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| /----------------------------------------------------------------------------- | --------------| A COLLECTION OF IDEAS | by Raheman Velji | ------------------------------------------------------------------------------ * * * [must use a fixed-width font to view diagrams properly] * * * CONTENTS: --------------------------------------- (1) Inventions A) The Seesaw Newton Motor B) The Simple Newton Engine Two inventions which will have a lasting effect on transportation, especially in space exploration. --------------------------------------- (2) Law of Conservation of Energy A) Gravitational-density Dynamo B) Potential Energy C) Creating and Destroying Mechanical Energy Ideas which clearly demonstrate that the Law of Conservation of Energy is wrong. --------------------------------------- (3) Work and Energy A) Defining Force, Work and Mechanical Energy B) Relative Views Force, work and mechanical energy will be defined in more intuitive ways. Observations of force, work, change in mechanical energy and mechanical energy depend on the frame you claim is at rest. --------------------------------------- (4) Special Relativity A) Preliminary B) A Reality Check C) Simultaneity D) The Constancy of the Speed of Light E) Outsider System vs. Insider System F) Understanding the Michelson-Morley Experiment G) The Finale Simultaneity is absolute, not relative. The speed of light is not constant. How does light propogate? Why we get a "null" result from the Michelson-Morley experiment will be explained. Amongst other things.. -\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\- -|-|-| (1) INVENTIONS -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|- -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/- Inventions: A) The Seesaw Newton Motor B) The Simple Newton Engine Devices that use "self-sufficient propulsion" - like the two mentioned above - work on Newton's law that "every action has an equal and opposite reaction." The idea is to harness the "action" and eliminate the "reaction", or convert the "reaction" into useable energy. Thus, within the device, the "reaction" is lost allowing the "action" to propel the device. All devices that use "self-suffiecient propulsion" work without affecting the environment. That is, they don't need a road to push off of like cars, they don't have to push air like planes or spew out gases like space shuttles. Thus, they get the name "self-sufficient propulsion" because they are self- sufficient. In other words, you can put a box around the entire device and the box would move, and nothing would enter or exit the box, and the device itself wouldn't react with the environment that comes inside the box. It only reacts to the environment in the box, which it creates, which it uses to propel itself. Devices that use "self-suffiicient propulsion" would look like UFOs if they are strong enough. (I propose that any device that uses "self-suffiecient propulsion" should have the name "Newton" added to its full-name so that we remember how it relates to Newton's law. I will use that convention here; whether this convention should be adopted is debatable.) The idea of "self-suffiecient propulsion" will have a lasting effect on transportation (especially in space exploration). -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-A) The Seesaw Newton Motor=-=-=-=-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Top view: ___base || \/ _____________ | | | M1a---M2a | <--front | | electromagnets | m1 | | \ | | \ | /\ | \ | || | o | <--seesaw || | \ | ("o" = pivot) forward | \ | | \ | | m2 | | | | M1b---M2b | <--back |_____________| electromagnets Ideally, "M1a", "M1b", "M2a", "M2b", "m1", "m2" are all electromagnets. (Some of the electromagnets can be changed into permanent magnets where it is deemed fit.) "M1a", "M1b", "M2a", and "M2b" are fastened to the base, while "m1" and "m2" are connected to a "seesaw" whose "pivot" ("o") is connected to the "base". (It is possible to construct this without the back electromagnets.) The way this invention works is somewhat hard to explain. Here is a simplified version: When "M1a" and "m1" are nearly touching an electric current is sent through "M1a", "M1b", and "m1". "M1a" should repel "m1" while "M1b" should attract "m1". Thus, both "M1a" and "M1b" will experience a force in the forward direction, while the seesaw swings around bringing "m2" close to "M2a". As "M2a" and "m2" are close now, an electric current will pass through "M2a", "M2b", and "m2". "M2a" should repel "m2" while "M2b" should attract "m2". Again, the electromagnets connected to the base, "M2a" and "M2b", will experience a force in the forward direction while the seesaw swings back to its starting position to repeat the cycle. Since all the electromagnets that are connected to the base experience a force in the forward direction, the entire device will be propelled forward as the seesaw keeps swinging about. Notice that the seesaw does *not* rotate, it simply moves back and forth, like a seesaw. It should be noted that as the seesaw swings about a bit of the "backward" energy of the electromagnets on the seesaw will be conveyed to the base via the pivot, thus slowing down the entire device. That loss of speed, though, is negligible. The above explanation of the workings of the "Seesaw Newton motor" is incomplete. One must understand the following: Every action has an equal and opposite reaction. The main idea of the "Seesaw Newton motor" is to harness the "action". When the front electromagnet, back electromagnet and the electromagnet on the seesaw are activated, the front and back electromagnets experience a "positive" force by being forced forward. The electromagnet on the seesaw, however, experiences a "negative" force as it moves in the backward direction. One must get rid of the "negative" energy of the electromagnet on the seesaw. If the "negative" energy is not rid of, then it will somehow be transferred to the entire device, thus not allowing the device to gain velocity and move forward. The "Seesaw Newton motor" does not only get rid of the "negative" energy, it in fact uses it to propel the device further. Consider the following scenario: a "Seesaw Newton motor" at rest, and set-up similar to the diagram above. Now, let us initiate a current through "M1a", "M1b", and "m1". The electromagnets on the base ("M1a" and "M1b") will experience a "positive" force by being forced forward. The electromagnet on the seesaw ("m1"), however, will experience a "negative" force by being forced backward. However, at the other end of the seesaw, the electromagnet ("m2") seems to be approaching the front electromagnet ("M2a") and receding from the back electromagnet ("M2b"). Thus, at the other end of the seesaw, when those electromagnets are activated, the repulsive force between the electromagnet on the seesaw and the front electromagnet will be greater, thus propelling the device further forward. Also, at the other end of the seesaw, when those electromagnets are activated, the attractive force between the electromagnet on the seesaw and the back electromagnet will be greater, again propelling the device further forward. The fact that both magnets ("M2a" and "M2b") experience a greater forward force is due to the initial "negative" energy of the electromagnet ("m1") on the seesaw. Thus, both the "action" and the "reaction" are harnessed to propel the entire device forward. Thus, in a sense this invention is more effective than a space shuttle because it harnesses both the "action" and "reaction", unlike a shuttle which only uses the "action". If both "action" and "reaction" are to be harnessed, one must ensure that the electromagnets on the seesaw should not hit either the front electromagnets or the back electromagnets. That is because in a collision the "backward" forces will be conveyed to the base via the pivot. Thus, input sensors might be needed to calculate the speed of the seesaw so that the electromagnets can be perfectly timed to avoid collisions. Notice that for this invention to actually move the electromagnets must be very strong and the entire device must be light. Otherwise, the device will stay in the same spot and the seesaw will just "wiggle about" instead of moving. Even though when it is "wiggling about" there still is a forward force; it's just that the forward force isn't strong enough to overcome static friction. So, even if on Earth it merely "wiggles about" instead of moving then it can still be useful in space where there is no static friction. So, this invention can definetely compete with other devices like ones that use ion propulsion. Also, the entire "Seesaw Newton motor" can (with a battery) be put into a box and the box would move without interacting with the environment outside the box. Thus, we say it moves using "self- sufficient propulsion". -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-B) The Simple Newton Engine-=-=-=-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- START: \-----------\-----------\-----------\-----------\ Side-view (cross-section): forward --> | ___cylinder | || | \/ |/------------- || #X| <--magnet ("X") |\------------- | /\ | ||__piston ("#") | | |<--start line The engine is a cylinder with a piston in it. The piston may require wheels to move inside the cylinder. "Every action has an equal and opposite reaction." The main idea of the "Simple Newton engine" is to harness the "action" by getting rid of the "reaction". How do we get rid of the momentum of the "reaction"? One way is by using friction, which is discussed in "Step 3". The idea is to force the piston in the backward direction, down the cylinder. Since every action has an equal and opposite reaction, the cylinder will then experience a force in the forward direction. This force is ideally created by using electromagnets. Let us say that there is an electromagnet on the piston ("#") which repels the magnet ("X") that is connected to the front of the cylinder. (Also, one could make this similar to a "Linear Induction motor", with the piston as the projectile.) /-----------/-----------/-----------/-----------/ STEP 1: \-----------\-----------\-----------\-----------\ | forward --> | | ___ The magnet and the cylinder | || move forward... | \/ --> | /------------- | | # X| | \------------- | /\ <-- | ||__ ...as the piston moves backward | through the cylinder | | Now, activate the electromagnet on the piston. So the piston, which is repelled by the magnet, moves down the cylinder as the magnet and the cylinder accelerate forward. /-----------/-----------/-----------/-----------/ STEP 2: \-----------\-----------\-----------\-----------\ | forward --> | | | | | /------------- | | # X| | \------------- | /\ | ||__The piston must be stopped before | it hits the back of the cylinder | | In fractions of a second, the piston will have arrived at the back of the cylinder. The piston must be stopped before it slams into the back of the cylinder because if it does then the energy of the piston will cancel out the forward velocity that the cylinder has gained. So, the energy of the piston must be removed (by friction, e.g. brakes on the wheels) or harnessed (a method which converts the "negative" energy of the piston into something useable). If friction is used to stop the piston, the friction must cause the piston to lose velocity in decrements; should the brake make the piston stop abruptly, then the "negative" momentum of the piston will be transferred to the cylinder. Consider the following analogy: If I'm on a bike and I stop abrubtly by pushing down hard on my brakes, I (my body) will go hurtling forth until I hit a wall. In the presence of gravity, I might hit the ground before I hit a wall, but the point remains the same. However, if I push on my brakes and slowing come to a stop, I can avoid being thrown forward. And moreover, by coming to a stop slowing, the momentum of me and the bike is dissipated as heat, and perhaps sound, by the brakes. Thus, in the "Simple Newton engine" the "reaction" is lost due to friction (as heat and possibly sound) while the "action" is harnessed to propel the cylinder forward. /-----------/-----------/-----------/-----------/ STEP 3: \-----------\-----------\-----------\-----------\ | forward --> | | | | | /------------- | |# X| | \------------- | | | | | When the piston has reached the end, and has been brought to a stop, it must then be moved to the front of the cylinder, perhaps by hooking it to a chain which is being pulled by a motor. Or perhaps the piston can slowly move back on its wheels towards the front of the cylinder. Or perhaps the piston can be removed from the cylinder when it is being transferred to the front, and thus leave the cylinder free so that another piston can "shoot" through the cylinder. /-----------/-----------/-----------/-----------/ Return to STEP 1: \-----------\-----------\-----------\-----------\ | forward --> | | | | | /------------- | | #X| | \------------- | | | | | The piston has been returned to the front. Overall, the engine has moved and gained velocity. Now it is ready to restart at STEP 1. It should be noted that the "Simple Newton engine" creates a small amount of force for a relatively minute amount of time. Nonetheless, I'm sure this invention can be useful in space exploration. Also, like the "Seesaw Newton motor", the entire "Simple Newton engine" can (with a battery) be put into a box and the box would move without interacting with the environment outside the box. Thus, we say it uses "self-sufficient propulsion". /-----------/-----------/-----------/-----------/ -\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\- -|-|-| (2) LAW OF CONSERVATION OF ENERGY |-|-|-|-|-|-|-|-|-|-|-|- -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/- The fact that the Law of Conservation of Energy is wrong is perhaps nature's cruelest trick. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-A) Gravitational-Density Dynamo-=-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- The following is what I call a "Gravitational-density dynamo": _____ | \_____ | _ \_____ | | \_____ \_______ | | \_____ | | | \___ | | | | | | | | | | | | | | | | | | ------*------ <--\ | | | | | | | turbine | | | Tube B --> | | (contains | | | | perfluoro- | | | | octane) | | | | | | | | <-- Tube A | | | | (contains | |_________________| | water) | | | |____________|____________| /|\ \_ semi-permeable membrane (dialysis tubing) A "Gravitational-density dynamo" is to be used to create free energy. It is not necessarily a perpetual motion machine. Tube A contains 250ml of water. Tube B contains 750ml of perfluorooctane. Tube A and Tube B are connected to each other by dialysis tubing, which is a semi-permeable membrane. Water can permeate through the dialysis tubing but perfluorooctane can't. Due to osmotic pressure, the water in Tube A will pass through the dialysis tubing entering Tube B. Since water is insoluble in perfluorooctane, and since water is less dense than perfluorooctane, the water will rise to the top of Tube B. Once enough water has accumulated at the top of Tube B, it will fall, turning the turbine, and returning back into Tube A. Notice that this dynamo didn't require any input energy, and it will continue to work, creating electricity by turning the turbine (and generator, which is not shown), so long as the perfluorooctane does not seep into Tube A through the semi-permeable membrane. Eventually, the perfluorooctane will seep through the dialysis tubing (this is a slow process), and so this invention is not a perpetual motion machine. But how can this dynamo generate electricity without any input energy? First, let's observe that the water at the top of Tube B has gravitational potential energy. When it falls, the gravitational potential energy is realized and is converted into electricity by the turbine (and generator, which is not shown). But how did the water initially get its gravitational potential energy? It got its gravitational potential energy by being displaced upward in a fluid (perfluorooctane) that is more dense than it. Thus, we must conclude that insoluble objects immersed in fluids that are more dense gain gravitational potential energy by being displaced upwards. However, where is that energy coming from? By the Law of Conservation of Energy something must lose energy so that another can gain energy. Since we cannot find anything losing energy, we must conclude that the Law of Conservation of Energy is wrong, and that gravity creates forces which then create/destroy energy; in this case it created energy in the final form of electricity. As mentioned before, enough perfluorooctane will eventually seep through the dialysis tubing causing the level of the liquid in Tube B to lower such that the water cannot escape through the top of the tube. And so, the turbine will stop spinning. At such a point we can easily "unmix" both liquids by pouring all the liquid into a tall cylinder. If we leave the two liquids in the tall cylinder for awhile then the water will accumalate at the top and the perflourooctane will gather at the bottom. We know that originally there was 250ml of water. So, we need only take the top 250ml of liquid (water) from the cylinder and put it into Tube A; the rest of the 750ml of liquid (perfluorooctane) can be dispensed back into Tube B. Thus, this dynamo can continually produce electricity; when the turbine stops turning because the two liquids mix, then we need only "unmix" the two liquids and restart the dynamo. Notice again that this dynamo creates electricity without using any input energy! Some may argue that we used energy to "unmix" the two liquids. That is true *but* even though we used energy to "unmix" the two liquids we did not *give* the two liquids energy. That is, two liquids in separate beakers have the same amount of energy as the same two liquids in the same beaker. We can potentially get this dynamo to work using salt water in Tube B instead of perfluorooctane. If we use salt water, the water from Tube A will still permeate through the membrane entering Tube B. However, salt water will accumalate at the top of Tube B and so it will be salt water that falls, turning the turbine, entering Tube A. Having salt water in Tube A is obviously undesirable. So, we'd have to also put dialysis tubing at the top of Tube B so that only pure water falls into Tube A. By putting dialysis tubing on both ends of Tube B the salt will be "trapped" in that tube. But after time enough salt will permeate through the dialysis tubing stopping the device; I do not know of an efficient way how we can "unmix" the salt water solution. We can conclude by noting that energy is being created/destroyed all around us. Gravity and magnetism are prime examples. Both create forces. The immediate effect of the forces on the system is nothing (the vectors of the forces cancel each other out). However, after the immediate effect, and after a minute amount of real time, the forces will do work on the system. If "positive work" is done, then the system will gain energy. If "negative work" is done, then the system will lose energy. Whether "positive work" or "negative work" is done is relative to the frame of reference you are in. This dynamo may be a perpetual motion machine if it creates more energy than is needed to unmix the two fluids. So, it is possible that the "Gravitational-density dynamo" can be used to create electricity on a large scale. In any case, I am discussing it here simply to demonstrate that the Law of Conservation of Energy is wrong and that gravity and magnetism can be used to create energy. (ASIDE: We have shown above that gravity can create energy. It is always figured that the universe should collapse due to gravity. However, gravity doesn't always bring things together. For example, it is possible to have two planets attract each other but not collide because of the direction of their initial velocities. Instead of making a collision they can accelerate towards each other and then "exit" with a greater speed then what they "entered" with.) -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-B) Potential Energy-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- --------------------------------------- Suppose we have two magnets with like-charges. As the two magnets are moved closer to each other, potential energy will be gained and kinetic energy will be lost. As the two magnets move away from each other, potential energy will be lost and kinetic energy will be gained. Say, initially, that both magnets are far apart. Now, let us do work by moving the charges closer together. When we are done and the magnets are close to each other, the potential energy will have increased. The increase will be equivalent to the work we did pushing them together. Now, let's say that we took two hammers and pounded both magnets until they lost their magnetism. Then, the potential energy between the two magnets will dissappear. Thus, the system has lost energy without any part of the system gaining energy. We have demonstrated that the Law of Conservation of Energy is wrong. Let me recap: First, we did work to move two repelling magnets together. Thus, we lost kinetic energy while the magnets gained potential energy. We then destroyed the magnetism of the magnets, thus losing the potential energy. Thus, all-in-all, we lost energy. This idea, which works on magnetism, can also be applied to gravity, which follows. --------------------------------------- Consider two stationary gaseous planets, both made entirely of deutrium. As the two planets are moved closer to each other gravitational potential energy will be lost and kinetic energy will be gained. As the two planets move away from each other gravitational potential energy will be gained and kinetic energy will be lost. Let's do work on the planets, increasing the gravitational potential energy of the planets, by moving them apart. The increase in gravitational potential energy will be equivalent to the amount work we did separating the planets. Now, let's say that the deutrium of both planets began to fuse by the following equation: deutrium atom + deutrium atom => helium atom + neutron + 3.27 MeV (It is true that I didn't include the initial energy to start the fusion. However, the above equation is properly balanced, so we do not have to consider the initial energy required. That is, let us assume the initial energy to start the fusion is supplied.) Now, it is obvious that mass is being converted into energy. Since the masses of both planets are decreasing, the gravitational potential energy between both planets will also decrease. Thus, the work we did moving the planets apart (which is now graviational potential energy) will diminish. We have again demonstrated that the Law of Conservation of Energy is wrong. Let me recap: First, we did work by moving the two planets apart. Thus, we lost kinetic energy while the planets gained gravitational potential energy. We then converted some of the mass of the planets into energy. Thus, we lost mass and in the process we lost gravitational potential energy. So, all-in-all, we lost energy. --------------------------------------- Or, you can consider throwing a ball up. As the ball is heading upward kinetic energy is being converted into gravitational potential energy. The ball will reach a maximum height when it has a velocity of zero and a maximum gravitational potential energy. When the ball has reached its maximum height let us convert the mass of the ball into energy. I don't know how to do this, but nonetheless, it is within the realm of possibility. By doing that, the mass will disappear and so the gravitational potential energy will disappear. One might oversimplify the above to say: "What goes up does not *necessarily* come down." -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-C) Creating and Destroying Mechanical Energy=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- --------------------------------------- "Mechanical energy" is the energy which is possessed by an object due to its motion and its stored energy of position. When I use the term "mechanical energy" in this section I am referring solely to "the energy which is possessed by an object due to its motion" *not* "its stored energy of position". (I won't use the term "kinetic energy" because that term is related to the equation "½mv²", and I do not want to imply that I am using that equation.) --------------------------------------- Let's say we have two electromagnets (coils of wire) with air cores. Now, let's set them next to each other. And then, let's send an electrical current through them so that they repel each other. Because they repel each other they will begin to move away from each other. The two electromagnets were stationary and now they are moving - now they have "mechanical energy". Thus we have created energy (at least it seems that way since we observed the two electromagnets from this particular frame of reference). Now, let's have the two electromagnets move towards each other. Again, let's send an electrical current through them so that they repel each other. They will stop moving. The two electromagnets had "mechanical energy" and then they stopped. Thus we have destroyed energy (at least it seems that way since we observed the two electromagnets from this particular frame of reference). --> Some may argue that for both scenarios above the total energy of the system is zero because the momentum of both electromagnets when taken together is zero. However, the "mechanical energy" of both electromagnets can be turned into another form of energy; for example, we can let both electromagnets rub against a surface like ashphalt. The heat and sound which is produced is due to friction and it is energy. Thus, we must conclude that the electromagnets initially also had energy. Thus, the total energy of the system is not zero! We cannot simply add the "mechanical energy" of the objects in the system and derive a conclusion from that. The "mechanical energy" of a system depends on the addition of the *individual* "mechanical energies" of the objects in the system, not just the addition of the "mechanical energies" of the objects in the system. --> Some may argue that energy is not created or destroyed but simply converted from one type of energy into another. For example, if we were using a battery to power the elecromagnets then these people would say that the chemical energy of the battery is being converted into electrical energy which then causes a change in "mechanical energy" of the electromagnets which we perceive. If we were plugging the electromagnets into the outlet then these people would say that "mechanical energy" at the site of the power plant is being converted into electrical energy which then causes a change in "mechanical energy" of the electromagnets which we perceive. Now, if energy is not created or destroyed but simply converted from one type of energy into another then the amount of electrical energy used by the electromagnets should *equal* the change in "mechanical energy" experienced by the electromagnets. Notice that electrical energy is proportional to current. But what if we inserted iron into the cores of the electromagnets? Then the repulsive force between the electromagnets will be greater; thus, the change in "mechanical energy" will be greater. But the current remains the same!; we used the same amount of electric energy! Thus, we realize that the amount of electrical energy used by the electromagnets does not *equal* the change of "mechanical energy" experienced by the electromagnets because iron cores "amplify" the magnetic field and cause the change in "mechanical energy" to be greater than it would be if there were no iron cores! So, we can conclude that energy is not transformed from one type of energy into another on a fixed ratio, at least not in this case. --> Some may argue that "mechanical energy" is being transformed into potential energy and vice versa. But we know from the previous section that potential energy can disappear without being realized. So we can conclude that the Law of Conservation of Energy is wrong. -\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\- -|-|-| (3) WORK AND ENERGY-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|- -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/- As said before: "Mechanical energy" is the energy which is possessed by an object due to its motion and its stored energy of position. When I use the term "mechanical energy" in this section I am referring solely to "the energy which is possessed by an object due to its motion" *not* "its stored energy of position". (I won't use the term "kinetic energy" because that term is related to the equation "½mv²", and I do not want to imply that I am using that equation.) -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-A) Defining Force, Work and Mechanical Energy-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- --------------------------------------- Before we go on further I need to invent a word. When I say that A is "generally proportional" to B, I mean that as A increases so does B. --------------------------------------- It is worthwhile to define work in physics similar to how we define work in an intuitive way. So, how do we define work in an intuitive way? Well, as a human, work obviously depends on the magnitude/ difficulty of the task and the duration of the task. So I propose that in physics work should be generally proportional to a "magnitude" and a "duration". (The "magnitude" and "duration" of work will be defined later.) Also, as a human we realize that by doing work we can accomplish some task. Now, that can translate into physics to mean that work can cause a change in energy of the system. If all the work causes a change in "mechanical energy" we will say that the work is "effective"; if it does not cause a change in "mechanical energy" we will say that the work is "ineffective". If the work causes a change in "mechanical energy" but is hampered, that is, not all the work causes a change in "mechanical energy", then we will say the work is "semi-effective". Likewise, force and power can also be called "effective", "ineffective" or "semi-effective". The equation for "effective force" is: · where "f_e" is "effective force" "m" is mass "a" is acceleration The equation for "ineffective force" is: · where "f_i" is "ineffective force" "p" is pressure "A" is area We will define "whole force" as the summation of all "effective forces" and "ineffective forces". The equation for "whole force" is: · where "f_w" is "whole force" --------------------------------------- Consider the following scenario: two classmates, Jack and Jill, who are each going to hold a brick. The downward force of the brick due to gravity is going to be the same for either participant. Now, let's say that Jack held his brick for 20 seconds, and Jill held her brick for 10 seconds. Now, without using any scientific jargon, who did the most work? Jack obviously did more work than Jill. Thus, *intuitively*, work should be generally proportional to force and time. Now work is already defined. The definition of work as it stands today is wrong intuitively but it is *very* useful in making calculations. It calculates work where work is defined as causing an object to be displaced in a certain direction. So it looks like we have two different ways of defining work. Let us distinguish between the two by giving them names. Let the traditional meaning for work - which is generally proportional to displacement - be called "productive work" whereas the "new" definition for work - which is generally proportional to time - be called "general work". As said above, "productive work" is generally proportional to force and displacement. But physicists allow "productive work" to be directly proportional to force and displacement for simplicity's sake. Thus, we get the following equation for "productive work": · where "W_p" is "productive work" "s" is displacement The force in "productive work" is, by definition, always effective. As said above, "general work" is generally proportional to force and time. It is sensible to also allow "general work" to be directly proportional to force and time, again for simplicity's sake. Thus, we get the following equation for "general work": · where "W_g" is "general work" "t" is a period of time I propose that the unit for "general work" should be "P", for Prescott, Joule's middle name. Thus, "one prescott" equals "one newton second". (I realize that force multiplied by time is called an impulse. However, the term "general work" is more fitting because it relates to "productive work". Because in a sense, "productive work" and "general work" are two sides of the same coin; hence the reason why both units - joule and prescott - are two names of the same person.) --------------------------------------- When force is effective, "productive work" can be written in terms of "general work": general work" it becomes exponentially rewarding in productiveness. (2) A given amount of "effective general work" doesn't always give you the same change in "productive work". When force is effective then "f_w = f_e" and so: · where "v_a" is the average change in velocity This means that the rate at which "general work" becomes "productive work" - when the force is effective - is the average change in velocity of the object. Since average velocity (the rate) increases with time, we can conclude (again) that the productiveness of the "general work" increases exponentially. Because the productiveness of "general work" increases with time it is worthwhile to determine what the productiveness of "general work" is over a small (infinitesmal) duration of time. So, when "t" approaches zero the rate at which "general work" becomes "productive work" is the instantaneous change in velocity - which is acceleration. Say that we push a particle with an "effective force" "f_e" over a displacement of "s". The time it takes for the particle to be displaced is "(2ms/f_e)^½". In such a case the change in velocity is "(2f_e*s/m)^½". Now, if the work becomes semi-effective then that means that some of the "effective force" has turned into "ineffective force". So, "f_e" will decrease; thus, the period of time - "(2ms/ f_e)^½" - will increase and the change in velocity - "(2f_e*s/m)^½" - will decrease. When "general work" is fully productive (due to "effective force") the rate at which it becomes "productive work" is the acceleration, which can be written as "f_e/m". So, as mass increases it becomes harder to convert "general work" into "productive work". As the "general work" becomes less productive (less displacement due to "semi-effective force") the average change in velocity is less, and so the rate at which "general work" becomes "productive work" is less than the acceleration. As the "productive work" nears zero (no displacement due to "ineffective force") then the average change in velocity nears zero and so the work is almost entirely general. When force is effective, power equals "f_e*v_a". So, "effective power" is proportional to the rate at which "general work" becomes "productive work". --------------------------------------- Above, we observed that "productive work" depends force and displacement while "general work" depends on force and time. I propose that we now define the "magnitude" of work as "force". And, when we are considering "displacement" and "time" from the point of view of work we will call them the "duration" of work. --------------------------------------- We are now going to consider the energy of a system which has one particle with a mass of "m" moving at an initial velocity "v". "Effective work" will be applied on the particle. We will call the "magnitude" and "duration" of the work as "M" and "D" respectively. Notice that the "mechanical energy" of a particle is generally proportional to its mass and velocity. We will "measure" the "mechanical energy" of the particle in two different ways; we will name them "productive energy" and "general energy". If we are considering the "productive energy" of the particle, we will "measure" the energy of the particle using the equation "½mv²". If we are considering the "general energy" of the particle, we will "measure" the energy of the particle using the equation "mv". Both equations - "½mv²" and "mv" - can be considered to be two different "rulers" used to "measure" the energy of the particle in the system. Now, notice that the change in "productive energy" due to "productive work" and the change in "general energy" due to "general work" is "MD". So, we can create the following equations to determine the "mechanical energy" and change in "mechanical energy" of the system: When we are considering "productive work": When we are considering "general work": · where "E_p" is the equation for "productive energy" · where "E_g" is the equation for "general energy" · where "m" is the mass of the particle · where "v" is the initial velocity of the particle (prior to work) Now in Newtonian mechanics kinetic energy is equal to "½mv²" and momuntum is equal to "mv". So the equation for "productive energy" gauges the Newtonian kinetic energy of the system while the equation for "general energy" gauges the Newtonian momentum of the system. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-B) Relative Views-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- --------------------------------------- Now, "mechanical energy" depends on mass and velocity. But velocity is relative; so, we must conclude that the "mechanical energy" in a system is also relative! More precisely, "mechanical energy" depends on what frame of reference you claim is at rest. Here's a rule: · The relative velocity of two objects is constant no matter what frame of reference you are in (even accelerated frames) so long that the two objects are not accelerating relative to each other. For example, consider a skydiver plumetting to the Earth such that he has reached his terminal velocity. Someone on the Earth will claim that he is at rest and will observe the skydiver falling; he will say that the "mechanical energy" of his own system depends on the mass of the skydiver and the speed at which he is falling at. On the other hand, the skydiver will claim that he is at rest and will observe the Earth to be moving towards him; he will say that the "mechanical energy" of his system depends on the mass of the Earth and the speed at which the Earth is approaching him. In both cases the speed of the skydiver and the speed of the Earth are the same (because velocity is relative). But, the mass of the Earth is greater than the mass of the skydiver. So, the skydiver will claim that there is more "mechanical energy" in his frame of reference than what someone on the ground will claim! So, the "mechanical energy" of a system depends on what frame of reference you claim is at rest. --------------------------------------- The acceleration of the skydiver and the Earth due to gravity can be determined by tactile observations. That is, the skydiver and the Earth can feel the acceleration. (Of course, the acceleration of the Earth is so small that we cannot feel it, but that is just because our instruments aren't sensitive enough.) If we determine acceleration by tactile observations then we will say that it is a "real acceleration"; if we determine force using "real acceleration" then we will say that it is a "real force". The "real forces" of gravity on the skydiver and the Earth are equivalent: · where "f_s" is the "real force" on the skydiver "f_e" the "real force" on the Earth "G" is the Gravitational Constant "m_s" is the mass of the skydiver "m_e" is the mass of the Earth "r" is the distance between the skydiver and the center of the Earth Work is proportional to force. Now, when you are *doing* work then the work depends on "real forces". However, when you are *observing* work then the work depends on "apparent forces". "Apparent force" is determined by "apparent acceleration"; and "apparent acceleration" is determined by visual observations of acceleration, not by tactile observations like "real acceleration". When we are *doing* work we will call the work "real work" while when we are *observing* work we will call the work "apparent work". The "total acceleration" is the sum of the "apparent acceleration" of the skydiver and the "apparent acceleration" of the Earth: · where "a_t" is the "total acceleration" "a_s" is the "apparent acceleration" of the skydiver "a_e" is the "apparent acceleration" of the Earth Notice that the "total acceleration" is constant no matter what frame of reference you are in (even an accelerated frame!): Here's a rule: · The relative "apparent acceleration" of two objects (which is the "total acceleration") is constant no matter what frame of reference you are in (even accelerated frames) so long that the relative "apparent acceleration" of the two objects is not increasing/ decreasing (that is, the "apparent acceleration" isn't itself "accelerating"). If someone on Earth were to assume that he is at rest then he will say that an "apparent force" is being applied on the skydiver; if the skydiver were to say that he is at rest then he will say that an "apparent force" is being applied on the Earth. Now, "apparent force" is proportional to mass and "apparent acceleration". In both cases the "apparent acceleration" of the skydiver and the "apparent acceleration" of the Earth are the same (because "apparent acceleration" is relative). But, the mass of the Earth is greater than the mass of the skydiver. So, the skydiver will claim that a greater "apparent force" is being applied on the Earth and so, more "apparent work" is being done from his frame of reference than what someone on the ground will claim! And so, a greater change in "mechanical energy" will be witnessed by the skydiver. Of course, we can always claim that a certain frame is at rest such that an "apparent force" is being applied on the skydiver *and* an "apparent force" is being applied on the Earth. For instance, there is a frame which is at rest such that "apparent forces" equal "real forces". So, we saw above that the "mechanical energy" of a system depends on what frame of reference you claim is at rest. Likewise, we can now say that "apparent acceleration", "apparent force", "apparent work" and change in "mechancal energy" also depend on what frame of reference you claim is at rest. -\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\- -|-|-| (4) SPECIAL RELATIVITY -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|- -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/- -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-A) Preliminary=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- --------------------------------------- Here are Einstein's two postulates of Special Relativity: --> (1) The laws of physics take the same form in all inertial frames. That is, one cannot distinguish one inertial frame from the others or make one frame somehow more "correct" than another. --> (2) In any inertial frame, the velocity of light "c" is the same whether the light is emitted by a body at rest or by a body in uniform motion. That is, the speed of light will always be measured to be "c" when the light source is in an inertial frame. --------------------------------------- When you *measure* a quantity using an instrument we will say that that quantity is "measured". On the other hand, if you *just* use an equation to determine a quantity we will say that the quantity is "derived". It is often hard to determine whether a quantity is "measured" or "derived" because in certain cases we can either use an instrument to determine the unknown or use an equation to determine the unknown. I make a distinction between the two here; a "measured quantity" is always made by using an instrument (and perhaps an equation), and we assume here that "measured quantities" are always correct; "derived quantities" are merely "observations" (made *solely* by using equations) which may or may not agree with "measured quantities". (Side-tracking a bit: How do you measure a length? If the endpoints of the thing you wish to measure are at rest with your own frame then you can measure the thing using a ruler; otherwise, the endpoints of the thing you wish to measure are moving relative to you and so you need to measure the thing by perhaps using visual observations (which may include the use of something like a ruler, or other instrument).) Now, a "measured length" is determined by using a ruler or by using visual observations. A "measured time" is determined by using a clock. On the other hand, you could figure out the distance by using the equation "d=vt" or the time by using the equation "t=d/v" - where "d" is distance, "v" is velocity, and "t" is time; by using those equations we can determine "derived length" and "derived time". Now, we can determine velocity using the Doppler effect. If we use an instrument to determine the frequency then by the equation for Doppler's effect we will find "measured velocity". On the other hand, if we determine the frequency by other means then by the equation for Doppler's effect we will find "derived velocity". Of course, we can also find "derived velocity" by using the equation "v=d/t". Also, a "measured mass" is determined by using a scale. Of course, to use a scale you need to know the strength of the gravitational field you are emmersed in, and if there is no gravitation field then the scale will fail. "Derived mass" is figured out by using the equation for kinetic energy or the equation for momentum. "Measured mass" is usually called "rest mass"; "derived mass" is usually called "inertial mass". Now, there may be other ways to determine measured/derived length, time, velocity and mass. I wonder how they should be added to the mix.. Take note that when we measure *anything* our measurements may not be accurate; this is especially true when we make "visual measurements". There is always some error. "That there is a lower limit to this error merely asserts that our intellects are more delicate than our physical apparatus." I said above that "we assume here that "measured quantities" are always correct". If "derived quantities" do not correlate with "measured quantities" then it is - to put it bluntly - the "derived quantities" fault. It should be physic's goal in general to have all "derived quantities" equal "measured quantities" for this is not so in present day physics as we will see in what follows. --------------------------------------- I am now going to invent two "thought devices"; "ideal emitters" and "ideal receivers". Ideal emitters are used to send signals to ideal receivers. The signal goes from the emitter to the receiver *instantaneously*. So, there is absolutely no time lag; that's why they're called "ideal". In practice there is always some delay in our signalling devices; there is always some error. "That there is a lower limit to this error merely asserts that our intellects are more delicate than our physical apparatus." --------------------------------------- Also, we will be using three different devices; what I call "SD devices" and "SMD devices", and "light-clocks". All three aparatus have a light-source and a light-detector, and perhaps a clock and a mirror. To simplify verbiage, the "light-source" will be called the "source" and the "light-detector" will be called the "detector". In any thought-experiments, all devices are equipped with ideal emitters at the source and the detector. Anyone can get an ideal receiver and thus determine *exactly* when the source emits the light and when the light gets received by the detector. A "SD device" is an apparatus consisting of a clock, a source and a detector. The apparatus is set up such that the clock starts when the source emits a flash of light. The light then gets registered by the detector which causes the clock to stop. The device is called an "SD" device because light goes from the (S)ource to the (D)etector. For this entire section the distance between the source and the detector in a SD device will be "L". A "SMD device" is very similar to a "SD device" except that it has a mirror. The apparatus is set up such that the clock starts when the source emits a flash of light. The light is then reflected off the mirror. The light returns to the source where it is registered by the detector which causes the clock to stop. The device is called an "SMD" device because light goes from the (S)ource to the (M)irror and back to the (D)etector. For this entire section the distance between the source/detector and the mirror in a SMD device will be "L". It should be noted that "light-clocks" differ from SMD devices. Einstein used light-clocks in his famous thought-experiments. A light- clock is an apparatus set up like a SMD device but without the clock. The crucial difference between the two is that a SMD device *measures* an amount of time while a light-clock *derives* an amount of time. How does a light-clock derive time? Well, when you look at a light- clock in action you will see the light traverse a certain distance "d". A user using a light-clock assumes that the speed of light is the constant "c". Thus, the light clock - using displacement "d" and the speed of light "c" - derives the time "t" elasped by using the equation "t=d/c". For this entire section the distance between the source/detector and the mirror in a light-clock will be "L". The distance between the source/detector and the mirror in a light-clock is always "L"; this is true no matter what frame you are looking at the light-clock from. The displacement of light, "d", is what differs depending on your frame. --------------------------------------- I will refer to a velocity measured relative to the "absolute frame" as an "absolute velocity". -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-B) A Reality Check=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Now, when I looked at the moon a while ago it was a full circle. Today I look at the moon and it is half a circle. I can look at this from two angles. I can say that my observations are accurate and the moon is now half of what it used to be. Or, I can say that my observations are flawed and I can only see half the moon. Which is true? From the Earth, from my particular observations, I cannot say one is more right than the other. But, it is much better to believe that I am only seeing half the moon because it is hard to explain where half the moon suddenly disappeared to. Thus, when we examine a situation we must decide what is reality in such a way that we can easily describe the Universe. For each individual case we must ask ourselves are our observations an accurate description of reality or are our observations flawed? It is fundamentally impossible to prove one over the other; that is because our perception of reality is through our observations, and one cannot know whether to trust the observations or assume that there is a reality outside of our observations. These questions must be asked when we consider simultaneity, which follows in the next section. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-C) Simultaneity-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Einstein and relativity are wrong in their treatment of simultaneity. The failure of relativity's treatment of simultaneous events is best described by Professor W. D. MacMillan in "A Debate on the Theory of Relativity": "The notion of simultaneity in two distant places according to Newtonian mechanics is not ambiguous, as is so frequently asserted by the relativists. We can set two distant clocks to indicate the same time with a certain margin of error. That there is a lower limit to this error merely asserts that our intellects are more delicate than our physical apparatus. However fast or slow light may go, we can imagine a speed a million times as great, or any other ratio that may be desired, and there is no lower limit, save zero itself, to the determination of simultaneous events so far as the mind is concerned. To say that simultaneity does not exist because it is unattainable in practice is like saying that a straight line does not exist because it, too, physically is unattainable. Shall we then put geometry into the discard because it is ambiguous and without meaning? If we do the matter is ended, for there is nothing left for us to talk about." Different observers measure different events to be simultaneous. Is each observer correct in his own frame? Or is there an underlying reality unseen because our observations are faulty? What is reality? Relativity claims the former idea. Einstein claims that events which are simultaneous with reference to one frame are not simultaneous with respect to another frame. So, is simultaneity absolute or relative? Is only half the moon showing or has half the moon disappeared? The fact that we do observe events out of order is because our observations are faulty. If we had a way to transmit information instantaneously (like by using ideal emitters and ideal receivers) then our observations would correlate with reality and simultaneity would not seem to be ambiguous. The fact that we don't have such devices merely implies "that our intellects are more delicate than our physical apparatus". So, simultaneity is absolute. That is, two events are either simultaneous or not; it does not matter what frame you are in. Now, if you were to see two events occur at the same time then we will say that the events "appear to be simultaneous"; if you don't see two events occur at the same time then we will say that the events "do not appear to be simultaneous". If we had the use of ideal devices then all simultaneous events would appear to be simultaneous and all "non- simultaneous" events would not appear to be simultaneous; this is not always so when we do not use ideal devices. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-D) The Constancy of the Speed of Light=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- --------------------------------------- INTRODUCTION: To maintain the constancy of the speed of light we need to have time dialate and/or length contract. We will now examine the thought- experiments which are used to derive the equation for Special Relativity's time dialation and length contraction. This is how the "Time Dialation" thought-experiment is set up: There are two people, an "insider" and an "outsider". The "outsider" is standing on the Earth while the "insider" is sitting on a train. The train is travelling forward at a velocity "v" relative to the Earth. The velocity "v" is perpendicular to the line of sight of the "outsider". There is a light-clock on the train such that the source/detector is secured on the floor of the train while the mirror is fastened above the source such that it will (hopefully) reflect the light from the source directly back down to the detector. --------------------------------------- Einstein claims that the speed of light is always a constant. However, he never said from which frame does light always leave the source in a straight line. So, we will observe below that when light appears to travel from the source in a straight line as observed by an "outsider" then the "Time Dialation" thought-experiment fails. --------------------------------------- "TIME DIALATION" THOUGHT-EXPERIMENT: (assuming light leaves the source in a straight line as observed by an "outsider") As assumed, the flash of light will leave the source in a straight line as observed by an "outsider". While the flash of light is heading upwards towards the mirror the train has moved forward. Thus, if the train is fast enough then it may have moved forward enough such that the flash of light might not even hit the mirror at all! The light may not hit the mirror because the light is travelling upwards as seen from outside the frame, not inside. The "insider" will see light "bend". (Diagram A) (A) ---> WHAT THE INSIDER SEES: | | ______ | · | | · | | · | L forward --> | · | | · | | ·| \_________________________________ The experiment as stated by Special Relativity requires that the light gets reflected back to the detector on the floor of the train and so, this "Time Dialation" thought-experiment does not produce proper results when we assume that light leaves the source in a straight line as observed by an "outsider". --------------------------------------- So, we will now assume that light appears to travel from the source in a straight line as observed by the "insider". --------------------------------------- "TIME DIALATION" THOUGHT-EXPERIMENT: (assuming light leaves the source in a straight line as observed by an "insider") When the two observe the light-clock let the "insider" derive a time of "tI" to elaspe while the "outsider" derives a time of "tO" to have elasped. The "insider" is at rest with the light-clock so he sees the light travel a total distance "2L". Meanwhile the "outsider" sees the light travel a total distance "2[(vtO/2)²+L²]^½". (Diagram B) (B) ---> WHAT THE OUTSIDER SEES: | | ___ | | · | | ·|· | | · | · | L | · | · forward --> | | · | · | | · | · | _|_ ·_____|_____· | | |-----------| | vtO \_________________________________ And we assumed that both the "insider" and the "outsider" see light travel at the constant "c". Now, we will use the equation "t=d/ c", where "t" is an amount of "derived time", "d" is the "measured distance" the light traverses, and "c" is the speed at which light (supposedly) travels at. So the "insider" derives a time while the "outsider" derives a time Using the above two equations, the "Time Dialation" thought- experiment goes on to derive the following equation: · where "y" equals "1/[1-(v/c)²]^½" --------------------------------------- The above thought-experiment shows that if we want to maintain the speed of light as a constant then we need for time to dialate in a particular way. If time doesn't dialate, that is, if time is constant for the "insider" and "outsider", then the two will not agree that the speed of light is "c". --------------------------------------- For us to maintain that the speed of light is constant for everyone we need for time to dialate and/or length to contract in a particular way. Essen describes this perfectly in his book "The Special Theory of Relativity": "A critical examination of Einstein's papers reveals that in the course of thought-experiments he makes implicit assumptions that are additional and contrary to his two initial principles. The initial postulates of relativity and the constancy of the velocity of light lead directly to length contraction and time dialation simply as new units of measurements, and in several places Einstein gives support to this view by making his observers adjust their clocks. More usually, and this constitutes the second set of assumptions, he regards the changes as being observed effects, even when the units are not deliberately changed. This implies that there is some physical effect even if it is not understood or described. The results are symmetrical to observers in relative motion; and as such can only be an effect in the process of the transmission of the signals. The third assumption is that the clocks and lengths actually change. In this case the relativity postulate can no longer hold. "The first approach, in which the units of measurement are changed, is not a physical theory, and the question of experimental evidence does not arise. There is no evidence for the second approach because no symmetrical experiment has ever been made. There is no direct experimental evidence of the third statement of the theory because no experiments have been made in an inertial system. There are experimental results that support the idea of an observed time dialation, but accelerations are always involved, and there is some indication that they are responsible for the observed effects." This book was written a while ago and so things may have changed experimentally in the second paragraph above. Essen discussed three cases; they all attempt to maintain the speed of light as a constant for everyone by claiming that time dialates and/or length contracts in a particular way. In this case, why does time dialate and/or length contract? In short, either because.. CASE #1: .."measured quantities" change depending on your frame. OR CASE #2: ..we adjust our instruments and equations. OR CASE #3: ..it is a result of an intrinsic property of our observations. I will now discuss the above three cases in detail. --------------------------------------- CASE #1: Here we will consider that time dialates and length contracts because "the clocks and lengths actually change"; that is, "measured quantities" change depending on you frame. Now, since the "outsider" sees the light travel a greater distance than the "insider" Einstein and his friends then use the equation "t=d/c" to claim that the "outsider" will measure a greater amount of time to elapse than the "insider". The fact that the "outsider" sees the flash of light travel a greater distance than the "insider" is *directly* responsible for the fact that we then get an equation which demonstrates that time dialates. The time dialation equation means that since the "measured quantity" of distance the light traverses differs depending on your frame then "derived time" has dialated; this does not neccesarily mean that "measured time" has dialated. Einstein and his friends often make the mistake of saying "measured time" has to dialate because "derived time" dialates; this is wrong. As said above, the fact that "derived time" dialates does not necessarily mean that "measured time" dialates. Consider the outsider; "measured time" for him will pass at a certain rate. In fact, "measured time" will *always* pass for him at a certain rate whether there is a train in front of him or not. Now, the distance the light traverses (in the light-clock on the train) as observed by the outsider depends on the velocity of the train. So, using the equation "t=d/c" we find that "derived time" dialates according to the velocity of the train. This does not necessarily mean that "measured time" dialates because "measured time" will *always* pass for the outsider at a certain rate whether there is a train in front of him or not! Because "derived time" does not always equal "measured time" when we assume that the speed of light is constant we find that the equation "t=d/c" works only to find "derived time". But what equation should we use to determine "measured time"?? Now, on the other hand, if the speed of light is not constant and if light acted "normally" then "derived time" would always equal "measured time" and the following equation would always be true: "t=d/z", where "z" is the speed of the flash of light which depends on the frame you are in. Let me clarify things: Einstein and I both agree that during the above thought-experiment the "outsider" and "insider" will measure the distance travelled by the light to be different. Einstein then says that the speed of light is constant so time has to dialate. I say that time is a constant and so the speed of light is what "dialates"; that is, it is speed of light as observed by the "insider" and "outsider" which differs, not time. In any case, this is how most physics textbooks leave the subject. However, what if we moved the light-clock down to Earth beside the "outsider"? Then, in a sense, the "outsider" will become the "insider" and the "insider" will become the "outsider". So, if you repeat the "Time Dialation" thought-experiment one will derive the following contradictory equation: Now both equations - (1) and (2) - demonstrate that time dialates! If we are to say that "derived time" dialates then there doesn't seem to be much of a problem. But if we mean that "measured time" dialates then we have the following problem: Which equation is true and which is false? Both the "insider" and the "outsider" have equal rights to have their "measured time" dialate with respect to the other. In essence both equations together mean that "My time is faster than your time which is faster than my time which is faster than your time which is, etc..." Now, physics books and thought- experiments often allow one of the equations to be true while the other equation is dismissed (e.g. the famous "Twin Paradox" thought- experiment); such action is unjustified. Now, only one of the two equations can be true. Again, if we are to say that "derived time" has dialated then we seem to have no problems. However, if we are to say that "measured time" dialates then only *one* observer - in a unique frame - will not have time dialate; everyone else will. This leads us to the idea and necessity of creating an "absolute frame" if "measured time" dialates; this invalidates Postulate #1, the relativity postulate. This idea and necessity of creating an "absolute frame" also appears in Einstein's thought-experiment for length contraction. He introduced an equation for length contraction by using a similar thought-experiement. It is similar to his equation for time dialation in that it can be written in two contradictory ways; here they are: and · where "LO" is the length derived by the "outsider" · where "LI" is the length derived by the "insider" (The lengths "LO" and "LI" are in the direction of the velocity "v"; lengths perpendicular to the velocity "v" are not contracted.) Both equations - (3) and (4) - demonstrate that length contracts! Again, which equation is right and which is wrong? Many of the same problems encountered with the "Time Dialation" thought- experiment are also encountered with the "Length Contraction" thought- experiment. Now, many relativists claim that the "Length Contraction" thought- experiment means that "measured length" contracts. That is, lengths really contract; it's not just a "bad observation" due to solving an equation. Instead, it is more likely that "derived length" contracts and "measured length" doesn't. Also, Einstein and his friends never discussed whether length should contract in their "Time Dialation" thought-experiment! Oops.. Shouldn't the value "vtO" (in the above diagram) contract?! Now, even if "measured time" dialates then this actually does not save Special Relativity's second postulate! Let us assume here that the "insider" is in the "absolute frame", and that the "outsiders" view the velocity of the "insider" to be perpendicular to his line of sight. So, only such "outsiders" looking at the light-clock with "insider" (who's in the "absolute frame") will observe "measured time" to equal "derived time". And so it is only these "outsiders" who will have "measured time" dialate properly such that the speed of light remains a constant. If the "outsiders" are looking at a light-clock that is *not* at rest with the "insider" (who's in the "absolute frame") then the equation for time dialation cannot be properly used to maintain the speed of light as a constant; this is because "measured time" will no longer equal "derived time". Now, what happens when the velocity "v" of the "insider" is *not* perpendicular to the line of sight of the "outsider"?!? Special Relativity does not consider that scenario!!! And what if we move the light-clock around?!? Again, Special Relativity does not consider that scenario!!! Now, on the other hand, if the speed of light is not constant and if light acted "normally" then the two scenarios above would no longer be problems. Now, if "measured quantities" don't dialate and contract then Einstein's thought-experiments demonstrate that "derived time" dialates and "derived length" contracts. We are saying here that "derived quantities" do not correlate with "measured quantities". So, in this case the fact that "derived time" dialates and "derived length" contracts is due to our equations, not due to reality. But shouldn't our equations describe reality?! - shouldn't our equations describe "measured quantities"?! Nonetheless, in this case if "derived time" dialates and "derived length" contracts such that the speed of light is maintained a constant then we have essentially described "CASE #2", which is discussed next. --------------------------------------- CASE #2: Let us now consider the idea of creating "new units of measurements" "by making observers adjust their clocks" and rulers so that the speed of light *appears* to maintain the constant speed "c". By adjusting our instruments (clocks and rulers) we are essentially adjusting our equations. So, we are saying here that "derived time" dialates and "derived length" contracts, not that "measured time" dialates and "measured length" contracts. This method of maintaining that the speed of light is constant in all frames is the most seductive because we need not abandon any "pre- relativity" physics! So, we can say that the speed of light is not constant, and light acts "normally", and "measured time" does not dialate and "measured length" does not contract. But, if we let "derived time" to dialate and we let "derived length" to contract then we hope to find that the speed of light *appears* to be travelling at the constant speed "c" from any frame. We can let "derived time" dialate and "derived length" contract by adjusting our equations. Certainly, the equations (1) and (2) in "CASE #1" dialate "derived time" such that the speed of light is maintained a constant. However, what happens when the velocity "v" of the "insider" is *not* perpendicular to the line of sight of the "outsider"?!? And what happens if we move the light-clock around?!? In such cases "derived time" will dialate by a different factor and so the time-dialation equation - (1) and (2) - will no longer be able to be used to allow the speed of light in the light-clock to be maintained the constant "c". Now, I do not know of a way how we can have "derived time" dialate and/or "derived length" contract such that the speed of light is *always* maintained a constant. In any case, this method of maintaining the speed of light as a constant does not in any way clash with other theories, and so, we can actually say without doubt in this case that the speed of light is not constant. --------------------------------------- CASE #3: If time dialates and/or length contracts because it is an intrinsic property of our observations then we must ask "why is this so?". In this case we are saying that the dialation of time and the contraction of length is similar to an optical illusion. We have not explained "why is this so?", just that somewhere along the line time dialates and length contracts. So, this "explanation" does not really explain anything afterall. Moreover, this "effect" is "not understood or described" by any physics theories; without an explanation of what the effect is or how it's derived it is likely - by Occam's razor - that there actually isn't an effect to begin with. --------------------------------------- CONCLUSIONS: Above, we tried to maintain the speed of light as a constant by having time dialate and length contract in a particular way. However, in our attempts we found that when we had time dialate and length contract we ran into problems and contradictions and so, it is likely that the speed of light is not constant. --------------------------------------- SO WHY DOES TIME APPEAR TO DIALATE?: We have seen above that time cannot dialate and length cannot contract in a particular way such that the speed of light can be maintained a constant. Now, I have never seen a physical experiment that shows that "measured length" contracts. However, there have been physical experiments that demonstrate that "measured time" dialates. But notice that the fact that "measured time" dialates does *not* in this case maintain the speed of light as a constant. For example, it has been shown that muons created in the atmosphere are observed to have the time of their half-lives dialated. Why?: · Perhaps the "measured time" of the muon will dialate according to the velocity of the muon measured from the "absolute frame". This means that anything will have their "measured time" dialate according to its "absolute velocity". · Perhaps the "real acceleration" of the muon as it approaches the Earth causes time to dialate. This means that anything experiencing a "real acceleration" will have their "measured time" dialate. In this case we do not need to invent an "absolute frame". · Perhaps our observation of the muon *causes* time to dialate. The fact that the halflife dialates is directly because we made the *measurement* of the muon's velocity. It is the *act* of making the measurement which causes time to dialate. This means that if we *measure* the velocity of any particle then the time for that particle will dialate according to the observed velocity. Now, we've never observed that measuring the velocity of a train causes time to dialate for the humans on the train; afterall, the velocity of the train can be anything depending on your frame and so that means that time can dialate by any factor. So, why doesn't this work with humans and trains which are, afterall, just large conglomerates of particles? Now, quantum mechanics describes the "small world" (things like muons) but has trouble describing the "big world" (things like humans and trains). So, perhaps the dialation of time is like some kind of wierd "quantum effect". In this case we do not need to invent an "absolute frame". Physical experiments need to be done to know why "measured time" appears to dialate. --------------------------------------- "SPEED OF LIGHT" EXPERIMENT: We will now discuss the famous "Train" thought-experiment Einstein used to show that events which are simultaneous with reference to one frame are not simultaneous with respect to another frame. Einstein says that events which are simultaneous with reference to one frame are not simultaneous with respect to another frame; this allows him to maintain that the speed of light is constant. But we know from above (in the section on "Simultaneity") "that two events are either simultaneous or not; it does not matter what frame you are in". So, we are discussing the "Train" thought-experiment here as a method to determine whether the speed of light is constant for everyone. We know from physical experiments that "measured time" does dialate. At this point we do not know why; more physical experiments need to be done. Now, in this section we will say that "measured time" doesn't dialate; by the nature of this experiment you will find that this premise should not appreciably affect our conclusions. And when we determine why "measured time" appears to dialate we should update this discussion of the experiment. There is a train passing by an embankment. The length of the train is "2L". There is someone standing in the middle of the train; let that person be called the "insider". There is also someone standing on the embankment across the "insider"; let that person be called the "outsider". The train is moving forward with a velocity relative to the embankment. Now, two flashes of light strike the tracks simultaneously, one at the front of the train, the other at the back of the train. ---> DIAGRAM OF "TRAIN" THOUGHT-EXPERIMENT | | | train __ | || | \/ | _______________________ | * | I | * | FL * ------------------------- * FL --> forward | * Ø Ø Ø Ø Ø Ø * |--------------------------------------------- | O | /\ | embankment __|| | | | · where "I" is the "insider" | "O" is the "outsider" | "FL" is a flash of light \_________________________________ Both the "outsider" and the "insider" will see both flashes of light traverse the *same* distance "L". If the events appear to be simultaneous then it takes *equivalent* times for both flashes to cover the *same* distance "L"; this can only happen when the speed of light is *constant*. We can also reverse that fact: If the events do not appear to be simultaneous then it takes *different* times for both flashes to traverse the *same* distance "L"; and this can only happen when the speed of light is *different*. So, if light travels at a constant speed for all frames then the "outsider" and "insider" should *both* observe the events to appear to be simultaneous! If the "outsider" or "insider" do not see the events to appear to be simulataneous then we can conclude that the speed of light is not constant for everyone! I will now discuss how Einstein treats this "Train" thought- experiment in his book "Relativity: The Special and General Theory". I want you to notice that when Einstein conducts this "Train" thought-experiment he finds that the speed of the flashes of light reaches the "insider" and "outsider" at *different* times. This should imply to any rational person that the speed of light is not always constant. However, Einstein circumvents this issue by saying that both events are simultaneous for one observer, and *not* simultaneous for the other observer!!! It is this con which allows him to maintain that the speed of light is constant!!! This is quite ridiculous, because as discussed above "two events are either simultaneous or not; it does not matter what frame you are in". Let me explain the above paragraph clearly. This is how Einstein "sets up" the "Train" thought-experiment: Let us say that the flashes of light are simultaneous for the "outsider". In that case, the "insider" will not see the two flashes to appear to be simultaneous; the "insider" will see the flash from the front before the flash from the back. Now, the "insider" can explain this situation in two ways: --> (1) The speed of the flash of light from the front is faster than the speed of the flash of light from the back and so the speed of light is not constant, as observed by the insider. OR --> (2) The flash of the light from the front occured earlier than the flash of the light from the back and so the events are not simultaneous, as observed by the insider. Both options explain why the front flash is seen before the back flash. Now, Einstein vouches for option (2). But if the event is simultaneous for the outsider then it must also be simultaneous for the insider because "two events are either simultaneous or not; it does not matter what frame you are in". If we had the use of ideal devices then the insider would *certainly* agree that the events are simultaneous. So, option (2) goes to the garbage! And we are left with option (1). So, there is no reason to believe that the speed of light is constant! The only way that the speed of light can remain a constant now is if we conduct this experiment and both the "outsider" and "insider" observe the events to *appear* to be simultaneous. This is unlikely to happen. So, we should conduct the above experiment in reality to determine whether the speed of light is constant. (ASIDE: To conduct this experiment we'd have to consider at least three cases; one, when the source of flashes are at rest with the "outsider", the second, when the source of flashes are at rest with the "insider", the third, when the source of flashes are not at rest with the "insider" or the "outsider". Why do we have to consider (at least) three cases? Because, as we see in the section "Outsider System vs. Insider System" it is possible (and likely) that the speed of light depends on the motion of the source.) --------------------------------------- REMARKS: Now, Einstein claimed many many years ago that the speed of light is a constant in all frames. Why hasn't anybody checked this?!?! We should do many experiments, some on Earth, some in space, some in inertial frames, some in accelerated frames. We should observe the distance the light traverses and the time elasped from many different frames, and see if the speed of light is constant for everyone!!! And we should not be satisfied with thought-experiments; we must conduct real physical experiments to verify the integrity thought- experiements! -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-E) Outsider System vs. Insider System-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- --------------------------------------- INTRODUCTION: For convience sake let us make the following defenitions: · An "Outsider System" is true when all observers *outside* a frame measure the speed of light which emanates from a source *inside* the frame to be the constant "c". · An "Insider System" is true when all observers *inside* a frame measure the speed of light which emanates from a source *inside* the frame to be the constant "c". Now, for Postulate #2 to be true all observers *inside* a frame should agree with all observers *outside* the frame that the speed of light coming from a source *inside* the frame is the constant "c"; that is, the "Outsider System" and the "Insider System" should be compatible. We will be analyzing two situations. We will first consider both situations assuming that the "Outsider System" is true. Then we will consider both situations assuming that the "Insider System" is true. "Insider System" are compatible, that is, the speed of light is the constant "c" for everyone. These situations we will be analyzing are thought-experiments. They should be tested out in reality by physical experiments to verify their integrity. A reasonable physical experiment to determine which of these thought-experiments are correct will be outlined at the end of this section. We saw above that time cannot dialate and length cannot contract such that the speed of light is maintained a constant. So, we will use Galilean transformations here instead of Lorentz transformations. Nonetheless, we know from physical experiments that "measured time" does dialate. At this point we do not know why; more physical experiments need to be done. Now, in this section we will say that "measured time" doesn't dialate; by the nature of these thought- experiements you will find that this premise should not appreciably affect our conclusions. And when we determine why "measured time" appears to dialate we should update these thought-experiments. We will call the person outside the frame the "outsider" while the person inside the frame, on the space ship, will be the "insider". Here we go! --------------------------------------- SITUATION #1: (assuming "Outsider System" is correct) On the space ship is a SD device secured such that the source is at the back of the space ship and the detector is at the front so that the detector will (hopefully) register the light from the source. Now, to start off the space ship is at rest with the "outsider". It is the "insider's" job to start the SD device when we decide to do the experiment. Let the "insider" start the experiment. The "outsider" will say he saw light traverse a distance "L" in a time "t". Also, since we are using an "Outsider System" he will say that the speed of light is "c". Thus, the "outsider" will say that: Now, the "insider" will also say that he saw a flash of light travel a distance "L" in a time of "t". Thus, the "insider" will also say that the light was travelling at a speed of "L/t". From the above equation we can say that "L/t" equals "c" and so the "insider" will agree with the "outsider" that the speed of light was "c". Now, let's accelerate this space ship forward so that it ends up with a speed of "v" relative to the "outsider". The velocity "v" is perpendicular to the line of sight of the "outsider". Let's have the "insider" do the experment once more. (Diagram A) (A) ---> WHAT THE OUTSIDER SEES: | | ct | |--------------------------| | | |··················|·······| forward --> | | |------------------|-------| | L vt \_________________________________ Notice that this round it will take more time for the light to be detected. This is because the ship is moving forward, and so, the front of the ship will have moved forward by a factor of "vt" before the flash of light could reach the detector. So this time the "outsider" will say that he saw a flash of light travelling at a speed of "c" traverse a distance "L+vt" in a time of "t". Thus, we arrive at the following equation: Again, the "insider" will say that he saw a flash of light travel a distance "L" in a time of "t". Thus, the "insider" will say that the light was travelling at a speed of "L/t". From the above equation we can say that "L/t" equals "c-v" and so the "insider" will not agree with the "outsider" that the speed of light was "c"; he will say that the speed of the flash of light was "c-v". Thus, when we use an "Outsider System" somebody inside the frame where the source of the light is might not agree with someone outside the frame that the speed of light is the constant "c". But notice that the above equation can be solved for "v"!: So far we have said that "v" is the relative velocity of the "outsider" and the space ship. But we have a little problem. The "insider" will measure the time elasped during the experiment to be some "fixed value". This fixed value has nothing to do with the relative velocity of the "outsider" and the space ship! Even though the above equation is what the "outsider" observes, the "insider" can conduct the experiment on his own and thus get a value for "t" without any aid or reference to the "outsider"! Thus, using that value of "t" the "insider" can figure out the value of "v" using the above equation! Now, what exactly is this velocity relative to? It must be a velocity that is measured relative to some "absolute frame of reference"! Put another way: You can be alone on the space ship and conduct this experiment and get a unique value for the change in time. Now, "L" and "c" are constants, so we must conclude that "v" is also unique. That is, a unique value of "t" corresponds to a unique value of "v". Now, what is a "unique" velocity? It must be a velocity measured from some "absolute frame". And since we said above that "v" is the relative velocity of the "outsider" and the space ship then we must notice that we have inadvertently put the "outsider" at rest with the "absolute frame of reference". If the "outsider" is not at rest with the "absolute frame" then he will see the speed of light to be some constant, but that constant will not be "c". And so we have just proved that the first postulate is wrong! Look! We have distinguished one inertial frame from the others! We've derived an equation that determines the velocity of the ship relative to an "absolute frame". Now, let's accelerate this space ship backward so that it ends up with a speed of "v" relative to the "outsider". The velocity "v" is perpendicular to the line of sight of the "outsider". Let's have the "insider" do the experiment once more. (Diagram B) (B) ---> WHAT THE OUTSIDER SEES: | | ct | |----------| | | |··········| forward --> | | |-------| | vt | |------------------| | L \_________________________________ Notice that this round it will take less time for the light to be detected. This is because the ship is moving backward, and so, the front of the ship will have moved backward by a factor of "vt" before the flash of light could reach the detector. So this time the "outsider" will say that he saw a flash of light travelling at a speed of "c" traverse a distance "L-vt" in a time of "t". Thus, we arrive at the following equation: Again, the "insider" will say that he saw a flash of light travel a distance "L" in a time of "t". Thus, the "insider" will say that the light was travelling at a speed of "c+v". Thus, when we use an "Outsider System" somebody inside the frame where the source of the light is might not agree with someone outside the frame that the speed of light is the constant "c". Again, we can determine the "absolute velocity" of the ship: Again, we have inadvertently put the "outsider" at rest with the "absolute frame". If the "outsider" is not at rest with the "absolute frame" then he will see the speed of light to be some constant, but that constant will not be "c". Now let's consider an "outsider" that is travelling at a speed of "u" relative to the "absolute frame". If the "outsider's" velocity is in forward direction of the space ship then the "outsider" will say the light travelled at a speed of "c-u". Now, if the "outsider's" velocity is in the backward direction of the space ship then he will say he saw light travel at the speed of "c+u". Thus in this case only the "outsider" at rest with the "absolute frame" will measure the speed of light to be the constant "c". --------------------------------------- ADDING TO DEFINITIONS: Now, we need to add to the definition above of the "Outsider System" and the "Insider System" because they are incomplete. We avoided mentioning this before to avoid confusion: Sometimes light will appear to move from the source in a straight line only from one particular frame; all other frames will see the light "bend". Einstein claims that the speed of light is constant. However, he never decided from which frame does the light always seem to leave the source in a straight line. Big error. I claim here - without any justification - that the observer who witnesses light travel at the constant speed "c" is also the observer who always sees light travel from the source in a straight line. I claim this because my intuition tells me so and I will only be validated or discredited by physical experiments. If we are using an "Outsider System" then the direction of the light follows the direction the source is pointing in as seen by an "outsider". Now, all the "outsiders" are in different frames so that they will all (usually) disagree as to what the actual direction of the light is. Because only one "outsider" can be "right" as to what the actual direction of the light is, we are led to the conclusion that only one frame of reference is "right". This leads us directly back to the idea and necessity to create an "absolute frame". This means that (usually) only one "outsider" in a unique frame will see light follow from the source in a "straight" line. Everyone else will (usually) see light "bend", that is, the light will not follow from the source in a straight line. On the other hand, if we are using an "Insider System" then the direction of the light follows the direction the source is pointing in as seen by an "insider". Now, since all "insiders" are in the same frame then they will all agree as to what the actual direction the light is moving in. So, we have no need in this case to create an "absolute frame". This means that only the "insiders" will always see light follow from the source in a "straight" line. Everyone else ("outsiders") will (usually) see light "bend", that is, the light will not follow from the source in a straight line. The reason why we could leave these points out of the definitions before is because in "Situation #1" all "outsiders" and all "insiders" will agree as to what the direction the light is heading in; this is not always the case as "Situation #2" will demonstrate. --------------------------------------- SITUATION #2: (assuming "Outsider System" is correct) On the space ship is another SD device such that the source is secured on the floor of the space ship and the detector is fastened above so that the detector will (hopefully) register the light from the source. To start off the space ship is at rest with the "outsider". It is the "insider's" job to start the SD device when we decide to do the experiment. Let the "insider" start the experiment. The "outsider" will say he saw light traverse a distance "L" in a time "t". Also, since we are using an "Outsider System" he will say that the speed of light is "c". Thus, the "outsider" will say that: Now, the "insider" will also say that he saw a flash of light travel a distance "L" in a time of "t". Thus, the "insider" will also say that the light was travelling at a speed of "L/t". From the above equation we can say that "L/t" equals "c" and so the "insider" will agree with the "outsider" that the speed of light was "c". Now, let's accelerate this space ship forward so that it ends up with a speed of "v" relative to the "outsider". The velocity "v" is perpendicular to the line of sight of the "outsider". Let's have the "insider" do the experment once more. (Diagram C) (C) ---> WHAT THE INSIDER SEES: | | vt | ______ | · | | · | | · | L forward --> | c[1+(v/c)²]^½ * t · | | · | | ·| \_________________________________ Now, let's accelerate this space ship backward so that it ends up with a speed of "v" relative to the "outsider". The velocity "v" is perpendicular to the line of sight of the "outsider". Let's have the "insider" do the experment once more. (Diagram D) (D) ---> WHAT THE INSIDER SEES: | | ·| | · | | c[1+(v/c)²]^½ * t · | forward --> | · | L | · | | ·_____| | vt \_________________________________ In both cases above, the "outsider" will see exactly what he saw before. That is, he will see the light emanate from the source and move upward. But while the flash of light is heading upwards towards the detector, the space ship has moved forward or backward by a factor of "vt". Thus, if the space ship is fast enough then it may have moved forward or backward enough such that the flash of light might not even hit the detector! The light may not hit the detector because the light is travelling upwards as seen from outside the frame, not inside. So, the "insider" will see light "bend". Now, the light will hit the ceiling of the space ship at a certain point. So, we can measure the length "vt" using a ruler; let that length be "Z". We can also determine "t" using a clock. Then we can create an equation that solves for the "absolute velocity", "v": Again, we have inadvertently put the "outsider" at rest with the "absolute frame". If the "outsider" is not at rest with the "absolute frame" then he will see the speed of light to be some constant, but that constant will not be "c". In both cases, the "insider" will say he saw light travel a distance "((vt)²+(ct)²)^½" in a time "t". Thus, he will say he saw light travel at the speed of "c[1+(v/c)²]^½". So, the "insider" will measure the speed of light to be greater than or equal to the constant "c", but never less. Thus in this case only the "outsider" at rest with the "absolute frame" will measure the speed of light to be the constant "c". --------------------------------------- REMARKS: Before we move on, it should be noted that above in "Situation #1" and "Situation #2" we only examined the velocity in one dimension. So, if we are to try to actually implement the thought- experiments in real life then one would have to consider the other dimensions of the velocities of the spaceship and the flash of light. --------------------------------------- NEGATIVE CONCLUSIONS: From the above, if we are to say that the "Outsider System" is true then we are led to three inevitable negative conclusions: --> (1) Postulate #1 is wrong! There must be some "absolute frame" for "v" to be relative to, and so, we have distinguished one frame from the others. --> (2) Postulate #2 has errors! We've used the "Outsider System" and we've found that the original definition of the "Outsider System" is wrong! The speed of light is only the constant "c" when it is measured from the "absolute frame". --> (3) When observed from inside the frame where the light source is, the flash of light may seem to "bend", that is, it may not follow from the source in a straight line. --------------------------------------- CONCLUSIONS: We have seen above that the "Outsider System" is ridden with pitfalls. Now, many experiments have been done where the light source and the experimenter are inside the same frame. In such experiments the speed of light has never deviated from "c" and light has never appeared to "bend". So with these problems it is likely that we started with the wrong assumption. So instead let us now assume that the "Insider System" is right and redo the thought-experiments. --------------------------------------- SITUATION #1: (assuming "Insider System" is correct) On the space ship is a SD device secured such that the source is at the back of the space ship and the detector is at the front so that the detector will (hopefully) register the light from the source. Now, to start off the space ship is at rest with the "outsider". It is the "insider's" job to start the SD device when we decide to do the experiment. Let the "insider" start the experiment. The "insider" will see the light traverse a distance "L" in a time "t". Also, since we are using an "Insider System" the "insider" will say the light travelled at the speed of "c". So, Now let's consider an "outsider" that is travelling at a speed of "v" relative to the space ship. The velocity "v" is perpendicular to the line of sight of the "insider". Let the "insider" do the experiment once more. The "insider" will again see light traverse a distance "L" in a time "t". In fact, the "insider" will *always* observe the same thing because we are using an "Insider System", which means that the speed of light is always constant within the frame. If the "outsider's" velocity is in the forward direction of the space ship, the front of the ship will have seemed to move backward by a factor of "vt" before the flash of light could reach the detector. So, the "outsider" will see the light traverse a distance "L-vt" in a time "t". Using the above equation we can say that the "outsider" will see the light travel at a speed of "c-v". (Diagram E) (E) ---> WHAT THE OUTSIDER SEES: | | (c-v)t | |----------| | | |··········| forward --> | | |-------| | vt | |------------------| | L \_________________________________ Now, if the "outsider's" velocity is in the backward direction of the space ship, the front of the ship will have seemed to move forward by a factor of "vt" before the flash of light could reach the detector. So, the "outsider" will see the light traverse a distance "L +vt" in a time "t". Thus, he will then say he saw light travel at the speed of "c+v". (Diagram F) (F) ---> WHAT THE OUTSIDER SEES: | | (c+v)t | |--------------------------| | | |··················|·······| forward --> | | |------------------|-------| | L vt \_________________________________ This means that someone outside the frame will not agree with the "insider" that the speed of light is the constant "c"! --------------------------------------- SITUATION #2: (assuming "Insider System" is correct) On the space ship is another SD device such that the source is secured on the floor of the space ship and the detector is fastened above so that the detector will (hopefully) register the light from the source. Now, to start off the space ship is at rest with the "outsider". It is the "insider's" job to start the SD device when we decide to do the experiment. Let the "insider" start the experiment. The "insider" will see the light traverse a distance "L" in a time "t". Also, since we are using an "Insider System" the "insider" will say the light travelled at the speed of "c". So, Now let's consider an "outsider" that is travelling at a speed of "v" relative to the space ship. The velocity "v" is perpendicular to the line of sight of the "insider". Let the "insider" do the experiment once more. The "insider" will again see light traverse a distance "L" in a time "t". In fact, the "insider" will *always* observe the same thing because we are using an "Insider System", which means that the speed of light is always constant within the frame. The "outsider" will see the light "bend" because the light is travelling upwards in a straight line as seen from inside the frame, not outside. If the "outsider's" velocity is in the forward direction of the space ship, the "outsider" will see the light traverse a distance "(L²+ (vt)²)^½" in a time "t". (Diagram G) (G) ---> WHAT THE OUTSIDER SEES: | | vt | ______ | · | | · | | · | L forward --> | c[1+(v/c)²]^½ * t · | | · | | ·| \_________________________________ If the "outsider's" velocity is in the backward direction of the space ship, the "outsider" will see the light traverse a distance "(L²+ (vt)²)^½" in a time "t" (again). (Diagram H) (H) ---> WHAT THE OUTSIDER SEES: | | ·| | · | | c[1+(v/c)²]^½ * t · | forward --> | · | L | · | | ·_____| | vt \_________________________________ Both observations above are symetrical. Thus, we find that the "outsider" will measure the speed of light to be "c[1+(v/c)²]^½". This means that someone outside the frame will not agree with the "insider" that the speed of light is the constant "c"! --------------------------------------- NEGATIVE CONCLUSIONS: From the above, if we are to say that the "Insider System" is true then we are led to one inevitable negative conclusion: --> (1) Postulate #2 has errors! We've used the "Insider System" and we've found that the speed of light is the constant "c" only when measured from inside the frame where the light source is. --------------------------------------- CONCLUSIONS: Notice that two negative conclusions from when we considered the "Outsider System" have gone!: (1) We no longer need to "create" an "absolute frame" and (2) light does not seem to "bend" when the source and the observer are in the same frame. So, comparing the conclusions we find that it is likely that the "Insider System" is correct, not the "Outsider System". To recap, when we use the "Outsider System" then light travels at the constant "c" from the "absolute frame" but not "c" from all other frames. When we use the "Insider System" then light travels at the constant "c" from inside the frame (where the source is) but not "c" from all other frames. Thus, we can conclude that the "Outsider System" and the "Insider System" are incompatible. Postulate #2 is wrong no matter which way you look at it! Either the "Outsider System" is right or the "Insider System" is right, not both! The "Outsider System" means that the speed of light does not depend on the motion of the source while the "Insider System" means that the speed of light does depend on the motion of the source; contradiction ensues. --------------------------------------- ASIDE: If we are to assume that light travels abiding by an "Insider System" then that means that the speed of light depends on the motion of the source. This means that if two objects are heading *away* from each other such that the relative velocity of two objects is greater than "c" then the light from one object will never reach the other. Also, by the Doppler effect the frequency of the light would be an imaginary number. Now, we know that the universe is expanding so it is likely that our planet Earth has a relative velocity greater than "c" with many of the objects in the universe. Perhaps that is why we cannot see dark matter.. And what happens when the relative velocity is greater than "c" when the two objects are heading *towards* each other? Again, the frequency of the light will be an imaginary number. Again, is that why we cannot see dark matter?.. So, is the equation we use for the Doppler effect for light correct?.. --------------------------------------- "OUTSIDER SYSTEM VS. INSIDER SYSTEM" EXPERIMENT: We can create a simple experiment to determine (at last!) if light travels using an "Outsider System" or an "Insider System". We start with two sources, Source A and Source B, and two detectors, Detector A and Detector B. Source A is pointing at Detector A and Source B is pointing at Detector B. Both detectors are side-by-side. Source A is on the ground a fair distance away from Detector A. Source B is on a train quite far behind Source A. The idea of the experiment is to let the train (which has Source B) accelerate towards Detector B. When Source B reaches Source A (which is on the ground) both sources emit a flash of light. Both flashes of light will traverse the same distance to reach the detectors. We just have to see which flash of light gets recorded by the detectors first and draw our conclusions from there! I predict that Detector B will register the light first, and so the "Insider System" will be validated. If Detector A and Detector B register the light from the sources at the same time then the "Outsider System" is validated. Very simple idea. I wonder why I have never heard of such an experiment being performed.. If the "Outsider System" is validated then we run into difficulties. For instance, we can put Source B at the back of the train and Detector B at the front of the train. Let "L" be the distance between the source and the detector. Then we can redo the experiment and measure the time "t" (using a clock) it takes for the light to go from Source B to Detector B. Now, if you were a person on the train you'd expect that "t" would be a constant; this is not so. When the train is stationary then the light traverses a distance "L" with a speed "c"; when the train is moving (with velocity "v") then the light traverses a distance "L+vt" with a speed "c". Thus, when the train is stationary the time it takes to conduct the experiment is "L/c" while when the train is moving it takes "L/(c-v)". Now, you can be alone on the train and conduct this experiment and get a unique value for the change in time. "L" and "c" are constants, so we must conclude that "v" is also unique. That is, a unique value of "t" corresponds to a unique value of "v". Now, what is a "unique" velocity? It must be a velocity measured from some "absolute frame".. (Again, we have inadvertently put ourselves at rest with the "absolute frame" making the speed of light "c"; this assumption may very well be wrong. If we are not at rest with the "absolute frame" then we will see the speed of light to be some constant, but that constant will not be "c".) With these difficulties when we use the "Outsider System" it is likely that light travels instead by the "Insider System", which is why I predict it to be so above. --------------------------------------- ASIDE: Sound propagates through air using an "Outsider System". Consider two people, a pilot and a co-pilot, both sitting in the cockpit of a plane. The co-pilot is behind the pilot. The plane is travelling faster than the speed of sound relative to the ground and atmosphere. Now, if the cockpit is closed then when the co-pilot says something the sound of his voice will travel forward to the pilot. The speed of the sound of his voice will be travelling at the speed of sound relative to the air in the cockpit. However, if the cockpit is open and the co-pilot says something the sound of his voice will *not* travel forward to the pilot. The speed of the sound of his voice will be travelling at the speed of sound relative to the air of the atmosphere. But since the plane is travelling faster than the speed of sound relative to the atmosphere, the co-pilot's voice will not be heard by the pilot. *(I am interested in knowing how open the cockpit can be such that the pilot still hears the co-pilot's voice.)* Notice that if the cockpit is open then we can determine the velocity of the plane relative to the atmosphere as we did above with light. The velocity is zero when the plane is stationary with the atmosphere, the atmosphere being the medium through which sound propagates through. Thus, if we are to say that the "Outsider System" for light is true, then we can say that when the space ship's "absolute velocity" is zero then it is stationary with the "ether", the medium through which light (supposedly) propagates through. If the "Insider System" for light is true then we don't really need to introduce an "ether". -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-F) Understanding the Michelson-Morley Experiment=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- --------------------------------------- INTRODUCTION: My experiment is different from Michelson-Morley's setup but it essentially demonstrates the same thing. We will have two SMD devices, "SMD X" and "SMD Y", and we will do this experiment on the equator of the Earth. "SMD X" is set up parallel to the equator while "SMD Y" is set up perpendicular to the equator. "SMD X" has the source/detector west and the mirror east while "SMD Y" has the source/detector south and the mirror north. And there are two people, an "insider" and an "outsider". The "insider" is on the ground next to the two SMD devices. The "outsider" is in a space ship above the Earth such that he observes the SMD devices to be directly below him every 24 hours; so, the "outsider" will see the Earth rotating at a velocity of "3*10^4" meters per second. We assume here that the "insider" and the SMD devices are at rest; this is not so. The Earth is accelerating by rotating. But, if we conduct the experiment quickly, then we can dismiss the fact that the Earth is rotating. (ASIDE: I define perpetual motion as motion that continually causes a change in inertial frame without any external forces. An "ideal" planet in rotation is in perpetual motion. If you are attached to the planet you will be constantly changing inertial frames of reference as the planet rotates. If the planet is "ideal" then the planet will continue to rotate forever, thus making the motion perpetual. It rotates forever because the force that causes the rotation is the force that causes the rotation, which is the force that causes the rotation.. you get the point. Once a force has been applied to make it rotate, it will continue to rotate forever.) In the experiment done by Michelson and Morley, they themselves were the "insiders", and there was no "outsider". Now, let's do this experiment in our thoughts and see what we'd expect to happen. We saw above that time cannot dialate and length cannot contract such that the speed of light is maintained a constant. So, we will use Galilean transformations here instead of Lorentz transformations. Nonetheless, we know from physical experiments that "measured time" does dialate. At this point we do not know why; more physical experiments need to be done. Now, in this section we will say that "measured time" doesn't dialate; by the nature of this experiment you will find that this premise should not appreciably affect our conclusions. And when we determine why "measured time" appears to dialate we should update this discussion of the experiment. The Michelson-Morley experiment attempts to find the Earth's speed relative to the ether by observing a fringe shift in the interference pattern of two beams of light. The fact that the experiment fails is because there is no ether. In this experiment we are not finding "fringe shifts"; we are looking for a "time discreptancy" in the times of both SMD devices. But if there is a time discreptancy then that implies that in a Michelson Interferometer we should expect to find a fringe shift. Now, when you look at both SMD devices then you will see light traverse a different distance based on your frame. Everyone will agree to that. When we add to that the assumption that the speed of light is constant in all frames then you expect to find that "derived time" dialates. And because "derived time" dialates then you'd expect to find a time discreptancy which implies that the Michelson-Morley experiment should work, that is, we should see a fringe shift in the Michelson Interferometer. I will show that (1) when we assume that the speed of light is always "c" then we encounter a contradiction and (2) when we assume that light abides by an "Insider System" then we understand why we get a "null" result. Let's now activate the SMD devices in our minds. --------------------------------------- FOR "SMD X" and "SMD Y": (for the "insider") Now the speed of light from the "insider's" view is "c"; either we assume that the speed is "c" because of Postulate #2 or we infer that the value is "c" because we are using an "Insider System". For both SMD devices the "insider" will say he saw the light traverse a distance "L" twice. So, if "t" is the total time it takes for the light in both SMD devices to go from the source, to the mirror, and back to the detector, then: So, the "insider" will not observe a time discreptancy. And so, when using a Michelson Interferometer the "insider" will not see a fringe shift because the time elasped for both SMD devices is equal. --------------------------------------- DEFINING VARIABLES: The "outsider", on the other hand sees the experiment differently. As observed by the "outsider": In "SMD X": · let a time "tX1" pass as the light moves from the source to the mirror · let a time "tX2" pass as the light moves from the mirror to the detector In "SMD Y": · let a time "tY1" pass as the light moves from the source to the mirror · let a time "tY2" pass as the light moves from the mirror to the detector Also, We will derive two values of each: "tX1", "tX2", "tY1", and "tY2"; the first by assuming that Postulate #2 is correct, the second by assuming that the "Insider System" is right. When we are deriving the time variables for the "Insider System" we need to know the velocity of the light; one needs only refer to the two situations in the section "Outsider System vs. Insider System" where we assumed that the "Insider System" is right. --------------------------------------- FOR "SMD X": (for the "outsider") When the light is travelling towards the mirror the "outsider" sees the light traversing a distance "L+vt" in a time "tX1". (Diagram A) · if the speed of light is "c" (by Postulate #2) then "tX1 = L/(c-v)" · if the speed of light is "c+v" (by "Insider System") then "tX1 = L/c" (A) ---> WHAT THE OUTSIDER SEES: | | (c+v)tX1 or ctX1 | |--------------------------| | | |··················|·······| East --> | | |------------------|-------| | L vtX1 \_________________________________ When the light is returning back to the detector the "outsider" sees the light traversing a distance "L-vt" in a time "tX2". (Diagram B) · if the speed of light is "c" (by Postulate #2) then "tX2 = L/(c+v)" · if the speed of light is "c-v" (by "Insider System") then "tX2 = L/c" (B) ---> WHAT THE OUTSIDER SEES: | | (c-v)tX2 or ctX2 | |----------| | | |··········| East --> | | |-------| | vtX2 | |------------------| | L \_________________________________ --------------------------------------- FOR "SMD Y": (for the "outsider") When the light is travelling towards the mirror the "outsider" sees the light traversing a distance "[L²+(vt)²]^½" in a time "tY1". (Diagram C) (C) ---> WHAT THE OUTSIDER SEES: | | ·| | · | | c[1+(v/c)²]^½ * tY1 · | L East --> | or c * tY1 · | | · | | ·_____| | vt \_________________________________ When the light is returning back to the detector the "outsider" sees the light traversing a distance "[L²+(vt)²]^½" (again) in a time "tY2". (Diagram D) (D) ---> WHAT THE OUTSIDER SEES: | | |· | | · | | · c[1+(v/c)²]^½ * tY2 East --> | L | · or c * tY2 | | · | |_____· | vt \_________________________________ So, for both cases above: · if the speed of light is "c" (by Postulate #2) then "tY1 = tY2 = L/c * 1/[1-(v/c)²]^½" · if the speed of light is "c[1+(v/c)²]^½" (by "Insider System") then "tY1 = tY2 = L/c" --------------------------------------- ASSUMING POSTULATE #2 IS CORRECT: When we assume that the speed of light is always the constant "c" then the "outsider" observes a time discreptancy in both SMD devices. This means that using a Michelson Interferometer, if we assume Postulate #2 is correct, the "outsider" will see a fringe shift. --------------------------------------- ASSUMING INSIDER SYSTEM IS CORRECT: = 2L/c When we assume that the "Insider System" is right the "outsider" no longer expects to find a time discreptancy. This means that in a Michelson Interferometer, if we abide by an "Insider System", the "outsider" will not see a fringe shift. --------------------------------------- CONCLUSIONS: The truth is that the fringe shift doesn't exist as demonstrated by physical experiments. And so, we can conclude that there is no ether. Now, when we assume that the speed of light is "c" in all frames then we find that the "insider" does not observe a time discreptancy while the "outsider" does. This means that in a Michelson Interferometer the "insider" does not see a fringe shift while the "outsider" does. So, one of them is wrong because either the fringe shift exists or it doesn't; they can't both be right. Of course, we know that it doesn't exist. But with this contradiction we can conclude that the speed of light cannot be constant in all frames. And so, when we don't see a fringe shift then the Michelson- Morley experiment gets a "null" result. But when we assume the "Insider System" is right for light then we see why we get a "null" result. Michelson and Morley expected to find a difference in the speed of the flashes of light. The fact that they didn't implies that the speed of light is a constant for the "insider". The experiment says nothing about how an "outsider" would view the situation. Now, Einstein's second postulate claims that the speed of light is constant for the "insider" *and* the "outsider". Claiming that the "outsider" views the speed of light as a constant is totally unjustified. And, as we've seen above, the "outsider" cannot view the speed of light as being constant; when he does, we encounter a contradiction. So, Postulate #2 goes to the garbage and the "Insider System" is validated. This experiment should be conducted in reality to ascertain whether the above conclusions are correct. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-G) The Finale-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- --------------------------------------- Until more experiments are performed this paper leaves physics in a puddle of mud. In getting out of this puddle we have to check many things like the following: · why time seems to dialate · whether there is an "absolute frame" · whether velocity and acceleration are relative · does light propogate using an "Insider System" or an "Outsider System" · the Doppler effect for light --------------------------------------- When you discount all the major pitfalls of Special Relativity - and there are many - it turns out to be a very beautiful theory. I believe that that is the main reason why the average physicist believes that Special Relativity is a coherent theory. But watching someone who is explaining Special Relativity is like watching a good salesman trying to sell a bad vacuum. Or put more bluntly as a certain "Mike" put it on the usenet newsgroup "sci.physics.relativity": "Relativists are cranks because they deny the immediately given. they are also ad hominen animals, just watch how many of them will turn ad hominen because of this post. they are so ad hominen, they do not even get a job at MacDonalds and lurk in the usenet 24/7." hahahaha... --------------------------------------- · A great but short book which I have often consulted identifies the various failures of Special Relativity. I quoted it: "The Special Theory of Relativity" by Essen, L. · I have quoted this book: "A Debate on the Theory of Relativity" by Professor W. D. MacMillan. · Ardeshir Mehta has come up with many clever thought-experiments which debunk Special Relativity: [Only registered users see links. ] There must be many other people who have come to the same conclusions I have here. The faults of Special Relativity are too obvious. -\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\- -|-|-| THE END! -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|- -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/- by Raheman Velji [Only registered users see links. ] [Only registered users see links. ] June 14, 2007 you can also view this paper (and updated versions) at... ...[Only registered users see links. ] ...[Only registered users see links. ] ! ! ! BEWARE OF THE ILLUMINATI ! ! ! ! ! ! BEWARE OF CHEMTRAILS ! ! ! |
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