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Eugene Stefanovich:
Well, congratulations. You've just managed to assert that not only
is the principle of equivalence wrong, but that even inertial mass is
not simply inertial mass. (You can't have it both ways. If time dilation
depends upon the type of mass which interacts, then obviously mass is
not just mass.) So far, the evidence is against you at better than parts
in 10^13.
How do you explain the following:
(1) Differential cross sections transform properly from centerofmomentum
to lab coordinates, independent of the material. In fact, the standard
quantity that one uses in calculating the cross section is the lorentz
invariant phase space.
(2) Accelerators such as cyclotrons, which accelerate ions ranging
from deuterium through uranium have never noticed the kind of
dependence to which you refer. The relativistic corrections to
the magnetic fields are crucial to accelerating a beam. Those
corrections are determined from m/q and the resonance is very
sharp.
(3) The value measured for the weak coupling constant has no dependence
on the weak decay process used, i.e., all weak decays occur at the
same rate, regardless of the nuclues or the measurement. In other
words, whether you determine the ftvalue from the decay of rela
tivistically moving pi+, or determine the ftvalue for superallowed
fermi decays for a variety of nuclei, the number is the same.
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Eugene Stefanovich:
How do you know it's unlikely? According to you, you don't what the
probability is until you measure the ensemble, so there's no reason for
you to assume anything at all about what you should get. For the rest of
us, it's not a problem, but then again, the rest of us don't regard the
probability amplitude as an observable that depends upon an ensemble
of measurements in order to fix a value. The rest of us treat the
trials as independent, each having the same probability.
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"Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...


 jem wrote:
 > Eugene Stefanovich wrote:
 >
 >>
 >> jem wrote:
 >>
 >>> Eugene Stefanovich wrote:
 >>>
 >>>> I hope you will find this book not boring and thoughtprovoking.
 >>>> I would be glad to read your comments either on these newsgroups
 >>>> or at my email address [Only registered users see links. ]
 >>>> You can also visit my website [Only registered users see links. ]
 >>>>
 >>>
 >>> Re section 1.2.1  are you suggesting that a quartz clock and a
 >>> balance clock that are collocated and insynch when viewed from their
 >>> rest frame, could be observed to be out of synch by a moving
 >>> observer? And are you suggesting that a tungsten rod and a wooden
 >>> rod that are coincidental in their rest frame could be seen to have
 >>> different lengths by a moving observer?
 >>
 >>
 >>
 >> That's exactly what I am saying.
 >
 >
 > So what would the moving observer see if the 2 rods were lightly glued
 > together along their lengths?
 >

 That's a very good question. I am glad you asked. I actualy waited when
 somebody asks this kind of question, because it cuts to the heart of my
 approach.

 When you glue two rods together you introduce interaction between them.
 In my approach, interaction has effect on boost transformations.
 Therefore, from the point of view of moving observer, two glued rods
 will look different from two free rods. I can't tell you exactly what
 this difference will be, because such an answer requires a full
 dynamical solution for this system. For example, I can imagine that the
 two glued rods may become slightly bent.

 The main point is that until now we considered boost transformations as
 kinematical (universal) transformations, like translations and
 rotations. This is not correct. Boost transformations are dynamical,
 so they are more like time translations. You are not surprised that
 when time passes, objects can dramatically change their appearance and
 internal structure. If we take the same glued rods as an example, then
 as time passes by and glue hardens, the two rods may bend. The same
 with boost transformations. They are just as dynamical as time
 translations,
 and they may lead to rather drastic changes in the appearance of
 physical objects. (of course the primary effect will be the usual
 length contraction, and we are talking here about some miniscule
 corrections to this primary effect).

 You could invoke another example, which also seems impossible on the
 surface.
 Take two clocks of different design, but exactly the same rate
 (e.g., balance clock and quartz clock). Connect these clocks to
 an explosive device in such a way that when they start to show
 different time (e.g. 1 msec difference) the bomb goes off. The observer
 at rest may feel safe, because the clocks are guaranteed to go at the
 same rate and explosion never happens. The moving observer has different
 view: he may observe that clocks have slightly different rate and at
 some point in time, the difference of their readings may reach 1 ms.
 So, in principle, the moving observer can register an
 explosion while observer at rest can't.
 The idea that observer at rest does not see explosion
 and moving observer does see the explosion may seem crazy. But if you
 change in the preceding sentence words "at rest" and "moving" to
 words "today" and "tomorrow", respectively, then the statement doesn't
 look that stupid.

 Actually, in my book I discussed a similar effect in the case of
 unstable particle (see subsection 13.2.1). If at time t=0
 observer at rest prepares unstable particle (with 100% certainty),
 then for the moving observer there is a (very small) chance to see this
 particle as decayed (i.e., to register the decay products even at
 t = 0).
 If this particle is an unstable nucleus of Uranium 235, which can
 initate the chain reaction in the bomb, then, here you are: the moving
 observer sees an explosion while observer at rest doesn't.

 It is important to realize that we are dealing here with ridiculously
 small effects. In my treatment of the decay of fast moving unstable
 particles (subsection 13.2.2) I estimated the order of magnitude
 of corrections to the
 Einstein's formula as dM/M where dM is the width of mass distribution
 and M is the total mass. For example, for muon this ratio is only
10^{17}.
 I think this estimate is roughly true for other situations. Thus in the
 case of two rods glued together you should consider the ratio
 E/Mc^2, where E is the binding energy due to the glue and M is the
 mass of the rods. There is no chance such corrections can be observed.
 Even the much bigger effect of length contraction has not been directly
 observed yet.

 However, no matter how small these corrections are, they are nonzero,
 and they undermine the universality of Lorentz transformations
 proclaimed by Einstein and entire Minkowski spacetime picture.
 These corrections are unavoidable. If you accept

 1) Poincare group relationships between inertial observers
 (every relativist must accept it)
 2) dynamical (interaction dependent) character of (the representation
 of) time translations
 3) kinematical (interaction independent) character of (the
 representation of) space translations and rotations

 then you have no other choice but to accept the dynamical character
 of (the representation of) boosts.
This seems to be somewhat the same as SR and LET both being right only with
SR having the most effect by a long shot. But I arrive at that conclusion
by matter and spacetime being made of the same "stuff". What is going to
"distort" more? Spacetime or matter? Well, I would think it would be
spacetime. But matter should "distort" a tiny tiny amount also. Hmmm...
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Eugene Stefanovich:
As the selfdescribed independent thinker to claim to be, why on earth
do you need to find this spelled out in a textbook? Even us establishment
clones are able to figure this out simply understanding the basis of
relativity.
Hint: Relativity is a theory of spacetime. The lorentz transforms
may be derived from the first postulate alone, with the galilean
transforms as a limiting case. Light and the properties of
light belong in a theory about light, i.e., a theory of
electromagnetism. Maxwell's equations are one such theory
in which light propagates along null rays. Proca's equations
are a different theory in which light does not propagate along
null rays. It's a perfectly good relativistic theory but the
photon is massive and behaves just like every other particle
with a mass.
Well, being the simple establishment clone I appear to be, I wasn't
smart enough to go hunting for a book that spelled it out. I had to
settle for understanding the textbooks I had.
You mean, you're argument? Well, that is certainly the place to start
looking. You might try this argument to figure out where the gap lies:
Start with a vector v = (t, x, y, z). Perform an infinitesimal
spacetime displacement, v > v' = v + \delta v. Require that
the scalar product remain unchanged under that transformation.
Consider the various possible metric tensors you can construct,
i.e., signature 0,2 or 4. After deducing that only one of these
makes sense, construct the finite transforms. Note that you get
three rotations and three boosts (assuming you pick the only
metric that makes physical sense).
I'm afraid you haven't put on your independent thinking cap
enough to figure out how physical theories relate to each other.
If you don't want to treat spacetime as spacetime so that coordinate
transfor,ations are not interaction dependent, what possible reason
could you have for justifying the use of spacetime at all? You're
being silly. If spacetime is interaction dependent, then there's
no point in even considering poincare invariance to be of any value.
Obviously that will not explain anything. If you actually understood
what I just suggested you look up, you wouldn't have such difficulty
understanding the irrelevance of the ``light postulate'' to relativity.
[...]
The lorentz transforms are not a postulate. The lorentz transforms are
derived from the first postulate regarding the equivalence of inertial
systems.
[...]
No shit, sherlock. Why do you think I've been telling you the
``light postulate'' is irrelevant to relativity? That is the
ENTIRE point. The properties of light belong in a theory about
light.
You have apparently didn't notice that relativity was developed at
a time the world didn't know of any interactions other than E&M and
gravity. Einstein did not ``postulate such a bridge'' to ``all
physical systems''. He postulated a bridge to the only physical
systems anyone knew existed, i.e., electromagnetic systems.
``Independent thinking'' seems to be taking away from understanding
the basics.
Apparently one that seems beyond your ``independent thinking'' and
the assertions derived therefrom. I just pointed out a counter example
to your assertion that relativity depends upon the ``light postulate''.
[...]
Why? Are you going to tell my mother that I'm not being fair by
not claiming enough postulates to make you happy or something?
Download a new book on quantum mechanics and relativity.
Eugene Stefanovich:
You might want to keep a copy of this so I don't have to say it for
the N+1th time. Because you start with a hamiltonian in which the
electromagnetic interaction has two degrees of freedom, then perform
a socalled unitary transform and end up with (at least) one more
degree of freedom, then assert that as a physical result.
Not if your axiomatic structure includes any of the standard physics
you claim it does.
Sure they do. Your prediction of instantaneous interaction means you
have introduced an unphysical longitudinal polarization to the
electromagnetic interaction. p_u A^u = 0 and the coulomb gauge further
takes the fields to be transverse, i.e., div A = 0. You performed an
alleged unitary transform and declared the unphysical longitudinal
polarization you got to be a real interaction. But, I've already attempted
to explain why, in at least a halfdozen ways, so I can't see any point in
you asking again. All you have to do is reread anyone of my posts and
pick the explanation to which you most easily relate.
They disagree with your axiomatic structure, too. I told you many
posts ago that what you claimed as a result of your theory wasn't
the issue. The issue is that the socalled ``axiomatic structure''
you claim to employ is not consistent with the results you claim
to have derived from it.
You only demonstrated you know absolutely nothing about qed. The
propagation of the electromagnetic interaction at `c' is essential
to deriving the qed lagrangian. In qed, there is exactly one field.
The electromagnetic field. The electromagnetic field propagates at
`c' whether that refers to light or not.
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Ken S. Tucker wrote:
So far so good, except for the fact that one radio photon is not
enough to create detectable wave. You need to have a huge number of them
working together in order to create continuous "electromagnetic field".
Another objection is that gamma photon does not consist of two charges.
It can create an electronpositron pair when it hits some obstacle.
Otherwise I am with you.
Thanks for the advice. Do you know his email?
That's just indicates the inadequacy of our experimental devices.
Theoretically, if there existed radiophotography, then radio photons
would make tiny little dots on the "photograph". I cannot prove that,
I believe in that because I believe in unity of nature: photons
of different energy have exactly the same properties except
energy. How would you describe the radiophotgraphy experiment?
No, light has nothing (or very little) to do with electromagnetic
interactions. Light is a flow of photons. Electromagnetic interactions
are Coulomb and magnetic (and contact and spinorbit...) instantaneous
potentials (or I should better say "forces", so you not confuse them
with the scalar and vector potentials of Maxwell's theory) acting
between charged particles (see subsection 12.2.3).
The connection between light and electromagnetism appears in my theory
if
we take into consideration the bremsstrahlung terms in the Hamiltonian
(see Table 1 in section 12.1). In classical Maxwell's physics this
interaction has counterpart in "radiation reaction". Due to
bremsstrahlung (radiation due to acceleration or breaking), each time
a charged particle is accelerated or decelerated it emits (or absorbs)
photons.
So, when you make a call on your cell phone, the electrons in the
antenna start to move back and forth. This creates two effects in
the neighborhood. First there appear bremsstrahlung photons which
fly away with the speed of light and either go to space or hit receiving
antenna. Thanks to these photons we have radio communication.
Second, moving electrons in your antenna interact with neighboring
charges via Coulomb and magnetic forces. These forces are instantaneous.
In addition they decrease rather rapidly with the distance from the antenna.
For example, the Coulomb force decreases proportionally to the square of
the distance
(the variation in force decreases even faster). So, the effect of these
instantaneous forces is localized around your cell phone. Certainly,
you cannot use this force to communicate instantaneously with
alpha Centauri. You can use photons (or transversal radio wave,
in classical language) for communication, but, sadly, they move with
the speed of
light.
The original version of the theorem (I reproduce its simplified proof in
subsection 12.3.1) uses Poisson brackets between particle observables
and generators of inertial transformations. This theorem has been proven
in 1963, and since then there were many papers with generalizations of
this theorem to include many particles, spins, etc. I know at least
half a dozen such generalizations, but I am sure there are more. Maybe
some of them use tensor analysis, I don't know. Why do you ask?
I used another foundation for QM called "quantum logic" in section 4.1.
But this is not relevant. We both agree that QM is correct. Let's move
on.
Fine.
There is just an instantaneous potential, e.g., 1/R for the Coulomb
part, which is a part of the total Hamiltonian. There is no any
mechanical carrier for this interaction. Why you think the presence
of such a carrier is necessary?
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Bilge wrote:
I said that time dilation depends on the nature of the process and on
interactions responsible for this process. I haven't said anything
about mass.
I think I said several times during our discussion that yes,
Smatrix (and scattering crosssections derived from it) has
perfect Lorentz transformation properties. This is because
in the Smatrix, the time evolution is "integrated" over infinite
time interval. When you consider timedependent processes, e.g.,
trajectories, the Lorentz formulas are no longer valid.
For free particles, Lorentz transformations are valid exactly. I also
said that. When you speak about a particle in external (magnetic) field,
this is a situation which I haven't considered. My theory only works for
isolated systems, so in order to consider particles in accelerator,
I need to include the particle and charges in wires creating the field
in one isolated system. That's rather complicated. Can we discuss
something simpler, like two colliding electrons or hydrogen atom?
First, I asked you to stick to electromagnetic phenomena.
Second, what this has to do with the question we are discussing:
the dynamical character of boost transformations?
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Bilge wrote:
I agree that each trial is independent and has the same probability
associated
with it. The outcome of each trial is rather random, it is controlled by
the above probability (just as for rolling die). I didn't say that
probability amplitude depends on ensemble. Probability amplitude
depends on the state of the system. The (large) ensemble is needed to
measure the probability accurately.
Do we agree? Can we consider this part of discussion closed?
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Bilge wrote:
I agree that you can derive Poincare group as generalization of
the Galilei group. I actually did it in the book: see subsection 2.2.1.
I always said that Poincare group properties are unique and universal.
They do not depend on the physical system, on the interaction, on
anything. This is because Poincare group properties reflect
relationships
between freely moving inertial observers. However Poincare group,
by itself doesn't tell you how observables of particles in physical
systems transform from one reference frame to another. In order to find
these transformations, you need to construct REPRESENTATION of the
Poincare group in the Hilbert space of the system (see chapter 5). The
representation
of the Poincare group is ultimately responsible for the interaction in
the system (see section 8.2). You can construct a noninteracting
representation of the Poincare group in the multiparticle Hilbert space,
then all particles will move independently along straight lines,
and their trajectories will transform according to Lorentz formulas.
However, if you build an interacting representation of the
Poincare group
(note that the group is still the same, it is the representation that
changes) you will see that trajectories of particles become curved
(due to interaction) and they will no longer transform by Lorentz
(CurrieJordanSudarshan theorem)
In my approach light is a flow of photons, and I discussed at length
why Maxwellian electromagnetic wave is inadequate representation of the
properties of light.
Photon is a particle with zero mass, that's sufficiently well
established by experiment, so let us forget Proca's
equations.
The problem is not that it is difficult to find statements about
Minkowski spacetime. Quite opposite, books are full of them.
The problem is to find statement supported by logic. So far,
I have seen only logical jumps from light pulses to universal
spacetime. From what you are saying I gather that you haven't seen
the proof of the space and time unification either.
You assumed right from the beginning that there is certain background
space (or spacetime) with scalar (or pseudoscalar) product, and that
universal transformations of this spacetime are the same as
transformations of results of mesurements of particle observables.
You have nothing to prove.
I do not care if there is spacetime or not. I care about observers,
physical systems, and results of measurement of observables by
observers. For me, Poincare group is not a group of invariance of
some "spacetime". For me, Poincare group is a group of transformations
relating different inertial observers (see chapter 2). Maybe there exist
a spacetime, maybe not. I am not interested. I am interested in results
of measurements. I proved that results of measurements do not transform
by universal linear formulas when the velocity of the observer changes.
Since such universality is the cornerstone of the Minkowski spacetime
idea, I conclude, that most likely there is no such thing as
spacetime.
The difference between our views is the following. I do understand that
Poincare group (and its subgroup SO(3,1)) can be represented as a group
of linear transformations preserving interval in a certain 4D space with
pseudoeuclidean metric. You think that this 4D space is really existing
spacetime in which all of us are "embedded" as fish in a fishtank.
This is an assumption (or postulate) with far reaching consequences.
In my approach I do not make this assumption. There is no such postulate
in my book. However, I do respect the Poincare group. I even say at
some point
that commutators in the Poincare algebra are among the most
important equations in physics (see section 2.2.1). But for me, the
Poincare group is just
the group of transformations between inertial observers.
The fact that this
group is also a group of invariance of certain abstract 4D space
is just a coincidence, nothing more. And this 4D space has no
relationship to the physical 3D space (whose existence I of course
accept as selfevident) and time. I have one postulate less than you do.
And I also show that your postulate of spacetime (or of universality
of lorentz transformations) actually contradicts your other postulates.
I explained my point of view above.
I am interested only in electromagnetic systems in my book.
So, we then agree that the universality of Lorentz transformations
in such systems is a postulate?
Ok, let us then agree that Lorentz transformations are exactly
applicable to events related to light pulses (or massless particles)
and to noninteracting massive particles. This is Statement C of my book
(end of subsection 1.1.6). I think we also agreed that applicability
of Lorentz transformations to interacting systems is an independent
postulate (I call it Assertion D in subsection 1.2.1, I call it
Assertion before I am going to disprove it later). We are moving fast!
I wanted to hear from you that this is an independent postulate, because
in this case we can safely remove it from the theory and try to
construct a theory in which this postulate is not present. Then there
are three possibilities:
1) we may find out that reasonable theory cannot be built without this
postulate, and we will be forced to declare it valid
2) we may prove the statement of this postulate as a theorem.
3) we may find that this postulate actually contradicts our other
postulates, then we will declare it invalid.
The point of my book is that possibility 3) is actually realized.
I prove that the "Lorentz universality postulate" is not needed for
building a complete theory of interacting particles and that it
contradicts other respectable statements, so it should be dismissed.
I collected all major postulates from my book in one of my replies to
FrediFizzx. Let me copy them here, so we'll keep them handy during our
discussion. I list these postulates along with subsections of the book
where they can be found:
Postulate A: The principle of relativity (1.1.1)
Postulate H: Poincare group properties of inertial transformations
(2.2.1)
Postulates of quantum mechanics: I, J, K1 K11, K13, L, M.
They are summarized in statement N (4.3.2 and 4.3.7)
Statement N in subsection 5.2.4 (oops! I have two statements N):
Representation of inertial transformations by
unitary operators in the Hilbert space.
Postulate O: Hilbert space of compound system (8.1.1)
Postulate P: Kinematical character of space translations and boosts.
(8.2.3)
Postulate R: Cluster separability of interactions (8.3.3)
To study a particular theory I postulate in subsection (11.1.2)
the form of interaction in the Hamiltonian and boost,
which is exactly the same is in normal QED
(see, for example eqs (8.4.22)  (8.4.25) in
Weinberg's book vol. 1)
Postulate U: Charge renormalization condition (11.3.4)
Postulate V: Stability of vacuum and oneparticle states (12.1.1)