Time dilation - No Need to Do the Math

"sal" <[Only registered users see links. ]> wrote in message news:XJ8ob.13181$[Only registered users see links. ]...


Earth uses coordinates (x,t)
Right twin uses coordinates (x',t')
Left twin uses coordinates (x",t")
World line Earth: x = 0 (t-axis)
World line Right twin: x' = 0 (t'-axis)
World line Left twin x" = 0 (t"-axis)

Right twin is present at event R: (x,t) = (D,0)
where/when his clock is set to t' = 0,
and he approaches Earth with relative speed v
Left twin is present at event L: (x,t) = (-D,0)
where/when his clock is set to t" = 0,
and he approaches Earth with relative speed v

[M]
/|\
/ | \
t"/ t \t'
/ | \
/ | \
/ | \
/ | \
-----[L]------|------[R]------x

Transformation Earth coord --> Right twin coord:
{ x' = g( (x-D) + vt )
{ t' = g( t + v(x-D)/c^2 )
Transformation Earth coord --> Left twin coord:
{ x" = g( (x+D) - vt )
{ t" = g( t - v(x+D)/c^2 )
where in both cases
g = 1/sqrt(1-v^2/c^2)

Meeting of the 3 world lines at event M:
{ x = 0
{ x' = 0
{ x" = 0
==> 2 lines of algebra ==>
(x,t) = ( 0, D/v )
(x',t') = ( 0, D/(gv) )
(x",t") = ( 0, D/(gv) )
According to Earth D/v seconds have passed.
According to both twins D/(vg) seconds have passed.

Dirk Vdm

"Harry" <[Only registered users see links. ]> wrote in message news:3fa12183$[Only registered users see links. ].ch...

[snip]


Ha, but it *is* part of SRT:
http://groups.google.com/groups?&threadm=a3M1b.82977$[Only registered users see links. ] net-ops.be


I think it is not included in the standard twin paradox
treatment because it is irrelevant.
When the accelerations are taken large enough, such
that the cruising velocities are reached in a short time,
then what happens during these accelerating phases
can be ignored when compared with what happens
during the cruising phases.

Dirk Vdm

"Harry" <[Only registered users see links. ]> wrote in message news:3fa12123$[Only registered users see links. ].ch...

[snip]


Not sure yet. His style suggests a few candidates.
But I could be wrong of course, this one could be
brand-new after-all :-)

Dirk Vdm

"Paul Cardinale" <[Only registered users see links. ]> wrote in message news:64050551.0310300657.2f5a033d@posting.google.c om...

You are too kind, sparing him like that ;-)

Dirk Vdm

Stephen Bint wrote:
[snip}

No need to do the math, eh? Crackpot. Special Relativity is a set of
hyperbolic rotations in 4-space. Do those matrix multiplications
intuitively, git.

[Only registered users see links. ]
[Only registered users see links. ]

--
Uncle Al
[Only registered users see links. ]
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

Dirk,

When you warned me that G=EMC^2 Glazier <[Only registered users see links. ]> is a
troll, I didn't like the way you elected yourself judge and jury over who is
a troll and who isn't. Nor did I like the way you saw fit to speak on behalf
of the others on this newsgroup.

Dirk:

"I think you don't want to know what the Bert believes.
You might want to know that in the beginning the Bert
used to be a Herb. We all wonder whether next year
the Bert will call himself a Terp or a Terk, and the year
after, whether the Terp will call himself a Perd or a Perl,
or perhaps whether the Terk will become a Kerl or a
Kerm. To survive on this forum one needs patience.
But you'll find that out soon enough."

I will be the judge of whether I want to know what Bert believes.

Now you are accusing me of being a troll, I like it even less. I have
started one thread on alt.sci.physics.new-theories about my cranky
strobing electron theory and contributed to a couple of other threads.
I have started two threads about the twin paradox, which I have
cross posted to three groups. I have confined myself almost entirely
to discussing the topics of these threads with those adults who have
chosen to discuss them with me.

Who the hell are you to declare me a troll, or any sort of pest? The threads
I have started concern subjects of great interest to me and I have every
right to discuss them here. I suppose you think the people contributing to
these discussions are all fools who have fallen into my trap. They come
across as a good deal more intelligent than you.

What I really take exception to is this:


This is a lie. You are lying about me, though I have done nothing to you,
nor have I been rude to anyone on this list, except Uncle Al, who was much
ruder to me first.

I think you owe me an apology.

Stephen Bint


"Dirk Van de moortel" <[Only registered users see links. ]> wrote
in message news:3fa0df79$[Only registered users see links. ].hp.com...
news:bnqmjp$3q7$[Only registered users see links. ]...
news:3fa0893c$0$122$[Only registered users see links. ].. .
it is

"Paul Cardinale" <[Only registered users see links. ]> wrote in message
news:64050551.0310300657.2f5a033d@posting.google.c om...
news:<3fa07dad$0$118$[Only registered users see links. ]> ...

You can only resort to personal attacks. What you cannot do is face the
issue, which I keep bringing up for you to ignore. You call me names, you
bleat "do the math" and you run like a cur from the question at hand.

This is the question I have asked Jon Bell. You won't be able to answer it
and I suspect you won't even understand it:

Two skateboards glide past eachother at speed.

On each skateboard is an observer and a device which sends a light pulse
from a source which is 1m above the base, vertically down to a mirror on the
base, which reflects it directly vertically back to the source. To one of
the observers (either one) the light pulse on the other board traces a
V-shaped path, which is longer than the vertical one. If there is no time
dilation, the observer will see the pulse travel a greater distance in the
same time, and therefore, see it travelling faster than c.

Time dilation slows the event on the other skateboard, the exact amount
necessary to make the light pulse travel this longer path at exactly c. The
length of the V-shaped path and consequently, the time dilation required, is
purely a function of the relative velocity of the two skateboards.

Furthermore, the path that A sees the pulse trace on B's skateboard is
exactly the same length as the path seen by B, taken by the light pulse on
A's skateboard.

So the time dilation must be identical in both directions, regardless of how
they acheived their relative velocity.

So what if your travelling twin was passing earth and viewing such an
experiment there. Either he will see time slowed down there, or he will see
the light pulse travelling faster than c there. Is that not the case?

So there it is. Don't worry if you can't see the point or understand the
question. Just call me few names and bleat "Do the math!" over and over and
everyone will think you are mature and intelligent.

Stephen

"Dirk Van de moortel" <[Only registered users see links. ]> wrote
in message news:3fa12a93$[Only registered users see links. ].hp.com...
news:3fa12183$[Only registered users see links. ].ch...
the
the
mentioned
relative
http://groups.google.com/groups?&threadm=a3M1b.82977$[Only registered users see links. ] n
et-ops.be

Oops, I'll have a look! :-)
Einstein was certainly not aware of that in 1918, he simply declared that
SRT is for Gallilean systems and thought he needed his GRT for the answer...
So it's no part of the original SRT.. but of course, thinking has advanced
since then!

BTW, your second reference (Baez) from the above claims:
"
[TOTAL BALONEY FOLLOWS:]
"Einstein came up with special relativity, which handles
only unaccelerated frames of reference [...]
Then he realized that an accelerated frame of reference
is indistinguishable from a gravitational field - his famous
`elevator' thought experiment. This led him to invent general
relativity, which handles general frames of reference and gravity."
"
To the contrary, I can find no error, I'm sure it is historically accurate!


But it is included in elaborate treatments.
Einstein and later Moller understood the necessity to explain the time
acceleration of the stay-at-home according to the traveller.


No it can't - you still need an explanation for the time jump as "seen" by
the traveller -see Einstein's paper of 1918 or Moller's book. (I can find
the refs if anyone is interested).

Harald

Stephen Bint wrote:

[snip]

The twin paradox arose specifically to point out the inconsistency of
SR. So, way back in the early 1900's, intelligent people like you were
finding it hard to come to grips with SR because of things like the
situation you bring up. If velocities are relative, how can it be wrong
to say that, from each twin's perspective, the other twin ages less?

Take a look at
[Only registered users see links. ]
They have nice graphics and a decent explanation. You should be able to
convince yourself of the following scenarios:

1) Given twins, A & B,
--A accelerates left to relativistic speeds
--B stays put
--A reverses course and returns
**We find age(A) < age(B)

2) Given triplets, A, B & C,
--A accelerates left to relativistic speeds
--B accelerates right to relativistic speeds
--C stays put
--A & B have the same acceleration/deceleration profiles
--A & B reverse course and return
**We find age(A) = age(B) and both are younger than C

There is enough literature to support (1) and by symmetry you can glean
(2).

"Harry" <[Only registered users see links. ]> wrote in message news:3fa14846$[Only registered users see links. ].ch...

[snip]


(This was an extract from
http://groups.google.com/groups?&threadm=bi75vd$qbm$[Only registered users see links. ].edu )


The first line is obviously wrong already :-)
And I don't have much to add to John's surrounding remarks.



Of course, it can be a nice exercise to really take accelerations
into account to describe the twins paradox. You can use my
calculations for it :-)


Sure it can. Just look at the equations at the bottom of my
treatment at
http://groups.google.com/groups?&threadm=a3M1b.82977$[Only registered users see links. ] net-ops.be
Take for instance the equation that gives proper time T as
a function of coordinate time t and take the limit for
a --> infinity:
T(t) = c/a argsinh(at/c)
You clearly see that for all values of t (!)
Limit{ a->Inf; T(t) } = 0
which says that the accumulated proper times can be made
arbitrarily small by taking the acceleration large enough.

Some more limits at
http://groups.google.com/groups?&threadm=3f150372$[Only registered users see links. ].hp.com

Cheers,
Dirk Vdm