Re: The real twin paradox.

colp says...

On Nov 25, 3:57 am, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:

If the theory of relativity is wrong, then
there are two simple ways to demonstrate that
it is wrong: (1) Show that it makes predictions
that are contradictory, or (2) Show that it makes
predictions that are proved false by experiment.

In this thread I have pursued the first option.

No, you haven't. As I said, you have to look at
what relativity *actually* predicts, not your
own distorted version of relativity.

1. There is a special collection of coordinate systems,
the inertial coordinate systems. If x,y,z,t are coordinates
for an inertial coordinate system, then so are x', y',
z', and t' obtained from (x,y,z,t) through the following
transformations:

A. Translations: x' = A + x
y' = B + y
z' = C + z
t' = D + t

B. Rotations: x' = x cos(A) + y sin(A)
y' = y cos(A) - x sin(A)
z' = z
t' = t
(and similiarly for rotations about yz and xz planes)

C. Lorentz transformations: x' = gamma (x - vt), t' = gamma(t - vx/c^2)
y' = y, z' = z. (And similarly for boosts in the y and z directions)

The paradox that I have described incorporates the Lorentz
transformation for time.

No, they don't. The Lorentz transformations describe
the relation between two *inertial* coordinate systems.
They don't say anything about what an accelerated rocket
sees or measures.

The equation that I have referred to has a different form to the one
that you cite:

http://en.wikipedia.org/wiki/Time_dilation

Everything on that page is simply mathematical consequences
of the claims that I gave. What you seem to have not understood
is that time dilation is *not* a relationship between two
clocks. It is about the relationship between *one* clock
and an inertial coordinate system.

If an ideal clock is moving, then the relationship between the
time tau shown on the clock and the coordinate time t is given
by

tau = tau_0 + Integral from t_0 to t of
square-root(1-(v/c)^2) dt

where v and t are measured in any *inertial* coordinate system,
and tau_0 is the time shown on the clock when t = t0.

According to this formula, if two clocks accelerate identically
(as measured in an inertial coordinate system) then they will
always have the same time shown on the clock as measured in that
coordinate system. There is nothing contradictory about the
application of this time dilation formula.

--
Daryl McCullough
Ithaca, NY

.

Relevant Pages

  • Re: Androcles asks for Derivation of LT
    ... time on a rotating clock (or a clock moving along any continuous ... Let S be a fixed inertial coordinate system. ... Let T_Nbe the elapsed time for a constant-velocity clock ...
    (sci.physics)
  • Re: The Nanometre Twin
    ... Only a hypothetical light clock does this. ... what Newton's spacetime was. ... In your preferred coordinate system, ... than Newtonian physics. ...
    (sci.physics.relativity)
  • Re: The real real twin paradox.
    ... neither twin has an inertial coordinate ... inertial coordinate system is nonsense, ...
    (sci.physics.relativity)
  • WHAT IS AN INERTIAL COORDINATE SYSTEM
    ... WHAT IS AN INERTIAL COORDINATE SYSTEM ... upon a material body to which we attach the coordinate system. ... same way as in the case where do not exist gravitational forces. ...
    (sci.physics.relativity)
  • Re: On The Subject of The Mosquito And The Ladder
    ... preventing them from using a "mosquito clock" to measure the passage ... That gives them a perfectly good coordinate system. ... is at rest in Sam's frame. ...
    (sci.physics.relativity)