Re: For Seto: Theories incompatible with relativity


Dirk Van de moortel wrote:
<schoenfeld.one@xxxxxxxxx> wrote in message news:1167477840.886137.170650@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Sam Wormley wrote:
For Seto: Theories incompatible with relativity
http://en.wikipedia.org/wiki/Status_of_special_relativity#Theories_incompatible_with_relativity

That article needs to be cleaned up and its sources corrected.

Special relativity is not compatible with the physical existence of the
following objects, forces, or laws (except in the nonrelativistic limit
in which all speeds are much less than c):

1. Infinitely rigid rods, or any other object which transmits forces at
infinite speeds. Note that this would require the existence of a new
force which is not currently explained by any of the laws of physics.


I don't see how SR prohibits the existence of a 'rigid rod', from its
axioms.

Rigidity implies that when you push the rod on one end,
it either
- instantaneously starts moving as a whole, which requires
the disturbance to move at infinite velocity, or
- it never moves at all, which contradicts experience.

That considering such objects causes contradictory results in
the theory is insufficient to conclude that the theory prohibits such
objects. Maybe the theory has a 'bug' (using computer jargon)

Maybe you don't understand the theory.


For example:

[1] Suppose there is a rod 1m long, with respect to its own frame.

Yes, that is the proper lenght of the rod, by definition.


[2] Suppose that an instantaneous acceleration is applied
*simultaneously* everywhere on that rod, with respect to the rods
initial frame.

The kinematics of the rod allows it to be classified as 'rigid'.

The problem with this scenario is:

[3] Suppose the end velocity of the rod is 0.866c with respect to the
rods initial coframe.

[4] Relative to the rods initial coframe,
*Proper* length of Rod before acceleration = 1m
*Proper* length of Rod after acceleration = 1 /
sqrt(1-(0.866c)^2/c^2) = 2m

The transformation equation
Dx' = gamma ( Dx - v Dt )
reduces to your
Dx' = gamma Dx
provided
Dt = 0
i.o.w. provided the distances difference Dx between the endpoints
is measured in the rod's rest-frame. So Dx is the proper length here,
and the quantity
Dx' = gamma Dx
is useless because it is the distance difference between the end
points at different times
Dt' =/= 0 .
When you measure the front and the back of a train at different
times and calculate the difference between these distances, you
get a useless quantity.
Common error. Marcel Luttgens' specialty.

Thus the rod has doubled in physical size after the accelartion, and
this violates the supposed invariance of proper length. It would seem
that Special Relativity admits a contradictory result.

Actually, in this case it would seem that you haven't understood
special relativity.


What you misunderstood was that the acceleration was applied
_simultaneously_ everywhere on the rod with respect to the initial
frame. The *coordinate length* of the rod remains the same before the
acceleration and after the acceleration w.r.t to the initial frame. A
transformation into the rods frame at 0.866c gives a new proper length
of 2.

The solution is to avoid accelerations which are simultaneous
everwhere, but delayed from point to point (w.r.t to initial coframe)
such that the coordinate length contracts but the proper length remains
invariant.This special type of proper-length preserving acceleration
profile is called a Born rigid acceleration. In SR, the only types of
accelerations which don't break the theory are Born rigid
accelerations. But, out of the infinite possible ways to physically
accelerate an object, a Born rigid acceleration is only of them. That
the theory is violated by other types of acceleration profiles is
insufficient to show that the theory only admits Born rigid
accelerations - the other types must be ruled out axiomatically, but
they can't be.

.

Relevant Pages

  • Re: How can this work in relativity?
    ... > that as long as you do your calculations in a single frame, ... >>> uniform acceleration by applying the appropriate compensating ... >From the moving FoR that includes the rod, ...
    (sci.physics.relativity)
  • Re: Deriving the contraction of a moving rod
    ... This is different to the problem of showing that a rod will ... If you have a rod at rest in some inertial frame, ... In Born rigid acceleration, you actually need to apply a ... You then *must* apply forces that give proper ...
    (sci.physics.research)
  • Re: SR Length Contraction - how do physicists explain this
    ... >> reference frame. ... >> accelerated rod stops accelerating, the rod is 5 meters longer than an ... >> change length during the acceleration. ... It takes more energy to accelerate something and stretch it ...
    (sci.physics.relativity)
  • Re: How can this work in relativity?
    ... >> that as long as you do your calculations in a single frame, ... the same at all points of the rod. ... >> Uniform acceleration means that the ...
    (sci.physics.relativity)
  • Re: TomToms stupidity (re: was always TomToms stupidity)
    ... >> acceleration is immaterial, and Daryll was right to neglect it. ... >> relative to the stationary frame. ... and this "pulling" will stretch the rod. ...
    (sci.physics.relativity)