Re: Lorentz transformations - a derivation
From: RP (no_mail_no_spam_at_yahoo.com)
Date: 01/13/05
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Date: Thu, 13 Jan 2005 10:21:53 -0600
Androcles wrote:
> "RP" <no_mail_no_spam@yahoo.com> wrote in message
> news:34jnhkF4ajaq9U2@individual.net...
>
>>
>>Tom Roberts wrote:
>>
>>
>>>RP wrote:
>>>
>>>
>>>>An off topic question: Is light speed invariant wrt an accelerated
>>>>frame?
>>>
>>>
>>>Measured with standard clocks and rulers at rest in an accelerated
>>>system, the one-way speed of light is not isotropic, is equal to c
>>>only in some directions, and in other directions is not even
>>>constant. Using one standard clock and ruler, the round-trip speed of
>>>light is not isotropic and is equal to c only in directions
>>>perpendicular to the acceleration.
>>
>>Thanks Tom, though as you probably guessed, I already knew this, but
>>there seems to be an ongoing thread in which several otherwise
>>intelligent contributors are stating otherwise, and I just wanted them
>>to hear it from you.
>>
>>Richard Perry
>
>
> Roberts doesn't answer serious questions. He's useless.
> Why don't you ask him about this?
Whether a person agrees with the theory that's one question, the
question of whether Roberts relates it correctly is quite another.
When a theory is understood as well as Roberts understands this one,
then some unlearned questions, though serious, may seem to the expert
to be meaningless.
>
> "Roberts:
>
> Standard and well-known derivations of the Lorentz transform are
> based on the following assumptions/postulates/techniques:
> 1. The Principle of Relativity (Einstein's version)
>
>
> Androcles:
> Which one do we use?
> Is it
> a) "But the ray moves relatively to the initial point of k, when
> measured
> in the stationary system, with the velocity c-v..."
> or
> b) "It follows, further, that the velocity of light c cannot be altered
> by composition with a velocity less than that of light.
> For this case we obtain V = (c+w)/(1+w/c) = c."
Neither is the PoR.
>
> What does Roberts do? Snips:
> Is it [... irrelevant verbiage]
>
> Those two phrases in quotes are Einstein's.
> Roberts calls them irrelevant verbiage.
They're conclusions drawn from the PoR and Maxwell.
> Roberts is nothing but irrelevant verbiage himself.
>
> A standard ruler:
>
> "From 1889 to 1960, the metre was defined to be the distance
> between two scratches in a platinum-iridium bar kept in the
> vault beside the Standard Kilogram at the International Bureau
> of Weights and Measures near Paris.
>
> This replaced an earlier definition as 10^-7 times the
> distance between the North Pole and the Equator along a
> meridian through Paris; unfortunately, this had been based on
> an inexact value of the circumference of the Earth.
>
> From 1960 to 1984 it was defined to be 1650763.73 wavelengths
> of the orange-red line of krypton-86 propagating in a vacuum.
>
> It is now defined as the length of the path traveled by light
> in a vacuum in the time interval of 1/299,792,458 of a second."
> http://dict.die.net/metre/
>
> What happens to the light also happens to the standard ruler.
> "Measured with standard clocks and rulers" is self-referential,
> Roberts is mumbling again.
>
> "Thanks Tom" indeed!!
>
> Androcles
Yes, it's self-referential, but how does this make it wrong?
The Galilean transform makes an assumption that the length of a rod is
independent of it's state of motion, special relativity makes no such
assumption, and thus attaches a gamma term "just in case" this is an
incorrect assumption. Experiment (the MMX in particular) showed that
the length must vary with velocity. Though, the c+v model will account
for the MMX result "on the surface", it fails in other areas, namely
Maxwell's equations, since as Einstein noted, "asymmetries appear".
Here it was implicit that he meant "when the c+v model is applied".
Thus it is specifically considerations of symmetry that rule out the
c+v model.
If you are ok with those asymmetries, then you necessarily believe
that effects aren't repeatable, in contradiction to all empirical and
everyday experience. Repeatability and symmetry are intimately
related, and in some instances of these terms they are perfectly
synonymous. IOW, all else being equal, if we get result A in the first
experiment, then we must also get the same result A in a second
experiment, regardless of the relative motion of the experimental
setups wrt each other "all else being equal".
If you don't agree that "all else is equal" in the relatively moving
setups, then you are necessarily an aetherist of the original sort, or
else disagree with Maxwell. There is no way out of this, other than to
admit that your version of c+v is inconsistent with Maxwell, and that
you are thus an aetherist of the sort that believes in absolute
motion. If you disagree with this last conclusion, then you have to
show that your c+v model is consistent with Maxwell. And since Maxwell
predicts c and not c+v, then no such proof is possible.
Further arguments:
An accelerated rod will compress due to internal stresses, it's length
is also dependent on external pressure, on the presence of
electromagnetic and gravitational fields, and on temperature. The rod
isn't a reliable standard of length.
The distance that light propagates in a given time interval, OTOH, is
reliable, if for no other reason than light speed is defined to be
constant. If you're arguing that a mathematical system cannot be
derived from this premise and be consistent with the empirical
evidence, then the empirical evidence says that you're incorrect. In
fact, if any deviation from a prediction of this theory were observed,
then it would be amazing, since if the rules of measurement as
outlined are adhered to, then it is literally impossible to measure
anything other than what is predicted *because* the measurement system
is circular. The redefinition of meter in terms of light speed was a
requirement of the theory all along, and once having implemented it
the system became internally consistent.
Thus, if you are arguing against the theory, and your premises of
those arguments are the old Newtonian type standards, then the only
valid conclusions that you have derived is that these older standards
aren't consistent with special relativity, which apparently somebody
was inclined to agree with, else they wouldn't have changed the
definitions of the standards.
Your task has thus been simplified somewhat; prove that SR is
inconsistent with either itself or with the empirical evidence, by
comparing *its own* premises to each other, and its conclusions to the
empirical data. It's a lack of understanding of symmetry requirements,
combined with invalid argumentation, and lack of the knowledge of
correspondence of Maxwell to the known electromagnetic phenomena, that
allows you to continue in your acceptance of the c+v model. And we
might throw in your belief that circular self-referential definitions
are automatically wrong. An empirical definition is quite impossible,
that is, without first making assumptions that are non-empirical (i.e.
arbitrary). We are bound to implement fiat in any initial premises
that we care to initiate.
Richard Perry
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