Light Speed Invariance
Richard Perry
Here is a simple observation begging of a solution:
Given simply the premise that light speed is invariant wrt frames, the
mathematical form of this statement in terms of Cartesian coordinates is
simply:
x/t = c = x'/t'
Now interestingly enough the Lorentz transform simply cannot be derived
from this premise, that is, it requires an additional premise, and it
hasn't become clear to me what that additional premise is.
The best that we accomplish with the above premise is:
t' = x't/x
But x' = x + vt
Hence
t' = (x + vt)t/x
t' = t + vx/c^2
t' = t + vt^2/x
Hence the transform:
x' = x + vt
t' = t + vx/c^2
Now this is Lorentz transform devoid of the factor gamma attached
gamma = (1/sqrt(1 - v^2/c^2).
What purpose does gamma serve, it seems to be entirely redundant?
Note that with this form of the transform provides the following result:
Given an observer K in motion wrt another observer K', and an object in
motion wrt K, the speed of the object wrt K is x/t = w, the speed of K
wrt K' is v, the speed of the object wrt K' is x'/t' = W.
Hence
W = x'/t' = (x + vt)/(t + vx/c^2)
because x = wt this reduces to
W = x'/t' = (wt + vt)/(t + vwt/c^2)
or
W = (w + v)/(1 + vw/c^2)
Which is the special relativist velocity addition equation.
This occurs because given x'/t' the gammas in the Lorentz transformation
equations simply cancel out leaving exactly the same ratio as above,
Viz.
x'/t' = (x + vt)gamma/(t + vx/c^2)gamma
Why was the Lorentz 'gamma' introduced? What additional premise requires
the inclusion of gamma?
Moreover how can we decide on the final form of the equation before
declaring it valid for all other space-time velocities, e.g. for objects
moving at less than c? While yet considering the motion of a photon we
can produce as many perfectly equivalent forms of the fourth equation as
we have time to derive, for instance we could have retained either of
the two forms that preceded the final form above:
t' = (x + vt)t/x
t' = t + vx/c^2
Certainly if we decide at some arbitrary point in our manipulations of
the symbols to begin finally letting x and t apply to the motion of
something other than a photon, then we will get drastically disparate
results, but nonetheless each equally as internally consistent as the
other.
Note that the first of these provides for the invariance of "all" speeds
wrt "all" observers. It works, but hardly pertain to reality, since our
clocks don't differ in their readings by any measurable amount when
moving at low velocities, whereas this transformation predicts wildly
differing ticking rates at arbitrarily low speeds.
We might conclude that the final form adopted was simply the one that
buried this clock difference the deepest at low velocities, if for no
other reason than to render it an untestable and simultaneously
palatable theory.
In truth of fact, time dilation is a logical impossibility, of which I
have provided more than sufficient proof, and so none of the forms above
is any more empirically valid than the other. SR persists simply because
its predictions are consistent enough with the empirical evidence at low
velocities to avoid obvious contradictions between prediction and
evidence, and because it simultaneously maintains an element of
controversy that is aesthetically pleasing to those endowed with a bent
for the extraordinary.
--
Richard Perry
http://www.cswnet.com/~rper
S. Johnson
"Richard Perry" <no_mail...@yahoo.com> wrote in message
news:3EA36B14...@yahoo.com...
>
> Here is a simple observation begging of a solution:
please.
> Given simply the premise that light speed is invariant wrt frames, the
> mathematical form of this statement in terms of Cartesian coordinates is
> simply:
>
> x/t = c = x'/t'
>
> Now interestingly enough the Lorentz transform simply cannot be derived
> from this premise, that is, it requires an additional premise, and it
How do you know it can't be derived? Just because *you* can't? That's
awfully arrogant of you, don't you think? How about I can't see how Fermat's
theorem is correct since *I* can't prove it?
> hasn't become clear to me what that additional premise is.
Because there's none.
> The best that we accomplish with the above premise is:
The best *you* can accomplish...
> t' = x't/x
>
> But x' = x + vt
No, this is Galilean transformation that's not (and shouldn't be) assumed in
relativity. You clearly lack the basic knowledge of relativity.
> Hence
>
> t' = (x + vt)t/x
>
> t' = t + vx/c^2
>
> t' = t + vt^2/x
>
> Hence the transform:
>
> x' = x + vt
> t' = t + vx/c^2
>
> Now this is Lorentz transform devoid of the factor gamma attached
> gamma = (1/sqrt(1 - v^2/c^2).
Of course, *you* threw it away when you assumed Galilean transformation
above.
> What purpose does gamma serve, it seems to be entirely redundant?
It's redundant to *you*. Think harder or just read any basic textbook on
relativity. (Hint: the light doesn't only propagate along the relative
motion of the reference frames, i.e. the x axis here.)
<further derivations based on entirely false starting points snipped>
Tom Roberts
> Here is a simple observation begging of a solution:
>
> Given simply the premise that light speed is invariant wrt frames, the
> mathematical form of this statement in terms of Cartesian coordinates is
> simply:
>
> x/t = c = x'/t'
>
> Now interestingly enough the Lorentz transform simply cannot be derived
> from this premise, that is, it requires an additional premise, and it
> hasn't become clear to me what that additional premise is.
The additional postulate needed is the equivalence of inertial frames,
aka the Principle of Relativity. Einstein showed this back in 1905. One
also needs the "hidden postulates" -- that clocks and rulers have no
memory, that space is isotropic in any inertial frame, and that space
and time are each homogeneous in any inertial frame.
Tom Roberts tjro...@lucent.com
Richard Perry
LOL!
I've read the derivations, they all include mental masturbations.
For instance Einstein goes from:
t' = t + vt^2/x(gamma)
to
t' = t + vx/c^2(gamma)
Without so much as a howdy doo.
He provides no reason to prefer the latter form over the former, he
states simply that t^2/x = x/c hence it would seem because of this
equivalence in regard to a photon, he for some reason known only to him
found it requisite to make that substitution.
OTOH it was also true for the same photon that t = x/c hence by the same
illogic we are constrained to make this substitution as well, hence:
t' = x/c + vx/c^2(gamma)
or simply
t' = x/c(1 + v/c)gamma
Then again maybe the correct form for material objects is
t' = t(1 + v/c)gamma
or no, maybe it is
t' = t(1 + v/c)
Are you following? Here's another hint for you:
A spaceship leaves the Earth with two identical shuttle craft aboard.
Upon achieving some uniform velocity away from the Earth the shuttle
craft are launched symmetrically from the mother ship in opposite
directions wrt it along the line joining the mother ship and the Earth.
1) Will the twins piloting these shuttle craft be the same age upon
their return to the mother ship, that is, from the frame of reference of
the mother ship, assuming symmetrical shuttle trips wrt the frame of the
mother ship?
2) Will the twins be the same age upon their return to the mother ship
as perceived from Earth frame?
Show your work please.
Richard Perry
That's what I was hoping someone would say:)
SR does 'not' support the POR. It's meager (and mostly suspect)
successes are born of this simple fact, that light moves at c wrt Earth,
aka 'lab frame'. That it does so is no indication that light speed is
invariant wrt other frames moving in the near-Earth vicinity, and quite
frankly if you perpetually limit the domain to lab frame observations,
then you'll never do the required experiments that will without one
doubt contradict its predictions. Logic simply won't allow time dilation
'and' isotropic space to coexist. Note that a gravitating body presents
in contrast an anisotropic region of space, GR time dilation will
therefore be a bit more resilient to logical argumentation.
Dirk Van de moortel
>
> Given simply the premise that light speed is invariant wrt frames, the
> mathematical form of this statement in terms of Cartesian coordinates is
> simply:
>
> x/t = c = x'/t'
>
> Now interestingly enough the Lorentz transform simply cannot be derived
> from this premise, that is, it requires an additional premise, and it
> hasn't become clear to me what that additional premise is.
>
> The best that we accomplish with the above premise is:
>
> t' = x't/x
>
> But x' = x + vt
"Let's derive the Lorentz Transformation and start with x' = x+vt"
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/LorentzPerry.html
Stupid idiot.
Dirk Vdm
S. Johnson
order, but you don't have the mental capacity to understand it. Just like
the above when you start with x'=x+vt and wonder how you end up with x'=x+vt
without a gamma. You should LOL, but you're laughing at your own self.
> For instance Einstein goes from:
>
> t' = t + vt^2/x(gamma)
>
> to
>
> t' = t + vx/c^2(gamma)
>
> Without so much as a howdy doo.
Read the paper again, and this time try to understand how the letters form
words and words form sentences, and in the end, if you have the
intelligence, maybe you can at least realize not everyone is capable of
understanding relativity. You can then either choose to do something else,
or choose to display your own ignorance by deriving x'=x+vt from x'=x+vt.
LOL indeed.
Dirk Van de moortel
"Richard Perry" <no_mail...@yahoo.com> wrote in message news:3EA37B22...@yahoo.com...
[snip]
>
> LOL!
>
> I've read the derivations, they all include mental masturbations.
>
> For instance Einstein goes from:
>
> t' = t + vt^2/x(gamma)
>
> to
>
> t' = t + vx/c^2(gamma)
>
> Without so much as a howdy doo.
>
> He provides no reason to prefer the latter form over the former, he
> states simply that t^2/x = x/c hence it would seem because of this
> equivalence in regard to a photon, he for some reason known only to him
> found it requisite to make that substitution.
Out of which orifice did you pull the equation
t^2/x = x/c^2
?
As far as I can see the equations
t' = t + vt^2/x(gamma)
and
t' = t + vx/c^2(gamma)
are equivalent if
t^2/x = x/c^2
which is equivalent with
x^2 = (ct)^2
which is equivalent with
x = ct or x = -ct
the first of which is the equation describing a light
ray in the positive x-direction, while the second is
the equation of a light ray going in the negative
x-direction.
Is that enough, or do you want some more howdy doo?
Dirk Vdm
Dirk Van de moortel
"Richard Perry" <no_mail...@yahoo.com> wrote in message news:3EA37B22...@yahoo.com...
[snip]
> LOL!
>
> I've read the derivations, they all include mental masturbations.
>
> For instance Einstein goes from:
>
> t' = t + vt^2/x(gamma)
>
> to
>
> t' = t + vx/c^2(gamma)
>
> Without so much as a howdy doo.
>
> He provides no reason to prefer the latter form over the former, he
> states simply that t^2/x = x/c hence it would seem because of this
> equivalence in regard to a photon, he for some reason known only to him
> found it requisite to make that substitution.
Out of which orifice did you pull the equation
t^2/x = x/c
?
As far as I can see the equations
t' = t + vt^2/x(gamma)
and
t' = t + vx/c^2(gamma)
Tom Roberts
> Tom Roberts wrote:
>>Richard Perry wrote:
>>>Now interestingly enough the Lorentz transform simply cannot be derived
>>>from this premise, that is, it requires an additional premise, and it
>>>hasn't become clear to me what that additional premise is.
>>
>>The additional postulate needed is the equivalence of inertial frames,
>>aka the Principle of Relativity. Einstein showed this back in 1905. One
>>also needs the "hidden postulates" -- that clocks and rulers have no
>>memory, that space is isotropic in any inertial frame, and that space
>>and time are each homogeneous in any inertial frame.
>
> successes are born of this simple fact, that light moves at c wrt Earth,
> aka 'lab frame'.
This is simply not true. Perhaps you do not have a wide enough
knowledge of modern physics. There are literally ZILLIONS of
experiments in high energy physics that could not possibly work unless
SR described nature to within a few parts per million within its domain
of applicability. This includes such basic observations as:
particle accelerators operate as designed
pion beams exist
muon beams exist
And also more complicated observations:
4-momentum is conserved in elastic scattering
4-momentum is conserved in particle production experiments
4-momentum is conserved in decays
> That it does so is no indication that light speed is
> invariant wrt other frames moving in the near-Earth vicinity,
I grant you that no direct measurements of the speed of light have been
made in frames moving significantly wrt the solar system. But this is a
non-issue -- a physical theory like SR makes lots of predictions, and
to date no reliable and reproducible experiment has displayed any
discrepancy with its predictions, within its domain of applicability.
And literally zillions of experiments have confirmed its predictions.
Sure, there are other experiments which would be nice (e.g. measuring
the speed of light in a rocket moving .5 c wrt the earth; operating a
high-resolution MMX-like experiment in an airplane; doing just about
any SR test in deep space; etc.). But the lack of them does not
indicate any problem with SR; they merely display current limits on
technology and/or budgets.
> Logic simply won't allow time dilation
> 'and' isotropic space to coexist.
That is simply not true. What kind of "logic" are you using? -- it's
clearly invalid if it leads you to this conclusion.
But it's more likely that you have introduced unacknowledged
puns into your argument.... Or sloppy and ambiguous
terminology.... Or gross misunderstandings.... Or all the
above....
> Note that a gravitating body presents
> in contrast an anisotropic region of space, GR time dilation will
> therefore be a bit more resilient to logical argumentation.
Gravitation is a LOT more complicated than that....
Tom Roberts tjro...@lucent.com
Frodo Morris
> Here is a simple observation begging of a solution:
>
> Given simply the premise that light speed is invariant wrt frames, the
> mathematical form of this statement in terms of Cartesian coordinates is
> simply:
>
> x/t = c = x'/t'
>
> Now interestingly enough the Lorentz transform simply cannot be derived
> from this premise, that is, it requires an additional premise, and it
> hasn't become clear to me what that additional premise is.
moving with velocity v wrt S, then L(v).L(-v) should land us back in
frame S. This imposes the condition that L(v) should be linear:
(x') (A B C D)(x)
(y') = (E F G H)(y)
(z') (I J K L)(z)
(t') = (M N O P)(t)
From here it should be easy to get to the required form, gammas and all.
HTH
--
FM
shuba
> Out of which orifice did you pull the equation
> t^2/x = x/c
> ?
It came from the Orifice of Navel Communications, which was
funded by a law championed by former US Senator Dan Quayle
as an ongoing rememberance of his service in the Coast Guard.
---Tim Shuba---
John Anderson
Richard Perry wrote:
> Here is a simple observation begging of a solution:
>
> Given simply the premise that light speed is invariant wrt frames, the
> mathematical form of this statement in terms of Cartesian coordinates is
> simply:
>
> x/t = c = x'/t'
>
> Now interestingly enough the Lorentz transform simply cannot be derived
> from this premise, that is, it requires an additional premise, and it
> hasn't become clear to me what that additional premise is.
>
It's derived from assuming that the forward and backward light cones
are preserved:
ie. for x = c*t or x = -c*t then x' = c*t' or x' = -c*t'
plus the assumption that the coordinate transformation is linear,
that the inverse transformation for the +v transformation is the -v
transformation, and that spacetime is isotropic.
See Weinberg, Gravitation and Cosmology, for the details.
John Anderson