Reason 2/100 of why Special/General Relativity are entirely IMPOSSIBLE
(DO NOT POST HERE. Discuss any reasons here: viewtopic.php?f=3&t=232 )
The Relativistic "Lorentz Transformation" (Time Dilation) is impossible
Special Relativity (as developed by Einstein) obtains a set of equations, known formally as the
Lorentz Transformation formulae, which relates length and time units of two systems moving at uniform velocity relative to each other. However this name is entirely misleading as the original Lorentz Transformations had an Ether rest frame to derive absolute velocity and motion, which unlike relativity made them at least logically feasible despite the problems with the Lorentzian Ether model.
The relativistic Lorentz Transformations are impossible as they inevitably result in
different ontological (causal) effects for different observers, this is because the velocity derived physical effects are dependent only upon the observer (relativistic).
And
as shown in reason 1, even without these logical fallacies they have no mathematical basis in the proofs as Einstein ignored basic mathematical constraints in his relativistic derivation of the formal Lorentz Transformation. Such blatant mathematical errors today wouldn't even make it past peer review.
Lorentz Transformation
Unlike the equations of the usual Galilei Transformation, the Lorentz Transformations are not merely a linear transformation. The Galilei Transformation describes the change in distance between two points (co-ordinate change) in each reference frame due to their different relative motion). The Lorentz Transformations are non-linear in the velocity
due to an additional factor γ containing the ratio of the velocity and the speed of light γ= 1/√[1-(v/c)^2].
The relativistic Lorentz Transformations differ from the original Lorentzian theory in that velocity
is entirely dependent upon the observer, they have no absolute velocity to derive effects (as there is no Ether or medium to derive absolute motion) for things such as length contraction.
So objects can undergo a length contraction (and time dilation) for
one observer but not another, this produces contradicting effects that make Special Relativity impossible.
Time Dilation
The time dilation claim is based on the set of Lorentz transformation for the "space and time" coordinates relating the rest frame (observer A) (unprimed coordinates) and moving frame (primed' coordinates):
(1a) x'=γ(x - vt)
(1b) t' = γ(t - vx/c²)
Einstein derives the "time dilation" effect by considering the origin of the moving frame x'=0. Inserting thus (Eq.(1a)) x=vt into Eq.(1b) he obtains (considering that γ= 1/√[1-(v/c)^2])
(2) t' = t/γ
This would mean that the clock rates in the moving (primed') frame would be a factor 1/γ slower (time dilation) than in the rest frame (observer A). But as there is no rest frame to derive velocity (which is dependent upon the observer in SR) if we consider the previous primed' frame as Observer B - the effect for this primed frame observing the original frame would be reversed, producing entirely opposite effects.
Using the Lorentz transformation for the Observer B now being the rest frame now:
(3a) x=γ(x' + vt')
(3b) t = γ(t' + vx'/c²)
And applying (like before) the condition x=0 i.e. x'=-vt' (from Eq.(3a)):
(4) t = t'/γ,
So we have
opposite time dilations, i.e. a "Twin Paradox" if the dilations are both true and both happen, comparatively there is actually no time dilation. Rendering Special Relativity useless as no times would even get dilated in the Universe (relative to the observer) in the first place as it would always be a mutual dilation.
t = t'/γ
t' = t/γ
We will now demonstrate how relativity still utterly fails to deal with this twin paradox, and why the observer based Universe of relativity with no local rest frame to derive velocity is impossible and results in logical fallacies and contradicting effects.
Why the Twin Paradox (done correctly) still invalidates relativity (Thomas Smid example)
Relativists always claim that the twin paradox situation is not symmetric as one observer has to turn around and change reference frames to share the time, but this is a lackluster excuse for this complete logical debacle. Because by stopping both clocks BEFORE any return journey to share the time, no change in a state of motion is even required and cannot undo what time dilation just happened either.
If we take a symmetrical example where two frames
are moving at a uniform velocity v toward each other,
And a
MECHANICAL INTERACTION starts and
stops both clocks simultaneously, NO change in reference frame is even required to derive the time.
|-----A-----
| -> v.............
.............v <-
|-----B-----|
.........Clocks Start......
....|-----A-----
|>.................
...............
<|-----B-----|...
........Clocks running.....
......|-----A-----
|>..............
..............
<|-----B-----|......
........Clocks Stop.........
..................
|-----A-----|>..
...<|-----B-----
|...............
..(Identical Time Dilation)...
....................
|-----A-----|>
<|-----B-----
|...................
The signal propagation time for both mechanical clock activation in the above example is also irrelevant,
if the corresponding distances are identical in both systems, then the delay times will also be IDENTICAL. So any claims of non-symmetry by relativists cannot hold.
So it is clear that the final recorded clock readings MUST be identical
or you get a logical contradiction (i.e. if the observer who had the slower time gets a pie in the face after the time is reconciled). But Special Relativity theoretically predicts t'= t/γ, it predicts
one observer expects the other to have a slower clock, but as shown in the above example this is simply impossible as this paradox cannot be resolved by an accelerating frame (like in the famous twin paradox) in the above example the clocks are already stopped while the frames are still uniform.
Faced with this, a small number of relativists will claim that the 'relativity of simultaneity' is responsible for the asymmetry, this is a false claim that "relativity wouldn't even theoretically predict/require different time readings in this uniform instance" i.e. the term vv.x/c^2 in the Lorentz transformation formula t'=γ(t-v.x/c^2). But this claim has no basis as the coordinate x is equal to vt (for uniform motion, as used in the above example). Such an argument also contradicts all formally recognized interpretation of Special Relativity and also Einstein's own papers.
As x=vt the original argument that t'= t/γ still holds and theoretically relativity
requires this time dilation to happen (as is seen easily by inserting the gamma factor γ= 1/√[1-(v/c)^2].
Einstein actually derives the same expression for the alleged transformation of the clock readings in his paper "Electrodynamics of Moving Bodies" (
http://www.fourmilab.ch/etexts/einstein/specrel/www/), which depends only on the absolute value of the speed and neither on its direction nor the x-coordinate (i.e. it does not depend on the 'relativity of simultaneity').
Just to reiterate this in a different time dilation example, if the velocity reverses at some point, this has no impact whatsoever on the clock reading as t' depends only on v^2 (by re-defining the origin x=0 as the reversal point for the 'return-journey' the same expression t'= t/γ does indeed apply to the outward AND return journey for both frames).
So even such an alleged 'asymmetrical' situation where the relativistic effects apply (such as the famous Twin Paradox) is in fact also a paradox
if the Lorentz transformation is applied correctly. The relativistic "time dilation" caused from an observer based relative velocity and the solution to the famous paradox using accelerating frames actually shows in itself that relativity is an internally inconsistent theory.
But the point of this reason - even without this problem (as shown above and below), the solution to the famous paradox only works in that
specific type of example with different accelerating frames (and not symmetrical or uniform examples as shown in this reason).
A more familiar (an easier) example (from S. N. Arteha)
A --
>-------------
O--------------
<--
B
> ship A
< ship B
If we have two colonies of Earth’s inhabitants
A and
B be at a large distance from each other.
The beacon
O is at the middle of this distance. It sends a signal (the light sphere), and when it reaches both colonies (simultaneously), each launches a spacecraft piloted by one "twin". The laws of acceleration (to reach a large equal speeds) are chosen equal in advance.
At the time each twin passes the beacon, at a high relative velocity,
each will believe that his counterpart should be younger.
A --------------
>--
O--
<---------------
B
This is impossible, since they can photograph themselves at this instant and write their age on the back side of a picture (or even exchange pictures by the digital method). It is nonsense, if for example wrinkles will appear on a pictured face of only ONE astronaut during the deceleration of another one. This is a paradox.
The Famous Twin Paradox
It is important to remember the explanation for the famous paradox of twins (one an astronaut and one an Earth’s inhabitant). Since only one of them accelerates and changes inertial frames it is just this person who was declared to be younger than the other one in eventuality. But before this acceleration
each of the twins thought that the other one should be younger.
This itself is a contradiction and entirely impossible,
any resolution after the fact is superfluous because this first part of the paradox can be exploited by a minor change to the example.
And, in fact, if one twin is accelerated, then the other grows old faster.
Even the ”explanation” of the classical twins paradox certainly contains some contradictions. First, as shown in this reason everything could have been done symmetrically anyway (an example which easily invalidates Special Relativity's assumptions of "observer dependent time dilation"); but also the astronaut twin and the Earth twin can take photographs before and after the acceleration that changes inertial frames at a given age. If the astronaut is expected to be younger just before the acceleration in one frame but not the other we have an impossible situation that has causal eventualities even before the standard mathematical trick of accelerating frames "saves the paradox".
Accelerating frames doesn't save the paradox,
because the paradox is still there and can be exploited in situations before and without it.
All of this logically and empirically demands a different (non-relativistic, non observer based) physical explanation for all experimentally observed "time dilation". One that is logically consistent and based in physical reality. Not the purely mathematical construct of Special Relativity derived from an assumption of light invariance in all frames, which is replete with causal errors and logical fallacies that make the entire related theory simply impossible.
Electromagnetic Retardation
Other non-relativistic theories such as Oleg Jefimenko's Electromagnetic Retardation also mathematically predict the exact same (experimentally) observed "Time Dilation" effects instead by using Oliver Heaviside's equations (which are well tested in electrodynamics), he uses these equations rather than the Lorentz Transformation to derive a theorem based on Electromagnetic Retardation. In this theory a metric of "time" itself isn't being dilated either, it should be mentioned there is no definitive proof either that a metric of "time" even exists because time itself is just a measure of magnitudes - so to say each observer has a "time" dependent on velocity with nothing physical (or an Ether) as a causal basis for this dilation is nonsensical in any serious physical scientific theory.
Final Note
There is actually NO NEED for us to hold onto Special Relativity and its explanation of "time dilation" when it is logically, mathematically, and physically impossible. There are consistent alternatives out there, many of which are likely still undiscovered because many people simply cannot apply an ounce of skepticism to relativity, it essentially gets a "special treatment" that other theorems never receive as it is embedded into academia and its popular culture derivatives in General Relativity only have added further to this problem.
*examples discovered by Thomas Smid, PhD. Astronomy and S.N. Arteha, original explanation modified from writings of Thomas Smid and S.N. Arteha
[color=#0000FF][b][i][size=108]Reason 2/100 of why Special/General Relativity are entirely IMPOSSIBLE[/size][/i][/b][/color]
[size=85](DO NOT POST HERE. Discuss any reasons here: https://www.thunderbolts.info/wp/forum3/phpBB3/viewtopic.php?f=3&t=232 )[/size]
[u][b]The Relativistic "Lorentz Transformation" (Time Dilation) is impossible[/b][/u]
Special Relativity (as developed by Einstein) obtains a set of equations, known formally as the [b]Lorentz Transformation formulae[/b], which relates length and time units of two systems moving at uniform velocity relative to each other. However this name is entirely misleading as the original Lorentz Transformations had an Ether rest frame to derive absolute velocity and motion, which unlike relativity made them at least logically feasible despite the problems with the Lorentzian Ether model.
The relativistic Lorentz Transformations are impossible as they inevitably result in [b]different ontological (causal) effects for different observers[/b], this is because the velocity derived physical effects are dependent only upon the observer (relativistic).
And [b][color=#0000FF]as shown in reason 1[/color][/b], even without these logical fallacies they have no mathematical basis in the proofs as Einstein ignored basic mathematical constraints in his relativistic derivation of the formal Lorentz Transformation. Such blatant mathematical errors today wouldn't even make it past peer review.
[u]Lorentz Transformation[/u]
Unlike the equations of the usual Galilei Transformation, the Lorentz Transformations are not merely a linear transformation. The Galilei Transformation describes the change in distance between two points (co-ordinate change) in each reference frame due to their different relative motion). The Lorentz Transformations are non-linear in the velocity [b]due to an additional factor γ[/b] containing the ratio of the velocity and the speed of light γ= 1/√[1-(v/c)^2].
The relativistic Lorentz Transformations differ from the original Lorentzian theory in that velocity[b] is entirely dependent upon the observer[/b], they have no absolute velocity to derive effects (as there is no Ether or medium to derive absolute motion) for things such as length contraction.
So objects can undergo a length contraction (and time dilation) for [b]one observer but not another[/b], this produces contradicting effects that make Special Relativity impossible.
[u]
Time Dilation[/u]
The time dilation claim is based on the set of Lorentz transformation for the "space and time" coordinates relating the rest frame (observer A) (unprimed coordinates) and moving frame (primed' coordinates):
(1a) x'=γ(x - vt)
(1b) t' = γ(t - vx/c²)
Einstein derives the "time dilation" effect by considering the origin of the moving frame x'=0. Inserting thus (Eq.(1a)) x=vt into Eq.(1b) he obtains (considering that γ= 1/√[1-(v/c)^2])
(2) t' = t/γ
This would mean that the clock rates in the moving (primed') frame would be a factor 1/γ slower (time dilation) than in the rest frame (observer A). But as there is no rest frame to derive velocity (which is dependent upon the observer in SR) if we consider the previous primed' frame as Observer B - the effect for this primed frame observing the original frame would be reversed, producing entirely opposite effects.
Using the Lorentz transformation for the Observer B now being the rest frame now:
(3a) x=γ(x' + vt')
(3b) t = γ(t' + vx'/c²)
And applying (like before) the condition x=0 i.e. x'=-vt' (from Eq.(3a)):
(4) t = t'/γ,
So we have[b] opposite time dilations[/b], i.e. a "Twin Paradox" if the dilations are both true and both happen, comparatively there is actually no time dilation. Rendering Special Relativity useless as no times would even get dilated in the Universe (relative to the observer) in the first place as it would always be a mutual dilation.
t = t'/γ
t' = t/γ
We will now demonstrate how relativity still utterly fails to deal with this twin paradox, and why the observer based Universe of relativity with no local rest frame to derive velocity is impossible and results in logical fallacies and contradicting effects.
[b]
[u]
Why the Twin Paradox (done correctly) still invalidates relativity[/u] [/b] (Thomas Smid example)
Relativists always claim that the twin paradox situation is not symmetric as one observer has to turn around and change reference frames to share the time, but this is a lackluster excuse for this complete logical debacle. Because by stopping both clocks BEFORE any return journey to share the time, no change in a state of motion is even required and cannot undo what time dilation just happened either.
If we take a symmetrical example where two frames [i][b]are moving at a uniform velocity v toward each other,[/b][/i]
And a [b]MECHANICAL INTERACTION[/b] [color=#008000]starts[/color] and [color=#BF0000]stops[/color] both clocks simultaneously, NO change in reference frame is even required to derive the time.
|-----A-----[b]|[/b] -> v.............
.............v <- [b]|[/b]-----B-----|
.........Clocks Start......
....|-----A-----[b]|>[/b].................
...............[b]<|[/b]-----B-----|...
........Clocks running.....
......|-----A-----[b]|>[/b]..............
..............[b]<|[/b]-----B-----|......
........Clocks Stop.........
..................[b]|[/b]-----A-----|>..
...<|-----B-----[b]|[/b]...............
..(Identical Time Dilation)...
....................[b]|[/b]-----A-----|>
<|-----B-----[b]|[/b]...................
The signal propagation time for both mechanical clock activation in the above example is also irrelevant, [b]if the corresponding distances are identical in both systems, then the delay times will also be IDENTICAL[/b]. So any claims of non-symmetry by relativists cannot hold.
So it is clear that the final recorded clock readings MUST be identical[b] or you get a logical contradiction[/b] (i.e. if the observer who had the slower time gets a pie in the face after the time is reconciled). But Special Relativity theoretically predicts t'= t/γ, it predicts [b]one observer expects the other to have a slower clock[/b], but as shown in the above example this is simply impossible as this paradox cannot be resolved by an accelerating frame (like in the famous twin paradox) in the above example the clocks are already stopped while the frames are still uniform.
Faced with this, a small number of relativists will claim that the 'relativity of simultaneity' is responsible for the asymmetry, this is a false claim that "relativity wouldn't even theoretically predict/require different time readings in this uniform instance" i.e. the term vv.x/c^2 in the Lorentz transformation formula t'=γ(t-v.x/c^2). But this claim has no basis as the coordinate x is equal to vt (for uniform motion, as used in the above example). Such an argument also contradicts all formally recognized interpretation of Special Relativity and also Einstein's own papers.
As x=vt the original argument that t'= t/γ still holds and theoretically relativity [b]requires this time dilation to happen[/b] (as is seen easily by inserting the gamma factor γ= 1/√[1-(v/c)^2].
Einstein actually derives the same expression for the alleged transformation of the clock readings in his paper "Electrodynamics of Moving Bodies" (http://www.fourmilab.ch/etexts/einstein/specrel/www/), which depends only on the absolute value of the speed and neither on its direction nor the x-coordinate (i.e. it does not depend on the 'relativity of simultaneity').
Just to reiterate this in a different time dilation example, if the velocity reverses at some point, this has no impact whatsoever on the clock reading as t' depends only on v^2 (by re-defining the origin x=0 as the reversal point for the 'return-journey' the same expression t'= t/γ does indeed apply to the outward AND return journey for both frames).
So even such an alleged 'asymmetrical' situation where the relativistic effects apply (such as the famous Twin Paradox) is in fact also a paradox [u]if the Lorentz transformation is applied correctly[/u]. The relativistic "time dilation" caused from an observer based relative velocity and the solution to the famous paradox using accelerating frames actually shows in itself that relativity is an internally inconsistent theory.
But the point of this reason - even without this problem (as shown above and below), the solution to the famous paradox only works in that[i] specific type of example[/i] with different accelerating frames (and not symmetrical or uniform examples as shown in this reason).
[b][u]
A more familiar (an easier) example[/u][/b] (from S. N. Arteha)
[b]A[/b] --[b]>[/b]-------------[b]O[/b]--------------[b]<[/b]-- [b]B[/b]
[size=85]
[b]>[/b] ship A
[b]<[/b] ship B
[/size]
If we have two colonies of Earth’s inhabitants [b]A[/b] and [b]B[/b] be at a large distance from each other.
The beacon [b]O[/b] is at the middle of this distance. It sends a signal (the light sphere), and when it reaches both colonies (simultaneously), each launches a spacecraft piloted by one "twin". The laws of acceleration (to reach a large equal speeds) are chosen equal in advance.
At the time each twin passes the beacon, at a high relative velocity, [b]each will believe that his counterpart should be younger[/b].
[b]A[/b] --------------[b]>[/b]--[b]O[/b]--[b]<[/b]--------------- [b]B[/b]
This is impossible, since they can photograph themselves at this instant and write their age on the back side of a picture (or even exchange pictures by the digital method). It is nonsense, if for example wrinkles will appear on a pictured face of only ONE astronaut during the deceleration of another one. This is a paradox.
[u]
The Famous Twin Paradox[/u]
It is important to remember the explanation for the famous paradox of twins (one an astronaut and one an Earth’s inhabitant). Since only one of them accelerates and changes inertial frames it is just this person who was declared to be younger than the other one in eventuality. But before this acceleration [u]each of the twins thought that the other one should be younger[/u].
This itself is a contradiction and entirely impossible, [i]any resolution after the fact is superfluous[/i] because this first part of the paradox can be exploited by a minor change to the example.
And, in fact, if one twin is accelerated, then the other grows old faster.
Even the ”explanation” of the classical twins paradox certainly contains some contradictions. First, as shown in this reason everything could have been done symmetrically anyway (an example which easily invalidates Special Relativity's assumptions of "observer dependent time dilation"); but also the astronaut twin and the Earth twin can take photographs before and after the acceleration that changes inertial frames at a given age. If the astronaut is expected to be younger just before the acceleration in one frame but not the other we have an impossible situation that has causal eventualities even before the standard mathematical trick of accelerating frames "saves the paradox".
Accelerating frames doesn't save the paradox,[u] because the paradox is still there[/u] and can be exploited in situations before and without it.
All of this logically and empirically demands a different (non-relativistic, non observer based) physical explanation for all experimentally observed "time dilation". One that is logically consistent and based in physical reality. Not the purely mathematical construct of Special Relativity derived from an assumption of light invariance in all frames, which is replete with causal errors and logical fallacies that make the entire related theory simply impossible.
[u]
Electromagnetic Retardation[/u]
Other non-relativistic theories such as Oleg Jefimenko's Electromagnetic Retardation also mathematically predict the exact same (experimentally) observed "Time Dilation" effects instead by using Oliver Heaviside's equations (which are well tested in electrodynamics), he uses these equations rather than the Lorentz Transformation to derive a theorem based on Electromagnetic Retardation. In this theory a metric of "time" itself isn't being dilated either, it should be mentioned there is no definitive proof either that a metric of "time" even exists because time itself is just a measure of magnitudes - so to say each observer has a "time" dependent on velocity with nothing physical (or an Ether) as a causal basis for this dilation is nonsensical in any serious physical scientific theory.
[u]
Final Note[/u]
There is actually NO NEED for us to hold onto Special Relativity and its explanation of "time dilation" when it is logically, mathematically, and physically impossible. There are consistent alternatives out there, many of which are likely still undiscovered because many people simply cannot apply an ounce of skepticism to relativity, it essentially gets a "special treatment" that other theorems never receive as it is embedded into academia and its popular culture derivatives in General Relativity only have added further to this problem.
[color=#004040]
[b][i][size=85]
*examples discovered by Thomas Smid, PhD. Astronomy and S.N. Arteha, original explanation modified from writings of Thomas Smid and S.N. Arteha[/size][/i][/b][/color]