Evidences for and against Einstein's Theories of Relativity

[Aardwolf]

I asked if the "change of inertial frame = change of velocity = acceleration" is the cause of A's slower elapsed time.

And I answered carefully and correctly. The time elapsed on the worldline of the Twin that changes frame is less.

And what caused this lower elapsing time? You have no answer, you have no theory. Just observing an effect; without any effort to attribute a cause. Faith based garbage.

The thread is about Einstein's theories not mine. I don't want to go off topic.

It's absolutely on-topic. If you think it is a valid question to ask for the "cause" of one clock reading less time , beyond the fact that they have followed different worldlines, then it is a valid question for me to ask you for the "cause" of separated and reunited clocks reading the same. What keeps them reading the same? If one question is not valid, then neither is the other.

Where did I state they read the same? Is making all this stuff up part of the faith? I'm asking for the action that differentiates them so a reasonable theorist can determine which stayed and which travelled. A presumably simple question you refuse to answer. We can all only wonder why.

You have in no way attempted to explain the physical cause behind the effects you want us to accept in faith.

I am not asking you to accept anything on faith. I was challenged on the self consistency of SR, and I demonstrated its self-consistency - I did not ask you to accept anything on faith. SR is a description of the world which stands or falls on whether it is an accurate description of what we observe, in the same way that Newton's law of gravity is a description of the world. You might think that Newton's laws are deficient in that they do not propose a "cause" for one massive body to attract another at a distance, but that is no different from your insistence that there must be a "cause" for clocks following different worldlines to read differently. If you think these are both deficiencies, that's your prerogative - but physics is not bound to conform to your desire for mechanical causes. In the one case we have come to accept the explanatory power of fields (and in fact we found that fields are actually primary), and in the other that space and time are not absolute under Lorentz boosts.

The cause of gravity is also a problem which is why the current theories are shaky at best. Relying on the failure of other theories to explain your failure isn’t much of a defence.

If H & A are in sealed compartments and A accelerates away at 1g, returns at 1g and decelerates at 1g, how can they tell which stayed and which travelled?

A experiences acceleration, H does not. We have been over this before.

Describing what happened as an outsider doesn’t answer the question. You said H and A both know which accelerated. How does A’s experience differ from H?

…physics is not bound to conform to your desire for mechanical causes

Comedy gold. Obviously God just wills stuff to happen.

[Higgsy]

I'm asking for the action that differentiates them so a reasonable theorist can determine which stayed and which travelled. A presumably simple question you refuse to answer. We can all only wonder why.

I have told you several times that the one who travelled changes frame and therefore experiences acceleration. The other does not. Are you finding that difficult to understand - or just refusing?

The cause of gravity is also a problem which is why the current theories are shaky at best. Relying on the failure of other theories to explain your failure isn’t much of a defence.

OK - so you think both Newtonian gravity and GR are shaky because the "cause" "is "a problem"? You must also think that electromagnetism is shaky because the "cause" of the Coulomb force and the Lorentz force is a problem. That's exactly the same. How about the strong and weak forces? We have now dispensed with the four fundamental forces in physics, so you must think physics generally is "faith based garbage". One wonders why you even bother to contribute to a physics forum.

Physics is not religion. It is not ontology. It is a humble process by which we observe the natural world and describe how it goes mathematically. Allowing us to predict events within the limitations of our models.

If H & A are in sealed compartments and A accelerates away at 1g, returns at 1g and decelerates at 1g, how can they tell which stayed and which travelled?

A experiences acceleration, H does not. We have been over this before.

Describing what happened as an outsider doesn’t answer the question. You said H and A both know which accelerated. How does A’s experience differ from H?

I just told you: A experiences an acceleration and H does not. What is it about that explanation that you don't understand? I can't say it more plainly.

And I must say that I don't feel that you are conducting this discussion in good faith.

[EtherQuestions]

The second link, Stephen J Crothers – On Einstein's Time Dilation and Length Contraction – 2017, has exactly the same trivial mistakes (word for word) as the one I demolished.

My response your invalid criticism of SJ Crothers "logical inconsistencies of length contractions" paper (and condescendingly inappropriate rude replies to crawler)



Higgsy: "He then says: "It follows from the Lorentz Transformation for a system of stationary observers that there is no place in the 'stationary system' K from which the moving sphere of radius R in k undergoes length contraction. All stationary observers report length expansion."

But eqn 2 is the expression for an ellipsoid in x, y and z, displaced from the origin by vt and where the radius in the y and z axes is R and the radius in the x axis is R contracted by 1/beta.

His own equation confirms that all observers in the frame moving with respect to the sphere see it contracted by the same factor."


First of all that is not SJ Crothers equation. It is the same sphere but according to the co-ordinates stationary system K from Einstein's very own paper (Have you even read Einstein's papers?).

In other words this equation 2 by Einstein doesn't show length contraction, rather it shows length expansion by merely showing the perfect sphere in the other primed co-ordinate system where the x-axis is contracted. Otherwise the gamma factor would be the inverse,

According to you Einstein's eq 2 would be x^2 /(1/sqrt[1-(v/c)^2 ])^2

NOT x^2/(sqrt[1-(v/c)^2 ])^2 ).

So you've just misunderstood Einstein's equation from the Electrodynamics of Moving Bodies (German translation here; http://www.fourmilab.ch/etexts/einstein/specrel/www/) which is a (comparative) expansion equation superposing the co-ordinate systems, not a contraction equation for the sphere and you therefore you misunderstood the entirety of SJ Crothers paper. It is a critique of Einstein proof from superposing two co-ordinate systems.

It is analyzing the point of view of the center of the sphere in the contracted co-ordinate system, and then showing how the original sphere would look from that contracted point (a stretched sphere, "ellipsoid").

So you have it completely upside down, this equation (2) is just expressing the same perfect sphere relative to the adjusted co-ordinate system x,y,z (where it would otherwise be an ellipsoid) but it isn't applying the Lorentz Transformation to turn it into a contracted ellipsoid (relative to the primed' frames sphere) at all.
It is just comparing it to the primed contracted co-ordinate system without contracting it, and then assuming this observers point of view of it (just as Einstein did). So it is an "ellipsoid" in the sense it is comparatively expanded compared to the contracted co-ordinate system (even when it doesn't physically exist in the contracted system) Einstein is comparing the systems to generate his proof, and this is the source of the mathematical error as in superposing the co-ordinates Einstein forgets the time transformations of the moving frame when creating his original proof.

This isn't SJ Crothers trying to obfuscate things either, this is Einstein's equation directly picked from Einstein's example, which you have entirely misunderstood.

The whole point of the paper is that Einstein's superposing of the coordinate systems to display the primed' sphere relative to the unprimed coordinates creates a logical inconsistency due to the offset times (in the primed frame), so the zero time origin point Einstein used to derive his proof of LC being "only a function of velocity" simply cannot work as Einstein forgets his own Lorentz Transformation of the time and SJ Crothers demonstrates this invalid proof must therefore produce opposite effects.

The point Crothers makes is that if two or more "stationary observers" are clock synchronized, yes of course Δξ/β = Δx for a moving object; but this must be at the expense of the identical time dilation of the observed moving object and therefore resultantly at the expense of being "stationary" to each other - all due to Einstein's equivocation blunder in superposing what an absolute shape might look like to two co-ordinate systems that are contracted/uncontracted from a zero point time scale (whilst ignoring the time adjustments for each co-ordinate system).

However this problem of non-simultaneity contradicting the foundational proofs of relativistic length contractions can be made more concisely than SJ Crothers has made it (a lot people even in the EU community misunderstand his papers, but that is ONLY because he is directly referencing Einstein's papers which use purposeful obfuscations to hide Einstein's own errors, a clever psychological trick to create "dependency" due to mental investments spent in understanding something. Einstein even alludes to doing this in interviews later in his life. He was a genius in that regard, or as Nikola Tesla put it "a beggar in purple clothing, whom ignorant people mistake for a king").

The example you should be referring to with your very plain argument "He then calculates the equation of the sphere/ellipsoid in the observers' frame in equation 2" is instead the resultant "ellipsoid of revolution" from an actual length contraction which would create the length contraction with the 3 radii: R/gamma,R,R. But merely stating this doesn't invalidate Crothers argument, you should try and understand Einstein's paper before making any criticism.

This equation 2 (of Einsteins) Crothers is generating proof that Einstein made a blunder in his comparative expansion equation (again Einstein's equation here is not a Lorentz Contraction, it is the opposite (an expansion, it is R*gamma) used by Albert Einstein in his paper "The Electrodynamics of Moving Bodies" (German translation; http://www.fourmilab.ch/etexts/einstein/specrel/www/) to generate a Length Contraction proof in a given state of motion by comparative co-ordinates superposing).




Just like 90% of the time you throw around invalid arguments followed with extremely condescending preemptive victory declarations, when you don't even understand the critique to begin with. Before I believed you knew your stuff and at least respected that, but I'm starting to wonder how well versed you actually are in physics or if you are just a troll relativity fanboy trying indulge in some sort of entirely misplaced superiority "intellectual vanity" complex by posting on here all the time. You're not proving anything here by down talking users like crawler, not understanding a critique in the first place only proves ignorance, not intellectual superiority.


Higgsy:"Turning to the rod, his unnumbered equation before eqn 4 is incorrect (it should be Δξ/β = Δx; he is equivocating between which frame the observer is in and in which frame the rod is at rest)"

He already used ξ/β = x at t = 0 for the contracted co-ordinate system. He isn't confusing the frames the observer is and which frame the rod is at rest, he just derived the reverse effects from Einstein's own blunder in forgetting the time offsets in his clock synchronized example. This is why ξ1 can be equivalent to x1/β because if x=0 at ξ=0, according to Einstein's proof example when we consider time offsets of the superposed co-ordinate systems at ξ=R due to the Lorentz Transformation the k time is not the same in the traveling superposed "absolute" sphere in both co-ordinate systems.

Because of this as the displacement through space at vt is a function of time, the superposed sphere cannot work as a universal mathematical proof for other stationary observers not at the 0 origin point. Einstein is the one who equivocated the frames to generate a false example by superposing a sphere of absolute length onto a contracted co-ordinate system (contradicting his own logic).

Again eq 2 is just displaying the absolute sphere in the contracted co-ordinate system whilst also accounting for the motion of the x (r/gamma) radii offset to the left with x-vt. It is not contracting the sphere, it just superposing it onto the contracted co-ordinates.
The problem in Einstein's proof therein lies that the traveling origin point in the contracted co-ordinate system cannot coincide with the absolute sphere which in later examples Crothers renders identical time dilations/contractions in all stationary frames mathematically inconsistent.

Where SJ Crothers often fails is that he usually isn't concise enough, so I'll make this paper more clear:

In short their cannot be reason/mathematical proof for a universal contracted co-ordinate system to apply both Length Contractions AND time offsets/dilations in the Lorentz Transformations to all objects (or observers) in the identical relative motion, because Einstein's mathematical rigid sphere "proof" example generates inconsistencies and is not a valid proof for all observers as it doesn't work if the co-ordinate systems aren't locked at a 0 space-time co-ordinate origin. As soon as Einstein uses velocity in his proof, he undoes himself because after t=0 his proof proves meaningless.

Does this alone debunk Special Relativity? No it doesn't, but considering the fact all of Einstein's other proofs of the relativistic Lorentz Transformation also fail (see my reason 2), yes it does.


Higgsy:"And his claim that this expression comes about by considering eqn 2 is nonsense"


It isn't for the simple fact Einstein forgot to apply time adjustments to the contracted co-ordinates, he assumed simultaneity of events/spacetime co-ordinates by superposing an uncontracted sphere onto a contracted co-ordinate system as a means of comparing it and deriving a proof.

Einstein's error is by superimposing the unprimed frames time (ultimately velocity) readings onto the primed' contracted co-ordinate system to derive a "contracted" sphere in the primed frame (which according to Einstein the contracted sphere would look like x^2 + y^2 + z^2 = R, as Einstein earlier defines the uncontracted perfect sphere as (x*gamma)^2 + y^2 + z^2 = R (when shown in the contracted (x,y,z) co-ordinate system)). //


Higgsy:"I have reviewed one of your links above and showed it to be gibberish. I have no intention of wasting time on the others."



I wouldn't call that a "review" of the SJ Crothers paper "On the Logical Inconsistency of Einstein's Length Contraction" crawler just posted.

You don't even understand the Einstein paper's example it came from let alone SJ Crothers, Einstein is not strictly writing about just applying the Lorentz Transformation, he is superposing incompatible frames to derive an invalid proof of the Length Contractions from an "absolute shape" by retroactively defining x^2 + y^2 + z^2 =0 as a "contracted" sphere because the x-coordinates are comparatively contracted.

I'm surprised you don't know this (I was taught all the ins and outs of Einstein's papers used to formulate the scientific proofs early on, I'm not sure if every educational establishment does this though).

You've literally just skirted through the Length Contraction paper and made an entirely false criticism, added a bit of ad-crotherhominem (relativists always do this "oh SJ Crothers that foolish crank" etc.) then you went on and declared victory in the same old condescending insulting fashion (yet again). These condescending preemptive victory declarations are like putting a cherry on a pile of your own excrement, serving it on a shiny silver platter, and forcing people to digest it.

You aren't proving anything, and you aren't better than anybody here either by just being insulting and condescending to other members and also to SJ Crothers who is a good person and has sacrificed/risked so much personally just to point out flaws in Special/General Relativity.

[EtherQuestions]

And what did the other "relativists" have to say about this "paradox"?

They answer it by stating that the phase velocity can be variant, it exceeds c for the approaching observer. They just believe that light isn't displaced through space at a velocity >c for the approaching observer because the phase velocity is confined within a traveling "wave packet" (which has a constant group velocity c). As for my critique of the invariant group velocity explanation (in the case of continuous emission) I haven't had any answer, because there isn't one for cases when the wave packet isn't detached from the source.

Why not? The frequency is the frequency in the frame of the source. The wavelength is the wavelength in the frame of the source. For an observer approaching the source, the wavelength is reduced (the length of a wavetrain is reduced by the same amount) and the frequency is increased. What's the problem?

No, the created wavelength is not the same in the frame of the source.

In the frame of the source the phase velocity exceeds c for the approaching observer (or reflector) so more peaks hit the observer, but this only increases the frequency just for the approaching observer. The rate of creation is the same (not increased) as light is invariant in the source frame (no compressed wavetrain), this effect is not too different to the standard Doppler (Ether) model. The frequency increase is defined by the
increased peaks/troughs per second hitting the observer, but nothing happens to the wavetrain or wave creation rate.

In the frame of the approaching observer the phase velocity is c for the approaching observer, so the wavetrain is now compressed as light has to "slow down" from the velocity defined in the source frame (to remain c). So to increase the frequency you must now increase the rate of creation at the source, the whole wavetrain must be effected and the wave creation rate.



Lorentz Transformation Topic

No it's not - this is exactly the definition of symmetry - each sees the other's clock running slow.

No, this is actually "asymmetry" by definition in each frame. But even if we supplant the word "asymmetry" for "symmetry", the contradiction still applies. As you put it "each sees the other's clock running slow". This proves reason 3/100, a paradox occurs because relativity theoretically predicts "each sees the other's clock running slow". If we stop the start and stop the clocks simultaneously (in each frame) one expects the other to be slower, this is impossible as it causes a paradox.

There is no such thing as a clock rate in a frame which is the same for all frames. Maybe that's where your misconception is. As long as two frames are moving with respect to one another each will see the other's clock running slow.

Proving reason 3/100 correct. You just admitted it again. As shown in reason 3 if the clocks are started and stopped before the change in reference frame by a mechanical interaction, relativity predicts a paradox. It predicts opposite effects in each frame, which is impossible.

When the clocks are stopped, each observer reads his clock to be the reading the same, but each observer sees the other's clock as running slow. That's all there is your scenario. The thing ends when the clock's stop. Each observer sees the other's clock as running slow. There isn't an impossible situation here.

Lol. As you condescendingly wave Michael Mozina's quote around like a flag on your profile, I might just keep this one:

Higgsy: "The thing ends when the clock's stop. Each observer sees the other's clock as running slow. There isn't an impossible situation here."

Of course this is impossible. Tell me Higgsy. What happens when the observers meet up? Who's clock is slower? The clocks already stopped, as you said. Both reading slower than the other in each frame:

"The thing ends when the clock's stop. Each observer sees the other's clock as running slow." You just effectively admitted Reason 3/100. Congratulations.

For the muon we are in one frame looking at the other. And we observe clocks in that other (moving) frame running slow. That's all we observe. For the muon, no-one said anything about synchronisation. How do you propose we synchronise clocks with the muon?

I don't. No problem here. Merely pointing out you contradicted yourself in your earlier claims a while back where you implied in reason 3/100 mutual time dilation occurs (no relative dilation, or synchronized clocks).

[Aardwolf]

I'm asking for the action that differentiates them so a reasonable theorist can determine which stayed and which travelled. A presumably simple question you refuse to answer. We can all only wonder why.

I have told you several times that the one who travelled changes frame and therefore experiences acceleration. The other does not. Are you finding that difficult to understand - or just refusing?

I already acknowledge that one travelled and the other didn’t, keep up the straw man. However, without any mechanism offered by you I can accurately state that H travelled away, A remained and H’s clock run 2 hours slower. Ergo paradox. Ergo garbage theory.

The cause of gravity is also a problem which is why the current theories are shaky at best. Relying on the failure of other theories to explain your failure isn’t much of a defence.

OK - so you think both Newtonian gravity and GR are shaky because the "cause" "is "a problem"? You must also think that electromagnetism is shaky because the "cause" of the Coulomb force and the Lorentz force is a problem. That's exactly the same. How about the strong and weak forces? We have now dispensed with the four fundamental forces in physics, so you must think physics generally is "faith based garbage". One wonders why you even bother to contribute to a physics forum.

I'm only concerned with gravity in this thread but still nice of you to acknowledge that gravity and electromagnetism are “exactly the same”.

Physics is not religion. It is not ontology. It is a humble process by which we observe the natural world and describe how it goes mathematically. Allowing us to predict events within the limitations of our models.

And what observation of the natural world causes A’s time to run slower? Was it the acceleration? Oh yes, I forgot, that’s the bit of the natural world you would rather not describe.

If H & A are in sealed compartments and A accelerates away at 1g, returns at 1g and decelerates at 1g, how can they tell which stayed and which travelled?

A experiences acceleration, H does not. We have been over this before.

Describing what happened as an outsider doesn’t answer the question. You said H and A both know which accelerated. How does A’s experience differ from H?

I just told you: A experiences an acceleration and H does not. What is it about that explanation that you don't understand? I can't say it more plainly.

Plainly explain how when In A’s shoes you know that you are travelling. You said A would know. Put yourself in the natural world of A and humbly describe how he knows he accelerates. To keep describing the process as an outside observer isn’t really an answer is it.

And I must say that I don't feel that you are conducting this discussion in good faith.

Just looking for a simple answer to a simple question. Apologies if that causes you angst. Belief in blind dogma can have that effect when propositioned with logic.

[Higgsy]

I'm asking for the action that differentiates them so a reasonable theorist can determine which stayed and which travelled. A presumably simple question you refuse to answer. We can all only wonder why.

I have told you several times that the one who travelled changes frame and therefore experiences acceleration. The other does not. Are you finding that difficult to understand - or just refusing?

I already acknowledge that one travelled and the other didn’t, keep up the straw man. However, without any mechanism offered by you I can accurately state that H travelled away, A remained and H’s clock run 2 hours slower. Ergo paradox. Ergo garbage theory.

I keep telling you that A experiences acceleration and H doesn't. What more do you want to know?

The cause of gravity is also a problem which is why the current theories are shaky at best. Relying on the failure of other theories to explain your failure isn’t much of a defence.

OK - so you think both Newtonian gravity and GR are shaky because the "cause" "is "a problem"? You must also think that electromagnetism is shaky because the "cause" of the Coulomb force and the Lorentz force is a problem. That's exactly the same. How about the strong and weak forces? We have now dispensed with the four fundamental forces in physics, so you must think physics generally is "faith based garbage". One wonders why you even bother to contribute to a physics forum.

I'm only concerned with gravity in this thread but still nice of you to acknowledge that gravity and electromagnetism are “exactly the same”.

So that's what I mean about bad faith. Any reasonably intelligent reader would understand that I am not claiming that electromagnetism and gravity are the same, but that the effect of action at a distance (what gravity is or what electro-magnetism is) for the two forces (and for the weak and strong nuclear forces) are equally unexplained. I suppose you are reasonably intelligent, so the only explanation for your conflation is a deliberate attempt on your part to score points by the cheap trick of misrepresenting what I said.

If H & A are in sealed compartments and A accelerates away at 1g, returns at 1g and decelerates at 1g, how can they tell which stayed and which travelled?

A experiences acceleration, H does not. We have been over this before.

Describing what happened as an outsider doesn’t answer the question. You said H and A both know which accelerated. How does A’s experience differ from H?

I just told you: A experiences an acceleration and H does not. What is it about that explanation that you don't understand? I can't say it more plainly.

Plainly explain how when In A’s shoes you know that you are travelling. You said A would know. Put yourself in the natural world of A and humbly describe how he knows he accelerates. To keep describing the process as an outside observer isn’t really an answer is it.

Who said anything about an external observer. I said that A experiences accceleration. Not X sees A change frame (although X would). A experiences acceleration. How is acceleration experienced? By forces acting on bodies in the accelerated frame, which can be measured.

And I must say that I don't feel that you are conducting this discussion in good faith.

Just looking for a simple answer to a simple question. Apologies if that causes you angst. Belief in blind dogma can have that effect when propositioned with logic.

Yes, I can see you are struggling with logic.

[Higgsy]

In other words this equation 2 by Einstein doesn't show length contraction, rather it shows length expansion by merely showing the perfect sphere in the other primed co-ordinate system where the x-axis is contracted. Otherwise the gamma factor would be the inverse,

According to you Einstein's eq 2 would be x^2 /(1/sqrt[1-(v/c)^2 ])^2

NOT x^2/(sqrt[1-(v/c)^2 ])^2 ).

Don't put words in my mouth. Equation 2 represents an ellipsoid contracted in x. It's exactly the same as for the case where t=0 except the origin is displaced by vt. According to me equation 2 is correct, as is the equivalent equation at t=0 from reference 3 in that paper. When y =z =0, (x - vt)^2 = (R/beta)^2. I'll leave you to solve for x-vt and work out the diameter of the ellipsoid in the x-axis. I haven't time for the rest of your very long posts at the moment.

[Aardwolf]

I keep telling you that A experiences acceleration and H doesn't. What more do you want to know?

According to you A experiences acceleration.
According to you A’s clock runs slower.
So, does the acceleration cause A’s clock to run slower? Yes or no?
It’s an incredibly simple question.

So that's what I mean about bad faith. Any reasonably intelligent reader would understand that I am not claiming that electromagnetism and gravity are the same, but that the effect of action at a distance (what gravity is or what electro-magnetism is) for the two forces (and for the weak and strong nuclear forces) are equally unexplained. I suppose you are reasonably intelligent, so the only explanation for your conflation is a deliberate attempt on your part to score points by the cheap trick of misrepresenting what I said.

No opportunity to be misrepresented if you just stick to the thread topic and answer the question clearly. If it has no relevance don't bring it up.

Who said anything about an external observer. I said that A experiences accceleration. Not X sees A change frame (although X would).

You (as the observer) are stating what happens. Is that difficult for you to understand?

A experiences acceleration. How is acceleration experienced? By forces acting on bodies in the accelerated frame, which can be measured.

And as I said before if A travels away at 1g and returns at 1g in a sealed ship how does he know the difference between just standing on a 1g planet.

Yes, I can see you are struggling with logic.

But not struggling to answer very simple questions.

[Zyxzevn]

Can we get back to science and experimental results please?
Let me first start with Special relativity.

If you measure a fast moving object relative from an observer..
..so you have a delay and movement between the observer and the object's reality.

Time: Will there be any change of a clock? And what kind of clock?

Position: At what position would you expect to see a moving object?
At what speed would it seem to move?

Any other things that are important?

What do real observations tell us?
I have not seen much about this in this whole thread.

Starting with the basic Aether model, and the basic Emission model..
What kinds of modifications do we need to apply to fit certain observations?

Do we still have magnetism as a separate force?

In an aether model, do we need to add movement? Relative to what?
In a emission model, do we need to add time and/or length relativity? What transfers force?
For both: Do we need to add dimensions?

[Higgsy]

In other words this equation 2 by Einstein doesn't show length contraction, rather it shows length expansion by merely showing the perfect sphere in the other primed co-ordinate system where the x-axis is contracted. Otherwise the gamma factor would be the inverse,

According to you Einstein's eq 2 would be x^2 /(1/sqrt[1-(v/c)^2 ])^2

NOT x^2/(sqrt[1-(v/c)^2 ])^2 ).

Don't put words in my mouth. Equation 2 represents an ellipsoid contracted in x. It's exactly the same as for the case where t=0 except the origin is displaced by vt. According to me equation 2 is correct, as is the equivalent equation at t=0 from reference 3 in that paper. When y =z =0, (x - vt)^2 = (R/beta)^2. I'll leave you to solve for x-vt and work out the diameter of the ellipsoid in the x-axis. I haven't time for the rest of your very long posts at the moment.

So I have looked more carefully at EQ's enormously wordy and lengthy post. There is no further content beyond it, other than his fundamental misunderstanding of how to transform between inertial frames in relative motion. It seems that he (and Crothers) fail to recognise eqn 2 as the equation of an ellipsoid where the ellipsoid radius along the x-axis is contracted with respect to a sphere. There is nothing more to be said about this supposed "disproof" of SR - it is badly conceived. In SR the proper length of a body, defined as the length observed in the rest frame of the body is always longest. Observers in all other frames perceive the length in the direction of relative mortion as contracted. This is guaranteed by the form of the Lorentz transform for position-like co-ordinates. As for EQ's gratuitous insults against me (and against Einstein!), they would carry more sting if EQ (and Crothers) weren't hopelessly wrong.

[Higgsy]

And what did the other "relativists" have to say about this "paradox"?

They answer it by stating that the phase velocity can be variant, it exceeds c for the approaching observer. They just believe that light isn't displaced through space at a velocity >c for the approaching observer because the phase velocity is confined within a traveling "wave packet" (which has a constant group velocity c). As for my critique of the invariant group velocity explanation (in the case of continuous emission) I haven't had any answer, because there isn't one for cases when the wave packet isn't detached from the source.

Then they don't know what they are talking about. In both source and observer's frames we have a monochromatic wave propagating in a non-dispersive medium. In both frames the phase velocity = group velocity = c. As I told you earlier, forget about phase versus group velocities - the distionction is irrelevant to this discussion.

Why not? The frequency is the frequency in the frame of the source. The wavelength is the wavelength in the frame of the source. For an observer approaching the source, the wavelength is reduced (the length of a wavetrain is reduced by the same amount) and the frequency is increased. What's the problem?

No, the created wavelength is not the same in the frame of the source.

You need to set out your objection mathematically.

In the frame of the source the phase velocity exceeds c for the approaching observer (or reflector) so more peaks hit the observer, but this only increases the frequency just for the approaching observer. The rate of creation is the same (not increased) as light is invariant in the source frame (no compressed wavetrain), this effect is not too different to the standard Doppler (Ether) model. The frequency increase is defined by the
increased peaks/troughs per second hitting the observer, but nothing happens to the wavetrain or wave creation rate.

You need to set it out mathematically. There is no discrepancy. In the frame of the source and in the frame of the observer, the phase velocity = c.

In the frame of the approaching observer the phase velocity is c for the approaching observer, so the wavetrain is now compressed as light has to "slow down" from the velocity defined in the source frame (to remain c). So to increase the frequency you must now increase the rate of creation at the source, the whole wavetrain must be effected and the wave creation rate.

The phase velocity in the source frame = the phase velocity in the observer frame = c. That is the basic tenet of SR. If you have an objection relating to that you need to set it out mathematically.

[EtherQuestions]

Let me first start with Special relativity.

If you measure a fast moving object relative from an observer..
..so you have a delay and movement between the observer and the object's reality.

Time: Will there be any change of a clock? And what kind of clock?

Position: At what position would you expect to see a moving object?
At what speed would it seem to move?

The space-time co-ordinates get adjusted by the Lorentz Transformation.

For time, before a change in reference frame, t' = t/gamma in each frame (so for each observer the other experiences time slower). Defined by the Lorentz Factor, with v being the relative motion of the observer.

Starting with the basic Aether model, and the basic Emission model..
What kinds of modifications do we need to apply to fit certain observations?

Do we still have magnetism as a separate force?
In an aether model, do we need to add movement? Relative to what?

Define the Lorentz Factor, by v being the object's relative motion to a local Ether rest frame to derive the "time dilation" as an absolute physical effect in all frames. Further adjustments can be made based on Ether density and the motion of the Ether to explain gravitational time dilation effects, and analogous gravitomagnetic effects ("frame dragging") within the error margins.

[Higgsy]

"The thing ends when the clock's stop. Each observer sees the other's clock as running slow. There isn't an impossible situation here."

Of course this is impossible. Tell me Higgsy. What happens when the observers meet up? Who's clock is slower? The clocks already stopped, as you said. Both reading slower than the other in each frame:

Up until the clocks are stopped the situation is symmetric. Each observer sees his own clock running at proper time, and each observer sees the other clock running slow. Stop the clocks and they will both read the proper time - ie, the time each observer sees in his own clock. Bring them together and they will read the same time, the time the clocks stopped according to each observer in each clock's rest frame.

Furthermore, both observers will agree that both clocks read the same when they are stopped, even before they are brought together. In the rest frame of one observer, say A, n years pass and he stops his clock. He observes the other observer's, B's, clock running slow by a factor 1/γ. After γn years in his own frame he observes B's clock stop reading n years. B observes the same thing about A. The situation is symmetric.

Bring them together you say - but you have prematurely truncated the experiment. Let the clocks continue running, and how you bring them together will determine whether they then read the same or whether one reads more than the other, and which one.

[Higgsy]

And as I said before if A travels away at 1g and returns at 1g in a sealed ship how does he know the difference between just standing on a 1g planet.

In this case, A is not in an inertial frame at any stage in the process, so the scenario is not relevant to the discussion which is about doing Lorentz transforms between inertial frames.

And in any case, if there is acceleration throughout the process and we take acceleration away to be positive and acceleration back negative, then A spends longer (three times as long actually) under negative acceleration, as under positive (since he has first to slow down and stop before he starts to accelerate back). He will know that he is not standing on a 1g planet, because the direction of the acceleration vector reverses.

(Note that if we include GR in the discussion, acceleration and gravity are equivalent, so standing on a 1g planet has the same effect as accelerating at 1g - and indeed GR predicts time dilation as a consequence of being in a gravity well.)

[Higgsy]

And in any case, if there is acceleration throughout the process and we take acceleration away to be positive and acceleration back negative, then A spends longer (three times as long actually) under negative acceleration, as under positive (since he has first to slow down and stop before he starts to accelerate back).

Not three times longer - 2.41 times longer (2 + (sqrt(2)-1)).