Real Lorentz–FitzGerald contraction

[Mentz114]

heldervelez:

If we must consider the real length contraction then we must also be prepared to consider a change in the geometrical atomic shape. Idem to a real change of time unit.

So the same object can have many 'real' lengths or shapes at the same time ?

 

[Dale]

I think that there is a huge diference between a 'real effect' and 'an illusion' (coordinate-dependent origin).

What are your definitions of "real" and "illusion"?

 

[heldervelez]

heldervelez:

So the same object can have many 'real' lengths or shapes at the same time ?

Of course not.

Einstein did the treatment using an IRF (Inertial Reference Frame, like CMB, or VLBI, not any other class of reference frames). And this represents 'absolute space' (accelerometer and sagnac effect with zero readings).

One object at rest there has his 'natural' length mass and shape. If the object is moving then everyting change.

 

[Dale]

this represents 'absolute space' (accelerometer and sagnac effect with zero readings).

There are an infinite number of such frames.

 

[Mentz114]

...If the object is moving then everything change.

Absolute motion ?

[EDIT]Now I think you may be referring to length contraction under acceleration, which is not Lorentz contraction.

 

[heldervelez]

There are an infinite number of such frames.

Then they are not all equivalent. Only one of such will be at rest in relation to VLBI.
Or expressed in other words: where we can define an observer with a motion such that one-way light speed in relation to him is isotropic.

 

[Dale]

Then they are not all equivalent. Only one of such will be at rest in relation to VLBI.

What are you talking about? VLBI is a technique. That is like saying that you are at rest in relation to frequency modulation.

Or expressed in other words: where we can define an observer with a motion such that one-way light speed in relation to him is isotropic.

Any of the infinite number of inertial frames fit this description, that is the whole point of the second postulate.

 

[heldervelez]

What are you talking about? VLBI is a technique. That is like saying that you are at rest in relation to frequency modulation.

http://journals.cambridge.org/actio...28&jid=IAU&volumeId=2&issueId=14&aid=1432424"

"...From 1 January 1998 the IAU adopted the International Celestial Reference System
(ICRS) oriented by distant extragalactic objects in the framework of general relativity
with the underlying assumption that the ensemble of such objects has no global rotation.
The initial fundamental realization of the ICRS is the ICRF (International Celestial
Reference Frame) based on positions of 212 defining radio sources measured with VLBI
along with 396 other sources with consistent positions..."

Any of the infinite number of inertial frames fit this description, that is the whole point of the second postulate.

IMO Einstein 1905 use c0=(v1+v2)/2 and it is somewhat similar to the above statement (isotropy of light)

 

[Dale]

"...From 1 January 1998 the IAU adopted the International Celestial Reference System
(ICRS) oriented by distant extragalactic objects in the framework of general relativity"

The ICRS (quite a different thing from VLBI) is general relativistic, so it does not in any way define a preferred reference frame.

IMO Einstein 1905 use c0=(v1+v2)/2 and it is somewhat similar to the above statement (isotropy of light)

http://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf" says "light is always propagated in empty space with a definite velocity c". That means that it is isotropic, finite, and constant. Again, the one-way speed of light is isotropic in all inertial reference frames.

heldervelez, there is a http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html" supporting special relativity and the idea that there is no preferred reference frame. You can continue to produce objections to the contrary but they are contradicted by data. Nature has spoken quite clearly and emphatically on the topic and neither of our opinions really matter. Experiment is always the final judge, and the ruling is clear.

 

[heldervelez]

The ICRS (quite a different thing from VLBI) is general relativistic, so it does not in any way define a preferred reference frame.

http://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf" says "light is always propagated in empty space with a definite velocity c". That means that it is isotropic, finite, and constant. Again, the one-way speed of light is isotropic in all inertial reference frames.

heldervelez, there is a http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html" supporting special relativity and the idea that there is no preferred reference frame. You can continue to produce objections to the contrary but they are contradicted by data. Nature has spoken quite clearly and emphatically on the topic and neither of our opinions really matter. Experiment is always the final judge, and the ruling is clear.

about anisotropy/isotropy from here (and many other references)
http://www.fiu.edu/~hawkinsl/paper/synchronize2.htm"

"...For example, the common belief that the SRS incorporates isotropy and homogeneity of space and time has no operational presence in the theory. The customary association of special relativity with spatial homogeneity and isotropy arises from the insistence of the mind on a prior and absolute synchronization being somehow achievable, i.e., if the clocks were already synchronous, and if space were homogeneous and isotropic, then exactly the same situation as in relativity would result. But such "conceptualizing" is pointless: within the relativistic scheme, no amount of experimentation could ever reveal, say, a possible anisotropy. One would always find that light propagates "isotropically," but only because the relevant clocks had been synchronized to give that result. So within the SRS, isotropy could not be said to be a property of space, but rather of the SRS itself. ..."

from Poincaré "http://en.wikisource.org/wiki/The_Measure_of_Time" "
quote
XII
...When an astronomer tells me that some stellar phenomenon, which his telescope reveals to him at this moment, happened nevertheless fifty years ago, I seek his meaning, and to that end I shall ask him first how he knows it, that is, how he has measured the velocity of light.
He has begun by supposing that light has a constant velocity, and in particular that its velocity is the same in all directions. That is a postulate without which no measurement of this velocity could be attempted. This postulate could never be verified directly by experiment; it might be contradicted by it if the results of different measurements were not concordant. We page 233 should think ourselves fortunate that this contradiction has not happened and that the slight discordances which may happen can be readily explained.
..."

on the same document of Einstein we find c + v and c - v (pags 5 & 6)
the phrase you mentioned above refers to 'two-way velocity' or 'closed loop velocity' = 'c' was made equal to the mean value (pag 3) "we further assume the quantity
2AB / (tA'− tA ) = c, to be a universal constant—the velocity of light in empty space."
then as we see, at least imo, my expression "where we can define an observer with a motion such that one-way light speed in relation to him is isotropic." is also good, but not exactly equal to 'c= mean value of one-way'. My expression is a specialization of the Einstein way, and so it is also included.

Your expression "Again, the one-way speed of light is isotropic in all inertial reference frames." can not hold because SR is only about the closed loop (two-way).

ICRS and VLBI from quote http://aa.usno.navy.mil/faq/docs/ICRS_doc.php
"...The International Celestial Reference System (ICRS) is the fundamental celestial reference system adopted by the International Astronomical Union (IAU) for high-precision positional astronomy. The ICRS, with its origin at the solar system barycenter and "space fixed" axis directions, is meant to represent the most appropriate coordinate system for expressing reference data on the positions and motions of celestial objects..."

I understand our problems and questionings about 'Absolute space/motion/velocity' but this theme is mandatory if really the motion induces a physical length shortening.
Your idea that this is only a semantic problem is unfounded.
Lets pursue the original intention of the OP: Real Lorentz–FitzGerald contraction ?
I put forward at least tree distinct ways to show my point, namely:
1) my 'art work' i.e. my visualizations in first posts
2) Hans de Vries book (it is delicious)
3) Aleksandar Gjurchinovski paper

Instead of insisting that I'm wrong it is better to declare either 1 or 2 or 3, or ...:
1) Your way has this ...and this... errors because ...
2) Hans de Vries book (it is delicious) (chapter 4) is wrong because he is saying other things that you say that he said. And those are ... and... and... because ...
3) Aleksandar Gjurchinovski paper is wrong because ..., ...

Can you cite one experiment from the mountain of evidence that supports the idea that there is no preferred reference frame?
MMX is no good for that purpose and I have in mind that all experiments were done at the Earth Lab that is known not to be elegible as a inertial reference frame (because we are not only moving at 370 Km/s but also accelerating at x? km/s/s, and also it seems conceptually dificult to make such a test.

 

[Al68]

I understand our problems and questionings about 'Absolute space/motion/velocity' but this theme is mandatory if really the motion induces a physical length shortening.

If it does, it's a different effect from Lorentz contraction. Just look at the Lorentz equations. The v in them refers to the relative velocity between the object and any inertial frame, not just a "preferred" one.. The v has a different value in different reference frames.

If you are claiming that there is a "physical length shortening" due to an object's motion relative to a single preferred reference frame, then you might want to give such an effect a different name so it won't be confused with Lorentz contraction.

Can you cite one experiment from the mountain of evidence that supports the idea that there is no preferred reference frame?

We are free to "prefer" any reference frame we choose. But that doesn't stop all the other inertial reference frames from existing.

MMX is no good for that purpose and I have in mind that all experiments were done at the Earth Lab that is known not to be elegible as a inertial reference frame (because we are not only moving at 370 Km/s but also accelerating at x? km/s/s, and also it seems conceptually dificult to make such a test.

Why would Earth not be eligible as an IRF for that reason? For the purposes of MMX, Earth is in inertial motion aside from insignificant second order effects. It was specifically Earth's motion through space that was the basis for MMX.

Are you under the impression that the word "inertial" means lack of motion?

 

[Dale]

Your expression "Again, the one-way speed of light is isotropic in all inertial reference frames." can not hold because SR is only about the closed loop (two-way).

This is simply false, as I already showed the isotropy of the one-way speed of light is a postulate in special relativity. It is also clear from the Lorentz transform and the Minkowski spacetime formalism. If you cannot even understand this bare minimum level of SR then the remainder of the conversation is pointless.

I encourage you to re-read the second paragraph of Einstein's seminal paper:
http://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf

And Wikipedia's intro to SR:
http://en.wikipedia.org/wiki/Introduction_to_special_relativity

Once you have done so and are clear on what SR states then we can return to the rest. You are free to disagree that the postulates of SR accurately reflect reality, but you are not free to falsely change what the postulates of SR say nor their logical conclusions.

 

[heldervelez]

sensing the Absolute Space ?

Are we sensing the Absolute Space ?
(my bolds)

PROGRESS IN PHYSICS (vol 4 October, 2009)

Is not acceptable ? ( I searched now and seems not clearly peer-reviewed)
I will unpost that part
I'm sure I will have to study the document first.

-------------
-------------
about Mr. Al68 comment "Are you under the impression that the word "inertial" means lack of motion?"
Inertial is a property of space and not of 'mass':
the way space allows mass to move
the way space allows light to move.

(Obs: light has not a ballistic motion because its speed is independent of the motion of the source so light speed must be dependent on the field/vacuum/aether/physical space )
----------------------

 

[Mentz114]

Heldervelez:

This is a quote from Gjurchinovski -

Consequently, it emphasizes the fact that the length of a uniformly moving object will be physically contracted along its velocity vector by the usual Lorentz factor.

The Lorentz factor applies between any two inertial frames. This statement says that a rod has a physical length corresponding to every possible inertial observer !

This is such an obvious contradiction/paradox that I cannot see how anyone can think for a moment it can be true.

The author seems to be under the impression that there is only one factor that can be applied, which must be assuming an absolute frame in which velocity is measurable.

Even if this were the case the Lorentz factor applies between two frames and is based on their relative velocity.

Get a grip, man !

 

[GRDixon]

If we must consider the real length contraction then we must also be prepared to consider a change in the geometrical atomic shape. Idem to a real change of time unit.

---------

I really think you'll enjoy the link in #27 (or at least find it thought provoking).

 

[heldervelez]

Heldervelez:

This is a quote from Gjurchinovski -

"Consequently, it emphasizes the fact that the length of a uniformly moving object will be physically contracted along its velocity vector by the usual Lorentz factor."

The Lorentz factor applies between any two inertial frames. This statement says that a rod has a physical length corresponding to every possible inertial observer !

That sentence is the the last one there. It is Gjurchinovski conclusion, with an conceptual experiment that is not observer dependent. He concluded a reallity of contraction on the 'object', not observer/light dependent.

Before disagreeing with the conclusion one's must point a faulty step along the derivation of the conclusion.

What he said is along with the references cited in the paper. The author merit becames clear after he imagined an experiment that is observer independent, and cristal clear.

This is such an obvious contradiction/paradox that I cannot see how anyone can think for a moment it can be true.

I see no paradox, nor contradiction, not clashing with SR.
Einstein paper does not rule out 'absolute space', it just do not need it.

The author seems to be under the impression that there is only one factor that can be applied, which must be assuming an absolute frame in which velocity is measurable.

Yes, it cames with the conclusion. The Einstein SR is observer/light dependent.
Things change when we remove the constraint imposed by light travel time/observer.

Even if this were the case the Lorentz factor applies between two frames and is based on their relative velocity.

observer dependent applies to SR not to this perspective.

Get a grip, man !

At last I agree with you .

If it exists a 'really' an object contration, as it seems, and a cumulative observer dependent contraction, as it seems,
then the observed contraction would be lambda^2.
Am I wrong?

 

[Mentz114]

Heldervelez,
The problem with Gjurchinovski's paper is this

Obviously, simultaneity of the events A′ and B′ becomes irrelevant because the rod is stationary.

which is not true. In the frame of the ground, where the scorch marks are, the rod is not stationary. When the marks are measured, we are in the ground frame, not the moving rod frame. If we had fired the crackers without moving the rod, the distance between the marks would be the 'natural' length of the rod ( ie measured in its own frame). Because the rod was moving when the crackers were fired the distance between the marks is foreshortened. It is an observer dependent effect ! It depends on the relative velocity when the crackers were fired.
( remember, in the ground frame the crackers did not go off simultaneously, which accounts for the foreshortening ).

You are entitled to hold any view you like, and I respect your freedom to do so, but you are being mislead if you believe Gjurchinovski's nonsense.

Some of your remarks lead me to believe that you may be talking about something other than Lorentz contraction ( or doing a quick sidestep ). If this effect depends on lambda ( cosmological constant ) it has nothing to do with SR and Lorentz.

I wish you goodnight.

 

[heldervelez]

I really think you'll enjoy the link in #27 (or at least find it thought provoking).

I have read it (and others pages on your site) and I'm glad that you, independently, derive it simply after established theory. All we know that even with strict SR the shape had to change.
GR is all about rulers/clocks change. They are not invariants.
We can find software in the net with a visual approach (find: relativity software renderer download)

I do not understand so much 'horror' just because things are broader than what we are used to.
Physics is about evolving concepts and Einstein is not the end of story.
The study of relativity under the perspective of an 'instant observer' (not dependent on light to ackowledge events) is welcome, to my enlightment, and to challenge the intelectual criticism of those that do not believe in the 'absolute space'.
I already know that the study is available. It does not destroy the Einstein work, it makes the analise from a different perspective and spread the horizont.

Lorentz work gives us a real length contraction, time dilation, shape modification, based on the properties of electromagnetic field (not observer dependent).
Matter can move and survive (i.e. Maxwell equations are Lorentz invariants).
With a change on the geometrical properties of the atom we can expect, and explore, the consequences. GR is also about changing rods/matter/clocks/time.

 

[heldervelez]

its gamma, not lambda. Sorry. I'm not proficient in English and Greek
I will study the paper next.
Good nigth to you too.

 

[yuiop]

Let us analyse length contraction from the point of view of Lorentz Ether Theory (LET) and see if it gives us any insights. LET is widely accepted as giving the same predictions as classic SR so I think it valid to use LET in some circumstances. Consider 2 rods, A and B that have equal proper length that are moving with respect to each other. For the sake of argument let us assume A is at rest with the ether and B is moving with respect to the ether. In this situation rod B is "really" length contracted because of B's motion relative to the ether. B also experiences "real" time dilation due to motion relative to the ether. The "real" length contraction and time dilation experienced by B (and a difference in simultaneity) causes the illusion that rod A is length contracted from B's point of view. We can now reverse the situation and assume B is at rest with the ether and now it is A that is "really" length contracted. Now it is A that is under the illusion that B is length contracted due to physical changes in the measuring apparatus of A. The end result is that we have no way of determining whether it is rod A or B that is really length contracted and consistent with SR both measure the other be length contracted. All we can say in LET terms (by applying simple logic) is that if A and B have motion relative to each other, then at least one of the rods is really length contracted. What we can NOT say, is that if B is moving relative to A, that B must be "really" length contracted, because it might well be that B is the rod that is "really" stationary in LET terms.

However we can look at length contraction in terms of a rotating ring and this has the benefit that rotation has an absolute nature that is missing when considering purely linear inertial motion in SR. Imagine that we have a hollow tube formed into a ring to create a circular tunnel. This tunnel is non rotating and supported on the outside by rocket thrusters or hydraulic pistons so that its radius does not alter under stress. Inside the tunnel we have a train moving at relativistic speeds relative to the tunnel. The train and its carriages completely occupy the tunnel comfortably without any stresses parallel to its length. Let us say speed of the train is such that the gamma factor of the moving train is 2.0 and we now try to bring the train smoothly to a stop relative to the tunnel. The train would be physically crushed when it stopped because its rest length is now twice the circumference of the non rotating tunnel it was moving inside of and can no longer fit inside the tunnel. Hopefully, this demonstrates the physical nature of length contraction because the physical crushing of the train can not be explained as an illusion brought about by differences in point of view.

Conversely, we could take a stationary train that completely occupies the circular tunnel and is connected all the way around. If we try to smoothly accelerate the train it would be ripped apart by length contraction forces as it tried to contract to a length that is shorter than the non rotating tunnel it occupies. Essentially this is the Ehrenfest paradox, which is only a paradox if you do not consider length contraction to be physically real.

 

[Dale]

Good point kev, even in LET the measured length contraction is frame dependent. There is some "real" length contraction, but it cannot be observed.

In any case, heldervelez, as I have said to you several times before, if you are philosophically comforted by LET then you are free to use it. You are just wasting your time trying to convince others of its superiority over SR since there is no evidence supporting (nor opposing) your preference. It is entirely a matter of taste and not really worth arguing for or against.

 

[Mentz114]

In my opinion, heldervelez and others do not accept the first tenet of relativity - 'one cannot distinguish between rest and a state of uniform motion'. They believe there is absolute motion and can't let go of that idea.

Have we unequivocally ruled out the existence of a "primary" (or "ether" or "dark matter" or ...) frame? In truth we have not, although we must acknowledge the possibility that no experiment can differentiate such a frame from all the other inertial frames. Perhaps, with advances in astronomy, we can attempt to narrow the search and define the "primary" frame to be the frame in which the center of mass of the known universe is at rest. Perhaps. But what will such an exercise gain us?

One thing does seem certain. The length contraction of moving systems appears not to be an illusion, even though K and K’ each measures such effects for systems moving relative to himself. Such effects are real, and are predicted by the remarkable fact that the physics of Newton, Maxwell and Lorentz work equally well in every inertial frame of reference.

This is from http://www.maxwellsociety.net/LovingLorentz.html .These two paragraphs show that GRDixon has not grasped the meaning of motion and rest. "Primary Frame" ? Center of the universe at rest ? Always the insistence on absolutism.

I don't think this thread is about LET vs SR. These guys don't believe relativity.

 

[Dale]

I don't think this thread is about LET vs SR. These guys don't believe relativity.

You are probably right. Heldervelez in particular has repeatedly tried to assert some measurement of absolute speed, which is inconsistent with LET as well as SR.

However, to the extent that he correctly understands and applies LET then I have no problem with his philosophical preference for that over SR. His trying to proselytize it is annoying, but harmless.

 

[heldervelez]

Why should somebody in the Department of Theoretical Physics, University of Lodz, dedicate time and money exploring such an old subject as MMX?

This paper seems interesting:

http://versita.metapress.com/content/9740621616717848/fulltext.pdf"
Bogus law Broda and Marcin Ostrowski
Department of Theoretical Physics, University of Lodz,
published in Concepts of Physics (Lodz University, Poland)

Abstract
The idea of the Michelson–Morley experiment is theoretically
reanalyzed. Elementary arguments are put forward to
precisely derive the most general allowable form of the directional
dependence of the one-way velocity of light.

-------------------------------
I stated here, without any reserves, that the SR is correct. But we can not dismiss other viewpoints. They have been explored (but not completelly) and the subject is not a dead end.
I am not trying to convince anyone of this or that.
We are free to explore, (I think that it is the very essence of this forum) and I follow the rules.
I'm in this forum to explore my limits and I tanks anyone that show me the errors based in reasoning and knowledge. I can learn.
The building of Physics will never be fully writen. IMO it is unfounded the common belief that Teoretical Physics can only progress within the walls of academia.
Mr Dixon contributed with calculations and showed, what is known in SR, that bodies change shape under motion because, for now, only the longitudinal component is affected. The Lorentz paper showed also a transversal effect (later he droped it, I think).

OK, there is no way to distinguish experimentally the existence of an 'absolute referential'.
By the rules of this forum I will not try to show you differently.
But the its existence is a different issue and, in another thread, having the time, I will try to show why I consider it mandatory.

In post #1 I quoted Einstein, Lorentz, and other papers, relative to the subject that do not contradict me.
In post #2 I show that a body under acceleration must shorten physically. I urge anyone to show that the reasoning contains errors.

 

[Dale]

In post #2 I show that a body under acceleration must shorten physically.

Sure, but as I already mentioned several times, that is simply not what Lorentz contraction is.

 

[A.T.]

OK, there is no way to distinguish experimentally the existence of an 'absolute referential'.

Then it is not physics.

But the its existence is a different issue

In physics it is the same.

 

[GRDixon]

a real length contraction must exist.
Then I searched the words of Lorentz, Einstein and also what others are saying.

Good Stuff! Here's more fodder for the realness of length contraction:

"In classical physics it was always assumed that clocks in motion and at rest have the same rhythm, that rods in motion and at rest have the same length. If the velocity of light is the same in all coordinate systems, if the relativity theory is valid, then we must sacrifice this assumption. It is difficult to get rid of deep-rooted prejudices, but there is no other way." A. Einstein and L. Infeld, "The Evolution of Physics" (1938.

 

[Al68]

any[/i] two inertial frames. This statement says that a rod has a physical length corresponding to every possible inertial observer !

This is such an obvious contradiction/paradox that I cannot see how anyone can think for a moment it can be true.

That would depend on how "physical length" is defined. If it's defined as the distance between the coordinate positions of an object's endpoints at a specified time, then the rod would have a different "physical length" in each inertial frame with no contradiction or paradox.

 

[Mentz114]

Good Stuff! Here's more fodder for the realness of length contraction:

"In classical physics it was always assumed that clocks in motion and at rest have the same rhythm, that rods in motion and at rest have the same length. If the velocity of light is the same in all coordinate systems, if the relativity theory is valid, then we must sacrifice this assumption. It is difficult to get rid of deep-rooted prejudices, but there is no other way." A. Einstein and L. Infeld, "The Evolution of Physics" (1938).

I'm glad to see you're quoting the latest works available to defend your absurdist position !

That would depend on how "physical length" is defined. If it's defined as the distance between the coordinate positions of an object's endpoints at a specified time, then the rod would have a different "physical length" in each inertial frame with no contradiction or paradox.

What you have described is just the length of the rod measured from another frame, which is an observer dependent quantity.

 

[Dale]

That would depend on how "physical length" is defined. If it's defined as the distance between the coordinate positions of an object's endpoints at a specified time, then the rod would have a different "physical length" in each inertial frame with no contradiction or paradox.

What you have described is just the length of the rod measured from another frame, which is an observer dependent quantity.

This is exactly my point from https://www.physicsforums.com/showpost.php?p=2494738&postcount=3" in this thread. The reality of length contraction is purely semantic based on the definition of "real" (I have yet to find a definition of "real" that I like).

 

[Hans de Vries]

There is a very convincing argument for physical length contraction:All relativistic wave equations exhibit physical Lorentz contraction. These wave equations can be implemented with ordinary mechanical mass/spring
systems which show physical Lorentz contraction. For example: A mass/spring grid
with a characteristic speed of 1 meter/second shows the same Lorentz contraction
at 0.9 meter/second as matter wave packets show at 0.9c.It is actually very easy to proof. To start with the classical wave equation:

$$\frac{\partial^2 \Phi}{\partial t^2}\ -\ c^2 \frac{\partial^2 \Phi}{\partial x^2}\ -\ c^2 \frac{\partial^2 \Phi}{\partial y^2}\ -\ c^2 \frac{\partial^2 \Phi}{\partial z^2}\ =\ 0$$

This equation governs propagation in all kinds of classical situations as well as the
propagation of the electromagnetic (potential) field. c is the characteristic speed.

Mathematically, any arbitrary function which is stable (doesn't change in time) and
which shifts along with a velocity v obeys mathematical relations like:

$$\frac{\partial \Phi}{\partial t}\ =\ -v \frac{\partial \Phi}{\partial x} \qquad \qquad \frac{\partial^2 \Phi}{\partial t^2}\ =\ v^2 \frac{\partial^2 \Phi}{\partial x^2}$$

These expressions are always valid independent of the shape of the wave function.
We can use the quadratic one to eliminate the dependence on t from the equation:

$$\left(1-\frac{v^2}{c^2}\right) \frac{\partial^2 \Phi}{\partial x^2}\ +\ \frac{\partial^2 \Phi}{\partial y^2}\ +\ \frac{\partial^2 \Phi}{\partial z^2}\ =\ 0$$

This shows that the solutions are Lorentz contracted in the direction of v by a factor
gamma, The first order derivatives are higher by a factor gamma and the second order
ones are higher by a factor gamma^2. It shows that velocities higher as c are impossible.

The proof can't hardly be any simpler.
It is from this chapter of my book: http://physics-quest.org/Book_Chapter_EM_LorentzContr.pdfRegard, Hans

 

[matheinste]

This is exactly my point from https://www.physicsforums.com/showpost.php?p=2494738&postcount=3" in this thread. The reality of length contraction is purely semantic based on the definition of "real" (I have yet to find a definition of "real" that I like).

An interesting quote from an early Rindler book. Special Relativity, Oliver and Boyd Ltd. First published 1960, second edition 1966. Page 26. Unfortunately his use of the word "real" is also open to interpretation.

-----Although relativity offers no detailed explanation in terms of cohesive forces or the like, yet it predicts the contraction phenomenon as inevitable. (This is comparable to some of the predictions based on the energy principle.) It must be stressed that the phenomenon is not to be regarded as illusory, due perhaps to some peculiarity in our methods of measurement: relative to a given frame it is real in every possible sense. But for the practical difficulties involved, the following experiment, for example, could demonstrate the existence of length contraction----

He then goes on to describe a well known demonstation which, as far as I know, has not yet been carried out due to these practical difficulties.

Matheinste.

 

[Mentz114]

Hi Hans,

as far as I can see you have only 'proved' that an observer from a moving frame will see a wave packet contracted. This is not surprising because its momentum observed from the moving frame is different. Lorentz contraction is a function of the relative velocity between the frames and so cannot be real in the sense that in the rest frame of the wave packet something changes.

Suppose I am in my kitchen eating a shami kebab, and being watched by someone from a spaceship at rest wrt to me. They zoom off and reach a high velocity; according to you my kebab shrinks to half its previous length. But what about all the other 'observers' in the universe. Are you saying that my kebab will vary in size according my relative velocity wrt them also ? That's more like a sort of Machian kebab principle than Lorentz contraction.

The only things I can regard as real are those that are agreed by all (IRF) observers. Einstein's principle of covariance explicitly states that anything that can be altered by a change of coordinates ( eg LT) is not a real physical effect !

 

[jtbell]

Suppose I am in my kitchen eating a shami kebab,

This cries out for a relativity limerick that starts with something like "There was a young fellow named Bob".

 

[Mentz114]

There was a young man called Hans
who thought he could tell at a glance
that things on the move
(it is easy to prove)
are somewhat in length a bit sans

Sorry I had to use French.

matheinste,

since Rindler's name is associated with accelerated frames, are you sure that the quote you gave isn't referring to those, rather than IFR's ?