The law of reflection can be found by applying Huygens Method. If the mirror is moving, the incident wavefront reaches the mirror at different times which alters the angle of the wavefront. It remains entirely compatible with SR when the various effects of motion are correctly included.

Whether Einstein stated it, or not, isn't relevant-and, in fact, the statement is wrong, as given. It's the other way around. But that's relevant for the history of physics, not for physics.

Maxwell's equations are invariant under Lorentz transformations, which don't leave Newton's second law of motion invariant; which are invariant under Galilean transformations. Galilean transformations are a limiting case of Lorentz transformations.

The example with reflection is too vague. If one doesn't focus on Lorentz invariant quantities, any comparison is meaningless. But it is known how to apply Lorentz transformations to electric and magnetic fields. The boundary, of course, breaks Lorentz invariance, so doesn't define an inertial frame.

This is another homework problem.

Dear Stam

Thanks for your answer. The statement is in fact from Einstein, the reference is given in the attached article.

A scientific statement is science not history, unless it is proven wrong.

I am not sure why the counter example is vague as a response to Einstein's statement. Please note the same response also applies to light as considered in the article.

Once more: this concerns the history of physics, not physics. It doesn't matter what Einstein, or anybody else said-what matters are impersonal statements-like the invariance of Maxwell's equations under Lorentz transformations, when the electric and magnetic fields transform, also, as do the sources.

In the presence of boundaries Lorentz invariance is explicitly broken, that's why the example discussed isn't relevant.

Dear Stam

I do agree with you that Einstein’s statement written in his famous 1905 paper is not correct. But Einstein introduced special relativity (SR) in the paper which is still considered as physics and definitely it is not personal, unless you also think SR is not anymore physics but history. My reason is that relativistic physics is based on a huge blunder when M&M experiment was analysed. Please see the attached article to the following RG question.

https://www.researchgate.net/post/Does_Michelson_and_Morley_experiment_support_length_contraction

Please clarify what do you mean that the example is not relevant. We know that in a light clock incidence and reflection angles do exist and we cannot overlook their sizes, measured from a different inertial frame. Do you agree that the reflection law does not apply anymore if it is observed by a moving observer?

Dear Ziaedin Shafiei

I find your example very interesting however I'd like to point out the following:

1_ The motion of the ball cannot be compared to the motion of a light ray. The velocity or light has a vary important character that does not have the motion of any material(massive) object, i.e., it is invaritant with respect IRF's

2_ For the case of light if we accept that the refflections laws of optics is a consequence of the fundamental equations of electrodynamics then since in both frames the same equations hold then the "reflections laws" must be the same in both frames.

Furthermore, the simple naive geometrical analysis of the angles does not apply, the moving observer suffers relativistics effects like length contraction for intance.

The law of reflection can be found by applying Huygens Method. If the mirror is moving, the incident wavefront reaches the mirror at different times which alters the angle of the wavefront. It remains entirely compatible with SR when the various effects of motion are correctly included.

Dear Justo

Many thanks for your comments. Here are my answers:

• For the ball case the law does not hold when the ball is observed from a second frame and this example is enough for refutation of Einstein’s statement. That is why I have highlighted this case in the question.
• For light, the issue is more complicated. However, as it is pointed out in the article length contraction and time dilation do not help here. In fact, the angle of incident can increase with length contraction, as well as decrease depending on the direction of v. In the former case diversion from the law is aggravated in comparison to the ball case. I wanted to add this to the article but as length contraction is not scientifically valid and it diverts us from the main point I decided not to include this fact. Maybe I should add it as an appendix.

Dear Ziaedin,

When a ball bounces off a moving surface, its speed changes. That is not the case for light. You cannot use a low-speed ball as an analogy for light, their behaviour is completely different.

Questions like this can only be correctly answered when it is recognized that a physical medium exists for the purposes of transmitting electromagnetic waves and for causing the inertial forces.

Dear George

Of course the mechanism of reflection between the ball and light is completely different but this is not the issue here. The fact is that the light bounces back when it hits a mirror and the angles of incident and reflection are equal, similar to the case of the ball, when it is observed from the same frame.

To visualize this issue, imagine a light clock in your own frame. the beam of light moves vertically up and down between top and bottom mirrors. Now imagine the same clock in a second frame moving at the speed of v related to you. As illustrated in any special relativity textbooks the beam is not anymore vertical. The conclusion is that v causes the angle to change, even for light. The textbooks always use this specific case for time dilation. That is why the issue of this forum does not show up.

GD - " When a ball bounces off a moving surface, its speed changes. That is not the case for light. "

You are right. The angle of incident and reflection, if the speed of light assumed constant, is different from the ball case when both cases are observed from a second frame. This is sufficiently discussed in the article attached to the following RG question.

https://www.researchgate.net/post/Does_Michelson_and_Morley_experiment_support_length_contraction

Dear Ziaedin,

ZS: To visualize this issue, imagine a light clock in your own frame. the beam of light moves vertically up and down between top and bottom mirrors. Now imagine the same clock in a second frame moving at the speed of v related to you. As illustrated in any special relativity textbooks the beam is not anymore vertical.

That is correct, if you consider the structure of the source producing the light, its movement means that the light path has different coordinates in the second frame.

ZS: The conclusion is that v causes the angle to change, even for light.

Obviously. This is also the origin of the effect called "relativistic beaming".

https://en.wikipedia.org/wiki/Relativistic_beaming

Dear George

GD- You cannot use a low-speed ball as an analogy for light, their behaviour is completely different.

I did not argue from analogy. The optical behaviour of light, as you now agree, is already well known. Thus, based on optical law, the counter example is also correct for light. But I need to repeat my main point in response to your comment:

GD- When a ball bounces off a moving surface, its speed changes. That is not the case for light.

The difference has no effect on the reflection law. Still the angles of reflection and incidence are equal if observed in the same frame. It is shown in the article, Michelson and Morley Experiment Does not Validate Length Contraction, that the difference only has an effect on the quantity of angles, when observed from a second frame. Special relativity tried to remove this difference, in the unique textbook example, by introducing length contraction.

Ziaedin Shafiei > Are the laws of electrodynamics and optics valid for all inertial frames of reference?

Yes, when interpreted correctly, to the best of all available experimental evidence (which is quite a lot).

Ziaedin> the equality of the angles of reflection and incidence, say, when an ideal-elastic ball is thrown with a specific angle at a flat wall.

That is not a law of electrodynamics or mechanics! You have just flunked both topics in an embarrassing way :-).

at a flat wall. -> at a flat wall at rest in the inertial frame of reference.

For earthly walls, that law is equally valid on March 15 as September 15 (throughout the days, everywhere on earth), although the (approximate) inertial frame of the earth changes by a relative speed of about 60 km/s between these dates. The reflection laws for walls in motion relative to the inertial frame of reference look different, but (to the best of our knowledge) they also remain equally valid throughout the day (as the earth rotates around its own axis), year (as it orbits the Sun), and (we expect) even as the Sun rotates around the galaxy centre.

Can you imagine the nightmare if the laws of physics did not admit the relativity principle, but changed from hour to hour and day to day???

As for the calculation of described/observed angles, when the wall is in relative motion, this is a simple exercise which even my neighbours cat can carry out, starting from the conservation laws of energy and momentum. I once gave it as a homework problem to him, for a finite mass wall/mirror (to make it sufficiently difficult), and refusing him to make the problem trivial by employing Lorentz transformations (to maintain it sufficiently difficult). He, of course, managed magnificently. But, as a clever cat, he sneakingly circumvented my restriction by algebraically introducing variables which were Lorentz invariant, or behaves in a very simple way under Lorentz transformations.

You can find a report of his calculation here:

Working Paper Reflections on Relativistic Moving Mirrors

Ziaedin Shafiei >

"It is claimed that MRI exists because of special relativity. In general, the claim applies to any equipment which uses electromagnetism. But the claim is only based on explanations. One explanation is as follows;

“Electromagnets work via relativity. When DC current flows through a single wire the conducting material is electrically neutral with no net positive or negative charge. Now lets put another identical wire next to the first.Assuming the currents are moving and same strength, in the same direction, the electrons in the first wire "see" the electrons in the second wire as motionless. From the electrons' perspective, the protons in both wires appear to be moving. Due to relativistic length contraction, they appear to be more closely spaced, so there's more positive charge per length of wire than negative charge. Since like charges repel, the two wires also repel. Reverse one of the currents in one of wires and you'll get the opposite effect and they will attract creating you electromagnet”

There are a few issues with this explanation..."

I have lifted this question of yours from another blog, where it is https://en.oxforddictionaries.com/definition/off-topic.

A theory is not refuted by misunderstood, badly explained, or perhaps plain wrong attempts of explanation (however enthusiastic). The above quoted description in bold is taken from https://interestingengineering.com/10-ways-can-see-einsteins-theory-relativity-real-life-keyword-theory-relativity, which appear to be a webpage maintained by a (somewhat enthusiastic, but perhaps too hurried) Master in Geology. It is hardly authoritative, and a bad starting point for any discussion.

Some comments can nevertheless be made:

If we, in one frame of reference, have an electrically neutral (ρ=0) wire carrying a non-zero net current j≠0, there will be a magnetic field B around that wire, leading to magnetic forces on other current carrying objects in the vicinity. Then, in another frame moving parallel to the wire, there will appear to be a net charge ρ'≠0 on the wire, together with a different net current j'≠0. By Lorentz invariance we will have^* that j'2 - ρ'2 = j2. Hence, in the new frame the net current must appear to be larger, together with the magnetic forces it causes. This is compensated by the presence of an electric field E' caused by the charge density ρ'. Note that this charge density, proportional to the relative velocity v of the two frames, does not have any immediate explanation in terms of length contraction, which to lowest order depends on v2.

As for the electromagnetic fields, they are Lorentz transforming quantities, but restricted by the two relativistic invariants E2 - B2 = E'2 - B'2 and E · B = E' · B'. This implies that it is impossible to explain pure magnetic forces in one frame as pure electric forces in another frame, or vice versa. No matter the amount of enthusiasm exerted.

A quantitative analysis of this problem may be an interesting problem in introductory relativity. But any attempts of qualitative interpretations should be postponed until such analysis is digested, to assure proper agreement with reality.

^*) All formulas in units where c=1.

Added note to my previous post:

The interestingengineering.com webpage mentioned in my previous post refers to another site, https://www.livescience.com/58245-theory-of-relativity-in-real-life.html, presenting the following "information":

"Assuming the currents are moving in the same direction, the electrons in the first wire see the electrons in the second wire as motionless. (This assumes the currents are about the same strength). Meanwhile, from the electrons' perspective, the protons in both wires look like they are moving. Because of the relativistic length contraction, they appear to be more closely spaced, so there's more positive charge per length of wire than negative charge. Since like charges repel, the two wires also repel."

Do I need to remind you that in electrodynamics two parallel wires with currents in the same direction attract each other? In "real life" the apparent charge densities "seen" on the wires from the moving frame is unobservable (I think of relative importance 10-20 in the rest frame of the current carrying electrons, hence utterly irrelevant); it also leads to a wrong-sign (repulsive) force, contrary to the correct searched-for explanation.

There is a lot a balderdash on the web. Belief in relativity theory does not automatically assure proper understanding of it.

Another addition:

These kind of explanations appears to emerge from an approach introduced in a textbook by Purcell in the 1960's (Electricity and Magnetism). Serious quantitative discussions of this approach can be found here:

http://physics.weber.edu/schroeder/mrr/mrrtalk.html

http://physics.weber.edu/schroeder/mrr/MRRnotes.pdf

The main points are

i) to explain the Lorentz force on a single charged particle moving parallel to a current carrying wire, which appears to be neutral in the laboratory frame. In this frame the force has a purely magnetic (v × B) origin. How can this force be explained in the inertial frame of the particle, where the particle is at rest? The answer, by a Lorentz transformation, is that the wire appears to have a non-zero charge density in this frame, leading to an electric force (of the correct direction and magnitude) on the particle. A magnetic field is still present, but this does not contribute any force on a particle at rest.

ii) to explain the origin of the apparent non-zero charge density. This can indeed by explained as a difference of length contraction effects; they are different because the positive and negative charges are in relative motion. (I didn't find that part to be explained very clearly by Schroeder, at least not on a first reading.)

Problems arise when one try to apply this kind of explanation directly to a configuration of many particles with different motion, as in a second current carrying wire. There are also some interesting dynamical aspects of the problem.

It's amazing how many answers to the question haven't mentioned that the answer is Yes, since ``all'' inertial frames of reference are equivalent. And the reason they are is that Maxwell's equations-that describe electrodynamics and optics-take the same form in all inertial frames. So there's simply no way to say ``which'' inertial frame is used, when solving Maxwell's equations: they're the same equations!

It all depends on your understanding of an inertial frame of reference. This article here takes a closer look at the physical origins of the inertial forces,

Article The Double Helix and the Electron-Positron Aether

The Double Helix ..., page 1> Special relativity is however notorious for its internal contradictions, ...

Oh dear, oh dear...☂✋

Inertial force = oxymoron. An inertial frame is something else, entirely, of course. For electrodynamics and optics it's defined by the Minkowski metric.

Stam, An inertial force is not an oxymoron. They appear in inertial frames of reference with respect to a polar origin in conjunction with Newton's Laws. It's the Minkowski metric which is the problem. Read here,

Article Pythagoras's Theorem and Special Relativity

There's no problem with Pythagoras' theorem-there exist other metrics, beyond the Euclidian metric, that's all-and not all are Riemannian, either. No problem.

Stam, I didn't say there was a problem with Pythagoras's Theorem. The article simply claims that it can only operate in 3D space. The 7D example is worked through as an illustration.

It's the cross product that illustrates that Pythagoras's theorem only works in three dimensions.

"Pythagoras's theorem only works in three dimensions."

The Pythagoras theorem works in all Euclidean spaces of dimension D>=2. It can even be been extended to infinite dimensional Hilbert spaces. The notion of cross product can be generalised to every finite-dimensional (D>=2) space, as the wedge operator ^ of Grassmann (exterior) algebra. It can be defined on spaces where no metric is defined, i.e. where the Pythagoras does not make sense. But additional properties, like the * operator, can be defined for metric spaces.

https://en.wikipedia.org/wiki/Exterior_algebra

The only other case that might have been considered is 7D. No matter how hard you try, you won't be able to fit the Pythagorean trigonometric identity into 5D. And not to any even numbered case. Read this article carefully. It works through the 7D case.Article Pythagoras's Theorem and Special Relativity

I think Frederick's article "Pythagoras's Theorem and Special Relativity" is intresting in the sense that it show a definiton of "cross product".

The problem is with the definition he uses and its relation to Pythagoras' Theorem so all boils down to a problems of semantics and defintions.

All this is irrelevant with respect to its consequences for the theory of relativiy.

Justo, That depends upon to what extent Einstein's relativity hinges on the requirement that Pythagoras's theorem can apply in 4D. The Pythagorean trigonometric identity yields a 3D vector cross product, and only a 3D one. The 7D case was the only other contender. So how do you justify the extension of it to 4D?

In the derivation of the time dilation formula in special relativity, what appears to be a 4D application of Pythagoras's theorem is in fact just a double application of the 3D Pythagoras's theorem. If this fact is accepted, then it's not so much relativity itself that is the issue here as it's the notion that it operates in a 4D space-time continuum.

Dear Frederick

In relativity theory, you only need to use a Riemannian metric. There is no logical relation to the definition of cross product you use.

You can use Phythagoras' formula independantly of the cross product you chose to use.

Justo, This is not so much about relativity itself as its about the commonly held belief that relativity operates in a 4D space-time where Pythagoras's theorem operates as normal. I pointed out that when deriving the STR time dilation equation, we use two successive applications of the 3D Pythagoras's theorem. One for the triangle involving ct and ct0 and another to split length into the three Cartesian components. This does not mean that we are operating in a 4D space. The Pythagorean Trigonometric Identity is clearly linked to the 3D vector cross product and so it only exists in 3D space. The article examined 7D as a possibility because you can't have a cross product in any other dimensions than 3 or 7.

Christian,

That's right as you said in this context "..cross product is neither required nor included". However, there exists a definition of cross product that apparently only works in three and seven dimensions, of course all this is irrelevant with respect to its consequences for the theory of relativity.

The cross product may not have been known to Pythagoras himself, but the Pythagorean Trigonometric Identity incorporates both the scalar dot product and the vector cross product. So how could you apply the Pythagorean Trigonometric Identity to 4D? The conclusion is that when Pythagoras's Theorem is being used in relativity, it is just successive applications of the 3D Pythagoras's Theorem, and so we cannot deduce the existence of 4D space-time as a reality in its own right where Pythagoras's Theorem continues to hold.

Christian,

The real problem with Frederick's views is of logical nature rather than philosophical.

Aparently he claims that whenever one uses a sum of squares, this expression is logically bound to a certain definition of cross product.

Justo,

Yes. If it is to have any geometrical significance.

The result of the cross product of two vectors is a vector, in Pythagoras, the sum is the squares of scalars and the result is a scalar.

George, We were looking at the Pythagorean Trigonometric Identity and how it involves the 3D vector cross product. It's hardly going to do that if it can hold in 4D. See section IV here Article Pythagoras's Theorem and Special Relativity

Christian, You are correct to not be sure. Only 3D space has any physical reality.

Frederick David Tombe

In your preprint (linked to above), the rules for your "cross product" is unclear. One understands that it should be antisymmetric, but what are the underlying geometric motivations? Is it associative? How should the entries in table 1 be understood? F.i., what is the meaning of the line

i = j × k, m × n, k × o

If it is meant to be understood as

i = j × k = m × n = k × o,

why is that not written out explicitly?

Kåre,

It's because the emphasis was on the fact that there are three possible cross products for every unit vector, rather than that these three cross products are all equal to each other, which ought to be quite obvious. I didn't want to make an equation out of each line. I was constructing a table.

Cross products are not associative.

As for the geometrical motivations, in the 3D case, it can be shown to be tied up with the area of a parallelogram enclosed by the two vectors, but I've never considered that to be of any importance. For me, the most important aspect of the cross product is how useful it is, especially when used in conjunction with the curl operator, in formulating the laws of electromagnetism.

Kåre, You made me look up my original notes from 1993. See the attached pdf file. I see that I used the "equal to" signs in the table on the second page, down at the bottom. So thanks for bringing this to my attention. I might amend the publication accordingly for clarity.

Ziaedin Shafiei ~

The angle of incidence and angle of reflection (for light bouncing off a mirror or a ball bouncing off a wall) are equal when measured by an observer for whom the surface is at rest. If the surface is moving, the two angles are not the same − as you yourself have pointed out. This conclusion doesn't invalidate Relativity. Indeed, calculation of the angles in a given situation is an exercise in the application of the relativity principle.

Dear Ziaedin Shafiei ,

"the laws of nature are the same for all inertial reference frames"

unfortunately, as already mentioned, your mechanical example does not provide a falsification of Special relativity since it would provide a falsification of the Galilean one first which is not the case...

The postulates of SR are quite straightforward hence SR is virtually unassailable:

this is the reason why the SR had such level of success, very few assumptions, inevitable logical conclusions and experimental evidences...

IRF are all the same and the speed of light is constant as c in every IRF. It seems that there is no way out!!!

Let's have a look at how difficult it is to break it down:

On one hand it is quite out of mind to argue, having defined the IRF, as entities with cartesian axes going at constant speed, that you can find any difference from one to the other. On the other hand for the same reason, having measured the speed of light in a two-ways experiment as 2c, I cannot see something which can make a difference between one IRF to another in the measurement of c, hence c has to be the same.

The Lorentz Invariance is the necessary consequence of the two assumptions, and the group of transformations came out thanks to Poincare', extending the Galilean Transformations which also form a group.

But there is a "but" in every construction built on axioms since we are not talking about math but Physics, and reality "is" , whatever formalism you use to describe it, well beyond the limitations of our definitions...

What is a Inertial reference frame in the real world? The IRF is an abstraction, comfortable to us to make things more understandable.

We can imagine to attach our physical stuff to entities going at constant speed. Unfortunately though it can be done

a) under a certain level of accuracy

b) only for a very limited amount of time

both statements have an importance in our choices, since eventually we have to perform experiments to test formulas behind theories and conjectures...

TO BE CONTINUED..

Dear Eric

Many thanks for your response. You are right for saying “The angle of incidence and angle of reflection … are equal when measured by an observer for whom the surface is at rest.” However, this has been my point too. That is why the same article criticizes the idea of including the movement of inertial reference frames (IRF) as a setting for investigating the law of the nature, resulting in ideas such as “time slows down or objects shrink”. The title of the section in the article is “Adding Speed of Objects to Scientific setting?”. Please note ”?” at the end.

There is no "if" and "but" in the two principles of special relativity, knowing that we are passing judgement on physical laws in IRFs moving related to each other. Consequently, like various paradoxes created by relativistic physics there are also exceptions which needs to be explained away. But, law with exception is not law anymore.

Preprint Special Relativity: The Revival of Metaphysics

Dear Stefano

“The postulates of SR are quite straightforward hence SR is virtually unassailable:”

My answer is the same as before which yet to be refuted. If one accepts that an analytical mistake to be the foundation of science then let it be. If one does not, then one should prove that length contraction is, in fact, based on correct scientific principle.

I repeat: the idea of length contraction and then Lorentz transformation equations (LTE) are based on a false analysis of M&M experiment. The claim is simply illustrated in Figures 12 and 13 of the attached article.

Preprint Michelson and Morley Experiment Does not Validate Length Con...

Thanks Christian

A quote from the same wiki page

" In 1892, with the attempt to explain the Michelson-Morley experiment, Lorentz also proposed that moving bodies contract in the direction of motion (see length contraction; George FitzGerald had already arrived at this conclusion in 1889).[10]"

This question cannot be answered in the absence of a definition for "inertial frame of reference" that takes into account its physical structure. This is tackled here in sections I, VII, and VIII.

Article The Double Helix and the Electron-Positron Aether

And most of the problems in modern physics will end when people stop trying to fit a 3D cylindrical symmetry into a 4D spherical symmetry. It doesn't fit. See here,

Article Pythagoras's Theorem and Special Relativity

Dear Frederick David Tombe ,

that is exactly what I began to explain to Ziedin...

But there is a "but" in every construction built on axioms since we are not talking about math but Physics, and reality "is" , whatever formalism you use to describe it, well beyond the limitations of our definitions...

What is a Inertial reference frame in the real world? The IRF is an abstraction, comfortable to us to make things more understandable.

We can imagine to attach our physical stuff to entities going at constant speed. Unfortunately though it can be done

a) under a certain level of accuracy

b) only for a very limited amount of time

both statements have an importance in our choices, since eventually we have to perform experiments to test formulas behind theories and conjectures...

Dear Stefano and Frederick

IRF is well defined in relativity. But the mistakes I am talking about is nothing to do with IRF. It is a clear analytical mistake. I should also add that relativity also rely on a thought instrument for time measurement which shift the subject right to the heart of metaphysics. But for the time being I only concern about this fact, why scientists find it hard to abandon a theory which is founded on a mistake?

It is not a matter of define it clearly or not!! it is a matter of applying it correctly or not!!

Dear Eric

After reading my own article and refreshing my memory, I should say that your answer is completely wrong. Here is a clear example why:

Bob and Alice travel in two parallel spaceships moving at a constant speed relative to each other. Bob throws a ball vertically up at constant speed which hits the ceiling and comes back vertically to him. Alice sees the ball travels at certain angle and comes back at exactly equal angle so that it reaches Bob who have also moved to a new position. Now, according to Alice the ceiling of the first ship is moving but the angle of reflection is the same as the angle of incidence, contrary to your statement.

The last paragraph of the section of the article is quoted below:

“This experiment is shown in SR sources only when the flat surface is parallel to the relative speed. In this case the angle of reflection is the same as the angle of incidence. This is not the first time that SR is demonstrated to be true only in very limited cases. The author has already shown[13] that the light clock is also positioned only perpendicular to the relative speed between two IRFs to function as it is desired by SR. Any deviation from perpendicular position is not even imagined.”

Preprint Special Relativity: The Revival of Metaphysics

Dr. Shafiei, Unless you define the inertial frame of reference in terms of a physically real medium you will find yourself arguing in a hall of mirrors, not knowing what relates to what.

Dear Frederick and Stefano

As an example of correct interpretation/definition of inertial frame of reference, can you please show the correct analysis of M&M experiment?

Dr. Shafiei, It's my opinion that the 1887 Michelson-Morley result follows from the fact that the luminiferous medium in the vicinity of the Earth is entrained within the Earth's gravitational field as the Earth orbits the Sun.

Hello, Frederick. I am just curious, according to your last comment you accept the 19th-century interpretation of M&M and defend the existence of an "ether wind". Do you also accept the existence of a Newtonian absolute time?

Dear Ziaedin,

the two postulates of SR bring naturally to Lorentz Invariance.

Constancy of the speed of light in every IRF is the key.

What is compliant with the Lorentz Invariance and singles actually out the Aether is the longitudinal Doppler effect.

In other words it is not possible for two bodies going at constant speed along the same direction of motion in deep space to say who moves more or less within a "medium" by exchanging EM waves. In material media (acoustics), where there is a moving source and moving detector version which are quantitatively different, the distinction can be made. In such case the speed within the medium can be determined.

The gamma factor makes the two formulas of the Doppler the same, in the one dimensional case, it is possible only to state that two bodies approach or depart from each-other, nothing else...the motion gets totally relative if analysed in one dimension. The Doppler and the RADAR Doppler work beautifully. No material medium like a luminiferous Aether can be adimitted...this is basically the counterexample against the presence of an Aether.

The gamma factor in the one dimensional Doppler formula is gist of the symmetry or the Lorentz Invariance which singles out the existance of "material" media to drive light in vacuum.

What instead is not in compliance with the Lorentz Invariance, hence singles out also the ill-posed concept of the space-time, is the pure Transverse Doppler...which is bi-dimensional.

Here we see that the concept of IRF cannot be fully applied....the Transverse Doppler needs more degrees of freedom to work properly, Lorentz transformations are not able to determine the values of frequency shifts other than the redshift between bodies going at constant speed and with transverse radiation.

It is easy to show that while the Lorentz transformations predict a non vanishing red-shift for moving bodies, in the same symmetrical configuration, the transverse frequency shift between moving bodies has to be identically null.

Dr. Lambare, Yes I accept the existence of Newtonian absolute time. If the Earth orbits the Sun once, relative to the background stars, then one year will have passed for everybody in the universe, no matter what speeds relative to what that they have been moving at over the course of that year.

Dear Frederick

From a logical standpoint Newtonian mechanics is sound and so is SR and according to modern scientific standards, physicists prefer SR because experimental evidence favors SR and not Newtonian mechanics. The phenomenon of time contraction/delation has very sound experimental support.

Dear Justo

One important point is that the relativistic physics is based on an original error. Please have a look at the attached article to see the analytical mistake made by Lorentz. Simply, Lorentz did not look at the movement of the half-silvered-mirror in M&M experiment to realize that his length contraction ides does not apply to the mirror in the experiment. I have simplified the case in figures 12 and 13. Your negative feedback is welcomed.

Preprint Michelson and Morley Experiment Does not Validate Length Con...

JPL “according to modern scientific standards, physicists prefer SR because experimental evidence favors SR”

If you check these experiments you will find out that these experiments consider length contraction as a proved theory and then try to prove time dilation. You need to read my article fully to appreciate my criticism and then have a look at the Introduction of the following article.

Preprint Special Relativity: The Revival of Metaphysics

Dr. Lambare, The illustration that I gave you regarding the Earth's solar orbit marking out a year for everybody in the universe clearly indicates that all is certainly not correct with SR.