A Disproof of the Principle and Theory of Relativity

[swansont]

1 minute ago, Halc said:

Alternate theories that posit absolute velocity and time and non-isotropy of light speed (such as LET) still do not predict any empirical differences.

We are dealing with a specific idea with its own predictions. Other theories are irrelevant to to conversation.

 

1 minute ago, Halc said:

 

  Yes, the clock rates on Earth would change over the course of the day and year, but none of those effects would 'show' (my bold). If it were, we'd have a method to empirically determine the preferred frame and one of SR or LET would be falsified.

I did not posit clock rate changes. I am focusing on the transit time that is predicted by this idea. The time-of-flight would deviate from D/c in a predictable way.

1 minute ago, Halc said:

So asking for 'evidence of this' is unreasonable.  Lidal is claiming the possibility of 'evidence of this' by incorrectly calculating that the signals would reach the detector at different times in the moving lab frame.  It is his calculations that are necessarily wrong, and not his assertion of absolutism, which is merely 'probably wrong' and not necessarily wrong.

Their predictions are based on there being an absolute frame. I am endeavoring to show that the calculations do not match observation, and was asking for observations that match prediction, which is a requirement, and not at all unreasonable.

[lidal]

Just now, studiot said:

Since you propose measuring a time difference of the order of 10-11 seconds, please explain the electronics of your 'start pulse', which must be several orders of magnitude smaller.

Please also evaluate the accuracy to which the synchronisation must be achieved.

Yes, you are right. The pulse widths of the synch pulse and the pulses sent from the sources to the detector need to be around 1 pico second or less ? , for the time difference of 11 picoseconds, which I think is not feasible.

Perhaps if distance D is 100km, the time difference will also increase by the same factor, 1100 picoseconds= 1.1 nanosecond. The synch pulse width will be about 0.1 nano second (if we take it to be ten percent of the time difference). But then I am not sure if it is possible to transmit such a small pulse width successfully over a distance of 100km because it may not have sufficient energy to detect.

But I need to study all this this in detail. Overall, I think it is a very challenging experiment, if feasible at all.

May be some one with better experience can help.

 

 

[lidal]

Just now, swansont said:

But what if D were ~35,000 km? You send a signal to a geostationary satellite and back to the source. The error is now almost a microsecond. When the satellite is in the opposite direction, it’s that much, but in the opposite direction.

Wouldn’t we notice this happening? The source clock, good to much better than a nanosecond, being almost a microsecond off by more or less than expected?

 

Yes, by assuming a maximum absolute velocity of 390 km/s I also obtained about 0.4 micro seconds discrepancy.

                                              -----> v = 390 km/s

           ∆                                    D= 35000km                               ∆         Earth clock                                                              GPS clock

 

( the diagram may not be correct. Please note that the clock on the left is the Earth clock and the clock on the right side is the GPS clock)

Let the Earth clock transmit the synch pulse at t = 0 . The GPS clock  actually receives the synch signal at t = D/(c-v), that is when the time of the Earth clock is t=D/(c-v). However, due to the assumption of isotropy of light speed, the GPS clock is set to t =D/c. Therefore, the GPS clock will be actually behind the Earth clock by an amount:

             δ =  [   D/(c-v) ] -  D/c

The  c - v  is because the GPS clock is moving away from the synch signal as shown.

Now, let the GPS transmit the time signal to Earth later at some time t=t₀ .

At this instant the clock on Earth will be ahead of the GPS clock by an amount δ. That is, the time of the Earth clock when the GPS transmits the signal will be:

         t₀ +  δ

Therefore, the GPS signal arrives on Earth when the time of the Earth clock is:

        (t₀ + δ ) + [ D/(c+v) ] = t₀ +   [   D/(c-v) ] -  D/c  + [ D/(c+v) ]

The  c + v is because the Earth clock is moving towards the GPS signal.

However, due to the assumption of isotropy of light speed, the GPS receiver calculates the 'correct' time to be:

                   t₀ + D/c

Therefore, the difference between the actual time of the Earth clock and the calculated time (using GPS signal) will be: 

          t₀ +   [   D/(c-v) ] -  D/c  + [ D/(c+v) ]    -   (  t₀ + D/c ) =

[ D/(c-v) ] +  [ D/(c+v) ]  -  2D/c

Substituting D = 35000 km, v = 390 km/s  we get about 0.4 micro seconds.

To estimate the order of magnitude of error in distance/position we multiply this by the speed of light : 118 meters.

 

 

 

 

 

 

 

Edited November 4, 2023 by lidal
Diagram to be corrected.

[swansont]

GPS is at a lower orbit, but the same principle applies. 

GPS satellites at different positions in the sky would give errors in positioning owing to this discrepancy, depending on the time of day they were synchronized with the ground station. Tens of meters is a big error. Has anyone noticed?

[lidal]

On 11/3/2023 at 11:31 PM, joigus said:

 It really, really lets you see behind corners that otherwise stay in the dark. So yes.

A theory gives you a 'big picture' perspective. It affords you a tool to predict new range of phenomena. So @Bufofrog was spot on, I think, when saying you don't really have a theory.

 

I think you are saying I don't have a theory because it doesn't give a big picture. My view is to let the big picture emerge from the facts  because I can't impose a big picture on the universe.

[joigus]

45 minutes ago, lidal said:

My view is to let the big picture emerge from the facts

Then I suggest you stop ignoring the facts. The facts say special relativity is correct.

[lidal]

Just now, joigus said:

Then I suggest you stop ignoring the facts. The facts say special relativity is correct.

We can agree to disagree.

8 hours ago, swansont said:

GPS is at a lower orbit, but the same principle applies. 

GPS satellites at different positions in the sky would give errors in positioning owing to this discrepancy, depending on the time of day they were synchronized with the ground station. Tens of meters is a big error. Has anyone noticed?

Sorry, I mistook it for GPS satellites.

Thank you for bringing up the idea of sending time signals between an Earth clock and satellite clock. Unlike sending signals between two clocks on Earth,  the big distance is a great advantage. 

I propose the same experiment I analyzed above. The experiment consists of two clocks, one on Earth and one on a satellite. The experiment is carried out when the Earth clock, the satellite and Leo are aligned. But full alignmeent may not be possible, neither is it necessary. A closest satellite off the line can be used, and a component of the velocity can be calculated and used.

However, for this the distance of the satellite from the Earth clock should be precisely determined. This must be done by reflecting radar pulses off the satellite ( not by interrogation!). Also the radial velocity of the satellite relative to the Earth clock must be near zero (Brian G Wallace effect). Under these conditions, the satellite distance D can be determined from the round trip time (T) of the radar signal, from: T = 2D/c .

The Earth clock sends time signal to the satellite clock, which sets its time using the standard procedure (assuming isotropy). The satellite clock after some delay sends time signal to the Earth clock. The actual time of the Earth clock and the calculated time (assuming isotropy) can then be compared.

[joigus]

57 minutes ago, lidal said:

We can agree to disagree.

No. You want to make it look like we've reached some kind of a stalemate, "we agree to disagree",

when the truth is that you've been awash in facts, valid criticism and analysis, and your arguments don't stand any ground.

You have no theory. You have no valid criticism. You have nothing and you must go back, either to the drawing board or, rather, to the books on basic physics and learn it all. Learn why we believe SR is right to zeroth, first, second, and third order --in a manner of speaking-- and, if proven wrong one day, it will be in a much more subtle way than what you're suggesting here. Along with the explanation of why it looks so damn right.

As I said, the whole thing is ludicrous.

[lidal]

How does the GPS Sagnac correction support my argument that the pulses from S1 and S2 will not arrive simultaneously at the detector ?

Consider both the proposed thought experiment and the GPS in the ECI frame. In both cases, the source and the observer are moving in the ECI frame. In both cases the clocks are synchronized by assuming light speed isotropy. In the GPS , the point of signal emission is fixed in the ECI frame and the motion of the observer in the ECI frame is considered. ( so called GPS Sagnac correction). Therefore, in the thought experiment also the point of signal emission is fixed in the ECI frame and the motion of the observer needs to be considered, and therefore we conclude that the pulses will not arrive simultaneously at the detector.
 

Edited November 5, 2023 by lidal

[swansont]

3 hours ago, lidal said:

We can agree to disagree.

Well, no. Unless you can show where SR disagrees with experiment, under a situation where it applies, there is no basis to claim that it’s incorrect.

3 hours ago, lidal said:

Sorry, I mistook it for GPS satellites.

Thank you for bringing up the idea of sending time signals between an Earth clock and satellite clock. Unlike sending signals between two clocks on Earth,  the big distance is a great advantage. 

I propose the same experiment I analyzed above. The experiment consists of two clocks, one on Earth and one on a satellite. The experiment is carried out when the Earth clock, the satellite and Leo are aligned. But full alignmeent may not be possible, neither is it necessary. A closest satellite off the line can be used, and a component of the velocity can be calculated and used.

However, for this the distance of the satellite from the Earth clock should be precisely determined. This must be done by reflecting radar pulses off the satellite ( not by interrogation!). Also the radial velocity of the satellite relative to the Earth clock must be near zero (Brian G Wallace effect). Under these conditions, the satellite distance D can be determined from the round trip time (T) of the radar signal, from: T = 2D/c .

The Earth clock sends time signal to the satellite clock, which sets its time using the standard procedure (assuming isotropy). The satellite clock after some delay sends time signal to the Earth clock. The actual time of the Earth clock and the calculated time (assuming isotropy) can then be compared.

Why bother, when current time transfer experiments show your idea to be wrong? People do “common view” observations of GPS satellites to tell what time it is. If the satellites had errors between zero and a few hundred nanoseconds, depending on the location when they were calibrated using D/c for the time delay, this would not be possible. The GPS clocks would not be synchronized if relativity was wrong.

[lidal]

Just now, lidal said:

How does the GPS Sagnac correction support my argument that the pulses from S1 and S2 will not arrive simultaneously at the detector ?

Consider both the proposed thought experiment and the GPS in the ECI frame. In both cases, the source and the observer are moving in the ECI frame. In both cases the clocks are synchronized by assuming light speed isotropy. In the GPS , the point of signal emission is fixed in the ECI frame and the motion of the observer in the ECI frame is considered. ( so called GPS Sagnac correction). Therefore, in the thought experiment also the point of signal emission is fixed in the ECI frame and the motion of the observer needs to be considered, and therefore we conclude that the pulses will not arrive simultaneously at the detector.
 

At this point one might accuse me of mixing the classical and the relativistic, assuming constancy of light speed but not relativity of simultaneity, etc. as someone already did.

We know that the special relativity theory is based on the two postulates:

1. The principle of relativity 

2. The constancy of the speed of light. ( Actually the independence of the speed of light from the velocity of the source)

Everything else in SRT is a consequence of these two postulates: Lorentz transformations, relativity of simultaneity, length contraction, time dilation,  etc.

Therefore, these two postulates need to be tested and established experimentally before accepting their consequences, such as relativity of simultaneity, as facts.

If one or both of the two postulates is shown to be wrong, then we can conclude that the consequences (relativity of simultaneity, etc.) are not correct. If somehow it can be  shown experimentally that the speed of light is not constant, one cannot bring relativity of simultaneity, for example, into the argument because the latter is a consequence of the former, and not the other way round.

Therefore, the proposed experiment is a test of one of the two pillars of relativity: the constancy of the speed of light. 

[Bufofrog]

54 minutes ago, lidal said:

Therefore, the proposed experiment is a test of one of the two pillars of relativity: the constancy of the speed of light.

I believe you have been informed several time that the invariance of light has been tested.  I also believe you have been informed multiple times that the term is invariance not constancy.  You seem to be trying very hard to ignore all attempts to help you.

[studiot]

24 minutes ago, Bufofrog said:

I believe you have been informed several time that the invariance of light has been tested.  I also believe you have been informed multiple times that the term is invariance not constancy.  You seem to be trying very hard to ignore all attempts to help you.

Yes indeed knowing the difference between invariant and constant is vitally important.  +1

[Markus Hanke]

2 hours ago, lidal said:

2. The constancy of the speed of light.

It’s invariance of the speed of light, not constancy. That’s an important difference.

2 hours ago, lidal said:

Therefore, these two postulates need to be tested and established experimentally

All aspects of SR have, over the past 100+ years, extensively tested in hundreds, perhaps thousands, of different experiments - it is arguably among the most well-tested theories in all of physics. At the heart of SR lies the symmetry of Lorentz invariance, so ultimately the aim is to look whether this symmetry is ever violated or not:

https://en.m.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation

No such violations have ever been observed within the domains we are able to experimentally probe, so SR stands firm.

[studiot]

1 hour ago, studiot said:

Yes indeed knowing the difference between invariant and constant is vitally important.

Perhaps I should add related words 'steady' and 'uniform' to the list of oft misapplied words.

[lidal]

Just now, Bufofrog said:

I believe you have been informed several time that the invariance of light has been tested.  I also believe you have been informed multiple times that the term is invariance not constancy.  You seem to be trying very hard to ignore all attempts to help you.

How was the theory of relativity born? 

Special relativity was born after all classical/conventional approach failed to explain the Michelson-Morley and earlier experiments. Physicists resorted to unconventional ideas such as length contraction, time dilation etc. It is crucially important to note that physicists resorted to these unconventional ideas only after they tried the classical/conventional approach. Even Einstein seriously considered classical approaches before he abandoned them.

Ever since the null result of the MM, many experiments have been performed. The Sagnac effect, the Ives-Stilwell experiment, moving source and moving mirror experiments, the GPS and the GPS Sagnac correction,the Marinov and the Silvertooth experiments, etc.

After the almost universal and premature acceptance of Einstein's relativity theory by the scientific community, particularly after the 1919 solar eclipse expedition, the physics community appeared to have forgotten the crucial fact that led to the birth of relativity theory: that is the failure of the classical and conventional approaches. This is to say that relativity was born ONLY AFTER THE CLASSICAL APPROACH WAS TRIED AND FAILED. 

My point is that the physics community should have followed the same approach it followed for the MM to all later experiments: FIRST CONSIDER THE CONVENTIONAL APPROACH AND THEN RESORT TO UNCONVENTIONAL APPROACH ONLY IF/AFTER THE CONVENTIONAL APPROACH FAILED, AND ADOPT THE RELATIVISTIC APPROACH ONLY IF IT EXPLAINED THE PHENOMENON IN A COMPELLING WAY.

Crucially, this means that the failure of classical theories itself should never have been interpreted as the evidence for relativity unless relativity provided its own explanation in a unique and compelling way.

In this regard, the only success of relativity I know is the Ives-Stilwell experiment.

If the scientific community had followed this approach during the past century, Einstein's relativity would never have achieved universal acceptance and the classical theories would not have been completely abandoned.

Now returning to your assertion that light speed constancy, as it is understood in relativity, is an experimentally established fact, I think that you are referring to the Michelson-Morley and other experiments. But what if the MM null result has other unconventional explanation? What if other unconventional explanation exists for the Ives-Stilwell  experiment? What if a model of the speed of light exists that can explain not only the small fringe shifts observed in the MM and Miller experiments, but also the complete null result of modern MM experiments, but also the large first order effects in the Marinov and the Silvertooth experiments, but also the Brian G Wallace effect? What if constancy of the speed of light has other novel interpretation?

When I proposed my thought experiment, this was the same problem that I noticed: not trying the conventional/classical approach first and, in fact, considering such an approach ridiculous despite the fact that it provided an almost trivial explanation.

 

 

 

Just now, Bufofrog said:

I believe you have been informed several time that the invariance of light has been tested.  I also believe you have been informed multiple times that the term is invariance not constancy.  You seem to be trying very hard to ignore all attempts to help you.

I will see if 'invariance' vs 'constancy' makes any difference.

Edited November 5, 2023 by lidal

[swansont]

22 minutes ago, lidal said:

This is to say that relativity was born ONLY AFTER THE CLASSICAL APPROACH WAS TRIED AND FAILED. 

I have to point out that relativity is a classical theory. As in, it is not a quantum theory.

Yes, Einstein’s relativity was born after the failure to detect motion through the aether, long after the observation of stellar aberration indicated that such motion was present. But Einstein said that the M-M result was not an influence on his work published in 1905.

Quote

the only success of relativity I know is the Ives-Stilwell experiment.

What about the Hafele-Keating experiment?

[studiot]

26 minutes ago, lidal said:

will see if 'invariance' vs 'constancy' makes any difference.

My freezer is kept at a constant temperature of -20^oC, but this is not invariant as I can turn the control knob up or down.

[lidal]

13 hours ago, Bufofrog said:

I believe you have been informed several time that the invariance of light has been tested.  I also believe you have been informed multiple times that the term is invariance not constancy.  You seem to be trying very hard to ignore all attempts to help you.

Since I couldn’t find any sources, here is my own understanding. Correct me if I am wrong.

The constancy of the speed of light is the assertion that the speed of light as measured in any inertial lab is constant c and isotropic. The invariance of the speed of light is the assertion that the speed of light in the experiment in that lab as 'seen' by a relatively moving observer is also equal to c.

Like relativity of simultaneity, the invariance of the speed of light is also a consequence of the constancy of the speed of light (and the principle of relativity). If the latter cannot be established experimentally, the former cannot be accepted as a fact. Like relativity of simultaneity, the invariance of the speed of light is not something that can be tested directly, but that can be inferred from the two postulates. You can test constancy of the speed of light directly, but not the invariance of the speed of light.

10 hours ago, swansont said:

 

What about the Hafele-Keating experiment?

I give more weight to the Ives-Stilwell experiment because this experiment was meant to test another theory but confirmed a prediction of special relativity. Moreover, I haven't seen any 'anti-relativist' questioning the integrity in the Ives-Stilwell experiment. 

[Markus Hanke]

1 hour ago, lidal said:

The constancy of the speed of light is the assertion that the speed of light as measured in any inertial lab is constant c and isotropic. The invariance of the speed of light is the assertion that the speed of light in the experiment in that lab as 'seen' by a relatively moving observer is also equal to c.

Constancy means that c always has the same value under all circumstances - which it evidently does not, since its value depends on the permittivity and permeability of the underlying medium. For example, c is different in glass than in vacuum. This is a direct result of Maxwell’s equations.

Invariance means that its value remains the same irrespective of the relative state of motion between emitter and receiver. For example, light emitted from high-velocity particles (e.g. northern lights) propagates at the same c as light emitted from a stationary flashlight. In other words, the form of the laws of physics do not change if you introduce relative motion.

2 hours ago, lidal said:

Like relativity of simultaneity, the invariance of the speed of light is also a consequence of the constancy of the speed of light

No, these are independent concepts. For example, kinetic energy in an inertial system is constant, but not invariant; mass of that same system is invariant, but not necessarily constant. You can’t conflate these terms.

13 hours ago, lidal said:

Crucially, this means that the failure of classical theories itself should never have been interpreted as the evidence for relativity unless relativity provided its own explanation in a unique and compelling way.

That’s not how it works. A model is considered valid and successful if it is able to produce correct and accurate predictions for the largest possible domain of applicability. Newtonian physics works just fine for classical, low-energy, low-velocity scenarios (which is why we all still learn it at school), but it fails miserably in the quantum realm, are for high-energy, high-velocity situations. Relativity has a much larger domain of applicability (ie it works for a much wider range of situations), which is why it has been adopted as a useful model. 

Remember, physics makes models, not ontological claims. You are welcome to disregard relativity and try to describe the world in Newtonian terms, if that’s what you wish - but you’ll find that you very quickly run into major problems with this. 

[lidal]

1 hour ago, Markus Hanke said:

Constancy means that c always has the same value under all circumstances - which it evidently does not, since its value depends on the permittivity and permeability of the underlying medium. For example, c is different in glass than in vacuum. This is a direct result of Maxwell’s equations.

Then what should we call the assertion that the speed of light in vacuum in any inertial lab is measured to be c and isotropic ? I have always read and known the constancy of the speed of light to mean constancy as measured in any inertial lab.

 

1 hour ago, Markus Hanke said:

Invariance means that its value remains the same irrespective of the relative state of motion between emitter and receiver. For example, light emitted from high-velocity particles (e.g. northern lights) propagates at the same c as light emitted from a stationary flashlight. In other words, the form of the laws of physics do not change if you introduce relative motion.

 

Can we also talk about 'invariance' of the speed of sound?

 

I am just trying to figure out how all this changes the argument.

 

[swansont]

9 hours ago, lidal said:

I give more weight to the Ives-Stilwell experiment because this experiment was meant to test another theory but confirmed a prediction of special relativity. Moreover, I haven't seen any 'anti-relativist' questioning the integrity in the Ives-Stilwell experiment. 

That’s different from claiming that it’s the only success.

Besides, people with an agenda will find fault wherever they want; some (most?) of the critiques of H-K are from people who clearly don’t understand timekeeping, and/or don’t understand relativity. 

5 hours ago, lidal said:

Can we also talk about 'invariance' of the speed of sound?

Only if it’s about how it’s not invariant.

A sound source inside a train car, or a plane, will acquire the speed of the train or plane.

[Bufofrog]

5 hours ago, lidal said:

Can we also talk about 'invariance' of the speed of sound?

Sure.  The speed of sound is not invariant.  You need to look up the meaning of invariant.

 

5 hours ago, lidal said:

I am just trying to figure out how all this changes the argument.

Your argument is that the speed of light is not invariant.  IOW you think that an inertial observer should measure the speed of light as c + v or c - v, where v is the speed of the inertial observer.  That is not true, all experiments show the speed of light is invariant, IOW the speed of light is always measured as c for all inertial observers.  So there really is no argument, because experimentation falsifies you proposal - end of story

[Markus Hanke]

On 11/6/2023 at 10:45 AM, lidal said:

Then what should we call the assertion that the speed of light in vacuum in any inertial lab is measured to be c and isotropic

That’s principally invariance - but so long as you specifically talk about c in vacuum, and so long as there is no gravity involved, then it is also constant. Just bear in mind that it won’t be constant if you go from vacuum into another medium.

On 11/6/2023 at 10:45 AM, lidal said:

Can we also talk about 'invariance' of the speed of sound?

No, sound is different from light, it’s neither invariant nor constant.

The thing is this - even if you didn’t know anything about the theory of relativity, and just worked off Maxwell’s equations alone, you would still find c to be invariant. You can derive the electromagnetic wave equation from Maxwell, and solve it for a fast moving emitter - the resulting wave still  propagates at exactly c. Special relativity simply describes the logical consequences of this fact in a coherent and simple way - something which Newtonian mechanics fails to do. Of course, we now know that Maxwellian electrodynamics is essentially a relativistic phenomenon, but Maxwell himself didn’t know this.

[lidal]

On 11/2/2023 at 5:15 PM, studiot said:

Thank you for the long response.

 

Can we please separate the history of the study of the nature and propagation of light from this discussion as you have several important omissions that you are perhaps not aware of.
By itself the history is an interesting subject and we could certainly discuss that in another thread where all might learn something new.

 

As far as I know Galileo did not offer a principle of relativity.
He did, how ever offer a principle of inertia, which is what perhaps you are referring to.
But for the purposes of this thread if you know of some reference showing that Galileo made the statement you claim above please post it.

 

Neither was this The Principle of Relativity of Einstein.

His exact words from the 1905 SR paper were

No mention of physicists locked in sealed rooms determining anything!

However he adds a further comment which many readers miss, as all the words in the paper are packed with import:

I will now develop the import of this latter statement in terms of the homogeneity and isotropy of space and link that to Einsteins two postulates.

When we say there is an event such as a light pulse from your source we need to specify two things. Where is it ? and When is it?
To do this we require up to five pieces of information. These are : up to 3 spatial coordinates, one time coordinate one reference base or origin for the time coordinate and one combined reference base or origin for the spatial coordinates.

The issue of the 'absoluteness' of the references bases will come out in the subsequent treatment.

It is no use just offering x, y, z, t values  - they are meaningless without knowing where and when they are measured from.

The good news is that these last two pieces of information 'drop out' of the calculations when wew measure the distance beteen two events and the time difference between them as

l²  = (x₂ - x₁)² +(y₂ - y₁)² and (z₂ - z₁)².

and

dt = (t²  -  t¹)

dt and l are examples of invariants.

dt is invariant with regard to translations of the origin of the time axis and l is invariant with regard to translations of the space origin.

When following Einstein's original paper the significance of the second quoted remark becomes apparent.
Although the paper is entitled the electrodynamics of moving bodies, most of the paper follows their kinematics only. Dynamics is only introduced in the last two sections at the end.

Are you comfortable with the distinction between kinematics and dynamics ?

1) Homegeneity

The arbitraryness of the origins of space and time are referred to as the homogeneity of space and time respectively.

This is equivalent to postulate that every chunk of space looks and behaves like every other chunk of space and that every chunk of time looks and behaves like every other chunk of time oe in other words they are homogeneous.

 

2) Isotropy

That the length l is the same (invariant) when measured in a coordinate system that is rotated, but not translated, with respect to the first is a simple piece of elementary geometry.

This leads to the conclusion that there is no preferred direction in space. So space is regarded as isotropic.

Since space has the property if transmitting light we have your isotropic light velocity.

 

With regard to the example in your post,

Please explain why there is a problem with the observer viewing light from S1 and S2 (with the maths).

Note that we cope with this everday day almost everywhere, but it really only interests the astronomers where the distances involved makes a difference to light sources.

 

 

I would like to directly reply to your comment regarding isotropy and homogeneity of space and time and to your question of why the observer sees the two sources differently. However, I can't do this without discussing my new theory to the problem of the speed of light, which I would prefer not to do here because my argument (as described in the OP and comments ) can stand on its own without the need for bringing in an alternative explanation.

 

 I think the scientific community should be able to disentangle two problems: 1. The fact that relativity theory has problems, which many physicists are increasingly becoming aware of.  2. The lack of alternative theories.

These two problems need to be treated independently. That is, the lack of alternative theories should not be seen as evidence for relativity anymore.

 

Therefore, I would prefer not to discuss my alternative explanation here. All I can say is that there is a deep quantum mystery not only behind phenomena traditionally known as quantum phenomena (such as quantum entanglement) , but also behind the mystery of the speed of light, as far as I have understood. Note that current physics is in the dark regarding any connection between quantum phenomena and the speed of light and treats the two differently as unrelated problems.