History of a subject is distinct from its logic. The latter matters for understanding it, not the former. So how Einstein described special relativity, is only of historical interest.

Special relativity describes spacetime, i.e. a manifold, with the Minkowski metric. Particles are described by worldlines, x^μ(λ), where λ is the parameter of the worldline.

So the action of a particle is a function of the Lorentz-invariant quantitiy, (η_μν u^μ u^ν)^(1/2), where u^μ=dx^μ/dλ.

The action is invariant under local reparametrizations of the worldline, λ->f(λ), with f'(λ)>0. Indeed it’s possible to show that demanding invariance under local reparametrizations of the worldline is equivalent to demanding global Lorentz invariance.

The Minkoswki metric, in turn, is the unique solution of the Einstein equations of general relativity, upon imposing appropriate boundary conditions. Matter couples to the metric through the energy-momentum tensor and the perturbation to the Minkowski metric, for ``small" values of the energy can be seen to be negligible. For `` larger" values, spacetime does get affected and that deformation of the spacetime geometry can be described by the Schwarzschild metric.

Eric Baird,

The third postulate,which is not a main or fundamental postulate or assumption,is the conservation of momentum,where the momentum is defined as the product of the relativistic mass and velocity.The clock postulate and the reciprocity postulate, each can also be called a third postulate.What the clock postulate and the reciprocity postulate are is kept to you as homework.According to Einstein et al.,special relativity has only two main or fundamental postulates or assumptions.

Page 2 describes Einstein’s 2 postulates:

1. The principle of relativity

2. The principle of the constancy of the velocity of light.

Unfortunately, the first postulate is not correct because the principle of relativity is founded on the mutual relations between observable/detectable phenomena. Therefore the principle of relativity is not “absolute” (and it violates the aim of theoretical physics to get a unified theory). Like the quantum of energy – Planck’s constant – isn’t a fundamental constant because it is a quantized relation between phenomena. Thus if we build a realistic model of space itself we will observe the emerging of Planck’s constant from underlying properties.

The principle of relativity is comparable with Planck’s constant. Relativity is a “theoretical construct” because we can only measure mutual relations. Actually, the constant speed of light – as a basic property of the structure of space itself – shows that the principle of relativity is a misinterpretation of physical reality. Because every local change in the universe – the real quanta transfer – has the speed of light. That means accelerating the velocity of a particle will slow down the rate of its internal changes (e.g. rate of decay).

With kind regards, Sydney

Stam Nicolis : " History of a subject is distinct from its logic. The latter matters for understanding it, not the former. So how Einstein described special relativity, is only of historical interest. "

No, It's a lot more important than that. Because Einstein promoted the idea that special relativity could be derived from only the two standard historical postulates, and nobody called him on it ... and because most physics people believe that those two postulates can't be wrong, most physics people seem to believe that the validity of SR is effectively proven and that only idiots or anti-relativity fringe people would try to find fault with it.

It's widely considered to be geometrically unavoidable, and the only possible relativistic option (encouraged by Einstein promoting his SR and SR-based approaches as "THE theory of relaitvity", in the singular) .

All of that changes when we realise that Einstein was never able (or willing) to present a legal derivation of SR as a physical theory.

Once we realise that the two postulates aren't sufficient,

Point [1] suggests the possibility (for instance) of a different general theory of relativity that regulates local c-constancy gravitomagnetically. This sort of "alternative GR" would be more in keeping with GR principles, and its non-SR relationships would seem to be more compatible with QM.

Most of the relativity community have spent a century failing to notice that there was at least one relativistic alternative to SR, and the reason they failed to see the alternative possibilities is because they were hoodwinked by Einstein's "two postulates" story into believing that SR was inevitable. They were presented with a false choice between SR and non-relativistic theories. Suggest a modern non-SR theory of relativity, and most practitioners will go, "... Huh?" According to the definitions that were instilled into them as students, a non-SR theory of relativity, or a general theory that doesn't include SR physics, is a contradiction in terms.

They've been taught to understand the word "relativistic" as meaning "SR-defined". Without the wider context, they aren't capable of making scientific assessments of the likely validity (or invalidity) of SR. They don't know what physics would look like if "relativity" was right but SR was wrong. Because of that, they don't know how to carry out experiments to show whether or not SR is the correct foundation theory of relativity, or whether its equations are a better or worse match to the data than the alternative set(s).

Without knowing what the competition might have said, we don't know how to assess the scientific significance of apparently pro-SR results. The success of special relativity has been like the success of a horse in winning a race where it was the only horse running. The success is almost meaningless without that wider context ... we can't tell whether SR is a thoroughbred at the top of its form, or a decrepit three-legged nag.

Point [2] suggests that a proper three-postulate derivation of SR would have revealed the theory's true dependencies, and resulted in the theory being quickly rejected or downgraded to the status of a useful engineering theory. If Postulate Three is "the law that the propagation of light is in no way affected by the presence and motion of matter", than that's an idea that Einstein went on record as saying was "against the mode of thinking in science". I don't think that there is any way of framing or phrasing a third postulate in a way that seems to be supported by experimental evidence, and/or that Einstein himself would have considered acceptable.

Without a third postulate, SR is not a legitimately-derived physical theory, and with a third postulate, it's a physical model whose explicit simplifying assumptions are difficult to take seriously.

====

Back when we believed in the "two-postulate" narrative, special relativity sometimes seemed like the front view of an impregnable fortress. It could seem as if there was no way we could attack and overrun it, and it seemed as if the stonework was perfect, and free from any little cracks or holes that would take a crowbar.

Now that we know that the public derivation of the theory was in effect an example of Einstein "bluffing", the situation is very different. Instead of accepting the view presented to us, we can choose to wander around the side of the fortress, and realise that the front wall was purely for show, intended to intimidate us into not exploring further -- the fortress turns out to have no side walls, and also no back wall. Getting past the "impregnable" defences is simply a matter of mapping the scene from a wider range of viewpoints, and then taking a leisurely stroll around the front wall.

There’s just one postulate in special relativity: Invariance under global Lorentz transformations. That’s necessary and sufficient. That's what defines special relativity. Matter belongs to a representation of the Lorentz group and is labeled by the two Casimir operators, that describe the mass and spin respectively.

The principle of relativity and the principle that the speed of light is independent of the reference frame are just two expressions of the property that Maxwell's equations are covariant under global Lorentz transformations, where the parameter, that has the dimensions of velocity is the speed of light.

This is now a standard exercise in any course in classical electrodynamics.

Stam Nicolis : " There’s just one postulate in special relativity: Invariance under global Lorentz transformations. "

Oh-kay ... and in a derivation of a physical theory of the behaviour of matter, this postulate is justified ... how, exactly?

I've said in the paper that there's no definitional ambiguity about what the equations of SR need to be, and I've also cheerfully agreed that for many modern researchers, we can define SR as being a theory with one statement: "the laws of physics must correspond to the geometry of MInkowski spacetime"

Definitional laxity is not the problem. The problem is derivational laxity.

====

Stating one condition that fully defines a possible physics is not a derivation, but a definition. I could, similarly, play the "single condition" game by modifying the above statement to read, instead, "the laws of physics must correspond to the geometry of a relativistic acoustic metric", which would give us non-SR laws and non-SR equations.

Would you then say that I'd proved my case that the laws of physics must be non-SR? Of course you wouldn't -- you'd say (quite correctly) that I had simply declared a correspondence between reality and the characteristics of a system that I liked, but that I hadn't proved a damned thing. Where would I have argued the case for acoustic metrics having correspondence to physical reality? What correspondences would I be drawing between acoustic metric predictions and known physical behaviours? How would I have established that these correspondences were superior to those obtainable from other classes of potential theory?

This is where we rely on either a set of supporting arguments (that are necessarily open to ongoing reevaluation), or more rigorously, present a physical derivation, which says that for given known behaviours, some options are impossible, or that a specified theory is the only possible logical way to satisfy them. General supporting arguments are often very messy and subjective, and rely on our being able to correctly assess a balance of probability. It requires us to be able to think. Compared to this, a derivational proof can be considered a logical "black box" that takes certain inputs and provides a deterministic output, and frees us from the obligation to think, because the derivation tells us that if A and B are correct, then C is the only possible answer. If the derivation is logically sound, we only have to ask ourselves "are A and B true?" and if so, the theory is unavoidable.

Snag is, Einstein mis-claimed for SR all the legitimacy and prestige and status that goes with a "derived" theory ... without actually managing to produce a derivation.

The internals of his "black box" were surreptitiously hard-wired to give the result he wanted. In reality, the inputs A and B could give output theory C, but they could also give the different theory D ... and without further study of the dependencies, it was (just) conceivable that there might even potentially be a competing theory E, F, or G.

What should have happened over the following decades is that the research community should have explored the landscape of potential classical relativistic theories, catalogued and categorised them by their properties and testable behaviours, established which results seemed to rule out which equation-sets, and, if SR survived that process, we would now be in a position to assess whether SR was as good a match to reality and fundamental principles as its competitor(s) (if there were other survivors). We would then be in a position to say why we believed SR to be right (or wrong), and defend our arguments.

This background research would normally be considered a matter of "due diligence" -- the sort of research that a community would have an obligation to carry out, to avoid being accused of negligence.

But nobody seems to know of any such work ever having been carried out by the mainstream.

... And it seems that the reason why nobody appears to have done the necessary work is that everyone assumed that it had either already been done by someone else, or assumed that it was known not to be necessary ... because if Einstein's "two postulate" story was true, then there were no other possible competing relativistic theories for SR to be compared against.

Right now, without a survey, map or guidebook to the relativistic landscape, the relativity community is flying blind.They are trusting to blind luck that the theory that they've ended up with just happens to be the right one. Since they don't know the options and possibilities, they don't even know how to do scientific testing of which relativistic system is best.

If you're a mainstream relativity person, I goes that what it currently comes down to is -- do you feel lucky?

Postulates aren’t ``justified"-they’re definitions. Assuming Lorentz invariance, certain consequences follow, which can be compared to experiment.

It’s the other way around: Having understood what Lorentz invariance means, it’s possible to describe how it may not hold globally-and how it’s possible to parametrize such violations.

The landscape of Special Relativity SR is actively being studied today. From gamma ray bursts showing that SR holds at the Planck scale, to showing that the Lorentz connection always carries torsion, to describing how a Lorentz-boson exists to maintain Local Lorentz invariance before the SR light cone even emerges, and to injecting rigor into standard model quantum field theory math, etc. Modern Lorentz invariance seems to be lurking at the center of everything.

Stam Nicolis " Matter couples to the metric through the energy-momentum tensor and the perturbation to the Minkowski metric, ... "

That's a reasonable statement

Stam Nicolis " for ``small" values of the energy can be seen to be negligible. "

... and then this is where modern relativity theory goes off the rails thanks to wishful thinking.

If the mainstream had studied the actual consequences of the general principle of relativity, without allowing the desire for SR compatibility to override everything else, they would have realised that, in the context of matter, there is no such thing as a "small" perturbation of the Minkowski metric.

• For a massed particle with zero gravitation (impossible under GR), the equations of motion are those of SR. But this class of purely hypothetical SR-compliant particles cannot exist according to our modern understanding of massenergy. It's not a physical solution.
• For a massed particle with maximal gravitation (whose interaction surface is a curvature horizon), gravitomagnetic effects are major. The gravitomagnetic shift on the moving mass is of the same magnitude as a traditional Doppler shift, the moving horizon drags light totally, and momentum exchange means that the energy of light entering or leaving the vicinity of the moving particle is modified. This means that the shift equations and equations of motion of an extremal-gravity particle are strongly non-SR.

The next point that researchers conveniently forget is that we are not allowed to have multiple equations of motion and multiple motion-shift equations. The principle of relativity, and the principle of wave-compatibility, and the principle that we can describe spacetime using a metric approach, all forbid it.

So under a working gravitational theory there is no such thing as a "low-gravity" realm or limit (except perhaps the low-velocity limit) where SR equations apply to matter. This is not a problem that you can solve with approximations that never get resolved -- you have to nail the exact solution, perfectly. Since the shape of the equations depends on the strength of gravitational and gravitomagnetic effects at a particle's interaction surface, And the equations have to be the same for the smallest possible particle and for a collapsed galaxy core with a horizon, Relativity forbids the existence of particles with "small" deviations from flat spacetime. Either all particles have zero deviation from flat spacetime (perfect SR solution), and out universe has no such thing as gravity, or all particles have maximal deviation from flat spacetime (perfect gravitomagnetic solution), and SR has the wrong set of fundamental equations.

General relativity principles, applied stringently, quantise gravity in the sense that they assign precisely the same relative gravitational field intensity to all "stationary" particle surfaces that are exposed to a mass-observer. if we place a particle in a stronger background field, its effective interaction surface (its relative horizon, for us) simply extends with its effective horizon. It's a gravitationally and gravitomagnetically self-regulating system, Since local lightspeeds are regulated for every mass by grvaitomagnetic differentials, there is no need for SR, and in fact the SR equations in that context are toxic to the physics.

This is not a flight of fancy on my part, it's what we can derive from the strict conditions required by the general principle of relativity.

• In terms of physics, a general theory and SR are two utterly incompatible logical systems -- General theory makes gravitomagnetism compulsory and universal, while SR/Minkowski makes gravitomagnetism illegal.
• In terms of mathematics, then ... yes, special relativity can be derived as a form of homogenised average of the correct equations, and this trick works for every relativistic theory, regardless of whether a solution is right or wrong -- once you time-average the thing, you always end up with SR. So SR does have a place at the heart of relativity theory, but it's not for the reasons that people think ... it's not for having the correct equations.

Stam Nicolis : " For `` larger" values, spacetime does get affected and that deformation of the spacetime geometry can be described by the Schwarzschild metric. "

Well, if the characterisations of the Schwarzchild metric that I've read are correct, and the Schwarzchild metric generates the SR shift equations

(i.e. for a gravitational differential with an associated relative velocity v, the gravitational shift is calculated by using v with the SR shift equations).

, then the Schwarzchild metric doesn't really work, does it? because if the gravitational source generating that curvature also has relative motion to the observer, then everything breaks down:

Preprint Gravitomagnetic horizons and the comprehensive failure of Ei...

I'm thinking that perhaps I shouldn't be trying to explain who non-SR relativity theory works in this thread. That really shouldn't be my problem. Once we accept the abstract hypothetical possibility of non-SR relativity theory, then really, the mainstream physics community is obliged to investigate non-SR solutions themselves.

The reasons why they haven't already done this work, despite having had over a century to think about it ... is something that perhaps I should leave to them to explain.

Issam Mohanna : " The third postulate,which is not a main or fundamental postulate or assumption, is the conservation of momentum,where the momentum is defined as the product of the relativistic mass and velocity. "

Hi Issam!

Conservation of momentum is another reason why SR equations can't be applied correctly to gravitational problems (and under a general theory, all problems involving masses are gravitational problems)..

Conservation of Momentum, plus gravity, leads directly to gravitomagnetism, and gravitomagnetism destroys the geometrical basis of SR.

According to the "slingshot effect" arguments:

... If you throw a ball at 20kph, and it bounces off the front of a train approaching at 60kph, then the driver is supposed to see the incoming ball to be approaching at 80 kph, and therefore also leaving at 80 kph, with the result that the ball comes back to us at about ~80+60=~120kph

This result is explained by saying that the interaction of the ball with the approaching train transfers some of the train's forward momentum to the ball.

We say that he interaction involves momentum exchange.

Suppose that we now replace the approaching train with a distant approaching planet, and instead of throwing the ball directly at the planet, we throw it so that the ball follows a horseshoe-shaped orbit that loops around the planet and brings it back to us.

Similar arguments then apply: the ball interacts gravitationally with the approaching planet, and comes away from the encounter approaching is faster than we originally threw it. The planet's own velocity should be reduced by an unmeasurably small amount due to the momentum that it donates to the ball. This is the principle used by NASA to slingshot probes around the solar system.

So the planet's gravitational interaction with the ball is causing a deflection component, pointing in the direction that the planet moves. If we assume that passing light is affected in the same way as passing matter, then the moving planet must also be deflecting nearby light in the same direction, and we have a gravitomagnetic field.

====

Now we can switch to the problem of light leaving the planet's surface. That light has to move through the same field to reach us, and should show a gravitomagnetic blueshift if the planet approaches and a gravitomagnetic redshift if it recedes.

• If the gravitomagnetic shift applies in addition to the nominal SR motion shift, then the total combined motion shift will be non-SR
• If the gravitomagnetic shift is the motion shift, calculated outside the time domain as a curvature effect, then it is already built into the motion-shift equations, and doesn't have to be calculated as a separate effect. But those equations will need to fit a geometry in which the relative motion of a source is associated with a distortion of the region's spacetime geometry. In other words, the equations again cannot be those of SR

So gravitomagnetism forces SR's flat-spacetime equations to be wrong, and kills special relativity.

Since all moving masses in the universe have to obey the same shift equations and equations of motion, if we calculate the the "worst-case" scenario of a moving collapsed star with a curvature horizon, giving the maximum possible gravitomagnetic deviation from the SR predictions, then those are the same equations that then have to apply universally, to all other moving-matter problems.

Conservation of momentum, applied within gravitational theory, lets us conclude that the shift equations and equations of motion within a "gravitational" universe cannot be those of special relativity.

Eric Baird,

https://youtu.be/iMDTcMD6pOw

Eric Baird Eric Baird said, "That really shouldn't be my problem." I accept this problem as homework. First, I write general relativity as a gauge theory in flat spacetime. A gauge theory where the energy-momentum real (not pseudo) tensor of only the gravitational field interacts with a matter fields real energy-momentum tensor at some location in spacetime. To maintain local Lorentz invariance a boson that exchanges your gravitomagnetic force is created. Note that this is not the magnetic field of electro-magnetic type, but rather a gravitational-magnetic field. The new boson is the massless spin-one Lorentz boson that minimally couples to fermion number at gravitational strength. This Lorentz boson is predicted by aikyon theory as fermions localize during wave function collapse and as the SR light-cone emerges out of pre-spacetime and its coupling to fermion number is described by Kevin Cahill, “Is the local Lorentz invariance of general relativity implemented by gauge bosons that have their own Yang-Mills-like action?” Phys. Rev. D 102, 065011, arXiv:2008.10381 [gr–qc] (2020).

George Soli : " The landscape of Special Relativity SR is actively being studied today. "

The full landscape of relativity theory appears to have two unconnected islands, one for theories based on flat spacetime and SR, and one for theories based on curved spacetime and the general principle of relativity.

The "landscape" of SR is a flat desert compared the the lush nonlinear landscape generated by the general principle of relativity. But that larger island isn't properly available to current researchers, because its incompatible with SR physics.

The GPoR landscape includes the principles of relativity of acceleration and rotation, the principle of the equivalence of inertia and gravitation, compatibility with expanding-universe principles, an arrow of time, wider support for observerspace principles, further equivalence principles, more dualities (allowing us to calculate the same outcomes in more ways), and support for the classical counterpart of Hawking radiation.

None of that "good stuff" works if we believe that SR has the correct fundamental equations.

George Solii : " Modern Lorentz invariance seems to be lurking at the center of everything. "

Oh, it is. Just not in the way that current theorists think.

Once we leave the flat confines of SR behind and look at the wider spectrum of potential theories of relativity, all with their own different shift equations and different equations of motion, with each related to its neighbours by a "Lorentzlike" factor ( [1 - v2/c2 ]gd ) we find that one thing that every possible non-SR theory of relativity has in common (including nasty old C19th ballistic emission theory), is that they are all time-asymmetrical. Apart from SR, they all have different equations for physics that apply for calculations in forward and reversed time.

BUT ... if we artificially impose time-symmetry by averaging out the forward-and reversed time predictions together, every relativistic theory then generates flat spacetime and the SR equations

(SR then slots back into the wider pattern: the time-reversed version of SR is SR, and the time-averaged averaged version of SR is also SR).

Where textbooks typically present Newtonian theory as being an approximation of the more correct SR, it's arguably more accurate to write this the other way around, and say that SR is an averaged approximation of Newtonian theory (and also, in the same way, an averaged approximation of every other relativistic theory, including itself).

SR and Minkoski spacetime connect mathematically and geometrically to every other conceivable theory of relativity, but not necessarily by having the correct equations for inertial physics, and not through being a physical limiting case of a valid GTR (which it isn't).

The connection appears because SR is the universal homogenised version of the equations and geometry of every other currently-conceivable theory of relativity.

... But we're getting ahead of ourselves.

We now know that one of the founding beliefs of special relativity, the "fact" that SR is the unique result of just two basic postulates, is demonstrably wrong. Einstein's derivation and justification for SR was never completed, and the omitted third postulate has to be something along the lines of "we know that the presence and motion of matter has zero effect on lightbeam geometry"

This immediately points us towards a range of hypothetical other theories of relativity that diverge from SR in how strongly moving matter is thought to influence lightsignals, and how strongly they diverge from the third postulate. We can then generalise and parameterise, invent a variable "gd" for the supposed strength of gravitomagnetic dragging effects in a theory (0>=gd>=1), use gd as an identifier for any potential relativistic theory, and then survey which solutions appear to be at least broadly compatible with the available physical evidence, which experimental results depend critically on gd and which results come out precisely the same regardless of the value of gd (like E=m0c2).

I appreciate that GR was still fresh in the 1920s, and people had other things to look at in the 1930s, but this basic comparative survey of possible relativistic models should have been in print by at least the 1940s.

It's now 2022, and nobody in the mainstream yet appears to have done a basic review of relativity theory. They are sure that the system that they inherited MUST be true, but without knowing the wider picture, they have no way of constructing a scientific argument that assesses the probability of the SR-based approach being right or wrong. They are relying on faith -- faith in the system, and faith in their fellow professionals.

I'd suggest the reason why the community failed to do this basic "discovery" exercise was that they also had faith in Einstein, and when Einstein repeatedly provided them with the two-postulate story, they believed it.

... so they never did a survey of hypothetical relativistic theories of inertial physics that might compete with SR, because they thought that Einstein had already shown that there were no other competing relativistic theories. They couldn't parameterise a range of non-SR theories by their divergences from SR's third postulate, because Einstein didn't tell them that there was a third postulate.

Einstein effectively wrong-footed everyone.

In fact, special relativity is never derived from *only* two postulates. There are a number of additional implicit assumptions in any derivation, such as homogeneity of space and time and isotropy of space. Sometimes, it is argued in derivations "from the two postulates" that these additional assumptions follow from the relativity principle, but that is not so clear. An anisotropic homogeneous space would not lead to any obvious violation of the relativity principle.

And then there is the statement, that actually only *one* postulate is necessary. The second postulate (uniformity of the speed of light) can be dropped. It is possible, using only the first postulate and the aforementioned implicit assumptions, to derive the Lorentz transformations as the general form leading from one inertial system to another one. This establishes that there exists a characteristic velocity (which could be infinite, then the Galilei transformations would ensue as a special case). That this velocity is the speed of light would then be established by experiment, not by a second postulate. (Or else the second postulate could be weakened to only state that the limit speed following from the first is finite. That there can be only one such speed and not several ones follows without the second postulate.)

Dear Eric Baird ,

K. Kassner clearly explained that there is only one postulate at the end of the day.

Just the Galilean postulate suffices. That allows performing Physics locally (the famous Galilean Vessel), Inertial frames of references abstract entities equivalent by definition.

The constancy of the speed of light is just a consequence of that equivalence: once "c" is measured, how would it be possible to detect a different speed of light, by performing the same experiments, in different frames of references indistinguishable by definition?

Einstein resorted to that equivalence in order to derive "logically" the Lorentz Transformats which are at the base of SR.

So as a matter of fact it is not appropriate to say that there are two postulates but there is only one postulate and a corollary to derive the Lorentz Transformations (LT).

The corollary is a constraint on physics that limits its degrees of freedom. That is the price to pay : time becomes also a consequence of relative simultaneity, no anymore an independent variable, it depends also on space, mixing with space to define space-time... The compliance to such transformation is what the Lorentz Invariance (LI) is about....

Not everything obtained logically is necessarily right if it starts from unwarranted premises. The construction initiated by Galilei is certainly valid up to a first-order approximation (classical physics), as experimentally verified, Galilean invariance.

LT based on the same postulates, but a further constraint, are valid to what order of approximation? This is the question....

To which extent the Lorentz Invariance is followed by Physical phenomena?

Probably to an extent far lower than what so far expected...

LTs do not necessarily reduce to GTs in the low-speed limit v

Hi Stefano Quattrini ,

I'm afraid that you're wrong. The simplest way to demonstrate this is to throw away all the technical jargon and provide a simple, basic, geometrical counter-example:

Suppose that all moving masses dragged light completely at their interaction surfaces. Hertz produced such a model in the 1890s, and Einstein later agreed that it was internally logically consistent.

Such a model would:

• Obey the principle of relativity. If all masses drag light, then there is no preferred frame for the propagation of light. Light is then always emitted travelling at at cemitter and is always received travelling at creceiver
• Obey the principle of the constancy of the speed of light, if lightspeed only has to be constant locally (to each observer-mass).

Hypothetically ... a fully dragged-light model has a different geometrical structure to SR, it has a dynamic spacetime geometry rather than the fixed spacetime geometry of Minkowski spacetime, and so its spatiotemporal relationships must be different, too. So it would be a physically different theory to SR, with physically distinct predictions, and not just another "SR clone".

If we then have two different theories that both combine the principle of c-constancy with the principle of relativity, then these two conditions are quite clearly not sufficient to generate SR as a unique solution.

Case closed.

----

We either have to amend the two standard postulates to make them more specific (which would open up special relativity to new lines of attack), or, if we have some other argument or reason for not liking a dragged-light model, we have to add that in as a third postulate (overturning that third postulate then giving another potential way of invalidating the theory).

Einstein's derivation is based on the hidden third implicit assumption that the geometry of spacetime in a region R' containing multiple masses with different states of motion is necessarily the same as the geometry of a region R, that is completely empty. Einstein derives the "law" that c is (globally) flat throughout a region based on the idea that the region is empty, and then applies the same law to the region when it is NOT empty. Naughty Einstein! :)

That's where his logic has a disjunct.

It's easy enough to fix the problem ... we might say (as a third postulate) that we know that the geometry for an empty space carries over to the case of a populated space ... which is equivalent to saying that we know that the presence and motion of matter has zero effect on the behaviour of light.

While that would have fixed Einstein's derivation, he seems to have been unwilling to make that change, presumably because (a) from his other writings, he seems not to have believed that the behaviour of matter doesn't affect light, and (b) because if that had been an explicit third postulate, a lot of contemporary physicists would simply have cited the Fizeau light-dragging result as proving that the third postulate, and therefore the whole special theory of relativity, was disproved by the available experimental data.

Einstein's special theory was successful, partly because he managed to bluff the scientific community and get away with it. I'm not aware of any mainstream source examining that third postulate, because nobody realised that there WAS a third postulate.

K. Kassner " It is possible, using only the first postulate and the aforementioned implicit assumptions, to derive the Lorentz transformations as the general form leading from one inertial system to another one. "

Really? Without using "inertial frame" arguments, or the assumption of flat spacetime in the presence of moving matter?

The problem (in general) with "inertial frame" arguments is that while they can be an incredibly useful and efficient abstraction, the point of an abstraction is to eliminate unneeded data that is cluttering up the description -- so someone somewhere has to make a value judgement as to which data is considered "important" and what is "discardable".

In the case of inertial frames, we keep relative velocity vector data and discard positional data. Discarding positional data means discarding any distance-dependent effects, which means discarding any fields that represent any curvatures of spacetime due to stationary or moving masses.

So while "inertial frame" arguments are quite excellent for describing problems in special relativity, the moment that one switches to a frame-based logic, one is pretty much presupposing that inertial physics is a flat-spacetime problem, and that SR is correct.

It's using SR to derive SR.

For the same reason, frame logic is pretty dangerous under GR, too.

If we accelerate a mass, the relativity of acceleration requires the accelerated body to physically warp the region's spacetime (Einstein, 1921). But in an accelerated frame, there's no intrinsic distortion, and any apparent curvature is due to our considering a curved path through flat spacetime.

So an "accelerated frame" argument under a proper working general theory does not necessarily give the correct physics of an accelerated body.

Modern relativity theory is full of these lame-brained techniques that make the geometry simpler, but force the calculations to then give qualitatively wrong answers. A lot of the problems stem from Einstein trying to make GR a natural progression from SR, and carrying over techniques and definitions that really have no place in a general theory.

Stam: " Postulates aren’t ``justified"-they’re definitions. "

Yes, they are definitions. But for physical theories, one is expected to be able to justify why those particular definitions are to be considered physically reasonable. It's the "GIGO" principle, "Garbage In, Garbage Out".

A theory based on junk is likely to be a junk theory, even if its logic is impeccable.

I'm saying that Einstein should, in a perfect world, have declared (as a third postulate) "the identity of the geometry of a populated space with the geometry of an empty space". Because he derives the relativistic geometry of an empty space, and then applies it to a populated space without flagging up he change in environmental conditions.

Einstein provides no reason, explanation, justification or philosophical argument for why the presence and behaviour of matter shouldn't affect light. Now it's perfectly fine to make an unjustified assumption that your entire theory hinges on, as long as you flag it up as such .

Einstein didn't do this, and judging by the expertise with which the offending passages were written (either by Einstein or his English translator), it feels a hell of a lot as if whoever wrote that section was deliberately trying to obfuscate the logic, and conceal the theory;s dependency on that third assumption.

Somebody was faking, and judging by the fact that the fake "SR only depends on two postulates" storry is still being used by people, it seems to have been one of science's more successful pieces of fakery.

Stam: " Assuming Lorentz invariance ... "

You mean, "presupposing that special relativity is correct ..." !

There seem to be two fundamental solutions to relativity theory: one assumes that spacetime is necessarily flat, that there's no such thing as gravity or gravitomagnetism, and the basic relationships are Lorentz ...

.... and another, that assumes that all masses are associated with curvature, that cg=c, that gravitomagnetic curvature exists wherever masses have relative motion, and that the relationships are Lorentz-squared.

Current textbooks only have half the story regarding how Lorentz relationships apply to physics

(and I would suggest, that IMO they seem to have the wrong half).