space, time and philosophical considerations from an experimentalist's point of view

[RedshiftDrift]

This is a copy of part of a note I posted on another discussion forum on general relativity. This may be of interest.

Dear ... , let me express a more philosophical point of view. Like you, I have learned special relativity and general relativity (although at a very elementary level). Then I spent a career working with atomic clocks that can measure time intervals with 16 significant digits. It didn't take long to understand that these clocks are influenced by the environment in a very sensitive way: temperature in the lab, atmospheric pressure, humidity, vertical alignment (direction and strength of the gravitational acceleration), magnetic field of the truck in the nearby parking lot, tides (gravitation of moon and sun), etc. etc. etc. The accuracy of atomic clocks makes them so sensitive to the environment it becomes an experimental nightmare.

Now we want to move the atomic clock and bring it to another lab. While giving it a velocity we change the de Broglie wavelength of all the atoms in the clock. Guess what, it also has an influence on its ticking rate. Then we push the clock uphill from Ottawa to Boulder and notice that the climb in the gravitational potential has, once again, changed the clock's rate. For the experimentalist, everything you do to the clock changes its rate, therefore, time is certainly not what a clock displays.

Years of experimental work with clocks will convince anyone that it's the clock and the ruler that changes when you give it a velocity. We know that because the clock in the other lab, which has not been touched, is still ticking at the same rate. The Lorentz transformations give numerical values describing this change, but this is different from what I have learned 40 years ago (supposedly "space and time are modified following the Lorentz transformations"). The experimentalist knows that it's the clock that changes because you accelerate it. And with that in mind, the so-called "twin paradox" is not a paradox at all. You are pushing one twin around, can anybody really expect it won't affect its ageing rate?

Same thing for moving the Ottawa clock to Boulder (1500m above Ottawa), we know that the Ottawa clock has changed since the clock in Boulder has not been touched. General relativity gives the numerical values of the change, but the change is not because "space and time are curved by gravity" as I have learned in graduate school. Despite the mathematical convenience obtained by treating space-time as a field that can be stretched and distorted, the idea of space expansion is not at all what is observed by the experimentalist. Time is not only defined as "a number of oscillations of the Cs atom", but this is to be measured "on the Earth's geoid". If you take the cesium to Boulder, you've ruined it by moving it up 1500 meters in Earth's gravity.

We've been told "matter tells spacetime how to curve, and curved spacetime tells matter how to move", but what is observed is that "moving matter changes clock and rulers, and we measure acceleration".

Einstein's equations describe the change of "space-time" for mathematical convenience, but what is described is a change of "clocks and rulers". These are material objects inside the universe, not conceptual "space-time" coordinates. What does this have do to with cosmology? The attempt by Einstein, Lemaître, Friedmann et al. to describe the entire universe with "space-time" is meaningless because Einstein's equation actually describe the behaviour of objects moving inside the universe.

I agree with you that the mathematics that brings us LCDM is an impressive piece of work, but it is just that: mathematics. The physics described by LCDM does not make sense because it uses a theory that describes objects inside the universe, and then tries to describe the entire universe. The error is to confuse the container with the content. Unfortunately for the scientists who thought they were doing science, they spent their life doing mathematics.

That's why cosmology is heading toward a complete crisis: the inconsistencies are not due to mathematical errors - relativity is a good theory, but the mathematical language that uses space-time-distortions does not (and cannot) be used to describe the physical universe but only the content of the universe.

[Francois-Zinserling]

A great read.

There is something amiss though, in that it explains above how the observer sees the clock.
For the clock itself, (observer no.2 riding on the clock) if its clock is slowed (which we know it is), it doesn't see itself as slowed, but therefore it must see all other clocks to be faster.

This would be - in my opinion - the biggest paradox of SR, since SR proposes both clocks see each other as slowed, because you cannot determine who is actually moving. Impossible. This is a real problem though because as Michelson and Morley showed, we cannot determine who is moving!

This can be corrected though by afixing that only 1 is moving, and the other is not. That the stationary observer will see a slowed moving clock (which is really slowed), and the moving clock will see the stationary one as 'faster' which it must then know the observed effect is not real, (because we tell it that it is moving) and then acknowledge this by realising its own clock was slowed.

However, by fixing this, you have to acknowledge that there is an absolute frame - an aether.

One example I like to quote - and these are not apparent observations - these would be real, as in the Boulder examples above by Redshift.

1. If you travel in space at a velocity of ~11km/sec, your clock is slowed by γ = 1.00000000067315. This is SR time dilation, due to velocity. We know it is experienced in GPS clocks and it is very real.
2. On the surface of the earth your clock is also slowed by the exact same factor of γ = 1.00000000067315. This is GR time dilation, due to gravity. This is also experienced by GPS clocks and it is a real effect.

No.2 has nothing to do with velocity. It is an effect of gravity.
But here comes the clincher: Escape velocity on the surface of the earth is 11km/sec.

Now we know with certainty that everone on the surface of a round earth is not diverging at 11km/s from the centre. (although there are some 'growing earth theories)
And we can reasonable conclude that space is not falling into earth at 11km/s.
(although there are 'space as a river' model theories)

Yet somehow gravity is very closely related to velocity. How is this?

While I'm rambling, and apologies in advance.
Another way of thinking of escape velocity - if you take a mass infinitely far away from earth and release it, and by extension give the earth an infinite amount of time to accelerate it, earth will only accelerate it to 11km/s. No more.

This is not a rare coincidence. I quoted earth figures, but it applies to all.
Grief - now this sounds like an advert :)

[HanDeBruijn]

@Francois-Zinserling .

No.2 has nothing to do with velocity. It is an effect of gravity.

On the contrary, No.2 has everything to do with No.1. Because gravity potential is linked to escape velocity $v_e$ via kinetic energy:

$$ \frac{GMm}{R_e} = \frac{1}{2}mv_e^2 \quad \Longrightarrow \quad v_e^2 = \frac{2GM}{R_e} $$

where $R_e$ is e.g the earth's radius, $M$ its mass and $G=$ gravitational constant. The corresponding SR/GR dilated time is

$$ t' = \frac{t}{\gamma} = \frac{t}{\sqrt{1-(v_e/c)^2}} = \frac{t}{\sqrt{1-2GM/(R_e c^2)}} $$

The latter is precisely the formula for time dilation as found in Gravitational redshift for a Spherically symmetric gravitational field.

[Francois-Zinserling]

@HanDeBruijn I think that's pretty much what I said above, or at least intended to.
You said it nicer though. I need to practice my equations so I can also roll them out like you do!

But then you'll have to explain to me how a clock in gravity would know what its escape velocity is. Yes, yes, I know, it 'feels' the gravitational potential. Not good enough though. What is it feeling?

Let me throw a curve-ball. And I'm going to reach far with this one. Hear me out.
If you were to jump off a cliff into a pool below, and then later out of a high hot-air balloon into the same pool, (and let's ignore friction, because we can) your velocity when you reach the water will be higher and higher, as you jump from a higher point each time. Basic stuff, yes. But your velocity will never be as high as the escape velocity. (I say never, because it will take you forever to go infinitely far, and then return as well. (Like There and back again, by Billbo Baggins) :)

But let's say you can go that far, and come back again. Then, for your entire journey to the surface of the earth, you are travelling at the escape velocity as it would be at each point in your approach. Yes, it's already in your equation in the $R_e$ component. It works from any radius, not just from the surface.

Then, by this long reach of mine - what if gravity is just an attempt of space to accelerate us to the (minus value of) local escape velocity. In the case above gravity had infinite time to do it in so actually gets it right. But you are never infinitely far away, so cannot reach escape velocity because you will always crash before you do, and you also cannot reach it instantly because, well, mass is a resistance to acceleration, and acceleration takes time.

In other words - gravity is a 'velocity push' downward, which only appears to us like a force, because there is a $dv/dt$, an acceleration that ensues.
Then we can say a clock can 'feel' that velocity, as if it were at the same SR velocity in open space.

Am I saying space is flowing into earth at $V_e$? No, others do but I don't. I maintain; If space is energy (with zero mass) then it must move at c.

Just a note that this is not some quackery or pseudoscience I'm selling. Mansuripur and Pfeiffer (independent from each other) derived that a beam of photons do not exert a continuous force on glass while it travels through, but a stream of photons will try to accelerate the glass up to a fixed (low, limited, << c) velocity.

[budrap00]

@Francois-Zinserling

I maintain; If space is energy (with zero mass) then it must move at c.

Energy with zero mass moving at c is a good definition of electromagnetic radiation. So, you've discovered for yourself that what everybody calls space is just all the ambient electromagnetic radiation moving between massive bodies. That's what's there. That's what we observe. Unfortunately modern theoretical physicists don't care about what's there. They're much more interested in things that aren't there like dark matter, etc.

There's a bit of an elaboration on this point here.

[Francois-Zinserling]

@budrap00 I agree with your conclusion (on the link), as to the curving of light around large masses. On the other hand, once we can show that 'space' is electromagnetic, then we can answer to both sides - GR and Electrodynamics.

Some points to consider though

• Gravity cannot be a direct result of electromagnetic radiation: (and hereby I mean EM as spin=1 photons)

1. EM radiation does not have enough penetration into matter, and e.g. most of it will be absorbed in the surface of an object. Even X-Rays have limited penetration, and at even higher energies the collisions would be catastrophic and very visible. If gravity were to be of pure EM origin, it's force effect would drop off rapidly underground.
2. A very very low frequency has some promise, but just not enough energy to actually cause what we know as gravity. Also, gravity is very predictable, and varying frequencies of photon energies would cause measurable fluctuations in gravity, e.g. it should be noticeably different during day or night.
3. An EM wave can only push - as far as I know. I know of no mechanism where a single wave exerts a pull, as if a photon can transfer negative momentum. Then by extension 'primordial' gravity as a pure EM wave cannot be emitted by e.g. the sun, or even earth, as we would be pushed away, and not attracted.

This does not mean that I think EM waves are not involved in gravity, but the properties would have to be different. I propose the primordial aether to be such 'different' waves, as others e.g. Arto Anilla, Wolfgang Bentz, Rueda and Haisch, and Matt Edwards have already proposed for the ZPF or the Quantum Vacuum. (why can't I link Matt?) @ExpEarth?
One relatively simple solution may be 'coupled photons' - 2 photons with same vector but out of phase - which present as a spin=2 photon-like particle but appears to have 0 energy. Because the waves interfere destructively, the coupled pair does not interact as EM, but can travel right through mass, unless it actually collides with a particle of mass at which point it disassembles into 2 x spin =1 electromagnetic waves. In the 'empty space of an atom' scenario, vast majority of these pairs go right through matter, and we have the makings for the mechanics of gravity.

[budrap00]

@Francois-Zinserling

... once we can show that 'space' is electromagnetic...

There is no evidence, to the best of my knowledge, showing that 'space' is anything but EMR. That claim is based strictly on observations. The onus of demonstrating the existence of an independently existing 'space' falls solely on those who believe it exists. Non-believers do not have to demonstrate space's non-existence.

I agree that EMR by itself cannot account for all gravitational effects but I think it is likely that all gravitational effects can be explained by various aspects of EMR-matter interactions. For one example we both agree on the radiation density gradient account of gravitational behavior in the vicinity of a gravitating body.

On a cosmological scale it is possible to account for the cosmological redshift of a galaxy by simply calculating the gravitational redshift for an expanding spherical wavefront of light emitted by a galaxy using a mass term calculated from a realistic value of mass-density for the Cosmos. Repeated calculations at increasingly larger radial distances will yield a redshift-distance correlation. An elaboration can be found here.

[budrap00]

@RedshiftDrift

I agree with much of what you say here but there are a couple of points on which our views diverge.

...time is certainly not what a clock displays.

That is only true if you think that there must be a universally constant "true" time that exists independently of the local conditions. As your discussion and examples illustrate, there ain't no such animal, at least not in empirical reality. That "universal time" exists in the same place as perfect geometric shapes, the universally constant speed of light, and the unitary Universe concept that underlies modern cosmology. Those are all theoretical ideas that exist only in the minds of those who choose to believe in them; they have no correlates in physical reality.

The error is to confuse the container with the content.

I would say that the container concept is the error. There is no evidence for it; there seems only to be a philosophical disposition that the Cosmos has (or is) a container. Container also implies a boundary condition. It seems more logically consistent with everything we now know about the Cosmos to think of it as unbound (container-less) content the extent of which is inherently unknowable due to known physical constraints, not technological limitations..

It is not that GR describes objects moving within a universe - it does not describe a universe at all. It only describes the behavior of objects relative to each other. The existence of a Universe is irrelevant to GR. The FLRW mistake was to impose a universal metric on GR. The results of that misbegotten effort, I think we agree, speak for themselves.

@Francois-Zinserling

There are no paradoxes in Relativity Theory as long as you are clear about the distinction between SR and GR. SR was Einstein's initial foray into developing his theory and it hinges on a simplifying assumption - the absence of gravity and acceleration called an inertial state. True inertial conditions do not exist in physical reality but there are near or approximate inertial conditions where SR based calculations can be used. Here is where a lot of confusion arises:

In the SR thought experiment with two inertial observers moving with some relative velocity to each other, each observer sees the other's clock running slower but, and this is the key point, neither clock is running slower than the other. In each inertial frame the remote clock appears to run slower but that is a point-of-view consequence of SR not a physical consequence of their relative velocity.

The GR situation is completely different. In a gravitational field, observers at a lower potential in the field will observe their clock to be running slower than a clock at a higher potential. Observers at the higher potential will also observe the clock at the lower potential to be running at a slower rate than their own. In the GR case there is a real physical effect (gravity) causing a real physical time dilation that observers in both frames agree on. This is because the observers are in two physically different frames which the observers can also agree on.

So under SR (inertial) conditions there is no physical time dilation only apparent (POV) time dilation and therefore there is no paradox that needs to be resolved. Under GR (non-inertial) conditions time dilation is a real physical effect and there is also no paradox.

Yet somehow gravity is very closely related to velocity.

It is acceleration (a change in velocity) and gravity that are closely related - they are both GR conditions. Constant velocity is an SR state.

[genotics]

A truly stimulating discussion, and reminiscent of the countless articles and books of criticism of SR that have appeared since Dingle, and even before. There is much that I would agree with here, but I will spare you my ignorant ruminations and proffer instead a note from the late Thomas E. Phipps Jr which he sent me years ago. It has not been published as far as I know. In my view, the LT may be physics, but SR is not.

The Lorentz Transformation is not Physics
Like the inhabitants of Laputa (the subjects of Lemuel Gulliver’s third voyage), today’s academic physicists are highly proficient in mathematics and possibly in music, but not in physics. They not only make a basic mistake at the start of their studies, but make it in unison, parrot-fashion, in the lock-step manner of GPS clocks.
I am aware that such an introductory remark is no way to win hearts and minds. But I am also aware of being immensely old and immensely tired of fruitless repetitions of the lesson I shall here attempt one last time to teach. The lesson comes in two stages. About the first stage there will be no controversy. This simply notes that the time part of the Lorentz transformation (LT) of special relativity theory (SRT) asserts an explicit symmetry between any two inertial systems. That is, if systems A and B are in uniform relative motion, and a clock initially at rest in A is moved into a state of rest in B, then that moved clock runs slower in B than it did in A. Similarly, the inverse LT shows that if A and B are interchanged in the foregoing proposition, then a clock initially at rest in B, when moved to rest in A, will run slower in A than it did in B. These propositions are purely kinematic. That is, no inquiry is made or allowed into how the clocks were transferred, whether energy was gained or lost by the clocks during transfer, etc. In other words, physics is deliberately excluded from the analysis. We are required to prejudge the physics to be irrelevant by our basic terms of reference, defined by the very nature of SRT. The LT calls for timekeeping symmetry and allows no doubt about it (whence, from the earliest days, the notorious twin “paradox”).
The second stage of discussion addresses the real world. Consider, for instance, the timekeeping of the Global Positioning System (GPS). If A is the earth’s surface system and B is a (relatively) moving earth satellite, simplified by neglect of the gravity difference, then we know for a physical fact that an uncorrected (proper-time) clock initially at rest in A and moved to rest in B will run slower in B than it did in A. To compensate for this, the actual GPS protocol speeds up the clock it intends to put in orbit by just the amount of slowing specified by the LT. This causes all clocks, both in A and B, to run in step and to register the same “time.” That is an important point, because it shows that the relativity of simultaneity is an artefact of human choice; namely the choice to leave all clocks permanently uncorrected, so that they always show only their own proper times. That is Einstein’s choice. It has nothing to do with physics, but is a perfectly general and invariable (hidden) assumption of SRT. It was not the choice of the GPS engineers, bless them!
So, is the symmetrical inverse proposition realized in the GPS example? The question is, is a slow-running (uncorrected) proper-time clock at rest in B (that has previously been transferred from A) going to run still slower when transferred back to A? If it does so, it must show a sort of timekeeping “hysteresis,” such that with repeated transfers back and forth between A and B the moved proper-time clock runs slower and slower. Such hysteresis is non-physical. What happens is that when transferred back from B to A the proper-time clock that was slowed by the opposite transfer is speeded back up, so that when once again at rest in A it runs at the same rate as all other clocks at rest in A, the ones that were not transferred. Don’t take my word for it – think about it.
But that implies a basic physical asymmetry among inertial systems. For the back-transfer speeding-up of the moved clock is asymmetrical with the forward-transfer slowing down of the same clock. Is it not so? I know the reader has been filled to the brim with complacency on this issue by the experts who tell him [him? Goodness, what has happened to my political correctness?] quite rightly that Einstein’s formulas have been used for the GPS corrections, so go back to sleep. But the fact is we have stumbled upon a direct physical contradiction of the LT timekeeping symmetry claim. That is fatal to the survival of any theory … for a symmetry error is structural, therefore ineradicable. No worse error can a physical theorist make.
In appraising the GPS the parrots all reproduce the same howler: they focus on the fact that special and general relativity give the right clock-correction formulas, but they overlook entirely that the resulting GPS time refutes the relativity of simultaneity and in fact constitutes a return to Newton’s time, the time that defines an unambiguous “now” throughout the universe. It does this by simply not playing by Einstein’s (hidden) rule, that clock running rates are sacrosanct products of Mother Nature, which must never be messed with by human intervention. If Einstein were developing thermodynamics in the same spirit, he would forbid thermometer corrections, thereby making a dog’s breakfast of that discipline.
It is worth concluding with a look at the specifics of clock-rate correction in the GPS. This is a real part of the physics. While the clock to be put in orbit is still at rest on the earth’s surface, the “second” of “time” is redefined from n oscillations of the cesium clock to n’, where n’<n. Consequently a real (objective) physical slowing of clock running rate in orbit is prevented by a real setting adjustment of the counter accompanying the clock (to shorten the “second,” so that more “seconds” occur in any given lapse of proper time). As a result of this prior adjustment, the slowing in orbit is compensated by a clock speeding-up and thus time-slowing in B is avoided (“time” being what is measured by “seconds”). A little reflection will show the objective asymmetry of this procedure between surface and orbiting systems, viewed as a pair of inertial systems in relative motion. There is never any concern with “appearance,” the crowd-pleaser in many twin paradox pseudo-analyses.
We have to consider the specifics of the clock transfer, the work done on the clock. Only by bringing in that physical aspect can we begin to recognize where Einstein went astray in supposing that physics could be finessed in favor of kinematics. The two inertial systems, A and B, are not symmetrical; but the difference is subtle. It would have to be, since it means the relativity principle is not quite right. The difference can never be discerned by observations confined strictly to one or the other of the individual systems. The systems are distinguishable only by the (different) energetics through which their states of motion are attained. Oddly enough, that subtle distinction is enough to affect timekeeping within the systems in verifiable ways. My conclusion: the Lorentz transformation is not physics because it has the wrong symmetry properties.
I am well aware of the havoc this wrecks. It means that SRT fails, which means that general relativity (whereof SRT is the flat-space limit) fails, which means that the whole of modern cosmology fails, which means that for a half-century physicists have piled cloud castles of conjecture upon cloud castles of speculation, all balanced on a pinpoint of assumed solidity that was never solid. Surely this is an indictment of a profession. Being that as it may, one would hope at least for a widespread learning experience, preferably leading to a new-found dash of professional humility, as well as a bit broader recognition that all science is tentative … and profits from being kept that way.
Thomas E. Phipps
2210 CR 0E, Mahomet, IL 61853
tephipps137@gmail.com

[Francois-Zinserling]

@genotics I think there might be a mismatch in the proposed properties of A and B by Phipps, or maybe I tried to read too fast, but the main point is taken.

It seems for all of us the discrepancies arise in SR, not so much GR (if we can agree about A and B)

However, the GPS corrections are real, not just GR corrections, but also SR corrections. We also have an ISS, with observers on board.
To further illustrate this point, the ISS clocks are adjusted to be in sync (1) with earth clocks, and corrections match calculations, as they do for GPS clocks, with a GR and SR component. But for the astronauts on the ISS, they agree to the GR correction, but according to SR they should see earth clocks slowed due to our relative velocity. This is not the case, and no further corrections are needed to remain synced (as per 1) from them or from earth. That is simply explained because they are moving, and we are not.
This confirms:
A clock in a gravity well is slowed. This is agreed by all clocks
A clock in motion will be slowed. A stationary clock is unaffected. According to SR the clocks do not agree on who is moving, but ISS shows that at least a part of SR is incorrect because a moving clock can be synced with a stationary clock.

Then we have to acknowledge that all our clocks are already skewed by our local gravity and our velocity through space. Problem is, we don't know what our gamma is, and M&M have shown it is not possible to measure it. <- This is not a proof of non-existence though. It's merely a failure to measure. So we carry on and set our own gamma = 1.

@RedshiftDrift part of my next answer was presented by @budrap00 above, and I also don't think the answer to SR lies in the acceleration.
Let's say it is correct that the clock slows during the acceleration, and then remains slowed there-after during constant velocity. Being in a 'new' frame of reference, the next acceleration must slow the clock again, but what if it is a deceleration back to the initial frame? It's still an acceleration from the new frame, but a deceleration from the old frame, so what must the clock do? See the problem here? By rules the clock must keep on slowing down. (Yes, this was already said above, but I think this is crucial to rule out acceleration from SR)

[budrap00]

@genotics

I'm curious what you mean when you say SR is not physics. Could you elaborate? Thanks.

[HanDeBruijn]

The accuracy of atomic clocks makes them so sensitive to the environment it becomes an experimental nightmare.

Precisely! And why? Because the errors involved have become larger with every "improvement" of the clocks.
Time is assumed to be continuous. Right?
Then take a look - I mean a good look - at the mathematical definition of a Continuous function.

Let everything be real valued in: A function $f(x)$ is continuous in $a$ if and only if
for all $\epsilon\gt 0$ there exists $\delta\gt 0$ such that for $|x-a|\lt\delta$ it follows that $|f(x)-f(a)|\lt\epsilon$.

Now what is the physical meaning of $\delta$ and $\epsilon$ for an experimentalist? Think about it. $\delta$ and $\epsilon$ are (the idealizations of) errors, yes: errors.
Mathematicians are continuously trying to make everything "exact", meaning that they don't want anything to be like an error. They get rid of those things they don't want by declaring errors non-existent, zero to be precise, using the verb "for all". But, unfortunately, nobody knows what for all means. And errors seem anyway to be inevitable in a continuous context.

Okay, so here is, after some further thought, our bold statement: Continuity is (empirically) DEFINED by errors.

No joking. There are plenty physical examples that confirm this.
For example, a fluid consists of molecules. But if you consider large enough (erroneous) volumes in a fluid then you don't "see" the molecules anymore. What we have then is continuization of the discrete. The (Navier-Stokes) equations of Fluid Mechanics are based upon that continuous description. I have encountered a more extreme, but still very realistic example from my own engineering practice: the Fluid-Tube Continuuum.

A further consequence of the above is Brouwer's Continuity Theorem. For an experimentalist this Theorem is actually easy to understand. Because $|x-a|\lt\delta$ is empirically the same as $x\approx a$ and $|f(x)-f(a)|\lt\epsilon$ is empirically the same as $f(x)\approx f(a)$. And so, when idealized: continuous means that $[x=a] \mbox{ } \Rightarrow \mbox{ } [f(x)=f(a)]$ , which in turn simply means that $f(x)$ is a function. Grossly speaking: in a real valued context every function is continuous.

For the experimentalist, everything you do to the clock changes its rate, therefore, time is certainly not what a clock displays.

Have people ever thought of the following. Maybe (y)our atomic clocks simply have become too accurate for comfort.
Anyway, there is an absolute bound on the accuracy of atomic clocks. It is given by the Compton time, as follows.
Let $h = 6.62607015\times 10^{−34}\mbox{ }J.s$ , $m_e=9.1093837\times 10^{-31}\mbox{ }kg$ , $c=299 792 458\mbox{ }m/s$ . Then:

$$ \mbox{error} \gt \frac{h}{m_ec^2} = 0.8(093299794) \times 10^{-20} \mbox{ } s $$

Motivation is found in The Limited Validity of Special Relativity ; Albert Einstein's Gedanken-Experimente reexamined for small masses. At present, we are only a few orders of magnitude remote from this ultimate limit !!

And if time is certainly not what a clock displays, then what is it? Something very metaphysical perhaps?

[budrap00]

@HanDeBruijn

And if time is certainly not what a clock displays, then what is it?

Time is a relational concept that humans employ when discussing the behavior of observable objects and events. In that regard it is just like the concept of distance but whereas there is no ontological angst with regard to the nature of distance there is a great deal of confusion about the nature of time (and space). For this we can thank the same mid-20th century mathematicists who also gave us a fictitious, universally constant, light speed. Wheeler's empirically baseless aphorism regarding the causal interaction between spacetime and matter and energy is at the root of the confusion.

Nobody wonders how distance manages to keep things separated but thanks to Wheeler and his cohort we are left with the queasy notion that something that cannot be directly observed or detected (spacetime) can nonetheless affect the behavior of observable objects and events.

If you simply discard Wheeler's quaint aphorism as unscientific nonsense you can revert to viewing spacetime in the same way you do distance and temperature - as ways of describing the behavior of observable entities and events - as relational concepts. As long as you do not attempt to reify those relational concepts into substantival entities there is no ontological problem. And if you don't reify it, the answer to the question, what is time?, is straightforward. It is a relational concept used to describe the behavior of objects and events.

WRT your broader point it seems that you are saying in mathematical terms what I see in physical terms - that physical reality does not conform to idealistic human concepts (Platonism) and the relentless pursuit of (or belief in) the perfect in modern theoretical physics is the enemy of scientific advancement. For instance, the notion of dark matter and dark energy arises from the belief that we possess universally applicable laws (Newton-Einstein) of gravity so any discrepancy between observations and predictions of the laws is the fault of reality, not our perfect laws.

[HanDeBruijn]

@budrap00 .

MATHEMATICS (Stack Exchange), MSE for short, is a worldwide forum consisting of over 1,000,000 participants.
Unfortunately, many of them are sitting there waiting to get cheap answers to their homework questions.
Unfortunately, many of the more skilled members are gaining cheap reputation by answering those questions.
Unfortunately, there is a sort of Dark Matter present in Mainstream Mathematics as well. It's called Set Theory.
The forum is an Questions & Answers site. This means that one cannot promote ideas directly.
Ideas can only be advertized by "abusing" a question and eventually answering this question yourself.
Here is a list of such questions and what I really wanted to say by posting them: the hidden messages.

• Propositional Logic and Redundancy
  Mathematical logic is highly redundant, because it is combinatorial instead of sequential. This causes a mismatch with common language.
• Non-Euclidean Geometrical Algebra for Real times Real?
  Non-Euclidean Geometry is always embedded in Euclidean Geometry; even elementary algebra is impossible without classical geometry.
• Additive functions and measure theory
  Measure theory by Lebesgue is pure mathematism. There are no other addditive functions than linear ones: $f(x)=c.x$ .
• Is any real-valued function in physics somehow continuous?
  All real-valued functions in physics are continuous everywhere. They are simply not a function where they are discontinuous.
• Uniform Probability and Riemann Sum
  Uniform Probability does not exist in mainstream mathematics, while it is easy and highly practical to define it.
• Is this serious mathematics?
  Question renamed by moderation (i.e. censorship): Can $f(\infty)$ be defined if the sequence $f(n)$ is divergent?
• Double Think about Numerosity
  Actual Infinity is nonsense; there is only Potential Infinity in the real world.
• Leibniz' Law and that good old riddle
  There is no exact equality in reality. Absolute rigor is a phantom.
• Why does Group Theory not come in here?
  Group Theory is much less powerful than is claimed in some circles (e.g. Particle Physics)
• Iterated Limits Schizophrenia
• Commutativity of iterated limits
  The hidden message is that iterated limits are always commutative.
• Cauchy distribution instead of Coulomb law?
  It does no harm to physics if Coulomb's law is replaced by a function that approximates it without a singularity at the origin.
• How about Cantor's Theory in a Finite context?
  This question was removed from Mathematics Stack Exchange for reasons of moderation.
  Okay, I know which high reputation guy is responsible for this.

Mathematics is general. So general that most of it applies, if at all, only to mathematics.

[genotics]

Hello Bud, Thank you for your question. Actually, if you wish to learn why Tom Phipps felt that the LT was not physics you need only read the essay I appended to the post. Myriads of physicists have rejected SR for various reasons, from before the time of Dingle. I cannot count the number of critiques of SR that were published in Apeiron alone. Phipps preferred to replace Maxwell with what he called neo-Hertzian equations. My own simple view of the SR controversy, which may be shared by others, is that it was stillborn and no theory at all--or rather 2 theories, each of which could be adopted according to taste. In the 1905 paper , section 4, a contradiction appears which has left physics in a confused state ever since. Bodies and rods and clocks in motion relative to an observer are described with the terms "viewed from the stationary system", "X dimension appears shortened", "moving objects—viewed from the “stationary” system"; or conversely, " bodies at rest in the “stationary” system, viewed from a system in uniform motion"; and further, "rate of this clock, when viewed from the stationary system", "time marked by the clock (viewed in the stationary system) is slow", all of which is quite reciprocal, as there is no distinction between a moving and stationary system in terms of the results: viewed from one system, the rods and clocks in the other appear shorter or slower. There is no absolute frame. But in the next paragraph Einstein changes his stripes, abandoning the reciprocity: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B... It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide." In my view, no amount of prestidigitation can reconcile the first part with the second part. Yet an entire edifice of physics has been raised on this contradiction. Cheers, Roy

[budrap00]

Hi Roy,

I will admit that Einstein was remiss in not explaining the outcome of the second paragraph. Nonetheless it is easily explicable in relativistic terms. Einstein didn't abandon reciprocity in the second case, he abandoned the SR framework by introducing an acceleration and that acceleration introduces a physical slowing of the moved clock as specified by GR. There is no contradiction and no inconsistency of results unless you fail to account for the non-SR piece of the experiment.

The misuse of SR as a general model for physical reality (due to the so-called Einstein Equivalence Principle) has been a disaster for modern physics. Historically, the analytical development of RT was deliberately restricted to inertial conditions as a way of forming a baseline for subsequent elaboration to GR. While SR math can be useful to a first approximation in low acceleration/gravity systems it is always a mistake to use it as an analytical tool in the real world because gravity and acceleration are always present. It is in that sense that I would agree that SR is not appropriate for doing real physics.

[genotics]

Good day Bud, Methinks appealing to GR to save SR's skin is akin to playing with a loaded deck. As far as I am aware, Einstein did not begin discussing accelerated motion until several years after the 1905 paper: the first I can recall was 1911, but I don't think it involved an attempt to salvage the confusion wrought by the faulty logic of 1905. Of course you may say that the LT is supported by experiment, but that is not vindication for SR in my book. Here's a snippet from a note I wrote to myself 30 odd years ago: "Einstein states that his method is simply a technique for solving problems in the optics of moving bodies, which consists in eliminating the inconveniences introduced by moving bodies by reformulating the problem so that it can be solved with standard methods. This is achieved by arbitrarily normalizing the speed of light to c in all frames, which has the effect of transforming the forces into a system of coordinates which is at rest relative to a moving body. An analogous situation exists in the field of aerodynamics, and it will be instructive to compare the experiences in the two fields. In the early decades of this century, the discipline of aerodynamics was reaching maturity. By around 1920, the problem of supersonic flight was being addressed, at least in theory, by engineers working in Germany. At speeds approaching the velocity of sound, the compressibility of air causes significant increases of drag and unstable flow in straight airfoil designs. Standard methods of calculating the properties of foils that would provide the right properties of lift broke down near the speed of sound, so a method was sought for dealing with the problem of compressibility. The resulting method consists in applying a factor, known as the Prandtl-Glauert Transformation, to the chord of the wing. This factor was originally derived by Prandtl in 1918 (apparently), and it is defined as the root of [1-(mainstream velocity/velocity of sound in mainstream)^2], or root(1-M^2), M being the Mach number. The factor is applied to a wing in order to calculate a flow pattern in a compressible gas by assuming a wing of larger chord in an incompressible gas. (Jones 1990, Hilton 1951) The effect of the Prandtl-Glauert transformation is thus exactly the same as the Lorentz factor. In the terminology of relativity, a wing travelling near the speed of sound "sees" the air through which it travels "contracted" due to its velocity. Since it was first introduced, the technique has been refined further; the chief result of the refinement is that it "circumvents the real problem and reduces the calculation of compressible flow to that of incompressible flow." Perhaps special relativity kinematics, where "all problems in the optics of moving bodies [are] reduced to a series of problems in the optics of stationary bodies", could benefit from some of the the progress made in aerodynamic theory. While Einstein relativists are convinced that the symmetric effects (time dilation, length contraction) inherent in the Lorentz transformation are proved by asymmetric effects due to non-kinematical causes, aerodynamics engineers have apparently also been tempted to draw "relativistic" conclusions from the Prandtl- Glauert transformation. One writer warns his readers thus: "This concept of compressibility factors has proved so powerful that we tend to think in these terms as though they expressed some physical quality of these flows. Thus, rather too easily, we tend to regard pressure distributions in compressible flow as scaled-up or stretched versions of those in incompressible flow." A similar admonition should perhaps be affixed to the Lorentz transformation...." References Petr Beckmann, 1987. Einstein Plus One, Boulder, Colo., Golem Press. Howard C. Hayden, 1990. Experimentum crucis, in Galilean Electrodynamics, Vol. 1, No. 1, Jan 1990. Howard C. Hayden, 1991. Yes, moving clocks run slowly, but is time dilated?, in Galilean Electrodynamics, Vol. 2, No. 4, July/August 1991. Howard C. Hayden, 1992. Distinctions between Galilean and Einsteinian physics, in Galilean Electrodynamics, Vol. 3, No. 2, March/April 1992. Robert T. Jones, Wing Theory, Princeton, 1990. W. F. Hilton, High Speed Aerodynamics, NY, Longmans, 1951. D. Kuechemann, The Aerodynamic Design of Aircraft, Oxford, Pergamon, 1978." On the kinship between hydrodynamics and electrodynamics, see this excerpt from "Fundamentals of hydro- and aeromechanics" by Tietjens based on the lectures of Prandtl: "The analogy between velocity fields of vortex filaments and magnetic fields produced by electric currents is so great that many theorems and examples in electrodynamics can be applied directly to hydrodynamics by simply replacing electric currents by vortex filaments and magnetic fields by velocity distributions." ... "...the contribution of this element is perpendicular to ds and a, is Tr proportional to the sine of the angle between ds and a, and is inversely proportional to the square of the distance a from the point in question. This however is exactly the law of Biot and Savart in electrodynamics from which the magnetic field in the neighborhood of a current-carrying wire can be calculated." My late friend Adolphe Martin developed a theory of a gaseous ether to account for the forces and the structure of elementary particles.

[budrap00]

Hello Roy,

...Einstein relativists are convinced that the symmetric effects (time dilation, length contraction) inherent in the Lorentz transformation are proved by asymmetric effects due to non-kinematical causes...

As an Einstein relativist, as opposed to a Dicke-Wheeler relativist, I have to say that you are mischaracterizing my view on this particular matter. There is no issue of "proof" involved, only of logical consistency. All I am pointing out is that this type of thought experiment which allegedly demonstrates some logical flaw or inconsistency in SR rests on a witting or unwitting failure to properly account for non-inertial events when they are introduced into the experiment.

GR does not in any sense bail out SR; GR is a completion of SR. If you do a thought experiment to test SR and introduce non-inertial events into that experiment while clinging to an SR-only analysis the results will be inconsistent with SR based expectations. In that case the flaw lies entirely with the logical inconsistency of the analysis - not with SR.

If Einstein didn't invoke GR in his 1905 analysis that is understandable given that Relativity Theory was in its early stages of development. Quibbling with that failure to anticipate future developments seems trivial and pointless. At this point in time, deliberately not invoking the completed version of RT (GR with SR as a limiting case) when the imagined scenario implies the necessity of doing so, seems logically inexcusable to me. As an effort to 'disprove' SR it cannot be considered very convincing simply because of its logical inconsistency.

[genotics]

Hi Bud, Thank you for your further thoughts on the SR issue. I'm sorry to have to tell you that I am not convinced that invoking GR to prove SR, especially in thought experiments as opposed to actual empirical tests, represents a departure from the way I feel science should work. Though the discussion probably lies outside the scope of the CG terms, I will simply venture this definition from Wikipedia. "[SR] is presented as being based on just two postulates <https://en.wikipedia.org/wiki/Postulates_of_special_relativity>:[p 1] <https://en.wikipedia.org/wiki/Special_relativity#cite_note-electro-1>[1] <https://en.wikipedia.org/wiki/Special_relativity#cite_note-Griffiths-2013-2> [2] <https://en.wikipedia.org/wiki/Special_relativity#cite_note-Jackson-1999-3> 1. The laws of physics <https://en.wikipedia.org/wiki/Laws_of_physics> are invariant <https://en.wikipedia.org/wiki/Invariant_(physics)> (identical) in all inertial frames of reference <https://en.wikipedia.org/wiki/Inertial_frame_of_reference> (that is, frames of reference <https://en.wikipedia.org/wiki/Frame_of_reference> with no acceleration <https://en.wikipedia.org/wiki/Acceleration>). 2. The speed of light <https://en.wikipedia.org/wiki/Speed_of_light> in vacuum <https://en.wikipedia.org/wiki/Vacuum> is the same for all observers, regardless of the motion of light source or observer." Regards, Roy

[sahil5d]

The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively.
The term "theory of relativity" was based on the expression "relative theory" (German: Relativtheorie) used in 1906 by Planck, who emphasized how the theory uses the principle of relativity.
https://en.wikipedia.org/wiki/Theory_of_relativity

'Relativity Theory' is a set containing 'Special Relativity' and 'General Relativity', each of which has a dependency on the 'principle of relativity'. The way you write about them, it's as if they're not connected to each other and then you blast me for calling a spade a spade. That is absurdity.

The half-assed story of "stretching and shrinking space" has nothing to do with Einstein's RT.

It does have to do with it. See SR addition of velocities, https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity. This is a special formula that distorts lengths between objects for the illusion that every particle has a particle-centric reference frame where its speed is 0 and photons move at c wrt to it. That is a Ptolemaic model of the particle, a model of schizophrenic reference frames, stretching and shrinking lengths, and stars revolving around planets.

Do you still think SR is physics? Does the Milky Way revolve around the Sun?

[HanDeBruijn]

@budrap00 replying to @sahil5d :

It suggests you don't know this subject very well.

I find this one and further remarks in your discussion with Sahil close to personal attacks.
It is certainly not up to you to throw doubt on the competence of someone else in this group.
As a participant in this discussion, I would like to rise a red flag, but can't find anything appropriate.
So instead, Bud, please show some restraint and read ACG's code of conduct, especially the first few lines:

• Demonstrating empathy and kindness toward other people
• Being respectful of differing opinions, viewpoints, and experiences
• Giving and gracefully accepting constructive feedback
• Accepting responsibility and apologizing to those affected by our mistakes, and learning from the experience
• Focusing on what is best not just for us as individuals, but for the overall community

[budrap00]

Hi Han,

Yes, of course, you are right. I understand the need for such rules and apologize to you and the rest of the community, including Sahil. To prevent any further outbreaks of incivility, I will return to my previous policy of not engaging with Sahil's remarks. Thanks for bringing this up.

Peace,
Bud

[HanDeBruijn]

@sahil5d writes:

Huh?? The literal quote is "Could we build a real relativistic physics valid in all CS; a physics in which there would be no place for absolute, but only for relative, motion?"

To begin with, a better name for a CS is Reference Frame (RF). According to Léon Brillouin in Relativity Reexamined the difference is that Coordinate Systems are weightless, while Reference Frames are "heavy laboratories". On page 45 we read: Let us sum up : A frame of reference does not constitute a piece of unreal geometry anymore; it is a heavy laboratory, built on a rigid body of tremendous mass, as compared to masses in motion. The confusion between CS and RF is one of the further problems with SR and GR.

Second, it is suggested that the "true" laws of physics should be independent of any Coordinate System / Reference Frame.
Even classical physics is infected by this False Framing (pun intended). An example is the Wikipedia page about Rotating reference frames, where it is stated that All non-inertial reference frames exhibit fictitious forces. I beg to differ ! The forces on a rotating earth are not at all "fictitious". They are very real. They can be felt. For example weather systems are unthinkable without these forces. If there is different physics in different reference frames, who cares? Kinematics has always been an integral part of physics. The idea of a real relativistic physics valid in all CS is nonsense.

Note.

It is not widely known that Lorentz Transformations (LT) are "hyperbolic rotations", as is explained in the first few lines of Relativity Special at my website. In contrast with others, I have no problems with the incorporation of some abstract mathematics in physics, but in this case I find one detail worrysome: how the LT relates to a given velocity $v$ via

$$ \tanh(p) = \frac{v}{c} \quad \mbox{where} \quad p = \mbox{hyperbolic angle} $$

Referring once again to Relativity Reexamined, on page 4: For the moment, let us concentrate on the word " given." What do we mean by a given velocity? Who is giving us this velocity, and how? I become very suspicious whenever I hear the word " given."

[budrap00]

@HanDeBruijn
The ludicrous naming of a real physical effect like Coriolis force as "fictitious" while purely fictitious dark matter is treated as "real" is another example of how daft modern theoretical physics has become. In this case the proclivity for reifying relational concepts into physical things is most likely the culprit. The term force describes an effect not a cause.

A golf club is not a force but it can exert a force on a golf ball. Modern science has defined four fundamental forces, electromagnetic, gravitational, weak and strong. Of those only electromagnetic radiation and charged particles can be said to exist in the way that a golf club exists - not as forces but as physical phenomena that can exert a force on other physical phenomena. The other three fundamental forces are fictitious. They essentially attribute an observed effect to a "force" without describing the mechanism by which the "force" is actually exerted.

[genotics]

Good day Bud and Sahil, I confess that, having trod this ground in the past, my expectations of any consensus emerging here are rather thin. Nor do I particularly relish a protracted discussion that leads nowhere. There is a long history of debate about the empirical evidence for SR, and disputes over its internal consistency are likewise nothing new. I concede that some evidence may be interpreted to support the LT, but generally only if the second postulate is conveniently ignored, such that evidence for SR is wholly lacking. The reason I referenced the two postulates is to remind that one cannot be claimed without the other. As you point out, "second postulate only holds under the first postulate which in turn, only applies to inertial frames." Yet you and others invoke non-inertial frames to retro-validate the clock paradox. The framing of the so-called clock paradox--the legacy of Einstein's "peculiar consequence"--and its evolution into the "twins" paradox, has long been a dominant focus of debate and the subject of varied attempts at solution, some resorting to accelerations, some not. Hence it is surprising that criticism of what I and many others have viewed as a fatal logical contradiction in the framing of SR and its widely accepted meaning should be trivialized as a "general aesthetic dissatisfaction." Rather than try to convince, I will recommend some light reading. For empirical evidence against SR--or for light entertainment--the curious may consult this essay by Hector Munera: < http://redshift.vif.com/JournalFiles/V20NO4PDF/HORS-20-MUN.pdf>. For a more serious critique of the contradiction/paradox of SR, interested readers might delve into this piece by Thomas Phipps, written not long before he passed away. <http://redshift.vif.com/JournalFiles/V20NO1PDF/V20N1PHI.pdf> Sahil, it is interesting that you make reference to Infeld. About 40 years ago I signed up for a class on cosmology for poets, which was taught by someone--the name eludes me--who I was told had been a student of Infeld. After one class I approached him to enquire whether an alternative explanation of cosmological redshift might be worth considering. Quicker than a jackrabbit, he snatched up his briefcase and dashed out the door. Anyone interested in brushing up on the evolution of the notion of physical spacetime in Einstein's thinking may wish to consult the book "Einstein and the Ether" by Ludwik Kostro, available on Amazon. Should you prefer a PDF copy I will gladly supply one. Since both Maxwell and the LT exhibit strong affinities to fluid dynamics, I prefer a gas ether so as to avoid obscure metaphysical concepts like spacetime and curvature. Rather than a fixed spacetime fabric, I prefer to conceive of the vacuum as a flowing and swirling medium; in the words of Heraclitus, panta rhei. Cheers, Roy

[sahil5d]

But in practice, γ cannot be distinguished from approximations like 1 + (v/c)^2 / 2.

No. In practice, they can be distinguished. These experiments
https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments
https://en.wikipedia.org/wiki/Tests_of_relativistic_energy_and_momentum#Precision_measurements
accelerated particles to 0.5c, 0.6c, 0.7c and higher, and the gamma term described the data well.

there does not exist a Grand Unified Theory and never will

I think that's partially wrong, maybe even totally wrong. Review the greatest successes in science and how they unified multiple areas of study at once. Mass-centric gravity, the periodic elements, the tree of life and evolution, B2FH stellar nucleosynthesis.

Weber's theory

Check out Weber's work on c. He figured out the connection between charge and light before Maxwell.

[Francois-Zinserling]

@sahil5d
"The attraction toward an object moving with a steady velocity is towards its instantaneous position with no delay, for both gravity and electric charge."

The Newton equation (very similar to Coulomb equation)
$F = GMm/r^2$
relates to an attraction of any object at distant r. The earth orbiting around the sun is already travelling on that radius r so anywhere on the circle the attraction will be the same, and will be vectored toward the centre of the ring. Orbits are generally too slow to notice a velocity component (as is witnessed in high-speed electrodynamics) so it only appears as if Newton is 'instant action' is valid. A high orbit speed in sol is Mercury, and lo and behold - there's an anomaly.

Yes, if a small object is magically placed at distance $r$ from earth it will immediately experience the force of attraction, but that is because the gravity field is already there. Because it was magically placed, its own field is not there yet, but this goes unnoticed for a small object, and since we cannot 'magically' place masses, and only move them around at v<<c, it just seems as if their fields are always there.

It is unfortunate that the author of your link discards the ether so vehemently. I'm also not a fan of Mach's principle. It is no longer a question in my mind that aether exists, and that gravity is a result of an energy gradient in the aether. No particles need to fly back-and-forth betweeen ALL masses.

The basic wave equation
$∇^2Φ = 1/c^2 * ∂^2Φ/∂t^2$
also holds true if you replace $Φ$ with $E$ or $B$ from electromagnetics. This means they are a wave, and they only propagate at the speed of light - not faster - not slower.
Looking at the equation above, the left describes changes in space (as in x,y,z) while the right describes changes in time (t). The delimiter is that these changes in space happen at the speed of light $c$ in vacuum, or less, depending on ε or μ if not in vacuum, but that's still the speed of light in that material.

In other words, it is forbidden that a local change (e.g in position or velocity) can instantly be observed in the $E$ or $B$ field some large distance away. It will take as long as light takes to that point before an 'update' is observed.
Simply said, updates occur from the source and spread radially outward.

Now for gravity we don't have the luxury of throwing things around at close to 'c', so we are still trying to figure it out. But we have long supspected gravity moves (updates) at the speed of light, and it has recently been confirmed with gravitational waves. So we will find velocity dependent components eventually, just as we have for EM waves.

So I would implore you to not follow the 'instant action' path for too long.

[sahil5d]

In other words, it is forbidden that a local change (e.g in position or velocity) can instantly be observed in the E or B field some large distance away. It will take as long as light takes to that point before an 'update' is observed. Simply said, updates occur from the source and spread radially outward.

Forbidden according to Maxwell's theory. Meanwhile, the problems abound. Retarded potential theories break down for even the slightest elliptical orbit. Also, Feynman worked on a half-retarded and half-advanced theory because the retarded theory alone had problems.

Also, [photons] are not [attraction and repulsion due to charge]. There is confusion between [directed pulses of electromagnetic energy] and [electrostatic and magnetostatic attraction and repulsion]. Photons are things moving at c in a volume, and electric and magnetic forces are instant calculations based on the state of things in the volume.

Now for gravity we don't have the luxury of throwing things around at close to 'c', so we are still trying to figure it out. But we have long supspected gravity moves (updates) at the speed of light, and it has recently been confirmed with gravitational waves.

After reading Louis's analysis of LIGO, https://github.com/orgs/a-cosmology-group/discussions/82#discussioncomment-7165969, I have a lot of doubts about LIGO's claims of "gravitational waves".

[HanDeBruijn]

There is another lesson to be learned. Some people think that reference frames can be defined at will. They also think that General Relativity has given people the freedom to choose any metric they like. These choices are supposed to be meaningful, because the laws of nature are said to be independent of such arbitrary frames of reference. This is blatantly wrong. Another metric means another physics. And it is not allowable to adopt a metric if that metric is not attached to a reference frame that has a physical meaning. An outstanding example is the reference frame called earth. The earth is not an universal frame. We have seen that it allows us to describe star trails, but these are not the true motions of stars, because in that case the speed of any star would exceed the speed of light. It requires a great deal of non-trivial transformations to find a proper reference frame (earth orbit & sun) for defining the Parallax enabling us to measure the distance to a star.

[budrap00]

@HanDeBruijn

The earth is not an universal frame.

True and I would only add that all physical frames are local not universal. The quaint notion that there are universal laws which we have discovered by observation and experiment in our local frame(s) is nothing but a sad display of human hubris. Our "universal" law of gravity does not work on the scale of galaxies and above. The unchallengeable belief that they (ND-GR) are universal laws leads directly to the ad hoc dark matter and dark energy hypotheses.

Another metric means another physics.

Again I agree with you, but would reverse the implied dependency - different physics requires different metrics.

And it is not allowable to adopt a metric if that metric is not attached to a reference frame that has a physical meaning.

Agree again, this time without qualification. This begs the question though, does the concept of a universal frame have physical meaning? My view is that it does not because of the hard limit implied by the maximum speed of light relative to material bodies (3 x $10^8$ m/s) and the scale of the Cosmos that we currently observe from our local frame.