Why two mass attracts each other?

[Tach]

That was to Markus, not pryzk.

Did I say that you said it to przyk? I just said that you stated a crackpottery, that's all. I corrected it, yet you persist.

 

[Undefined]

My questions to you again, Tach; please answer and stop playing games to avoid answering:

...I read the scientific literature and understood naively that light there is "frozen" (not moving much either way) until its energy dissipates and vanishes into quantum fluctuations background. What do you disagree with exactly? You haven't said what your "falls straight out of Scwarzchilds solution EFE" explains about what is happening physically to light there, or say why it was "meaningless" to physicists to think about it and ask questions and discuss it?

 

[Undefined]

Did I say that you said it to przyk? I just said that you stated a crackpottery, that's all. I corrected it, yet you persist.

It is the questions about your "correction" that remain unanswered by you. Please see my above post.

 

[Tach]

It is the questions about your "correction" that remain unanswered by you. Please see my above post.

The correction explains why repeating Farsight's claims and arguing with Markus and przyk is wrong.

 

[Undefined]

The correction explains why repeating Farsight's claims and arguing with Markus and przyk is wrong.

In your own mind it does. Not in the real world where you are a troll who pretends to know but doesn't. I believe them when they say you are infantile poison to any thread because of your troll games. The management is either stupid or just incompetent to let you keep getting away with your evasions and games. Not a good site after all. You are to be ignored from now on since you know nothing that others cannot tell me and more correctly at that. Goodbye.

 

[przyk]

Unfortunately people who consider themselves to possess some degree of expertise often treat MTW as the "bible" of GR, and sometimes react emotionally when presented with contrary information and evidence.

First, that's not true, since the purpose of any good textbook, including MTW, is to give students a working understanding of the theory (and not merely tell them what to believe), and most students will consult more than one source when learning general relativity. (Why do you think textbooks tend to be peppered with "exercises"?) It's also not true that everyone learns general relativity from MTW. I didn't, for example. Not that there's all that much variation between textbooks anyway. Anyone who studies from MTW for example will learn pretty much the same general relativity as they would from reading Einstein's 1916 paper.

Second, I find it particularly ironic that you attack MTW since it has a section devoted to the Hamiltonian formulation of general relativity (chapter 21, around section 4). That involves an explicit splitting of spacetime into spacelike slices and is the most formally developed "separate space + time" view of general relativity that I am aware of.

 

[Markus Hanke]

I am confused what you are trying to say to Farsight, Marcus Hanke. I can think of at least one situation where both local proper and remote frame coordinate speed of light is practically zero. My naive understanding of the professional physics literature says the event horizon of a non-rotating black hole has a location somewhere just above it where light virtually stops moving both ways and just fades away to infinite wavelength while not moving from the spot? No observer can say there is light speed of any kind (except that part of motion vector shared with the black hole's motion through universal space surroundings overall). Where is the null geodesic for that lightwave 'frozen' there and fading to nothingness into the quantum vacuum background fluctuations energy contribution? Can anyone tell me where that fits into what you claim about light speed never being less than 'c' if in that case both proper and remote coordinate speed is effectively 'c'=zero?

What you are referring to here is the distinction between coordinate time and proper time.
Coordinate time is a purely mathematical construct; it is what an idealized observer who is located infinitely far away at rest "outside" the gravitational field would see, because only in those circumstances does coordinate time coincide with proper ( measurable ) time. It is immediately clear that this is unphysical, because there is nowhere in the universe where gravitational fields are completely absent. The far bigger problem is that coordinate time, as the name implies, is dependent on the coordinate system used; in other words, if we decide to choose a different coordinate system ( which is perfectly permissible, since coordinates are arbitrary ), we will suddenly get a different coordinate time, even if the rest of the scenario is unchanged. This makes the notion physically meaningless; coordinate time is only useful as a mathematical abstraction in some calculations. Coordinate time can not be physically measured, it is only apparent, and so are all effects based on it. It is of crucial importance to understand this simple fact.

Proper time, on the other hand, is what an observer physically measures in his/her own frame of reference. It is the arc length of the world line of that observer in space-time between two events, so it is what a clock that "travels" with the observer along that same world line will physically measure and show. Proper time is independent of the coordinate system chosen, it is an invariant in space-time.

In your concrete scenario of a particle falling into a black hole the situation is as follows - an observer at rest "outside" the black hole will approximately see the coordinate time of the infalling particle. In the case of a Schwarzschild black hole ( uncharged, static and without angular momentum ) this means that the particle appears to our observer to be going slower and slower the closer it gets to the event horizon; at the same time it will grow dimmer and dimmer as the light that arrives at the observer becomes increasingly red shifted. The observer will therefore say that the particle slows down more and more, and never reaches the event horizon. For him, it will remain forever "frozen" just outside the event horizon, but never reach it. The physical reason for this apparent effect is that the light which travels from the particle to the observer has to traverse an increasingly curved space-time the closer it gets to the event horizon, so the perceived "length" of a photon's geodesic in space-time increases steadily. At the event horizon itself the light literally goes "in circles" around the black hole. Beyond the event horizon, all time-like and null geodesics spiral only inward, and terminate at the singularity - that is why nothing can escape from a black hole.
That was the situation from the point of view of a far-away observer. However, an observer travelling together with the infalling particle will disagree. For him, nothing special happens; his clock ticks as normal, he reaches the event horizon in a finite, well defined time, and he hits the singularity in a finite, well defined time. This time can be physically measured, so you could let a clock fall into a black hole, and at any point in its trajectory it would show a finite, well defined reading. This proper time is the only physically meaningful measurement, because it is what actually happens. The infalling particle will get destroyed in the black hole; it does not somehow magically hover above the event horizon into all eternity; that coordinate time effect is only apparent, it is not what happens, only what appears to happen.

Btw, the time it takes for a particle to fall from rest into a black hole can be calculated. I have done the calculation recently on Cosmoquest; for a supermassive black hole ( ca 15 billion solar masses ) the result was just over 72 hours. So, for a massive BH like that you'd be falling more than three days before you perish at the singularity. Interestingly, you'd be alive almost all the way, the tidal forces in such a BH will only kill you just before you reach the singularity.

As for the speed of light, the situation is clear - it never varies, nor does it have to. The coordinate speed of light mentioned before is only apparent, just like the coordinate infall time of a particle is only apparent, it is not what physically happens. The proper speed of light is always constant at exactly c, simply because, the closer we get to the event horizon, the more space-time is curved, and the "longer" the null geodesics in that space-time become globally. You will never measure anything else but exactly c, so, in other words, the physical laws of electrodynamics will always hold everywhere, even in the vicinity of a black hole. So in reference to what I quoted you on, let me make it clear again that the local proper speed of light is never anything else but exactly c. In particular it never becomes "effectively zero". Thinking that the speed of light somehow "slows down" is based on the misconception that light travels on a straight line through flat space from the event horizon to the far-away observer; however, that is not what physically happens in the vicinity of a black hole.

You may perhaps also be interested to play around with this handy little visualisation tool : http://www.adamtoons.de/physics/gravitation.swf. If you make the mass zero, you get a flat space-time and hence a "straight" trajectory of the moving particle. As you increase the gravitational field, space-time becomes more and more curved, and the trajectory of the particle becomes more and more complex. Do make sure though that you understand that this little visualisation is a just an analogy, since it is missing two dimensions.

 

[Markus Hanke]

First, that's not true, since the purpose of any good textbook, including MTW, is to give students a working understanding of the theory (and not merely tell them what to believe), and most students will consult more than one source when learning general relativity. (Why do you think textbooks tend to be peppered with "exercises"?) It's also not true that everyone learns general relativity from MTW. I didn't, for example. Not that there's all that much variation between textbooks anyway. Anyone who studies from MTW for example will learn pretty much the same general relativity as they would from reading Einstein's 1916 paper.

Second, I find it particularly ironic that you attack MTW since it has a section devoted to the Hamiltonian formulation of general relativity (chapter 21, around section 4). That involves an explicit splitting of spacetime into spacelike slices and is the most formally developed "separate space + time" view of general relativity that I am aware of.

I didn't learn from MTW either ( have recently purchased a copy though, and will go through it in detail ), but just by leafing through it I can see why it is considered the "gold standard". It is extremely detailed, and extremely well presented and written. For any GR related question you will find an answer there.

It is obvious and predictable that Farsight ( or is it Fargone ? ) will dismiss it, because it contradicts his claims from start to finish, and also because he has made it clear that he isn't interested in learning more about GR. Hence a textbook, any textbook, is of no use to him. He prefers to just quote bits and pieces of text taken out of the overall context.

Go on then Farsight - have your usual rant about addressing non-existent points, and the Leyden speech...

 

[wellwisher]

The speed of light is the same in all references based on experimental data. If you look at a photon, it travels at the speed of light. If you plug the speed of light into the special relativity equations, photons should always appear as d=point and t=instant. However, photons are not singular and unique but rather can display a wide range of variable expressions in distance and time (wavelength and frequency). What we also observe is the wavelength and frequency are reference dependent and can red and blue shift based on reference, while the speed of light is always constant.

This tells us that photons exist in two references at the same time. One reference is absolute, does not change and is independent of inertial reference (v=c), while the other is relative and dependent on reference (wavelength and frequency). Using this distinction I like to think of the absolute aspect of the speed of light as the zero state since it is only reference that is consistent to all.

Say we are moving away from a huge energy output source and notice a red shift due to our relative motion. Based on our reference, since the energy is red shifting, the amount of observed energy is less than the amount of real energy being generated by the source, since red shift implies lower energy photons. This is not due to energy decay of the original photons, but simply due to our observational reference which can be a tiny satellite without energy conversion capacity.

The result is the wrong energy balance and a violation of energy conservation, because motion is not an energy sponge that can remove energy from the universe; it is more of a reference illusion. Is the difference between the real energy (as defined by source) and the relative energy (defined by reference based red shift) called dark energy?

 

[Farsight]

Ad hominems instead of a considered response to my post #158 Markus? Tut tut. What are we to make of that?

przyk: thanks for your response and your intellectual honesty. Rest assured I'll get back to you on it.

Undefined: it can be difficult having anything resembling a discussion with Tach. I recommend that you don't bother. And that when Markus gives an unsatisfactory reply, that you press your point.

 

[Markus Hanke]

Ad hominems instead of a considered response to my post #158 Markus? Tut tut. What are we to make of that?

The reply is post #222. Where's the ad hominem in there ? Care to point it out ?

The replies are also all over the rest of this thread. And on many other threads. And on other forums. You have been spreading the same old nonsense for years and years, and many different people have pointed out to you in detail how wrong you are. Yet you just go on, regurgitating the same cranky stuff, oblivious of any responses already provided. The trail you left behind is a matter of public record on various science forums, including this one. Now, what are we to make of that ?

But regardless, you can make of it what you wish - I, and others on here and elsewhere, will continue to call woo when we see it. We are doing that purely for the benefit of other readers; no one here is expecting you to ever come around.

And that when Markus gives an unsatisfactory reply, that you press your point.

Any reply I give will always be unsatisfactory for you, because they expose the fallacies and misconceptions in your claims. I am thus not expecting any praise in return.

Rest assured I'll get back to you on it

...with more quotes. Yes, it is fairly predictable what you are going to post.

 

[OnlyMe]

The speed of light is the same in all references based on experimental data.

This is not really an accurate statement. The universal constancy of the speed of light is a postulate introduced in the second paragraph of Einstein's 1905 paper On The Electrodynamics of Moving Bodies (The introduction of The Special Theory of Relativity), in the following text,

"...and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."​

Experimentally the speed of light has only been "experimentally" proven the be constant with any degree of accuracy, in our locally defined frame of reference. So while the statement is supported by the success of SR generally, it has not been proven, as stated in the sentence quoted from your post above.

There are even additional theoretical issues that arise as we move from a locally flat spacetime to the curved spacetime of GR and frames of reference where gravitationally significant interactions are present.

We accept the constantcy of the speed of light based on the success SR and its introduction as a postulate, within that context. All experimental evidence, with an accuracy sufficient to support the postulate, has been conducted here on Earth in frames of reference which within the context of SR are inertial with respect to one another, and within the context of GR were conducted under experimentally equivalent effects of the Earth's gravity and thus experimentally equivalent curvatures of spacetime.

The point is that your statement as quoted above, raises a portion of the theory of relativity from postulate, to proven experimentally, while it remains a postulate, only locally supported by experimental evidence.

This in some respects is a technical issue, but because in lay oriented discussion it is often misinterpreted to be a "fact of evidence", and can lead to complications when moving beyond the confines of a SR theoretical, it is worth making the distinction.

 

[Farsight]

This has been addressed, I'd say, about 10 times now on this thread alone. The speed of light does not vary. The GIF does not represent what is actually happening, thus it is nonsensical, as stated. In reality light traces out null geodesics in curved space-time. No changes in speed anywhere. Yes, the light does indeed go at the same speed. You will find no experiment and no observation which will ever show light to be propagating at anything else but c. You only find curved null geodesics in curved space-time.

The Shapiro delay is the experiment. If light passes between two massive bodies it travels in a straight line, and reaches the detector later than when the bodies aren't there. All local observations will of course show light moving at the speed of light, but the coordinate speed of light varies in a non-inertial reference frame.

OnlyMe: your post #225 noted. Good stuff IMHO.

 

[Markus Hanke]

The Shapiro delay is the experiment. If light passes between two massive bodies it travels in a straight line, and reaches the detector later than when the bodies aren't there. All local observations will of course show light moving at the speed of light, but the coordinate speed of light varies in a non-inertial reference frame.

OnlyMe: your post #225 noted. Good stuff IMHO.

No, wrong once again. The Shapiro delay demonstrates that we are dealing with geodesics in space-time and a constant speed of light; an outside observer will measure no light deflection angle, but the null geodesic of the light/radar signal is curved in space-time, and hence spans a longer distance than in flat space-time in the absence of the bodies. Since the speed of light never varies, but the geodesic spans a longer distance on the space-time manifold, we naturally get a delay, i.e. the signal takes a longer time to arrive.

A very good demonstration of curvature and the constancy of the speed of light ! And you are still trying to separate space from space-time...

 

[OnlyMe]

OnlyMe: your post #225 noted. Good stuff IMHO.

Though, I am fairly certain how your interpret what I was attempting to say and how I interpret it, would not be entirely in agreement.

 

[Markus Hanke]

Face it Farsight - you are not going to be able to provide any experimental data which actually shows light propagating at anything other than exactly c in vacuum. On the other hand anything and everything you quote will always be consistent with light tracing out null geodesics in a curved space-time, both in terms of physics and maths - not surprising, because that is precisely what physically happens, and it is also what every single textbook and article about GR tells us.

Your "inhomogenous space" and "varying speed of light" are just personal fantasies of yours, which you cannot physically substantiate.

Btw, you have never explained to me where that additional degree of freedom which would need to appear in the Maxwell equations to support your fantasy can be found; where is it ? I don't see it anywhere, neither in the classical vector field formulation, nor in the tensor formulation or the differential forms formalism. In all of these the permittivity and permeability of vacuum must be perfectly homogenous for the equation to work.

 

[Farsight]

I am disappointed that you seem reluctant to show much willingness to consider the points of view of others. One has to wonder why you find this so difficult, since merely acknowledging that someone has a certain opinion is in no way an entrapment for you.

I am przyk. What I don't show much willingness about is stuff like "nonsense" and "meaningless" salted with ad-hominems in lieu of sincere discussion of the physics.

Here are my responses (again) to the three points I summarised in [POST=3067397]post #200[/POST]. Many of them I made, in even more detail, in [THREAD=105796]this[/THREAD] (starting around page 5) and subsequent threads, as well as in a PM discussion about six months ago. If you think they are unfair representations of your end conclusions, or that I have misunderstood something, then now is your opportunity to say so.

OK.

Of course, this is a reference to the first few sentences in [POST=3066616]post #158[/POST]:

Spacetime is an abstract mathematical space in which motion does not occur because it models space at all times. You can draw world-lines in it, and you can draw them curved, but that worldline represents the motion of a body through space over time. The body doesn't actually move through spacetime. People tend to talk of "the spacetime around the Earth" and suggest that light moves through it, but that's wrong.

This is the least interesting point to deal with because most physicists would see it as vacuous. To the extent you are right, you are not saying anything that anyone needs to be educated about.

Apart from Markus. Like you said, I'm right, but Markus reacts very badly to it.

Your argument "spacetime is an abstract mathematical space" is pointless because the same could be said of any mathematical notation or formalism used in physics.

I beg to differ. I can hold up my hands and say look przyk, there's a space between them. In this respect space is empirical. I can also waggle my hands and say look przyk, this is motion. So motion is empirical too. These things aren't abstract. You can't show me spacetime in any similar way.

There is no testable difference between the "spacetime" view and the "space + time" view, and consequently no meaningful distinction as far as most physicists are concerned.

Come off it, przyk. Go out into the garden later and look up at the night sky. You're gazing up at space, not spacetime. You see a shooting star, something moving through space. You don't see world-lines and light-cones. The difference is utterly testable.

It is simply a question of which notation is the most practical or useful, and in relativistic physics the "spacetime" view and notation just better reflects certain symmetries in relativistic theories. In some cases, the difference is as minor as writing something like $$\phi(x^{\mu})$$ as opposed to $$\phi(\bar{x};\,t)$$.

I reject that, and counter with it's simply a question of which accurately reflects the world we see. Talking of which, sit down in your chair, and take a look at your watch. See the second hand going round? You can see it moving, that's empirical. Your watch clocks up some kind of regular cyclic motion, probably that of a quartz crystal, and shows you a cumulative result that you call the time. It isn't actually measuring "the flow of time", and nor is it actually measuring "your motion along your worldline". You're just sitting in your chair.

The next part, "[...] in which motion does not occur" is silly.

Try not to use words like "silly".

When a physicist talks about "motion" in the context of spacetime without further qualification, they are almost certainly referring to exactly the same type of "motion" you might in space: changing position over time.

The whole point of our conversation is that they aren't. They're talking about "motion through spacetime" instead of "motion through space". They confuse spacetime with space.

You even explain exactly how to describe that in the language of spacetime (with worldlines and so on). Same thing, different notation and language. That's it. A Minkowski diagram of a worldline is essentially the same thing as the distance-time graphs we make kids draw in highschool physics, except with the space and time axes inverted.

No problem with that. We represent motion through space with a slanting worldline drawn in spacetime. Like the red streak in the stack of film frames represents the motion of the thrown ball.

The response to the rest of that passage is pretty much the same: when you read someone say something with the word "spacetime" in it, don't simply invent the stupidest interpretation you can come up with and attribute it to that person. That's an instant strawman that serves only to derail the discussion.

I don't. I'm just alert for people conflating space and spacetime and suggesting that light moves through the latter.

Continued.

 

[Farsight]

Next point:

2) General relativity is, or can be interpreted as, a theory about flat but inhomogeneous space.

As the person claiming this, the burden of proof of course falls on you to adequately support it.

You're rather putting words into my mouth with this. General relativity is laden with curvature, so the word "flat" goes against the grain. The point ought to concern that cause of curvilinear motion, which Einstein made clear. Light doesn't curve because spacetime is curved.

Specifically, you have to successfully show that general relativity can be formulated this way and, most importantly, that it actually works. However, what you offer up in support falls far short of this.

This is a straw-man, przyk. I'm not saying GR should be reformulated, I'm saying it should be understood.

Note that merely finding an instance where someone says something is not proof that the idea actually works. That pretty much disqualifies any nontechnical source you might try to use, since the point of nontechnical expositions is just that -- exposition -- and not proofs or derivations.

Whilst I quote Einstein, what he said isn't as important as hard scientific empirical evidence. Which we have. Optical clocks go slower where gravitational potential is lower. And those clocks don't literally measure the flow of time.

First, we get the elephant out of the way. Einstein's 1916 paper was the first complete and general formulation of Einstein's theory that was developed to the point that it could make arbitrary predictions. For some reason you cite it as supporting your case in post #158, despite the fact it is 3+1 dimensional pseudo-Riemannian geometry from beginning to end. The 3+1 dimensional "spacetime" bit is spelled out in the introductory sections that set the stage and define notations for the rest of the paper. For instance, there's a sort of preface on the first page which includes:

The generalization of the theory of relativity has been facilitated considerably by Minkowski, a mathematician who was the first one to recognize the formal equivalence of space coordinates and the time coordinate.​

So there already, apparently we're getting from Einstein that Minkowski's spacetime language and formalism is really helpful for understanding and generalising relativity. The very next sentence is:

The mathematical tools that are necessary for general relativity were readily available in the "absolute differential calculus," which is based upon the research on non-Euclidean manifolds by Gauss, Riemann, and Christoffel, and which has been systematized by Ricci and Levi-Civita and has already been applied to problems of theoretical physics​

Unsurprisingly, the content of Einstein's paper is pretty much what you would expect from this preface. In fact, the first several section can be read as an abridged recap of special relativity in Minkowski's notation followed by a tutorial on the methods of (pseudo) Riemannian geometry in 3+1 dimensional spacetime. Note the references to "space-time", "four-dimensional", and such language, including definitions of four-vectors, tensors, and so on. Of course, pointing out specific instances like this just amounts to a bit of quote mining, and there is no substitute for actually reading Einstein's paper and understanding why he's doing things that way (which anyone following so far is of course encouraged to do).

There's no problem with any of that. But how do we measure a distance? With a metre rod, wherein the metre is the distance travelled by light in 1/299,792,458th of a second. How do we measure a time? With our light clock.

That's not to say that Einstein uses the Minkowski "spacetime" language exclusively throughout the whole paper and never uses the "space + time" language, but the general pattern that emerges is that Einstein uses the "spacetime" language when he's speaking in generalities (i.e. developing the general theoretical framework), and reserves the "space + time" language for far more specific and restricted problems in the latter part of the paper, e.g. low velocity and weak field approximations that make the correspondence with Newtonian physics.

Note that the general "equation of motion" that Einstein (re)derives in this paper, which you refer to in post #158, is the geodesic equation in 3+1 dimensional spacetime given as equation (20d) in section 9 on page 168. (In Minkowski notation, Greek indices run over the four spacetime coordinates. This is more or less explicitly stated toward the end of page 155 in section 4). In [POST=2727436]this post[/POST], I also showed that the time component part of the geodesic equation was vital for the recovery of Newtonian gravity in the weak field approximation. As I also pointed out back then, a more detailed discussion of this approximation is given by Einstein in section 21 around pages 194--195.

No problem with that. A geodesic in spacetime is a static curved worldline which relates to motion through space.

Your statement that "metric is to do with measurement" is also false.

What do you mean also? And it definitely isn't false. Go and look at the etymology: that by which anything is measured. When Einstein refers to the metrical qualities of the continuum of space-time he's talking about measurements of distance and time.

The metric components are basically the coefficients that appear in a generalised differential version of Pythagoras' theorem, and are defined and discussed on page 155. They are not defined as being measurable.

Absolutely not so. Einstein says "and is ascertainable by measurements of space and time". Lower down he says "ds² is a quantity measurable by rod-clock measurement". See the Simple Derivation of the Lorentz Transformation where Einstein says things like we suppose a light-signal sent out from the origin of K at the time t = 0.

Continued.

By the way, aren't you supposed to be responding to my post #158? There's no much wrong with it, is there?

 

[Farsight]

It is clear from the definition in equation (3) and surrounding discussion that they are coordinate-dependent: pick an arbitrary coordinate system, then $$\mathrm{d}s^{2}$$ is an invariant and the $$g_{\mu\nu}$$s are just whatever they need to be in that coordinate system such that $$\mathrm{d}s^{2} \,=\, g_{\mu\nu} \mathrm{d}x^{\mu} \mathrm{d}x^{\nu}$$. In particular, this implies that the metric components transform according to

$$g'_{\alpha\beta} \,=\, \frac{\partial x^{\mu}}{\partial x'^{\alpha}} \, \frac{\partial x^{\nu}}{\partial x'^{\beta}} \, g_{\mu\nu} \,.$$​

This is a special case of the (covariant) rank 2 tensor component transformation rule given in equation (11) on page 159.

So then what? Honestly as far as your case goes, that's pretty much it, really.

You've said nothing! In special relativity ds² is invariant because whether you sit in your chair or go on a fast out-and-back trip, the light-path-length in your parallel-mirror light clock is the same. Subtract one from the other and you get zero. And don't forget "According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν)..." Take your out-and-back trip through space where gμν is not constant, and I can pan with my gendaken telescope watching your parallel-mirror light clock, and plot a curvature that you don't detect locally.

Of the various sources you cited, Einstein's 1916 paper is by far the most important for two reasons: 1) it is the only one that defines general relativity formally and precisely enough that predictions can be derived from it (which he does for certain specific circumstances in all the gory details), and 2) being a technical paper it is addressed primarily at physicists who needed to fully understand his work. This is how Einstein wanted his scientific peers to understand his theory.

Not good enough. He wrote material both before and after, and you haven't made anything like a convincing case to refute my post #158.

Your case is undermined by the absence of any paper by Einstein or anyone else establishing a formal equivalence between the 3+1 dimensional Riemannian geometry and an alternative formulation that is based around some idea of inhomogeneous space. The best evidence you have is that some Chinese researchers had a shot at it in 2008. (!) I thought I already made this point as clearly as possible at the conclusion of [POST=3051334]this post[/POST]:

If there is an alternative version of GR, why isn't there a complete treatise on it in the literature, say something analogous to Einstein's 1916 paper?

That's a weak argument. It's saying you must be wrong because we can't be, and it's saying "die Ausbreitungs-geschwindigkeit des Lichtes mit dem Orte variiert must be wrong because we can't be." Or more succinctly "Einstein was wrong because we can't be". He said what he said. He referred to the variable speed of light time and time again. The underlying problem is the "paradigm shift" that occurred in the "Golden Age" of general relativity which threw away Einstein's variable speed of light and his inhomogeneous space. It comes with Einstein didn't mean what he said, he meant what we say he meant.

(I [POST=2707463]previously responded[/POST] with regard to the Chinese Physics Letters paper too, by the way.)

You said In this theory, curvature of space-time is not synonymous with inhomogeneity of space, as shown by the FRW solutions. The FLRW metric starts with the assumption of homogeneity and isotropy of space, which absolutely contradicts Einstein. Again it's Einstein was wrong because we can't be, and nothing else.

Continued.

 

[Farsight]

Of course, you're thinking about the Leyden address, which finally brings us to the last point:

3) Albert Einstein was personally a proponent of point #2.

As explained above, and many times to you before, you won't find anything to back this up in Einstein's 1916 paper.

I do. Extension of the postulate. Observable fact of experience. Law of causality. Laws of motion conditioned by distant masses. Not laws of curved spacetime conditioned by distant masses. Take a look at the bottom of page 150. It will also be obvious that the principle of the constancy of the velocity of light in vacuo must be modified. The word was Geschwindigkeit. And the principle, the postulate, was the constant speed of light.

Instead, you offer what seems to be one of your all-time favourite Einstein quotes, from the 1920 Leyden address:

According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν), has, I think, finally disposed of the view that space is physically empty.​

from which you somehow jump to "Space is inhomogeneous, not curved." But the part you bolded doesn't support that.

It does. As does A curvature of light can only occur when the speed of light varies with position. It veers, przyk. It doesn't curve because it moves through curved spacetime. lt moves through space, and space isn't curved. It's inhomogeneous. Read what the guy said.

First, it merely states that "empty space" is inhomogeneous, which is not controversial (e.g. the geometry or curvature of spacetime within the solar system is inhomogeneous).

No! He said spacetime in the previous sentence. Now he says space. Not spacetime. Spot the difference!

You don't explain where you get this dichotomy between inhomogeneity and curvature -- that's not in your quote.

What dichotomy? Inhomogeneous space is (nearly) equivalent to curved spacetime. Light moves through the former, and its motion is modelled using the latter.

And since we're happily quote mining, did you notice the bits I highlighted in red for you?

Yes. Did you notice metrical qualities? That's measurement qualities. You measure seconds and metres via the motion of light. And did you notice space as opposed to space-time?

The whole passage basically amounts to arguing that spacetime should be viewed as having properties.

Noooooooo! The whole passage amounts to spacetime being n abstract "continuum" of measurements made using light moving through inhomogeneous space. The motion of light defines the standards of space and time, and gμν describes the state of space. The space that light moves through.

That is entirely consistent with Einstein's 1916 paper, and there is no indication that Einstein is recanting anything from his original formulation of the theory. Once again, I point out that there is no article by Einstein formally establishing a version or interpretation of general relativity specifically based around inhomogeneity of space. All you have are a few isolated quotes mined from various places.

I've got more than that pryzk. I've got Shapiro, and GPS, and optical clocks, and the parallel-mirror gif. And all this:

1911: If we call the speed of light at the origin of co-ordinates cₒ, then the speed of light c at a place with the gravitation potential Φ will be given by the relation c = cₒ(1 + Φ/c²)
1912 : On the other hand I am of the view that the principle of the constancy of the speed of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential.
1913: I arrived at the result that the speed of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the speed of light is incompatible with the equivalence hypothesis.
1915: the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the speed of light is to be abandoned.
1916: In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the speed of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the speed of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light).

What have you got? A rebuttal of my post 158? Nope. A rebuttal of everything I've said previously, delivered umpteen times already? Nope. A convincing argument? Nope. Sorry przyk, but you've got nothing. I've got Einstein and the evidence. It is empirical, and the game is up: