Why two mass attracts each other?

[Farsight]

Um, what case? You just posted a knee-jerk reaction to the particular language AlphaNumeric used without saying anything about the substance of his post. This is exactly what I was criticising you for.

The case I won. That's no knee-jerk reaction. That's a perfect demonstration of the confusion between space and spacetime that I cleared up in my post #158. Markus refuses to address it, and in our recent dialogue you didn't really address it either. Alphanumeric said something moves through space-time along some worldline. You know that's wrong. And Alphanumeric knows that It is very important to be precise about these things.

You did the same with me in [POST=3067812]this[/POST] post:

In this particular instance, what I said about spacetime also applies to space. In fact, I might be wrong but my impression is that "inhomogeneity" is normally a reference just to the spatial part (e.g. the FLRW metric is typically said to be "homogeneous" despite the fact it is time-dependent). So an "inhomogeneous spacetime" would mean a spacetime in which the spatial slices were inhomogeneous, which makes "inhomogeneous spacetime" pretty much synonymous with "inhomogeneous space".

I'm sorry przyk, but you're still missing the point, which is that inhomogeneous space is synonymous with curved spacetime. Pick through my post 158. When you can't find much wrong with it, hopefully you'll understand the point.

The distinction between "space" and "spacetime" was not relevant to the point I was making. Yet you jumped on it anyway and left the actual point I was making unaddressed: there is an alternative and more literal interpretation of what Einstein said that is perfectly in accord with the mainstream understanding of general relativity. (Incidentally, if you can't tell the difference between something Einstein said and something I'm saying in response, then we're really in trouble.)

I rather thought I went to the heart of the problem. But perhaps I should have said this: Inhomogeneous space is synonymous with curved spacetime. When space is homogeneous, then if it doesn’t expand, spacetime is flat. Light moves in straight lines, there is no gravity, and things don’t fall down. There’s an interesting little side issue with the “uniform gravitational field”, but we can talk about that another time. Again, pick through post 158. I'll go back through the thread looking at your posts in reply to mine. I'll try to be brief in my responses.

 

[przyk]

The case I won. That's no knee-jerk reaction.

Yes it is. You responded to a particular sentence fragment the same way you always do without thinking further about it. The important part of that sentence -- the point AlphaNumeric was trying to make -- was actually the second half of that sentence that you didn't quote at all. So that is a knee-jerk reaction.

And Alphanumeric knows that It is very important to be precise about these things.

He doesn't need to be precise here for a simple reason: the precision is already given by the Minkowski formalism that he was clearly referring to. It's that you should be criticising if you have a problem with it.

I'm sorry przyk, but you're still missing the point, which is that inhomogeneous space is synonymous with curved spacetime.

There is nothing in the passage you quoted from the Leyden address that supports that. Einstein certainly talks about "empty space" being inhomogeneous. But he says nothing to the effect that this is equivalent to curved spacetime. That just isn't in there, and it isn't in his 1916 paper either.

While homogeneous space and a variable (coordinate) speed of light are certainly things you encounter in general relativity, these are not synonymous with curved spacetime. It is possible to construct examples where you have one but not the other.

For instance, are you familiar with the common introductory thought experiment concerning a ray of light in an accelerating rocket (as illustrated here)? In that case you get a light ray passing through the rocket with variable (coordinate) speed and even a curved trajectory, despite the fact the spacetime is flat. (Spacetime curvature is an invariant in GR, so spacetime doesn't curve just because you started accelerating.)

 

[Markus Hanke]

If light (a photon) is not leaving the bh horizon or dropping into it, then it is going nowhere in fact despite any theoretical coordinate manipulations to make it "virtually" appear as if it is. The local measurement would also be zero for 'c' in that situation no matter what a theory interpretation is put on it by "abstract coordinate" theories and "arbitrary choices" we mentioned before.

I also asked where is the null geodesic for that photon if it is not moving in fact but only in some "chosen coordinate theoretical interpretation" which hasn't explained what is actually happening to that photon as it fades away in situ? Also my naive understanding asks about that rock sitting on the Earth's surface? It is going nowhere, so what "null geodesic" is it tracing out when it does not move down in "freefall"?

Obviously I wasn't successful in getting the point across, so I'll try again.
Firstly, do not confuse an infalling object with the light that it is sending out; they are not the same thing. An object in free fall follows time-like geodesics, whereas photons trace out null geodesics. They aren't the same. Also, if a photon became "trapped" at the event horizon, then an outside observer obviously wouldn't detect it at all.

Anyway, consider a simple scenario - an astronaut sufficiently far away from the BH to be considered stationary "at infinity". The astronaut now takes off his wrist watch and lets it go; the watch will commence a freefall into the BH. For the first bit nothing special will happen, the watch just accelerates towards the BH in the usual Newtonian fashion, i.e. the light eminating from it propagates in more or less straight lines back to the astronaut. However, there comes a time when relativity can no longer be ignored; as the watch approaches the BH space-time becomes more and more curved, and so do the null geodesics which it traces out. Since a curved geodesic between two points is longer than a straight line, that means that the light from the watch takes more of the astronaut's own time to reach him. At any given point of the lengthening null geodesic, however, light always propagates at exactly c.
In the immediate vicinity of the event horizon space-time is curved to such degree that the null geodesics actually trace out spiral-like patterns, traversing long curved trajectories before reaching the far away astronaut; this is why the infalling object looks to him like stuck in extreme slow motion. But again, at any point of those geodesics, the propagation speed remains exactly c. There is a very narrow region at the horizon where null geodesics can actually become closed, i.e. light will be trapped in circular and elliptical orbits, going around the BH forever. But even here, the propagation speed at any given point will remain exactly c. If light falls below the event horizon, then all null geodesics can only spiral inward, and terminate at the singularity, which is why nothing can "escape" a BH.

I referenced those visualisation tools simply to show how the shape of geodesics change as you approach the event horizon; play around it with them a little, it really does illustrate the principle.

So, to sum up, light never slows or "freezes", it always propagates at exactly c. What happens is rather that the null geodesics which it propagates on become complex and complicated curves through a curved space-time the closer you get to the event horizon, which is why such light takes more of the far-away astronaut's own time to reach him. Hence he will see everything at the event horizon as happening in extreme slow motion. That effect is real, but only to himself; other observers at other points in space-time may not agree.

 

[Farsight]

The reply is post #222.

Here's my post #158. Here's your post #222. No way is that a reply to post #158. You've totally ducked it, and everybody here knows it.

Where's the ad hominem in there? Care to point it out ?

Do you seriously expect to get away with ducking the discussion and saying things like Fargone and dismiss and rant?

The replies are also all over the rest of this thread. And on many other threads. And on other forums.

No they're not. All you ever say is...

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...

When they haven't. You can't point out in detail where I'm wrong. All you say is nonsense! and meaningless!.

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.

If I was some crank peddling woo, you'd be able to take post #158 apart. You can't. So you avoid it like the plague and call me names instead. Don't you get it get Markus? I'm not wrong. Einstein wasn't wrong. You're wrong.

 

[Farsight]

No, wrong once again. The Shapiro delay demonstrates that we are dealing with geodesics in space-time and a constant speed of light;

No it doesn't. It demonstrates a delay.

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.

The spacetime manifold is an abstract thing. The spatial distance between star A and star B does not increase when star C moves between them. But the coordinate speed of light does vary in a non-inertial reference frame.

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...

It's a very bad and very circular demonstration. Here's a reasonable explanation of the Shapiro delay. The respondent refers to contributory factors 1) and 2). Factor 1) contributes nine-tenths of the Shapiro delay. And it is this:

Close to the sun, the effective rate at which time passes is slowed. According to local clocks there, the light is traveling at the usual speed, c, but we think those clocks are slow so from our point of view the light is going slower.

Time of course, does not literally "pass". In the parallel-mirror gif it isn't time passing back and forth between the two mirrors. It's light.

 

[Farsight]

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.

No problem. We discuss our differences, and sometimes we agree to differ.

 

[Farsight]

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.

The speed of light is c. So I can't provide experimental data showing light propagating at something other than the speed of light. But I can easily provide experimental data that the coordinate speed of light varies in a gravitational field. And that 299,792,458 m/s at one location is not the same as 299,792,458 m/s at another.

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.

It doesn't physically happen. Light moves through space, not spacetime.

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

Would you like the Einstein quotes again?

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.

Well they're not. And c = √(1/ε[sub]0[/sub]μ[sub]0[/sub]) is one for another day.

 

[Farsight]

Let me be clear: you are right only to an extent that nobody with a physics background, including Markus, needs to be educated about.

I'm right, but it is hard to fill a cup that is already full. Markus needs to be educated about it. So do you, and here we are, furthering your ed-u-ca-tion.

And... so what? You are making the dangerous assumption that things are always as simple as they look to you.

It's no assumption. I refer to Einstein and the evidence. I don't just make this stuff up. I'm not some "my-theory" guy. I don't go round saying Einstein was wrong. Markus does that.

The reason for the popularity of the "spacetime" view is that, at the level of fundamental physics, we have discovered a (local) spacetime symmetry -- Lorentz symmetry -- that mixes up space and time to a significant degree. We didn't discover that until around the turn of the last century. That is a good 200 years or more after the scientific method as we know it today really got started with Galileo and Newton. It's several millenia after modern humans emerged. It's not something you would see just by looking at your hands.

There's no issue with Minkowski spacetime. But there is an issue with general relativity if you don't appreciate that spacetime isn't the same thing as space.

You shouldn't dismiss such a subtle discovery so casually.

I don't dismiss it. I point out that it's an all-times model and therefore light doesn't move through it.

It's testable... if you substitute the Minkowski spacetime view used in physics for something else that we are most certainly not using.

There's no motion in spacetime. You see that shooting star. So you can't be looking up at spacetime. You have to be looking at space.

What do you see when you look at the sky at a specific point in time? You see the sky at that specific point in time. It's really that simple, and that's the answer the spacetime view gives you.

And what is spacetime at a specific point in time? Space.

It's just a matter of caring to ask it the right question. Ditto with any similar question you ask in the context of the spacetime view: the language might be a bit different but the answer you get will always fundamentally be the same.

Yes. Light moves through space, not spacetime.

If you think the Minkowski spacetime view implies that you should see all of history at once, or see worldlines and lightcones dancing around you, or be able to feel time "flowing" like you could feel water flowing over your fingers, then you have misunderstood it and the point of it. You are mistaking it for something far more extreme than it actually is.

I'm not. I understand it perfectly. I don't mistake it for space.

That's why I say physicists don't need to be educated about this. They're people with eyes just like you and they see the same world you do in their daily lives. I interact with such people every day -- some of the people you're speaking about are colleagues of mine. To see what they see and yet believe that they should be able to see all of space and time at once, or whatever it is you think the spacetime view implies, simply doesn't make sense. It's not your mere everyday contradiction or indoctrination. It would require a level of cognitive dissonance and selective blindness so extreme that I've only heard about it in fiction.

I don't know what they all think, but if they think light moves through spacetime rater than space, they are wrong and they need to be educated. Do not underestimate people's capacity for groupthink, and their capacity to get things spectacularly wrong. Ask them if light moves through spacetime. Or through space.

So I propose you consider this simple resolution: physicists don't actually believe all that stuff, and it's not the point of nor is it implied by the spacetime formalism used in mainstream physics.

An awful lot of physicist believe that light curves because spacetime is curved. That confuses cause and effect, and it is wrong. Find somebody whom you respect, somebody whom you consider to have some special expertise in relativity. Tell him what I've told you. See what he says.

 

[Tach]

Obviously I wasn't successful in getting the point across, so I'll try again.
Firstly, do not confuse an infalling object with the light that it is sending out; they are not the same thing. An object in free fall follows time-like geodesics, whereas photons trace out null geodesics. They aren't the same. Also, if a photon became "trapped" at the event horizon, then an outside observer obviously wouldn't detect it at all.

Anyway, consider a simple scenario - an astronaut sufficiently far away from the BH to be considered stationary "at infinity". The astronaut now takes off his wrist watch and lets it go; the watch will commence a freefall into the BH. For the first bit nothing special will happen, the watch just accelerates towards the BH in the usual Newtonian fashion, i.e. the light eminating from it propagates in more or less straight lines back to the astronaut. However, there comes a time when relativity can no longer be ignored; as the watch approaches the BH space-time becomes more and more curved, and so do the null geodesics which it traces out. Since a curved geodesic between two points is longer than a straight line, that means that the light from the watch takes more of the astronaut's own time to reach him. At any given point of the lengthening null geodesic, however, light always propagates at exactly c.
In the immediate vicinity of the event horizon space-time is curved to such degree that the null geodesics actually trace out spiral-like patterns, traversing long curved trajectories before reaching the far away astronaut; this is why the infalling object looks to him like stuck in extreme slow motion. But again, at any point of those geodesics, the propagation speed remains exactly c. There is a very narrow region at the horizon where null geodesics can actually become closed, i.e. light will be trapped in circular and elliptical orbits, going around the BH forever. But even here, the propagation speed at any given point will remain exactly c. If light falls below the event horizon, then all null geodesics can only spiral inward, and terminate at the singularity, which is why nothing can "escape" a BH.

I referenced those visualisation tools simply to show how the shape of geodesics change as you approach the event horizon; play around it with them a little, it really does illustrate the principle.

So, to sum up, light never slows or "freezes", it always propagates at exactly c. What happens is rather that the null geodesics which it propagates on become complex and complicated curves through a curved space-time the closer you get to the event horizon, which is why such light takes more of the far-away astronaut's own time to reach him. Hence he will see everything at the event horizon as happening in extreme slow motion. That effect is real, but only to himself; other observers at other points in space-time may not agree.

Nice post. You should realize that you are being trolled by two of the foremost trolls in the forum, Farsight and his newfound disciple Undefined,. No matter how good your answers are, they will find a way to come back and deny that your explanations are valid.

 

[Markus Hanke]

You can't point out in detail where I'm wrong.

Yes I can. You are trying to separate space from space-time. That is where you are wrong. All physics in the universe take place in space-time. GR is a model of space-time, not space. This immediately invalidates everything you claim.

Well they're not. And c = √(1/ε0μ0) is one for another day.

That day is now, me thinks. Whatever your answer is, it would have to fit into the relativistic version of Maxwell's equations. I am waiting.

 

[Markus Hanke]

Nice post. You should realize that you are being trolled by two of the foremost trolls in the forum, Farsight and his newfound disciple Undefined,. No matter how good your answers are, they will find a way to come back and deny that your explanations are valid.

I understand this. And so will most casual readers; it is for the benefit of those readers that I keep replying, otherwise I simply wouldn't bother.

 

[Markus Hanke]

An awful lot of physicist believe that light curves because spacetime is curved. That confuses cause and effect, and it is wrong

...says someone who is not a physicist !

Find somebody whom you respect, somebody whom you consider to have some special expertise in relativity. Tell him what I've told you. See what he says.

Simple - he'll say that you have not the first clue what you're talking about.
Besides, what's the point ? There are physicists here and on other forums who have already told you exactly what they think; you just keep dismissing it.

Ignorance is a choice.

 

[Markus Hanke]

I'm sorry przyk, but you're still missing the point, which is that inhomogeneous space is synonymous with curved spacetime.

What complete and utter nonsense. The two are not synonymous, certainly not in the context of GR, which deals only with space-time.
Tell us, in the GR field equations

$$\displaystyle{G_{\mu \nu }=\kappa T_{\mu \nu }}$$

what range of values do the greek indices $$\displaystyle{\mu, \nu}$$ cover ? What does that range of values represent ? Do you know the difference between the use of greek and latin letters in a tensor equation ? Do you agree that these are Einstein' equations ?

Enough now with all the rhetoric - time to make the discussion technical.

There's no issue with Minkowski spacetime. But there is an issue with general relativity if you don't appreciate that spacetime isn't the same thing as space.

This is just getting crankier by the minute. You do realize that Minkowski space-time is just a special case of Riemann space-time, where the metric is constant, don't you ? It would seem not.

I'm not some "my-theory" guy. I don't go round saying Einstein was wrong. Markus does that.

Einstein gave us a model of curved space-time, as just one glance at the above field equation shows us. This is just what I said all along. You however keep ignoring the equation above - no surprise, since it makes your fallacy all too obvious.

Would you like the Einstein quotes again?

Much rather I would like to know why you never quote the actual publication of Einstein's address to the Prussian Academy of Science dated 25th November 1915, which is where GR was first presented in its final form. Here's a scan of the archived original document :

http://echo.mpiwg-berlin.mpg.de/zog...nstein/sitzungsberichte/6E3MAXK4/pageimg&pn=1

Interesting to note that there is no mention anywhere here of "inhomogenous space", but plenty usage of the terms "space-time" and "space-time coordinates" throughout the paper, specifically in the first sentence, and in the conclusion. Furthermore, the meaning of the maths given is clear - it is curved space-time. Varying speeds of light, inhomogeneities in space, non-constant permittivity and permeability of vacuum etc are not to be found in this text, just Riemann curvature. As a matter of fact you may turn to this sentence, which he writes in the context of having talked about GR as an explanation for gravity :

"Dagegen vermag das allgemeine Relativitätspostulat uns nichts über das Wesen der übrigen Naturvorgänge zu offenbaren (...) Meine in dieser Hinsicht neulich an dieser Stelle geäusserte Meinung war irrtümlich."

which means

"On the other hand the postulate of General Relativity does not offer any insight into the other processes of nature. (...) My earlier opinion which I had stated here in this regard was mistaken."

If you wish to refer to what Einstein said, then do it from this text, because this is where GR was published; it shows quite clearly that Einstein not only makes no mention of anything other than space-time curvature when talking about gravity, but also explicitly rules out that GR has any effect on processes other than aforementioned curvature. Specifically, there is no mention of changing speeds of light, and nowhere is this to be found in his maths either.

 

[Markus Hanke]

It isn't often that I am on a talking basis with someone who knows GR so well. Your reponse brings up a question. In GR there are three "curvatures" or "shapes" of the universe and the real shape is determined by the cosmological constant, I think. We are now thought to be in a very nearly flat "shape" with slight "open" curvature, if I'm not too wrong. My question takes the title of this thread to the extreme "closed" curvature option which has as its fate a final big crunch where all the matter and energy accumlate at the end of the game. What is the current thinking as to the size, in light years, of the diameter of such a final crunch, or have you never thought about it?

Are you referring to the maximum size of the universe before it starts collapsing again ? That would be a function of the cosmological constant, so it depends on the value of the vacuum energy density in such a universe. I don't think there are any actual numbers, since this does not appear to describe the universe we are actually in.

 

[Farsight]

You're already getting things wrong here. Einstein specifically derives and uses the geodesic equation as his "equation of motion" for test particles, including light. That's a concept from Riemannian geometry. If general relativity is a theory about stuff curving in space, and not the geometry of spacetime itself, then how do you explain that he wrote a paper that is 3+1 dimensional Riemannian geometry from beginning to end, and used that to make many of the predictions that the theory is now famous for?

The map is not the territory. General relativity certainly isn't about curved space. See my previous posts, the geodesic equation lets you work out a curved worldline which the motion of light through space matches.

We already know how to model, say, the path that light will take in an inhomogeneous medium. We don't need Riemannian geometry to do that.

Agreed. But the flip side of that is the use of Riemannian geometry doesn't mean space is homogeneous.

I didn't necessarily say you did think it needed to be reformulated. I said "General relativity is, or can be interpreted as, a theory about flat but inhomogeneous space".

Noted.

How far does your commitment to considering empirical evidence actually go?

All the way.

Are you willing to actually go through calculations in detail?

No. Mathematics isn't empirical evidence. Optical clocks running at different rates is empirical evidence. The total absence of time flowing in those clocks is empirical evidence.

If you understand what, say, a "metric" is, are you willing to show you understand exactly how to derive one from the Einstein field equation, and then use that metric to make numerical (i.e. the most falsifiable of all) predictions?

No, because it will be a lengthy distraction, you'll slip off the hook, and Markus will hide behind mathematics. I'll keep my line tight instead: address my post #158.

Because if you are simply taking it on faith that certain math means what you assume it does and ends up spitting out the right numbers, then the way I see it you care a lot less about evidence and falsifiability than the average physicist does. In physics we care about evidence to the point that if the theory says 12.3 and the evidence says 12.9 +/- 0.2, then we think the theory is wrong.

No way. I'm not taking the constant speed of light on faith contrary to what Einstein said and contrary to that parallel-mirror gif that is a simplification of the optical clocks.

There is no such quantity as "gravitational potential" in general relativity. It's a relic from Newtonian gravity, and Einstein only uses the term in the weak field limit where general relativity approximately reduces to Newtonian gravity.

Come off it przk: “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν).

And what does that have to do with the material you quoted and were presumably responding to? Why is Einstein's paper Riemannian geometry practically from beginning to end?

Because the world is painted in light. Light moves in a local light clock and we say we measure time. And light moves in space and we say we measure distance.

Do you know what an "etymological fallacy" is? Example: look up the etymology of the word "atom". What does it tell you about atoms?

Indivisible. Now go and look up the etymology of metric.

Really? Which measurements? How are they made? How do they result in a "measured" metric?

Measurements of time and space using rods and clocks. Only we use the motion of light instead of clocks these days. The metre is the distance light moves in 1/299,792,458th of a second.

What full set of measurements should I perform that tells me the metric is exactly $$\mathrm{d}s^{2} \,=\, -\, (1 \,+\, h) \mathrm{d}t^{2} \,+\, \mathrm{d}x^{2} \,+\, \mathrm{d}y^{2} \,+\, \mathrm{d}z^{2}$$ with a certain value of $$h$$, and not $$\mathrm{d}s^{2} \,=\, -\, (1 \,+\, h') \mathrm{d}t^{2} \,+\, \varepsilon \mathrm{d}t \mathrm{d}x \,+\, \mathrm{d}x^{2} \,+\, \mathrm{d}y^{2} \,+\, \mathrm{d}z^{2}$$ with some different value of $$h'$$ and nonzero $$\varepsilon$$?

Your speed and position, the time on your clock, the time according to a remote clock such as a pulsar,and other local measurements that remain unchanged. Your t is given by your local light clock, you don't see it changing because you're measuring it with a light clock, and you use the local motion of light to define your second. Now go and look up the etymology of metric. The metric is not space. It's an abstract thing derived from measurements made using light. Moving.

Do you understand how the mathematical symbols used in GR are related to measurement results at the level of detail I'm asking here? Honest answer, please.

I know something about it. For example $${ds^2=g_{\mu \nu }dx^{\mu }dx^{\nu} }$$.

You've cited an essay about special relativity.

It was relevant. Stop wriggling.

I found plenty wrong that I explained in post #227. I wasn't even trying to be exhaustive. It was a deliberate choice that I more or less only responded to the first half or so of your post #158.

Your post #227 doesn't address my post #158. You still haven't addressed it. What was that about intellectual honesty? This is getting tedious, przyk.

 

[Markus Hanke]

Optical clocks running at different rates is empirical evidence.

Precisely. Because space-time is curved.
Finally we can agree on something.

General relativity certainly isn't about curved space.

Precisely. It is about curved space-time.

No. Mathematics isn't empirical evidence.

So you are not willing to do any maths. Yet you consider yourself in a position to discuss GR, or any physics ? I call BS.
Until you are ready to prove your personal theory with maths you have exactly nothing. Pretty little animated GIFs just don't cut it, you know. Especially if they depict something which is physically wrong.

 

[Markus Hanke]

I am awaiting your answer, Farsight. In the Einstein field equations, what range of values do the greek indices run over ? What do these values represent ?
We are now talking about the question whether Einstein made a model of space, or of space-time. Remember, your assertion has been all along that Einstein's GR is about space.

 

[Farsight]

So, to hell with the principle of general covariance that Einstein spends the first several sections of his paper on?

No. Don't put words into my mouth.

I did. It's you who didn't read all of it. Be honest: you skipped all the mathematical derivations in Einstein's 1916 paper, didn't you? Have you noticed that everyone capable of understanding the whole paper, and doesn't skip all the details that you skip, walks away with a completely different impression of it than you do?

No I didn't. And really przyk, you're clutching at desperate straws trying to play the you don't understand the mathematics card. It just doesn't counter It will also be obvious that the principle of the constancy of the velocity of light in vacuo must be modified.

Reading through Einstein's paper, including all the details which you aren't taking into account, in terms of substance it looks remarkably similar to me to the first general relativity course I followed in university. It's not identical, but the similarities far outweigh the differences. It's hardly some unrecognisable alien I've never seen before.

Sure it does. But Einstein's inhomogeneous space is an unrecognisable alien, isn't it? So much so that you took it to be inhomogeneous spacetime instead of synonymous with curved spacetime.

Did I say otherwise? No. Did you address my point? No.

I addressed it. Read what he said and accept what he said. Don't translate inhomogeneous space into inhomogeneous spacetime because that matches your relativity course.

Yes. Did you notice he put "empty space" in quotes? Did you notice he didn't put "space-time" in quotes?

Yes. Read on:

"...has, I think, finally disposed of the view that space is physically empty."

He put it in quotes because it isn't empty. He's talking about space as a something. An aether. Doubtless your relativity course told you Einstein dispensed with the aether. He did when he was doing SR. But when he did GR, he resurrected it.

And no idea how to make a quantitative prediction from first principles.

I'm the one teaching you first principles here przyk. Light doesn't curve because spacetime is curved.

Already addressed many times. Einstein thought of general relativity as including a variable speed of light (note: not the same as actually basing his theory around that idea). History already acknowledges this and respectfully decided to disagree for a reason you have never addressed: the variable speed of light he is referring to is a coordinate-dependent quantity. Quotes that tell me what I already know aren't going to change my mind.

This should change your mind: View attachment 6263. Now look at it. I will hold your nose to the grindstone until you do. It's a simplified exaggerated version of the super-accurate NIST optical clocks separated by a vertical foot. In the upper clock light moves at 299,792,458 m/s. In the lower clock light moves at 299,792,458 m/s. But those two speeds are not the same. Look at it przyk. Be empirical. You know there is no literal time flowing through a clock. It employs cogs, or a crystal, or microwaves, or something else that moves And when the clock runs slower, it isn't because "time runs slower", it's because the regular cyclical local motion that the clock accumulates is going slower. Do not dismiss that because history respectfully disagrees. Physics is empirical and evidential. It is not decided by some popular vote that dismisses what's in front of your nose and Einstein to boot.

You are making the fundamental error of assuming that because you have an explanation of some of the evidence (and only at a qualitative level), then it must necessarily be the explanation. Science isn't just about explaining evidence. It is about coming up with the best and most detailed explanation of as much evidence as possible. You have done nothing to rule out alternative possible explanations of the same evidence, most notably the one we've had all along: general relativity as a gauge field theory based on the principle of general covariance and the Einstein field equation.

But light moves through space, not spacetime. Doesn't it? It doesn't move along its worldline, does it? And it doesn't curve because your model is curved, does it? By the way, you might want to pay attention to this: The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature. Coordinates are artifices. So is your coordinate system. So is your metric.

 

[Farsight]

No, that is something else I said that had little to do with the Chinese Physics Letters article. My criticism of that article was this:

In the process, it was revealed that you hadn't read the fine print. I specifically asked you [POST=2705111]here[/POST] if there was anything in the paper that might restrict its validity:

You failed to notice the authors only considered static and spherically symmetric gravitational fields,

despite the fact it is explicitly stated in the very passage from the article that you quoted in your support. (For context, your post is [POST=2707320]here[/POST].)

You're clutching at straws. The paper is what it is, and those guys aren't the only people talking about inhomogeneous vacuum.

 

[Farsight]

Alternative explanation for why we are having this discussion: you don't understand general relativity, because you have never made a sincere effort to, while everyone else understands it just fine.

OK przyk. That's enough. Until you respond with intellectual honesty to my post #158 and to the parallel-mirror gif, our conversation is at an end. And since you patently won't, everybody can see that you've ducked the issue and dismissed not just Einstein, but the evidence. Your position is now reduced to bleating you don't understand the maths. So you lose. I recommend that you don't try it on with I've debunked your argument previously again.