Why two mass attracts each other?

[Tach]

As does A curvature of light can only occur when the speed of light varies with position.

Bzzt, Duffield, the above clearly demonstrates that you don't know the difference between speed and velocity. You have reached a new low.

I've got Shapiro, and GPS, and optical clocks, and the parallel-mirror gif.

You obviously do not have any knowledge, though you pretend to do. I also think that someone like you, spending all day posting nonsense, doesn't have a job. So, I think that you must be on the dole, Duffield.

 

[Farsight]

This has been addressed, I'd say, about 10 times now on this thread alone. The speed of light does not vary.

Oh shut up Markus. You know f*ck all physics, you flake.

 

[przyk]

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

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 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.

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

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.

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

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.

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

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. 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.

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.

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.

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.

 

[brucep]

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.

There are no 'apparent' empirical measurements in relativity theory. Measurements are valid in all frames. Direct measurements made in local proper frames are invariant. Measurements made from remote coordinate frames are frame dependent not apparent. When physical measurement isn't technically possible or practical then we can substitute the theoretical prediction to fill the role of the remote measurement. We've confirmed this empirical relationship in many experiments. For example: The Hubble Space Telescope made this remote measurement which confirms the theoretical prediction that an object emitting a electromagnetic signal, while falling into a black hole, will exhibit a 'dying pulse train'.

http://hubblesite.org/newscenter/archive/releases/exotic/black-hole/2001/03/text/

Lets choose the HST again. Observing a black hole candidate to determine it's mass based on an object orbiting the black hole candidate. Lets model this using invariant tick rates in both the local proper frame of the HST and the local proper frame of the orbit.

dTau_remote orbit = (1-3M/r_remote orbit)^1/2 dt_remote bookkeeper / dTau_HST orbit = (1-3M/r_HST orbit)^1/2 dt_remote bookkeeper

The ratio

dTau_remote orbit/dTau_HST orbit = (1-3M/r_remote orbit)^1/2 / (1-3M/r_HST orbit)^1/2

We can also designate the HST orbit as a remote coordinate frame and find the ratio

dTau_remote orbit/dt_ remote bookkeeper = (1-3M/r_remote orbit)^1/2

The difference in tick rate between dTau_HST orbit and dt_bookkeeper is a nanosecond. So for this experiment we can use the clock in the local proper frame, of the HST, to time observations associated with events occurring in the local proper frame of r_remote orbit.

All empirical measurements are valid. None are apparent. The reason for the huge delta between local proper frame measurements [theoretical prediction] at the event horizon and the theoretical predictions associated with the remote bookkeeper coordinates is the local proper frame measurement are conducted in the tangent space that approximates a flat manifold while the global bookkeeper prediction takes into account the entire spacetime curvature over the natural path of the object falling from remote coordinates far away into the black hole. I think I know what you meant but introducing non scientific terms tend to confuse the uninitiated and 'gives nonsense fodder' to cranks.

Peace

 

[Farsight]

I did not "repeat Farsight" on that, 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?

Your posts noted, Undefined. It's nice to see somebody who understands that putting a frozen observer in front of a frozen light-clock doesn't make it start ticking again in his Kruskal-Szekeres coordinate system. The light is stopped, he is stopped, he sees nothing forever. So his proper time isn't proper at all, it's a mathematical fiction. Light can't go slower than stopped, the coordinate speed of light can't go lower than zero, so gravitational potential is at rock bottom and the gμν gradient is as flat as a board. Hence the frozen star, where the Schwarzschild singularity at the event horizon is not some mere artefact. See the somewhat-similar gravastar where This region is called a "gravitational vacuum", because it is a void in the fabric of space and time. When light doesn't move space is undefined, and so is time. Note however that when light is stopped quantum fluctuations are stopped too, so Hawking radiation is a dead duck.

 

[PhysBang]

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.

Can you please explain how waggling your fingers is evidence of motion?

 

[Tach]

Your posts noted, Undefined. It's nice to see somebody who understands that putting a frozen observer in front of a frozen light-clock doesn't make it start ticking again in his Kruskal-Szekeres coordinate system. The light is stopped, he is stopped, he sees nothing forever. So his proper time isn't proper at all, it's a mathematical fiction. Light can't go slower than stopped, the coordinate speed of light can't go lower than zero, so gravitational potential is at rock bottom and the gμν gradient is as flat as a board. Hence the frozen star, where the Schwarzschild singularity at the event horizon is not some mere artefact. See the somewhat-similar gravastar where This region is called a "gravitational vacuum", because it is a void in the fabric of space and time. When light doesn't move space is undefined, and so is time. Note however that when light is stopped quantum fluctuations are stopped too, so Hawking radiation is a dead duck.

I think the above deserves the all time "ultimate BS post" crown.

 

[Farsight]

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)

It doesn't deliver an understanding. If it did, we wouldn't be having this discussion, now would we? Light curves because spacetime is curved. Ye Gods.

...and most students will consult more than one source when learning general relativity.

So consult the source where Einstein said what he said. Don't dismiss it because it doesn't square with the pap you've been fed in Sunday school.

(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.

Baloney. I've read what Einstein said, it isn't the same. People who learn from contemporary textbooks dismiss Einstein with words like nonsense and meaningless. Whilst spectacularly failing to address the fabulous post #158 and falling for the speed of light is absolutely constant. Despite what Einstein said. Despite the evidence. Their monumental arrogance is only exceeded by their towering stupidity. And their predilection for ad-hominems and censorship. You know Markus is the moderator of a forum? He won't have me there whupping his ass and exposing his p*ss-poor knowledge of physics. Oh, and if he "accidentally" posts a link, narrow your eyes and ask yourself if he's only here for the poaching.

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 mean to single it out, even though I disapprove of Thorne and Wheeler peddling time-travel woo. It's just a totem for the "paradigm shift" that doomed relativity to be the Sleeping Beauty, the Cinderella of modern physics. One day you'll know what I'm on about.

 

[brucep]

It's hard to believe that he actually 'believes' his nonsense. He thinks any disagreement, with the bullshit he conjures up, is with the posters in these forums while those reading think he's brilliant. Delusional. The gravitational vacuum is between his ears.

 

[brucep]

It doesn't deliver an understanding. If it did, we wouldn't be having this discussion, now would we? Light curves because spacetime is curved. Ye Gods.

So consult the source where Einstein said what he said. Don't dismiss it because it doesn't square with the pap you've been fed in Sunday school.

Baloney. I've read what Einstein said, it isn't the same. People who learn from contemporary textbooks dismiss Einstein with words like nonsense and meaningless. Whilst spectacularly failing to address the fabulous post #158 and falling for the speed of light is absolutely constant. Despite what Einstein said. Despite the evidence. Their monumental arrogance is only exceeded by their towering stupidity. And their predilection for ad-hominems and censorship. You know Markus is the moderator of a forum? He won't have me there whupping his ass and exposing his p*ss-poor knowledge of physics. Oh, and if he "accidentally" posts a link, narrow your eyes and ask yourself if he's only here for the poaching.

I didn't mean to single it out, even though I disapprove of Thorne and Wheeler peddling time-travel woo. It's just a totem for the "paradigm shift" that doomed relativity to be the Sleeping Beauty, the Cinderella of modern physics. One day you'll know what I'm on about.

More than anything you're just a liar. Intellectually dishonest crank. You don't have the intellectual abilities to read a book such as MTW. Phoney baloney crank.

 

[Farsight]

Beat it, troll.

pryzk: see this from another thread.

...So what you really mean is something moves through space-time along some worldline...

I rest my case.

 

[przyk]

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.

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?

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.

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

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".

Whilst I quote Einstein, what he said isn't as important as hard scientific empirical evidence. Which we have.

How far does your commitment to considering empirical evidence actually go? Are you willing to actually go through calculations in detail? 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?

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.

Optical clocks go slower where gravitational potential is lower.

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.

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.

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?

What do you mean also? And it definitely isn't false. Go and look at the etymology: that by which anything is measured.

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

When Einstein refers to the metrical qualities of the continuum of space-time he's talking about measurements of distance and time.

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

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.

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.

You've cited an essay about special relativity.

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

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.

 

[przyk]

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.

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

Read what the guy said.

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?

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.

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

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

And did you notice space as opposed to space-time?

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

I've got more than that pryzk. I've got Shapiro, and GPS, and optical clocks

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

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).

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.

I've got Einstein and the evidence. It is empirical

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.

 

[Undefined]

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.

Thanks Marcus Hanke for reply. I already naively understood all about what a infalling body just about to pass into bh event horizon would "appear" like to an observer remotely. That was not my question focus. I focused on speed of light at that same location which tries to escape and also is being gravitationally accelerated towards bh horizon simultaneously. That photon would just smear out and go nowhere. Hence 'c' for that photon is effectively "zero" in both proper frame at that location and at emote frame of remote observer (because observer would never see that photon since it does not get away from event horizon position but fades away into quantum fluctuations background in situ?). No need to explain about coordinate frames being "virtual constructions". I already knew that too. What I was focusing on was the actual motion, or lack of it, of that photon away from horizon location where its outwards and inwards speed/motion is effectively zero no matter what coordinate frame you create to make a "virtual" fantasy out of it so you can say the photon has some speed 'c' when it doesn't according to the description of what happens in fact as per professional literature. Also, if a photon "frozen" there just above the horizon and fading away to nothing is not actually moving, then there is no "null geodesic" to describe via the photon motion. Anything else you claim by "choosing suitable coordinate frames" doesn't change the fact that something not moving in a gravity well is no longer "following null geodesic motion path" as the jargon says. For example, something sitting on the ground on Earth and no longer "free falling" towards center of Earth is no longer "following null geodesic" because it is stationary in the Earth gravity well frame (ignoring motion shared with Earth rotation and motion through solar system, galaxy, universe and such). If photon cannot escape and does not keep falling into horizon, then it is effectively "zero" lightspeed no matter what else we arbitrarily or abstractly (like you said) coordinate graphing you use to describe it? That is why I want naive understandings not just sophist jargon and constructs which explain nothing in fact at that position for the photon energy and motionless state? My naive understandings don't let me just ignore the physical fact that the photon is "stuck there" in fact and no switching frames of references or other theoretical ploys can change that physical fact of effective zero speed either way?

Edit/ Please take notice that I do not speak of photons directed inwards to begin with, or going around horizon; only a photon directed upwards away from horizon and trying to escape but is trapped there by gravity.

 

[przyk]

]You said In this theory, curvature of space-time is not synonymous with inhomogeneity of space, as shown by the FRW solutions.

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:

That's actually impossible, again by a simple counting argument: the gravitational field is specified by ten functions, while a refractive index is only one function. Now part of the metric is just a matter of how you pick your coordinate system, but even accounting for that you're still left with about six parameters after fixing the coordinate system, and you can't interpret six parameters as just one parameter. It's only going to be possible if the authors restrict their attention to special cases. If you check the paper this is indeed what you find. For example near the end of the first page:

Landau and Lifshitz have derived from the general relativity Fermat’s principle for the propagation of light in a static gravitational field as $$\delta \int g_{00}^{-1/2} dl = 0$$​

In other words, it only works for a particular class of gravitational fields that don't vary in time. The Eq. (3) referred to in your quote also looks like it's only valid for the Schwarzschild solution, and the authors themselves say:

A(R) and B(R) come from a static and spherically symmetric metric of the standard form​

Finally, and most obviously, they only consider light. What about massive particles that don't travel along light-like geodesics? In order for the analogy to hold in general they'd have to show that they could predict the motion of matter as well using the same refractive index they do for light.

Learn to check the fine print when reading scientific papers. That the authors were limiting their attention to static, spherically symmetric gravitational fields is even mentioned in the text you quoted above:

Equations (6) and (7) provide a general method for finding the vacuum refractive index profile of a static spherically symmetric gravitational field, where the coefficients A(R) and B(R) can be obtained from the Schwarzschild solutions​

yet apparently you didn't notice. Little details like these will bite you if you don't look out for them.

So, if you're claiming that the behaviour of light in static, spherically symmetric gravitational fields is analogous to the behaviour of light in a refractive medium then fine. But if you want to claim that space-time curvature is analogous to inhomogenous space in GR then you're on your own: your paper only shows that the analogy works in a special case.

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 keep dumping this article on us as if the title alone is supposed to prove something. Before I delve into it, here's a question: have you checked that this article actually supports your position? For example, do the authors claim they've shown a general equivalence between curved spacetime and inhomogenous space, or does it hold only under certain restricted conditions?

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

Yes, the paper supports my position. It includes this: "The strong similarity between Eqs. (3) and (5) indicates again that an inhomogeneous vacuum may be the physical reality of the curved spacetime. From these two equations and the boundary conditions at infinity, the refractive index of this inhomogeneous vacuum can be derived as follows... Equations (6) and (7) provide a general method for finding the vacuum refractive index profile of a static spherically symmetric gravitational field, where the coefficients A(R) and B(R) can be obtained from the Schwarzschild solutions....

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].)

 

[przyk]

It doesn't deliver an understanding. If it did, we wouldn't be having this discussion, now would we? Light curves because spacetime is curved. Ye Gods.

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.

Explanation for why you might not have made a sincere effort to understand Einstein's work: reading only Einstein's words is easier than trying to follow and understand mathematical formulations and derivations. Reading and thinking about inhomogeneous space is easier than trying to grapple with and understand what a gauge field theory is.

So consult the source where Einstein said what he said. Don't dismiss it because it doesn't square with the pap you've been fed in Sunday school.

You once again present an explanation for a fact without attempting to rule out plausible alternatives. Maybe you can't imagine another explanation. But lack of imagination has never been a good argument for anything.

Observable fact: I personally don't buy what you're trying to sell me about Einstein's theory of general relativity.

Candidate explanation #1: I am too indoctrinated by what I learned in "Sunday school" to be able to part with it.

Candidate explanation #2: I know full well you're right and I'm wrong, but can't bring myself to openly admit it and let the matter rest. Maybe I'm doing this because I'm worried about job security, but since I'm doing research that is unrelated to gravitation, the more likely explanation is my fragile and threatened ego.

Candidate explanation #3: I am basing my opinion on an understanding of all the technical details and derivations in standard formulations of general relativity, including Einstein's, that I consider critical to understanding the theory and that you aren't even trying to take into consideration. I genuinely think most of the examples and arguments you come up with are either irrelevant or trivially and embarrassingly wrong, and, in short, you can't effectively debate with me or convince me of anything because you have ensured you have no way of understanding my point of view on the matter.

 

[Tach]

Thanks Marcus Hanke for reply. I already naively understood all about what a infalling body just about to pass into bh event horizon would "appear" like to an observer remotely. That was not my question focus. I focused on speed of light at that same location which tries to escape and also is being gravitationally accelerated towards bh horizon simultaneously.

Photons are not "accelerated towards bh horizon". They travel at c=constant.

Hence 'c' for that photon is effectively "zero" in both proper frame at that location and at emote frame of remote observer (because observer would never see that photon since it does not get away from event horizon position but fades away into quantum fluctuations background in situ?).

Nope, c is effectively NOT zero but the good old 300,000 km/s. This was also explained to you previously.

 

[quantum_wave]

Somebody clue me in. Is what we have here a general pissing contest between those who believe that GR corresponds precisely with reality, and those who believe that reality has a few surprises for those who think it is settled by GR?

 

[Tach]

Somebody clue me in. Is what we have here a general pissing contest between those who believe that GR corresponds precisely with reality, and those who believe that reality has a few surprises for those who think it is settled by GR?

nah, it is a debate between people who know GR and people who pretend to know (Farsight and his new-found disciple, Undefined).

 

[Undefined]

Photons are not "accelerated towards bh horizon". They travel at c=constant.

So they are not affected by gravity well strength acceleration effect like all energy and matter in gravity wells? You make me laugh.

That "c" is a proper frame relativity-calculated constant, not an absolute constant outside proper frame calculations. You don't know any real physics but pretend to correct people. Ignorant troll is what you are.

Nope, c is effectively NOT zero but the good old 300,000 km/s. This was also explained to you previously.

You explained nothing, ignorant troll. And Markus Hanke hasn't respond yet to my answer to his attempt at explanation using imaginary changes in reference frames and coordinate systems which did not explain what was happening to the photon there in fact.

I also saw this from you to Pete:

Please stop playing games.

Very thick of you saying that to someone else. You could do with taking your own advice there, troll. No wonder I can ignore any "corrections" from you on anything that matters. Others here are to be trusted, not you. Troll away, but no one is taking you seriously because you play the games and pretend to correct when you haven't.