The Arrow of Time: The Laws of Physics and the Concept of Time Reversal

[Dale]

I worked it out ages ago.

Then please post your work.

The biggest problem with maths is that it can work fine on paper but be completely impossible in reality.

I agree and so does every scientist I know of, particularly physicists. That is why we value experiments so highly and why we continually strive to test and re-test every aspect of our equations to ever greater precision.

Thus far, the GR equations have passed all tests to date, so any alternative theory you would like to invent will need to reduce to the GR values for each experiment's conditions.

 

[PeterDonis]

I do believe that the accelerometers in your example would read a non-zero amount of proper acceleration, because the tidal force they would be experiencing would be increasing, so they would be accelerating. You can have objects in free-fall that feel zero proper acceleration though, in an idealised setting. They would have to have a perfectly circular orbit so that the distance between them and the source of the gravity, and the amount of tidal force they experience remains constant and in fact cancels itself out if they're perfectly spherical objects.

Ok, this clarifies where you're coming from. I wish we'd been able to get to this point a few hundred posts ago. That does lead to a couple of further questions, though.

First, do you have any way of quantitatively predicting what the accelerometers in my example should read, or do you just wave your hands and say, "Well, it's got to be smaller than whatever the most accurate accelerometers can read today"? I ask because, although nobody has done the precise experiment I described as far as I know, experimenters have certainly attached accelerometers to single objects in free fall (e.g., in orbit in the Space Shuttle), and those have read zero to within the precision of the instruments. So it seems to me that you would have to take the position that, whatever nonzero acceleration your model predicts, it must be smaller than the smallest acceleration that today's accelerometers can measure. In other words, is your model basically not empirically testable at our present level of technology?

(Btw, the orbits followed by satellites such as the Space Shuttle are never perfect circles, so by your reasoning there should be *some* nonzero acceleration that could in principle be read. I have no idea how your model would predict quantitatively what it would be, though.)

Second, even though you disagree with me (and everyone else who studies gravitation physics) about what the accelerometers in my example would read, do you agree that, even if GR predicts (incorrectly, by your reckoning) a zero acceleration reading on those accelerometers, it predicts correctly the worldlines that the objects in my example would follow? I don't see how you can disagree, since GR's predictions on this point have been verified countless times, but I'd like you to confirm that you agree. I'm going to assume you do for the rest of this post.

SR predicts that two objects under the influence of different amounts of acceleration will separate. They can separate because one is closer than the other to a gravitational source, and so one is always undergoing a higher amount of acceleration. SR models it just fine.

You can model acceleration with SR, so you can model gravity with it as well. It's just easier using GR because it looks at it as the space-time between objects being curved rather than the movement of the objects themselves. Ironically GR is literally just a generalisation of SR than modelling each objects acceleration individually.

There's a problem here that you haven't considered. On your model, the "shape" of a worldline (its covariant derivative) is no longer equivalent to the acceleration measured by an accelerometer following that worldline. How, then, does your model predict the "shape" of an object's worldline? You can't just say "by its acceleration" any longer, because your premise is that they're not connected. But all the SR modeling you're referring to assumes they are; it assumes that the acceleration measured along a worldline is equal to its covariant derivative. For example, the SR prediction that objects under different amounts of acceleration will separate depends on that connection; if you remove that connection, the prediction is no longer valid, and your model can no longer rely on SR's modeling of acceleration. So what justifies your even using SR at all in your model? It seems to me that you need to start entirely from scratch, throw away SR (and GR), and develop your own account of how all this works--which, by the way, will still have to match all the experimental facts (like the fact I referred to in a previous post, that using the covariant derivative along a worldline to predict the acceleration measured is experimentally confirmed to work for accelerations we *can* measure, so it seems reasonable to predict that that method will still work for accelerations too small for us to measure, including the case of zero covariant derivative = zero acceleration).

I don't agree with this. I don't see how the tidal force could possibly anything other than infinite at the horizon because anything that made it that far would be moving at infinite speed relative to everything else. When you calculate the proper time and tidal force to be non-infinite you're overlooking the fact that the time dilation and length contraction are infinite at this range, which is why you get an event horizon in the first place. you can substitute any of those infinities with c because it's the same thing.

As I've already said many times, the GR calculations I've been referring to all already take into account all of the "time dilation" and "length contraction", and the answers I'm giving are all *after* all that has been taken into account. You don't understand how those calculations work, mathematically, so you're just going to have to take my word for it that I (and everyone else in gravitation physics--I've checked my work against multiple sources) am doing the math correctly. You may not agree with the result, but that's because you don't even agree on the basic physical fact that objects following freely falling worldlines experience exactly zero proper acceleration (accelerometers read zero), so from your point of view the math is starting from an incorrect premise, so it will give an incorrect result even if all the intermediate steps are done correctly.

No. A freely falling observer *can* in principle pass a hovering observer at every point on its worldline, which can't extend to the horizon. There doesn't need to be any observers at or inside the horizon since this is impossible anyway.

You want more? Do I have to do everything?

Not everything; just justify the assumption you just made in the above quote (again) without any justification. If you can prove it, fine. But you can't just assume it, because it is logically possible for it to be false, and assuming its truth is logically equivalent to assuming that the spacetime must end at the horizon. So you can't use this reasoning to prove that the spacetime ends at the horizon, because you're assuming what you're supposed to be proving. You have to find a starting assumption that is *not* logically equivalent to your conclusion.

 

[PeterDonis]

A-wal, one other question I just thought of. In an earlier post, you said:

I know you said the tidal force is negligible but if there was no tidal force then they couldn’t be free-falling, so it can never really be negligible in this sense.

Actually this raises two questions (which may be connected, I'm not sure). First, what do you mean by "if there was no tidal force then they couldn't be free-falling"? I don't understand what that means, even in the light of your later post about what the accelerometers read.

Second, what does your model predict for the idealized case of a spacetime with absolutely no gravity present? What would an idealized point-like accelerometer, floating in empty space in such a spacetime, with no force acting on it, read, according to your model? Would it read exactly zero?

 

[PeterDonis]

experimenters have certainly attached accelerometers to single objects in free fall (e.g., in orbit in the Space Shuttle), and those have read zero to within the precision of the instruments.

Just to expand on this a little more, we have data about free-falling objects that are not on nearly circular orbits as well--for example, the Apollo spacecraft transiting to and from the Moon. The astronauts and everything else inside were weightless to within the precision of their measurements (I don't know for sure that there were actual accelerometers on board, but I would think there were, since NASA instrumented everything they could think of--certainly the astronauts reported *experiencing* weightlessness). It seems to me that your model would predict that those astronauts should have felt some non-zero acceleration, but again I have no idea how your model would predict quantitatively what it should have been.

 

[PeterDonis]

You would be able to tell that you're accelerating if you're falling towards the source of the gravity, but not if you were in a circular orbit.

And this brings up still another question. In SR, it's impossible for an object that feels zero acceleration to move in a circular orbit. It has to move in a straight line. Yet you say you can model gravity entirely with SR. How can that possibly work in the light of the above?

 

[PAllen]

English isn't pointless with me. Explain using words how an object could possibly reach an event horizon in time in a way that's self-consistent and that will be that. I don't think it can be done.

You think I can't be serious about learning GR if I don't want to do it using equations? You're trying to tempt me over to the dark side aren't you Mr Sith? It won't work. My heart is pure, ish. Seriously though, cheers for the offer but I don't see the point of learning the mathematics of something I don't even think is right.

So, by analogy, I can learn tennis without lifting a racket or moving my arms. I can know without trying that ping pong paddles would work better than tennis rackets.

More seriously, with no math and no science background, you can not even learn 'about' GR let alone learn GR. The more math and physics background, the more about it you can understand. To say you 'know GR' enough to be a modern practitioner (and I definitely wouldn't say that about myself), you need a great deal of math and physics. Unfortunately, as with any field that evolves, the level of 'knowing GR' is much higher than it was, say, in 1940.

[EDIT: 'unfortunately' is a very bad choice of words. It is certainly fortunate that knowledge is not static.]

 

[PeterDonis]

In SR, it's impossible for an object that feels zero acceleration to move in a circular orbit. It has to move in a straight line. Yet you say you can model gravity entirely with SR. How can that possibly work in the light of the above?

A-wal, on consideration, this point is even more of an issue than I thought. If objects in circular orbits feel exactly zero acceleration, then it's simple to set up a scenario where even your model is forced to predict that two objects can both feel no acceleration and yet will still separate. Just consider two idealized point-like objects, both in exact circular orbits, but at different altitudes. Consider the particular instant at which both objects lie along the same radial line; i.e., they differ only in their radial coordinates at that instant. At that instant they will both be moving in the same direction, but at different speeds. But as they move, they will not only move apart because of their different speeds; they will also change direction, and they will do so at different rates, because they are orbiting at different altitudes. So after some time, the two objects will no longer be moving in the same *direction*, even though, on your model, they both feel zero acceleration. How can that possibly be modeled in SR?

(In GR, of course, what I've described is just another example of tidal gravity and is modeled just fine using the spacetime curvature model, which allows two objects to both feel exactly zero acceleration and still change speed and direction relative to each other. It's not purely radial tidal gravity, which is why we haven't really talked about it in this thread before, but I've mentioned several times that radial tidal gravity is not the only kind there is.)

 

[A-wal]

Oops, just realized that "acceleration relative to the river bed" in your version of the model is not the same as proper acceleration in GR. A "hovering" observer's "acceleration relative to the river bed" is zero, since the hovering observer is at rest in Schwarzschild coordinates. It doesn't change the main point I was making, but I phrased it wrong. Here's what I should have said:

In the limit where gravity is weak (i.e., very far away from the hole), I believe you can say that tidal force is equal to the *rate of change* of the "acceleration of the river relative to the river bed" (*not* the acceleration itself). I say "I believe" because I haven't actually worked out the math to confirm that, when you compute the "acceleration of the river relative to the river bed" far away from the hole, you do in fact get the correct Newtonian formula, - GM/r^2, for "acceleration due to gravity". If you do, then the (radial) tidal gravity, in the Newtonian approximation, is equal to the (radial) rate of change of that acceleration, i.e., 2GM/r^3.

If all that is the case, then the equality would continue to hold approaching, at, and inside the horizon, because, as I've already pointed out, the formula for tidal gravity remains the same as the Newtonian formula all the way into r = 0, even though the "acceleration due to gravity" does not (it acquires an extra sqrt(1 - 2GM/c^2r) term in the denominator, so the acceleration diverges as the horizon is approached). The formula for "acceleration of the river relative to the river bed" should also remain the same as the Newtonian formula all the way into r = 0 (since the formula for the velocity of the river remains the same, and the acceleration is just the radial rate of change of that velocity), so radial tidal gravity should continue to equal the radial rate of change of that acceleration. (This means, of course, that as the horizon is approached, reached, and passed, the "acceleration of the river relative to the river bed" is no longer equal to the correct relativistic "acceleration due to gravity", since that diverges as the horizon is approached.)

All this depends, however, on the formula for "acceleration of the river relative to the river bed" working out as I said it needs to above. I'll have to check that when I get a chance.

You’re right. That’s why there’s no acceleration in a circular orbit. I shouldn’t have said tidal force is equivalent to acceleration, I should have said an increase (or decrease I suppose) in tidal force is equivalent to acceleration.

Then please post your work.

I have been. The bit above was the summary of it. You can make the difference between them whatever you like, but if it takes an infinite amount of time for an observer to see an object cross the event horizon then it takes an infinite amount of time for that object to cross the horizon. In other words if it doesn’t ever cross the horizon for one observer then it doesn’t ever cross the horizon.

I agree and so does every scientist I know of, particularly physicists. That is why we value experiments so highly and why we continually strive to test and re-test every aspect of our equations to ever greater precision.

That's why I prefer doing it without the maths. It's so much easier.

Thus far, the GR equations have passed all tests to date, so any alternative theory you would like to invent will need to reduce to the GR values for each experiment's conditions.

I don't think anything I've said would contradict those results would it?

Ok, this clarifies where you're coming from. I wish we'd been able to get to this point a few hundred posts ago. That does lead to a couple of further questions, though.

I only just thought of using circular orbit. I'm not a physicist.

First, do you have any way of quantitatively predicting what the accelerometers in my example should read, or do you just wave your hands and say, "Well, it's got to be smaller than whatever the most accurate accelerometers can read today"? I ask because, although nobody has done the precise experiment I described as far as I know, experimenters have certainly attached accelerometers to single objects in free fall (e.g., in orbit in the Space Shuttle), and those have read zero to within the precision of the instruments. So it seems to me that you would have to take the position that, whatever nonzero acceleration your model predicts, it must be smaller than the smallest acceleration that today's accelerometers can measure. In other words, is your model basically not empirically testable at our present level of technology?

(Btw, the orbits followed by satellites such as the Space Shuttle are never perfect circles, so by your reasoning there should be *some* nonzero acceleration that could in principle be read. I have no idea how your model would predict quantitatively what it would be, though.)

Whatever amount of proper acceleration is needed to stop an object reaching an event horizon, and it could be tested for by firing an accelerometer into the sun. The faster it’s moving the more acceleration there should be, so it could be conventionally accelerated as much as possible until just before it burns up. If you’re right as soon as the conventional acceleration stops the accelerometer will read zero. If I’m right then it won’t.

Second, even though you disagree with me (and everyone else who studies gravitation physics) about what the accelerometers in my example would read, do you agree that, even if GR predicts (incorrectly, by your reckoning) a zero acceleration reading on those accelerometers, it predicts correctly the worldlines that the objects in my example would follow? I don't see how you can disagree, since GR's predictions on this point have been verified countless times, but I'd like you to confirm that you agree. I'm going to assume you do for the rest of this post.

The world line would be curved by the acceleration as normal. It would have to be tested in very high gravity, just like the proper acceleration when free-falling towards a source of gravity.

There's a problem here that you haven't considered. On your model, the "shape" of a worldline (its covariant derivative) is no longer equivalent to the acceleration measured by an accelerometer following that worldline. How, then, does your model predict the "shape" of an object's worldline? You can't just say "by its acceleration" any longer, because your premise is that they're not connected. But all the SR modeling you're referring to assumes they are; it assumes that the acceleration measured along a worldline is equal to its covariant derivative. For example, the SR prediction that objects under different amounts of acceleration will separate depends on that connection; if you remove that connection, the prediction is no longer valid, and your model can no longer rely on SR's modeling of acceleration. So what justifies your even using SR at all in your model? It seems to me that you need to start entirely from scratch, throw away SR (and GR), and develop your own account of how all this works--which, by the way, will still have to match all the experimental facts (like the fact I referred to in a previous post, that using the covariant derivative along a worldline to predict the acceleration measured is experimentally confirmed to work for accelerations we *can* measure, so it seems reasonable to predict that that method will still work for accelerations too small for us to measure, including the case of zero covariant derivative = zero acceleration).

I said before that if you class time dilation and length contraction as curvature then it’s always curved and you don’t need gravity to do it.

As I've already said many times, the GR calculations I've been referring to all already take into account all of the "time dilation" and "length contraction", and the answers I'm giving are all *after* all that has been taken into account. You don't understand how those calculations work, mathematically, so you're just going to have to take my word for it that I (and everyone else in gravitation physics--I've checked my work against multiple sources) am doing the math correctly. You may not agree with the result, but that's because you don't even agree on the basic physical fact that objects following freely falling worldlines experience exactly zero proper acceleration (accelerometers read zero), so from your point of view the math is starting from an incorrect premise, so it will give an incorrect result even if all the intermediate steps are done correctly.

But I don’t why time dilation and length contraction wouldn’t be infinite at the horizon.

Not everything; just justify the assumption you just made in the above quote (again) without any justification. If you can prove it, fine. But you can't just assume it, because it is logically possible for it to be false, and assuming its truth is logically equivalent to assuming that the spacetime must end at the horizon. So you can't use this reasoning to prove that the spacetime ends at the horizon, because you're assuming what you're supposed to be proving. You have to find a starting assumption that is *not* logically equivalent to your conclusion.

The starting assumption is that reaching an event horizon is no different to reaching c in flat space-time. The event in flat space-time is c. A black hole creates an area where you would need to go faster than c to reach.

Actually this raises two questions (which may be connected, I'm not sure). First, what do you mean by "if there was no tidal force then they couldn't be free-falling"? I don't understand what that means, even in the light of your later post about what the accelerometers read.

Just that there’s always some tidal force present in free-fall, apart from point like objects that can’t actually exist.

Second, what does your model predict for the idealized case of a spacetime with absolutely no gravity present? What would an idealized point-like accelerometer, floating in empty space in such a spacetime, with no force acting on it, read, according to your model? Would it read exactly zero?

Again this is actually not possible, but if it was then yes, apart from the tidal force from the gravity of the object itself.

Just to expand on this a little more, we have data about free-falling objects that are not on nearly circular orbits as well--for example, the Apollo spacecraft transiting to and from the Moon. The astronauts and everything else inside were weightless to within the precision of their measurements (I don't know for sure that there were actual accelerometers on board, but I would think there were, since NASA instrumented everything they could think of--certainly the astronauts reported *experiencing* weightlessness). It seems to me that your model would predict that those astronauts should have felt some non-zero acceleration, but again I have no idea how your model would predict quantitatively what it should have been.

A very, very small amount.

And this brings up still another question. In SR, it's impossible for an object that feels zero acceleration to move in a circular orbit. It has to move in a straight line. Yet you say you can model gravity entirely with SR. How can that possibly work in the light of the above?

It is moving in a straight line. Time dilation and length contraction create the circular orbit. If you want to look at it as actual curved space-time then standard acceleration works the same way, but in the opposite direction and *c squared more powerfully.

So, by analogy, I can learn tennis without lifting a racket or moving my arms. I can know without trying that ping pong paddles would work better than tennis rackets.

More seriously, with no math and no science background, you can not even learn 'about' GR let alone learn GR. The more math and physics background, the more about it you can understand. To say you 'know GR' enough to be a modern practitioner (and I definitely wouldn't say that about myself), you need a great deal of math and physics. Unfortunately, as with any field that evolves, the level of 'knowing GR' is much higher than it was, say, in 1940.

[EDIT: 'unfortunately' is a very bad choice of words. It is certainly fortunate that knowledge is not static.]

I see learning it with the equations as equivalent to learning tennis without moving your arms or using a racket and you can only learn 'about' GR if you’re doing it that way.

A-wal, on consideration, this point is even more of an issue than I thought. If objects in circular orbits feel exactly zero acceleration, then it's simple to set up a scenario where even your model is forced to predict that two objects can both feel no acceleration and yet will still separate. Just consider two idealized point-like objects, both in exact circular orbits, but at different altitudes. Consider the particular instant at which both objects lie along the same radial line; i.e., they differ only in their radial coordinates at that instant. At that instant they will both be moving in the same direction, but at different speeds. But as they move, they will not only move apart because of their different speeds; they will also change direction, and they will do so at different rates, because they are orbiting at different altitudes. So after some time, the two objects will no longer be moving in the same *direction*, even though, on your model, they both feel zero acceleration. How can that possibly be modeled in SR?

(In GR, of course, what I've described is just another example of tidal gravity and is modeled just fine using the spacetime curvature model, which allows two objects to both feel exactly zero acceleration and still change speed and direction relative to each other. It's not purely radial tidal gravity, which is why we haven't really talked about it in this thread before, but I've mentioned several times that radial tidal gravity is not the only kind there is.)

Just give them some inertia. They’re both moving towards the source of gravity but the closer one has more inertia and is moving faster towards it. The difference between the time dilation and length contraction that they experience changes the direction they’re moving in. I think it would be easier if you think of using the curvature of GR to model SR rather than the other way round.

 

[PeterDonis]

I only just thought of using circular orbit. I'm not a physicist.

Um, let me get this straight. You say you thought this model of yours up a long time ago. You've been giving out little bits and pieces of it for hundreds of posts, but all along you've been talking like you have a well-developed system of thought behind those little bits and pieces--well-developed enough, anyway, for you to be quite, quite confident that you are right and GR is wrong about whether or not a black hole horizon can be reached. And yet you have *never considered* how your model would deal with a circular orbit? Pardon the expression, but wtf?

Whatever amount of proper acceleration is needed to stop an object reaching an event horizon, and it could be tested for by firing an accelerometer into the sun.

How would that accomplish anything? The sun doesn't have an event horizon; it's about a hundred thousand times larger than a black hole of the same mass would be.

The faster it’s moving the more acceleration there should be, so it could be conventionally accelerated as much as possible until just before it burns up. If you’re right as soon as the conventional acceleration stops the accelerometer will read zero. If I’m right then it won’t.

Does this have to be done into the sun, or would any spacecraft in interplanetary space that undergoes a "rocket burn" qualify? I'm pretty sure there were accelerometers aboard the Apollo spacecraft , at least, and that they read zero whenever the rocket engine wasn't firing. Would that count?

A very, very small amount.

I said "quantitatively". This is not a quantitative prediction; it's just a hand-waving assertion that whatever your model predicts, it's too small to currently measure. Can you be more precise about what "very, very small" is?

It is moving in a straight line. Time dilation and length contraction create the circular orbit.

Nope, this won't do. See next two comments.

Just give them some inertia. They’re both moving towards the source of gravity

No, they aren't. They are both in exact circular orbits at a constant radius (just a slightly different radius for each one); they each remain always at exactly the same distance from the source. Their velocity is entirely "sideways" at every instant. See next comment.

The difference between the time dilation and length contraction that they experience changes the direction they’re moving in.

Nope. They each remain always at exactly the same distance from the source, so there is *no* change in the time dilation or length contraction they experience; it remains always the same. (This should be obvious in any case, since you have already agreed that they feel exactly zero acceleration, and the only way to *change* the amount of time dilation/length contraction of an object, in your model, is for it to actually feel some acceleration--so if they feel no acceleration, they can't change their time dilation or length contraction.)

 

[Dale]

I have been. The bit above was the summary of it.

A hand waving verbal summary isn't showing your work. If you have not done the math then you have not worked it out. You are making wrong statements simply because you haven't done the math yourself and have ignored it when others have done it for you.

If your claim were logical then it could be shown mathematically.

That's why I prefer doing it without the maths. It's so much easier.

You can't do it without math at all. It is not possible to make a quantitative prediction for an experimental outcome without math.

Your disdain for math is unacceptable for someone who honestly wants to learn modern physics.

I don't think anything I've said would contradict those results would it?

You predict that the proper time for a free falling observer going towards the event horizon is infinite, so your formula for proper time is not the same as GRs. Since you haven't provided that formula it is impossible to tell if the difference is larger or smaller than experimental error, but I suspect that it is larger. In any case, it is up to you as the theorist to prove that your theory is quantitatively consistent with current results, which you have not done.

 

[Dale]

I see learning it with the equations as equivalent to learning tennis without moving your arms or using a racket and you can only learn 'about' GR if you are doing it that way.

It is amazing how you tout ignorance as a virtue. That somehow your learning less and doing less allows you to understand more. How does that make any sense?

Can you give an example of any other skill or field of study where that is the case, that people are more skillful or knowledgeable the less they do or learn?

 

[Lost in Space]

I hope this is equivalent to what I said? Newton's laws can be a second order differential equation or two first order differential equations, and in both cases initial (or final) conditions on position and momentum are needed. In time reversal, the final conditions become initial conditions, and the momentum initial condition gets reversed by definition of time reversal. I thought A-wal was confused by forgetting to reverse the momentum initial condition. In any case, A-wal seems to have understood PeterDonis's point.



There is no arrow of time in general relativity either. In physics, the only arrow of time comes from the second law of thermodynamics (with a small caveat on the weak interactions) which says that the change in entropy is *monotonic* in time. By convention, the direction in which entropy increases is called the future.

Can things 'unhappen'? Is the future already written? Can this view be reconciled with the uncertainties of quantum physics? The 'present' cannot be quantified as anything else but a flux between future and past but the past is fixed and can't be changed. If the future is uncertain and exists as uncollapsed wave functions, do these originate in the past or the future? Doesn't the many worlds hypothesis imply that decoherence and continual branching creates the present as we experience it from any number of possible futures?

So wouldn't any kind of time reversal imply the dissolution of a fixed state into infinite potential?

 

[A-wal]

Um, let me get this straight. You say you thought this model of yours up a long time ago. You've been giving out little bits and pieces of it for hundreds of posts, but all along you've been talking like you have a well-developed system of thought behind those little bits and pieces--well-developed enough, anyway, for you to be quite, quite confident that you are right and GR is wrong about whether or not a black hole horizon can be reached. And yet you have *never considered* how your model would deal with a circular orbit? Pardon the expression, but wtf?

A well developed system? Er, no. The main points, yes. The rest I'm making up as I go along.

How would that accomplish anything? The sun doesn't have an event horizon; it's about a hundred thousand times larger than a black hole of the same mass would be.

Well if there was a black hole in the Solar system then I would suggest we use that. The Sun is the best we have, as we'd just testing for proper acceleration when being pulled into a higher gravitational field.

Does this have to be done into the sun, or would any spacecraft in interplanetary space that undergoes a "rocket burn" qualify? I'm pretty sure there were accelerometers aboard the Apollo spacecraft , at least, and that they read zero whenever the rocket engine wasn't firing. Would that count?

The faster the gravity/tidal force increases the better.

I said "quantitatively". This is not a quantitative prediction; it's just a hand-waving assertion that whatever your model predicts, it's too small to currently measure. Can you be more precise about what "very, very small" is?

Yes. Like I said, trying to reach an event horizon is like trying to reach c. They're exactly equivalent, so you could work out the exact amount of proper acceleration that should be felt.

Nope, this won't do. See next two comments.

No, they aren't. They are both in exact circular orbits at a constant radius (just a slightly different radius for each one); they each remain always at exactly the same distance from the source. Their velocity is entirely "sideways" at every instant. See next comment.

Nope. They each remain always at exactly the same distance from the source, so there is *no* change in the time dilation or length contraction they experience; it remains always the same. (This should be obvious in any case, since you have already agreed that they feel exactly zero acceleration, and the only way to *change* the amount of time dilation/length contraction of an object, in your model, is for it to actually feel some acceleration--so if they feel no acceleration, they can't change their time dilation or length contraction.)

It's moving in a straight line but the distance between it and the source of gravity is constantly shortening due to length contraction. This creates a curve. When it's the right amount of inertia relative to the distance between it and the gravitational source and the mass of the gravitational source you get a circle. What's the problem.

A hand waving verbal summary isn't showing your work. If you have not done the math then you have not worked it out. You are making wrong statements simply because you haven't done the math yourself and have ignored it when others have done it for you.

If your claim were logical then it could be shown mathematically.

You can't do it without math at all. It is not possible to make a quantitative prediction for an experimental outcome without math.

Your disdain for math is unacceptable for someone who honestly wants to learn modern physics.

Just because I can't do it mathematically doesn't mean it can't be done. It's not a disdain for maths. Every time we discuss something and you fall back on your equations as the sole gateway to enlightenment it very much gives the impression of ‘turtling up’.

You predict that the proper time for a free falling observer going towards the event horizon is infinite, so your formula for proper time is not the same as GRs. Since you haven't provided that formula it is impossible to tell if the difference is larger or smaller than experimental error, but I suspect that it is larger. In any case, it is up to you as the theorist to prove that your theory is quantitatively consistent with current results, which you have not done.

It's the same as an accelerating observer trying to reach c if its acceleration increases by an inverse square relative to an imaginary object.

It is amazing how you tout ignorance as a virtue. That somehow your learning less and doing less allows you to understand more. How does that make any sense? Can you give an example of any other skill or field of study where that is the case?

Martial arts. You must empty your cup grasshopper. It really bothers you that I can do any of it without the maths doesn't it?

 

[Dale]

Martial arts. You must empty your cup grasshopper. It really bothers you that I can do any of it without the maths doesn't it?

You have obviously never done any martial arts either if you think that you could be better at martial arts with less knowledge and practice. Your suggestion that knowing and doing less makes you a better expert is absurd on the face of it, regardless of whether you are talking about GR, martial arts, or any other field of study.

 

[PeterDonis]

A well developed system? Er, no. The main points, yes. The rest I'm making up as I go along.

I see.

It's moving in a straight line but the distance between it and the source of gravity is constantly shortening due to length contraction.

But if I interpret this in the "obvious" way, you are saying that length contraction would have to occur perpendicular to the orbiting object's motion. That doesn't happen. Length contraction only occurs in the direction of motion of the object.

The only other way I can see to interpret this, by analogy with your previous claims that "length contraction" is what keeps a "hovering" object at the same radius even though it is firing its rockets to accelerate outward, would be that the *change* in length contraction due to acceleration is responsible. But that only applies if an object is feeling acceleration (because the change in length contraction is in the direction of the felt acceleration). You have already said that the orbiting objects feel zero acceleration, so this won't happen either.

 

[nitsuj]

This is the problem. A black hole occurs when the escape velocity needed to move away exceeds c. The trouble is that this can never happen because you would need to exceed c to be in that situation in the first place. You would need an infinite amount of energy to reach c in flat space-time because of time dilation/length contraction, which means c in fact represents infinite velocity. For an object to reach an event horizon the time dilation/length contraction associated with gravity means that the object would have to be moving at infinite velocity when it reaches the horizon. Therefore any maths or reasoning that allows an object to reach an event horizon is flawed in the same way that any form of maths or reasoning that allows an object to reach c in flat space-time is flawed.

wow A-wal your posts are fantastic! why waste them here? These should be in a published journal for some peer review by "highly trained physicists" (those fools, know nothing about physics unlike you!).

I got to ask A-wal, I have always wondered about the difference between acceleration from energy (physical fuels) and acceleration from gravity.

a spaceship powered by anything cannot accelerate to c because of mass increasing (and infinitely) for example. So, do you envision (in your imagination) the same implications of c velocity for "powered" vehicles as vehicles accelerated due to a black hole.

In case one, it seems the spaceship would have to distort the spacetime itself, with "physical" fuels. In case two, it seems the spaceship is merely following spacetime distortions already there (i.e. something else has spent the energy in distorting spacetime for you.

Lastly, the social deficits in your exchange of posts with these bright (and generous) respondents makes it rather transparent that you are quite young.

Which can be to your advantage! You have time to learn some math! Cause by the look of it, only you could prove yourself wrong.

Edit: after re-reading post 385, it looks like SR & GR are all mixed together.

 

[A-wal]

You have obviously never done any martial arts either if you think that you could be better at martial arts with less knowledge and practice. Your suggestion that knowing and doing less makes you a better expert is absurd on the face of it, regardless of whether you are talking about GR, martial arts, or any other field of study.

I used to do three clubs at the same time and train every night for a while. Both times when I've had a space of years without doing it, I was much, much better at it after a little bit of practice.

But if I interpret this in the "obvious" way, you are saying that length contraction would have to occur perpendicular to the orbiting object's motion. That doesn't happen. Length contraction only occurs in the direction of motion of the object.

The only other way I can see to interpret this, by analogy with your previous claims that "length contraction" is what keeps a "hovering" object at the same radius even though it is firing its rockets to accelerate outward, would be that the *change* in length contraction due to acceleration is responsible. But that only applies if an object is feeling acceleration (because the change in length contraction is in the direction of the felt acceleration). You have already said that the orbiting objects feel zero acceleration, so this won't happen either.

In flat space-time the curved path is caused by frame dragging.

wow A-wal your posts are fantastic! why waste them here? These should be in a published journal for some peer review by "highly trained physicists" (those fools, know nothing about physics unlike you!).

Thanks.

I got to ask A-wal, I have always wondered about the difference between acceleration from energy (physical fuels) and acceleration from gravity.

a spaceship powered by anything cannot accelerate to c because of mass increasing (and infinitely) for example. So, do you envision (in your imagination) the same implications of c velocity for "powered" vehicles as vehicles accelerated due to a black hole.

That's one way of looking at it. My favourite way of looking at it is you can't move faster than light because that's the speed of time. Everything that's in the same frame as you isn't moving through space and is moving through time at c. It could accelerate to a frame where some of its speed through space-time is through one of the spatial dimensions, but it always has to move through at least a little bit of time or it wouldn't be able to slow down, or do anything.

In case one, it seems the spaceship would have to distort the spacetime itself, with "physical" fuels. In case two, it seems the spaceship is merely following spacetime distortions already there (i.e. something else has spent the energy in distorting spacetime for you.

In both cases the object is moving through curved space-time. In the case of energy it's curved outwards instead of the inwards curvature of gravity, and it's *c squared more powerful because E=mc squared. In both cases no objects are moving. It's the space-time between them that isn't constant. Or in both cases space-time is flat and it's the objects themselves that are accelerating. Either way it's objects moving relative to other objects.

Lastly, the social deficits in your exchange of posts with these bright (and generous) respondents makes it rather transparent that you are quite young.

lol I'm 30. I keep getting asked for ID though.

Which can be to your advantage! You have time to learn some math! Cause by the look of it, only you could prove yourself wrong.

I don't want to learn the sodding equations! I'm using the other side of my brain.

Edit: after re-reading post 385, it looks like SR & GR are all mixed together.

They're equivalent.

 

[PeterDonis]

In flat space-time the curved path is caused by frame dragging.

Huh. First it was "length contraction", now it's "frame dragging". They're not the same thing, and I'm not confident you're using either term with its standard meaning anyway. Instead of using technical terms, where I'm not sure we have a common understanding of their definitions, can you just describe in plain English what you think is going on?

 

[nitsuj]

In both cases the object is moving through curved space-time. In the case of energy it's curved outwards instead of the inwards curvature of gravity, and it's *c squared more powerful because E=mc squared. In both cases no objects are moving. It's the space-time between them that isn't constant. Or in both cases space-time is flat and it's the objects themselves that are accelerating. Either way it's objects moving relative to other objects.

I don't want to learn the sodding equations! I'm using the other side of my brain.

They're equivalent.

1.) I have no idea what you are describing, my understanding is particles move in a straight line. "with energy the spacetime is curved outwards and with gravity its curved inwards" Pucky!

2.) whatever.

3.) SR / GR may share principals, but in my opinion are not equivalent.

 

[A-wal]

Huh. First it was "length contraction", now it's "frame dragging". They're not the same thing, and I'm not confident you're using either term with its standard meaning anyway. Instead of using technical terms, where I'm not sure we have a common understanding of their definitions, can you just describe in plain English what you think is going on?

It's still easier to view gravity as curvature and energy as acceleration, and there's nothing wrong with tis way of looking at it except that it gives the false impression that they're different. But it would mean you could use either to describe either. In flat space-time I think gravity could be explained by frame dragging if you look at a massive object as lots of individual massive objects spinning (the atoms). As I understand conventional frame dragging (caused by the spin of the whole object) it acts as gravity and creates additional time dilation and length contraction towards the object so in principle I don’t see anything wrong with describing all gravitational effects this way.

1.) I have no idea what you are describing, my understanding is particles move in a straight line. "with energy the spacetime is curved outwards and with gravity its curved inwards" Pucky!

It depends on what you mean by straight line. What the hell does pucky mean?

2.) whatever.

Why would that bother you?

3.) SR / GR may share principals, but in my opinion are not equivalent.

If the distance between two objects increases or decreases then did the objects move (relative to each other), or did the space-time between them increase/decrease? There's no difference.

 

[nitsuj]

It depends on what you mean by straight line. What the hell does pucky mean?

Why would that bother you?

If the distance between two objects increases or decreases then did the objects move (relative to each other), or did the space-time between them increase/decrease? There's no difference.

My last post in this thread that should be titled "informal debate with A-wal"

"It depends on what you mean by straight line" - you must be remarkably imaginative, what's else would i mean by "straight line"? (rhetorical)

2.) Your statement - "I don't want to learn the sodding equations! I'm using the other side of my brain." doesn't bother me, personally my math doesn't go beyond + - / * and =. But know this, if you don't want to learn the math, learn to trust what the more mathematically inclined are telling you. Using your imagination and claiming your thoughts as fact (let alone science) is spewing pucky. Claiming otherwise is laughable. (and nearly certifiable :)

3.) Oh yes I forgot that well known postulate for SR & GR. Yes I too agree there is no difference between increasing spacetime and increasing distance. Also note that is by definition, credit goes to Webster's.

 

[A-wal]

"It depends on what you mean by straight line" - you must be remarkably imaginative, what's else would i mean by "straight line"? (rhetorical)

It may have been rhetorical but there’s more than way to define a straight line. You need to compare your path to the path of other objects to define a straight line. In curved space-time there’s no such thing, unless you view the paths through curved space-time as straight lines. A straight line on Earth would make a big circle. You could class any non accelerating object as traveling in a straight line, or you could describe it as motionless.

2.) Your statement - "I don't want to learn the sodding equations! I'm using the other side of my brain." doesn't bother me, personally my math doesn't go beyond + - / * and =. But know this, if you don't want to learn the math, learn to trust what the more mathematically inclined are telling you. Using your imagination and claiming your thoughts as fact (let alone science) is spewing pucky. Claiming otherwise is laughable. (and nearly certifiable :)

Laugh all you want. It might do you some good. I don’t put as much faith in maths because I know you can use it to describe practically anything, whether it actually makes sense or not.

3.) Oh yes I forgot that well known postulate for SR & GR. Yes I too agree there is no difference between increasing spacetime and increasing distance. Also note that is by definition, credit goes to Webster's.

That well known postulate for SR & GR is only applied to limited cases. Increasing distance could be classed as increasing space-time (curvature) or as movement of the objects through flat space-time. Currently physics does distinguish between the space-time between objects changing and the movement of the objects themselves. Physicists use this distinction to allow objects to move faster than c and to cross an event horizon.

 

[PeterDonis]

As I understand conventional frame dragging (caused by the spin of the whole object) it acts as gravity and creates additional time dilation and length contraction towards the object

No, it doesn't. The "dragging" of inertial frames is tangential; an object free-falling towards a rotating mass does not just fall straight down (radially); it acquires a tangential component to its motion, as thought the rotation of the mass were "dragging" it around in the direction of the rotation. This does not affect the radial motion itself; that is, there is no change in the "length contraction" or "time dilation" towards the object.

In any case, I asked you to drop technical terms and explain what you think is going on with the case we were discussing in plain English. That case, just to recap, is the case of idealized point-like objects in perfectly circular orbits around a static (non-spinning) mass. You have agreed that these objects feel zero acceleration; how, then, can they change direction? What causes the direction change, and why does it not also cause them to feel acceleration?

The reason I don't want you to use technical terms like "frame dragging", "length contraction", or "time dilation" is that as these terms are used in standard SR and GR, *none* of them can account for the phenomenon I just described in the previous paragraph. If your interpretation of those terms makes them able to account for that phenomenon, then your interpretation is not the standard one, so you will need to explain it in plain English anyway. (Which also means, btw, that it's no good explaining one technical term in terms of another: saying that frame dragging causes more length contraction/time dilation, even if it were true, would not help, since those are technical terms too and can't explain the phenomenon I've described using the standard understanding of those terms.)

I suppose, for completeness, I ought to give the standard GR explanation for the phenomenon. It is simply that, in standard GR, any object moving solely under the influence of gravity is in free fall, and therefore feels zero acceleration. The only way for an object to feel acceleration is to have some force other than gravity act on it: examples are a person standing on a planet like the Earth, who feels the force of the planet's surface pushing up on him; and a person in a rocket firing its engine, who feels the engine pushing on the rocket. (This differs from your model because your model says radially infalling objects, even if they are falling solely under the influence of gravity, feel a non-zero acceleration; but that alone is enough to throw out the standard understanding of all those technical terms, since none of them cause an object to feel acceleration in the standard understanding of those terms.)

The above GR explanation is completely general; however, for the special case of the spacetime surrounding a static, spherical mass, there is an alternate model that may be easier to visualize, called the "river model", which has been mentioned before in this thread. I bring it up because it may be that your model can be visualized as an alternate version of the river model, where the "river bed" is an actual SR global inertial frame that physically restricts the motion of objects, instead of just being a Galilean "background space" that helps in the visualization but has no physical effects.

In the standard river model, the river can move at any speed relative to the river bed, even faster than light--which it does inside the horizon. Objects in the river can therefore also move at any speed relative to the river bed (which is why it is called a "Galilean" background space). But objects can only move at or less than the speed of light relative to the river; that is how the speed of light limit is realized in this model. Also, the rule about which objects feel acceleration is simple, since it's just a translation of the rule I gave above into the language of the river model: an object is in free fall, and feels zero acceleration, if the only changes in its motion (relative to the river bed) are due to the motion of the river (which is the same as saying the object is moving solely under the influence of gravity).

 

[PeterDonis]

You need to compare your path to the path of other objects to define a straight line.

Just to keep the record straight, in standard GR this is false. The test for whether you are moving in a "straight line" in standard GR is simple: if you feel zero acceleration, you are moving in a straight line. If not, you're not. (GR normally uses the term "geodesic" instead of "straight line" to forestall objections about how these aren't "straight lines" because spacetime is curved. It is, but that doesn't change the physical criterion for geodesic motion, which I just gave, and which is perfectly well-defined regardless of the global structure of spacetime.) No comparison with other objects' worldlines is required. A-wal even realizes this, because he says a couple of sentences later that

You could class any non accelerating object as traveling in a straight line, or you could describe it as motionless.

And once you realize that "straight line" means "straight line in spacetime", you realize that these two cases are really describing the same thing, just as they do in SR (where you can't tell uniform, non-accelerated motion from rest). Again, no comparison with the motion of other objects is required; all you need is an accelerometer.

 

[A-wal]

No, it doesn't. The "dragging" of inertial frames is tangential; an object free-falling towards a rotating mass does not just fall straight down (radially); it acquires a tangential component to its motion, as thought the rotation of the mass were "dragging" it around in the direction of the rotation. This does not affect the radial motion itself; that is, there is no change in the "length contraction" or "time dilation" towards the object.

Crap! There has to be a way of describing it I flat space-time and it must be to do with spin. Come to think of it I don’t even need to do this to make them equivalent because there’s no explanation of how gravity curves space-time in GR. I’ll have a go anyway. The angular frame dragging is from the overall spin of the object and happens because the spin is in the same direction but if the object as a whole isn’t spinning then the atoms are going in different directions and the angular frame dragging cancels itself out. But there should also be what I’m going to call radial frame dragging caused by the time dilation and length contraction from their relative velocity. Normally this would be symmetric, but they’re spinning so it can’t be. With angular velocity it creates gravity. Little atomic pack-men eating the space-time to shorten the distance.

In any case, I asked you to drop technical terms and explain what you think is going on with the case we were discussing in plain English. That case, just to recap, is the case of idealized point-like objects in perfectly circular orbits around a static (non-spinning) mass. You have agreed that these objects feel zero acceleration; how, then, can they change direction? What causes the direction change, and why does it not also cause them to feel acceleration?

I suppose they would feel some proper acceleration because it’s the equivalent to being spun around very slowly on a very large centrifuge?

The reason I don't want you to use technical terms like "frame dragging", "length contraction", or "time dilation" is that as these terms are used in standard SR and GR, *none* of them can account for the phenomenon I just described in the previous paragraph. If your interpretation of those terms makes them able to account for that phenomenon, then your interpretation is not the standard one, so you will need to explain it in plain English anyway. (Which also means, btw, that it's no good explaining one technical term in terms of another: saying that frame dragging causes more length contraction/time dilation, even if it were true, would not help, since those are technical terms too and can't explain the phenomenon I've described using the standard understanding of those terms.)

I thought frame dragging included length contraction and time dilation already. I knew that it literally drags them round with it but I thought it included radial ‘length shortening’.

I suppose, for completeness, I ought to give the standard GR explanation for the phenomenon. It is simply that, in standard GR, any object moving solely under the influence of gravity is in free fall, and therefore feels zero acceleration. The only way for an object to feel acceleration is to have some force other than gravity act on it: examples are a person standing on a planet like the Earth, who feels the force of the planet's surface pushing up on him; and a person in a rocket firing its engine, who feels the engine pushing on the rocket. (This differs from your model because your model says radially infalling objects, even if they are falling solely under the influence of gravity, feel a non-zero acceleration; but that alone is enough to throw out the standard understanding of all those technical terms, since none of them cause an object to feel acceleration in the standard understanding of those terms.)

I don’t quite agree with that. You’re saying that if radially free-falling objects do feel a certain amount of proper acceleration then we should throw out the standard understanding of proper acceleration.

The above GR explanation is completely general; however, for the special case of the spacetime surrounding a static, spherical mass, there is an alternate model that may be easier to visualize, called the "river model", which has been mentioned before in this thread. I bring it up because it may be that your model can be visualized as an alternate version of the river model, where the "river bed" is an actual SR global inertial frame that physically restricts the motion of objects, instead of just being a Galilean "background space" that helps in the visualization but has no physical effects.

Yes! That’s what I was saying before. That’s why I filled the space-time with hovering observers. To make it real and limit their speed.

In the standard river model, the river can move at any speed relative to the river bed, even faster than light--which it does inside the horizon. Objects in the river can therefore also move at any speed relative to the river bed (which is why it is called a "Galilean" background space). But objects can only move at or less than the speed of light relative to the river; that is how the speed of light limit is realized in this model. Also, the rule about which objects feel acceleration is simple, since it's just a translation of the rule I gave above into the language of the river model: an object is in free fall, and feels zero acceleration, if the only changes in its motion (relative to the river bed) are due to the motion of the river (which is the same as saying the object is moving solely under the influence of gravity).

You have to accelerate relative to the riverbed, and the river would always be accelerating relative to it because we’re talking about gravity. It would seem to follow that this would be proper acceleration and would be measurable. It's being caused by the length shortening around the massive object as I described for flat space-time. Circular orbit creates a mote.

Just to keep the record straight, in standard GR this is false. The test for whether you are moving in a "straight line" in standard GR is simple: if you feel zero acceleration, you are moving in a straight line. If not, you're not. (GR normally uses the term "geodesic" instead of "straight line" to forestall objections about how these aren't "straight lines" because spacetime is curved. It is, but that doesn't change the physical criterion for geodesic motion, which I just gave, and which is perfectly well-defined regardless of the global structure of spacetime.) No comparison with other objects' worldlines is required. A-wal even realizes this, because he says a couple of sentences later that

Which goes along with what I was saying. My point was it depends what you mean by straight line.

And once you realize that "straight line" means "straight line in spacetime", you realize that these two cases are really describing the same thing, just as they do in SR (where you can't tell uniform, non-accelerated motion from rest). Again, no comparison with the motion of other objects is required; all you need is an accelerometer.

Yea I meant that they’re the same. You could class any non accelerating object either as traveling in a straight line or as motionless. Outwards ‘curvature’ would push an object away in a ‘straight’ line just as the inwards curvature of gravity pulls an object radially inwards if there’s no inertia.

 

[PeterDonis]

Little atomic pack-men eating the space-time to shorten the distance.

I *think* this is more or less the same as your "modified river model" where space flows inward on an SR background. See further comments below.

I suppose they would feel some proper acceleration because it's the equivalent to being spun around very slowly on a very large centrifuge?

This would be more consistent with the other features of your model. However, you would still have to explain why no such acceleration has been measured; on the "centrifuge" model you would think the acceleration would have been enough to be measured on, say, the Space Shuttle, but it hasn't been; the accelerometer readings have always been zero to within the accuracy of the measurement.

I thought frame dragging included length contraction and time dilation already. I knew that it literally drags them round with it but I thought it included radial length shortening.

It may be an issue of terminology. The term "frame dragging" is standardly used (at least, to the best of my knowledge) to refer *only* to the tangential component caused by a rotating mass (to differentiate that from the non-rotating case, where the effect of gravity on inertial frames is purely radial). But of course the *total* effect of the rotating mass on inertial frames includes the radial component as well (just as it does for a non-rotating mass); that component just isn't included in the term "frame dragging".

You're saying that if radially free-falling objects do feel a certain amount of proper acceleration then we should throw out the standard understanding of proper acceleration.

Well, technically it's standard GR saying it, not me, but yes, that is an implication of standard GR: that if free-falling objects do feel any actual acceleration, the model of standard GR, including the "standard understanding of proper acceleration", can't be right, because it requires that they feel zero acceleration. Experimentally, nobody has ever measured any non-zero acceleration felt by a free-falling object (remember that objects falling in the Earth's atmosphere are affected by air resistance and so aren't truly "freely falling"), so the model of standard GR is consistent with the facts as we know them. If anyone ever *does* measure a non-zero acceleration for a "free-falling" object (i.e., one with *no* force acting except gravity), standard GR will be out the window.

Yes! That's what I was saying before. That's why I filled the space-time with hovering observers. To make it real and limit their speed.

You have to accelerate relative to the riverbed, and the river would always be accelerating relative to it because we're talking about gravity. It would seem to follow that this would be proper acceleration and would be measurable. It's being caused by the length shortening around the massive object as I described for flat space-time.

Okay, so your model is basically a "modified river model" where the river bed, instead of being a non-physical Galilean background that is only there to aid visualization, is an actual, physical, flat SR background that physically constrains the motion of objects. What you are calling "length shortening" would be better described, IMO, as "space flowing inward"; one reason for that is that the "river flow" is a continuous process, so describing it as "length shortening" implies that the lengths of *objects* should be continuously shortening, which is not the case; the "length contraction" of a "hovering" observer at a given radius is constant (relative to an observer very far away--the hovering observer himself sees all lengths as normal in his immediate vicinity, and would see the far away observer as "length expanded" in the radial direction).

In any case, a bigger problem with your "modified river" model is this: what happens at the horizon radius? The "rate of inward flow of space" at that radius becomes equal to the speed of light, which in your model is as fast as it can go; but it's not at zero radius, and gravity is still pulling inward on it, so it stands to reason it should accelerate further. If you're saying that the spacetime ends at the horizon, then there would be a big "hole" in the spacetime at the horizon radius, because that radius is not zero. And you can't hand-wave this away by saying that "length contraction" becomes infinite because that only occurs in the radial direction; tangential lengths are not contracted, so the circumference of a circle at the horizon radius, r = 2GM/c^2, is still 2 pi times the radius, or 4 pi GM/c^2. That means the "river", flowing inward from different angular directions, will "hit" the horizon at r = 2GM/c^2 at *different places*, since each value of the angular coordinate corresponds to a different point on the circle.

This means the "background", or "river bed" in your model, *cannot* be a standard SR flat spacetime, because that has no "hole" in it. So again, either your model predicts that the horizon is *not* the end of the spacetime, or your model's "river bed" is *not* an SR background, and you can't use any of the machinery of SR (or GR) to draw your conclusions, including its predictions about proper acceleration being required to separate objects. You have to start from scratch to build up your model.

Circular orbit creates a mote.

Mote? I don't understand.

 

[A-wal]

I *think* this is more or less the same as your "modified river model" where space flows inward on an SR background. See further comments below.

It’s the flat space-time version.

This would be more consistent with the other features of your model. However, you would still have to explain why no such acceleration has been measured; on the "centrifuge" model you would think the acceleration would have been enough to be measured on, say, the Space Shuttle, but it hasn't been; the accelerometer readings have always been zero to within the accuracy of the measurement.

It would be a very big circle though. It should be easy enough (not for me) to work out the amount of proper acceleration that they should feel.

It may be an issue of terminology. The term "frame dragging" is standardly used (at least, to the best of my knowledge) to refer *only* to the tangential component caused by a rotating mass (to differentiate that from the non-rotating case, where the effect of gravity on inertial frames is purely radial). But of course the *total* effect of the rotating mass on inertial frames includes the radial component as well (just as it does for a non-rotating mass); that component just isn't included in the term "frame dragging".

Okay. That makes sense.

Well, technically it's standard GR saying it, not me, but yes, that is an implication of standard GR: that if free-falling objects do feel any actual acceleration, the model of standard GR, including the "standard understanding of proper acceleration", can't be right, because it requires that they feel zero acceleration. Experimentally, nobody has ever measured any non-zero acceleration felt by a free-falling object (remember that objects falling in the Earth's atmosphere are affected by air resistance and so aren't truly "freely falling"), so the model of standard GR is consistent with the facts as we know them. If anyone ever *does* measure a non-zero acceleration for a "free-falling" object (i.e., one with *no* force acting except gravity), standard GR will be out the window.

But it wouldn’t automatically invalidate the rest of it. GR doesn’t through SR out the window using the standard interpretations, even though it does technically.

Okay, so your model is basically a "modified river model" where the river bed, instead of being a non-physical Galilean background that is only there to aid visualization, is an actual, physical, flat SR background that physically constrains the motion of objects. What you are calling "length shortening" would be better described, IMO, as "space flowing inward"; one reason for that is that the "river flow" is a continuous process, so describing it as "length shortening" implies that the lengths of *objects* should be continuously shortening, which is not the case; the "length contraction" of a "hovering" observer at a given radius is constant (relative to an observer very far away--the hovering observer himself sees all lengths as normal in his immediate vicinity, and would see the far away observer as "length expanded" in the radial direction).

In any case, a bigger problem with your "modified river" model is this: what happens at the horizon radius? The "rate of inward flow of space" at that radius becomes equal to the speed of light, which in your model is as fast as it can go; but it's not at zero radius, and gravity is still pulling inward on it, so it stands to reason it should accelerate further. If you're saying that the spacetime ends at the horizon, then there would be a big "hole" in the spacetime at the horizon radius, because that radius is not zero. And you can't hand-wave this away by saying that "length contraction" becomes infinite because that only occurs in the radial direction; tangential lengths are not contracted, so the circumference of a circle at the horizon radius, r = 2GM/c^2, is still 2 pi times the radius, or 4 pi GM/c^2. That means the "river", flowing inward from different angular directions, will "hit" the horizon at r = 2GM/c^2 at *different places*, since each value of the angular coordinate corresponds to a different point on the circle.

This means the "background", or "river bed" in your model, *cannot* be a standard SR flat spacetime, because that has no "hole" in it. So again, either your model predicts that the horizon is *not* the end of the spacetime, or your model's "river bed" is *not* an SR background, and you can't use any of the machinery of SR (or GR) to draw your conclusions, including its predictions about proper acceleration being required to separate objects. You have to start from scratch to build up your model.

Why? There’s no hole. It only looks like that from a distance. There would be an area that would be impossible to reach in any finite amount of proper time. It’s like trying to reach c. It’s a Rindler horizon. When you accelerate in flat space-time it doesn’t create a hole. Remember the event horizon wouldn’t be fixed. At the horizon the circumference of the horizon would be zero, the singularity. I was using the term length shortening because I'm tired of typing length contraction and time dilation, and you told me not to use terms you're familiar with in a way that you're not.

Mote? I don't understand.

I just meant the flow of the river would create a circle around the massive object. Let’s expand this because there wouldn’t be a riverbank. It’s a four-dimensional ocean with whirlpools where there’s less water pressure (gravity) and geezers that create areas of higher pressure (energy). Each river as we’ve been describing it is a current. The sea level’s rising at c locally, so you can’t dive. An event horizon marks the edge of an area where the sea level’s dropping instead of rising, but you can’t get there because any current would be taking its energy from the rising of the sea. So it would rise slower in a stronger current (length contraction/time dilation).

 

[PeterDonis]

It would be a very big circle though. It should be easy enough (not for me) to work out the amount of proper acceleration that they should feel.

How is anyone but you supposed to do that? You haven't given any rule for determining what an accelerometer in your model should read. Remember that standard GR predicts an acceleration of zero.

But it wouldn't automatically invalidate the rest of it.

Yes, it would. The rule that objects moving solely under the influence of gravity feel zero acceleration is critical for constructing models in GR. Without it there's basically no way to set up a correspondence between the mathematical model of a spacetime and actual physical predictions.

GR doesn't through SR out the window using the standard interpretations, even though it does technically.

GR includes SR as a special case, in the idealized situation where spacetime is globally flat (zero gravity everywhere). It also includes SR as a local approximation, over a region of spacetime small enough that the curvature (= tidal gravity) can be neglected. That's a very different situation from what would happen to GR if we were to discover that objects moving solely under the influence of gravity feel a nonzero acceleration. (Bear in mind that this rule also applies in SR, in the sense that objects moving inertially are "moving solely under the influence of gravity" in a spacetime where gravity is zero. In fact, the rule is critical to the "embedding" of SR within GR that I just described.)

At the horizon the circumference of the horizon would be zero, the singularity.

How do you figure that? In the standard "river model" it's certainly not true; the "standard" river model predicts a non-zero circumference for the horizon. The standard river model (since it is just a version of standard GR) predicts length contraction radially, but not tangentially--in other words, although radial distance at radial coordinate r is not measured directly by r, but by r times the "length contraction" factor 1 / sqrt(1 - 2GM/c^2r), *circumferential* distance *is* measured directly by r, so the circumference of a circle at radial coordinate r is just 2 pi r, which is nonzero at the horizon. As far as I can tell, your model makes the same predictions for "length contraction" as the standard model. That means your model also predicts a nonzero circumference for the horizon.

I just meant the flow of the river would create a circle around the massive object.

The flow of the river is purely radial; there is no tangential, "circular" component. So the river flow by itself can't move an object in a circle around the central mass; it can only move objects directly radially inward. (Remember we're talking about a non-rotating central mass, so there is no tangential "frame dragging".)

 

[A-wal]

How is anyone but you supposed to do that? You haven't given any rule for determining what an accelerometer in your model should read. Remember that standard GR predicts an acceleration of zero.

I meant it literally. It would be the same as if you were to swing it around on a rope in a vacuum.

Yes, it would. The rule that objects moving solely under the influence of gravity feel zero acceleration is critical for constructing models in GR. Without it there's basically no way to set up a correspondence between the mathematical model of a spacetime and actual physical predictions.

Surely some minor tweaking wouldn’t necessarily pull the whole thing apart, especially if it’s needed. It would mean it’s able to make more precise predictions.

GR includes SR as a special case, in the idealized situation where spacetime is globally flat (zero gravity everywhere). It also includes SR as a local approximation, over a region of spacetime small enough that the curvature (= tidal gravity) can be neglected. That's a very different situation from what would happen to GR if we were to discover that objects moving solely under the influence of gravity feel a nonzero acceleration. (Bear in mind that this rule also applies in SR, in the sense that objects moving inertially are "moving solely under the influence of gravity" in a spacetime where gravity is zero. In fact, the rule is critical to the "embedding" of SR within GR that I just described.)

I know SR applies to idealised situations where gravity can be neglected. And if I’m right you could say the same for GR, replacing gravity with proper acceleration.

How do you figure that? In the standard "river model" it's certainly not true; the "standard" river model predicts a non-zero circumference for the horizon. The standard river model (since it is just a version of standard GR) predicts length contraction radially, but not tangentially--in other words, although radial distance at radial coordinate r is not measured directly by r, but by r times the "length contraction" factor 1 / sqrt(1 - 2GM/c^2r), *circumferential* distance *is* measured directly by r, so the circumference of a circle at radial coordinate r is just 2 pi r, which is nonzero at the horizon. As far as I can tell, your model makes the same predictions for "length contraction" as the standard model. That means your model also predicts a nonzero circumference for the horizon.

You could never reach it in time. The proper acceleration from the acceleration of the river would cause the proper time it would take to reach the horizon to always be longer than the lifespan of the black hole.

The flow of the river is purely radial; there is no tangential, "circular" component. So the river flow by itself can't move an object in a circle around the central mass; it can only move objects directly radially inward. (Remember we're talking about a non-rotating central mass, so there is no tangential "frame dragging".)

I’m replacing river with current.

 

[PeterDonis]

I meant it literally. It would be the same as if you were to swing it around on a rope in a vacuum.

Well, that answer is obviously wrong: if you swung an object on a rope around a circle in empty space with the radius of the Earth (plus, say, a couple of hundred kilometers for the altitude of a low Earth orbit) at the same velocity as the object would have orbiting the Earth at that radius, the acceleration the object felt would be 1 g (or a little less since the radius is a little larger than that at the Earth's surface; but that is only a difference of a percent or so at most).

Surely some minor tweaking wouldn't necessarily pull the whole thing apart, especially if it's needed. It would mean it's able to make more precise predictions.

In a hypothetical situation where it has been experimentally verified that a small, "point-like" object in free fall does feel a non-zero acceleration, yes, a modified theory would make more accurate predictions than standard GR. But I don't see how such a modification could be made to GR itself; the "modified" theory would have to be some brand-new theory with a completely different model, not a "minor tweak". I say this because there have been a number of "modified" theories of gravity proposed by relativists in order to have something against which to compare GR (all of which have been falsified by experiments done after they were proposed), and all of them, as far as I know, share with GR the prediction that objects in free fall feel exactly zero acceleration.

You could never reach it in time. The proper acceleration from the acceleration of the river would cause the proper time it would take to reach the horizon to always be longer than the lifespan of the black hole.

There you go giving the black hole a finite lifespan again. We are talking about an "eternal" black hole that exists forever, and you've confirmed that you believe even for such an "eternal" black hole, the horizon would not be reachable. Please try again with an "eternal" black hole.

I'm replacing river with current.

What's the difference? The "river" is just another name for a "current" that makes space flow radially inward.

 

[A-wal]

Well, that answer is obviously wrong: if you swung an object on a rope around a circle in empty space with the radius of the Earth (plus, say, a couple of hundred kilometers for the altitude of a low Earth orbit) at the same velocity as the object would have orbiting the Earth at that radius, the acceleration the object felt would be 1 g (or a little less since the radius is a little larger than that at the Earth's surface; but that is only a difference of a percent or so at most).

Hmm. Looking at in flat space-time it would seem that it would have to work like that, but it doesn't as you say. I'll have to think about that one.

In a hypothetical situation where it has been experimentally verified that a small, "point-like" object in free fall does feel a non-zero acceleration, yes, a modified theory would make more accurate predictions than standard GR. But I don't see how such a modification could be made to GR itself; the "modified" theory would have to be some brand-new theory with a completely different model, not a "minor tweak". I say this because there have been a number of "modified" theories of gravity proposed by relativists in order to have something against which to compare GR (all of which have been falsified by experiments done after they were proposed), and all of them, as far as I know, share with GR the prediction that objects in free fall feel exactly zero acceleration.

If the amount of proper acceleration has never been detected then if it does exist I don't think it would be enough to make GR completely wrong. I don't think GR's that fragile, just as SR wasn't.

There you go giving the black hole a finite lifespan again. We are talking about an "eternal" black hole that exists forever, and you've confirmed that you believe even for such an "eternal" black hole, the horizon would not be reachable. Please try again with an "eternal" black hole.

It makes no difference whatsoever. NO amount of time would be enough because no amount of acceleration would be enough to reach an event horizon, just as no amount of acceleration would allow you to reach c.

What's the difference? The "river" is just another name for a "current" that makes space flow radially inward.

The current in the expanded 'ocean' model describes acceleration from energy as well.

 

[PeterDonis]

If the amount of proper acceleration has never been detected then if it does exist I don't think it would be enough to make GR completely wrong. I don't think GR's that fragile, just as SR wasn't.

It's not that GR is fragile; it's that GR is a very precise model making very precise predictions. You can't just "tweak" it to make slightly different precise predictions, because there's nothing to tweak; GR is a complete, self-consistent logical structure, and the only "free parameter" in it that could be "tweaked" is Newton's gravitational constant. Finding a slightly different value for that than the one we currently use would not affect the prediction that objects in free fall feel exactly zero acceleration.

It makes no difference whatsoever. NO amount of time would be enough because no amount of acceleration would be enough to reach an event horizon, just as no amount of acceleration would allow you to reach c.

And as I've noted many times, in the standard GR model, an object doesn't have to "reach c" to fall through the horizon. It just floats at rest, and gravity pulls it in. In terms of the "river model", the object just floats along on the river, which carries it inward across the horizon. It never feels any acceleration at all.

Your model needs to rule out this picture, and the only way I can see it doing that is if your model, unlike the standard GR model, predicts that as the "river" of space flows inward towards the horizon (I still don't understand why you think you need to add in a tangential "current", since we're talking about a non-rotating central mass whose gravity acts solely in the radial direction, so I'm not considering that here), an object "flowing along with the river" will feel an increasing acceleration--increasing without bound as the object, along with the "river", approaches the horizon. The only way I can see that happening is if your model predicts that the acceleration felt by an object moving with the "river" is the *same* as the "acceleration due to gravity", which is given by the relativistic formula:

$$a = \frac{G M}{r^2 \sqrt{1 - \frac{2 G M}{c^2 r}}}$$

And, as I've already noted, we know that's false; objects in free fall, including radially infalling ones, feel zero acceleration to within the limits of accuracy of our current measuring instruments, which are certainly accurate enough to detect a 1 g acceleration (which is, of course, what this formula gives for objects falling in vacuum near the surface of the Earth). So I ask again: what is the rule in your model for determining what acceleration a "freely falling" object feels?

 

[A-wal]

It's not that GR is fragile; it's that GR is a very precise model making very precise predictions. You can't just "tweak" it to make slightly different precise predictions, because there's nothing to tweak; GR is a complete, self-consistent logical structure, and the only "free parameter" in it that could be "tweaked" is Newton's gravitational constant. Finding a slightly different value for that than the one we currently use would not affect the prediction that objects in free fall feel exactly zero acceleration.

Yes, because they're being pulled along with the river, so they're not accelerating relative to it. But the river is accelerating as gravity gets stronger.

And as I've noted many times, in the standard GR model, an object doesn't have to "reach c" to fall through the horizon. It just floats at rest, and gravity pulls it in. In terms of the "river model", the object just floats along on the river, which carries it inward across the horizon. It never feels any acceleration at all.

It has to reach c relative to a hoverer to reach the horizon.

Your model needs to rule out this picture, and the only way I can see it doing that is if your model, unlike the standard GR model, predicts that as the "river" of space flows inward towards the horizon (I still don't understand why you think you need to add in a tangential "current", since we're talking about a non-rotating central mass whose gravity acts solely in the radial direction, so I'm not considering that here), an object "flowing along with the river" will feel an increasing acceleration--increasing without bound as the object, along with the "river", approaches the horizon.

The current is because I'm trying to expand the model to describe acceleration as well as gravity in curved space-time, just like I was trying to explain gravity in flat space-time. I'll go into that more in the next post. I'll just stick to the river model for now.

The only way I can see that happening is if your model predicts that the acceleration felt by an object moving with the "river" is the *same* as the "acceleration due to gravity", which is given by the relativistic formula:

$$a = \frac{G M}{r^2 \sqrt{1 - \frac{2 G M}{c^2 r}}}$$

And, as I've already noted, we know that's false; objects in free fall, including radially infalling ones, feel zero acceleration to within the limits of accuracy of our current measuring instruments, which are certainly accurate enough to detect a 1 g acceleration (which is, of course, what this formula gives for objects falling in vacuum near the surface of the Earth). So I ask again: what is the rule in your model for determining what acceleration a "freely falling" object feels?

The acceleration isn't relative to a fixed riverbed because that would require an ether and a preferred frame to accelerate against. That's obviously not right. The riverbed isn't fixed so it's the increase in the rate of acceleration relative to riverbed that should be felt as proper acceleration.

 

[PeterDonis]

The acceleration isn't relative to a fixed riverbed because that would require an ether and a preferred frame to accelerate against. That's obviously not right. The riverbed isn't fixed so it's the increase in the rate of acceleration relative to riverbed that should be felt as proper acceleration.

And how do you determine "the increase in the rate of acceleration relative to the riverbed" if the river isn't fixed, and now you're saying the river bed isn't fixed either? (And if the river bed itself isn't fixed, what is it "moving" relative to?)

 

[A-wal]

And how do you determine "the increase in the rate of acceleration relative to the riverbed" if the river isn't fixed, and now you're saying the river bed isn't fixed either? (And if the river bed itself isn't fixed, what is it "moving" relative to?)

The riverbed can’t be fixed because that would mean there’s a preferred frame.

Things just keep on falling till they hit something. The only limit to how far an object can fall towards an event horizon is c, which is constant. The only way an event horizon could be reached is if gravity had accelerated you past c, but it’s constant. ‘Distance shortening’ is relative to c, so traveling any distance in any amount of time won’t be enough to reach it. You’re still cheating.