# 3 dimensions of space and 1 of time

• Hoku
In summary, the perception of spacetime as "3 dimensions of space and 1 of time" is a symptom of our inability to maintain an objective view on the matter. Relative velocity is what gives control through space and time. Same thing, right?

#### Hoku

I'm wondering if the perception of spacetime as "3 dimensions of space and 1 of time" is a symptom of our inability to maintain an objective view on the matter.

I believe the reason we separate them in our minds is because we seem to have some control over space but no control over time. But this is due to our limitations of velocity, right, not because spacetime is actually "3+1". Relative velocity is what gives control through space and time. Same thing, right? I mean, we don't even really have control over 3-dimensions of space. We only have control across Earth's surface and we only really have that control in 2-dimensions. We need to build machines (airplanes, etc.) to gain control of the 3rd dimension. We'd need another machine to gain control of the 4th. So couldn't we just as easily say that spacetime is "2+2"?

Do you think it would help us to view spacetime not as "3+1" or "2+2" but as it really is; as "4"?

Experiments performed to date agree with the 3+1 model, not anything else.

http://arxiv.org/abs/gr-qc/0604027
Hamiltonian analysis of the double null 2+2 decomposition of Ashtekar variables
R. A. d'Inverno, P Lambert, J. A. Vickers

http://arxiv.org/abs/gr-qc/9510040
Covariant double-null dynamics: (2+2)-splitting of the Einstein equations
P. R. Brady, S. Droz, W. Israel, S. M. Morsink

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Well, time is definitely different. Whereas I can walk backwards and forwards in space with no difficulty, I can only move forward in time...unless H.G. Well's is right.

I suppose a spacetime is 3+1 or 2+2 if it is globally hyperbolic - are there physically important spacetimes that are not globally hyperbolic? I remember reading somewhere that the Schwarzschild solution isn't, but don't remember where, or if it is even true.

BTW, there is an interesting quote from Hawking about the canonical approach "However the split into three spatial dimensions and one time dimension seems contrary to the whole spirit of relativity. Moreover it restricts the topology of spacetime ..." http://books.google.com/books?id=pxA4AAAAIAAJ&dq=hawking+and+israel&source=gbs_navlinks_s

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Matterwave, I think your point hits the nail on the head as to why we make the 3+1 distinction. However, my point still stands. Our inability to travel backwards in time is OUR limitation and not a fundamental limitation of spacetime itself. Velocity moves us through space. Velocity also moves us through time - both forwards and back - IF we can achieve a relative velocity that equals or exceeds the speed of light. But we can't even gain enough velocity to leave Earth's surface without the aid of a machine. Doesn't it seem like we're projecting our limitations onto spacetime?

Hoku said:
Matterwave, I think your point hits the nail on the head as to why we make the 3+1 distinction. However, my point still stands. Our inability to travel backwards in time is OUR limitation and not a fundamental limitation of spacetime itself. Velocity moves us through space. Velocity also moves us through time - both forwards and back - IF we can achieve a relative velocity that equals or exceeds the speed of light. But we can't even gain enough velocity to leave Earth's surface without the aid of a machine. Doesn't it seem like we're projecting our limitations onto spacetime?

While the 3+1, 2+2 or 4+0 views are all equivalent in certain regimes, I hope you know that the distinction between timelike and spacelike at every point in spacetime is absolute - it comes from the signature of the metric being 2?

When we make the 3+1 distinction, we are folliating one of the space dimensions as a hypersurface. So, we are actually trying to visualize "1 time dimension + 2 space dimensions." Wiki up '3+1 Formalism' and 'ADM.'

A good way of clearly seeing the difference between space and time is with the formula for computing the space-time interval in special relativity. The interval between two space-time events is the same for all reference frames. This interval is:
dS = sqrt (dX^2 + dY^2 + dZ^2 - dT^2)

Notice that the three space dimensions have + signs and the time dimension has a - sign.
The formula will not hold true if you put in four + signs or two + signs and two - signs.

I hope this helps clarify things.

Hoku said:
Matterwave, I think your point hits the nail on the head as to why we make the 3+1 distinction. However, my point still stands. Our inability to travel backwards in time is OUR limitation and not a fundamental limitation of spacetime itself. Velocity moves us through space. Velocity also moves us through time - both forwards and back - IF we can achieve a relative velocity that equals or exceeds the speed of light. But we can't even gain enough velocity to leave Earth's surface without the aid of a machine. Doesn't it seem like we're projecting our limitations onto spacetime?

Our inability to reach the speed of light is not a practical limitation like space-travel, but a theoretical limitation put there by Special Relativity. According to SR, we will never be able to move at the speed of light. This speed limit is, as far as we know, absolute.

Matterwave, I believe the speed limit you are referring to is a restriction of matter, not spacetime itself. Black holes have a force that surpasses this speed limit. Entangled particles do to. And what information passes between two light particles that pass each other from opposite directions? All of these scenarios produce a net value that is greater than the speed of light and spacetime allows them all.

Kochanskij, I like the formula that you called upon. It speaks loudly and, although it leaves questions, it really puts those questions in a new light. I'll be pondering that one for a while. Thanks!

kochanskij said:
A good way of clearly seeing the difference between space and time is with the formula for computing the space-time interval in special relativity. The interval between two space-time events is the same for all reference frames. This interval is:
dS = sqrt (dX^2 + dY^2 + dZ^2 - dT^2)

But it would work equally well, wouldn't it, to make time the vector and length the scalar? Of course that would require a re-structuring of most equations.

PhilDSP said:
But it would work equally well, wouldn't it, to make time the vector and length the scalar? Of course that would require a re-structuring of most equations.
That wouldn't actually change anything. If one of the terms in the line element has a different sign than the others, that variable takes the role of time in the theory regardless of what you call it.

Hoku said:
Black holes have a force that surpasses this speed limit. Entangled particles do to. And what information passes between two light particles that pass each other from opposite directions?
Black holes do not have a 'force' that surpasses the speed of light. Are you suggesting that they can accelerate infalling objects to greater than light speed? That's also not right. You should read up on some GR, the generalization of special relativity to non-inertial frames.

As far as being unable to surpass the speed of light: this is an axiom of special relativity. Surprisingly, it is not 'derived'. Special relativity (and its constancy of the speed of light) are not accepted theories because we've empirically noticed that, try as we might, we simply can't go faster than light. Instead, we test the consequences of relativity -- the consequences of a theory based on the supposition that there is an ultimate speed in the universe. The predictions of special relativity (and, by extension, general relativity) have been well tested (time dilation, photon deflection by stars, QED, etc...there are many examples.)

Lastly, your comment about entangled particles. Do you mean quantum entanglement of wavefunctions? If so, it's not immediately clear that entangled systems violate causality. Not my field, but I've read that the jury is still out on whether meaningful information can be transferred between the components of an entangled state.

bapowell said:
Lastly, your comment about entangled particles. Do you mean quantum entanglement of wavefunctions? If so, it's not immediately clear that entangled systems violate causality. Not my field, but I've read that the jury is still out on whether meaningful information can be transferred between the components of an entangled state.
It's definitely impossible for us to transmit information using measurements on entangled particles, see Eberhard's theorem. Whether or not there are some "hidden" FTL effects coordinating the behavior of the particles depends on your interpretation of quantum mechanics, Bohmian mechanics says there would be but the many-worlds interpretation says there wouldn't, for example.

Relativity says that no information can be sent faster than light. If we could, then a paradox would always result.
JesseM is correct in that we can never use quantum entanglement to send information faster than light.
Even at the event horizon or inside a black hole, nothing ever passes the locally measured speed of light. A photon will always pass you at the usual speed.
However, space itself can expand faster than light. It did so at the big bang during inflation. But still, this expansion can not be used to send information.

If an object or signal is sent thru a wormhole to another part of space, it could get there faster than light. This would lead to time travel into the past and all those paradoxes. So many physicists think wormholes would collapse so quickly that nothing could ever pass thru. It is still unknown if there is a way to hold a wormhole open using negative mass-energy.

kochanskij said:
It is still unknown if there is a way to hold a wormhole open using negative mass-energy.

You should read up on the http://arxiv.org/abs/gr-qc/9702049" [Broken].

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Gatchaman said:
You should read up on the http://arxiv.org/abs/gr-qc/9702049" [Broken].
This paper says that the Krasnikov tube also requires negative energy densities, and mentions that with multiple Krasnikov tubes GR would predict the possibility of closed timelike curves (so if you believe the chronology protection conjecture quantum gravity would somehow rule out this possibility)

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JesseM said:
This paper says that the Krasnikov tube also requires negative energy densities, and mentions that with multiple Krasnikov tubes GR would predict the possibility of closed timelike curves (so if you believe the chronology protection conjecture quantum gravity would somehow rule out this possibility)

I don't want to bet causality on a conjecture.
Seriously, the only time I hear about NEGATIVE energy densities are in discussions of the ergoregion of a Kerr BH really close to the event horizon. Call me nutty, but I don't see those conditions being harnessed anytime soon. Then again, I DO find the CPC really very compelling. That also doesn't make it any more than a conjecture however...

Frame Dragger said:
I don't want to bet causality on a conjecture.
Seriously, the only time I hear about NEGATIVE energy densities are in discussions of the ergoregion of a Kerr BH really close to the event horizon. Call me nutty, but I don't see those conditions being harnessed anytime soon.
Usually when physicists talk about speculations like holding a wormhole open with negative energy, they mention the Casimir effect which allows a region of space between two parallel plates to have an energy density lower than the vacuum energy of quantum field theory. Of course the vacuum energy itself is usually treated as being greater than zero in GR, so this doesn't necessarily mean the space between plates actually has a negative energy in the GR sense--according to this the vacuum energy is probably about 9*10^-10 joules per cubic centimeter if we assume the vacuum energy is responsible for the cosmological constant. But hellfire said in post #51 of this thread that the energy density between plates could be lower than the vacuum energy by an amount even greater than the vacuum energy is assumed to be greater than zero in cosmology, as long as the plates were less than about 10^-5 meters apart, so that would suggest that for sufficiently small separations the energy density between plates can be negative in the GR sense. I suppose there's no way to be completely confident about this without a theory of quantum gravity though!

Bapowell,

bapowell said:
Black holes do not have a 'force' that surpasses the speed of light. Are you suggesting that they can accelerate infalling objects to greater than light speed?

Um, yes? There are two forces at work here: 1) gravity, 2) lights own velocity. From what I understand, the theory of relativity has linked these forces in a balanced way. Let's use the example of a "disappearing" Sun. If the Sun suddenly disappeared, it wouldn't be there to exert a gravitational influence on the Earth, but the effects of this wouldn't be seen until spacetime flattened out at Earth's location. This "flattening" of spacetime begins at the Sun's old location and "ripples" out until it reaches Earth. This happens at the speed of light. However, these changes in gravity don't affect the light. The light maintains it's own velocity; it still travels and without any blue or red-shifting. This is why I say that the forces of gravity and light are linked "harmoniously". They move at the same rate but maintain independance. Not so with a black hole...

Light looses it's independance around black holes. So, if light maintains independance from gravity when their forces are equal, then what does that say about the force of gravity when light looses it's independance? It says that force of gravity has surpassed that of light.

Hoku said:
Um, yes? There are two forces at work here: 1) gravity, 2) lights own velocity. From what I understand, the theory of relativity has linked these forces in a balanced way. Let's use the example of a "disappearing" Sun. If the Sun suddenly disappeared, it wouldn't be there to exert a gravitational influence on the Earth, but the effects of this wouldn't be seen until spacetime flattened out at Earth's location. This "flattening" of spacetime begins at the Sun's old location and "ripples" out until it reaches Earth. This happens at the speed of light. However, these changes in gravity don't affect the light. The light maintains it's own velocity; it still travels and without any blue or red-shifting. This is why I say that the forces of gravity and light are linked "harmoniously". They move at the same rate but maintain independance. Not so with a black hole...

Light looses it's independance around black holes. So, if light maintains independance from gravity when their forces are equal, then what does that say about the force of gravity when light looses it's independance? It says that force of gravity has surpassed that of light.
The http://www.aei.mpg.de/einsteinOnline/en/spotlights/equivalence_principle/index.html [Broken].

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JesseM said:
Usually when physicists talk about speculations like holding a wormhole open with negative energy, they mention the Casimir effect which allows a region of space between two parallel plates to have an energy density lower than the vacuum energy of quantum field theory. Of course the vacuum energy itself is usually treated as being greater than zero in GR, so this doesn't necessarily mean the space between plates actually has a negative energy in the GR sense--according to this the vacuum energy is probably about 9*10^-10 joules per cubic centimeter if we assume the vacuum energy is responsible for the cosmological constant. But hellfire said in post #51 of this thread that the energy density between plates could be lower than the vacuum energy by an amount even greater than the vacuum energy is assumed to be greater than zero in cosmology, as long as the plates were less than about 10^-5 meters apart, so that would suggest that for sufficiently small separations the energy density between plates can be negative in the GR sense. I suppose there's no way to be completely confident about this without a theory of quantum gravity though!

Exactly! That Planck scale is a real killer for current theories. I'm familiar with the Casimir Effect, but even if we assume that kind of "closeness" and a subsequent negative... I don't see how it could be applied in this case. You'd need to shape and control that 'region' of negative density relative to surroundings, and I can't even imagine how that could be accomplished.

The region of lower density is after all, confined between the plates which give rise to the effect. The only time I can still think of negative energy densities being seriously discussed on a macroscopic scale (in the classic sense, not the term of art) really is in the ergoregion. Even then, the uncertainty about whether or not LOWERING density ever reaches NEGATIVE density is just as you say. Ah well...

EDIT: @Hoku: You might find some reading into "Spacetime Geodesics" and "Degrees of Freedom" and "Refraction" both helpful and quite interesting. I'm not being sarcastic; I really believe that those topics will help you to come to a better understanding of the relationship between... hmmm... the "riverbed" and "the water" if you catch my drift.

Frame Dragger said:
Exactly! That Planck scale is a real killer for current theories. I'm familiar with the Casimir Effect, but even if we assume that kind of "closeness" and a subsequent negative... I don't see how it could be applied in this case. You'd need to shape and control that 'region' of negative density relative to surroundings, and I can't even imagine how that could be accomplished.
With flexible plates? ;) You only need a very thin layer of negative energy to keep a wormhole open, I believe. And anyway I'm not talking about whether this could be achievable in practice in the near future, just whether it's permitted by the laws of physics and could therefore be done by a "sufficiently advanced civilization" (to use a phrase that comes up a lot in discussions about wormholes and other weird spacetime geometries that wouldn't happen 'naturally')

JesseM said:
With flexible plates? ;) You only need a very thin layer of negative energy to keep a wormhole open, I believe. And anyway I'm not talking about whether this could be achievable in practice in the near future, just whether it's permitted by the laws of physics and could therefore be done by a "sufficiently advanced civilization" (to use a phrase that comes up a lot in discussions about wormholes and other weird spacetime geometries that wouldn't happen 'naturally')

You're my new hero for the "flexible plates" comment... I hope you know that. :rofl:

I see your point however... makes me hope the CPC really is more than mere conjecture!

Hoku said:
Um, yes? There are two forces at work here: 1) gravity, 2) lights own velocity. From what I understand, the theory of relativity has linked these forces in a balanced way.
Velocity isn't a force, the units are wrong.

Hoku said:
Let's use the example of a "disappearing" Sun. If the Sun suddenly disappeared, it wouldn't be there to exert a gravitational influence on the Earth, but the effects of this wouldn't be seen until spacetime flattened out at Earth's location. This "flattening" of spacetime begins at the Sun's old location and "ripples" out until it reaches Earth. This happens at the speed of light.
I don't know of any such solution to the Einstein field equations.

Hoku said:
However, these changes in gravity don't affect the light. The light maintains it's own velocity; it still travels and without any blue or red-shifting.
Gravitational red shifting is a very well-documented phenomenon. Google the Pound-Rebka experiment.

Hoku said:
This is why I say that the forces of gravity and light are linked "harmoniously". They move at the same rate but maintain independance. Not so with a black hole...
Light follows null geodesics, both in flat spacetime and also in a black hole.

Hoku said:
Light looses it's independance around black holes. So, if light maintains independance from gravity when their forces are equal, then what does that say about the force of gravity when light looses it's independance? It says that force of gravity has surpassed that of light.
Again, none of this is correct. The behavior of light is unaltered around black holes, so it doesn't lose anything that it had, and the units of force and velocity just don't match so you can't compare the two and say that one has surpassed the other.

Thank you all for your responses. One of my disadvanages is that I don't have the scientific vocabulary that most of you do. Dale, I understand what you're saying about velocity not being the same as a force. If they were parts of speech, you might say that velocity is an adjective and force is a verb. Clearly different. What I mean to compare is the force behind light's velocity with the force of gravity. Light contains a force that allows independant movement, right? Gravity is a force that affects the movement of things. These two forces are what I'm trying to "match".

I think I understand gravitational redshifting. I believe it's a relative phenomena that happens when light changes speed as it moves through gravitational fields. The disappearing Sun example is one that I picked up from The Elegant Universe (Nova DVD. Haven't read the book). I would assume that Brian Greene knows what he's talking about. Can you prove to me that he is wrong? If spacetime normally moves at the speed of light yet does not overpower lights independance, then my logic that black holes must exceed the speed of light in order to overtake light seems valid. Don't you think? My statement about red or blue shifting may not have been appropriate. All I meant to say was that light at the "event horizon" of ordinary spacetime as it flattens still maintains independace.

JesseM said, "...an free-falling observer will measure the same things that she would if she were moving inertially in flat spacetime..." and DaleSpam said, "Light follows null geodesics, both in flat spacetime and also in a black hole. ... The behavior of light is unaltered around black holes...". I think each of these statements are making the same point. But it's not clear to me that these contradict my line of reasoning. Here's why...

Let's say that we invented a way to travel faster than the speed of light - a time machine. We get inside and set the date for our 3rd birthday. We step out of the time machine and remember what a great time we had as we watch the festivities. Now, let's not get lost in grandfather paradoxes or whatever, because I don't want to loose the point. The point is that we are still "measuring the same thing" we are still following null geodesics. Do we expect to step out of the time machine as a three year old? No. The integrity of spacetime does not change for us, we are still moving into our future, even though we have traveled to a past time. Do you understand what I'm trying to say? Our "c" remains constant relative to us.

Does this take us back to the issue of "Spacetime...3+1"? 3+1 is kind of asymetrical, which makes it a bit "ugly". Do you think other possibilities would open up if it was "3+3"? 3dimensions of space + 3 of time; past, present and future? Might this inclusion change the geodesic possibilities?

Hoku said:
I think I understand gravitational redshifting. I believe it's a relative phenomena that happens when light changes speed as it moves through gravitational fields. The disappearing Sun example is one that I picked up from The Elegant Universe (Nova DVD. Haven't read the book). I would assume that Brian Greene knows what he's talking about. Can you prove to me that he is wrong?

The spacetime around a strong gravitational field changes a photons wavelength, not its velocity! This is the same reason why distant galaxies at very large redshift are 'reddened' due to cosmological expansion. Its also the reason why a distant observer will see an infinitely red-shifted photon as it approaches a black hole's event horizon.

Greene's not wrong (although I'm not a fan of string theory). Your understanding of some of the ideas he presents is wrong.

Thank you Gatchaman. I know that semantics are important and I keep missing the mark with my wording. I had already acknowledged that bringing red or blue shifting into the equation was a mistake and irrelevant to my point. I hope you are able to see past that and find the heart of what I've been trying to address.

You may be right that my understanding is wrong. That's why I'm pursuing this discussion. However, it would be more productive to pinpoint my error so that I can understand correctly rather than simply stating that I am wrong without explanation.

Hoku said:
Thank you all for your responses. One of my disadvanages is that I don't have the scientific vocabulary that most of you do.
I think it is more than that in this case. I think that because you haven't studied the material not only do you lack the vocabulary, but you also have a basic misunderstanding of the concepts. My recommendation would be to really try to learn the current material before trying to propose new theories. Learn what is well explained and experimentally verified and what is not.

Hoku said:
What I mean to compare is the force behind light's velocity with the force of gravity. Light contains a force that allows independant movement, right?
Here is an example where you simply have a wrong concept. A force is not required for uniform movement. This is Newton's first law, which is several centuries old by now.

Hoku said:
I think I understand gravitational redshifting. I believe it's a relative phenomena that happens when light changes speed as it moves through gravitational fields.
No, light never changes speed locally. What does change is the color.

Hoku said:
The disappearing Sun example is one that I picked up from The Elegant Universe (Nova DVD. Haven't read the book). I would assume that Brian Greene knows what he's talking about. Can you prove to me that he is wrong?
I didn't say that it was wrong, I just said that I have never seen such a solution to the Einstein field equations. Without such a solution I think it is impossible to make definitive statements about what would or would not happen in that situation.

Hoku said:
If spacetime normally moves at the speed of light yet does not overpower lights independance, then my logic that black holes must exceed the speed of light in order to overtake light seems valid. Don't you think?
No, you cannot logically base a correct conclusion on an invalid premise.

Hoku said:
My statement about red or blue shifting may not have been appropriate. All I meant to say was that light at the "event horizon" of ordinary spacetime as it flattens still maintains independace.
What do you even mean when you speak of "independence" in the context of light?

Hoku said:
The point is that we are still "measuring the same thing" we are still following null geodesics.
No, light follows null geodesics. We follow timelike worldlines that are not generally even geodesics.

Hoku said:
Do we expect to step out of the time machine as a three year old? No. The integrity of spacetime does not change for us, we are still moving into our future, even though we have traveled to a past time. Do you understand what I'm trying to say? Our "c" remains constant relative to us.
I don't get your point here. Are seriously trying to make some sort of definitive conclusion based on a hypothetical feature of some fictional time travel machine?

Hoku said:
Does this take us back to the issue of "Spacetime...3+1"? 3+1 is kind of asymetrical, which makes it a bit "ugly". Do you think other possibilities would open up if it was "3+3"? 3dimensions of space + 3 of time; past, present and future? Might this inclusion change the geodesic possibilities?
Certainly. If spacetime had a different signature (e.g. 3+3) you could obtain closed timelike curves in flat spacetime. Heinlein really enjoyed that idea towards the end of his career. I will remind you, however, that it was science fiction, not science.

Hoku said:
However, it would be more productive to pinpoint my error so that I can understand correctly rather than simply stating that I am wrong without explanation.
1) Forces are not required for uniform motion
2) The local speed of light is always c (even inside a black hole)
3) Gravitational redshifting is a change in the color (frequency) of light
4) Massive objects do not follow null geodesics
5) Light does follow null geodesics (even inside a black hole)
6) The existing evidence all points towards 3+1 being the correct signature

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I tried to tell him to research geodesics, and other topics that would have illuminated this subject by now. Clearly he never bothered to do that, for if he did you *DaleSpam* wouldn't be having to post what you just did.

I know this site is educational in its mission, and I respect that, but if someone is unwilling to educate themselves and is more interested in the "fantasy" of physics... well... maybe there needs to be a better mechanism to rapidly address that. It's not as though the world is filled with qualified science advisors and staff with unlimited free time. This seems... wasteful... when we all know Hoku needs to go back to some basics.

I don't believe that it's disrespectful to say so, rather the opposite! There is a level of polite discourse here, which I appreciate, but can sometimes stray into the realm of... if not actually toying with people, then at least stringing them along. A lot of people seem to come here to share their internal "breakthrough", and then resent it when the forum and world alike don't see the LIGHT.

@Hoku: You should really go to the books section here and read some of the classics and the basics. EVERYONE has to learn somewhere, somehow, but making assumptions and delving into fantasy isn't the way. You can draw your own conclusions and theories either way, but having educated yourself a bit more, or drawing on less... intense... resources you'd be in a better position to express them.

An unkind person would mock the source of your knowledge as being more about entertainment for the mass market, and ignore that you HAVE latched on to some very interesting concepts. You've had a glimpse of page 50... but now it's time to go back to page 10 and work up to a deeper understanding of what was being discussed on 50... if you catch my meaning.

Again, I don't mean to insult or offend you. If I believed that you were just some deluded fool, I wouldn't have bothered to write the preceeding.

Wow. I'm really saddened right now. Does nobody understand what I'm saying? I'm not making up any theories here, I'm just trying to understand what I've learned.

1) Brian Greene says that normal spacetime moves at the speed of light.
2) In normal spacetime, light has freedom of movement, which means it is free to travel away from a source of gravity.
I think both of these premises are true and I haven't made them up.

3) Light is not free to travel away from a black hole.
This is also true.

Why, then, should it not be concluded that spacetime at a black hole moves faster than light?

But I can see that there is no compassion for this logic and I must be content with my confusion. I don't mean to waste peoples time but people are certainly free to ignore my threads and posts. Thanks to everyone for trying. And Frame Dragger, I know how cruel you can be so I thank you for going easy on me. I'll research geodesics more.

:yuck: