Exploring Space-Time: Dilation & Concentration

[Dale]

Ok, and this is where the rubber hits the road - how can it have properties, 'information' and still be space?

All spaces have properties, so I don't know what would lead you to believe that having properties is antithetical to being a space.

Personally, I think that this is your key misconception. Spacetime is not nothing, it is a 4D pseudo Riemannian manifold. 4D pseudo Riemannian manifolds are topological spaces with a metric structure, and as such they have topological and geometrical properties. Any assumption that it should not have properties is simply a bad assumption which needs to be discarded.

And then, if it does have said properties, in what 'space' does it exist in? A higher dimension of some sort? Multiverse?

There are many embedding theorems about how a curved manifold may be isometrically embedded into a higher-dimensional flat manifold. However, none of those are necessary (nor even useful) for describing physics. All of the physics can be described from within the curved 4D manifold without reference to any higher dimensional manifolds.

 

[phinds]

AT, read what I wrote in my second response to you. Eucledian Geometry seems to be nothing more than a logical, mathematical, self-supporting construct existing outside of any actual 'eucledian', three-dimensional space. [read: it exists insofar that we know of it and understand it, like fiat currency (plus understanding)]

Yes it does. So does Riemann geometry (exist as a math model divorced from physicality). The fact that one (Riemann) describes space in GR and the other (Euclidean) seems to make some sort of profound difference to you, and the other folks here are just trying to ascertain WHY it makes such a difference.

 

[Dale]

Adrian2000, phinds makes a very good point above. Both Riemannian geometry and Euclidean geometry are "logical, mathematical, self-supporting constructs". They are both equally valid as mathematical frameworks and both self-consistent (logical).

There is no reason, a priori, why one should be a better model for reality than the other. That is a question that can only be determined by experiments. It turns out that Riemannian geometry predicts the experimental data better than Euclidean geometry.

So, we have to recognize that our preconceptions favoring Euclidean geometry over Riemannian geometry are simply that: preconceptions. Nature need not conform to our preconceptions, and in this case does not. When this happens, we always need to change our preconceptions because we cannot change Nature.

 

[Adrian2000]

What may be throwing you here is that we all have a very strong bias that Euclidean space is somehow what's "natural", so that parallel lines not intersecting, the Pythagorean theorem holding, and the like require no explanation; whereas any observed deviations from these behaviors must be explained in terms of something acting to change the behavior away from its "natural" Euclidean behavior. You see evidence of this bias when you consider how long it took for people to accept that the two-dimensional surface of the Earth is not a Euclidean plane embedded in a three-dimensional Euclidean space - it's a non-Euclidian non-flat two-dimensional surface embedded in a three-dimensional Euclidean space.

You are quite right with regards to Euclidean space, however..

It has nothing to do with 'natural' vs 'unnatural' - persons who advocate the wholesale discarding of what's 'natural' only replace one biased framework for another - it has to do with a logical, tangible understanding of what space actually means. Ok, great, we have space that has conditional properties like objects do. That makes it a zone of some sort, not a space. Which begs the follow-up question - how is this zone defined? By what? From where? Is there a higher plane of existence? And so on and so forth. It's wonderful that everybody here wants to re-assure me of the fact that human beings are human, but that's kind of beyond the point.

Yes it does. So does Riemann geometry (exist as a math model divorced from physicality). The fact that one (Riemann) describes space in GR and the other (Euclidean) doesn't seems to make some sort of profound difference to you, and the other folks here are just trying to ascertain WHY it makes such a difference.

Betrayal! (On a serious note, it makes absolutely zero difference to me - I have no idea where you got that from, and it actually makes me scared I made a blunder in my rhetoric earlier)

Adrian2000, phinds makes a very good point above. Both Riemannian geometry and Euclidean geometry are "logical, mathematical, self-supporting constructs". They are both equally valid as mathematical frameworks and both self-consistent (logical).

There is no reason, a priori, why one should be a better model for reality than the other. That is a question that can only be determined by experiments. It turns out that Riemannian geometry predicts the experimental data better than Euclidean geometry.

So, we have to recognize that our preconceptions favoring Euclidean geometry over Riemannian geometry are simply that: preconceptions. Nature need not conform to our preconceptions, and in this case does not. When this happens, we always need to change our preconceptions because we cannot change Nature.

Fellas, is this a joke? First triangles, now I'm the luddite hanging on to my Eucledian wheelbarrow while you're selling me Riemannian iPods? I couldn't care less about the nomenclature of the 'space' part of 'space-time'. I truly couldn't. Nevermind basic English comprehension, does anyone here have a lick of Physics knowledge and give me an elementary response to two basic questions??

Question 1: Is it true that space curves around gravity?
Question 2: If this is the case, does it not seem funny to anyone here that space itself, devoid of matter, radiation and anything else we understand to exist in this universe has the potential to warp under gravitational strain?? (Phinds seems to agree :/ )

 

[Dale]

Fellas, is this a joke? First triangles, now I'm the luddite hanging on to my Eucledian wheelbarrow while you're selling me Riemannian iPods?

Basically, yes (although without the unkind connotation of "Luddite", this is a normal learning process). It appears that you accept Euclidean space without question (and consider it to have no "properties"), but seem to consider for some reason that Riemannian spacetime has properties which are incompatible with it being a model of space.

Question 1: Is it true that space curves around gravity?

Yes. There is substantial experimental evidence for that.

Question 2: If this is the case, does it not seem funny to anyone here that space itself, devoid of matter, radiation and anything else we understand to exist in this universe has the potential to warp under gravitational strain?? (Phinds seems to agree :/ )

Sure it is funny. Everyone has to adapt their thinking when they are learning GR. However, once you do so, you see that it is completely logically self consistent and it is more consistent with the experimental data than any other model proposed to date.

 

[Adrian2000]

Sure it is funny. Everyone has to adapt their thinking when they are learning GR. However, once you do so, you see that it is completely logically self consistent and it is more consistent with the experimental data than any other model proposed to date.

It makes for a convinient explanation, and a good one too, but I'm wondering if it's more of a band-aid than a model of reality. Insofar that all the effects it describes indeed exist, and I don't dispute them, but the actual description of space-time has already been proven to break-down at the point of singularity, which can serve as a reductio-ad-absurdum counterargument to the theory, as well as a launchpad to a more comprehensive model of the universe. Other scientists have appeared to concede as much, with, if I recall correctly, Hawking stating that Einstein's model of space-time is functional for a macroscopic view of the universe, while quantum mechanics, the apparentely more sound model, being more appropriate for a microscopic view of the universe.

But that's not really what I want to argue;

I don't want to beat a dead horse, but I still have trouble understanding how empty, naked space that we can all experience, as we all exist in it, even if it's filled with matter and energy, is then conditional on something like gravity. It just doesn't add up to me. Not intuitively, not logically, not rationally or tangibly. I don't have the geometry to make heads or tails of Riemannian space, but I doubt it would convince me otherwise even if I did.

 

[Dale]

It makes for a convinient explanation, and a good one too, but I'm wondering if it's more of a band-aid than a model of reality. Insofar that all the effects it describes indeed exist, and I don't dispute them, but the actual description of space-time has already been proven to break-down at the point of singularity, which can serve as a reductio-ad-absurdum counterargument to the theory, as well as a launchpad to a more comprehensive model of the universe.

The same can be said of all physical theories. So while this is true, it is also not something that is new and unique to GR nor is it something that is likely to change any time soon for any physics theory.

I don't want to beat a dead horse, but I still have trouble understanding how empty, naked space that we can all experience, as we all exist in it, even if it's filled with matter and energy, is then conditional on something like gravity. It just doesn't add up to me. Not intuitively, not logically, not rationally or tangibly.

It doesn't add up to most beginning students intuitively either. As far as logically, rationally, and tangibly, you simply don't have the required background to judge. If you are interested in learning, then I would recommend starting here:
http://preposterousuniverse.com/grnotes/

It takes effort, but that effort is required before an informed claim regarding its logical consistency can be made.

 

[Adrian2000]

The same can be said of all physical theories. So while this is true, it is also not something that is new and unique to GR nor is it something that is likely to change any time soon for any physics theory.

Well hold on a minute there, that's not exactly true, is it? When has Quantum Mechanics been proven to have holes in its theory? And what of the Theory of Gravity, Big Bang/Higgs Boson stuff aside?

 

[PAllen]

AT, read what I wrote in my second response to you. Eucledian Geometry seems to be nothing more than a logical, mathematical, self-supporting construct existing outside of any actual 'eucledian', three-dimensional space. [read: it exists insofar that we know of it and understand it, like fiat currency (plus understanding)]

This is just wrong. You have to make other assumptions. Those assumptions prescribe geometry. Mathematically, there is nothing that favors Euclidean geometry as 'neutral' or 'natural'. It was physical experience that made it natural, for a long time, to e.g. assume the parallel postulate. As soon as the question was asked, mathematically, 'what if the parallel postulate was not true? ', it was found that there were no contradictions, and you simply got other geometries.

 

[Adrian2000]

This is just wrong. You have to make other assumptions. Those assumptions prescribe geometry. Mathematically, there is nothing that favors Euclidean geometry as 'neutral' or 'natural'. It was physical experience that made it natural, for a long time, to e.g. assume the parallel postulate. As soon as the question was asked, mathematically, 'what if the parallel postulate was not true? ', it was found that there were no contradictions, and you simply got other geometries.

Oh for god's sake, I already covered this, I said 'Eucledian' because I did not know of Riemannian space - the precise descriptor is the 'space' part of spacetime (as we observe it in reality).

 

[Adrian2000]

Right, unless anyone has anything else to add, I suppose the mature option would be to agree to disagree. (and for me to go back to the books, so I could make some independent conclusions with a measure of confidence rather than asking all of you to help me out, which you have, in your own way :) )

So thank you and adieu :)

 

[PAllen]

Oh for god's sake, I already covered this, I said 'Eucledian' because I did not know of Riemannian space - the precise descriptor is the 'space' part of spacetime.

No, you did not cover it. You claim trianges adding up to 180 degrees is natural. This is false. It is a consequence of other axioms. In particular, it is false if you assume the parallel postulate is false.

 

[Adrian2000]

No, you did not cover it. You claim trianges adding up to 180 degrees is natural. This is false. It is a consequence of other axioms. In particular, it is false if you assume the parallel postulate is false.

180 degrees is natural? What? It's logical and deductive, as you say, a result of a self-supporting framework of the definition of a 2-dimensional triangle.

I covered it at the bottom of the 2nd page, in my response to Dale.

 

[Dale]

Well hold on a minute there, that's not exactly true, is it? When has Quantum Mechanics been proven to have holes in its theory?

Sure, infinities crop up all the time in QM. The whole topic of renormalization was invented specifically to address those infinities.

 

[PAllen]

Where the hell are you getting your information from, pal? 180 degrees is natural? What? It's logical and deductive, as you say, a result of a self-supporting framework of the definition of a 2-dimensional triangle.

I covered it at the bottom of the 2nd page, in my response to Dale. So have a coke and relax. Bad enough with one AT, now we have a second one.

I saw no understanding of how properties you claim are natural and neutral are anything but that. Other choices are equally logical and deductive. It is nothing but our low precision physical experience that makes particular choices for geometric axioms seem natural.

 

[Bandersnatch]

You know this is why nobody talks to you people.

Hey, I resent this statement! I talked to the mailman back in 1996. He seemed to enjoy it, though I haven't seen him since.

 

[Adrian2000]

Hey, I resent this statement! I talked to the mailman back in 1996. He seemed to enjoy it, though I haven't seen him since.

Hehe, at least some of us still have a sense of humour ;)

 

[Dale]

It's logical and deductive, as you say, a result of a self-supporting framework of the definition of a 2-dimensional triangle.

Only in Euclidean geometry.

Consider a triangle on the surface of the Earth (idealized as a 2D curved manifold called a 2-sphere). You can draw a triangle with three right angles (270 degrees). Just start at the equator, go due north to the north pole, turn 90 deg, go due south to the equator, turn 90 deg, and go back to where you started where you will need to turn 90 deg again to face the direction you were originally facing.

In a positively curved manifold, like a 2-sphere, a triangle's interior angles will add up to greater than 180 deg. The 180 deg result only holds for Euclidean geometry, and does not hold for other geometries. The Euclidean geometry is called "flat" and deviations from the 180 deg are an indication of intrinsic curvature.

 

[Adrian2000]

Only in Euclidean geometry.

Consider a triangle on the surface of the Earth (idealized as a 2D curved manifold called a 2-sphere). You can draw a triangle with three right angles (270 degrees). Just start at the equator, go due north to the north pole, turn 90 deg, go due south to the equator, turn 90 deg, and go back to where you started where you will need to turn 90 deg again to face the direction you were originally facing.

In a positively curved manifold, like a 2-sphere, a triangle's interior angles will add up to greater than 180 deg. The 180 deg result only holds for Euclidean geometry, and does not hold for other geometries. The Euclidean geometry is called "flat" and deviations from the 180 deg are an indication of intrinsic curvature.

I agree wholeheartedly.

 

[PAllen]

I get it, you know more physics than me and are apparentely more up for a confrontation than I am at this hour; that doesn't mean you can put words in my mouth that I never said. So try to understand what I was actually trying to say.

It seems to me that you are not not listening, and I am trying my best to understand where you are coming from.

I still don't see, from your posts, that you understand that Euclids axioms that you learned in plane geometry include arbitrary choices. That consistent, logical systems follow by making different choices. If you change just one assumption (the parallel postulate), then the angles of triangles no longer add up to 180 degrees. I have not seen an indication that you at least understand this mathematical fact.

[Edit: well now maybe I do, for the first time: #54, made after I posted this.]

 

[harrylin]

Hi Harrylin!

Yes, and this is what I meant - IF said measuring rod appears shorter to an outside observer, does it have to do with the actual object (rod) being physically shortened, or does it have to do with space contracting around a gravitational field? And if it is the latter, then clearly this space, nothing IS actually something, and has internal properties, does it not? (according to GR, whether explicitly or implicitly?)

Imagine a "stationary" observer in "deep space" with an equally stationary rod in a reasonably stationary universe; and he sends the rod in vertical orientation slowly down to Earth with an Earth lander. Most people would then agree with the point of view that the stationary observer has not significantly changed, which logically implies that actually (or "really") it's the rod's length that has changed, and thus the rod has become shorter. And as you may have seen, a clock will similarly tick slower.

Moreover, the speed of light is also governed by space, even far away from matter. Therefore we must conclude that "empty space" is of course empty of matter, but it has properties. GR can say nothing more than that; Einstein was smart but he was not a prophet or a medium! And probably no serious book will tell you about "space contraction".

Ok, and this is where the rubber hits the road - how can it have properties, 'information' and still be space? Surely that means that it's not space at all, but some sort of 'zone' (if you like)? And then, if it does have said properties, in what 'space' does it exist in? [..]

"Space" means a volume that is free to move in, and "empty space" only means that there is no matter inside. ;)
And near a heavy mass such as the Earth there certainly is a "zone" of which the properties are affected by the mass: the common term is "gravitational field". :)

 

[Adrian2000]

Imagine a "stationary" observer in "deep space" with an equally stationary rod in a reasonably stationary universe; and he sends the rod in vertical orientation slowly down to Earth with an Earth lander. Most people would then agree with the point of view that the stationary observer has not significantly changed, which logically implies that actually (or "really") it's the rod's length that has changed, and thus the rod has become shorter. And as you may have seen, a clock will similarly tick slower.

Moreover, the speed of light is also governed by space, even far away from matter. Therefore we must conclude that "empty space" is of course empty of matter, but it has properties. GR can say nothing more than that; Einstein was smart but he was not a prophet or a medium! And probably no serious book will tell you about "space contraction".

"Space" means a volume that is free to move in, and "empty space" only means that there is no matter inside. ;)
And near a heavy mass such as the Earth there certainly is a "zone" of which the properties are affected by the mass: the common term is "gravitational field". :)

Harrylin, I love your avatar, and you are hands-down the most helpful member on this forum :) That is *exactly* what I was wondering about, and you hit the nail square on its head. I was confused by the prescriptions of space-time as described by GR, but am calmed by the fact that its prescriptions appear to be more tame than I thought. I don't dispute the effects of space-time dilation, but was confused with regards to what it actually meant for the nature of our universe (specifically, the nature of spacetime). As I've already mentioned (before Paul here managed to drag me back into the discussion) I think the wisest thing to do here is to say thank you for all of your help, and to go back to the literature so I could make some informed conclusions of my own. :)

Thank you all,
Farewell, Godspeed, LL&P, Gesundheit & Adieu
Adrian

 

[Dale]

With that I think we will close the thread