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Einstein's Curvature

sleeker
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Posted 11/19/04 - 02:43 PM:	#1
We all know about how Einstein's theory states that gravity is the cause of the curvature of space-time. The problem I have with this is that I've only ever seen a model like this with a curved plane being the space-time continuum (a ball bending a paper at the middle). How do you transfer that into our three dimensional world? It's obvious that this curvature cannot occur in two dimensions, but I don't know if it could happen in the third dimension. The only way I can understand it is if the space-time continuum exists in four dimensions, which would allow our universe to be placed on it so the gravitational curving would be correct. If I need to explain it more, I will because it all of a sudden got hard to transfer my thoughts to words now. I'd also like to ask if the graviton and the gravitational curvature of space are two seperate theories, and if not, how can they be mixed?

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Posted 11/19/04 - 02:53 PM:	#2
General relativity does not say that gravity causes the curvature of spacetime, it says that gravity is the curvature of spacetime. The only way I can understand it is if the space-time continuum exists in four dimensions, which would allow our universe to be placed on it Spacetime is our universe (and is by definition four dimensions), so placing our universe "on it" makes no sense.

Socrastein
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Posted 11/19/04 - 03:01 PM:	#3
Of course the space-time continuum exists in 4 dimensions: 3 "spacial" dimensions and 1 "time" dimension. Space-time curvature that results in the force of gravity belongs to the General Theory of Relativity, while the theoretical graviton (Scientists have predicted it's existence and what properties it would have, but have yet to experimentally verify it's existence) belongs to quantum mechanics, more specifically the Standard Model, as one of the many "foce carrying" particles, the graviton being responsible for carrying/transmitting the gravitational force, naturally. How can they be mixed? Superstring theory is expected to do just that. String theory proposes that all the various "elementary" point particles that quantum mechanics and the standard model operate with aren't really elementary or points at all, but are rather composed of TINY, looped, one dimensional strings, strings being the most fundamental constituent of mass and energy, or mass/energy. Rather than quarks and gluons and neutrinoes and electrons (among others) being elementary point particles, they are all manifestations of various vibrational frequencies and amplitudes of those tiny little fundamental strings. The "mixing" comes in when one recognizes that string theory mathematically predicts a certain vibrational pattern of a string that results in a particle who's properties and forces match those of the predicted graviton. So string theory actually explains/encompasses not only quantum mechanics and the various particles of the standard model, but also gravity as well. This incredibly delicious feature, that string theory has the potential to unite and explain all four of the fundamental physical forces, is what has so many physicists working hard to try and develop the theory. Unfortunately, the mathematics of string theory are incredibly complicated, so much so that the very equations of which it is composed are not even known! All scientists have been able to do so far is approximate what the equations should look like, and further they have to approximate the various values to input into these approximated equations. So right now, because of our lacking mathematical prowess (Many believe it will be quite some time before we can "solve" string theory, because it requires the invention of a whole new mathematics, much in the same way Newton had to invent Calculus to encompass his theories of gravity) the best we have are approximate approximations. However, this has deterred very few, because the exciting thing is that even with as little as we understand about this promising theory, we have already seen incredible things and derived amazing explanations. Not to mention Einstein's Special and General Relativity equations are actually found within string theory itself! As well as quantum mechanics. The past 100 years of physics just naturally arise out of the mathematics of string theory. A very tantalizing treat, if you ask me, and one that keeps the physicists thirsting and plugging away, hoping one day to substantiate all the excitement that has been generated by the most promising candidate for the Unified Field Theory, or Theory of Everything! Sorry if I got a little long-winded If you have any questions, just let me know, I'll do my best to answer with what humble knowledge I have.
"The time has come for people of reason to say enough is enough. Religious faith discourages independent thought, it's devisive, and it's dangerous." -Richard Dawkins

Kwalish Kid
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Posted 11/19/04 - 06:02 PM:	#4
Bringing up string theory is not an appropriate answer to the question at hand. Almost everyone in the physics community believes that general relatvitiy is correct to some extent. The jury is out on string theory. Sleeker, I recommend that you begin to think about spacetime curvature as just that space-time curvature. Gravity determines the straight line (or free-motion) paths in the geometry of spacetime. Thus the proper straight line that the Moon is following is the orbit around the Earth. This is a path in the four dimensions of spacetime. So, you aren't thinking of paths that are curved in space, you're thinking of paths that are curved in spacetime.
"Scientific truth is always paradox, if judged by everyday experience, which catches only the delusive nature of things." - KM, V, P and P "A fishnet is made up of a lot more holes than strings, but you can't therefore argue that the net doesn't exist. Just ask the fish." - Jeffrey Kluger "…Love of God and compassion and empathy leads you to a very glorious place, and science leads you to killing people." -Ben Stein [This is included for the irony.]

Socrastein
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Posted 11/19/04 - 07:43 PM:	#5
He asked how can they be mixed, string theory is the best contender. Hence I "brought it up". Unless you have a better theory that you have personally created that can unite QM and GR, I am confused as to why my answer was "inappropriate". Or did you simply not read his entire post, missing the part where he essentially asks for possible unification?
"The time has come for people of reason to say enough is enough. Religious faith discourages independent thought, it's devisive, and it's dangerous." -Richard Dawkins

Kwalish Kid
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Posted 11/20/04 - 08:19 AM:	#6
I'm sorry, I thought that "graviton" was "gravitation". Personally, I'm not even sure that there is anything like a graviton. I'm convinced of gravity waves and the finite propogation of gravity. I'm waiting for some actual evidence to be able to relate to these theories before giving them much credence. Especially if they infer the existence of a preferred frame of reference. On both of these counts, it seems that Loop Quantum Gravity (Ashtekar, Smolin and others) is doing the best. But I'm not buying anything from them yet.
"Scientific truth is always paradox, if judged by everyday experience, which catches only the delusive nature of things." - KM, V, P and P "A fishnet is made up of a lot more holes than strings, but you can't therefore argue that the net doesn't exist. Just ask the fish." - Jeffrey Kluger "…Love of God and compassion and empathy leads you to a very glorious place, and science leads you to killing people." -Ben Stein [This is included for the irony.]

Machiveli
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Posted 11/20/04 - 10:47 AM:	#7
"curvature" in this context does not require space to be curved within a higher dimentional space. Rather it refers to "intrinsic curvature" which is to do with path lengths. e.g. imagine if you could not percieve height - you could still discover the presence of hills because walking from point A to point B takes longer if you need to go over a hill. http://164.8.13.169/Enciklopedija/math/math/c/c854.htm
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Socrastein
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Posted 11/20/04 - 05:04 PM:	#8
Machiveli - if you can't percieve height, then you're living in a two-dimensional world (from your perspective) which is curved in a higher dimension - 3D. Not too good of an example to use right after saying curvature does not require space to be curved within a higher dimension of space, seeing as how your example is curvature within a higher dimensional space
"The time has come for people of reason to say enough is enough. Religious faith discourages independent thought, it's devisive, and it's dangerous." -Richard Dawkins

sepia
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Posted 11/20/04 - 06:53 PM:	#9
Socrastein wrote: Machiveli - if you can't percieve height, then you're living in a two-dimensional world (from your perspective) which is curved in a higher dimension - 3D. Not too good of an example to use right after saying curvature does not require space to be curved within a higher dimension of space, seeing as how your example is curvature within a higher dimensional space You know that isn't what Mach meant. Here's a thought: I wonder how many proponents of string theory actually understand the mathematics behind it to the fullest. Because I don't, and that is why I don't (yet).

sepia
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Posted 11/20/04 - 06:59 PM:	#10
sleeker wrote: The only way I can understand it is if the space-time continuum exists in four dimensions, which would allow our universe to be placed on it so the gravitational curving would be correct. Exactly. However...I still do not understand what you are asking. Sorry. Though I try to remember that some things are created for postulates' sake.

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