Is space discrete ?

[kevin1981]

The world as i understand it, is made up of tiny particles (and fields) so at the deepest level what is actual "space" made out of? Is it tiny bits of matter like everything else, do we even have any theories/ideas on this subject.

I ask this as i was trying to think of a question but could'nt come up with anything else for the moment.

I know space can "warp", "twist" and "curves" in the presence of matter/energy and the theory of general relativity is geographical. So to be able to "warp", "twist" and "curve" it must be "made" from something?

I hope that makes some sense and look forward to reading what others think.

[tdvance]

Well, the ultimate underlying nature of reality is not known (and the reality of nature is debated by philosophers), but so far, it appears fundamentally, the universe is not discrete---worse, the "probabilities" that govern quantum mechanics seem to be complex values rather than real values--but that (the phase information as opposed to the amplitude which *is* a real number) only shows up in interference between two waves; can't be measured absolutely as far as is known. Penrose had some kind of twistor theory that was somewhat discrete, but even Penrose doesn't think that's panning out anymore.

[WayneFrancis]

I think the closest you can get to that idea would be the Planck length but even this is speculative on its real effects. I might have a bearing on quantum gravity but we don't know yet. If space is a field then I'm not sure how much you can say its made up of "something" besides the field. I think the key here is not to necessarily equate "what makes up space" with anything you can easily relate to. Just like you can't treat photons as just a wave or just a particle. Space might be loosely analogous to stuff that is more tangible to use but step to far in the association and you'll end up with a wrong model of what space actually is.

[kevin1981]

So it is probably best to view space as a field then. I do anyway, i was just thinking out loud, but sometimes when i think about how "reality" really is at those tiny distance scales i find it truly bizzaire and fascinating at the same time. Like how a particles location is based on probability and an electron can be in 3 places at the same time ect.. It seems like proper chaos down there !

[DrRocket]

So it is probably best to view space as a field then. I do anyway, i was just thinking out loud, but sometimes when i think about how "reality" really is at those tiny distance scales i find it truly bizzaire and fascinating at the same time. Like how a particles location is based on probability and an electron can be in 3 places at the same time ect.. It seems like proper chaos down there !

It apparently is "proper chaos" speaking loosely.

I seem to recall a comment, I think from Steven Weinberg, that lattice models (the correct term for discrete models of spacetime) have been attempted but that there are big problems with formulating physics in that setting.

There have also been suggestions, originally from John Archibald Wheeler, that spacetime on the smallest scales is not simply connected and has a quantum character -- what he called "quantum foam". I don't think that idea has ever been made precise or gone anywhere, though one sees references to it writings by the loop quantum gravity crowd.

"There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe that there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper, a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I can safely say that nobody understands quantum mechanics." – Richard P. Feynman in The Character of Physical Law

[Jens]

The question of whether space and time are discrete or continuous is one that has been thought of by people throughout history. The famous paradoxes of Zeno deal with that very issue. I think the honest answer is that nobody really knows. We do not understand the essential structure of the universe, and in my opinion we probably never will, or never can if you want. We can get better approximations, but I think that any answer we find will in fact lead to more questions.

[DrRocket]

The question of whether space and time are discrete or continuous is one that has been thought of by people throughout history. The famous paradoxes of Zeno deal with that very issue. I think the honest answer is that nobody really knows. We do not understand the essential structure of the universe, and in my opinion we probably never will, or never can if you want. We can get better approximations, but I think that any answer we find will in fact lead to more questions.

Zeno's "paradox" has nothing to do with whether space is discrete or a continuum.

Zeno's "paradox" (there are several but I think you are referring to the "dichotomy paradox") is not even a paradox, but rather just bad reasoning. In any case it does not depend on a discrete version of space.

Whether or not there is an ultimate "theory of everything" is up in the air. But history is on your side. So far our understanding has progressed as series of successive approximations, with no limit point in sight.

[gzhpcu]

As Dr. Rocket mentions, Loop Quantum Gravity postulates the minimum size of space.

source: http://universe-review.ca/R01-07-quantumfoam.htm

A theory to describe space with the size of the Planck length has been developed lately. It is called theory of loop quantum gravity, which postulates that the minimum linear size of space is of the order of the Planck length.

One aspect of the loop models, though, is easy to grasp: Space, in general relativity, is a continuum. In every part of it, one can define regions of arbitrarily small volume, and every little region can be divided further into smaller regions still, ad infinitum. In the loop models, the basic structure of space-time turns out to be discrete. Just as, with a childrenīs lego set where you cannot build a structure smaller than the smallest block, in such discrete space times, there are smallest values for volumes and areas that are not divisible any farther. The fabric of space is what is called a spin network with lines and nodes

source: http://www.aei.mpg.de/einsteinOnline...ops/index.html

[kevin1981]

Thanks for your answers, it makes interesting reading. I have another question about Inflation at the start of the universe but don't want to start a thread about it as i could just as easy ask here.

I have just read this and i understand what it is saying but do have some questions also which hopefully someone could help me with.

"The Cosmic Inflation theory proposes that there was a period in the very early stages of the cosmos in which extremely rapid, exponential expansion of the universe took place prior to the more gradual Big Bang expansion. During the period of inflation, the energy density of the universe was dominated by a cosmological constant-type of vacuum energy. Later, the vacuum energy decayed to produce the matter and radiation we see in our universe at present. Inflation was rapid. It increased the size of the universe by a factor of ~1026 in only a small fraction of a second. When the period of inflation had ceased, essentially, the universe, which began as a quantum fluctuation about 1020 times smaller than a proton, had grown to a sphere about 10 centimeters in diameter in 15 X 10-33 seconds. The inflation was rapid enough to overcome gravity and in fact had expanded faster than light."

I know it is basically saying that in an instant (well very quick) it grew from a billion times smaller than a proton to the size of an apple, but how much quicker than light was inflation and after the inflation period when it slowed down how quick was space expanding ?

[DrRocket]

Thanks for your answers, it makes interesting reading. I have another question about Inflation at the start of the universe but don't want to start a thread about it as i could just as easy ask here.

I have just read this and i understand what it is saying but do have some questions also which hopefully someone could help me with.

"The Cosmic Inflation theory proposes that there was a period in the very early stages of the cosmos in which extremely rapid, exponential expansion of the universe took place prior to the more gradual Big Bang expansion. During the period of inflation, the energy density of the universe was dominated by a cosmological constant-type of vacuum energy. Later, the vacuum energy decayed to produce the matter and radiation we see in our universe at present. Inflation was rapid. It increased the size of the universe by a factor of ~1026 in only a small fraction of a second. When the period of inflation had ceased, essentially, the universe, which began as a quantum fluctuation about 1020 times smaller than a proton, had grown to a sphere about 10 centimeters in diameter in 15 X 10-33 seconds. The inflation was rapid enough to overcome gravity and in fact had expanded faster than light."

I know it is basically saying that in an instant (well very quick) it grew from a billion times smaller than a proton to the size of an apple, but how much quicker than light was inflation and after the inflation period when it slowed down how quick was space expanding ?

Just do the calculatoin. It the radius of the sphere was about 5 centimeters after 15x 10^-33 seconds then a hypothetical point on the "edge" moved at about 3x10^32 cm/sec away from the "center" (you can assume that it started at radius 0 since the radius of a proton is orders of magnituce less than a centimeter). Since c is 3x 10^10 cm/sec the recession speed was 22 orders oif magnitude greater than the speed of light -- that is a lot.

There really is no "center" or "edge" but in this case you can take any point as the center and any other point as the edge. It is just easier to visualize what is going on with the imagery of "edge" and "center".

I don't know the answer to your second question off the top of my head.

[astromark]

The really big questions do have answers. We just can not see them., or if we can, fail miserably to convey such.
What is contained in empty space ? ... The ether., ( What ! ) and everything else. All that we can know of is in space. This would include some things we know almost nothing of. Dark Matter. Energy. and its also filled by waves of photons and Dark Energy and a great deal of things we have no knowledge of. Yet we still describe it as empty... space. The foam is very very thin...
Then you ask of the expansion rate in the earliest moments of 'Creation' Oh I so did not want to use that word...Lol
I must stride in here and remind you that at those moments 'Mater' as we know it had not yet materialized. Super hot super dense and almost pure energy... We can not test. and therefore can not know. With each and every new paper we might get closer to what we think as fact... can we ever be sure.

[DrRocket]

The really big questions do have answers. We just can not see them., or if we can, fail miserably to convey such.
What is contained in empty space ? ... The ether., ( What ! ) and everything else. All that we can know of is in space. This would include some things we know almost nothing of. Dark Matter. Energy. and its also filled by waves of photons and Dark Energy and a great deal of things we have no knowledge of. Yet we still describe it as empty... space. The foam is very very thin...
Then you ask of the expansion rate in the earliest moments of 'Creation' Oh I so did not want to use that word...Lol
I must stride in here and remind you that at those moments 'Mater' as we know it had not yet materialized. Super hot super dense and almost pure energy... We can not test. and therefore can not know. With each and every new paper we might get closer to what we think as fact... can we ever be sure.

That is most flowery "beats the hell out of me" that I have seen in a long time. But it is pretty accurate.

[kevin1981]

That is most flowery "beats the hell out of me" that I have seen in a long time. But it is pretty accurate.

LOL Well at least he had a go !

Thanks for the answers