# Is Space Continuous?

1. Jul 23, 2011

### Nano-Passion

Or do we have no idea?

2. Jul 23, 2011

### samsracecar

You mean infinite? No, the universe is actually donut-shaped (seriously) and very much finite, but is expanding at such a fast pace that it can be considered infinite. But not really.

3. Jul 23, 2011

### Naty1

We have no idea.

Nobody knows exactly what space or spacetime actually is...

try this discussion:

A search will turn up hundreds of discussions closely related to this subject.

My own suspicion is that it is likely discrete because at Planck length and smaller, about 10-33 cm quantum foam seems to destroy conventional ideas of space,time,matter,etc.
But the continuous perspective works very well in most of classical physics...like relativity.

4. Jul 29, 2011

### Naty1

I came across these notes of mine which might be of interest.

from Lee Smolin, THREE ROADS TO QUANTUM GRAVITY:

5. Jul 29, 2011

### bcrowell

Staff Emeritus
A little over a year ago I asked for comments on Smolin's arguments as presented in that book, and got some very helpful responses: https://www.physicsforums.com/showthread.php?t=391989

6. Jul 29, 2011

### Nano-Passion

Can you tell me exactly what quantum foam is? I've watched a lecture that mentioned it but I don't have much of an idea about it.

7. Jul 30, 2011

### tom.stoer

There are many indications for spacetime-discreteness: holographic principle, T-duality in string theory, spin networks in LQG, even in the asymptotic safety program something like an effective cutoff may emerge from a smooth manifold.

But these are mathematical models only and none of them has a chance of becoming directly (!) accessable experimentally.

8. Jul 30, 2011

### Naty1

Quantum foam is the quantum fluctuations which seem inevitable at small scales....say about Planck size....it ruins the ability to make measurements of space,time,mass,etc...they all become blurred. A crude analogy: smooth rolling waves in the sea become frothy when strong winds are present, tops are blown off, and the form of the wave becomes blurred. What's water and what's air...where is the top of the wave???

A simple related way to think about it from an observable perspective, is that at such small scales even if everything was smooth and well behaved, we need really short wavelengths....very high frequency... to be able to see anything...but that means high ENERGY...E = hf, so we disturb what we are trying to observe!!!

But the foam idea says it's already bouncing all around for very similar reasons anyway....lots of virtual energy at small scales...

http://en.wikipedia.org/wiki/Quantum_foam

all check: vacuum energy, zero point energy, Planck scale, Infrared-ultraviolet connection, Heisenbery uncertainty, etc....all related concepts.

Last edited: Jul 30, 2011
9. Jul 30, 2011

### Naty1

10. Jul 30, 2011

### Nano-Passion

Thanks, it was a very intersting read.
Thanks it was intersting though I found it harder to understand at a non-superficial level because I haven't even begun calculus based physics in college. :shy:
Its pretty interesting. Is quantum foam an accepted theory or in great debate?

What is T duality in string theory?

11. Jul 31, 2011

### tom.stoer

In string theory a closed string can wrap around a compact surface with size L (just like a rubber band can wrap around a garden hose). There are two different modes, namely
vibrational modes with quantum number n and "momentum" p ~ n/L,
and winding modes with winding number w and "momentum" p ~ wL/a.

For m² ~ p² you get contributions both with n²/L² and w²L²/a².

Physically the different contributions to m are not directly accesssable, but the total mass m of the string is. That means that interchanging L with a/L does not change its mass spectrum. Therefore for every string on a compactified dimension with size L and n,w you can find another string on a different compactified dimension with size L'=a/L and n',w'.

That means that the two (mathematically different) theories with compactified dimension with size L and a/L are physically identical. Decreasing the size of L below Planck length in one theory can be interpreted as increasing the size L' in a second theory. So these two theories are related by a so-called T-duality which mathematically describes the map between L,n,w d w and L',n', w'.

Last edited: Jul 31, 2011
12. Aug 22, 2011

### yoda jedi

continuous at least to 10-48 mt and maybe beyond, and maybe continuous.

at least less than 10-33 mt (not cm)
<10-48 mt

http://arxiv.org/PS_cache/arxiv/pdf/1106/1106.1068v1.pdf

.

Last edited by a moderator: May 5, 2017
13. Aug 22, 2011

### PAllen

Can't help this (mods may delete if desired). From a very old science fiction story:

character one: I have discovered that time is particular and space is discrete.

character two: How very nice of them.

14. Aug 22, 2011

### Finbar

One needs really to ask a well thought out question. Space and even spacetime are immaterial
in some sense so it may well be that there is real answer to the question. What is probably true is that gravity exchanges information/energy in discrete amounts with other fields such that some observables become quantised. I would expect these to ratios of lengths and not lengths themselves. For example maybe the ratio wavelength of a particle and its Schwarszchild radius has a smallest value even though each as an individual quantity have no well defined value and are not in themselves observables.

$\lambda/r_s = 2 \pi/ 2GM^2 \to 1$

say, even though we could have $r_s \to 0$ and $\lambda \to 0$ we couldn't measure either value only their ratios.

15. Aug 22, 2011

### marcus

Space consists of geometrical measurements---it is not a material substance, it is geometry.
Or so I think anyway. Space is a network of geometric relationships.

So when you ask questions like discrete/continuous, I would say you are asking questions not about a a physical material but about measurement itself. Measurement of areas, measurement of volumes. Observers. Observables.

Operators on the Hilbert space of quantum states of geometry. That is what it must come down to. What else could it be? The universe has a geometry. Therefore it has quantum states of geometry. Therefore according to our current ideas of quantum theory there must be a Hilbert space of all those states. And geometric measurements or observables must correspond to operators on that Hilbert space of states.

The question of discrete/continuous then boils down to nothing else but asking about the spectra of those operators.
======

there is no "space itself"there is only geometry---geometric relationships. So you are asking about measurement (at the scale where quantum theory is important.)
========

People who like to think about this kind of question might be amused by Achim Kempf's paper on the topic
Spacetime could be simultaneously continuous and discrete in the same way that information can
http://arxiv.org/abs/1010.4354
He published it in December of last year in the New Journal of Physics.

Sample quote:
"The equivalence of continuous and discrete information, which is of key importance in information theory, is established by Shannon sampling theory: of any bandlimited signal it suffices to record discrete samples to be able to perfectly reconstruct it everywhere, if the samples are taken at a rate of at least twice the bandlimit."

If geometry is a kind of information about the world it can be both discrete and continuous

Last edited: Aug 22, 2011
16. Aug 23, 2011

### Fra

This shows is a duality between discrete and analog representations that are and bandwith limited; but the information content is finite.

But I think a real problem when talking about this is how to KNOW (ie how to INFER) that it's bandlimited in the first place; when your measurement apparatous always has finite resolution and sampling rate in the first place?

In real measurements, you typically apply an anti aliasing filter to make sure the signal ARE bandlimited before beeing sampled, thereby discarding any information in the higher frequencies that might be there, this means that it's actually the inference machinery that imposes the bandwidth limitation. You have a given bandwith of any measurement apparatous, the bandwith of the "actual signal" is unknown.

This is reasonably clear from a generic inference perspective, if you take seriously also how information that is measured is retained.
One question where people seem to differ is: what is the ontological status of this "network of measurement results". This is exactly where I personally have problems with rovelli's logic.

It seems rovelli thinks of this in terms of elements of realist. While I think that even this network of measurements must be represented on the inside (by an observer). Meaning that the complexity of the network needs to be bounded (but I realized this has nothing to do with OT sorry).

I think Rovelli's view is baggage from classical GR, in which you only consider "test observers" that has no mass, and that the networks and maps have not mass thesemelves, in which case they would also distord geometry.

/Fredrik

17. Sep 6, 2011

### Fineliner

Purely theoretical there could be more bigbangs more then we will ever be able to observe (too far away), in such a case space and time might not be made by it..
It could have been always there and even have no beginning, empy space just exist (and wel basicly empty space is nothing so why wouldnt nothing exist not ?..
oops ...now it becomes rather philosopical.

You know its far more easy to think of someone made brick wall at the border.
Although you might fear what would happen if the walls break down
And dont put windows in this wall, they would only make you wonder who is looking through them...

18. Sep 15, 2011

### emlbiltek

Black hole physics suggests a discrete nature of space and time (spacetime). The idea that there is an absolute limit to information on the other side of a horizon is known as Bekenstein’s bound. There is no way to reconcile this with the view that space is continuous.

On the Planck scale space seems to be composed of fundamental discrete units. String bits are one view of this, the Bekenstein bound from black hole thermodynamics is another. It’s possible these are three different approaches to the quantum world.

19. Sep 15, 2011

### Nano-Passion

Empty space is not empty, there is what physcists call negative energy/virtual particles.

Even empty space is not considered nothing in philosophy, because its a field that you can interact in.

20. Sep 15, 2011

### ZapperZ

Staff Emeritus
Closed, pending moderation.

Zz.