# Is the Planck Length real? How do we know?

1. Sep 15, 2010

I've heard of Stephen Hawking talking about the Planck Length and how nothing could exist at a level smaller than that length. I'd like to know how we know this to be certain.

It seems that history has always repeated itself in that when humans see as far as we possibly see we simply just believe that is the edge of the universe. Etc. Similarly I have to wonder if that is the case here. Are we seeing as small as we can see and deciding that's it? What if we were wrong?

Say I have a glass bottle how do we know that an INFINITE number of molecules couldn't fit within that bottle so long as those molecules were scaled down to an infinitely small size somehow?

Would appreciate some insight.

2. Sep 16, 2010

### Chronos

The planck length is the mathematical limit of resolution.

3. Sep 16, 2010

interesting, apparently, stephen hawking says that such a limitation exists in the real universe... but if so... how do we know this?

i just think it could change a lot of ideas if we found that there was no end or limitation to the size of things... Wouldn't it mean that the universe, whatever its measurable size... was in fact, infinite?

4. Sep 16, 2010

### twofish-quant

At plancks length our current understanding of physics breaks down. If you were able to define a particle to planck's length then the uncertainty in it's momentum would create a black hole that would swallow it up.

No. Planck's length is much smaller than the scales that we can see, and we can see atoms start becoming fuzzy.

Oh that one is easy. If you had an infinite number of molecules that you shrink down forever, you couldn't heat the bottle up.

Imagine, that you have a bottle with a gas with infinite number of molecules with zero size. Now lets add energy to it. Because you are distributing a finite amount of energy to an infinite number of molecules, each molecule will not increase in its energy by very much. What this means is that the temperature of the gas is never going to increase.

(This is called the Gibbs Paradox.)

5. Sep 16, 2010

### friend

Some have suggested that spacetime breaks down at the Planck length because you could never probe and measure anything smaller than that. It would take so much energy to probe that small a region that your measuring apparatus would collapse into a black hole. So they say if we cannot measure it, then it does not exist.

I beg to differ on that point. For by that logic nothing inside a black hole exists because we cannot measure it. But observers traveling into a black hole do not see an event horizon. So the inside of a black hole has observable structure from their point of view. Same with the Planck length. Just because we cannot observe it doesn't mean that it does not exist. A sufficiently small observer might see structure there.

Last edited: Sep 16, 2010
6. Sep 16, 2010

### Rebound

"The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the ‘quantum of length’, the smallest measurement of length with any meaning.

And roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton.

The Planck time is the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length. This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds. No smaller division of time has any meaning. With in the framework of the laws of physics as we understand them today, we can say only that the universe came into existence when it already had an age of 10-43 seconds."

I think the bold text explains.

7. Sep 16, 2010

### Parlyne

I strongly object to the statement that lengths smaller than the Planck length have no meaning or the statement that lengths only exist in quantized units of the Planck length. First of all, this can't be a frame invariant statement (at least not in the usual relativistic sense). And, second, the basic problem regarding the Planck length is that we know that quantum gravitational effects must be relevant on that scale. But, since we don't have any good working understanding of quantum gravity, all we can say meaningfully is that we don't know what it would mean to talk about smaller lengths. This is not the same thing as saying that there is no meaning to such statements. It might be the case that lengths shorter than the Planck length are meaningless and it might not. Any statement making a claim one way or the other is entirely speculative or is based on an unproven model of quantum gravity.

8. Sep 16, 2010

### Rebound

I don't know to whom you are responding, but I agree with you as stated in my post. It merely states that at such distances quantum effects take over from classical interactions so they can no longer be thought of in that way. It is the Plank time that is a fundamental unit.

9. Sep 16, 2010

### PhanthomJay

10. Sep 17, 2010

### twofish-quant

No. That's not the problem.

The problem is that you have two theories of how things work. Quantum mechanics and general relativity. Quantum mechanics works well at small scales and low gravity. GR works well at large scales and high gravity.

If you try to stitch them together, then you end up with a mess. The trouble is that at planck's length you have to stitch them together to figure out what is going on.

Yes. The trouble is that then you have a hidden variable theory, and for that to work you have to have all your structures in the universe communicating with each other at faster than the speed of light. (see the wikipedia article on Bell's theorem)

11. Sep 17, 2010

### twofish-quant

I agree with your objection. One problem with these sorts of things is that subtle points get garbled when people repeat statements. I'd be interested in see Hawking's original quote.

One other thing that is often unclear when physicists talk is how much of what they say is "personal opinion" and how much is "consensus belief." It may well be that Hawking thinks that space is quantized below Planck's scale or not, but that's his own personal opinion.

12. Sep 17, 2010

### Rebound

I disagree. It is the essence of the Scientific Method all that is certain is what has been observed empirically. The results are used to exclude alternative hypotheses as much as they are to confirm them. This process is critical to everything from criminal investigations to General Relativity. GR, for example, was not widely accepted until effects it predicted were observed. Until a testable prediction has been confirmed by experiment, it remains firmly in the realm of the hypothetical. This is the major knock on String Theory. It doesn't appear to make any testable predictions.

Any scientist worth his salt is normally going to make a clear distinction when speaking to the public.

13. Sep 17, 2010

### diggy

Planck units are special because they are formed from quantities directly found in nature, i.e. speed of light, gravitation constant, etc. Those natural units have dimensions like length and time and such, and when the natural units are combined together they can be expressed directly as a time scale or length scale.

As far as I know, these scales have no other physical significance. For example the planck charge is 10 times bigger than the electrons charge. So obviously that isn't a bound. The planck length is very small, but that doesn't limit a size scale. It just defines a unit.

There may be other arguments that near those sizes/scales laws of physics break down, but its not clear to me that they actually come directly from the units.

14. Sep 17, 2010

### diggy

Just to clarify, planck length is a unit.

Planck *scale* refers to a physics argument.

15. Sep 17, 2010

### Rebound

As stated above,
"This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds. No smaller division of time has any meaning. With in the framework of the laws of physics as we understand them today, we can say only that the universe came into existence when it already had an age of 10-43 seconds."

This is clearly of physical significance.

 It occurs to me that I may appear to be off target since the discussion has been mostly about length; however, the connection between distance and time is such that this becomes relevant.

Last edited: Sep 17, 2010
16. Sep 17, 2010

### diggy

I'm not going to argue with Stephen Hawking, but I'm not convinced that the argument leading to 10^-43 seconds as an absolute quanta of time is really that solid. I don't think many people would disagree with the statement that we don't understand nature very well at that time/space precision. Are ~black holes created at the single particle level at those energies, I don't know. I know we do observe cosmic rays ~10 more energetic (than the energy of photons that are supposed to create mini-black holes). Its not quite the same (since those are most likely nucleons), but I think that it does at least challenge that limit.

17. Sep 17, 2010

### Rebound

There's not much more I can say about this other than to reiterate that the point is that nothing meaningful can be said about time at any smaller scale.

18. Sep 17, 2010

### diggy

Rebound, sorry but its not clear to me what you are saying. (1) That we can't say anything meaningful, i.e. our theories breakdown as gravity converges with quantum. Or (2) that nature does not meaningfully operate below the planck scale, i.e. mini-black holes and such. I think those are the distinctions that are being discussed.

19. Sep 17, 2010

### petergreat

Planck Length is untested theoretical fantasy

Planck length is derived from G, c, and h. If special relativity or general relativity breaks down at length scales much smaller than the reach of LHC, but much larger than Planck length, then G and c loses meaning before Planck length is even approached. In this case the Planck length would become physically meaningless. If QM ever breaks down, h would also become meaningless.

Therefore, as a combination of these 3 physical constants, the Planck length is only meaningful if both relativity and QM remain valid up to 10^19 GeV. There is certainly no reason why this can't be true, but at the same time, there's no experimental evidence whatsoever.

20. Sep 17, 2010

### Chronos

For a good discussion on the meaning and physicality of the planck length, see:
Planck-scale physics: facts and beliefs
Diego Meschini
http://arxiv.org/abs/gr-qc/0601097