Is the Planck Length real? How do we know?

[sorad]

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.

 

[Chronos]

The Planck length is the mathematical limit of resolution.

 

[sorad]

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?

 

[twofish-quant]

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.

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.

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?

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

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?

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 let's 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.)

 

[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.

 

[Rebound]

The following is quoted from http://www.physlink.com/education/askexperts/ae281.cfm

"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 traveling 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.

 

[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.

 

[Rebound]

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.

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.

 

[PhanthomJay]

I hope this is applicable, but I liked Chalnoth's response in this thread below:

https://www.physicsforums.com/showthread.php?t=398153&highlight=planck+length

(I always thought the Planck time was the time it takes for a fly to get out of the way when the swatter is within a Planck's length of squooshing it..)

 

[twofish-quant]

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.

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.

Just because we cannot observe it doesn't mean that it does not exist. A sufficiently small observer might see structure there.

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)

 

[twofish-quant]

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.

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.

 

[Rebound]

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.

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.

 

[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.

 

[diggy]

Just to clarify, Planck length is a unit.

Planck *scale* refers to a physics argument.

 

[Rebound]

<snip>
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.

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.

[Edit] 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.

 

[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.

 

[Rebound]

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.

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.

 

[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.

 

[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.

 

[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

 

[petergreat]

@Chronos: Thanks. I'm glad to see an article discussing this in detail.

Just two remarks to add.
1. Extrapolations are often unreasonably effective in physics. Among other examples, Coulomb's inverse square law was established under 18th century experimental conditions, but modern experiments confirmed its accuracy to the order of 10^-15. Another example is the fact that Michaelson-Morley's null result has been improved over many orders of magnitude by Fermi Gamma Ray Telescope.
IMO physicists have a mentality that's more friendly to extrapolation than anyone else. That's how the talk about Planck scale even started.

2. I'm surprised no one here has mentioned large extra dimensions, which can drastically lower the quantum gravity energy scale and make BHs possible at LHC... Anyway, this is far too speculative.

 

[Chronos]

It is a difficult problem [inserting meaning to Planck length], but, I believe we are not far off the mark. I also believe extra dimension ideas will fail in LHC. We already have much more energetic events in the atmosphere [cosmic ray collisions] that tend to run contrary to this idea.

 

[Rebound]

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.

OK, just to be totally explicit:
My last post was referring to the measurement of time only. Classical meaning of time completely stops making sense at intervals shorter than the Plank time.

The Plank length is a totally different thing. It is the distance below which gravity ceases to have a meaningful effect, not the shortest meaningful distance.

 

[sorad]

OK, so can I get some layman's terms :)

Its sounding from many of you that the Planck Length mainly describes a length or measurement at which gravity no longer works the same way as it does to us? However it still may be possible that things exist at smaller measurements than this? Or is this refutable as well?

 

[RLutz]

Black holes are also relevant to this issue. Black holes represent the highest possible entropy a given region of space can have, they have maximal entropy since anything one would do inside the event horizon (move stuff around, change the spin of particles, reorder your DVD library) would go completely unnoticed by anyone outside the black hole. I think it was Hawking that proved that this entropy is determined not by the volume of the black hole, but by the surface area. Specifically, if you lay a grid of Planck squares out over the event horizon of a black hole (where a Planck square is a square with all sides equal to the Planck length), then the black hole's entropy will be equal to the number of Planck squares it takes to cover the black hole. Therefore it would seem the Planck square is a fundamental unit of space which can carry a single unit of entropy. Therefore, nothing, even in principle, could take place within a Planck square, because anything that could happen could increase disorder (thereby making the Planck square contain more than a single unit of entropy, which is impossible).

If you have a copy of Brian Greene's The Fabric of the Cosmos, he explains it pretty thoroughly from pages 477-481. If you want a really thorough explanation though, I think you'd have to thoroughly research the holographic principle.

 

[twofish-quant]

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.

On the other hand there are very strong theoretical reasons to believe that QM breaks down eventually. If you assume that QM works to infinite energy scales, then you run into some huge problems because a lot of quantities suddenly become infinite. To get finite values for things, you have to assume that QM breaks down at some unknown scale.

 

[PhanthomJay]

I may be off topic, but what is the hypothesized length of a 1 dimensional string in String Theory? I had heard that it was in the order of the "planck length" in that dimension. Presumably, it would have no length in the other directions?

 

[nismaratwork]

I may be off topic, but what is the hypothesized length of a 1 dimensional string in String Theory? I had heard that it was in the order of the "planck length" in that dimension. Presumably, it would have no length in the other directions?

That's a good description, but additionally string theory says that there is NOTHING below the Planck Length, and in that way it claims to unify forces and smooth out the weirdness of the QM universe. AFAIK "on the order of" is as close as ST gets to an actual length, and yes, a string is supposed to possesses only length, nothing else.

This dovetails with Twofish-Quant's point, in that ST essentially says that without the issue of infinitely divisible scales you eliminate some of the funky "quantum foam" or other issues; no breakdown occurs because such distance scales only exist on paper.

 

[Kevin_Axion]

Just for a clarification of scale, if an object of the order of Planck Scale were to expand in size to be equivalent to a tall tree then tall tree would be approximately 150,000,000,000,000,000 (150 quadrillion) light years long, much larger than the Observable Universe.

 

[nismaratwork]

Just for a Clarification of scale, if an object of the order of Planck Scale were to expand in size to be equivalent to a tall tree then tall tree would be 11,000,000,000,000,000,000,000 (11 sextillion) light years long, much larger than the Observable Universe.

Well, around 10^-33 is pretty damned tiny

 

[petm1]

Is a Planck length relative, after all it does define a meter but it is based on time which is a variable in space-time depending on the position and age of the photon you are measuring.

 

[nismaratwork]

Is a Planck length relative, after all it does define a meter but it is based on time which is a variable in space-time depending on the position and age of the photon you are measuring.

I don't understand what you mean... for any given photon (its own frame of reference) there is no relative effect.

 

[friend]

The Planck length is derived from G, h-bar, and c. But how do we know if these constants stay the same at very small scales or in very tightly curved spacetimes?

 

[petergreat]

The only safe thing to say is that the Planck energy scale is the absolute upper bound of the region of validity of our current understanding of physics. It remains a possibility that our theory breaks down much faster than that. But there's absolutely no chance that it ever works beyond Planck scale.

 

[nismaratwork]

The Planck length is derived from G, h-bar, and c. But how do we know if these constants stay the same at very small scales or in very tightly curved spacetimes?

If such spacetimes exist in accordance with String Theory, then there is nothing smaller than the constant, and if they exist in some other context... who the hell knows? One clarification: c is a constant... $$\hbar$$ is not a fundamental natural constant, it's just a number.