# POLL: Planck's length

1. Oct 13, 2004

### peter8

Hi all,
I have a question driving me crazy about Planck length:
1.- PL is the minimum length possible. This is, there is no length under PL.
2.- Of course there are lengths under PL, but our laws stop in PL (in the meaning that they can say nothing under PL BY NOW)

THANKS

-sorry for my english-

2. Oct 13, 2004

### Fredrik

Staff Emeritus
Your english is fine, but there's no poll here. We should be able to click "one" or "two" here somewhere. I vote "one".

3. Oct 14, 2004

### peter8

If 1,
1.1-if you are moving at a constant velocity 'u' you should measure PL and this number must be the same measured by a static observer. So, relativity concerns not only c, but PL too. Isn't it? There is not length contraction when we are talking about PL?
1.2 How does cinematics is possible? If there is no length under PL, movement is quantizied: where is a moving body between PL and PL+1? I'm not thinking about atoms, I'm referring to ordinary 'big' solids.

4. Oct 14, 2004

### nisophy

My view

Your English is good and I choose 1 since at quantum level that must be most expected minimum value where the limits on length converges.

5. Oct 14, 2004

### Stranger

thats sounds kinda interesting...if nothing can cross the barrier of PL...then does it mean, that an object travelling close the the speed of light cannot get smaller than PL...i mean if the object somehow manages to travel fast enough to break the PL barrier, will it still not go beyond PL....or is it that it is relative to me...

6. Oct 14, 2004

Staff Emeritus
I think the best answer is 2, although the laws don't stop, they just become irrelevant. At the Planck scale gravity and atomic forces are equal.

7. Oct 15, 2004

### peter8

I think that any quantization of the space, via PL (as proposed in DSR) or via LGQ, introduces an space quantum. Then, if there's an space quantum (PL or a quantum area or an quantum volume), there is nothing smaller than it. Then special relativity is wrong because this quantum, as Stranger pointed, cannot get smaller. There is no length contraction in a quantum of because there is nothing under it. So,we have
i.-Space is quantizied. Then, special relativity, as we know, is not complete. We must rewrite it.
ii.-Space is not quantizied. Then LGQ is false, and the answer to the question is 2: PL is no more than a formal limit but no a real limit to space.

What do you think? Am I speaking logically? Or maybe I am an Spanish engineer blasting my time in absurds considerations?
THANKS

8. Oct 19, 2004

### Stranger

so is this considered one of the problems in making relativity complatible with quantum theory....

9. Oct 21, 2004

### jnorman

on a related note, i tried to use PL in an argument with a mathematician over pi. i have long held that since the definition of pi is the ratio of a circle's circumference to its diameter, and that both are finite lengths, then pi cannot be an irrational number - the only way this could be possible is if either the diameter or the circumference was an irrational number itself. the mathematician argued that this is not a "real world" issue, it is pure math, which is not limited. so i brought up PL indicating that you cannot avoid "real world" constraints, even when discussing pure math - ie, that at the most fundamental level of reality, there is no such thing as a circle - it is a polygon made up of PL-sized segments. he got really p'''ed at me after a few minutes of that... i had to laugh.

10. Oct 21, 2004

### ZapperZ

Staff Emeritus
Actually, I think it is you who were over-extending what we can and cannot say. Even stating that a circle is made up of a polygon at the PL scale ASSUMES that there is such a thing as "straight-line" segments within that scale. If there's no curve, then there's no straight lines either! A length of anything is undefined within that scale. So if you want to invoke PL (which, BTW, we have NOT yet verified the existence of), the last thing you want to do is talk about a length scale of anything.

Secondly, you are confusing "geometry" with numerology. The Gregory (or Leibnitz) series formula for pi is purely an exercise in numerology that is devoid of "real world" implications.

Zz.

11. Oct 21, 2004

### Dr. Oberheimer

2 is right. Our laws stop if something is under the planck-length. If something is smaller then it it has too much mass and become a black-hole.
There is also a planck-time, a planck-temperature, ...
p.e. if something has a higher temperature then the planck-temperature we can't calculate anymore with our laws of physics that we have today.
(sorry my English isn't perfect).

12. Oct 21, 2004

### marcus

I agree with what you say. As I see it you are speaking logically.

If it is possible to have a general relativistic quantum physics----via LQG or some other approach---then precisely what you say: special relativity, as we know, is not complete. We must rewrite it.

SR has only one invariant scale: the speed of light.
SR must be modified so as to have more than one invariant scale---it must have not only an invariant speed but also an invariant length (or alternatively energy): a length which appears the same to all observers.

Some form of modified SR----some multiple-invariant-scale version like DSR---must be formulated and tested by astronomical observations. then maybe it will test positive or maybe negative.

If all forms of DSR fail then LQG and several other approaches to QG must be wrong. Because these Loop-and-allied QG approaches need the PL to look the same to all observers.

this is merely my opinion, but I think it is also shared by others. In fact I think this is what you are saying---so I am simply agreeing with you.

I will look for some links to articles about DSR and variations of it, and about testing QG (i.e. QG phenomenology) via testing suitable versions of DSR.

13. Oct 21, 2004

### marcus

By the way, peter8,

I am not sure that one can answer the POLL question now.
How can one speculate that the answer is I or II? One needs empirical observations.
What I can agree with is that you have asked the correct logical question.

This is such a good question that many people are excited now about
the opportunities for testing DSR versions in the near future.

This was what the Karpacz conference ( Winterschool-2004 ) was all about. It was a 10-day symposium (4 Feb-14 Feb) about Quantum Gravity Phenomenology. Various types of astronomers were there discussing possibilties of testing with CosmicRay, GammaRayBurst, Xray, Neutrino, astronomy, etc. I don't know if you have looked at the conference website. If not, here is the link:

http://ws2004.ift.uni.wroc.pl/html.html

here is another link, showing all the Amelino-Camelia papers on the arxiv:

http://arxiv.org/find/grp_physics/1/au:+amelino_camelia/0/1/0/all/0/1

14. Oct 21, 2004

### marcus

let's think what this could mean.

in science things must have an operational meaning. to say there is a length one must imagine a measurement (of some length)

in quantum physics the measurements correspond to operators on some hilbertspace. there is nothing more basic than the spectrum of these operators.

to say that there is no length under PL means that no matter what length observable, or operator, you construct in whatever experiment, that this operator will have a discrete spectrum

it will have a smallest non-zero eigenvalue, and this (we will say) is no smaller than PL.

This is the physical meaning of saying there exists no length smaller----namely: that you cannot measure and get a smaller reading

we know space empirically as relationships between things we observe
and beyond the smallest we can measure----the question of what space really IS ----I am not sure the question is even meaningful.

As you know, in LQG it is found that the spectrum of the area and volume operators is discrete. There is a smallest positive area, and a smallest positive volume, which it is possible to measure. This is what one expects of a quantum theory of spacetime. BUT IT COULD BE WRONG
Maybe it will turn out that one can in principle measure infinitely small volumes and areas! LQG is only preliminary, it is not yet tested.

For me, the unsureness is why it is entertaining. Have a look at Smolin's recent article---it has an interesting list of solved problems, unsolved problems, and near-term testing prospects, and an FAQ. I think you might like it if you have not alread read it.

Smolin
Invitation to Loop Quantum Gravity
http://arxiv.org/hep-th/0408048

15. Aug 12, 2005

### dimitrimikhalinos

I think that the quark is occupying a Planck' volume ( 10^-99 cm^3).

16. Aug 12, 2005

Staff Emeritus
Why would you assume that? In string theory a quark would be a vibration mode of some string configuration, on a scale considerable bigger than the Planck length.

17. Aug 12, 2005

### Juan R.

Let me vote 3.

3.- Of course there are lengths under PL, and our laws say thing on that scale.

18. Aug 12, 2005

### WhiteWolf

I would say 1. But I got another question that I thought of while reading this. If speed isn't quantized, then if you approached light speed, you can continually get closer and closer to the speed of light and your length will continually contract infinitely. So either Plank length is wrong or special relativity is in my view. And if I'm wrong, someone tell me where I'm wrong. Thx.

19. Aug 12, 2005

### marcus

this short paper might interest you, WW

http://www.arxiv.org/abs/gr-qc/0311032
Quantizing speeds with the cosmological constant
Florian Girelli, Etera R. Livine

4 pages, 3 figures
published in Physical Review D.

certainly this little paper by a couple of postdocs is not the last word
but at least they play around with considering if speed might be quantized

there are more recent papers of Livine that deal with possible deformation of special relativity---modification of Poincare invariance----aimed at
taking into account the kind of concern you expressed in your post. you ask how can there be this important length, planck length, if lengths are shrinkable by Lorentz transformation. a number of people have been working on ways to resolve the apparent contradiction. I am personally not ready to chose one proposed solution over another

20. Aug 12, 2005

### DaTario

I have the impression that PL must be converted into a space time volume element to fit within the frame of SR. Would this reasoning be correct ?

Note: I have once read that if consider only the first 18 digits of pi, the formula for the largest circunference lenght in the universe (with the radius of the universe itself) would be correct with the precision of the radius of Hydrogen nucleus.

Best Regards

DaTario