# What is REALLY the value of the Plank energy?

1. Jul 30, 2011

### MTd2

$E_p = \sqrt{\frac{\hbar c^5}{G}}$

But in many theories, like QEG, the G runs to infinity. So, actually, it should be lower, much lower. What do you think?

2. Jul 30, 2011

### Dickfore

This result is obtained by dimensional analysis and is determined up to a numerical factor. So, to answer your question, one must have a precise theory that would give an equation that would spit out a result that has the meaning of 'Planck energy'. What do you mean by 'Planck energy'?

3. Jul 30, 2011

### MTd2

In which quantum gravity becomes important, so I gave an example, QEG, Quantum Einstein Gravity.

http://arxiv.org/PS_cache/arxiv/pdf/0708/0708.1317v1.pdf

Basically what I am asking what is the energy to which a particle can be accelerated probe quantum gravity, considering, say, QEG.

4. Jul 30, 2011

### Dickfore

I see this had been posted on the arXiv in August 2007. Has there been any publication resulting from these notes in a peer reviewed journal?

5. Jul 30, 2011

### MTd2

6. Jul 30, 2011

### Dickfore

Seems like the authors are versed in the field and have published in many high-impact journals. Among the list of articles by F. Saueressig, there were three that contained the term 'Quantum Einstein Gravity' (QEG) in the title:

1. Bimetric Renormalization Group Flows in Quantum Einstein Gravity
2. Functional Renormalization Group Equations, Asymptotic Safety, and Quantum Einstein Gravity
3. A class of nonlocal truncations in Quantum Einstein Gravity and its renormalization group behavior

The last one (PRD 66, 125001 (2002)) is the oldest publication, so I thought I would read there what QEG actually means. The article is 34 pages long, so I will need some time. If you have any suggestions or you would like to reformulate your question, please post in the meantime.

7. Jul 30, 2011

### MTd2

I am not well versed on this too.

I hope marcus can help us, since he is the one that keeps the development of QEG.

8. Jul 30, 2011

### Finbar

Don't you mean higher, much higher???

The real meaning of the planck energy should be the energy at which E/M_pl(E) = 1. Which may not be to much larger than the classical estimate even if M_pl goes to infinity as E does.

9. Jul 30, 2011

### marcus

Well I can try to help, but I haven't been following QEG much lately. It's worth listening to Finbar about this (also called Asymptotic Safe gravity.)
That points in the right direction. With QEG you have a momentum parameter k and the two main parameters G (newton) and Lambda (cosmo contant) run with k.

As k --> ∞ that is like scale getting very small, energy getting very large.

A key assumption is that there is a k --> ∞ FIXED POINT that the dimensionless versions of Lambda and G approach.

Lambda is an inverse area so naturally its dimensionless version is Lambda/k2

and if that approaches a finite value then obviously the dimensionfull version must be growing without bound. So near "big bang" for example, the cosmo constant can be considered near infinite.

The dimensionless version of G is denoted by a little letter g and is defined by

g = k2G

(when c = 1 that is how the units cancel)

so for that g to converge to a finite value as k -->∞ you obviously need G --> 0 at small scale and high energy.

So again at the start of expansion the QEG presumption is that G is very small.
=====================

I am not sure what Planck mass means at such conditions.
Or Planck energy. Finbar may have some interesting ideas about that.

10. Jul 30, 2011

### MTd2

11. Aug 5, 2011

### MTd2

Any idea? If the cosmological constant goes to infinity, would we have a repulsive field around the particle, that is, the particle would stat to behave as a white hole?

12. Aug 5, 2011

### marcus

I don't know MTd2. It's really speculative.
In AsymSafe QG cosmology I think we are talking about extreme density. I don't imagine that particles exist. Only fields make sense to me. the usual philosophcal concepts of localization and particle-ness don't seem to mean anything (to me). Maybe you can give them meaning and explain.

I would imagine that if density is extreme and Lambda is extreme you would have an extreme acceleration of expansion (Lambda is what accelerates expansion). Expansion of distance is not equivalent to motion.

(when the U experiences expansion of distance, nobody goes anywhere. nobody travels toward an destination, distances simply enlarge).

So your guess is as good as mine. If Lambda is extremely large positive it would just mean that distances are expanding incredibly fast. I think.

We are talking early universe conditions, not what you diddle around with using colliders.

13. Aug 5, 2011

### MTd2

I mean particles as the classical definition allows, like a charged point and accelerating in a tube. If they collide at really high energies, instead of decay into black holes, they'd decay into white holes?

14. Aug 5, 2011

### marcus

You are considering a regime in which essentially G=0. What does "black hole" mean?

I think you wanted us to consider how, in some high energy density regime, G --> 0 and
Lambda --> ∞
as AsymptoticSafe QG tells us must happen at the UV fix point.

So I think you need to look at the Einst. eqn. and what its solutions are under that conditions, when the parameters G and Lambda run to their UV fix point values. What then is meaningful?
What does "point particle" mean, if it means anything?
What can observables be? Does what we ordinarily think of as geometry exist? What is the meaning of the word "matter". Does it refer to anything under those circum stances.

Your guess is as good as mine. I can't tell you about the AsymSafe beginning of expansion.

Loop does not seem to have these problems. You can run a smooth computer simulation through the bounce, as has been done countless times. A matter field will go thru the bounce and continue evolving. One is not bothered by infinities. One can say what the maximum value of the Hubble expansion rate is, that is achieved at the time of bounce.
It is not infinite.

In that sense everything is under control in LQC, at the start of expansion, and everything is out of control in AsymSafe.

That is why I do not read AsymSafe papers so much any more. It does not go anywhere, that I can see, and there is a big output of new Lqg research now to keep track of.

But maybe you can answer these questions, or someone else, and make sense of it.

15. Aug 5, 2011

### MTd2

It means that the Schwarzschild radius, $M=\frac {Gm} {c^2}$, shrinks and you can have arbitrarily high density of matter without any gravity.

16. Aug 6, 2011

### Chronos

Particles decompose at exotically high energy levels, afaik. All we have to play with are fields.

17. Aug 6, 2011

### MTd2

What do you mean by decompose?