# Quantum gravity - Planck's constant as a scalar field?

1. Jan 4, 2013

### soothsayer

"Quantum" gravity -- Planck's constant as a scalar field?

I was just reading about a fascinating new theory on the solution to the quantum gravity problem:

http://arxiv.org/pdf/1212.0454.pdf

I really like it, but I have one big problem with it:

The author states that
$G = \frac{\hbar c}{m_{Pl}^2}$
where $m_{Pl}^2$ is the Planck mass, and says that gravity can then be considered to be coupled to Planck's constant. But my issue is: if $m_{Pl}^2$ is defined to be $\hbar c/ G$, then isn't this an empty statement? Specifically, the author goes on to say that Planck's constant could in fact be a scalar field, and the observed nonzero value of the Planck constant could be due to symmetry breaking after the big bang, much like in the Higgs mechanism. When defining Newton's gravitational constant, the author casually mentions that the Planck mass is constant, but how can that be true if it is tied to the Planck constant, which the author says is not actually a constant? Does the author mean that the Planck mass is equal to $\hbar_0 c/G$ where $\hbar_0$ is the current, experimental value of Planck's constant (The ground state of the field)? Is that valid?

Just wanted to get PF's thoughts on it. Thanks!

2. Jan 4, 2013

### DiracPool

Re: "Quantum" gravity -- Planck's constant as a scalar field?

Is this article published in a Journal? All I can see is that it is from a Cornell U archive site. It looks like it could be some student's homework assignment. That may important in trying to address your question because I'm not seeing how Sabine derived that equation. Does it come out of a dimensional analysis of the planck units? Or did he/she just make it up? That would be good to know as a start.

3. Jan 4, 2013

### soothsayer

Re: "Quantum" gravity -- Planck's constant as a scalar field?

Well, it comes from the fact that the planck mass, $m_{Pl}$ is DEFINED to be = $\hbar c/ G$, which basically comes from first principle. The thing is, everything besides G cancels out, so you basically get G = G, which gives you nothing.

The expression for the planck mass can be found on its wikipedia page. I am unsure as to the source of this article. I do not know if it was published in a journal.

Last edited: Jan 4, 2013
4. Jan 4, 2013

### pervect

Staff Emeritus
Re: "Quantum" gravity -- Planck's constant as a scalar field?

I managed to trace this to "third prize winner in the FQXi" essay contest.

I'm not familiar with FQXi, and I tend to be suspicious of sources I'm not familiar with.

A quick check into the author, Hossenfelder, shows they have some publication history in reputable journals (Physics Letters, for example).

My thoughts - overall I agree with the author's summay

And I think the idea is interesting and genuine, but needs more development (hence the publication in a rather off-the-beaten-track source. This is a bit of a red flag, but from my perspective the article doesn't seem obviously silly (unlike a lot of ideas one sees in off-the-beaten track journals). But I'm not terribly familiar with more than the basics of QM, so I can't say that someone more familiar wouldn't see flaws I don't.

I do give the author credit for fairly representing the status of the idea - it's apparently an idea he/she has been trying to work on to "beat into shape".

5. Jan 4, 2013

6. Jan 6, 2013

### cosmik debris

Re: "Quantum" gravity -- Planck's constant as a scalar field?

I agree with this, Bee, as she is sometimes known, is far from being a crackpot, as well as her excellent blog she has posted on this site.