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

• soothsayer
In summary, the author of this paper, Sabine Hossenfelder, proposes that Planck's constant could be a scalar field and the observed value could be due to symmetry breaking after the big bang, similar to the Higgs mechanism. However, there are still some unanswered questions and the idea is still in its early stages. Despite being published in a less mainstream source, the author is reputable and not considered a crackpot.
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!

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.

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:

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

I have argued that the fundamental theory can be neither classical nor quantized, but that quantization may be a phase that results from spontaneous symmetry breaking. Needless to say, this proposal is presently very speculative and immature.

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".

1. What is quantum gravity?

Quantum gravity is a theoretical framework that attempts to unify the principles of quantum mechanics and general relativity. It seeks to explain how gravity works at the smallest possible scale, where the laws of quantum mechanics govern the behavior of particles.

2. What is Planck's constant?

Planck's constant (represented by the symbol h) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is also used to determine the quantum behavior of particles at the atomic and subatomic level.

3. How is Planck's constant related to quantum gravity?

In quantum gravity, Planck's constant is thought to play a role in the quantization of space and time. This means that at the smallest scales, space and time may be discrete rather than continuous, and Planck's constant helps determine the smallest possible units of these quantities.

4. What is a scalar field?

A scalar field is a mathematical concept used in physics to describe a quantity that has only magnitude, but no direction. In the context of quantum gravity, Planck's constant is considered a scalar field because it has a fixed value regardless of the direction in which it is measured.

5. What are the implications of Planck's constant as a scalar field in quantum gravity?

One implication is that it may help explain the behavior of gravity at the smallest scales, where quantum effects are dominant. It also suggests that space and time may be fundamentally discrete rather than continuous, and that the laws of quantum mechanics play a role in the behavior of gravity.

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