As the Standard Model in elementary particle physics is not only a huge achievement in science, but something that works as a model of quantum mechanics amazingly well, why is gravity considered a fundamental force like electromagnetism; therefore hypothesizing an associated gauge boson (currently dubbed the graviton) in the Standard Model?
That is, couldn’t gravity simply be a side/accumulative effect of energy/mass in the universe bending spacetime—or something to that effect? Or is there something about symmetry-breaking or another esoteric theory that would discourage such thinking?
There are theories such as induced gravity and entropic gravity in which gravity is not a fundamental force, but an emergent force.
I think it is fair to say that whilst emergent gravity is definitely not the main line of attack to explaining gravity by quantum theory, it’s still seen as a serious avenue of investigation by many.
Of course though gravity in some ways is very amenable to being described by a quantum field just like electromagnetism. If you take a general spacetime metric and subtract a chosen "background metric"from it, you’re left with a classical spin-2 field which can be quantitized giving you a quantum field mediated by a spin-2 graviton. The problem with this approach though is, firstly, that the tools used in QFT to extract physical predictions from the theory have so far proven not that useful as far as gravity is concerned and, secondly, the starting point of choosing a background metric doesn’t sit that comfortably with the philosophy of GR, where the background is strongly-related to the gravitational field.
Just to take this point up (bolding mine): this is essentially what GR already says,depending on how closely you tie the theoretical apparatus of GR to its physical predictions. It’s also the biggest obstacle to going from GR to a quantum field theory for gravity. Even semi-classical gravity (which is seen by the vast majority as an approximation of a full theory of gravity rather than a possible fundamental description), where gravity remains as a result of the “warping” of spacetime by quantum fields, runs into problems due to this aspect of GR.
Thanks for your responses AF. I’ll definitely check out those links into other theories on gravity as an emergent force. I wasn’t aware of those (although figured something like that must’ve been proposed somewhere within the 100 years Einstein unleashed GR).
Anyhow, it’s great to to be able to get informed answers from actual physicists about a very specific aspect of nature. Especially the relationship between QM and GR. So thanks again, and hopefully more will weigh in.
There must be some way of describing gravity in quantum mechanical terms, because without it, one can reach truly absurd physical scenarios. Consider, for instance, a black hole that’s slowly evaporating and thus losing mass. As the mass of the black hole decreases, the energy per particle that it’s emitting increases. So smaller black holes emit more energetic particles than larger ones.
At least, that’s what happens in the semiclassical description. But if the pattern continues indefinitely, then somewhere in the vicinity of the Planck mass, you’d start getting a hole that’s emitting particles with more energy than the hole itself has available. This is absurd, and so there must either be some other relationship at such small masses, or some mechanism that prevents black holes from ever getting that small. But either way, that new relationship or mechanism must inherently be quantum gravitational.
What does actually happen in that regime? We don’t know yet, since we have no practical means of producing or finding black holes of that size. But even though none might exist yet, they’re still something that can exist in the Universe, so there must be rules for governing them.
Are we talking almost specifically about Hawking Radiation there? Can you explain to a layman why in a universe without quantum gravity, a sufficiently small black hole (near the Planck length) might emit more energy than it has available?
Yes, when I speak of black holes evaporating, I mean Hawking radiation.
Well, yes and no. I can tell you some of the relevant formulas, some of which might perhaps seem intuitive, but I can’t explain why those formulas hold without a lot more background.
First of all, the radius of a black hole (by which is meant the radius of the event horizon) is proportional to its mass. Surface gravity of an object is proportional to mass divided by radius squared, so the surface gravity of a black hole is inversely proportional to its mass (hence, smaller black holes have a larger surface gravity). Hawking found that the temperature of a black hole is proportional to its surface gravity, which means inversely proportional to its mass. And we’ve known for over a century that the average energy per particle in a system is proportional to its temperature. So the energy in a Hawking radiation particle is inversely proportional to the hole’s mass.
Black holes are a case where General Relativity and Quantum Mechanics bump heads- the infamous firewall problem for example. We’d love to be able to observe a micro-black hole just for the clues it might give us to the quantum gravity problem.
Another problem with leaving gravity unquantized is that it’s a nonlinear theory, while QM is a linear one. For a linear theory, any sum of solutions is again a solution—in QM, this is what gives you superpositions. But now consider a superposition of different mass configurations of a system, say placing an electron into a superposition of moving along different paths in an interference experiment. What’s the gravitational field of such a configuration? The problem is that the sum of the gravitational fields of the electron moving along each path is not in general a solution of the Einstein equations (even if it were, though, it’d be far from clear if that would be the right thing to do).
So the basic problem is that we know that matter has quantum characteristics, and GR couples matter to spacetime; so if we left spacetime unquantized, we have something quantum on the right, and something classical on the left side of the equation, and there’s no good way to couple the two, as far as anybody knows. There’s something known as semiclassical gravity, where the matter term is basically replaced with an averaged-over version, but it’s been argued that this also leads to inconsistencies.
So while that doesn’t settle whether it’s fundamental or not, it seems that basic consistency requirements lead to the quantization of gravity—or, should that turn out to be impossible, perhaps even a modification of the quantum framework alongside with that.
It certainly appears as though gravity is a different kind of fundamental force than the others, and general relativity provides a description of it that is completely incompatible with our best theories about the others. That people have spent a lot of time and effort looking for a way to make them compatible and don’t have a very good explanation suggests that we may be going about looking for it the wrong way. String theory has been developed for awhile as an attempt to do something in a different way that would explain everything, but from what I understand has never made any testable predictions, and it may be that the theories are fundamentally untestable besides deriving logical contradictions. Understanding how gravity and the other forces interact may very well require a fundamental leap of logic that is too weird for anyone to even consider theoretically possible. If you had told physicists in 1800 about the nature of quantum mechanics, they probably would have said you were insane.
Thanks HMHW. Bringing up something like superpositions of electrons is an interesting thought experiment that I hadn’t considered in trying to think about what the curvature of spacetime would be during such phenomena.
That actually helps me to visualize how QM and GR should be related quantumly, somehow, even more so than thinking of it from the very big, such as the aforementioned interface of the event horizon of a black hole and Hawking Radiation.