Would a theory that unified ‘the quantum’ with gravity be likely to influence our interpretation of classic quantum results and conundrums such as the double slit experiment, EPR Paradox, Schrodinger’s Cat, etc.?
I doubt I will understand the answers, but simply learning whether those results/interpretations have an ’ independent’ framework of their own or whether they could change depending on the properties of a unified theory (of quantum gravity) would be interesting to know.
Thanks!
What do you mean by “the quantum”?
Deliberately vague to indicate all those results and processes governed by quantum theory such as electrons as waves, discrete states, and discrete quanta of energy, etc.
There’s no conundrum in the double slit experiment, and there’s only one in Schrödinger’s Cat if you want there to be one. And it’s impossible to say what ramifications a theory of quantum gravity would have for either gravity or quantum mechanics, because we don’t yet have one, and have only vague ideas of what one would be like.
Just as auto mechanics fix autos, so do quantum mechanics fix quantums. The OP obviously has only one quantum, so he uses the definite article to refer to his quantum.
That depends a lot on what route to quantum gravity will eventually work out. The most ‘mainstream’ routes (like e.g. string theory or loop quantum gravity) are basically ‘quantum theories of gravity’, in the same sense we have a quantum theory of electromagnetism—they’re in a sense applications of the framework of quantum mechanics (or more accurately, quantum field theory) to a particular setting. Thus, such theories won’t modify the phenomena you mention, since they come part and parcel with the quantum framework.
Besides ‘quantizing gravity’, there are other possibilities, however, such as for instance showing that, contrary to the above approaches, quantum mechanics actually emerges from some deeper geometric theory—an approach sometimes known as ‘geometrizing the quantum’. The third possibility would be that both, quantum mechanics and gravity, are just approximations, valid in their respective domains, to some deeper theory that is neither quantum nor geometrical. Both of these could result in changes of our understanding of quantum phenomena.
One example I can think of right know is due to Roger Penrose, who thinks that the ultimate synthesis of quantum mechanics and gravity will be a nonlinear theory. However, quantum mechanics itself is completely linear, and in some nonlinear generalization, things like superpositions can’t exist in general—this means that the state spontaneously ‘collapses’, and thus, that there’s no cat paradox: everything macroscopic will have a very high likelihood to spontaneously take on either one state, or another.
Another possible implication would be if one of the holographic models turns out to be correct. Holography is inherently nonlocal, and the nonlocality just might turn out to be of a form which can satisfy the EPR paradox.
Thanks, all!
I think I understand non-locality (as much as I can say I understand anything about relativity and quantum theory).
I don’t really have any feel for what is meant or implied by a non-linear theory (as used to characterize a ‘quantum gravity theory’). Is there any way to elaborate?
With respect to holographic models, I have long wanted to post on that topic if for no other reason than to ask ‘is it even possible for a non-specialist to get a feel for an entropic theory of gravity?’ I’ve looked Verlinde’s famous paper (with looked being the key word ;)) and, although I really do think I get how entropy can give rise to an elastic force, that’s pretty much my limit.
“Linearity” basically just means that you can use the Principle of Superposition in some form. What precisely that means depends on context, but in general, it means that you can somehow break up a problem into parts, solve those parts individually, and then add the solutions back together to get the solution of the whole thing. For instance, to get the electric field due to a collection of charges, you can find the electric field due to each individual charge, then add up all of those electric fields to find the total field: Thus, the electric field is linear in this sense.
The gravitational field, meanwhile, is not linear in this sense, though it almost is, because there’s energy associated with the arrangement of masses, and that energy itself is a source of gravity. In most cases (i.e., not right next to a black hole), gravity is close enough to linear that you can use a perturbation approach: Solve for the gravitational field as if it were linear, then find the energy associated with that, and then find the field from that “extra” energy and add it in (and so on, though just taking that one extra step is almost always good enough.
That was a great help, Chronos! Thank you.
Naive question: is there a way to solve for the limit of the sum of those gravitational perturbations (in the example you gave)? Or does it not even (necessarily) converge?
Is there a general way to get an exact solution from a peturbation of an exact solution? No. Does the peturbation series necessarily converge? AFAIK, probably not. Even worse though, for a given exact solution there might not exist peturbed solutions, though from what I understand in the most useful cases it has been proven that peturbed solutions do exist.
Past thread for a starting point.
Wait. If the perturbation series doesn’t converge isn’t it inherently a wrong approximation? After all the gravitational force isn’t infinite or we’d ll be speeding someplace in a big hurry.
Every time I read anything about Quantum Anything, beyond the most elementary Dummies expositions, my mind sort of melts and becomes a perturbed solution.
That’s correct. With gravity, so far as I know it always converges everywhere outside of a black hole (though close to a black hole, the convergence might be too slow to be practical). With, say, the strong force, though, it converges only under certain circumstances (specifically, very high energies), and so we can’t use perturbative methods for the strong force except under those circumstances. There is some abstract sense in which the method is still correct, but that’s little comfort, because it’s not usable.
Thanks, I missed that thread.
In the linked thread, you give a neat example of 100 dice in a box, all initially showing ‘1’. Any agitation of the box, will lead to a much more homogenous state.
What, if any, may I ask, is the gravitational equivalent of the extremely rare occurrence where after shaking the box the dice are seen once again to all be showing ‘1’. Or, phrased differently, what is the entropic-gravitational equivalent of those states at either extreme of some bell-curve shaped distribution (whether we’re talking about states of dice, individual kinetic energies of a collection of gas particles, etc.)?
Unknown. Verlinde explicitly avoids giving a specific microscopic picture. The positions of gravitating objects are assumed to be described by information located on sheets or boundaries. That information is encapsulated through unspecified means and has unspecified dynamics, aside from operating with some sensible concept of time and having an entropy that varies in the right way as the gravitating objects move around. Causality is flipped, though: the objects are moving around because the surface information describing their locations is evolving to a higher entropy state (via unspecified dynamics acting on unspecified microstates).
Macroscopically, the unlikely state would be all matter far apart from all other matter, since the entropic force is exactly gravity.
So, basically not only does no one know, no one knows what they don’t know. I am not trying to sound sarcastic - that’s the way things can be at their earliest formulation, I suppose.
And, for the record, in my post two above from this one, I obviously meant much LESS homogeneous :smack:
As I did in that prior thread, I’d again like to point out Johannes Koelman’s excellent explanatory efforts regarding entropic gravity, in particular his mikado universe model, which provides for a 2d-universe an explicit realization of Verlinde’s idea in terms of microscopic degrees of freedom—infinite lines on the plane that can either be ‘on’ or ‘off’, and must be off if they cross the space occupied by a ‘particle’. ‘Off’ rays now don’t contribute to the entropy—think of it as degrees of freedom hidden behind the horizon of the particle, which we may think of as a model black hole—, and thus, there are more configurations in which the two particles are close together then there are configurations in which they are far apart, and so they will move inexorably closer to one another if the system is ‘updated’ randomly. There’s also some more in-depth explanation plus a simulation here.
However, just for completness’ sake, while the whole ‘entropic force’ formulation is due to Verlinde, using a thermodynamic approach to general relativity is somewhat older, due to a 1995 publication by Ted Jacobson entitled ‘The Einstein Equation as an Equation of State’. (Of course, there’s even earlier work by Bekenstein, Hawking and others on the connection between gravity and thermodynamics.) In fact, Jacobson’s approach is more complete, since he considers general relativity rather than (mainly) being concerned with Newtonian gravity. This is having something of a resurgence lately, due to the realization that in the string inspired version of the holographic principle, the entanglement on the horizon is related to the bulk spacetime (the connection being, in part, that entanglement can be quantified in terms of entropy).
The bit I don’t understand about “entropic gravity” models is that they all describe something that causes particles to move together… but gravity doesn’t do that. Gravity causes things to accelerate together, but acceleration is time-symmetric.