Quantum particles can feel the effects of gravitational fields
scienceinter.com
scienceinter.com
One way of interpreting the normal Aharonov-Bohm effect is that it implies that the electromagnetic potential is more "real" than the electromagnetic field. We tend to think of the electromagnetic field as what's "really" out there because if you stick a charge in an electric field you can measure the field strength by measuring the force the charge feels or you can measure the force on a moving charge and calculate the magnetic field. By contrast the electromagnetic potential is not uniquely defined which makes it feel like a mathematical construct. You can add any function with zero divergence to the electric potential and any function with zero curl to the magnetic potential and have a potential that behaves identically for any experiment you could do (these are different gauge choices in the parlance).
The classic Aharonov-Bohm effect is that you take a particle and pass it around a magnetic solenoid in a superposition of two states --- say one state goes to the left of the solenoid, the other goes to the right. In a sense the particle takes both paths simultaneously. The magnetic field is zero along both paths the particle takes. If you turn the solenoid on and off you would think it would make no difference because no matter what you do, the magnetic field the particle encounters is zero. The key, though, is that the magnetic potential is not zero along the particle's path, and the magnetic potential affects the particle's phase in measurable way when the two states recombine.
Sometimes I see interpretations that this means that there is a small but non-zero chance that the particle is found inside the solenoid where the magnetic field is non-zero, but I don't think that's right. You can construct the experiment in a way that the chance of this happening is negligible. The real implication seems to be that the electromagnetic potential is the more physically fundamental quantity even though it is not generally directly observable.
All the math for the Aharonov-Bohm effect applies for gravitational fields as well. But here it's not quite as "weird" a result because gravitational fields can't be shielded the same way magnetic fields can be. The particle always encounters the gravitational field along both paths, so it's not so spooky that the field has a measurable effect.
So if you turn the solenoid off, you could fix the gauge by setting the magnetic potential to zero, but you don't have to. You could still add any function whose curl is zero and have a valid magnetic potential. This would not change the observed phase difference. So there's still no preferred gauge. (Some choices of gauge may make the math easier in the same way that some choices of coordinate systems are more natural to the experiment, but any choice of gauge is valid, just as any choice of coordinate system is.)
> If you turn the solenoid on and off you would think it would make no difference because no matter what you do, the magnetic field the particle encounters is zero. The key, though, is that the magnetic potential is not zero along the particle's path, and the magnetic potential affects the particle's phase in measurable way when the two states recombine.
Imply that you can measure the potential somehow? That the particles phase is affected by the potential being non-zero, and therefore the gauge is at least somewhat fixed?
The centrifugal force, by contrast, is more a consequence of a particular choice of reference frame. Whether it exists or not picks out certain reference frames as being special. But something like the wavefunction or magnetic potential is not directly observable in any reference frame.
That said, one way in which the magnetic field is similar to the centrifugal force is that it is a direct consequence of special relativity. If you look at a stationary electron, you'll just see an electric field. But you can show that if you're looking at that electron in a moving reference frame, you'll see an extra force. We call that extra force the magnetic force.
AFAIR thats not quite accurate. Complex numbers are just the best representation. Altough, I can't seem to find the relevant article that I remember atm.
I'm sorry, but everything about forces is wondrously spooky to me.
When we arrive at the time when we find fields to be non-spooky, and the idea of material reality existing exclusively as field excitations to be ontologically comfortable, well - then I will finally get to meet my brothers and sisters!
Thank you so much for your excellent and informative comment, btw!
It means that (like with relativity) you end up dealing with some rather nasty intractable calculus, and in order to make sense of things you'll be looking to sound enough approximations of what's actually going on.
This consequences of this will be particularly amusing in near proximity to event horizons.
I am about as far from an expert as it's possible to be, but I always wondered what would happen if an entangled system exerted its gravity on something else.
Is there an argument for this rather than the other way?
I’m probably misremembering, but I thought I’d seen something about spacetime being continuous and particles being braids in that aether — but did that blow up when string theory didn’t happen at the LHC?
String theory isn't really possible to rule out via any experiment I've ever seen. At best you can rule out some versions of it, but even that is hard AFAIK.
If they both drop at the same exact speed (and it's not what it should be from a locality standpoint) it would confirm that local gravity is having an impact on both particles at the same time. In other words, if you drop a particle from 10 meters at sea level it would fall at a certain rate. However, if you entangle it with a particle that's 6,000 meters up that particle at sea level might drop at a rate equivalent to what it would at around 3,000 meters (assuming gravity influences both particles equally).
If that's how it worked then in theory you could entangle a large mass of particles here on earth with some out in space and you'd only need a fraction of the amount of energy for the particles here on earth to reach escape velocity.
Yes. The experiment is easy to run. The equipment that can detect the factor-of-10^-50 percent difference between them is not so easy to come by. The problem with quantum gravity is the lack of data brought on by the fact gravity effectively doesn't exist on Earth at what we typically call "quantum" scales, compared to the overwhelming influence of electromagnetism and the nuclear forces.
(The inhabitants of the Dragon's Egg in the science fiction novel of the same name, which are creatures made out of matter on the surface of a neutron star, presumably did not have such troubles making a theory of quantum gravity, because they could gather data directly. We creatures made of atoms in an environment that permits that are not so lucky!)
It's not that hard to come up with situations where you get less-than-Planck time expected differences in behavior. This is another frontier in science nobody knows the answer to. For as small as Planck time is, there are ways you can theoretically detect if the universe was "rounding" at that scale, and so far they have all consistently come up as "nope, the universe isn't rounding"... yet it is also almost inconceivable with modern physics how it couldn't be in one way or another. (The most interesting one was trying to pick up various effects of such quantization on photons travelling so far across the universe that the differences would be detectable.) There are still many mysteries!
It's gravity (approximately an inverse square law) operating across the probabilistic distribution of the locations of the system.
https://en.wikipedia.org/wiki/Three-body_problem
Actually, the gradient function is the probabilistic integral across the gradient functions of infinitely many three-body problems.
The actual solution is the integral of that.
Eh? That warping is the gravitational force.
"The world is... not analyzable into parts".
If there are no parts, what are numbers counting?
We just live in an age of hype.