When Gravity Breaks Down
nautil.us
nautil.us
Okay: Pass a photon, or electron, or other particle, through a beam splitter and, thus, get its wave function in two parts.
Then the question seems to be, do the parts also get bent by gravity? Is there any doubt they won't.
For a particle with mass, surely it has gravity. So, the two parts of its wave function no longer have gravity -- is that the question she is asking? Maybe depending on the beam splitter, the two parts of the wave function have 60% and 40% of the gravity of the whole particle?
Get a lot of particles, say, neutrons, that do feel and generate gravity and run them through a beam splitter. Bunch #1 goes north and bunch #2 goes east. So far they still generate gravity? Some miles away from the beam splitter we put detectors, one for each bunch. With a 50%-50% beam splitter, with the law of large numbers, we detect 50% of the particles at each detector. That is, each detector gets a part of the wave function for ALL the particles but detects only half of the particles.
Suppose the detector for bunch #1 is some miles farther from the beam splitter than the detector for bunch #2. So, the wave functions for bunch #2 hit their detector before the wave functions for bunch #1 hits their detector.
Now look at the wave functions for bunch #1: About half of those wave functions have already collapsed due to detections at the detector for bunch #2. So, the gravity generated by the remaining wave functions of bunch #1 are, from the law of large numbers, half what they would be without a detector for bunch #2. So, for bunch #1, we have had faster than speed of light communications from the detector for bunch #2 to a measurement of the gravity of bunch #1.
Yes, we can't get a gravity detector sensitive enough, but for that theory that's not important. Instead, for the bunches to generate gravity gets to be an issue anyway.
Also, remember that gravity waves move at the speed of light; you can't detect a photon's gravity from a distance without waiting for the same light speed delay that you would get from the photon itself.
I've wondered about that: The moving particle, photon, electron, neutron, is throwing off a gravity wave as it is moving if we don't have a gravity wave detector detecting that wave. So, just having the detector, maybe a second away, collapses the wave function?
My guess is that as a wave function is split into multiple parts going off in different directions and getting far apart, the particle is not yet "localized" in any of the parts. The idea that there is a particle, "localized" but we just don't yet know where it is I have a tough time accepting. Instead, until there is an interaction that transfers the energy, although maybe not the gravitational energy, there is no localization. Or, all the parts of the wave function both feel and generate gravity until the collapse from an interaction with, say, a detector.
Or, if only one part of the wave function has the particle, then when two parts of the wave function are combined, as in just Young's double slit, we should not get the interference we do get. Or, it seems we get the interference of the wave function parts, then get the detection; there never was anything localized until the detection at which time all the parts of the wave function have to collapse everywhere, instantaneously, even across 1 billion light years -- no I don't like to believe that, but I'm just looking at the interference of two parts of the wave function in Young's double slit: If the particle was really in just one of the two parts of the wave function, then tough to believe in the interference we do see.
This gets to to crux of the issue the author (and others in contemporary physics, Hawking included for that matter) was raising. We can conjecture, via theoretical physics, a whole slew of possible models of the universe that combine general relativity and quantum mechanics. But, there is a lack of experimental evidence (or interpretation of existing results) to resolve the ongoing "debates". And there hasn't been any real progress, in that respect, in the past 80 years.
We need to test the edge cases of both theories as best we know how. For example, tunnel to the center of the earth (or another planet?) and verify our existing models in the gravity well, maybe repeat the double-slit experiment remotely while we're there. I'd say a task much more difficult, engineering-wise, then flying a human being to another planet and back.
Not necessarily. Many kinds of motion do not cause gravitational wave emission. And even the kinds that do don't cause enough to detect with our best current technologies, by many, many orders of magnitude. You basically need huge masses in a situation where they are in very tight orbits, like merging black holes or neutron stars.
But in the Michelson interferometer, the Fabry-Perot, etc., the parts of the wave functions pass close to lots of mass, get reflected by mirrors, etc. without the wave function collapsing. So, a part of a wave function should be able to pass near a gravitational wave detector and be detected without causing the wave function to collapse?
Last night, in bed, lights out, no paper or pencil, nearly asleep, I had an idea. Here goes: There's the law of large numbers, the weak version and the strong version. Good authors for the details are M. Loeve, J. Neveu, L. Breiman. I've been through lots of proofs.
Likely the easiest proof of the strong law is from the martingale convergence theorem. It's so easy, just f'get about proving the strong law and concentrate on martingales!
But a few years ago I noticed that Breiman advised students to think of a simpler case. In a hurry, I didn't.
Then, yup, last night, trying to go to sleep, I thought: The simple case is coin flipping, say, 0 and 1.
Now flip a coin, say, 50 times. Get all the possible outcomes, that is, sequences of 1's and 0's. Now count the sequences with about 50%/50% 0s and 1s. Before getting out the little formulas on combinations and permutations, or just rederiving them, guess that the fraction of the sequences with 50/50 or near that start to dominate in the fraction of all the sequences. Do this for 1000 flips, 1 million flips, etc. Guess before looking into the details and just before going to sleep, if check the details will find that a the number of flips increase, just as the law of large numbers posits, will find that the 50-50 case so dominates that the rest, as fractions, as probabilities, head for zero. Presto, bingo, convergence! That's just a guess. I still haven't worked out the details. With the details, the guess might be right or might be wrong. But that's a little of how intuitive guessing goes. My guess now is that for guessing that guess was pretty good. I've published theorems that started with guesses less good looking than that one!
Lesson: For proving theorems, and finding new ones, intuitive guessing, sometimes starting with simple cases, at times can work.
Quantum mechanics does not say a particle can be in two places at the same time. A wave function does not say a particle is at point A AND point b. The wave function says the particele is at point A OR point B.
To take this a step further, if the particle has an electric field, then the wave function would look like the following:
(particle at A AND electric field around point A) OR (particle at B AND electric field around point B)
The wave function would NOT be:
(particle at A OR particle at B) AND (electric field around A OR electric field around B)
And also not:
(particle at A AND particle at B) AND (electric field around A and B)
Presumably the same applies to a gravitational field.
But to address your comment: the OR description is a bit better than the AND one because the possiblities described by the wave function are excluding one another (when a good basis is chosen). However neither the OR nor the AND description actually mention the fact that the "probabilities" interfere (which is what the double slit experiment tests). That experiment disproves both of these simplified descriptions.
Another reason I like the OR intuition better if I have to chose between these two wrong simplifications: if you do the double slit experiment with one photon at a time and repeat it multiple time then you do see only one photon at a time hit the screen (the OR intuition). But the image you get if you wait and average over many photons is indeed the interference pattern.
TLDR: OR acts more like probabilistic but not interfering particles. AND acts more like waves. Both are wrong, but in different contexts one or the other might be a convenient simplification.
https://www.smbc-comics.com/comic/the-talk-3
key quote:
'Superposition doesn't mean "and", but it also doesn't mean "or".' 'It means a complex linear combination of a 0 state and a 1 state. You should think of it as a new ontological category: a way of combining things that doesn't really map onto any classical concept.'
Sorry if this is a dumb question, I'm not formally trained in any of this stuff...
So if you have (a+bi)|0> + (c+di)|1>, the magnitude of this vector is a^2 + b^2 + c^2 + d^2 = 1
Edit: however, the vector only has to have magnitude 1 if it is describing the entire system, I think?
Some intuition: if you have a particle and you look everywhere for it, your chance of finding it must be 100%. It can't be 50% (where could it be?) and it can't be 200% (duh).
QM in one dimension is formulated as "a 1d complex unit vector", i.e. a complex number of magnitude 1, which is routinely represented in polar form (a complex exponential).
QM in two dimensions is a "2d complex unit vector" which is really 3d: you get three linearly independent components, and then the fourth one is decided for you. You can think of this as spherical coordinates, but complex numbers are much easier to manipulate, so that's what we do.
I'm a physicist and its true phsycist's don't always tell the whole truth when talking about quantum mechanics. I understand the different perspective between a person doing quantum computing and physicist thinking about the real world. In a quantum computer there are maybe 32 objects each with 2 states. In the real world something like an electric field has an infinite number of possibly values for each of an inifinte numbers of points in space. And then there are interactions between different objects which we can't hope to mathematcially solve but only approximate. And, on top of that, we have to relate the mathematcis to what people see around us.
So generally we have to create a straw man for a specific scenario, hence the line in the comic where phsycists don't tell the whole truth. And that's why all these people can look at the straw man example I gave and then say "No, that's not right. It's not "OR".
So, you can say a particle is in two places (AND) at the same time wihtin a given context. So that is fair. In the context of describing the connection of a field to its originating particle, that strawman is not useful. The elctric field is correclated with the position of the particle so the "OR" idea is helpful there, but if you try to take that example too far, sooner or later that strawman breaks down.
So you could look at the statement in the comic instead about wave functions. Does that provide an clarity to how a field relates to the particle from which it originates? Probably not unless you already know the answer.
Admitedly, I guess what I wrote didn't provide much clarity either. Any disucssion of quantum mechanics in a place like this usually devolves into everyone talking past each other.
Note though that quantum mechanics is itself just a simplified way of modeling what happens due to field theory. Under field theory, fields are central, and particles are just phenomena that happen under fields. It is of course possible that in a more fundamental theory, particles are central and their interaction just results in field-like behavior.
No, it doesn't. It doesn't say either of those things. It says the particle is in a superposition of being at point A and being at point B. There is no simple logical connective in ordinary language that captures that.
However, for the purposes of trying to figure out the gravitational field of the particle, being in a superposition of being at point A and being at point B is functionally equivalent to being in both positions at the same time, in the sense that we don't know how to treat either one quantum mechanically. See below.
> if the particle has an electric field, then the wave function would look like the following...
No, it wouldn't. It wouldn't look like any of the possibilities you wrote down. It would look like a superposition of "particle at A and electric field around point A" and "particle at B and electric field around point B". But since we know how to quantize the electromagnetic field, we know how to treat such superpositions quantum mechanically. We don't have a corresponding way to treat superpositions of gravitational fields quantum mechanically.
Yes, I'd agree with this. I was trying to say something aproximately true to convey a point. In your post you did agree with my salient point - the electric field moves with the electron, it doesn't do something funny when the elestron has some spread in its wavefuntion for position. This seemed to be the what the article was talking about, that the gravitational field behaved differently for a superposition of states.
I will try a more concrete example.
Suppose you have an electron gun and shoot a single elctron at a metal plate. Suppose the wavefunction is such that it is uniform over the surface of the plate (So the electron has an equal probability of hitting anywhere on the plate.) What does the damage to the plate look like? Is it spread uniformly over the plate? No. It is a single small mark at some specific place on the plate. The electron is not smeared over the plate, the probability of finding the electron is smeared over the plate. The electron is still a point particle (to the extent of our current laws of physics) and it will only interact with the plate at one point. (Some people will not like my language and tell me I am wrong. But it is true the electron will hit the plate at a single point - not smeared out like the wavefunction is.)
In actuality the electron didn't cause the damage to the plate. The electric field did. The electric field moves with the electron almost like you would expect in classical physics. It's not like the electric field is smeared around because the electron is in a superposition of states.
I'd expect gravity to work the same way. But seeing how we don't have a theory it is possible it could violate the above idea. To me that would be a pretty weird violation too. (This short writeup doesn't really do that justice.) I'd bet against it.
It isn't. It's a wave function (or, if we take relativity into account, a quantum field).
But that doesn't mean it can't have interference. Interference occurs because of the wave function. The wave function for the electron and the electron itself are two different things.
They did a electon double split experiment where they fired electons one at a time. The electrons each made a single point (or small mark) on the measuring screen, but over time, the interference pattern formed. (To be honest I heard this back when I was learning physiscs, which was along time ago. It could have actually been a thought experiment or it could have been something besides an electron. Anyway I believe it is true.)
Sort of. Describing it as an "electric field" assumes the electron is not moving; if it's moving, at the very least there will be a magnetic field as well as an electric field. Also, as I said, when we take quantum effects into account we need to quantize the electromagnetic field as well as the electron, so the field is no longer just something that "moves with" the electron; it's a separate thing of its own that happens to interact with the electron in a certain way.
> The electron is still a point particle (to the extent of our current laws of physics) and it will only interact with the plate at one point.
Not a point; the damage on the plate will have a finite size. But you're right that the damage on the plate won't look like the wave function as a whole. Also see below.
> In actuality the electron didn't cause the damage to the plate. The electric field did.
If this is true, you can't deduce that the electron is a point particle from the damage at all, since the damage tells you about the field, not about the electron.
> It's not like the electric field is smeared around because the electron is in a superposition of states.
You're mixing up two different things. If the electron hits the plate, it's no longer in a superposition, and neither is the field. If the electron is in a superposition, it's because it hasn't hit the plate yet, so we haven't measured it--and in that case, the field is in a superposition too. So the "smearing" of the electron and the field go together (in the oversimplified model we're using).
> I'd expect gravity to work the same way.
The issue with gravity is that the "field" in the case of gravity is the spacetime metric. All of the reasoning about the electron and the electric field assumed that the spacetime metric was known. But if gravity is quantized, the spacetime metric itself would be in a superposition if its source (say some massive object) were in a superposition. That's a crucial aspect that's unique to gravity.