Comment by graycat | Hacker News Reader

Comment by graycat | Hacker News Reader

As we know, the path of a photon can be bent by a large mass with gravity.

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.

If you have a gravity detector that can distinguish where a photon's energy is localized, it also works as a photon detector in the QM measurement sense, and will collapse the wavefunction in the same way.

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.

> If you have a gravity detector that can distinguish where a photon's energy is localized, it also works as a photon detector in the QM measurement sense, and will collapse the wavefunction in the same way.

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.

> So, just having the detector, maybe a second away, collapses the wave function? My guess is that (...)

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.

Gravity decreases as you move inside the Earth.

A gravity wave detector works by having mass which gets influenced by gravity. But this influence is a two-way street: the photon feels the detector's gravity at exactly the same time as the detector feels the photon's gravity. If the detector is sensitive enough to distinguish the location of photons, it must be very close to the photons and/or have a huge mass! So it's not surprising that its gravitational field can influence the state of the photon.

You might be interested in the following classic 1989 paper (famously discussed in the first year graduate physics textbook by Sakurai) - https://inis.iaea.org/collection/NCLCollectionStore/_Public/...

> The moving particle, photon, electron, neutron, is throwing off a gravity wave as it is moving

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.

> If you have a gravity detector that can distinguish where a photon's energy is localized, it also works as a photon detector in the QM measurement sense, and will collapse the wavefunction in the same way.

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?

The simplest answer, without getting bogged down in details that don’t change the answer, is found in the classic equation: E^2=m^2c^4+p^2c^2. We know that E=hf=pc, so we also know that the answer to your question is “Yes” and “No” respectively.

I wonder whether this exact thing is why we have dark matter...

I'll add a little to my post to you.

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.

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