When that waveform collapse happens, everything about the quantum state collapses: electromagnetic field, gravity, etc.
Grandparent did an excellent job setting up the hypothetical scenario by the way. It just turns out QM is awesomely weird like that. It does mean a mass which was de-localized by miles can, theoretically, localize to a single point instantly. However, any information about that localization is restricted to moving at the speed of light.
Sounds like when the wave function of the electron is moving, likely it is following the local geometry of space-time but otherwise is essentially lost to the universe.
Then whenever we do detect a field, gravity, electro-magnetic, strong, weak, etc., necessarily we are detecting just collapsing wave functions, each of which happens at essentially just a point in time. Then after the point in time of the collapse, the electron is just a wave function again off on its way to another collapse.
E.g., when an electron accelerates going around a circle and radiates photons, each photon radiated is from a collapse of the wave function of the electron at which time the electron creates a new wave function and continues on? Sounds like that.
Hmm ... So, all we are seeing, feeling, detecting, observing, measuring, etc. are just high rate point processes of collapsing wave functions? Gads. Why didn't they tell me that back in high school?
Where am I going wrong?
Regarding your electron-emitting-photons example: I would describe the photons being emitted as themselves in a quantum superposition of having been emitted/not emitted/emitted at different times, etc. It is when we detect or observe the photon that the state of the whole system collapses! The electron and the photon are entangled. Continue this line of thinking and you arrive at the famous Schrodinger's cat... it's a cascading entanglement of larger and larger groups of particles until you open the box and the waveform of every particle in the whole cat collapses to either alive or dead.
The waveform is not really a physical object; I think of it as a probability distribution about the state of the system when observed. These probabilities can be highly correlated; in this case, the probability of observing the electron at one energy level or another is 100% correlated to the probability of observing or not observing the photon at all - which is the definition of entanglement.
Yes, you are constantly observing collapsing wave functions. It might be some solace that most of said wave functions have highly-degenerate probability distributions. By this I mean that 99.999...% of the "mass" of the distribution lies in something reasonable happening. For example, each particle in a tennis ball is so highly entangled to every other particle, that when you throw it against a wall, it's exceedingly likely that the ball will bounce back. A single unentangled atom may have been able to pass right through the wall, but the tennis ball's "waveform" is much more stable and localized such that it's better approximated by classical mechanics.
- There's a huge sphere of a dense metal (something like 20 feet in diameter).
- The sphere can be moved closer to or farther away from an incredibly precise accelerometer.
- When the sphere is close to the accelerometer, the accelerometer's reading change very slightly due to the gravitational attraction of the massive sphere. (The change in acceleration was just barely detectable given the technology.)
- A radioactive isotope has a 50-50 chance of decaying or not in a particular time period. Under the Many Worlds Interpretation, the experimenter is in a superposition of having seen the decay and not.
- If the isotope decays, the experimenter pushes the sphere close to the accelerometer. Otherwise the experimenter pushes the sphere away. Now the sphere is in a superposition of affecting the accelerometer and not.
- The experimenter reads the accelerometer.
The point of the experiment was to see if the accelerometer would detect the deformation in spacetime caused by the superposition of the massive ball in parallel universes. The result of the experiment is that no acceleration was ever detected by other worlds' balls.
We have a gun that shoots electrons one at a time due north. A little ahead of the gun and in the path of the electrons we have a beam splitter, that is, a flat plate of material with horizontal normal along the line from south east to north west.
So, we fire the gun. The electron hits the beam splitter. The wave function splits with some going east and the rest passing through the beam splitter and going north.
One mile to the north of the beam splitter and in the line of the path of the wave function we have a very good electron detector. Similarly for one mile to the east.
So, we fire and some fraction of the time we get a detection from the north detector and the rest of the time, from the east detector.
Now, let's move some of the mass of the electron faster than the speed of light: A little ahead of each detector we have a very sensitive detector of gravity (or, maybe charge).
So, as the two parts of the wave function pass the gravity detectors, we get a signal from both. If the beam splitter sends 10% of the wave function north and the other 90% east, then from the north gravity detector we should get a signal of 10% of an electron, and from the east, 90% of an electron.
Then, soon, one of the electron detectors gives a signal, of 100% of the mass (and charge) of an electron. So, 90% or 10% of the mass (and charge) of the electron moved instantly, faster than the speed of light. along the line between the two detectors.
Is this wrong? Why?
In more detail, what about the electromagnetic field from the moving parts of the wave function? E.g., if the electron is detected at the east detector, is there an electromagnetic field still from the path of part of the wave function to the north?