Does photon interference violate causality?

Question

Suppose a hydrogen atom jumps down an energy level and emits a photon and that photon later goes through a double slit and gets absorbed by one atom of a screen making it jump up an energy level. Doesn't the photon have an extreme uncertainty in position and exist as a wave that travels in all directions until it suddenly collapses to have an uncertainty in position of about the diameter of an atom and gets completely absorbed by a single atom in the screen. That seems to violate causality because it's guaranteed that the screen will detect at most one photon from that atom so the detection by one atom sends the information to another atom faster than light to not detect it.

One possible explanation is that the universe follows de Broglie–Bohm theory and despite the fact that information can travel faster than light, it can never be sent in such a way to create a paradox. That in turn might be because those laws are a simulation by the fundamental laws which is that the universe is a Conway's game of life so it could not have simulated a universe with laws that allow for a paradox.

Another possible explanation is that the universe follows a different theory where it was already determined ahead by a hidden variable which atom will absorb the photon before the atom actually absorbs it. Maybe the photon emits a classical wave which stays a classical wave which gets gradually absorbed classically and the probability density of any atom on the screen jumping up an energy level at any time is completely determined by the rate of absorption of the classical wave so the jump down in energy level of the hydrogen atom actually can causing two atoms in the screen to jump up an energy level. Maybe it can actually be determined ahead which atoms will jump up in energy level but it seems random because the universe is chaotic. If that were the case, we would never be able to tell that the universe doesn't follow the accepted theory because we couldn't tell which jump ups in energy level of an atom in the screen came from which jump downs in energy level of a hydrogen atom. Just because a theory is consistent with observations doesn't mean the universe actually follows that theory.

Answer 1

Suppose a hydrogen atom jumps down an energy level and emits a photon and that photon

That is modeled by the hydrogen atom solution of the schrodinger equation, and the wave function is bounded by the existence of the proton and the electron and the leaving photon.

One quantum mechanical boundary condition problem.

later

not really too much later, consider the velocity of light

goes through a double slit

This is a second quantum mechanical problem with its solutions and its boundary values "photon scattering off two slits of given width and distance apart" . This gives a wave function which describes the probable path the photon will travel to a macroscopic screen

Here is the double slit one photon at a time:

One photon's path brings it to a point on a screen where a third quantum mechanical problem is seen, "photon scattering off atom on screen" and losing energy, the ionized atom seen as a dot from the dissipation of the energy it gained.

Three incoherent experiments with the quantum mechanical probabilistic distribution.

The accumulation of photons of the same energy and boundary conditions carries the information of the second experiment, the build up of the probability distribution, which shows the wave nature of the photon, not as an energy spread all over the place, but a probability wave.

The third experiment, detection by ionization due to energy loss of atom interacting with photon is used continuously in bubble chambers and other particle detectors to follow macroscopic tracks of elementary particles.

Doesn't the photon have an extreme uncertainty in position and exist as a wave that travels in all directions

No, it follows the probability distribution predicted by the solution of the specific boundary conditions.(the three independent setups)

until it suddenly collapses to have an uncertainty in position of about the diameter of an atom and gets completely absorbed by a single atom in the screen.

This collapse business is confusing you. It is only in the third phase that the interaction of a specific photon with an atom releases its energy in the confines of a few atoms. Of course once the interaction happens the wavefunction no longer is valid. The same is true for the second experiment, once the photons scatters off the two slits, the original hydrogen photon wave function is invalid.

Nothing happens faster than light. Consecutive interactions are incoherent, but certainly not faster than light, and this sentence is confused:

That seems to violate causality because it's guarenteed that the screen will detect at most one photon from that atom so the detection by one atom sends the information to another atom faster than light to not detect it.

Nothing is guaranteed in quantum mechanics except energy and momentum and quantum number conservations where appropriate. Everything else is governed by probabilistic quantum mechanical functions.

Answer 2

Congratulations, you’ve discovered the Einstein Bubble paradox! Every interpretation of quantum mechanics has its own way of dealing with this, and it’s up to you to decide which one you like.

Answer 3

For most physical theories, the way you work out what they imply about how the world works is to use the equations of motion of the theory. Now, in quantum mechanics, people use two distinct types of equations. The first type consists of equations like the Schrodinger equation that are well defined and relatively well understood. the send type is an ad hoc rule that sez that somehow under some unspecified set of circumstances the first kind of equation stops working. The second rule is the one that causes all the trouble in this case and in many others. So about 60 years ago Hugh Everett suggested that we should just ditch the second rule.

If we follow Everett's suggestion, then the photon propagates entirely locally. There are multiple different versions of the photon in different places. One version of the photon interacts with an atom, another version interacts with a screen and so on. At any particular place when the information about the photon's interactions arrive, the different versions of the information interact with one another and the versions where the photon is absorbed by the atom are paired up with versions of the screen that didn't absorb the photon.

So the theory that explains the causal interactions of the photon is quantum theory. No Bohmian particles are necessary. See

https://arxiv.org/abs/quant-ph/0104033

https://arxiv.org/abs/quant-ph/0107144

https://arxiv.org/abs/quant-ph/0403094

Answer 4

You are asking two questions.

1. How can the electron jump instantaneously.

2. How can the other atoms know instantaneously that this atom already absorbed the photon and there is nothing to absorb for the others.

The wavefunction is the probability distribution of the particle's position. For the photon, the wavefunction will give you a description of the probabilities of the photon's trajectory. For the electron in the absorbing atom, the wavefunction will give you a probability description of what energy level the electron is at as per QM.

Now you are saying that the electron in the absorbing atom will jump up an energy level when absorbing the photon and then it will jump back down when emitting a photon. But this is not right. As per QM, there is no quantum leap. The wavefunction describes the position of the electron at certain energy levels, and the probability that the electron is at a certain energy level is higher then the other ones. Classically we would say that the electron is at that orbit. But in QM, the electron is just at that energy level with a high probability and is at other energy levels with a lower probability at the same time.

At the same time is important. You could find the electron at other energy levels too, just with lesser probability. When the electron absorbs the photon, it does not jump. It does not travel to a higher energy level classically. What happens, is that the wavefunction changes. It will describe the electron's probability to find it at a higher energy level with higher probability. And at the original lower level with lesser probability. As per QM, the electron moved to a higher energy level. But the electron did not jump classically. The electron can be found at the same time at both energy levels, it is just the probability that changed, the higher energy level has now higher probability. Your confusion is about how the electron jumps instantaneously. It does not. It is the probability (of finding the electron at a certain energy level as per QM), and the wavefunction that changes instantaneously as per QM.

2.

It is not only the electron and the photon that have wavefunction. All the atoms have one.

The wavefunction is just information. It does not collapse classically. It changes. It is a probability description. The positions of the particles in this case are described and probabilities are assigned to them. That can change instantaneously.

When the atom absorbs the photon, the photon transforms into energy, and the photon does not exist anymore. It is added to the energy level of the electron.

This interaction is not instantaneous. It needs the average time of EM interactions.

You are asking then how is it possible that other atoms know they do not need to absorb the photon. It is because the photon is the excitation of the EM field. The EM field exists everywhere in space. The atoms nuclei (and their constituents) and the electrons are excitation of those fields. Those fields exist everywhere in space. The two kinds of fields can interact (the EM for the photon and the electron and the other fields of the nuclei's constituents).

When the two fields interact, and the atoms' energy level's gap is compatible with the energy level of the photon, it will be absorbed. The photon then does not exist anymore, it transformed into the energy level of the electron.

Though the photon travels as a wave, it's probability distribution will describe it's position in space for different positions at the same time. At the same time is important. When (at a point in time) the wave reaches the screen, there will be a position of the photon that has the highest probability at that time. Other positions of the photon at the same time have lesser probability around that area. The atoms around that position (the position of the photon with the highest probability at that time) have a wavefunction, that describe their positions and energy levels gaps. The atom that has the matching energy level gap that matches the photon's energy level will absorb it with the highest probability.

The interaction between the atom and the photon is not instantaneous. It needs the average time for EM interactions. But the change in the wavefunction can be instantaneous, and the probability description of the absorbing electron's energy levels has changed. The photon does not exist anymore. It transformed into the energy level of the electron.

The other atoms cannot absorb the photon for two reasons.

1. The photon's position has a probability description (wavefunction) and at the point in time when the photon hits the screen, there is a position with the highest probability. Only atoms around that area can absorb the photon. And only atoms around that area with matching energy gap can absorb the photon.

2. The wavefunction can change instantaneously. The photon after the interaction does not exist anymore. It transformed into the energy level of the electron.

No particle or object can travel faster then light as per SR. But the wavefunction is just information, and it describes the particles' characteristics' probabilities. Those probabilities can change instantaneously (because the wave function is not a physical object). But even if that changes instantaneously, no particle or object of information travels faster then light.

Answer 5

You are struggling with the central conundrum in quantum mechanics. The idea of collapse of a wavefunction is itself in conflict with causality, pretty much for the reason you've zeroed in on. As far as I know, the only resolution to this conundrum is the many-worlds interpretation of quantum mechanics: as long as the screen is kept isolated from the observer, then the states of the atoms in the screen are themselves describable as wavefunctions. An incoming photon's wavefunction alters all of the screen's atoms' wavefunctions. However, as soon as you peek inside the isolation box deeply enough to measure the wavefunctions of the screen's atoms, your own wavefunction is altered. In the many-worlds interpretation, at that point your world (that is, your wavefunction) splits into as many independent, non-interacting parts as there are possible outcomes to your peek inside the box.

Edit 8/10/18 Bottom line: you're right that wave function collapse violates the principle of causality. The term "measurement problem" encompasses that issue. This article discusses the measurement problem, but does not provide clear explanations. This paper: dives into the philosophical aspects of various approaches to resolving the measurement problem, but is a difficult read.

The frustration of trying to come up with an intuitively satisfying interpretation has led to the "stop worrying about it and just do the math" approach to quantum mechanics -- which works, but doesn't fulfill our desire to understand what the math means. End edit