Probability of finding a particle outside its light cone

[RickRazor]

TL;DR Summary

Nonzero implies faster than light communication. Zero implies contradictions.

Say we just created a particle (high probability of one-particle state), is the probability of a very far away detector getting triggered at the time of creation (probability of finding a particle outside of its light cone) zero according to QFT?

Since we can detect particles and make histograms of the positions where they're found using detectors, this seems like a reasonable question to ask. I hope that QFT says that detector cannot detect particles outside its lightcone because if that's not the case, we can imagine an experiment where information can be sent FTL:

Consider a ridiculous amount of hydrogen atoms/electrons near person A and a very far away B measuring the rate of particles he detects. So when A makes some movement, if the probability outside light cone changes immediately, B's rate of detection immediately changes and hence this can be used for communication.

If you say that the probability outside light cone doesn't change immediately, that leads us to a grave situation. Assume A himself has a detector, and if he sweeps/detects most of the particles (sweeps through the high probability region, peaks). It makes zero sense to say B observes a same rate of particle detection since particles are already 'used' up by A.

(Some clarification: When I say particles near A, I mean by this is that we intuitively have an idea that particles/fields must have some kind of probability distribution. It is reasonable to assume that the there is some peak in distribution of atoms/electrons of my phone in my hand and probability of electrons of phone's atoms is extremely low far away. So even if QFT doesn't have position operator or whatever, it should somehow be able to talk about this.)

 

[PeroK]

QFT sounds the death knell for the single particle quantum mechanics described in your thought experiment.

 

[PeterDonis]

Say we just created a particle (high probability of one-particle state), is the probability of a very far away detector getting triggered at the time of creation (probability of finding a particle outside of its light cone) zero according to QFT?

No. But that is because "high probability of a one-particle state" is not the same as "guaranteed to be a one-particle state, localized where you created the particle". There is always some nonzero probability that the state of the quantum field is not exactly a one-particle state and that a second particle appears at some faraway event outside the light cone of the first creation event.

if that's not the case, we can imagine an experiment where information can be sent FTL

This won't work, because the fact that there is a nonzero probability of a particle detection outside the light cone of the original creation event does not mean that you can control that particle detection, which is what would be required to send information FTL. You can't.

when A makes some movement, if the probability outside light cone changes immediately

QFT doesn't work this way. Probabilities are attached to events in spacetime, not times. The probability of a detection at a particular event cannot be "changed"; it is what it is.

The correct way to think of "locality" in QFT is that measurements at spacelike separated events commute: in other words, the probabilities of results are independent of the order in which the measurements are made. (This is an obvious consequence of the fact that the time ordering of spacelike separated events is not relativistically invariant.) What this means is that, even if the probabilities of results for A and B are correlated, those correlations cannot be used to send information, since any sending of information requires a dependence on the time ordering of the events.

 

[Dale]

Summary:: Nonzero implies faster than light communication. Zero also implies faster than light communication.

You really can’t have it both ways

 

[RickRazor]

You really can’t have it both ways

You're right. I misspoke. Edited

 

[Vanadium 50]

I think the question, even with all of its words, is ill-posed. Two detectors at different places detect a particle, say an electron, at the same time? Happens all the time: say an experiment at CERN and one at Fermilab.

If your answer is "No, no, they have to be the same particle," I would point out that electrons are indistinguishable. So I think you need to describe an experiment that shows what you want it to show. Ideally with calculations.

 

[RickRazor]

I think the question, even with all of its words, is ill-posed. Two detectors at different places detect a particle, say an electron, at the same time? Happens all the time: say an experiment at CERN and one at Fermilab.

If your answer is "No, no, they have to be the same particle," I would point out that electrons are indistinguishable. So I think you need to describe an experiment that shows what you want it to show. Ideally with calculations.

Sorry, I don't agree with you. I don't think it's ill-posed at all. I agree that electrons can be simultaneously measured at two different places. I meant to say that the number of electrons in the world (you can make this statement more rigourous using qm/qft) is almost equal to the number of electrons "person A has" (localization yada yada). The fundamental question now is that if B has a detector far away and A has lots of electrons/H atoms, will the rate of detection (number of particles detected/second) observed by B instantaneously change once A interacts will the electrons near him? If the detector observes a change in his rate instantly then we know we can send information faster than light. If the detector at B doesn't show a change in the rate we need to understand why the detection rate hasn't changed even though A completely altered their wavefunctions. We can hypothetically think of a method where A completely uses the electrons for electron capture and the number of electrons in the world decreases significantly (or to zero) and detector at B still observes electrons for long time.

I'm not talking about same electrons or anything.

I don't know what calculations you want me to do since that's the entire point of the question. How do I calculate the probability of detection as a function of time? Is the probability outside the lightcone zero?

 

[PeterDonis]

the number of electrons in the world (you can make this statement more rigourous using qm/qft)

If you think you can make this statement more rigorous, then do it. Don't just wave your hands and say it can be done; do it.

will the rate of detection (number of particles detected/second) observed by B instantaneously change once A interacts will the electrons near him?

No. This would amount to sending information faster than light, which is impossible according to QM/QFT.

If the detector at B doesn't show a change in the rate we need to understand why the detection rate hasn't changed even though A completely altered their wavefunctions.

No, A did not "completely alter their wave functions". You have to use relativistic QM, i.e., QFT, to analyze this, and QFT does not have "wave functions" the way you are using the term. There is no such thing as "the wave function of the system at an instant of time" in QFT; such a thing would not be relativistically invariant.

We can hypothetically think of a method where A completely uses the electrons for electron capture and the number of electrons in the world decreases significantly (or to zero) and detector at B still observes electrons for long time.

If you think there is such a method, then describe it. Don't just wave your hands and say "we can hypothetically think of" one. Describe it.

How do I calculate the probability of detection as a function of time?

You don't. There is no such thing in QFT. Detection probabilities are functions of events in spacetime, not "time".

 

[RickRazor]

If you think you can make this statement more rigorous, then do it. Don't just wave your hands and say it can be done; do it.No. This would amount to sending information faster than light, which is impossible according to QM/QFT.No, A did not "completely alter their wave functions". You have to use relativistic QM, i.e., QFT, to analyze this, and QFT does not have "wave functions" the way you are using the term. There is no such thing as "the wave function of the system at an instant of time" in QFT; such a thing would not be relativistically invariant.If you think there is such a method, then describe it. Don't just wave your hands and say "we can hypothetically think of" one. Describe it.You don't. There is no such thing in QFT. Detection probabilities are functions of events in spacetime, not "time".

Just as your first response you're just parroting stuff as impossible or preaching physics as bible instead of giving proper reasoning or trying to understand the question. I seriously doubt if you understand the point of the question or the reason why this question is important. "which is impossible according to QM/QFT" This statement shows it all. I'm trying to understand how qft shows that it is impossible and you aren't giving any points other than saying that it is impossible. So sorry, I'm not going to engage in this conversation with you.

 

[PeterDonis]

sorry, I'm not going to engage in this conversation with you.

Fine with me. Thread closed.

 

[Dale]

Sorry to come in after the lock, but I felt this was worth pointing out:

I'm trying to understand how qft shows that it is impossible and you aren't giving any points other than saying that it is impossible

He told you how QFT shows that it is impossible in post 3, his first post in the thread. He explained that it shows that it is impossible because measurements at spacelike separated events commute. He even closed that post explaining why commuting measurements can be correlated without sending information. So it simply is not the case that “you aren't giving any points other than saying that it is impossible”.