QED and Photons

[Amr Morsi]

In QED, it is well known that the electromagnetic field is also quantized (related to quantized electromagnetic sources) and that the quantum field is that of the wave function of photons.

 

But, I am just wondering if photons are deterministic, as confirmed by absorption and collision (Compton's effect). And, if not.... is the wave function of photons can be determined? Is there something mysterious in QED? Can any specialized expert comment?

[ajb]

In scattering calculations you take the in and out states to be described by plane waves. What happens in the middle is "taken care of" by the S-matrix.

[timo]

I don't know what you mean by "deterministic as confirmed by absorbtion and collision (Compton's effect)". If you mean that a collision of a photon is like the collision of two billiard balls, then "no". Loosely speaking, if you were shooting a single photon at a single electron at rest, you cannot know what happens in the sense that you don't know the momentum of the electron after the measurement. However, simply saying that the process is not deterministic is not appropriate to the complexity of the situation/scenario. Ultimately, it boils down to the problem that the part of quantum mechanics which breaks determinism, the process of measurement, is not fully understood (certainly not by me, but that's also what our mathematical physicists tell me).

 

You can directly write down a wave function for a free photon. The basis is simply plane waves.

[steevey]

Wait how is light deterministic? We don't even know which direction it will get emitted in...

 

If a photon hits an electron, they still hit each other as waves. The electron absorbs and jumps to a new state and probable location change. When the electron jumps back down, it re-emits the photon once again as a wave. That doesn't ell us anything about determining the position of either the photon or the electron.

Edited January 27, 2011 by steevey

[timo]

That's not how QM works. What happens is that if you shoot a photon at a free electron at rest (no need to complicate things by making it a bound electron), the electron and the photon will be in a definite state (note that "state" is a QM term). This state, let's call it "final state", is entirely determined by the state the electron and the photon were in before ("initial state") and the rules of physics. There is no randomness in there. However, the final state is not a state belonging to a definite direction, but a mixture of different direction. When you try to figure out which direction the electron went, you have to measure its direction. At this measurement process, randomness then comes into play, and a random direction will be picked (with the probabilities being dictated by the properties of the final state).

 

For this simple experiment, it seems like a rather cheap excuse to claim that everything was deterministic, and only the measurement process destroys determinism. It seems more natural (in the sense of being in the lines of everyday thinking) to assume that the transition from the initial state to the final state is a random process completely fixing the outgoing direction. However, in more sophisticated experiment (you don't measure the final state immediately but let a 2nd reaction happen first), one can tell the difference.

Edited January 27, 2011 by timo

[steevey]

That's not how QM works. What happens is that if you shoot a photon at a free electron at rest (no need to complicate things by making it a bound electron), the electron and the photon will be in a definite state (note that "state" is a QM term). This state, let's call it "final state", is entirely determined by the state the electron and the photon were in before ("initial state") and the rules of physics. There is no randomness in there. However, the final state is not a state belonging to a definite direction, but a mixture of different direction. When you try to figure out which direction the electron went, you have to measure its direction. At this measurement process, randomness then comes into play, and a random direction will be picked (with the probabilities being dictated by the properties of the final state).

 

But that would be suggesting that before the photon hit your retina which carried information, the properties were determined by measurement. But, light doesn't travel at infinite speed, so how can that be right?

[timo]

But that would be suggesting that before the photon hit your retina which carried information, the properties were determined by measurement.

It doesn't. Consider seeing with your eye as being the measurement. You either measure the photon as having gone your way (then you see it) or as not having gone your way (you don't see it).

 

sidenote: QM has the reputation of often being counter-intuitive. Hence, it should not be too surprising that it often works differently than you'd intuitively expect.

[steevey]

It doesn't. Consider seeing with your eye as being the measurement. You either measure the photon as having gone your way (then you see it) or as not having gone your way (you don't see it).

 

sidenote: QM has the reputation of often being counter-intuitive. Hence, it should not be too surprising that it often works differently than you'd intuitively expect.

 

But if things are determined by not seeing them, how did the electron act as a wave in the double slit experiment? Wouldn't it just be deitirmined in that the scientists specifically weren't observing the electrons?

[timo]

I don't understand what you are saying to trying to say with that. There should be plenty of texts to be found about the double slit experiment, though.

[steevey]

I don't understand what you are saying to trying to say with that. There should be plenty of texts to be found about the double slit experiment, though.

 

Your saying that the act of a particle not being observed is a form of determining it, but that doesn't make sense because you can't know you didn't observe it anyway. Also if it worked that way, then there should be no waves at all, since everyone is constantly having a photon "not go their way" and thus determining particles according to you.

Edited January 28, 2011 by steevey

[timo]

I don't see why measuring a photon as not having gone a certain direction seems to be such a catastrophy to you.

[steevey]

I don't see why measuring a photon as not having gone a certain direction seems to be such a catastrophy to you.

 

Because you can't miss what you never had.

 

Here's the situation we have: Measuring/observing determines a particle. But also, NOT measuring/observing a particle determines a particle. No particles would EVER be a wave state if both those statements were true, and its scientific consensus that when a particle is observed, that a particle becomes determined, not when its NOT observed.

Edited January 28, 2011 by steevey

[timo]

If you're seriously interested in a discussion and/or in learning something then I'd appreciate if you gave my posts and your replies more than ten minutes of thought - and subsequently be more accurate when referring to my statements (it's a huge difference to measure an object as not having a certain property and not to measure the property). At the moment, I consider this as a waste of my time.

[steevey]

If you're seriously interested in a discussion and/or in learning something then I'd appreciate if you gave my posts and your replies more than ten minutes of thought - and subsequently be more accurate when referring to my statements (it's a huge difference to measure an object as not having a certain property and not to measure the property). At the moment, I consider this as a waste of my time.

 

All I'm doing is pointing out things that don't seem to make sense, like this

 

What happens is that if you shoot a photon at a free electron at rest (no need to complicate things by making it a bound electron), the electron and the photon will be in a definite state (note that "state" is a QM term).

 

How does the act of simply shooting a photon at an electron determine either of them before before you observe them? I don't remember that anywhere. You wouldn't know where the photon has been or even where the electron his until after the photon hits your retina.

 

[steevey]

If you're seriously interested in a discussion and/or in learning something then I'd appreciate if you gave my posts and your replies more than ten minutes of thought - and subsequently be more accurate when referring to my statements (it's a huge difference to measure an object as not having a certain property and not to measure the property). At the moment, I consider this as a waste of my time.

 

All I'm doing is pointing out things that don't seem to make sense, like this

 

What happens is that if you shoot a photon at a free electron at rest (no need to complicate things by making it a bound electron), the electron and the photon will be in a definite state (note that "state" is a QM term).

 

How does the act of simply shooting a photon at an electron determine either of them before before you observe them? You wouldn't know where the photon has been or even where the electron is until after the photon hits your retina so I don't see why a photon hitting an electron anywhere in the universe determines it.

I think that maybe your applying classical physics to quantum mechanics, because in the classical world, if a photon hits an electron, there's only one possible place the photon could have hit and both of those particles would be defined classical particles. But, even at that stage, there's no way to determine the exact position of either of them at any point in time. You could figure out the energy level of the electron and probably of the light if you knew the material it was made up of and you analyzed the light afterwords, but that still doesn't tell you the position.

Edited January 28, 2011 by steevey

[timo]

You misunderstood that statement in at least two respects:

 

(1) More a detail: I am talking about a free electron. The only energy that a free electron can have is kinetic energy (momentum), which is not quantized in this case. Speaking about "energy levels" does not seem like a useful concept in this case. At least I don't know what you mean by it.

 

(2) The presumably crucial point: The term "state" in the context of QM is a technical term, which may not exactly be what a QM-layman expects from it (which is why I wrote "note that 'state' is a QM term"). In classical physics, the state of a free particle is determined by its position and momentum. In QM, that is not the case. In particular, an object's state might not uniquely determine its momentum (which is why I wrote "the final state is not a state belonging to a definite direction").

 

 

I understand that it might be difficult to understand statements that use abstract QM concepts. But since this sub-forum is called "Quantum Theory", I think it is appropriate.

[swansont]

 

How does the act of simply shooting a photon at an electron determine either of them before before you observe them? You wouldn't know where the photon has been or even where the electron is until after the photon hits your retina so I don't see why a photon hitting an electron anywhere in the universe determines it.

[/font]

I think that maybe your applying classical physics to quantum mechanics, because in the classical world, if a photon hits an electron, there's only one possible place the photon could have hit and both of those particles would be defined classical particles. But, even at that stage, there's no way to determine the exact position of either of them at any point in time. You could figure out the energy level of the electron and probably of the light if you knew the material it was made up of and you analyzed the light afterwords, but that still doesn't tell you the position.

 

The position isn't important to the analysis. The plane wave exists everywhere, and you only care about what happens if the photon interacts with the electron. Where it happens doesn't matter. If need be, you can say you are analyzing it in the frame of the electron, so it's at rest at the origin of its coordinate system.

[steevey]

You misunderstood that statement in at least two respects:

 

(1) More a detail: I am talking about a free electron. The only energy that a free electron can have is kinetic energy (momentum), which is not quantized in this case. Speaking about "energy levels" does not seem like a useful concept in this case. At least I don't know what you mean by it.

 

(2) The presumably crucial point: The term "state" in the context of QM is a technical term, which may not exactly be what a QM-layman expects from it (which is why I wrote "note that 'state' is a QM term"). In classical physics, the state of a free particle is determined by its position and momentum. In QM, that is not the case. In particular, an object's state might not uniquely determine its momentum (which is why I wrote "the final state is not a state belonging to a definite direction").

 

 

I understand that it might be difficult to understand statements that use abstract QM concepts. But since this sub-forum is called "Quantum Theory", I think it is appropriate.

 

So are you then saying THAT the position is determined and not that the actual position is known? Because even in a determined state, an electron still is a wave, but we only carries the information of a single particle upon our observation, which would make more sense for a photon to hit it at a specific location yet not have that location known...except...

 

Swan, if an electron is free and not bound to any particular atom, does it travel along a completely determined path? Is the state of the electron no longer a region where the electron acts as a virtual particle, but rather an actual particle with only one specific point to be in, in a linear movement?

[timo]

So are you then saying THAT the position is determined and not that the actual position is known? Because even in a determined state, an electron still is a wave, but we only carries the information of a single particle upon our observation, which would make more sense for a photon to hit it at a specific location yet not have that location known...except...

I'm not sure if that's what I said - I don't understand it. I'm not even sure if at least one of the sentences is grammatically correct.

[steevey]

I'm not sure if that's what I said - I don't understand it. I'm not even sure if at least one of the sentences is grammatically correct.

 

Ok, its scientifically proven that you cannot know the position of an electron in a determined state at any given moment. Are you arguing against that?

[mississippichem]

Ok, its scientifically proven that you cannot know the position of an electron in a determined state at any given moment. Are you arguing against that?

 

No. The more certain you are of an electron's momentum, the less certain you are of it's position. You can know the position of an electron quite well, but you'll be very uncertain of it's momentum.

[steevey]

No. The more certain you are of an electron's momentum, the less certain you are of it's position. You can know the position of an electron quite well, but you'll be very uncertain of it's momentum.

 

Except by the time you observe the photon for the electron of that particular spot, the electron has already gone to a different place.

 

The position of an electron even in a free state has randomness too. You can't even predict where it would be next even if you could somehow manage to find the exact position.

 

What you can do though, is find the most probable places for an electron to show up.

Edited January 29, 2011 by steevey

[Amr Morsi]

What is the Wave Function of Photons, in Q.E.D.? Has it been derived before in any problem?