A single photon traveling in space

[Mr Peanut]

Hard to know the proper forum here.

Say a photon is spontaneously generated in space with no initial trajectory imparted by the formation process. One year later, at a point on the sphere of radius 1 light year, a detector (a really good one) - by rare chance - just happens to detect it.

Had that detector not have been there to consume it, is there a chance -however slight -that the photon could be detected 1 second later at a point on the other side of the sphere (now having a radius 1 light year plus 1 light second)?

 

[jtbell]

If the source is isotropic (like an ordinary light bulb is, more or less), then until the photon is detected somewhere on the surface of the sphere, it can potentially be detected anywhere on the sphere.

If you're asking "what would have happened if we had removed that single detector," then there is of course a finite chance that the photon will arrive on the sphere at that location and not be detected at all.

 

[diegzumillo]

I think I understand your question.

What we can say for sure is what jtbell said: There is a probability of the photon be in anywhere in space.

Now, this is a tricky question because it concerns the nature of probability. Specially when you say "Had that detector not have been there...". The quantum Mechanics theory deals with it without much problems. If we had a twin universe, where the only difference would be the position of the detectors, when, in the first universe, the detector lits up, in the second universe the photon still is a probability cloud and can be measured in anywhere in space. Therefore it can be measured in the other side of the sphere one second later (or at the same time!)

I hope I didn't confuse you even more with this two universes.. :P

And don't forget that trajectories don't make much sense in quantum mechanics.

 

[Xezlec]

Had that detector not have been there to consume it, is there a chance -however slight -that the photon could be detected 1 second later at a point on the other side of the sphere (now having a radius 1 light year plus 1 light second)?

Yes.

The photon isn't somewhere until you measure it. Until then, it is everywhere on that sphere, all at once. Measurement forces it to immediately decide to be somewhere (random) in particular.

Therefore, if you don't measure it the first time, then it's still everywhere, and it can still pick any place on the sphere to exist whenever you get around to measuring it.

I've phrased all this according to the Copenhagen interpretation instead of the many-worlds interpretation, for your convenience.

 

[Phrak]

Hard to know the proper forum here.

Say a photon is spontaneously generated in space with no initial trajectory imparted by the formation process. One year later, at a point on the sphere of radius 1 light year, a detector (a really good one) - by rare chance - just happens to detect it.

Had that detector not have been there to consume it, is there a chance -however slight -that the photon could be detected 1 second later at a point on the other side of the sphere (now having a radius 1 light year plus 1 light second)?

Yes, but it depends upon how the field originated. I'm not sure I understand your explanation. A dipole antenna that emmits one photon at a time might be a good example. The relative probability of detecting the photon on a small region of the spherical shell is the same as relative field strength squared should the antenna be radiated large numbers of photons.

 

[jtbell]

Had that detector not have been there to consume it, is there a chance -however slight -that the photon could be detected 1 second later at a point on the other side of the sphere (now having a radius 1 light year plus 1 light second)?

If you're trying to get the photon to somehow jump back across the diameter of the sphere, you can't do it. Before the photon is detected at location A, it can potentially arrive at any point on the sphere. After you detect the photon at point A, if you now imagine "rolling time back" to before the detection, you simply return to the original state in which the photon's location is indefinite, and the photon could just as well arrive at location B on the other side of the sphere. There's nothing special about location A in this state.

 

[Mr Peanut]

OK, I do understand the concept of equal probability of location throughout the spherical surface.

However, would it be proper to say that the photon does have a location at time t - albeit unknowable unless detected?

Assuming that it does in fact have a location, then is it proper to conclude that it can be no further than one light second away, one second later?

 

[jtbell]

However, would it be proper to say that the photon does have a location at time t - albeit unknowable unless detected?

There is no generally-accepted answer to this question. QM (that is, the mathematical formalism that we use to predict the results of experiments) does not define the precise position of a photon (or indeed of any other particle) before it is measured or detected. Some interpretations of QM do. But there is no way to distinguish experimentally among these interpretations, because they are constructed so as to produce the same predictions for the results of experiments. All interpretations have strange features that some people object to, so people argue about them a lot.

 

[Xezlec]

OK, I do understand the concept of equal probability of location throughout the spherical surface.

However, would it be proper to say that the photon does have a location at time t - albeit unknowable unless detected?

No. If that were the case, you wouldn't be dealing with quantum physics, you would be dealing with ordinary classical physics, but with one quantity merely unknown to you. The whole point of QM is that what we are calling the "probability" is a real thing that exists and has real physical properties of its own.

The http://en.wikipedia.org/wiki/Double-slit_experiment" demonstrates that that probability wave can interfere with itself, a phenomenon that makes no sense in terms of a particle in classical physics where we "just don't know the direction". If the particle really did just go through one slit or the other, and not both simultaneously, you would never see an interference pattern build up from the individual photon hits.

Assuming that it does in fact have a location, then is it proper to conclude that it can be no further than one light second away, one second later?

As discussed above, assuming that it does have a location rules out quantum physics entirely. But yes, in that case.

There is no generally-accepted answer to this question. QM (that is, the mathematical formalism that we use to predict the results of experiments) does not define the precise position of a photon (or indeed of any other particle) before it is measured or detected. Some interpretations of QM do.

OK, if you want to get philosophical about it. But the point is, some information which is involved somehow in determining what we eventually measure as "position" certainly is spread out across the sphere before measurement (since we can't have local hidden variable theories). I think that's what he's asking.