Single photons and expanding spheres of light

[Zebulin]

This question has been bothering me for decades:

Imagine a point source in space that emits one photon per second. Would the photon expand in a globe in all directions until it strikes an object or would the photon shoot off in a random direction?

Suppose you have one target ten meters away and nothing else for light years. Would that target

1. receive most or all of the radiation (as the expanding globe of light encounters it first and the wave function collapses)

or would it

2. receive only a fraction proportional to the angle of the globe that it intersects?

If you say 1, then how is this consistent with what happens from regular light sources? Why would the multi-photon case not also focus on the nearest object?

If you say 2, then how is this consistent with the explanation of the two-slit experiments that says the photon passes through both slits at once?

 

[Let'sthink]

The photon shoot off in a random direction. If we allow sufficient time the hit record would show that all of the sphere will be uniformly covered. But if time is too short then you would watch photon hit a particular point on the spherical system depending upon the actual direction of Propagation of the photon.

 

[Nugatory]

The underlying problem here is that photons aren't what you're thinking when you hear that they are "particles" of light. They have no position, so the idea of them moving through space until they encounter something is very misleading.

But with that said... over time, the energy reaching the object will be proportional to the angle of the globe it subtends and to the (very very small) energy output of the source. If the object is a piece of photographic film, dots will appear on it over time and the number of dots times the energy per photon will be the total amount of energy absorbed.

The apparent conflict with the "photon passed through both slits at once" explanation for the double-slit experiment is resolved by noting that that explanation is itself a misleading oversimplification. It would be more accurate to say that both paths through both slits contribute to the probability of a photon being observed at a given point on the screen behind the slits.

We have a bunch of threads on how photons really behave, and Feynman's book "QED: The strange theory of light and matter" is a good layman-friendly start.

 

[Peter Morgan]

Better, IMO, to think in terms of wave/field duality than in terms of wave/particle duality. Our best theory for light is very arguably more a field theory than a particle theory. The formalism of quantum electromagnetic field theory doesn't support an idea that there are particles.

How, therefore, does the field know where to collapse? The simple answer is that there will be "events" wherever we put an exotic structure, with its own power supply and a storage device in which to make a permanent record, something like an Avalanche PhotoDiode (an APD), and there will be no "events" anywhere else. The formalism of quantum electromagnetic field theory does support an idea that there is an intrinsic noise, with amplitude fixed by Planck's constant, so that for a given point source we can only model statistics rather than individual events: our experience is that we will see event statistics more-or-less proportional to the intensity of the light source, the solid angle subtended by the APD, and the sensitivity of the particular APD to the particular frequencies emitted by the point source.
One point to note is that we only know how bright the point source is by knowing the statistics of events that we see in a characterized APD, because we don't watch light being emitted from the source. I suggest everything works out much more simply if you can stop yourself saying "Imagine a point source in space that emits one photon per second", insofar as we only measure "events", not "particles", and certainly not near the .

Think of a detector as just a way of creating $\mathsf{recorded}$ "events" that have been tuned to occur in proportion to the noisy waves/fields that surround it. We run an amplification circuit off exotic materials so that the current is mostly near zero, but occasionally the current transitions to a clearly non-zero value, when we say, "aha, an event, what time is it? Let's make a record." Note that we could have recorded the current every picosecond, [0.0001, 0.0000, ..., ..., 0.75, 0.82, ..., 0.6, 0.3, 0.02, -0.0003, ...], but we don't because we definitely don't have that much memory. Making the experiment be about events is just us conditioning and compressing the data. Nonetheless, at such a detailed level the properties of the current are presumably more about the way the particular APD has been constructed than about the noisy electromagnetic field that we nonetheless can be sure does affect the statistics. If we turn off the central source or increase the power to it, the statistics will change.

You should be clear that this is a new proto-interpretation of quantum field theory that doesn't have an official name, though I like to call it "the signal analysis interpretation of QFT", so don't take it too seriously, but try it for yourself and see. A wave/field approach of course is adaptable to double-slit experiments. If this seems too instrumental for your taste, it is possible to be realist about the quantum electromagnetic field.

 

[Derek P]

This question has been bothering me for decades:

Imagine a point source in space that emits one photon per second. Would the photon expand in a globe in all directions until it strikes an object or would the photon shoot off in a random direction?

Suppose you have one target ten meters away and nothing else for light years. Would that target

1. receive most or all of the radiation (as the expanding globe of light encounters it first and the wave function collapses)

or would it

2. receive only a fraction proportional to the angle of the globe that it intersects?

If you say 1, then how is this consistent with what happens from regular light sources? Why would the multi-photon case not also focus on the nearest object?

If you say 2, then how is this consistent with the explanation of the two-slit experiments that says the photon passes through both slits at once?

Photons present a peculiar problem that you probably didn't have in mind, namely that, for some extremely technical reasons, they don't have an ordinary wavefunction expressed in terms of position. So although we are allowed to think of the photon as a point particle we cannot say it has a position. However, we can gloss over this by replacing the photon with an electron which doesn't have the same issue. Or refer only to the photon's probability amplitude.

The particle's wavefunction does expand spherically - assuming a symmetrical source.

The same behaviour can be modeled with a point particle that leaves the source in a "random" direction provided you say that it takes all such directions at once, i.e. in superposition. It then gets complicated. It would be nice to be able to say that the superposition of every possible ray path gives the expanding sphere as the tips of all the rays, but, unfortunately, quantum mechanics does not allow infinitely narrow paths. Narrow objects spread out. But the behaviour can be modeled as the particle propagating in every direction at once all the time. This would make the particle explore every possible path to every possible destination, not just the straight paths and not just the ones that make sense. Remarkably, the superposition of all these paths does give you the wavefunction. This is Feynman's Path Integral Formulation. Interpreting it as the particle really taking all possible paths is generally discouraged but is not illegal in most jurisdictions .

That said, it seems you are thinking of a wavefunction as a physical wave. Bad idea. It's a description of the state of the whole system. If the system happens to be a quantum of electromagnetic radiation minding its own business in free space, the wavefunction/probability amplitude may very well map quite closely to the picture of the photon as a wave. Otherwise it's a mathematical function which need not be a recognisable wave at all.

I don't know why you say "until it strikes an object" and "encounters it first and the wave function collapses". That's not how wavefunctions behave. Nobody knows for certain whether wavefunction collapse occurs at all and many physicists think there is no such thing - especially now that we know that QM predicts the appearence of collapse and the emergence of probability without collapse actually occurring. But I suspect you're thinking of collapse as something that pretty well takes the whole wavefunction down. Zap! It isn't anything like that. The wavefunction is a superposition of every possible observable state. Collapse means that upon observation, or interaction, it becomes just one of the possibilities. And that's all it means.

So yes, the wavefunction collapses upon encountering the first target. And the second. And the third. If the particle is absorbed, its wavefunction disappears and the target is changed. If it is not absorbed, a new wavefunction carries on until the next target. Without collapse all the possibilities, now including the various target states, remain in superposition.

So there is no question of focussing on the nearest object!

The question of how much of the radiation the target receives is also meaningless. Under collapse-thinking, if the target absorbs the particle, the wavefunction ceases to exist completely everywhere, instantly (go figure!). If it doesn't then the wavefunction carries on with a shadow cast by the target. If you allow superposition as you should - no collapse - the particle and the target are entangled: you have to consider their joint wavefunction which is a superposition of "absorbed" and "not absorbed".

"The explanation of the two-slit experiments that says the photon passes through both slits at once" is just a loose way of saying that the wavefunction (PA!) represents both cases in superposition. Remember Schroedinger's Cat is a superposition of fully alive and fully dead. But there's only one cat. (Gratuitous diagram of a cat: ⇒ ⇐) Similarly, "photon to the left and photon to the right, but there's only one photon".

TLDR: Superposition is the key to every quantum puzzle, every paradox. It is totally counter-intuitive and yet it is inherent in QM.

 

[Mentz114]

[..]
TLDR: Superposition is the key to every quantum puzzle, every paradox. It is totally counter-intuitive and yet it is inherent in QM.

Superposing probability amplitudes or physical waves is valid and may be useful but actual physical macroscopic matter 'superposition' as you envisage it is a myth.
Please have a look at this review thread - particularly the later experiments.

There is one where a tiny piece of metal (Al) is apparently put in a (quantum ?) superposition of 'no-vibration' and 'vibration'. In order to do this the metal has to be cooled to micro-Kelvin temperatures - and it is still only mechanical WAVE superposition !

The point is that macroscopic objects are internally active all the time (unless cooled to very low temperatures) and this decoheres them and makes large matter superpositions impossible under everyday conditions.

https://www.physicsforums.com/threads/experiments-probing-macroscopic-limits-of-qm.903867/

 

[PeterDonis]

You should be clear that this is a new proto-interpretation of quantum field theory

Which makes it off topic for discussion here. Particularly since this is a "B" level thread.

 

[Derek P]

Superposing probability amplitudes or physical waves is valid and may be useful but actual physical macroscopic matter 'superposition' as you envisage it is a myth.

Superposing probability amplitudes or physical waves is valid and may be useful but actual physical macroscopic matter 'superposition' as you envisage it is a myth.
Please have a look at this review thread - particularly the later experiments.

There is one where a tiny piece of metal (Al) is apparently put in a (quantum ?) superposition of 'no-vibration' and 'vibration'. In order to do this the metal has to be cooled to micro-Kelvin temperatures - and it is still only mechanical WAVE superposition !

The point is that macroscopic objects are internally active all the time (unless cooled to very low temperatures) and this decoheres them and makes large matter superpositions impossible under everyday conditions.

https://www.physicsforums.com/threads/experiments-probing-macroscopic-limits-of-qm.903867/

Nah. Macroscopic superposition is just fine. Decoherence results in a second entanglement which after a bit of matrix-shuffling (representing a good few decades of theoretical work) turns out to put the subject system into an improper mixed state. The global system, including the environment, remains a pure state unless you postulate collapse ad hoc. If you want to argue that Schroedinger's Cat is not a true superposition but is entangled with the environment and therefore cat+environment is in superposition that's fine, but I don't think that going off on this line of hair-splitting is going to help the OP.

But if you think that decoherence can create a proper mixture (absent collapse) do say how!

The list is somewhat interesting but irrelevant. No-one disputes decoherence and the experiments are characterized by the extreme care that's been taken to isolate a mode of energization from the environment in order to sustain the coherent superposition as a separable sub-state. The need for coherence in order to demonstrate superposition is not the same thing as your point-blank description of macroscopic superposition as a myth.

 

[Zebulin]

Nuts. I posted that late at night, under sleep deprivation, and temporarily confused the QM wave function with the electromagnetic wave. The question was really about the electromagnetic wave (Maxwell style).

 

[Boing3000]

Nuts. I posted that late at night, under sleep deprivation, and temporarily confused the QM wave function with the electromagnetic wave. The question was really about the electromagnetic wave (Maxwell style).

And yet QM supersede and extend over Maxwell. Beside I don't think a single photon experiment can be understood in Maxwell's term...(which ignores what a photon is).
So I found your question simple and good. I also would like to know if the wave function 'position evolution' is spherical or 'packet like'. (for photon or electron).

 

[Eric Bretschneider]

You left out some critical information about the nature of the light source - is it a laser “pointed” at the nearby object? “Pointed” somewhere else? Is it an Omni-directional (uniform) emitter?

Light sources can all be characterized by an emission pattern. Until you establish the geometrical relationships it isn’t really possible to answers.

 

[Boing3000]

I think Zebulin's OP description is quite precise

Imagine a point source in space that emits one photon per second.

Light sources can all be characterized by an emission pattern. Until you establish the geometrical relationships it isn’t really possible to answers.

I kind of suspect as much. Let's say some unique exited atom is exited and is going to emit a photon anytime soon.
I suspect momentum conservation kind of point to some 'directional wave', but I have never heard that the two slits experiment (spherical/conical)wave" is build from a complete QM computation from the geometry of the zilion'th atom of a laser...

 

[Let'sthink]

And yet QM supersede and extend over Maxwell. Beside I don't think a single photon experiment can be understood in Maxwell's term...(which ignores what a photon is).
So I found your question simple and good. I also would like to know if the wave function 'position evolution' is spherical or 'packet like'. (for photon or electron).

If you talk of a particle then it has to be a wave packet like. If you forget about the particle till it is detected then it is spherical type.

 

[Boing3000]

If you talk of a particle then it has to be a wave packet like. If you forget about the particle till it is detected then it is spherical type.

I talk simply about one "emitted" photon or even an electron, and the way QM wave function position evolve in time.
Are you saying that that wave function should also contain the detector ? (changing it from spherical to packet like ?)
If so, I would guess that adding more or less detector "surface" would change it to a "many packet" wave... but not changing the probability at any point along some radius (otherwise that would be case 1 of the OP (that is obviously not correct))

 

[Let'sthink]

After reading till date, I conclude that it is possible to imagine an emitted electron at least after it has been emitted to move in some definite direction. But for a photon it is not so even after it has been emitted. Because for electron classically I can trace a track, for a photon I cannot. Just correct me if i am wrong. Even in photographs of cosmic showers we register tracks of particles only and not gamma rays. Am I right?

 

[Boing3000]

Just correct me if i am wrong.

I don't think I can do that, I am no physicist.

Even in photographs of cosmic showers we register tracks of particles only and not gamma rays. Am I right?

Sure, photon can't "trace" anything (at any interaction, it will vanish, so photon can only "spot")

Again, the question is this: What is the spatial shape of the volume of the time evolution of the WF (let's say where the photon has a >0.9 chance of being measured).
1) An expending sphere ?
2) A moving blob (whose "diameter" is probably proportional to its frequency) ?
3) Something else ?

I kind of think whatever the shape is it will be at average distance c/t from the source. But that's all I know.

 

[PeterDonis]

What is the spatial shape of the volume of the time evolution of the WF

A key difference between a photon and a massive particle like an electron is that there is no non-relativistic approximation for a photon. That means that thinking of a photon as having a wave function in space doesn't work. You have to use quantum field theory, which requires thinking about events in spacetime and probabilities of observing a photon at those events. On this view there is no "wave function" and no "spatial shape"; the photon is not a "thing" in space. See post #3 where @Nugatory already pointed this out.

 

[Boing3000]

See post #3 where @Nugatory already pointed this out.

Indeed, what he described is an expanding sphere, but strangely without acknowledging it.
Probability of events in spacetime is pretty much what I said in post #16. Thank's for the precision that it's not computed from a QM wave function but from something more complex described by QFT/QED

 

[PeterDonis]

what he described is an expanding sphere

No, he didn't. He didn't say anything about the specific mathematical form of the probability amplitude.

Probability of events in spacetime is pretty much what I said in post #16.

I don't see how that can be since in that post you gave three mutually exclusive possibilities and didn't make a choice between them.

I kind of think whatever the shape is it will be at average distance c/t from the source.

Strictly speaking, this is not the case; the amplitude is not exactly zero off the light cone. The amplitude does peak (take its largest value) on the light cone.

Whether or not the amplitude is spherically symmetric depends on how the source is prepared. But in any case we're talking about an amplitude, which is not the same as a "thing" moving in space.

 

[Boing3000]

No, he didn't. He didn't say anything about the specific mathematical form of the probability amplitude.

Yes he did.

over time, the energy reaching the object will be proportional to the angle of the globe it subtends

I don't see how that can be

No problem, I'll help you

What is the spatial shape of the volume of the time evolution of the WF (let's say where the photon has a >0.9 chance of being measured).

And since then,I have learn from you that it's not a wave function that allow such computation. But something more complicated ...

since in that post you gave three mutually exclusive possibilities and didn't make a choice between them.

I don't understand how this relate to probability of event. Anyway, when I ask question that's when a don't know the choice to make.

Strictly speaking, this is not the case; the amplitude is not exactly zero off the light cone. The amplitude does peak (take its largest value) on the light cone.

Is that fuzziness inversely proportional to the frequency/energy or not ?

Whether or not the amplitude is spherically symmetric depends on how the source is prepared.

The source is a single atom in an exited state (post#12)

But in any case we're talking about an amplitude, which is not the same as a "thing" moving in space.

I know that we are talking about probability, not about Maxwell classical equation

 

[PeterDonis]

I don't understand how this relate to probability of event.

Here is what you wrote:

What is the spatial shape of the volume of the time evolution of the WF (let's say where the photon has a >0.9 chance of being measured).
1) An expending sphere ?
2) A moving blob (whose "diameter" is probably proportional to its frequency) ?
3) Something else ?

These are descriptions of three different mutually exclusive possibilities for the probability amplitude for detection of a photon (or more precisely its distribution in spacetime). You might not have realized that that's what you were describing, but it is.

Is that fuzziness inversely proportional to the frequency/energy or not ?

It depends.

The source is a single atom in an exited state (post#12)

I understand that's what you were thinking, but I don't know if it's what the OP of this thread was thinking.

That said, "a single atom in an excited state" still isn't precise enough. Which excited state? And which possible transitions from that state to a lower energy state? AFAIK the spacetime distribution of the probability amplitude is not the same for all states/transitions.