Can one photon interfere with another photon?

[carrz]

These experiments are possible. See for example: Am. J. Phys. 68, 245 (2000) ("Interference fringes from stabilized diode lasers").

I don't have that book. Are you saying those experiments do not use any slits, they just cross the beams and get interference pattern?

"First of all, the things that interfere are not the photons themselves, they are the probability amplitudes associated with different possible histories..."

Possible histories? That's weird even as a mathematical concept, how can actual photons interact with an abstract idea? It's surreal.

 

[Cthugha]

So whereas this is commonly stated as intereference between two photons, Glauber's complaint is that it should be seen as intereference between two states, each with two photons? I do see probability amplitudes here, but not histories. So maybe histories has to refer to the path integral, but not the canonical formalism?

Well, there are two possible ways for two photons to end up at different detectors: Both are reflected or both are transmitted. These are the two "histories" and their probability amplitudes interfere destructively.

I don't have that book. Are you saying those experiments do not use any slits, they just cross the beams and get interference pattern?

Yes. They see the pattern for simple crossed beams if the detector integrates for less than 1 ms. For longer integration times the pattern loses contrast quickly.

Possible histories? That's weird even as a mathematical concept, how can actual photons interact with an abstract idea? It's surreal.

Is it that abstract? Consider a double slit. If you detect a photon somewhere behind the double slit, you cannot tell which slit it passed through. So you get two possible histories: the photon going through slit 1 and the photon going through slit 2.

In classical physics you just add the two fields and calculate the intensity. Here you add the probability amplitudes for the indistinguishable possible ways from A to B and calculate the probability density. The math does not change.

 

[carrz]

Instead, all that the emitter emits is a wavefunction which corresponds to an associated probability distribution which describes where the photon might be. The precise information about where the photon actually is and its direction, does not yet exist in any form at this point. The photon only obtains an exact location at the point of absorption.

That's a strange way to say we can't see photons unless we absorb them. Wave function is an abstract concept, it can not be materialized in the real world as such, it can not be "emitted" actually, only metaphorically.

It is the real photons that are emitted, at specific location, with specific direction, with actual electric and magnetic fields oscillating in a precisely defined geometrical plane, around actual axis that is their velocity vector, with actual frequency and wavelength.

Just because we can't see photons before the detection and don't know exact locations where they are emitted, reflected or deflected from, it does not mean they do not actually exist along their way following the shortest path between any two such interaction points.

 

[carrz]

Is it that abstract? Consider a double slit. If you detect a photon somewhere behind the double slit, you cannot tell which slit it passed through. So you get two possible histories: the photon going through slit 1 and the photon going through slit 2.

Shouldn't I be able to tell you which slit it passed through if I knew exact direction and location it was emitted from? Photons have to travel in a straight line to obey constancy of the speed of light, don't they?

 

[bhobba]

If photons cannot interfere with photons, then what in the world are they interfering with in a double slit experiment? There is nothing supposed to be there but the slit and the photons, and if it is not the photons, it must be the slit. Would edge-diffraction not produce the same pattern even without any interference?

Indeed it is the interaction of the slit and the photon. But as Dr Chinese points out its not the slit per se - its the fact it in effect is like a position measurement. I say like because photons, traveling at the speed of light do not have a frame where they are at rest hence to not have a position. A better way of looking at it is probably Feynmans path integral approach - the slits limit the paths the photon can take to reach the screen. Although it is called interference by analogy to wave experiments that's not the real reason - the real reason is the principles of QM:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

They start talking about interference and end up talking about entanglement. What does quantum entanglement have anything to do with wave interference?

Nothing. But, strictly speaking, quantum mechanically the double slit has nothing to do with interference either - as explained in the link I gave.

If two photons are entangled then they are partly in each others state so that means effects that would normally apply to only one photon are possible.

Thanks
Bill

 

[bhobba]

Shouldn't I be able to tell you which slit it passed through if I knew exact direction and location it was emitted from? Photons have to travel in a straight line to obey constancy of the speed of light, don't they?

No they don't - remember the path integral approach - they travel by all paths - not a single one.

They are emitted in a certain state, and that state, by the fact its emitted by a conceptual point source, means its position (loosely - as I said photons do not have position - its path going through that point is probably a better way of looking at it) is known at that time, hence its momentum is completely unknown. Since photons all travel at the speed of light that means its direction is unknown.

Again see the link on the QM analysis of the double slit experiment I gave that explains it entirely in these terms.

Thanks
Bill

 

[carrz]

No they don't - remember the path integral approach - they travel by all paths - not a single one.

There is only one path which is the shortest distance between two points, it's a straight line. If a photon doesn't interact with anything on the way and if it doesn't want to go faster than the speed of light it has no choice but to take that one path. We never measured otherwise.

Since photons all travel at the speed of light that means its direction is unknown.

Just because it is unknown doesn't mean the actual path was not precisely defined single direction.

Again see the link on the QM analysis of the double slit experiment I gave that explains it entirely in these terms.

I have, it does not contradict that photons, in real world actuality, always travel one specific path which is a straight line between any two interaction points.

 

[PeterDonis]

Since photons all travel at the speed of light

Strictly speaking, this isn't actually true, is it? Photons have a nonzero amplitude to travel faster or slower than light. More precisely, photons emitted from a given event in spacetime have a nonzero amplitude to be detected at events that are timelike or spacelike, rather than null, separated from the emission event. It's just that the amplitudes for timelike or spacelike separations die off very quickly with "distance", so for many experiments you can ignore them and treat the photons as traveling only on null paths.

 

[atyy]

Glauber has an opinion on that, too. The passage comes directly before the one I quoted earlier:
"When you read the first chapter of Dirac’s famous textbook in quantum mechanics [8], however, you are confronted with a very clear statement that rings in everyone’s memory. Dirac is talking about the intensity fringes in the Michelson interferometer, and he says,

Every photon then interferes only with itself. Interference between two different photons never occurs.

Now that simple statement, which has been treated as scripture, is absolute nonsense."

I guess you need a Nobel prize to be able to say it that way. As DrChinese already said correctly, in a common double slit self-interference is all you need.

Here is an argument against Glauber's claim that Dirac was in error. In the two photon case, the photons are identical, so one cannot talk about "each" photon. Therefore Dirac's statement that every photon interferes only with itself is true in cases in which "each" photon can be distinguished. In the case where there are two indistinguishable photons, it is the histories that interfere according to Glauber. If it is the histories rather than the photons that interfere, then it is true that "interference between two different photons never occurs".

 

[vanhees71]

Strictly speaking, this isn't actually true, is it? Photons have a nonzero amplitude to travel faster or slower than light. More precisely, photons emitted from a given event in spacetime have a nonzero amplitude to be detected at events that are timelike or spacelike, rather than null, separated from the emission event. It's just that the amplitudes for timelike or spacelike separations die off very quickly with "distance", so for many experiments you can ignore them and treat the photons as traveling only on null paths.

This is not correct. It doesn't make sense to say, "photons travel along a trajectory". One should not think about photons as miniature billard balls flying around at the speed of light. As a massless particle of spin 1 this picture makes never sense! A photon doesn't even have a clear definition for what's meant by "position" since there is no position operator in the strict sense.

The correct description of photons is QED and nothing else. An asymptotically free photon is defined as a single-particle Fock state. Here, "particle" must be read as a metaphor. As I stressed before, a photon cannot be viewed as a little particle in the classical sense. We "only" have a very abstract description about what's going on, and this is quantum field theory.

As for any "particle" you can calculate cross sections (S-matrix elements) for reactions. E.g., you can evaluate the probability for a detector (e.g., a photo plate) to find a photon at a certain location behind a double slit. Supposed you have prepared the photons such that they are pretty monochromatic you find an interference pattern as for macroscopic electromagnetic waves. It is clear from the formalism that for a single photon you get interference of the possibilities to move through one or the other slit, as long as you do not make it possible to decide through which slit the photon has gone. If you do so the interference pattern vanishes. This is a typical case of quantum behavior. It does not mean that one photon interferes with itself. It's not even clear to me what you mean by that.

 

[carrz]

This is not correct. It doesn't make sense to say, "photons travel along a trajectory". One should not think about photons as miniature billard balls flying around at the speed of light. As a massless particle of spin 1 this picture makes never sense! A photon doesn't even have a clear definition for what's meant by "position" since there is no position operator in the strict sense.

The correct description of photons is QED and nothing else. An asymptotically free photon is defined as a single-particle Fock state. Here, "particle" must be read as a metaphor. As I stressed before, a photon cannot be viewed as a little particle in the classical sense. We "only" have a very abstract description about what's going on, and this is quantum field theory.

I don't think we need to be metaphorical at all. Let's be practical instead. I'd say we got 'em photons pretty good actually:

They might not have sharply defined extent, but they do have have specific location and specific direction, actual em fields oscillating in a precisely defined geometrical plane, around actual axis that is their velocity vector, with actual frequency and wavelength. Photons travel along a trajectory, of course they do. There is nothing else to travel along but a trajectory. It is experimentally confirmed a photon will travel between any two emission and detection points with the speed of light. And you can bet your pants that if you place a detector anywhere along that straight line trajectory you will detect a photon exactly when and where it was supposed to be. What reason then could you possibly have to think photons are not always moving along such trajectories, and why would you suppose they are doing something else when we are not looking?

 

[Cthugha]

That's a strange way to say we can't see photons unless we absorb them. Wave function is an abstract concept, it can not be materialized in the real world as such, it can not be "emitted" actually, only metaphorically.

It is the real photons that are emitted, at specific location, with specific direction, with actual electric and magnetic fields oscillating in a precisely defined geometrical plane, around actual axis that is their velocity vector, with actual frequency and wavelength.

The photon concept means that you can only take a discrete amount of energy out of a field. It does not imply localized particles with well defined properties. This point of view is untenable at least since Bell.

Just because we can't see photons before the detection and don't know exact locations where they are emitted, reflected or deflected from, it does not mean they do not actually exist along their way following the shortest path between any two such interaction points.

You are considering "existing" to be the same as "being localized and having well defined properties". This is usually called local realism and is ruled out by experiments on entangled particles. See the Bell inequalities. DrChinese has a very good introduction on them.

Shouldn't I be able to tell you which slit it passed through if I knew exact direction and location it was emitted from? Photons have to travel in a straight line to obey constancy of the speed of light, don't they?

Photons are not bullets. Changes in the field need to travel at the speed of light. If you were able to know the exact direction and location it was emitted from so precisely that it could only have passed through one slit, you will not see an interference pattern. The exact time of emission is not well defined, but you get some superposition of the emitter being excited and no photon being present and the emitter in the ground state and a photon present. This is easy to understand if you consider fields. It is only confusing if you consider photons as localized bullets - mainly because they are not.

edit:

Photons travel along a trajectory, of course they do. There is nothing else to travel along but a trajectory. It is experimentally confirmed a photon will travel between any two emission and detection points with the speed of light. And you can bet your pants that if you place a detector anywhere along that straight line trajectory you will detect a photon exactly when and where it was supposed to be.

Do this with a detector placed behind a double slit at different distances and you will be surprised.

Fields travel outwards at the speed of light. Intensity is always a product of two fields. This can be a single field coming from a single source. In that case a trajectory may be a reaonable assumption. But these fields can originate from two light sources as well. These are the cross terms in an interference pattern. In that case, a linear trajectory picture is completely pointless. It is the changes in the fields which travel outwards at the speed of light. That does not imply that all products of two such fields (which is what gives rise to photons) will travel along linear trajectories at the speed of light.

 

[tim1608]

Consider the initial state, consider the final state and all the indistinguishable ways to get from one to the other. Add them, get the square and you are done.

Does anyone know of anything in macroscopic probability theory which operates on the basis of adding indistinguishables and then squaring?

 

[bhobba]

Strictly speaking, this isn't actually true, is it?

Yes Peter - true.

But that's QED mate. Understanding this is hard enough without introducing that.

Even the link I gave about the QM explanation of the double slit isn't true - there is a paper around explaining its issues.

But its like a lot of physics, one understands it at the basic level first then finds that basic level aren't the whole truth.

Thanks
Bill

 

[bhobba]

There is only one path which is the shortest distance between two points, it's a straight line. If a photon doesn't interact with anything on the way and if it doesn't want to go faster than the speed of light it has no choice but to take that one path. We never measured otherwise.

We have measured the consequence of the path integral approach which says it takes all paths. Many cancel out and we are often (but far from always) left with the shortest distance path.

Its precisely that that leads to Quantum effects.

Vanhees is also correct - there is one and only one correct treatment of this - QED. But that's a whole new and much more mathematically difficult ball game.

Thanks
Bill

 

[bhobba]

Photons travel along a trajectory, of course they do.

That's precisely what QM says they do not do.

Thanks
Bill

 

[carrz]

We have measured the consequence of the path integral approach which says it takes all paths. Many cancel out and we are often (but far from always) left with the shortest distance path.

What are you referring to? What was measured and how it says photons take all paths?

 

[bhobba]

What are you referring to? What was measured and how it says photons take all paths?

That's the path integral approach to QM:
http://en.wikipedia.org/wiki/Path_integral_formulation

You start out with <x'|x> then you insert a ton of ∫|xi><xi|dxi = 1 in the middle to get ∫...∫<x|x1><x1|...|xn><xn|x> dx1...dxn. Now <xi|xi+1> = ci e^iSi so rearranging you get
∫...∫c1...cn e^ i∑Si.

Focus in on ∑Si. Define Li = Si/Δti, Δti is the time between the xi along the jagged path they trace out. ∑ Si = ∑Li Δti. As Δti goes to zero the reasonable physical assumption is made that Li is well behaved and goes over to a continuum so you get S = ∫L dt.

S is called the action, and L the Lagrangian. The Lagrangian is the basis of Quantum Filed Theory. This is a very common way of approaching it, but some texts like Weinberg The Quantum Theory Of Fields takes a different, although equivalent approach.

What that weird integral says is in going from point A to B it follows all crazy paths and what you get at B is is the sum of all those paths. Now since the integral in those paths is complex most of the time a very close path will be 180% out of phase so cancels out. The only paths we are left with is those whose close paths are the same and not out of phase so reinforce rather than cancel. That's how you get the principle of least action in classical physics and Fermat's Principle which implies most of the time it follows the shortest path.
http://www.ms.unimelb.edu.au/~mums/seminars/variational_principle.pdf

Now we can start with the path integral formalism that it takes all paths and you get QM. Since QM has been verified by many many measurements this gives us great confidence that's what's really going on.

Thanks
Bill

 

[DrChinese]

They might not have sharply defined extent, but they do have have specific location and specific direction, actual em fields oscillating in a precisely defined geometrical plane, around actual axis that is their velocity vector, with actual frequency and wavelength. Photons travel along a trajectory, of course they do. There is nothing else to travel along but a trajectory. It is experimentally confirmed a photon will travel between any two emission and detection points with the speed of light. And you can bet your pants that if you place a detector anywhere along that straight line trajectory you will detect a photon exactly when and where it was supposed to be. What reason then could you possibly have to think photons are not always moving along such trajectories, and why would you suppose they are doing something else when we are not looking?

You realize you are posting in the Quantum Physics sub-forum, correct? What you are describing is classical physics. In quantum mechanics (QM), we have the Heisenberg Uncertainty Principle (HUP). You should probably read up on that. Quantum particles do not simultaneously possesses clearly defined position and momentum. There are strict limits on these such that the more you know one, the less you know the other.

The idea that a photon usually moves in a straight line only is completely incorrect. The net effect of the various paths/histories of a photon may be a straight line, but there are others involved and this has been demonstrated any number of times.

I might also refer you to forum rules on making statements about your personal views on how things work when you do not really know. Better to ask than to tell in this case. If you take the time to read up a bit on this subject area, I believe you will be amply rewarded in gaining some truly fascinating knowledge!

 

[DrChinese]

What are you referring to? What was measured and how it says photons take all paths?

QM is the theory. It makes specific predictions different than classical physics. Experiments are done to highlight the differences and they confirm QM.

In the case of multiple histories: shine a beam of light on a mirror and it reflects as if it is a straight line. However, if you make precise etching on spots on the mirror different from the apparent point of reflection, the intensity of the reflected beam increases. This is because the light actual reflects from many different points on the mirror OTHER THAN the apparent point of reflection on its way to the final destination. This is fully explained in the quantum view but not in the classical view.

 

[vanhees71]

The longer the thread gets, the more misconceptions are accumulated :-(.

Photons are massless quanta with spin 1. They are as relativistic as it can get, and you cannot apply naive one-particle wave-mechanics ideas from non-relativistic physics, let alone classical particle or wave concepts to them.

First of all, photons have no well-defined position observable in the strict sense. See Arnold Neumaier's Theoretical-Physics FAQ:

http://arnold-neumaier.at/physfaq/topics/position.html

It doesn't matter, in which of the different possible formulations of non-relativistic wave mechanics (position representation, matrix mechanics, or path integrals as integrals over single-particle trajectories) you try to treat photons. It doesn't work!

The only consistent way to treat photons is QED. That's very intuitive, because photons are created and destroyed all the time when interacting with other stuff, and quantum field theory is the way to describe precisely such annihilation and creation processes of quanta.

That QED actually works is demonstrated in many high-precision ways in both high-energy particle physics, where it is part of the Standard Model of elementary particles, which hitherto is the most successful theory ever, and in quantum optics experiments, where particularly photons are used to demonstrate all the features of quantum theory that appear "most weird" from the point of view of classical physics and our every-day schooled intuition like entanglement ("hypercorrelations").

A very nice article on the topic (particularly on the socalled "wave-particle dualism", which is another outdated point of view, which seems to be impossible to kill in the popular-science literature) is the following article on phys.org:

http://phys.org/news/2014-07-particle-optical-qubit-technique-photons.html

 

[D H]

The longer the thread gets, the more misconceptions are accumulated :-(.

I'm nipping that problem in the bud.

Thread closed.