Can one photon interfere with another photon?

[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.