Uncertainty principle and double-slit interference?

[Ken G]

But photons can defy SR, and can still show finite expressions even though this should not occur at C.

I'm not sure what you are trying to say here. SR was essentially built around photons, as kind of the asymptotic limit of a "relativistic particle". Photons do not "defy" SR, though they are outside of the constraints we put on "observers" in SR (an observer cannot zoom past another observer at a relative speed of c, so a photon is not allowed to "bear witness" to reality. Good thing, they'd have some weird notions-- nevertheless they'd be limiting examples of SR in the way that the concept of "infinity" is a limit of the concept of all the other real numbers).

 

[peter0302]

Agreed. Photons don't defy SR at all. The finite expressions siphon is referring to are special cases of more general equations.

For example, take the general Energy-Momentum relation:

E^2=(pc)^2+(mc^2)^2

For photons, m=0, therefore E=pc.

Another cool derivation from the above:

For a photon:
E = pc
ymc^2 = ymvc
v=c

So you can use the momentum-energy relation to show how V=C for a photon without even having to assume the constancy of the speed of light! So, photons don't defy relativity at all - they're a consequence of it.

 

[RandallB]

I should be more specific. When I say "punch hole" I mean something wider than a couple of millimeters. Like a hole punch in a piece of paper. Afshar used pinholes, much smaller. Point is making the holes/slits small is what makes the position measurement certain, leading to the uncertain momentum measurement.

I see what your saying, but don't forget "punch holes" are small if the source is far enough away to be "Far Field".

 

[xylai]

We can have an imaginary experiment. If a particle passes through one slit, left or right, then we can close the other slit, because it does not influence the partcle. However, after this experiment, we can get the diffractive pattern, but not the interference pattern.

We can get the pattern only when we have no idea, even in principle, which slit the photon went through. Mathematically, it's _equivalent_ to saying the photon went through both slits, but you whether it _really_ went through both is a matter of interpretation.

My point is that the two possibilities, which one was right we can never know, need to be very precise position measurements. If it was a "double punch hole" experiment instead of a "double slit" it wouldn't work.

 

[peter0302]

The _possibility_ of passing through either slit is what creates the interference pattern. When you close one slit, you remove that possibility. When you peek behind the slits, you remove that possibility.

You don't have to believe that it _actually_ passed through both, for one reason because no one can agree on what "actual" or "really" mean. All we can say is that possibilities influence the wave function, and the wave function influences where you'll end up finding the particle. What happened to the particle before it's detected is not something on which there is universal agreement. Quite the contrary.

 

[Ken G]

Yes, that's all true. Indeed, I would say that "what happened to the particle" is not even a scientific question, unless you make it part of the experimental setup to answer it-- in which case it is now a different question because it pertains to a different situation. If you can answer it in some systems that give all the same results for the measurables of similar systems not set up to answer that question, then you have a basis for giving a more general answer. But oftentimes, you will not get the same results when you do that (as with asking which slit the photon went through). Fortunately, quantum mechanics tells you when this is the case, and there is never a need to leave the Copenhagen interpretation to get that answer.

 

[lightarrow]

We can get the pattern only when we have no idea, even in principle, which slit the photon went through.

Exactly

Mathematically, it's _equivalent_ to saying the photon went through both slits, but you whether it _really_ went through both is a matter of interpretation.

On this I agree with you. Think that I believe the photon don't go through any of them!
(It was not irony, I really believe this).

 

[peter0302]

Haha. Well, that's why the double slit continues to be "the only mystery" because there are so many different ways of looking at it, all of which lead to the same result, that 83 years later we still don't have agreement.

 

[Schrodinger's Dog]

Haha. Well, that's why the double slit continues to be "the only mystery" because there are so many different ways of looking at it, all of which lead to the same result, that 83 years later we still don't have agreement.

It hasn't been heralded as the greatest experiment of the 20th century for nothing. There can be no agreement without measurement and no agreement with it? We're kind of at an impasse. Even if we measure where the wave is not, we still have the same problems.

 

[xylai]

I agree with you that What happened to the particle before it's detected is not something on which there is universal agreement. But the double-slit experiment is so weird. I need to think of it deeply. Thank you for your discussion.
If you have some good ideas on it, welcome to contact me. My email address is xylai2000@gmail.com . Thank you.

The _possibility_ of passing through either slit is what creates the interference pattern. When you close one slit, you remove that possibility. When you peek behind the slits, you remove that possibility.

You don't have to believe that it _actually_ passed through both, for one reason because no one can agree on what "actual" or "really" mean. All we can say is that possibilities influence the wave function, and the wave function influences where you'll end up finding the particle. What happened to the particle before it's detected is not something on which there is universal agreement. Quite the contrary.

 

[Robertalpac]

Just to be sure are you talking about the double slit quantum eraser experiment?

You would it is called the http://www.sciam.com/article.cfm?id=how-can-a-single-photon-p" which produces interference patterns when you fire one photon at a time.

Hi all,
I am searching for "quantum version conjugate of double slit" . Before photons reach the double slit, their wave function is delta function and after the double slit, on the screen, we have an interference pattern. The question is: Is there any mechanism to convert this interference pattern( this complex wave function of photons) to delta function as they had before double slit? It means the conjugate of double slit.
I appreciate it if one can answer this question.