About the behaviour of a beam-splitter

AnssiH

http://www.quiprocone.org/Protected/Lecture_2.htm

On the page you will find a video of Mr. David Deutsch talking about quantum computation, in terms of many worlds interpretation. At around 11:20 he mentions a curious feature about a beam splitter. He says that while a beam splitter makes the photon's direction of motion "unsharp", it can also do the reverse of that. I.e. if you pass a photon through a beamsplitter, and then have a mirror at both possible directions of the photon so that they reflect the photon back into the beam splitter, the photon will *always* end up back to the direction where it originally came from due to "an interference process" of some sort.

(Note: if you watch the whole lecture through, the final test setup is in fact this same setup of a beam splitter and two mirrors. I don't quite understand why at time 41:50 Deutsch makes a conflicting statement to the above, saying that the photon entering the beam splitter from two directions still has two possible directions of exit "...it again strikes the beam splitter, from which there are two possible directions of exit", although in fact the test setup he is talking about is still just two mirrors being aimed at a single beam splitter, and later he accounts the fact that the photon exits only at one direction, as an indication of many worlds).

In any case, this "joining" feature of a beam splitter is something that caught my attention. Do we know how and why does it work that way? What if you aim two different but identical lasers to a beam splitter from two different angles but from the same distance; will both of the laser beams end up exiting to a single direction, leaving one possible exit completely empty? If so, what decides which exit the beams take? Or is this something that only happens if you are to aim a single beam through a beam splitter and have it bounce back into a beam splitter over mirrors?

What happens physically at the mirrors for that matter; i.e. what does it mean to reflect a light beam?

Thanks

AnssiH

Anyone?

Is there a better category for the question?

Hurkyl

The easy answer is that it works because "joining" is just "splitting" done backwards.


The longer answer is that this is an interference process. When a photon returns to the beam-splitter and split again, it interferes with itself. You can place the mirrors so that one of the beams will be eliminated through destructive interference. (You can elimiate whichever one you like, I think)


Mathematically, the beam splitter may have the following effect on beams coming from the left (|L>), bottom (|B>), right (|R>), and top (|T>):

|L> --> (|T> + |R>) / sqrt(2)
|B> --> (|T> - |R>) / sqrt(2)
|T> --> (|L> + |B>) / sqrt(2)
|R> --> (|L> - |B>) / sqrt(2)


So, if you fire a beam in from the left (|L>), it splits into:
(|T> + |R>) / sqrt(2)

Then, if you place the mirrors carefully, so that the state going back into the beam splitter is:
(|T> + |R>) / sqrt(2)

then the beam splitter turns that into:

((|L> + |B>) / sqrt(2) + (|L> - |B>) / sqrt(2)) / sqrt(2) = |L>




This experiment is certainly proof that quantum superposition is real. However, it sounds like David Deutsch is making the mistaken assumption that other interpretations cannot work with superpositions. In particular, it sounds like he's assuming the Copenhagen interpretation necessarily says "either the photon went one way, or it went the other way", which is not correct. (Superpositions are certainly more natural in MWI than in Copenhagen, IMHO)



This is certainly a seam in my knowledge; maybe someone else can explain!

selfAdjoint

Superpositions are a feature of the formalism; the solutions of the Schroedinger equation are waves which can superpose by their nature.

The only difference between the CI and the MWI is that CI says the wave collapses and MWI denies that it does. But then MWI has to explain in what sense they mean "M", which gets them into science fiction or mysticism, take your choice. MWI also has problems with the assumption that experienced reality is the wave function (which it has to be since there's no collapse).

Farsight

I recall the David Deutsche lecture was discussed on another thread, where I think his basic premise came over as explainable via simple interference. I'll see if I can find it.

Edit: this was it, see post #35

http://www.physicsforums.com/showthr...=123590&page=3

AnssiH

Thanks to everyone for replying

Thanks! And "doh!" 180 degree phase shift, of course... :I This makes me believe that also in the case of pointing two different lasers into the same beam splitter, we can choose which way all the energy exits by adjusting the distances.

Yeah, it stroke me as a bit odd that he seems to assume that. Especially being that it is the whole original oddity of Copenhagen that it says there exists such a thing as a superposition. In fact I was just in a debate elsewhere about this very fact, when someone was claiming that this experiment is a proof for MW, which it certainly is not.

Yeah, well, also with CI, even though it says there is a wave collapse, it is impossible to actually define when and why it happens. I guess that's why Bohr talked about conscious observer and strange stuff like that.

And if we think about a regular double-slit experiment, there also the photon is passing through air molecules all the time. I would expect the light is actually refracted by the atoms of the atmosphere on its way to double-slit (being that the speed of light is lower than C through air), yet there is no wave collapse due to these atoms. So it seems to me that this experiment is already revealing the oddity regarding the concept of superpositions & wave collapse.

AnssiH

Oh, and Farsight, you mention in the other thread:
I've been wondering the same, and in John Gribbin's book "Schrödinger's Kittens", he mentions at page 115 that indeed, at 1950 David Bohm showed that photoelectric effect is already explained by just what Planck said; that atoms accept energy in definite amounts, and that "strictly speaking it means that Einstein did not deserve the Nobel Prize, at least not for the work he was given it for."

Then he goes on to explain how the experimenters have nevertheless observed photons to really exist. Hopefully you can find the book from the library for the details. Page 115 onwards.

vanesch

It should be noted that this is already the case in classical optics. The "secret" is (as is established in any good book on classical optics) the 180 degree phase difference between the transmitted and the reflected beam at the planar interface of a dielectric. In order to understand this setup, it is really much more helpful to look at the classical picture (and use that to fill in the quantum version of it, where the photons just follow the behaviour of a classical pulse in this case).

Be careful with Deutch's claims. Although I myself am rather sympathetic towards the many worlds interpretation (as many can testify here to their dislikings ), it doesn't do any good idea any service by overselling it in a religious way as Deutch does.
No experiment can *prove* any interpretation of QM over any other. In fact, MWI is more open to falsification than another interpretation like Copenhagen, because Copenhagen has an extra free "parameter" which is the place of the Heisenberg cut. So at best an experiment could show MWI to be false.


Only if they are phase-locked. And if they are phase-locked, "photons" are not localised into one beam, but are in a superposition of the two beams.

Really, these issues are better understood first using purely classical optics.