

Quantum Mechanics and Quantum Computation Course - austinlyons
https://www.edx.org/course/quantum-mechanics-quantum-computation-uc-berkeleyx-cs-191x

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jndsn402
I have a math background, no physics. Whenever I try educating myself about
this stuff I get hung up on the contradictions and can't/don't want to just
take certain concepts as given in order to understand more advanced concepts.

For example (from the pdf of the intro to this course,
[https://courses.edx.org/c4x/BerkeleyX/CS-191x/asset/chap1.pd...](https://courses.edx.org/c4x/BerkeleyX/CS-191x/asset/chap1.pdf)):

"Logically, we can ask which slit the photon went through, and try to measure
it. Thus, we might construct a double slit experiment where we put a
photodetector at each slit, so that each time a photon comes through the
experiment we see which slit it went through and where it hits on the screen.
But when such an experiment is performed, the interference pattern gets
completely washed out! The very fact that we know which slit the photon goes
through makes the interference pattern go away."

I read that and say, really? The fact that we _know_ about it? How does the
photon know that we know about it? I always feel like this is just a layman's
way of describing what happens, but there is actually a more rigorous
understanding among physicists. Is that the case? Because after reading that
sentence I want to stop right there and redo that experiment until we figure
out what's really going on.

~~~
tzs
> How does the photon know that we know about it?

The next sentence after the part you quoted is the key: "This is the first
example we see of how measuring a quantum system alters the system".

To measure the system in order to know which slit it went through, we had to
physically interact with it, and that changes its behavior. The experiment is
no longer "send photons through these double slits and then count them over
there". It's "send photons through these double slits, make them interact with
our measuring doohickey right behind the slits, and then count them over
there".

Take a look at Feynman's coverage of this in Chapter 1 of Volume III of "The
Feynman Lectures on Physics". You can find them online in a beautiful HTML
version here:
[http://www.feynmanlectures.caltech.edu](http://www.feynmanlectures.caltech.edu)

~~~
jndsn402
I will check out the Feynman lectures, thanks for the reference. But my
initial reaction is, isn't the measuring thing somewhere past the slit? So how
could its presence there influence which slit the photon goes through?

~~~
tzs
You kind of have to give up the notion that the photon goes through _a_ slit.

A striking illustration of this is given by the setup diagrammed in this
image: [http://imgur.com/UlFU7oi](http://imgur.com/UlFU7oi)

You have a source of photons at the bottom. It fires them them at a half-
silvered mirror. When a photon hits a half-silvered mirror, it randomly either
reflects or passes through. The first half-silvered mirror splits the photon
beam into two beams, labeled 1 and 3. Beam 1 hits a regular mirror, which
sends it down path 2 toward another half-silvered mirror. Beam 3 hits a
regular mirror which sends it down path 4 to that second half-silvered mirror.

At the second half-silvered mirror, photons coming in on path 2 can either
pass through and be registered at detector B, or reflect and be registered at
detector A.

Photons on path 4 can reflect into detector B, or pass through into detector
A.

Start out with the source at high intensity, so we have a lot of photons, and
can treat the light like a wave. The distances of the paths can be adjusted so
that light on path 2 that passes through to B is out of phase with light on
path 4 that reflects into B, and so we get destructive interference and B
detects nothing. We get constructive interference on path 5, so all the light
ends up at detector A.

Now, keeping the light at high intensity, block path 4 at the point labeled
"test point". Now half the light leaving the source takes path 3 and gets
blocked at the test point. The other half of the light takes 1 and 2, splits
at the second half-silvered mirror, and since there is no light on path 4
there to interfere, half of the light from path 2 goes to A and half to B. Net
result: 1/2 the light lost at the test point, 1/4 detected at A, and 1/4
detected at B.

Now, leaving the block in place at the test point, turn the light source down
so that it is emitting single photons, say a photon a second. What we will now
find is that 1/2 the photons get lost (the ones that took path 3 and 4, and
hit the block), 1/4 end up at A (the ones that took 1 and 2, then reflected at
the half-silvered mirror), and 1/4 end up at B (the ones that took 1 and 2 and
then passed through the half-silvered mirror).

So far, everything makes intuitive sense.

Now remove the block. Intuition says that we should have 1/2 the photons take
1 and 2, and 1/2 take 3 and 4. The photons, when they arrive at the second
half-silvered mirror, should end up distributed equally to A and B. So we
should see 1/2 the emitted photons at A and 1/2 at B.

What actually happens is that they all end up at A.

How can this be? We are somehow getting interference even though we are only
sending single photons through!

This lets us do something remarkable. Suppose I have been playing with the
equipment, and left it in an unknown state. You don't know if I have the block
at the test point or not, and it is inconvenient to reach the test point to
check.

So you send a single photon through, and it happens to register at B. You can
infer that I left the block in, because if I had taken it out, there would
have been interference and the photon would have come out at A.

Think about that...the photon came out at B, meaning it did not hit the block,
meaning it had to have taken that 1/2/6 path...but then how did it "know" that
the block was in place so that it was "allowed" to randomly take 5 or 6 (and
ended up taking 6)?

If you remove the block and then send one photon, and it takes 1/2, and then
has to "decide" whether to take 5 or 6, how does it know that the block is
gone and so that it is required to take 5?

It just doesn't work to say that the photon takes a path, in the sense that it
starts out at one place on that path, and as time goes forward it moves along
the path.

If you want more information on this particular setup, Google for "quantum
bomb tester" (the name comes from a hypothetical where you have a bunch of
light sensitive bombs, but some of them have defective light sensors, and you
want to find a way to figure that out without destroying all the working
bombs, and this kind of split path setup provides a solution--letting you
answer the question "would this bomb explode if I hit it with a photon?"
without actually hitting it with a photon).

~~~
jndsn402
Thanks for this detailed write-up. I guess I struggle more with the particle
aspect than the wave aspect. Meaning, if light were exclusively a wave, then
the half-silvered mirror doesn't 'randomly' either reflect or pass through, it
just splits the beam in two. And all the events described above would make
sense - the beam splits at each half-silvered mirror, so if the block is in
place you get hits at B, and if not, you don't. (Correct?)

Except that we are somehow convinced that we are sending single, indivisible
photons. Why is that?

And in general - I assume these experiments have actually been done, i.e. at
some point long ago someone tried this and was surprised to see that the
interference happened with individual photons. Is there a write up of one of
these experiments somewhere?

