Exploring Wave Function Collapse and the Double Slit Experiment

[curiousphoton]

I'm still wrestling with the whole uncertainty principal / wave function collapse idea. Obviously a basic building block of QM, I'm having a hard time understanding the real world evidence which supports these QM piles.

1. So from my understanding, the uncertainty principle tells us it is impossible to determine simultaneously both the position and velocity of a particle (lets say a photon). Instead, a 'wave packet' is used to describe the possible position of a photon. The photon may exist in any location of this wave packet. (This is a very general description but please take this as it is for now)

2. Why I'm thinking about this idea now is comparing this note to the double (or single for that manner) slit experiment. If you set up the experiment and turned your light source on and off 1 billion times (without making any changes to the setup) you would see the exact same diffraction pattern 1 billion times, correct?

I guess I'm just confused how 1. and 2. both can be correct. 1. tells us that these photons could be anywhere, yet 2. tells us those photons show up at the exact same location on our screen 1 billion times and counting?

Thanks for any thoughts.

 

[TheAlkemist]

In the double slit experiment when zapping a single 'particle' (photon) of light at the slit's the diffraction pattern created on the screen suggests that it passed through both slit's at the same time? And attempts to observe (measure) which slit it went through decoheres the quantum state ("collapses the wave function")? Hence the Uncertainty Principle?

 

[curiousphoton]

In the double slit experiment when zapping a single 'particle' (photon) of light at the slit's the diffraction pattern created on the screen suggests that it passed through both slit's at the same time? And attempts to observe (measure) which slit it went through decoheres the quantum state ("collapses the wave function")? Hence the Uncertainty Principle?

I'm talking big picture. Let's take the single slit for simplicity. If your turn your light source on and off an infinite amount of times (assume nothing changes in your setup) you'll get the exact same diffraction pattern on your screen.

How come we have 'wave pockets' or 'wave collapse' equations that tell us we don't know where these photons are? If they are hitting the same spots on the screen a billion times in a row, creating the same diffraction pattern, I don't see why we can't say they have definite locations prior to showing up the screen.

 

[nismaratwork]

I'm talking big picture. Let's take the single slit for simplicity. If your turn your light source on and off an infinite amount of times (assume nothing changes in your setup) you'll get the exact same diffraction pattern on your screen.

How come we have 'wave pockets' or 'wave collapse' equations that tell us we don't know where these photons are? If they are hitting the same spots on the screen a billion times in a row, creating the same diffraction pattern, I don't see why we can't say they have definite locations prior to showing up the screen.

It isn't the same, there is a statistical deviation of the HUP as you observe the many many "dots" on the screen.

 

[jtbell]

1. tells us that these photons could be anywhere,

Have you heard of something called a probability distribution? Even though we cannot predict exactly where any single photon will go, we can nevertheless predict that it is more likely to arrive at some locations than at others.

yet 2. tells us those photons show up at the exact same location on our screen 1 billion times and counting?

If you turn the source on and off rapidly enough that only one photon comes out, then repeat it, the photons will almost certainly not arrive at the same location on the screen. However, they are each subject to the same probability distribution.

If you repeat the process more and more times, you can watch the landing points build up on the screen according to the probability distribution. Eventually you get a pattern that looks just like what you get from classical wave optics.

 

[TheAlkemist]

Have you heard of something called a probability distribution? Even though we cannot predict exactly where any single photon will go, we can nevertheless predict that it is more likely to arrive at some locations than at others.

If you turn the source on and off rapidly enough that only one photon comes out, then repeat it, the photons will almost certainly not arrive at the same location on the screen. However, they are each subject to the same probability distribution.

If you repeat the process more and more times, you can watch the landing points build up on the screen according to the probability distribution. Eventually you get a pattern that looks just like what you get from classical wave optics.

Isn't this what happens when the light beam, which is thought of as a stream of multiple photons, passes through the slits, 'one at a time' so to speak?

 

[curiousphoton]

If you turn the source on and off rapidly enough that only one photon comes out, then repeat it, the photons will almost certainly not arrive at the same location on the screen. However, they are each subject to the same probability distribution.

3. This is exactly where I am confused. You're saying if we turn the source on so only 1 photon comes out at a time, the pattern on the screen will be different (because this photon is not arriving at the same location on the screen everytime, according to you).

4. Now back to our normal experiment where we turn a light source on, observe the pattern on the screen, then turn the light source off. We repeat this process, without changing anything, and notice that we see the same pattern on the screen every single time!

So now hopefully this makes sense : Account for what we said in 3. (one photon, different location on screen, hence different pattern) and 4. (light source emitting x number of photons, same exact pattern on screen).

If 3. and 4. are true, then there must be a certain number of photons (2, 10, 1 million ? ) where the pattern on the screen becomes the same for each trial. In other words, if we shoot 10 photons instead of 1, is that the point where we see the same pattern on the screen each trial?

Hopefully you can follow my logic. I'm trying to be as clear as possible. Thanks

 

[DrChinese]

3. This is exactly where I am confused. You're saying if we turn the source on so only 1 photon comes out at a time, the pattern on the screen will be different (because this photon is not arriving at the same location on the screen everytime, according to you).

4. Now back to our normal experiment where we turn a light source on, observe the pattern on the screen, then turn the light source off. We repeat this process, without changing anything, and notice that we see the same pattern on the screen every single time!

So now hopefully this makes sense : Account for what we said in 3. (one photon, different location on screen, hence different pattern) and 4. (light source emitting x number of photons, same exact pattern on screen).

If 3. and 4. are true, then there must be a certain number of photons (2, 10, 1 million ? ) where the pattern on the screen becomes the same for each trial. In other words, if we shoot 10 photons instead of 1, is that the point where we see the same pattern on the screen each trial?

Hopefully you can follow my logic. I'm trying to be as clear as possible. Thanks

I must admit that I do not understand the question. When you talk about the pattern for each trial, is each trial supposed to include many photons? You get similar patterns with large numbers of photons, so what is strange about that? And if you allow a pattern to build up by releasing a single photon at a time, what is strange about that?

On the other hand, you are in fact observing the final position of each photon without learning anything about which path it traversed to get there. That is how the Uncertainty Principle is being expressed.

 

[unusualname]

The pattern is always different, it just looks like interference bands as more particles are detected. Obviously for a single particle it won't look like an inteference pattern, just a single blip at a random position whose probability is predicted by wave interference (schrodinger wave in case of non-relativistic massive particles, like slow electrons, maxwell EM wave in case of photons (predicted mass 0, so travel at speed c), no idea what the wave is for neutrinos )

 

[DrChinese]

The pattern is always different, it just looks like interference bands as more particles are detected. Obviously for a single particle it won't look like an inteference pattern, just a single blip at a random position whose probability is predicted by wave interference (schrodinger wave in case of non-relativistic massive particles, like slow electrons, maxwell EM wave in case of photons (predicted mass 0, so travel at speed c), no idea what the wave is for neutrinos )

Well, I was diffracting neutrinos the other day in my neutrino detection lab, and I got...

 

[curiousphoton]

I must admit that I do not understand the question. When you talk about the pattern for each trial, is each trial supposed to include many photons? ?

For a better understanding, please re-read carefully my post with points 3. and 4. Two different experiments described. First, where one photon is released (3.) and second, where x amount of photons are released (4.).

You get similar patterns with large numbers of photons, so what is strange about that? And if you allow a pattern to build up by releasing a single photon at a time, what is strange about that?

Consider 4. (x amount of photons released). Again, please assume we release this x amount of photons on each trial (could be 10, or 1 million, doesn't matter as long as we release the same amount on each trial). Assuming this same number of photons was released for each trial, we would see the same diffraction pattern on the screen each trial, correct?

Consider 3. (one photon released). Again, we would see this photon at different locations on the screen each time we ran a trial, correct? Thus we would have a different diffraction pattern on the screen each trail, correct?

So I just find that 4. and 3. are contradictory. Please take them as two separate experiments. Why with the 10 photon experiment (4.) we see the same diffraction pattern each trial and with the 1 photon experiment (3.) we see a different diffraction pattern each trial?

 

[DrChinese]

So I just find that 4. and 3. are contradictory. Please take them as two separate experiments. Why with the 10 photon experiment (4.) we see the same diffraction pattern each trial and with the 1 photon experiment (3.) we see a different diffraction pattern each trial?

One photon = one blip. So that blip has a % chance of being in a certain spot (although not equal at all spots). If I ask one person what their street address is, I get a certain pattern of responses. If I ask 1000 people, I will get a predictable distribution.

So I don't exactly follow the contradiction.

 

[unusualname]

He doesn't realize that the 100-photon-pattern is different each time even though it usually resembles the same interference band pattern. ie looks the same but isn't the same.

In theory, if 1 million monkeys run 1 million double-slit experiments with 1 million particles each, some of them may see unusual patterns like a single band or graffiti describing the eq of quantum gravity)

@DrChinese, I'm impressed you got the neutrino diffraction working, I think my double slit was working but I couldn't tell because the damn detectors wouldn't blip

 

[DrChinese]

@DrChinese, I'm impressed you got the neutrino diffraction working, I think my double slit was working but I couldn't tell because the damn detectors wouldn't blip

My stomach is massive enough that I am able to detect them directly.

Of course, I must be at least a mile underground or there is just too much noise.

 

[TheAlkemist]

I must admit that I do not understand the question. When you talk about the pattern for each trial, is each trial supposed to include many photons? You get similar patterns with large numbers of photons, so what is strange about that? And if you allow a pattern to build up by releasing a single photon at a time, what is strange about that?

On the other hand, you are in fact observing the final position of each photon without learning anything about which path it traversed to get there. That is how the Uncertainty Principle is being expressed.

Exactly. This is what I thought. I think the OP's confusion is in pattern vs position.

 

[curiousphoton]

He doesn't realize that the 100-photon-pattern is different each time even though it usually resembles the same interference band pattern. ie looks the same but isn't the same.

In theory, if 1 million monkeys run 1 million double-slit experiments with 1 million particles each, some of them may see unusual patterns like a single band or graffiti describing the eq of quantum gravity).

Thanks that's all I needed. So follow up question : Is there actual experimental evidence where we've observed unusual patterns like a single band or graffiti? I'm having a hard time believing that we've performed a single or double slit experiment and actually have seen these strange patterns show up...

If so, there must be a source with pictures showing these strange patterns?

 

[unusualname]

Thanks that's all I needed. So follow up question : Is there actual experimental evidence where we've observed unusual patterns like a single band or graffiti? I'm having a hard time believing that we've performed a single or double slit experiment and actually have seen these strange patterns show up...

If so, there must be a source with pictures showing these strange patterns?

I don't think they could get enough monkeys to volunteer. ;)

But seriously, the point is that the pattern is randomly generated by a probability distribution determined by the wave functions involved in the interference (and in the case of photons it's just the classical em wave)

So just like you might toss 1 million coins and get all heads you might get the particles all hitting the detector at one small part of the probability distribution, but it's unlikely, and I don't think there are any reports or photos. But if you run the 10 electron/photon double slit experiment 1024 times (2^10), you're quite likely (but not certain) to see one case where all the electrons/photons hit just one side of the detector.

 

[curiousphoton]

I don't think they could get enough monkeys to volunteer. ;)

I know a couple we could use from the last adminstration...

But seriously, the point is that the pattern is randomly generated by a probability distribution determined by the wave functions involved in the interference (and in the case of photons it's just the classical em wave);)

This is what I'm questioning (see below)

But if you run the 10 electron/photon double slit experiment 1024 times (2^10), you're quite likely (but not certain) to see one case where all the electrons/photons hit just one side of the detector.

Yes this is what I've been trying to get at! All I'm trying to do is find where we experimentally confirm the probability distribution. I mean, I thought that if we performed the single or double slit experiment, not changing anything, each trial would result in the same pattern on the the screen.

Apparently though, the probability distribution tells us that we should see a different pattern every now and then (maybe 1 in a million, for instance). So if that is the case, I figured we must have performed the experiment 1 million times to observe a different pattern. It would be extremely interesting to see and document these different patterns, no?

It just seems like saying 'Oh the sun rises in the east and sets in the west' but never walking outside to check.

 

[nismaratwork]

I know a couple we could use from the last adminstration...



This is what I'm questioning (see below)



Yes this is what I've been trying to get at! All I'm trying to do is find where we experimentally confirm the probability distribution. I mean, I thought that if we performed the single or double slit experiment, not changing anything, each trial would result in the same pattern on the the screen.

Apparently though, the probability distribution tells us that we should see a different pattern every now and then (maybe 1 in a million, for instance). So if that is the case, I figured we must have performed the experiment 1 million times to observe a different pattern. It would be extremely interesting to see and document these different patterns, no?

It just seems like saying 'Oh the sun rises in the east and sets in the west' but never walking outside to check.

I think you are confusing issues of measurement with the fundamental statistical nature of the HUP. The pattern would be "the same", but the placement of each dot would not, and the deviation would be determined by the HUP. Think of it in cosmological terms: the same initial conditions for a Big Bang will always turn out a different CMB pattern.

 

[DrChinese]

Yes this is what I've been trying to get at! All I'm trying to do is find where we experimentally confirm the probability distribution. I mean, I thought that if we performed the single or double slit experiment, not changing anything, each trial would result in the same pattern on the the screen.

As nismaratwork indicates, each pattern is essentially unique and random. When you get down to that level, you see the essential randomness of particle property values (observables).

 

[unusualname]

To get a feel for the true randomness, here are some video clips of results from real double-slit experiments:

Electrons

Neon Atoms (?)

Photons

 

[nismaratwork]

To get a feel for the true randomness, here are some video clips of results from real double-slit experiments:

Electrons

Neon Atoms (?)

Photons

Oh now that was just fun to watch. Thanks unusualname, and thanks Dr. Chinese, for confirming that I am on the right path here. It's always good to be aware of these things.

 

[jtbell]

I thought that if we performed the single or double slit experiment, not changing anything, each trial would result in the same pattern on the the screen.

If by "pattern" you mean "collection of exact locations of spots", in general you will not get the same pattern each time. In fact, the odds are extremely small that two repetitions of the double slit experiment with a reasonably large number of particles will produce the same pattern.

As an analogy, consider tossing a coin a thousand times and recording the exact sequence of heads and tails. If you toss the coin another thousand times, how likely is it that you will get exactly the same sequence of heads and tails?

Nevertheiess, in both cases we can predict the probability of getting a spot at a particular location (in the double slit experiment) or the number of heads versus tails (in coin tossing), and the results of experiments confirm this, within the uncertainty imposed by the randomness of these processes. In both cases, the uncertainty decreases (in percentage terms) as the number of trials (number of photons or electrons, or number of coin tosses) increases.

Apparently though, the probability distribution tells us that we should see a different pattern every now and then (maybe 1 in a million, for instance).

It's far more often than "every now and then." Consider again, tossing a coin a thousand times. How often do you expect to get exactly the same sequence of heads and tails?

 

[TheAlkemist]

Exactly. This is what I thought. I think the OP's confusion is in pattern vs position.

Ah. So that WAS the confusion. I was starting to get a little confused myself there for a minute. Cool.