Quantum wave destruction question

[jimmylegss]

Now if you have a water surface of 2cm high. You create waves with a height of 1cm above that 2cm, and a through of 1cm. And if a +1 wave runs into a -1 wave they cancel each other out, or also called wave destruction.

But a similar pattern is seen with the double slit experiment. How is this possible? It is easy to visualize with water. But how can a photon or electron be canceled out? That should mean there is negative energy running into positive energy cancelling each other out? With my simple brain, the way I see it, there is either a photon in a vaccuum, or there is nothing. How can it cancel itself out? Does this mean a vacuum is not really empty?

I know the water waves and electron waves are very different and not comparable, but still the destruction of waves is still seen in similar ways in both cases.

If someone can give me some explanation on this, much appreciated!

 

[VantagePoint72]

The photon itself is not being 'cancelled out' when destructive interference occurs. Its wavefunction, which tells the probability of finding the photon here or there, is what undergoes interference as the photon propagates through the double slits. Constructive interference means there is a high probability of finding the photon in that spot on the screen, destructive interference means there is a low (possibly zero) probability of finding the photon there.

 

[jimmylegss]

Yes but if you open one or the other slit then,

slit 1 + slit 2 = what is on the wall

But if you open both slits at the same time then

Slit + slit 2 = less then the sum of those on the wall.

So if you look at the probability of finding the same amount of photons before the two opened slits as you find after the slits, that probability is lower? And as I am typing that sentence I am even more confused.

I guess since we cannot observe it, we cannot really find out what is happening exactly to have the probability of finding a foton go down after the two screens.

Everytime I think about this stuff, it just blows my mind really :D Cannot believe this actually happens in our reality.

 

[Nugatory]

But if you open both slits at the same time then

Slit + slit 2 = less then the sum of those on the wall.

The probability of a particle striking in the bright areas is greater than it would be if there were no interference, and this more than makes up for the lower probability in the dark areas.

 

[jtbell]

The probability of a particle striking in the bright areas is greater than it would be if there were no interference, and this more than makes up for the lower probability in the dark areas.

I would rather say that this exactly makes up for the lower probability in the dark areas. The interference between the two slits rearranges the probability distribution on the screen, i.e. it makes the photons arrive at different locations than they would have otherwise, but it does not create or destroy photons.

 

[jimmylegss]

Maybe this is outdated:
http://www.feynmanlectures.caltech.edu/III_01.html

But this one clearly states that a different amount of electrons arrive at the screen when there is interference?

P1 or P2, adding them up is P12. But both P1 and P2 open without being observed, and you do not get the same number of P12?

 

[jtbell]

But this one clearly states that a different amount of electrons arrive at the screen when there is interference?

At any particular location on the screen, this is true. However:

But notice! There are some points at which very few electrons arrive when both holes are open, but which receive many electrons if we close one hole, so closing one hole increased the number from the other. Notice, however, that at the center of the pattern, P12 is more than twice as large as P1+P2. It is as though closing one hole decreased the number of electrons which come through the other hole.

That is, at some locations, P12 < P1 + P2, but at other locations, P12 > P1 + P2. When you add up the numbers of electrons at different points all over the screen, the total is the same with and without interference.

 

[jimmylegss]

riight thanks. I misread, did not see the word 'intensity' in front of that statement. Thanks. It still makes you wonder how there is destructive interference. You see the exact same pattern as with water waves.

A wave can cancel out another one, because the starting point is NOT absolutley nothing like in a vaccuum. The surface of water is already some number. And with soundwaves, there is a certain number of molecules in the air. That number can go up, and it can go down, so that is why you see that interference pattern. It is peculair that you then see the same pattern with photons in a area where there is basicly nothing before the photons go in, and yet you see the exact same pattern.

 

[Nugatory]

I would rather say that this exactly makes up for the lower probability in the dark areas. The interference between the two slits rearranges the probability distribution on the screen, i.e. it makes the photons arrive at different locations than they would have otherwise, but it does not create or destroy photons.

Are we opening and closing a slit, or are we placing detectors at open slits? The interference neither creates nor destroys particles, but the total arrival rate summed across the entire screen will be greater with two slits open than with one - and this despite the appearance of areas where the arrival probability is less than with one slit open.

 

[jimmylegss]

Are we opening and closing a slit, or are we placing detectors at open slits? The interference neither creates nor destroys particles, but the total arrival rate summed across the entire screen will be greater with two slits open than with one - and this despite the appearance of areas where the arrival probability is less than with one slit open.

Are you saying the sum of either one open but not both is greater then if you open them both?

 

[Nugatory]

Are you saying the sum of either one open but not both is greater then if you open them both?

At some individual points (the ones in the "dark" areas of the interference when both are open) yes. At other points (the "bright" areas) the sum of the two either-but-not-both values is less than the both-open value.

As jtbell correctly stated above, as long as two slits are open the total number of particles reaching the screen in a given amount of time is the same whether there are detectors in the slits and hence an interference pattern, or no detectors and no interference pattern; all that's changing is how these particles are distributed across the screen.

If you close one of the slits, you eliminate the interference pattern just as happens with detectors at the slits. However, if you close the one of the slits, you also reduce the total number of particles reaching the screen in a given time.

 

[jtbell]

The interference neither creates nor destroys particles, but the total arrival rate summed across the entire screen will be greater with two slits open than with one

Yes. In the example discussed by Feynman (and which I assume we're discussing here), P1 is the probability of getting an electron at a certain location on the screen when only slit 1 is open; P2 is the probability of getting an electron at the same location when only slit 2 is open; and P12 is the probability of getting an electron at the same location when both slits are open.

Assuming the slits are the same size and are "illuminated" equally by an incoming electron beam, then I would expect that the integral of P1 across the whole screen would equal the integral of P2; and that the integral of P12 would be twice as large as either of those. That is, over the whole screen you get twice as many electrons with both slits open, than with only one slit open.

 

[jimmylegss]

Alright. And is there any info on why that wave pattern, that is basicly the same as with water and sound, exists? Because the set up is different then with for example water and sound. The medium through which they travel is empty.

 

[Nugatory]

Alright. And is there any info on why that wave pattern, that is basicly the same as with water and sound, exists? Because the set up is different then with for example water and sound. The medium through which they travel is empty.

The setup is different, but the differential equations that describe these problems are similar so the solutions have some similar properties. Google for "wave equation".

 

[jimmylegss]

So basicly we can describe them, predict the probabilities, but we haven't got the slightest clue why exactly they behave like a wave function if not observed?

 

[VantagePoint72]

So basicly we can describe them, predict the probabilities, but we haven't got the slightest clue why exactly they behave like a wave function if not observed?

I'm not really sure what you're asking. Their statistics are determined by wave functions because they're quantum systems, and quantum theory tells us how those behave. If you're asking why the universe obeys quantum mechanics/quantum field theory rather than some other set of rules, then, no, we can't answer that as it's not a scientific question. It could conceivably be possible to come up with a more fundamental model out of which quantum theory emerges in some limit, but then the question just becomes why those rules and not some others. You will have to consult a philosopher or theologian to get an answer to that sort of question.

 

[bhobba]

So basicly we can describe them, predict the probabilities, but we haven't got the slightest clue why exactly they behave like a wave function if not observed?

One of the problems here is the wave-particle idea the double slit is analysed with in beginning texts is basically a crock that is consigned to the dustbin once the full machinery of QM is available. See our FAQ:
https://www.physicsforums.com/threads/is-light-a-wave-or-a-particle.511178/

What texts should do is go back and analyse the double slit in terms on that newly developed formalism to see what is really going on - but don't.

The following fixes that issue up:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Note the above is not strictly correct either - but is an advance on the wave-particle idea. That however requires more advanced machinery than basic QM. Baby steps, baby steps - Rome wasn't built in a day :p:p:p:p:p:p:p:p. I know, it makes this stuff doubly hard - it annoys the bejesus out of me as well.

Thanks
Bill

 

[jimmylegss]

I'm not really sure what you're asking. Their statistics are determined by wave functions because they're quantum systems, and quantum theory tells us how those behave. If you're asking why the universe obeys quantum mechanics/quantum field theory rather than some other set of rules, then, no, we can't answer that as it's not a scientific question. It could conceivably be possible to come up with a more fundamental model out of which quantum theory emerges in some limit, but then the question just becomes why those rules and not some others. You will have to consult a philosopher or theologian to get an answer to that sort of question.

My question is this, the property of a wave is that energy is put into the system that always pushes something away. With water it starts by lowering the water level right around the machine that creates the ripples. The water surface tries to return to equilibrium, and you get a wave that travels to the screen. With sound waves it starts out by creating a area right next to the speaker that has less air molecules. So it just seems kind of peculiar that energy traveling through a vacuum behaves in the exact same way, yet there is nothing to push away or disturb (?). As the defining property of waves seems to be that they exchange whatever medium they travel through for energy (like a water surface that is lowered, causing the surface next to it to rise). You could make a hypothesis, that the light is pushing something away?

 

[Nugatory]

You could make a hypothesis, that the light is pushing something away?

You could, but you would have to assign a number of very unusual properties to that something. For example its speed would have be the same relative to all objects, even ones that are moving at very different speeds, to be consistent with the observed behavior of light (Google for "Michelson-Morley Experiment"). That's not a promising start.

 

[VantagePoint72]

With sound waves it starts out by creating a area right next to the speaker that has less air molecules. So it just seems kind of peculiar that energy traveling through a vacuum behaves in the exact same way, yet there is nothing to push away or disturb

Wavefunctions don't travel through the vacuum because they don't "live" in physical space. They live in Hilbert space. For a single particle, the wavefunction is a function of just the three spatial coordinates and time so it's easy to (mistakenly) imagine that it's a wave traveling through space. In general, though, the wavefunction of a multi-particle state is a function on the system's configuration space (plus time). So, for example, a system of two particles at $\vec{x_1}$ and $\vec{x_2}$ has a wavefunction $\psi(\vec{x_1},\vec{x_2},t)$. Unlike the one particle case, there is no well-defined value of the wavefunction at a single particular point. Contrast this with, say, the perfectly well-defined height of water at a point, the air pressure at a point, or the electromagnetic field tensor at a point for, respectively, water, sound, and (classical) EM waves which do "live" in real, physical space. The wavefunction doesn't transport energy through the vacuum; the particle(s) it describes does. Thinking of it like a time-varying field on space-time (which is what a physical wave is) is an overly classical way of thinking that can't, for example, account for entanglement and other uniquely quantum phenomena.