Interference in Quantum Mechanics (Basic)

[enceladus_]

I am doing some reading on Quantum Mechanics, and I do not understand this concept. Here is an excerpt from "The Universe and the Atom" by Don Lichtenberg. Sorry for the bad formatting.

13.4 Interference in quantum mechanics
If we shine light through a thin slit in an opaque object and place a
screen behind the slit, then the light will form a pattern on the screen.
Because light is a wave, it will bend as it goes through the slit (we call
this phenomenon “diffraction”), and the image on the screen will be
wider than the slit itself. We can also shine light through a double
slit, and again we get a pattern on the screen. However, the pattern
is not simply the sum of the patterns caused by the individual slits.
Because light is a wave, the light going through the two slits exhibits
interference. In particular, there are regions on the screen that are illuminated
if either slit is closed, but the regions are dark when both
slits are open. the reason is that the wave exhibits destructive interference
in those regions.
Let us now make the light source so dim that only one photon
goes through the slits at a time and makes a tiny spot on the screen
as if it is a particle. Suppose the spots on the screen are recorded
as more and more photons impinge on it. The pattern of recordings
is the same as the diffraction pattern from two slits. Those who say
that each photon must go through only one slit get the wrong answer,
because they predict, in contrast to experiment, that the pattern is the
sum of the patterns from one slit at a time.
The only way we can explain the phenomenon is to say that even
a single photon acts as a wave when it goes through the slits, somehow
“being aware” of both slits as it passes through, but the photon
acts as a particle when it makes a spot on the screen.
If we do the same experiment with a beam of electrons going through two slits and hitting a screen that scintillates when an electron
strikes, we get the same answer as with a beam of photons. The
conclusion is that an electron acts as a wave when it goes through
the slits and it acts like a particle when it hits the screen.
The question, “Which slit did the photon or electron go through?”
cannot be answered. According to quantum mechanics, the question
does not make sense unless an experiment is performed to measure
which slit the photon or electron goes through. It is a difficult measurement
to perform in practice, but it can be analyzed in principle.
Such an experiment is called a “thought experiment.” The result of
the analysis is that if a measurement determines which slit the photon
or electron goes through, the interference phenomenon is destroyed,
and the pattern on the screen is the result of the sum of the patterns
with a single slit open at a time. In Figure 13.1 we illustrate the
diffraction pattern after a wave (of light or electrons) passes through
a single slit. We also illustrate the interference pattern after the wave
passes through two slits.
If a two-slit interference pattern is observed, one cannot say that
the photons or electrons “really” go through either one slit or the
other. They act as waves that pass through both slits at the same
time. Our intuition does not allow us to “understand” how photons
and electrons can act both as waves and particles. There is no inherent
contradiction in the theory of quantum mechanics, as far as
we know, and furthermore, the calculations of quantum mechanics
lead to predictions that agree with experimental measurements. But
the human mind does not seem to be able to comprehend what is
“really” going on.

I don't understand why we can't answer which slit the particle when through. What else could it have gone though? This is probably a terribly literal way of viewing the event, but the whole concept is pretty fuzzy to me.

I also don't understand the significance of entanglement. If two observers agree on the same axis when total spin is 0, this seems incredibly obvious. If the axises are then changed to be perpendicular of each other, the probability of prediction is 50%. Again, this seems very obvious, and insignificant.

Thanks in advance to those who give wisdom.

 

[The_Duck]

I don't understand why we can't answer which slit the particle when through. What else could it have gone though? This is probably a terribly literal way of viewing the event, but the whole concept is pretty fuzzy to me.

The particle certainly passed through the barrier by going through the slits, but the point is that it has no single definite path over time intervals when its position is not being measured.

I also don't understand the significance of entanglement. If two observers agree on the same axis when total spin is 0, this seems incredibly obvious. If the axises are then changed to be perpendicular of each other, the probability of prediction is 50%. Again, this seems very obvious, and insignificant.

The weird behavior occurs not when the measuring devices are aligned, or when they are perpendicular, but for angles between 0 degrees and 90 degrees. In this case the correlation measured is slightly bigger than you would expect from naive classical ideas.

 

[enceladus_]

The weird behavior occurs not when the measuring devices are aligned, or when they are perpendicular, but for angles between 0 degrees and 90 degrees. In this case the correlation measured is slightly bigger than you would expect from naive classical ideas.

Ahh, ok then. I wondered about angles between 0 < x < 90 but my book didn't mention them at all.

The question, “Which slit did the photon or electron go through?”
cannot be answered. According to quantum mechanics, the question
does not make sense unless an experiment is performed to measure
which slit the photon or electron goes through. It is a difficult measurement
to perform in practice, but it can be analyzed in principle.
Such an experiment is called a “thought experiment.” The result of
the analysis is that if a measurement determines which slit the photon
or electron goes through, the interference phenomenon is destroyed,
and the pattern on the screen is the result of the sum of the patterns
with a single slit open at a time.

Could you possibly explain this as well? Thank you for your explanations.

 

[sophiecentaur]

First lesson about photons is that they are in no way like little bullets. They are a completely new type of entity which involves QM from start to finish. So 'the way they go through holes' is just not explicable in familiar terms. The diffraction / interference mechanism can be described in terms of the probability of a photon turning up at a certain point on the projection screen. But the sums involve exactly the same functions as when you do it using the wave model so why not do it using straightforward wave theory?

Any experiment which is designed to see which slot the photon went through will, of course, be affecting any photon (or the portion of any photon) that might have gone through the slot. Any photon that is detected as going into the slot will be destroyed and therefore can't contribute to any interference pattern.
From the wave point of view, if you imagine a detector that only partially blocked one slot then the pattern you would get would be the same as for two unequal width slots - namely a set of fringes in which the minima / nulls are just not as deep. This is a combination of a perfect set of deep fringes diluted by a broad, almost omnidirectional pattern which is produced by the extra bit on the un-occluded slot. In photon terms, the detector makes a random selection between photons that can go through it untouched - taking part in the interference phenomenon and photons which are not part of the statistics of the interference because, being detected, they 'had to have' gone through that slot. An equal number will get through the other slot and form an almost omnidirectional distribution on the projection screen because the can only have gone through that one slot. Result: an interference pattern with filled in nulls.

I reckon it's easier to stick with the model that works best in any situation. Let's face it, we are all quite happy to say that the photoelectric effect can only be described in terms of photons - so why not be selective about the way we treat interference and say it's a wave thing?

 

[movazi]

I appreciate answer to few questions :

1. When observed we get two lines, when not observed we get interference. But isn't the interference pattern on the screen an observation as well ?

2. When sending an electron ONE at a time, we can still get interference pattern, which raises the claim that quantum particles are waves as well. But if we send water waves ONE at a time (i.e. one cycle of the wave only ) we will not get interference pattern. Is there a way to send these particles with one cycle of their wave only ?

3. If we could only observe billiard balls by using other billiard balls then obviously the results would be completely messed up. Is this not the main problem here as far as observation goes ? (that I understand is why Heisenberg said you can not measure both the momentum as well as location of an electron, i.e. if you measure the location then the light photons have already effected the momentum)

 

[enceladus_]

Many thanks for the answers guys. I was told to check out a video by Dr. Quantum, and he mentioned that if one observes an individual particle entering a slot, its behavior is entirely different. Is this due to the Uncertainty Principle? If we know the exact position of a particle then our error in ρ is >= to h/2.

 

[sophiecentaur]

I appreciate answer to few questions :

1. When observed we get two lines, when not observed we get interference. But isn't the interference pattern on the screen an observation as well ?

2. When sending an electron ONE at a time, we can still get interference pattern, which raises the claim that quantum particles are waves as well. But if we send water waves ONE at a time (i.e. one cycle of the wave only ) we will not get interference pattern. Is there a way to send these particles with one cycle of their wave only ?

3. If we could only observe billiard balls by using other billiard balls then obviously the results would be completely messed up. Is this not the main problem here as far as observation goes ? (that I understand is why Heisenberg said you can not measure both the momentum as well as location of an electron, i.e. if you measure the location then the light photons have already effected the momentum)

In what way does this relate to QM?
A single impulse will not interfere with itself because the coherence length is just one cycle, for a start. A single impulse of a water wave is not a Quantum Particle and a photon is, by no means, a single cycle of an EM wave. Discussing the 'extent' of a photon is pretty meaningless, aamof. You are falling into the deadly trap of trying to picture a photon or an electron in your own familiar terms. Introducing de Broglie waves doesn't help the argument / issue. The de Broglie wavelength of an electron is not 'how big' the electron is, on the way through the diffracting structure. Billiard balls are not quantum particles so they are not relevant here.

What we observe on the screen is, of course, a measurement but it is measuring the result of the two slit interference. If you removed the screen and put another screen behind it, you would get a new interference pattern. If you removed only parts of the first screen, the pattern on the rear screen would not be the same as without the first screen - so a measurement on the way will still have an effect on the subsequent pattern.

 

[DrChinese]

I appreciate answer to few questions :

1. When observed we get two lines, when not observed we get interference. But isn't the interference pattern on the screen an observation as well ?

2. When sending an electron ONE at a time, we can still get interference pattern, which raises the claim that quantum particles are waves as well. But if we send water waves ONE at a time (i.e. one cycle of the wave only ) we will not get interference pattern. Is there a way to send these particles with one cycle of their wave only ?

3. If we could only observe billiard balls by using other billiard balls then obviously the results would be completely messed up. Is this not the main problem here as far as observation goes ? (that I understand is why Heisenberg said you can not measure both the momentum as well as location of an electron, i.e. if you measure the location then the light photons have already effected the momentum)

Welcome to PhysicsForums, movazi and enceladus!

sophiecentaur has already answered, I thought I might add a comment or two.

1. The question is whether you know which slit the particle passes through or not, in principle. The final result is observed of course, but you have the option of learning the slit as well.

2. You can send particles through one at a time.

3. The uncertainty principle has something to do with it, yes, but not in the manner you are saying. There are a number of ways to learn the which-slit information, and some of those do not involve disturbing the particle stream in the manner in which the HUP is a factor. An example is using polarizers in front of each slit. No interference is created when they are perpendicular, but there is interference when they are parallel.

 

[movazi]

Is it true that sending single atoms through the double slit will have the same results as sending electrons ? If so, then how about sending molecules ? I mean at what stage does this behavior stop ?

I assume all electrons in universe are exactly the same. Is this not strange ? Is it possible that we are dealing with only one electron in universe ? One that is everywhere at the same time ?

Sophiecentaur says it is not possible to send only one cycle of a photon wave. Is it because we can not do it yet or is it because the idea/suggestion itself does not make sense in the first place ?

If we observe the electrons after they pass the slits we get interference.

What do we get if we observe which slit the electron went though from the screen itself (i.e. looking from behind a semi transparent screen to see what is going on ?)

Sorry if I am throwing silly ideas, I am new to this fascinating paradox.

 

[jtbell]

Is it true that sending single atoms through the double slit will have the same results as sending electrons ? If so, then how about sending molecules ? I mean at what stage does this behavior stop ?

We don't know precisely where this behavior stops. The equivalent of double-slit interference was done with buckyballs (C₆₀ molecules) several years ago, perhaps with even larger things by now.

 

[sophiecentaur]

Is it true that sending single atoms through the double slit will have the same results as sending electrons ? If so, then how about sending molecules ? I mean at what stage does this behavior stop ?

I assume all electrons in universe are exactly the same. Is this not strange ? Is it possible that we are dealing with only one electron in universe ? One that is everywhere at the same time ?

Sophiecentaur says it is not possible to send only one cycle of a photon wave. Is it because we can not do it yet or is it because the idea/suggestion itself does not make sense in the first place ?

If we observe the electrons after they pass the slits we get interference.

What do we get if we observe which slit the electron went though from the screen itself (i.e. looking from behind a semi transparent screen to see what is going on ?)

Sorry if I am throwing silly ideas, I am new to this fascinating paradox.

This phrase has no meaning, I'm afraid - and I wouldn't have used it. Photons are not waves or bits of waves - which is one of those essential things about QM. A wave is not 'made up of' a string of photons.

It is only a "paradox" if you want to stay in the classical world; in which case it is nonsense rather than a paradox. QM says that, if you measure the presence of a particle going through one of the slits then you have resolved the question of which slit so there will no longer be interference for that particular particle. You will only get interference at the destination screen when there is the possibility that the quantum particle can be regarded as having taken a path through either slit. But the concept of it having actually gone through a particular slit is, itself, not in the spirit of QM.

 

[movazi]

This phrase has no meaning, I'm afraid - and I wouldn't have used it. Photons are not waves or bits of waves - which is one of those essential things about QM. A wave is not 'made up of' a string of photons.

If photons are particles yet somehow manage to go through both slits then where does the interference pattern come from ?

And to throw away classical physic's thinking means there are no set rules in the quantum world, i.e. everything goes, in which case why science is even trying to figure it out ?

Is there a definite answer as to at which point the wave/particle behavior stops ? Jtbell says C60 molecules or even larger ones still have double slit issues :- ) This behavior obviously stops at some point.

And if large molecules behave this way then why should'nt a grain of sand or a tennis ball ?

 

[DrChinese]

1. If photons are particles yet somehow manage to go through both slits then where does the interference pattern come from ?

2. And to throw away classical physic's thinking means there are no set rules in the quantum world, i.e. everything goes, in which case why science is even trying to figure it out ?

3. And if large molecules behave this way then why should'nt a grain of sand or a tennis ball ?

1. The pattern comes from the interaction of the possible paths the particle takes. The probabilities add in some spots, but decrease in others.

2. Science works according to rules regardless, doesn't matter if classical or not. If the model is useful, that is enough.

3. Theoretically you could diffract larger objects. However, the formula shows that the interference effect is inversely proportional to size. So the effect vanishes quickly as compared to accuracy.

 

[bohm2]

I thought you might find this experiment useful as it came out recently (relatively similar experiments have been done previously). The linked movies (third link below) are pretty cool:

Electrons Behaving Like a Particle and a Wave: Feynman's Double-Slit Experiment Brought to Life
http://www.sciencedaily.com/releases/2013/03/130313214031.htm

Controlled double-slit electron diffraction
http://iopscience.iop.org/1367-2630/15/3/033018/pdf/1367-2630_15_3_033018.pdf

Movies:
http://iopscience.iop.org/1367-2630/15/3/033018/media

Feynman's double-slit experiment gets a makeover
http://physicsworld.com/cws/article/news/2013/mar/14/feynmans-double-slit-experiment-gets-a-makeover

 

[NegativeDept]

I don't understand why we can't answer which slit the particle when through. What else could it have gone though? This is probably a terribly literal way of viewing the event, but the whole concept is pretty fuzzy to me.

Many (most?) quantum physicists consider this experiment the single most fundamentally confusing thing about quantum theory. A huge number of thought problems and real experiments have been performed based on it. (Even I got into the game by writing two lesser-known variations.) Here are some famous examples:

Teams at UT Vienna and MIT did the double-slit experiment with neutrons

Others sent an entire Carbon-60 "Buckyball" through a double-slit experiment; PhysicsForums discussions ensued.

Feynman's sum-over-all-paths method: "the particle goes whichever way it damn well pleases."

The de Broglie-Bohm "pilot wave" theory still starts arguments

Everett's many-worlds interpretation was mostly ignored, but is now taken very seriously

Wheeler's "delayed choice" experiment is even more confusing (and experimentally tested!)

I think the closest we have to a consensus is: nobody understands the double-slit experiment. I'm confident Feynman would agree.

 

[movazi]

One of the links you guys listed shows a wave pattern even when the electron goes through a single slit. I gather that if we do observe then the wave pattern will collapse here as well. But in a single slit we already know where the electron went through !
So what the observation has to do with it ?

Then take this observation phenomenon when two ships pass each other at speeds close to light. If there is no frame of reference then who is to say which one is moving and which one is not ? So each ship would observe the clock in the other chip going slower (or faster). So is it now correct to say that the mere observation of the other ship influences time ??

 

[sophiecentaur]

One of the links you guys listed shows a wave pattern even when the electron goes through a single slit. I gather that if we do observe then the wave pattern will collapse here as well. But in a single slit we already know where the electron went through !
So what the observation has to do with it ?

Then take this observation phenomenon when two ships pass each other at speeds close to light. If there is no frame of reference then who is to say which one is moving and which one is not ? So each ship would observe the clock in the other chip going slower (or faster). So is it now correct to say that the mere observation of the other ship influences time ??

I think we should deal with one thing at a time. SR is for another thread, I think.

When a particle is considered as going through a single slit, that slit must have a finite width - or nothing will get through. Considering it as a wave phenomenon, we just need to deal with the diffraction pattern of a single slit, which is the well known sin(x)/x pattern. There is no need to go further but, as you insist on the alternative, particle explanation I can just say that the photon (which has no actual 'extent') can take many paths through the slit and the probability function of where it will turn up is the same sin(x)/x. The process of "observing" the particle on the way through a single slit would take the form of narrowing the slit. This would exclude some of the photons - you could even imagine a thin light sensor down one edge of the slit which would actually 'observe' the photons which could be considered as hitting it. The previous 'diffraction' pattern is disrupted by doing this and ends up as a wider sin(x)/x function. The limiting case of an infinitely thin slit is an omnidirectional pattern (over +/- 90^o) because the possible destination of the particles is anywhere.
Imo, it is so well established that one can analyse these situations in terms of either waves and particles that it is hardly worth the effort of going through the agony of using the less convenient way through in every particular case. It isn't as if you are likely to find a case where it actually doesn't work. If you ever think you've found a paradox here then you should first examine your own argument before presenting it as an example where the Science doesn't work. Bigger brains then yours and mine have established things pretty well and it would need an even bigger brain to shake these foundations. Having said that, one of those could come along at any minute - but it won't be me and it probably won't be you either.

 

[jtbell]

One of the links you guys listed shows a wave pattern even when the electron goes through a single slit. I gather that if we do observe then the wave pattern will collapse here as well. But in a single slit we already know where the electron went through !

We know the electron went through the slit, but we don't know whether it went through the top part of the slit, or the bottom part, or the middle. There are an infinite number of positions across the width of the slit. To get the total amplitude for going through the slit, we have to integrate (add) the individual amplitudes for going through all the individual positions.

Mathematically, it's exactly like calculating the single-slit diffraction pattern for light.

 

[movazi]

jtbell

I do not see why it should matter if it went through upper or lower portion of the slit, that should not create a wave pattern. The experiment says that if individual atoms are shot through the single slit we get a wave pattern. I assume if we observe the atoms then we then get a single line pattern (as indeed some of the atoms went through the upper or lower portion of the single slit). So why they even had to do a double slit experiment ? In this particular experiment there is a paradox already in a single slit ! Sophie
I am not trying to solve this thing :-) I am merely trying to just understand the paradox :-)

 

[sophiecentaur]

jtbell

I do not see why it should matter if it went through upper or lower portion of the slit, that should not create a wave pattern. The experiment says that if individual atoms are shot through the single slit we get a wave pattern. I assume if we observe the atoms then we then get a single line pattern (as indeed some of the atoms went through the upper or lower portion of the single slit). So why they even had to do a double slit experiment ? In this particular experiment there is a paradox already in a single slit ! Sophie
I am not trying to solve this thing :-) I am merely trying to just understand the paradox :-)

What paradox?

BTW, We normally talk in terms of vertical slits and a diffraction pattern of vertical fringes - yet you seem to be introducing the idea of "upper and lower portion" of the slit. This is treating the slits as two dimensional and a 'tall' slit will have such a big aperture that the diffraction effect in a vertical plane will be negligible. It is better to confine your thoughts to a one dimensional case until you have that sorted out. (Perhaps I have got this wrong though(?))

On a practical level, the reason for doing the two (infinitely narrow) slit theory and experiment first is that it can be reduced to a simple sum of two vectors at any point on the 'screen'. If you pile in with the analysis of a finite width of slit then you need to integrate over the whole width of the slit and that involves an added level of complication, which is fine - but one thing at a time is best.

But, wherever you want to take this, there are two possible ways of viewing photons (or any other quantum particles). There is no point in expecting these things to go through holes in a familiar way.
You just need to come to terms with the fact that wave behaviour is far better explained by viewing Photons as part of a wave and that phenomena like the photoelectric effect are better explained by regarding Photons as particles. But there is one MASSIVE CAVEAT when you want to talk of Particles and that is that they are nothing at all like little bullets and that picture of them will lead you up the creek. I only wish that 'they' had never introduced such a loaded term as 'particle' and that they had invented a new term, for the sake of everyone who has ever been anywhere near QM. Once a particle starts to reveal its quantum nature by, for instance, 'orbiting' the nucleus of an atom or encountering a small space to go through then it (even a buckyball) ceases to be as you'd expect. You have to chuck out your intuition at that stage and go through Alice's looking glass. (Perhaps that's your "paradox")

 

[movazi]

Sophie
What you say reminds me of my Rabi, he also plays with words when he gets stuck and interprets the bible according to what is convenient : -) . I mean the damn thing acts both as a wave and as a particle depending on whether it is being watched or not ! A buckyball does it too but not a heavy insulin molecule. You send it through one slit only and you still get a wave pattern ! Something is going on here that Isn’t explained easily and as E=MCC himself once said : if you can’t explain it to a seven year old then you probably don’t understand it well enough (I realize there are various theories on the table but none has been reduced to scientific fact).
To say it acts as probability and the pattern comes from possible paths the element could have taken is a clever play with words. To say we should throw away the way we look at things may be correct but then how exactly should we start looking at them ? (the new way to look at things must still make sense or we might as well throw away the whole scientific way of thinking and go back to what the Rabi says).

 

[sophiecentaur]

Sophie
What you say reminds me of my Rabi,

That made my day!
Let me put this a different way. I imagine you know about algebraic equations. Many of them do not have solutions involving Real numbers. You absolutely have to introduce Imaginary numbers if you are ever going to solve even a simple equation like x²= -1.
No amount of insisting that you want an answer that doesn't involve something strange and confusing will allow you to progress further beyond the well known test b²>4ac (which is what we did when we first learned about quadratics.
It is strange that one never hears of people 'demanding' answers to Maths queries in terms of the Maths they already understand. They are quite content to say that they must either learn and accept the next step or just say "it's too hard guv and that's my limit".
Why, then, do you assume that someone will ever come up with an explanation for something like particles exhibiting diffraction effects which involves stuff that you can accept in terms of what you already know and love?

The quote about the seven year old child is not really in context. The fact is that it may be very difficult to give a seven year old child an answer that will satisfy them and yet will not conflict with what they later find to be true. He was not implying that you should be able to give a seven year old a complete answer but an appropriate one (not "because I say so"). You are trying to wear three hats at the same time for this problem. You want to have a "seven year old's" answer but then scrutinise that answer from a "seventeen year old's" point of view and then expect that to be sufficient for the "twenty seven year old", with a doctorate.

You are surprised that diffraction effects are limited to certain particles. If you consider the problem of producing optical diffraction, just in terms of waves, you run up against exactly the same situation. Initially, we are told that you need a 'coherent' source to get a diffraction pattern. We had no lasers when I was at school and the best we could hope for was 'monochromatic' light from a gas discharge tube. You will probably only have been shown diffraction of laser light and the practicalities may not have been pointed out as important to you. We later learned that 'how coherent' the source is will limit the range over which the diffraction can be observed. The smallest particles are the nearest to 'coherent'; they will have few possible quantum states are and the bigger particles will have progressively less coherence because their many possible quantum states. The conditions for buckyball diffraction will be very difficult to achieve and this may, in fact, be a real practical limit. Time will tell.

These are not 'Rabbi answers'. They are looking forward and not backward to ancient scripture. I am not just playing with words here but saying that you need to think differently about the problem from what you know already.