# B What is Quantum Interference?

1. Dec 22, 2017

### TheQuestionGuy14

What exactly is quantum interference (eg. Superposition, Double Slit Experiment) and what causes it?

I've heard some crazy explanations that its other universes interacting with ours, but what is actually causing quantum interference?

2. Dec 22, 2017

### Mentz114

In classical probability we can write ( if A and B are from a complete set of outcomes) $P( A\ or\ B) = P(A) + P(B)$. in quantum mechanics the wave functions are amplitudes ( 'square roots' of probability) and $P(A) = |\psi_A|^2$. The amplitudes can be added together and then squared. So $P(A\ or\ B) = |\psi_A + \psi_B|^2$. When we add those amplitudes together some parts may cancel out which affects the probabilities of outcomes. This is quantum interference.

It can happen whenever wave functions are split and recombined and amplitudes are added, like the double-slit experiment.

Last edited: Dec 22, 2017
3. Dec 22, 2017

### TheQuestionGuy14

So... erm... What does this mean in words instead of mathematical formulae?

4. Dec 22, 2017

### MichPod

I guess, nobody knows.

You can, though, think that the world actually consists of some sort of waves which can interfere (i.e., with some simplification, each particle is a wave so the interference is not a problem).
This view is quite good, but you may then get other questions for which the answer is not yet clear.

So, in the end, "nobody knows".

5. Dec 22, 2017

### Staff: Mentor

At the beginning level the following is about as good as you can get:
https://www.amazon.com/QED-Strange-Princeton-Science-Library/dp/0691164096

Once you have done some basic QM ie an actual first course at university level then the following is a better explanation:
https://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

But still not perfect:
https://arxiv.org/abs/1009.2408

Physics can be funny like that. You learn one thing when you start, another when you do a bit more, and still another once you are advanced. Its a bit weird like that.

Overall however I am not a fan of how its usually taught - I think the following is a better way to get to grips with it:
https://www.scottaaronson.com/democritus/lec9.html

Thanks
Bill

6. Dec 22, 2017

### Staff: Mentor

We do - its just not common-sensical and can only really explained mathematically.

Thanks
Bill

7. Dec 22, 2017

### Staff: Mentor

A lot of beginning students think that way and at that level it allows them to get by. The link I gave to the MIT lecture is much closer to what QM actually is.

In fact sometimes they never get over it leading to myths in QM:
https://arxiv.org/abs/quant-ph/0609163

Thankds
Bill

Last edited: Dec 24, 2017
8. Dec 23, 2017

### TheQuestionGuy14

So, if we do know, and its not other universes, does this mean the Many Worlds Interpretation is no longer viable?

9. Dec 23, 2017

### Staff: Mentor

MWI is as viable as ever - it's just a different way of describing the same math, and as @bhobba has already pointed out, the description of quantum interference is in the math.

10. Dec 23, 2017

### Lautaro

min. 3.25
John Preskill

11. Dec 23, 2017

### Staff: Mentor

This is the issue using a word like knowing - it has all sorts of baggage philosophers will argue about endlessly.

The more precise answer I will give, that avoids such issues, is physics is a mathematical model. In QM we know the why of that model - it has to do with what are called generalized probability models - QM is just the next simplest one after ordinary probability theory. Now what does it mean. Physicists have been trying to answer that one for a long long time without success. We have all sorts of possible answers, like Many Worlds, but unfortunately no way to experimentally tell the difference. This is hardly surprising since they were all concocted to be the same as the formalism which everyone agrees on, and as I explained we have a rather good idea of why it is that way - mathematically.

So - where does that leave your query - sorry to say - nowhere - its bogged down in so much philosophical baggage the exact answer is often unsatisfactory (ie a generalized probability model) or when we try to be more specific - as the other poster said - we don't know. Its maddening - but is not the only area like that. Although not as often discussed ordinary probability theory is exactly the same - but I will let you investigate that one yourself. In fact, John Baez thinks arguments about it are often simply the same arguments about probability in a different setting:
http://math.ucr.edu/home/baez/bayes.html

This is hardly surprising since we know QM is itself a generalized probability model so carries exactly the same issues with it - plus some others like Bell inequalities peculiar to QM.

Thanks
Bill

12. Dec 24, 2017

### vanhees71

You cannot express QT in words but only in math!

13. Dec 24, 2017

### TheQuestionGuy14

On the topic of Many Worlds, I have a question about it and its not really a big enough question to post a thread about it (I do ask a lot of questions; like my name suggests, sorry if I'm bothering you).

So, a lot of people say that every time you make any decision it makes a split universe. But I thought MWI was only about wave functions and quantum mechanics, not everday things? Is everyday decision making part of the interpretation?

14. Dec 24, 2017

### PeroK

If MWI applies to QM, then it must apply to "everyday" things.

15. Dec 24, 2017

### MichPod

16. Dec 24, 2017

### Staff: Mentor

Its the above link. The one you gave is the explanation of the double slit after a first course in QM. One generally uses the double slit to help motivate the usual QM formalism, but texts forget to go back and show how that formalism explains the double slit. It, at the beginning, is explained as a demonstration of how it sometimes is a wave so can go through both slits, interfering while doing so, and sometimes as a particle as indicated by flashes on a screen. But you have learnt in your QM course its not really a wave or a particle - its described by this thing called a quantum state that allows you to calculate the probabilities of observations. So we now need to use that to explain the double slit - which is what the paper does. Whats it is a demonstration of is the principle of superposition and the uncertainty principle. Directly behind each slit its in a state that gives that position with 100% certainty. With both slits open its in a state that is a superposition of being behind slit one or slit two. Consider slit 1 for a moment. We know its position with 100% certainty so we know nothing of it momentum. We haven't done anything to its energy so it still has the same speed, its now unknown momentum shows up in we do not know its direction. Where the flash occurs is a measurement of the direction, the probability of which, as the paper explains we can predict. Now we have both slits open and you get a superposition as explained before. You work through the same math as for a single slit, and low and behold you get an interference pattern. Its the same result as the wave-particle idea but an entirely different explanation.

IMHO you should not be learning and unlearning ideas - you should be told whats really going on from the start - and that's exactly what that MIT lecture does. Its not perfect, but better than the usual presentation IMHO.

Thanks
Bill

17. Dec 25, 2017

### vanhees71

18. Dec 25, 2017

### Staff: Mentor

We don't want to go through this one again.

You can certainly trust Feynman - so to the OP just use that.

In fact all the lectures are excellent.

What do they say to MIT students - get a copy and devour it. I have a copy, did just that and never regretted it.

Strangely though Landau - Mechanics had a stronger effect - this was my first exposure to the real power of symmetry - its life changing actually - at least for me.

Thanks
Bill.

19. Dec 25, 2017

### vanhees71

Indeed, getting exposed to Noether's theorem was one of the strongest impressions during my studies of physics. I think, I got introduced to it at the first time in the course lecture on classical analytical mechanics.

20. Dec 25, 2017

### MichPod

I am a bit confused as in Aaronson's lectures he did not mention MIT for what I can see.

But... anyway. How do you of Aaronson explain the interference pattern in the double slit experiment if not by waves? Say, we think of QM as of an alternative probability theory along the lines put by Aaronson in his lecture #9. And then what?

I definitely agree with you that things should better not be unlearned. I just do not understand well enough what you and Aaronson propose and besides I am not sure if this approach has a wide support. IMHO we are speaking of yet unresolved things on which there are many opinions and no any consensus. I'd be happy to learn I am wrong here.

21. Dec 25, 2017

### PeroK

In QM probabilities, or more precisely probability amplitudes, are complex numbers. It is sufficient, however, to consider them as being positive or negative, whereas, traditional probabilities are positive.

Aaronson explains this well but it terms of the double slit the heart of the matter is this:

Suppose the probability amplitude of a particle hitting the screen at a given point is:

$+0.1$ if slit one is open; and

$-0.1$ if slit two is open.

The probability, by the way, is the square of the amplitude.

Therefore, if slit one is open, the probability of hitting the given point is $0.01$. And, the same if slit two is open.

Bur, if both slits are open then the probability amplitude is $0.1 + (-0.1) = 0$. Hence, the probability of the particle hitting the given point is $0$.

The two probability amplitudes cancel out giving quantum interference.

In other words, if either slit is open, then the particle sometimes hits the given point, but if both slits are open, then it never hits the given point.

22. Dec 25, 2017

### MichPod

Ok, but how can we explain the change of the phase of the probability amplitude along the screen i.e. the interference strips?

And besides, having presented this nice variation of the probability theory with complex amplitudes, what can we say about what kind of reality stays behind, say, negative amplitudes? Is it that our theory works just as a calculation tool or because it corresponds more or less to some reality?

23. Dec 25, 2017

### PeroK

The change of phase is due to the nature of time evolution of a quantum system. That is why the complex amplitudes arise.

Reality, it seems to me, is what we measure. There are, incidentally, the same issues in classical gravitation, for example. How does the Earth know that the Sun is there? How does the Earth know the strength of the gravitational field and act accordingly? Both classical gravitation and QM are mathematical models that leave an underlying cause unexplained.

There is, however, one interpretation that is too bizarre. That is that a particle acts sometimes like a wave and interferes with itself and sometimes mysteriously turns back into a point particle!

24. Dec 25, 2017

### MichPod

For what I can see for myself now this picture brings not more understanding than early interpretations. Also, I cannot see how the probabilities of the measurements of other observables arise from it. I.e. if we interpret wave function as a probability amplitude of the coordinate measurement (as a pure math midel), this does not naturally resolve to the probabilities of the measurement of the momentum.
Now I personally do not like the idea of "quantum duality" either. Of course, saying that an electron may behave like a particle or like a wave is quite a poor science, even if it gives us right calculation results.

25. Dec 25, 2017

### PeroK

To understand these things you would have to learn QM, then all would be clear!

For example, if you do a Fourier transform of the position wave function you get the momentum wave function.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook