B The moment we observe superposition

1. Oct 23, 2016

Hi all,

I'm a computer scientist who has been getting an increasing fascination with quantum physics. I admit I am a novice in this respect. I had a question just for my own learning and understanding, not related to a class or anything like that. :)

In learning more about superposition and quantum states, I was wondering if someone can explain (in as layman's terms as possible :) ) if it's possible that one of the following is true regarding "superposition":
(1) At the moment we observe superposition, the "picture that we take" as evidence of superposition is itself taken too slowly and what we're seeing is actually analogous to an overexposed picture blur of someone moving quickly, i.e. they're really one thing existing in one place, but measured over too long a time it appears that they're in two places at the same time.
(2) alternatively, is it possible that these subatomic particles actually just move so fast that they "move faster than time moves" which is really all that superposition is, and that possibly using enough gravity to distort time this could be manipulated enough to slow down the superpositions enough to see discrete positions instead?

2. Oct 23, 2016

David Lewis

No. A photo of a fogbank is not the same as a photo that is blurry or out-of-focus.

3. Oct 23, 2016

Thanks for the quick response - I assume that answers (1) but not (2). Regarding your response, hmm a fogbank consists of separate particles, but isn't the idea of superposition that it's one thing, just in multiple places at the same time? Just wondering as the analogy doesn't make sense to me given that.

4. Oct 23, 2016

David Lewis

There are no pre-existing properties out there waiting to be measured. Superposition tells you what is possible. To bring possibility into actuality, you need a detector to pin it down.

5. Oct 23, 2016

Got it. So what I'm gathering here is that really the idea that something is in more than one place at the same time isn't necessarily true, but rather superposition suggests that there are various places something COULD be at a given time, not necessarily that it is in both those places at the same time.

6. Oct 23, 2016

Staff Emeritus
An object is never in two places at the same time in QM. Never.

7. Oct 23, 2016

David Lewis

A photon or electron must pass through two holes at once to create an interference pattern on a screen, for example, but otherwise you are correct, except that it’s not an ordinary probability function. It tells us where it could be if we measure it.
Otherwise where it is is undefined.

8. Oct 23, 2016

Thank you! This is very helpful and illuminates the whole thing for me. Cheers!

9. Oct 23, 2016

Staff: Mentor

We don't observe superposition.

A single "picture" (a better term would be "single measurement result") cannot provide evidence of superposition. We know that a system (more precisely, an ensemble of identically prepared systems) is in a superposition only by making many measurements and doing statistics on the results.

This doesn't make any sense.

It would help if you would give more details about the sources you are using to learn about QM. I suspect that they are pop science sources, which are not good ones to use.

10. Oct 23, 2016

Simon Phoenix

The formalism of QM, or the 'rules' if you like, can be interpreted in many different ways. As far as can be determined at the moment all of these various ways of looking at QM lead to the same experimental predictions. It's probably best to get an intro book (and I recommend "The Theoretical Minimum" by Susskind") and work through it to get familiar with the maths and how those rules get coded in the maths. If you try to figure out "what's going on" at too early a stage you'll get hopelessly bogged down. My advice would be to just accept the rules, work with them as a kind of recipe to begin with. Then when you have a good feel for the basic maths you can start to spend many a happy hour trying to figure out what the heck is going on

You can go surprisingly far with a smattering of elementary linear algebra, a bit of probability and some grasp of complex numbers - although to go further you'll have to add some more sophisticated stuff to your mathematical arsenal.

So to see whether your initial propositions make sense let's consider a 2 state system - and the archetypal example of this is the spin-1/2 particle. Spin is a fundamental quantum property that doesn't have any sensible counterpart in the classical world. If you need an initial picture then very, very crudely (and incorrectly) we can imagine a particle to be a sphere. Spin would then describe the sphere spinning about an axis - like the rotation of the earth about its axis. That picture turns out to be hopelessly incorrect though - so file it under "actually it's a rubbish picture, but it gives me somewhere to start from".

In fact any time you find yourself trying to 'picture' what things are, when you stray from the fairly narrow confines of the prescriptive rules, then associate the thought with a big red flag. It's not necessarily wrong to attempt to construct a picture, but if you find yourself doing so then do so with a bunch of alarm bells going off and big red flags waving.

QM associates a vector with a state - and we can prepare particles in known, definite, states. So for our spin-1/2 particle we can choose an axis - say spin-z, and prepare the particle in an 'up' state. We'd then associate the vector "up in the spin-z direction" to this particle. But it's a vector - so like any vector we can expand it in another basis. Spin-z up can be described as a sum of 2 spin-x states - in fact an equal sum of up and down states (vectors) in the spin-x direction. This is 'superposition'. So in your proposition we're trying to construct a picture in which our initial spin-z state is sort of flitting between the up and down spin-x states.

But we're dealing with vectors - so writing our initial state by picking one choice of basis is only one out of an infinite number of possible ways we can write things. We could also write our initial spin-z state as an equal sum (superposition) of up and down states of spin-y, for example. So in this new picture your proposition is saying that our initial state is flitting between spin-y up and down states.

But which is it? Is it a 'flit' between spin-x states or a 'flit' between spin-y states?

So you can see that your initial proposition isn't going to work - it's giving us a picture that makes less sense.

It's probably easier to put the maths around all these words - but I'm a bit of a novice with the LaTex code stuff and don't have time to do it at the moment - sorry. Hope my wordy explanation has helped clarify at least one thing that's wrong with your initial way of looking at things.

11. Oct 24, 2016

Thanks, this is also very enlightening! On some level I understand why pop science tends to be the go-to approach for many people to understand things like this; it requires a lot of patience and understanding to fully wrap one's head around all the detail and nuance here. :)​

12. Oct 24, 2016

Zafa Pi

We notice an interference pattern if we don't monitor which hole the photon passes thru. How do you know that it passes thru both holes at once?

13. Oct 24, 2016

David Lewis

That’s the only way a particle can interfere with itself.

14. Oct 24, 2016

Staff: Mentor

These statements are interpretations, not part of the basic theory of QM. Please bear in mind that interpretations are not the same as the basic theory, and discussion here should be focused on the basic theory.

15. Oct 25, 2016

Simon Phoenix

Yes, and even though often the mathematics involved in describing a given quantum system can be not too difficult, the subtleties and implications of QM can be quite alarming

In the quantum information field, a field that has grown massively over the last couple of decades, it is pretty standard to work with something called a qubit. This is nothing more than a 2-level system described quantum mechanically - it's one that only needs two states to be able to describe. So the spin-1/2 particle I mentioned above is kind of the archetypal example. The spin properties can be entirely captured (or coded, if you like) by working with 2 basis vectors (up or down in some specified direction is an example of 2 states that form a basis for this).

Think of taking a piece of paper and drawing a vector as an arrow on that paper - any journey from the tail to head of that arrow can also be represented as a sum of 2 other arrows - so $y$ units straight up from the tail, then $x$ units right gets us from the same beginning to the same endpoint. With a bit of experimentation you'll see that there are an infinite number of ways we can split our initial journey (the initial arrow) into 2 other arrows. With further experimentation you should be able to convince yourself that 2 is the minimum number we need (we can also do it with 3, or more, but in the jargon of linear algebra if we have 3, or more, mutually non-parallel vectors in a plane then they're not linearly independent). With a bit more experimentation still you can convince yourself that any initial journey you write down (an arrow of any length and direction drawn on the page) can be broken into a certain number of steps 'north' and a certain number of steps 'west'. So if we take 2 vectors 'north' and 'west' we'd say they form a basis, because any arbitrary arrow on the page can be written as a sum (superposition) of these 2, and 2 is the minimum number we need.

I suspect you probably know all that about vectors - but imagine if you were writing a pop science book - the target audience is likely going to include people who have a limited math background. It can't be assumed that words like 'vector' and 'basis' make any sort of sense to a reasonable fraction of your audience. It seems to me that getting the ideas of QM across to such an audience, getting some of the flavour across, whilst still maintaining strict rigour and not being a bit economical with the truth is a task of Herculean proportions. I take my hat off to all of those guys who attempt it!

I'm also going to disagree a bit with Peter here - whilst agreeing with what I think is the spirit of his comment. I think discussion of interpretations is important and useful. It helps us build a clearer picture of when and why our particular intuitions about QM can be on dodgy ground. We get a better understanding of the power of the basic formalism too by discussing the limitations and thorny issues of any given interpretation, at least in my opinion. It can all go horribly wrong and philosophical though which is why issues of 'interpretation' are partly clamped down on. I've done QM calculations in one given interpretation (a kind of collapse interpretation) for so long now that I often don't even know when I'm doing it

Trying to write things on here in a strictly 'interpretation free' manner is a bugger of a job

But I think your initial question was interesting. You proposed an interpretation and it's instructive (I think) to see why it doesn't work. It's not entirely daft to think of a quantum superposition as describing something that's flitting between the states in the superposition so fast that we have to describe it as a superposition, even though it's never really 'in' that superposition - but figuring out why it's actually not sensible is useful and instructive..