Is wave / particle duality linked to superposition?

[rede96]

I was watching a MIT opencourseware video on quantum mechanics. The first video is on superposition. The link is here:
http://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/lecture-videos/lecture-1/

In short the lecture shows a series of experiments done on electron spin in the X, Y or Z plane. He refers to them as 'Hardness' and 'Colour', which I am assuming refers to up and down spin in the Y axis and and left and right spin in the x-axis for example.

Anyway, one of the experiments (around 47 mins in) takes electrons of a know spin state, (e.g. 'Up' in the Y axis) and puts them through a device that tests for a different spin axis (e.g. left and right in the X axis). Depending on the what spin is detected the electron can take either of two paths, which then merge via the use of mirrors before the electron enters a final device that tests for the original spin state (e.g. Up and down in the Y axis)

The expected results are that the final device should detect 50% of the electrons in either the up or down state, but instead the results are 100% 'Up' spin state for example. However by blocking off one of the paths and repeating the experiment, the results change to 50% up and 50% down.

The lecture shows that the electron couldn't have taken the 'left' path, it couldn't have taken the 'right' path and it couldn't have taken both paths so it exists in a state of superposition.

My question... Is possible that the wave / particle nature of an electron plays a part in this outcome? So the 'particle' part of the electron may take one path, but the 'wave' part of the electron takes the other and so it interferes on itself. Hence the strange result. And when blocking one of the paths, this doesn't happen so the outcome is what may be expected when running the experiment with two devices in series without the mirrors?

 

[Nugatory]

Is possible that the wave / particle nature of an electron plays a part in this outcome? So the 'particle' part of the electron may take one path, but the 'wave' part of the electron takes the other and so it interferes on itself.

No.
There isn't a "wave" part of the electron and "particle" part of the electron. There's a single quantum object which is neither a wave nor a particle, but has some properties that we naturally associate with particles and other properties that we naturally associate with waves.

Although it's a popular metaphor and an OK visualization tool, "wave/particle duality" isn't a solid enough idea to build new theories on top of - it's more a user-friendly approximation of what quantum mechanics really says. Pillows are fuzzy, and tables have four legs, but when you encounter a sheep (which is fuzzy like a pillow and has four legs like a table) you aren't going to find the concept of "table/pillow duality" very helpful.

 

[rede96]

There isn't a "wave" part of the electron and "particle" part of the electron. There's a single quantum object which is neither a wave nor a particle, but has some properties that we naturally associate with particles and other properties that we naturally associate with waves.

Ah ok, thanks. But as you said there are wave and particle like properties of 'particles'. Another example would be like the double slit experiment. If you close a slit, then it acts more particle like etc.

EDIT: Sorry question should have read as follows:

So I guess my question was do we know enough to rule out this property which is responsible for what we see in the double slit experiment as having an effect in what we see with spin / superposition?

 

[Nugatory]

A
So I guess my question was do we know enough to rule out this property which is responsible for what we see in the double slit experiment as having an effect in what we see with spin / superposition?

All superpositions depend on the fact that the wave equation is a linear differential equation... and the most particle-like behavior of all is having a specific position and when a quantum object doesn't have a particular position it is because its state is a superposition of position states so superposition has something to do with how it isn't acting like a particle at the moment... and of course superposition is essential to the double-slit experiment. So yes, these concepts are all connected together.

But if you want to understand it you won't throw words at it, you'll look at what the math says.

 

[rede96]

so superposition has something to do with how it isn't acting like a particle at the moment...

In the simple experiments done where they are testing for different spin states, say just Up or Down, I'm guessing it is pretty much acting as a particle? Or in other words, those spin experiments aren't testing for the wave property of the electron. It just sends an electron through a magnetic field and depending on it's angular momentum it either comes out the Up or the Down aperture.

It's only when the mirrors are added as described previously that weird things start to happen. So superposition only comes into play in experiments that allow for the wave / particle properties to both have an effect on the outcome.

Which leads me to understand that it always has a wave and particle nature, but it just depends on what we are measuring as to how that manifests itself.

Excusing my poor terminology but is that a correct way to think about it?

 

[Nugatory]

In the simple experiments done where they are testing for different spin states, say just Up or Down, I'm guessing it is pretty much acting as a particle? Or in other words, those spin experiments aren't testing for the wave property of the electron... It's only when the mirrors are added as described previously that weird things start to happen. So superposition only comes into play in experiments that allow for the wave / particle properties to both have an effect on the outcome.

No. Superposition is clearly apparent in electron spins. Any spin state can be written as a superposition of spins along a different axis (spin-up is a superposition of spin-left and spin-right, spin-left is a superposition of spin-up and spin-down, all of those states are also superpositions of spin-3-degrees-left and spin-187-degrees-right, those two states can be written as superpositions of up/down or left/right, and so forth). It's easy, in principle, to perform measurements that demonstrate these superpositions.

In practice, it's easier to work with photons because they don't interact with air while experiments with electrons generally require working with a vacuum chamber and high voltages. If you put a vertically oriented polarizing filter in front of a horizontally oriented filter and send a beam of photons (note that this is "photons" not "light waves" - we're talking particle behavior here, not wave behavior) at it, none will get through. If you add a another filter at a 45-degree angle between these two filters, one in eight of the photons will get through - the additional filter increases(!) the number that can pass. It's impossible to explain this behavior unless 45-degrees is a superposition of vertical and horizontal.

So I'm going to repeat myself: Wave/particle duality is not what really happening, and trying to understand things in those terms is just wasting your time.

You might want to give Giancarlo Ghirardi's book "Sneaking a look at god's cards" a try.

 

[Schneibster]

First, @Nugatory, pillow/table duality may not be very useful, but I found it quite amusing, particularly when applied to sheep.

In the simple experiments done where they are testing for different spin states, say just Up or Down, I'm guessing it is pretty much acting as a particle?

Mmmmm, it's actually more a matter of them treating spin states in a particle-like manner, specifically, as having discrete values. To treat them in a wave-like manner would be what superposition is. But you must distinguish between treating a parameter of a particle in a wave- or particle-like manner from it having anything to do with the, pardon the expression, "particleness" of the particle.

Or in other words, those spin experiments aren't testing for the wave property of the electron.

Again, they're not testing the electron; they're testing the spin of the electron. A whole particle has many properties: spin, mass, charge, position, momentum, and more. When you deal with spin angular momentum you are dealing with only one of those properties. And that ignores the fact that while spin on a single axis can have a particle-like nature, i.e. discrete values like Up or Down, if it does then the spin on all other axes is undefined due to Heisenberg uncertainty; all those other spins are then wave-like (i.e. in superposition).

It just sends an electron through a magnetic field and depending on it's angular momentum it either comes out the Up or the Down aperture

Specifically its spin angular momentum on a single axis, that being the axis measured by the magnetic field.

It's only when the mirrors are added as described previously that weird things start to happen. So superposition only comes into play in experiments that allow for the wave / particle properties to both have an effect on the outcome.

No. Remember that all the spins on other axes are in superposition. This will be true for any parameter that is complementary to another parameter under Heisenberg uncertainty. What makes it weird is when you measure the spin on another axis, throwing the spin on the previously measured axis into superposition. That's ultimately why the experiment has the outcome it does. A very simple optical experiment that shows the same thing is the three polarizers experiment, which I recommend to your attention: https://www.physicsforums.com/threads/three-polarizers.500100/ @JesseM's post #3 on that thread has a couple good links in it.

On edit: I notice @Nugatory got in before me with the three polarizers experiment. It's very revealing.

Which leads me to understand that it always has a wave and particle nature, but it just depends on what we are measuring as to how that manifests itself.

That's true; once you see how I can agree with this and disagree as above, you'll be a long way toward grokking uncertainty, which is the intent of the lesson you're reviewing.

Excusing my poor terminology but is that a correct way to think about it?

You're getting there. Keep going the way you're going!

 

[Schneibster]

Wave/particle duality is not what really happening, and trying to understand things in those terms is just wasting your time.

I agree. What's really happening is Heisenberg uncertainty and resolution of a superposed parameter, along with de-resolution (technically, decoherence) of all complementary parameters.

 

[bhobba]

To treat them in a wave-like manner would be what superposition is.

Superposition simply expresses the fact pure states form a vector space. It's got nothing to do with treating them in a wave-like manner - whatever that is supposed to mean.

The full elucidation of, mathematically, what states are comes from Gleason's theorem:
http://www.kiko.fysik.su.se/en/thesis/helena-master.pdf

Thanks
Bill

 

[rede96]

It's impossible to explain this behavior unless 45-degrees is a superposition of vertical and horizontal.

I understood that with electrons, when the spin is tested along a certain axis, the test itself shifts the spin into the angle being tested. Or at least the test has an effect on the spin state of the electron. So does the polarisation filter have any effect on the polarisation of the photon? i.e. is changes the polarisation?

You might want to give Giancarlo Ghirardi's book "Sneaking a look at god's cards" a try.

Ok, thanks for that and thanks for your help. I'll do a bit more reading.

And that ignores the fact that while spin on a single axis can have a particle-like nature, i.e. discrete values like Up or Down, if it does then the spin on all other axes is undefined due to Heisenberg uncertainty; all those other spins are then wave-like (i.e. in superposition).

What happens with entangled particles? If I test one for spin in the x direction for example and get 'left' and the other in the y direction and get 'up' then don't I know the spin state for those two axis?

What makes it weird is when you measure the spin on another axis, throwing the spin on the previously measured axis into superposition. That's ultimately why the experiment has the outcome it does.

Ah ok, just so I understand this, is what you are saying that once I do the second measurement then the first measurement becomes obsolete in terms of current polarisation the photon?

You're getting there. Keep going the way you're going!

According to QM I already know everything there is about this topic, as it exists in state of superposition in my mind. I just can't find the right filter to access it! But thanks for your help.

 

[Nugatory]

What happens with entangled particles? If I test one for spin in the x direction for example and get 'left' and the other in the y direction and get 'up' then don't I know the spin state for those two axis?

It feels very natural to think that you do, but you don't. If it did work that way, then the correlations between spin measurements of the entangled pair would obey Bell's inequality; but experiments show that these correlations can violate that inequality.

If I measure one member of the entangled pair in the x direction, then I know what the result will be if I measure the other member in the x direction. But that's not the same thing as saying that the other member has that value of spin in the x direction whether I measure it or not.

 

[lox_and_whiskey]

No.
There isn't a "wave" part of the electron and "particle" part of the electron. There's a single quantum object which is neither a wave nor a particle, but has some properties that we naturally associate with particles and other properties that we naturally associate with waves.

Although it's a popular metaphor and an OK visualization tool, "wave/particle duality" isn't a solid enough idea to build new theories on top of - it's more a user-friendly approximation of what quantum mechanics really says. Pillows are fuzzy, and tables have four legs, but when you encounter a sheep (which is fuzzy like a pillow and has four legs like a table) you aren't going to find the concept of "table/pillow duality" very helpful.

Best explanation ever. lol @ table/pillow duality.