Entanglement question - how to prove that before one of a pair is measured, it's not well-defined?

Factual Questions
1

In his superb Ask the Particle Physicist thread (which I missed in January and only discovered today), Pasta gave this wonderful description of entanglement:

I have always wondered about this part of Pasta’s answer:

How does one demonstrate experimentally that the electron doesn’t have a well-defined spin until it’s measured, without measuring it? In other words, isn’t it the case that the only way you can prove it’s not well-defined is by interacting with it, i.e. measuring it, in some way, yet by doing so that would give it a definite value of spin (or whatever entangled property we’re looking at)? Obviously I’m missing something. Help! (please)

Thanks!

2

As no-one’s answered you yet, I’ll throw in my WAG, which is based on me trying to follow this explanation a minute ago.

Let’s say that our two detectors are set at arbitrary angles to the emitter.
If the particles already have an intrinsic spin as they’re emitted, we can make a simple prediction of what likelihood there is of correlation between the two detectors (detectors at any angle simply reporting opposite spins is a simplification, I think).
But what we actually get is a likelihood of correlation that implies that the particles somehow “knew” what angle the detectors were going to be at.

Which gives us (at least) 3 options:

  1. Particles can predict the future
  2. Particles can send FTL signals between each other
  3. Entanglement

Option 3 is the one most physicists go for. Although “something” might be said to happen FTL, it explicitly rules out useful info being sent, and therefore doesn’t affect relativity.

I think there are formats of option 1 which some theorists opt for. Obviously not quite as I’ve phrased it here, but some version of something being emitted into the past.

Oh and of course, option 2 isn’t completely out of the question in fact, though it probably breaks relativity.

3

Not that “it doesn’t affect relativity” is the reason for its popularity.
It is of course the simplest theory, that makes good predictions, that we currently have.

4

Are you familiar with the double-slit experiment? http://en.wikipedia.org/wiki/Double-slit

Essentially, you fire an electron beam (originally a photon beam, but electrons do it as well) at a screen through a wall with two small slits in it. Even if you fire one electron at a time, you get an interference pattern on the screen - indicating that the electron actually behaves as a wave and passes through both slits, constructively and destructively interfering with itself before reaching the screen. The position of the electron is not well-defined until it reaches the screen, where the position is “measured”.

If you put a detector on each of the slits, forcing the electron to take on a definite position before reaching the screen, the interference pattern disappears.

I don’t know exactly what experiment you can perform like this that involves spin instead of position, but I expect it will work the same way - you cause electrons to undergo some interaction that depends on their spin, measure the resulting state of the electrons after this interaction, and find that their behavior is incompatible with having a well-defined spin during the interaction.

5

:eek:

You just broke my brain.

6

Hmmm.

In the meantime, regarding the double slit experiment, I think I have the same problem - how do you know it’s not well defined unless you somehow observe, i.e. measure, it?

Same with spin and entanglement. How do you know there’s no well defined spin without observing it (i.e. measuring it, interacting with it, collapsing its wave) to have none (but thereby making it definite)?

And, thanks for the Bell’s theorem pointer.

7

You know the electrons’ positions are not well-defined at the slits because they produce an interference pattern on the screen. If their positions were well-defined, meaning they passed through one slit or the other like a marble or other macroscopic object, they would not produce an interference pattern. The interference pattern can only be produced if they act like waves, with no well-defined “position”, and pass through both slits at once.

When you force the electrons to have a well-defined position at the slits (either they pass through one of the slits or the other), they no longer produces the interference pattern.

At the point the electrons hit the screen, they are “measured”, so to speak, and their positions become well-defined. But you know that their positions were not well-defined when they passed through the slits, because that is the only way they can produce an interference pattern on the screen.

In short - you know the electron’s positions were not always well-defined because when you do observe them and cause them to have a definite position, you find them in places that they would not have gotten to if they had always had a definite position.

8

To the OP: This is an excellent question. Of course, one always could maintain that there are such things as well-defined but unmeasured (and potentially even unmeasurable) values of various kinds. The result is a bit more subtle than completely ruling that out, even if it is often described that way. The key issue, as noted above, is Bell’s theorem. Let’s illustrate this with a very loosely veiled analogy:

Imagine there are only two TVs in the world, one in NY and one in LA, far apart from each other. Each can be set to one of many channels. However, these TVs are so clunky that their channels can only be changed once every half hour, just at the stroke of the half-hour. Furthermore, in this dystopian future, there are precisely two kinds of programs: half-hour live comedies and half-hour live dramas (each also starting right on the stroke of the half-hour, naturally).

Yeah, so what? So you and your buddy, sitting on the two coasts, keep idly flipping between The Big Three (CBS, NBC, and ABC), trying to make the choice of which channel to watch as randomly as you can at the last moment, and then later comparing results over the phone. And over time, you notice something quite interesting: whenever you both tune into the same channel, you see the same program. However, overall (including the times you watch the same channel and the times you watch different channels), you tend to see programs of the same genre only about half the time.

So what? Well, I’ll draw the consequences out in a later post, but bonus points to anyone who can spot off the bat what’s so interesting about this situation…

9

Tentatively, I’ll take a stab at those bonus points; if the probability of you seeing the same genre were really .5, then the probabilities don’t quite add up.

With two kinds of programming and three channels, at any time at least two channels are showing the same kind of programme. My sums seems to indicate the chance of both TVs displaying the same kind of programme should be 2/3.

10

Excellent, you’re on the right track. But you’ve made some unwarranted assumptions… Certainly, if it were the case that the three channels each selected from comedy or drama at uniform random independently from everyone else’s choices, then the probability of the two TVs matching would be 2/3; since the actual observed facts are that the TVs match only 1/2 the time, we can rule that particular probability distribution out as not accurately modelling the empirical statistics. But that’s not the only probability distribution worth considering. What can you say more generally?

11

Hehe love this style of learning…

All I’ve got is:

[ul][li]There’s an equal probability of them watching the same kind of programme as each watching a different kind of programme.[/li][li]This doesn’t fit the probability distribution of “Both kinds of programme and all channel choices are equally likely, and independent”. Something in this statement must be wrong.[/li][li]At least some of the time, they’re watching the same channel. In this case, we’re told they’re watching the same programme (so this must be part of the 50% of matches).[/li][li]50% of the time, they don’t match. Therefore, we know they aren’t watching the same channel and that the channels are not all broadcasting the same kind of show.[/ul][/li]
The key thing here is the second bullet point, no? Either the channels are not independent, or the guys’ TV choices are not (or both).
Or something else.

12

OK. In the scenario with wavelike behaviour, why does “hitting the screen” count as measurement, but passing through the slit not count?
Parts of the wavefront must interact with the walls around the slits, why doesn’t that define the location of the electron?

13

A wee bump to see if anyone can add more, or approach things differently, at this time.

14

Excellent.

Alright, keep in mind, the situation I described, where it turns out the TVs match half the time… there’s nothing logically/mathematically incoherent about it. It’s something which could in fact happen. Indeed, experiment shows that it does in fact happen, for a certain kind of quantum mechanical “TV”.

But let’s get back to what’s interesting about it.

As we saw, it can’t be the case that every channel is independently randomly picking programming, since this would actually cause a 2/3 match rate. But that’s not so weird; perhaps the channels coordinate their schedules with each other in some way, or show biases towards certain genres. And certainly, one can achieve a lower match rate by doing so: if ABC and NBC always show comedies and CBS always shows dramas, then the match rate would actually be 5/9 (4/9 of the time you’d both see comedies and 1/9 of the time you’d both see dramas).

But 5/9 is still larger than 1/2. Indeed, as you came close to establishing yourself, this is the best one can “classically” do, in the following sense: as you noted, if we consider there to be a specific genre being shown on each channel in each timeslot, then at any moment, either two or all three channels are showing the same genre. If the viewers’ random channel selections are independent of the channels’ programming, then the viewers will match genres 5/9 of the times when just two channels show the same genre, and will match 100% of the time when all three channels show the same genre. Overall, therefore, the match rate must be between 5/9 and 100%; that is, at least 5/9.

But 1/2 is clearly less than 5/9. Therefore, any attempt to (even retrospectively) create a TV guide consistent with all viewers’ experiences will end up displaying some correlation between the viewers’ ostensibly random channel selections and the channels’ programming schedule.

This still isn’t so bad; why shouldn’t there be any correlation? For that matter, who’s to say there’s even any fact of the matter as to what’s being displayed on the unwatched channels; perhaps the TVs just make it all up as they go along in response to the viewers’ channel selections, the latter of course influencing the former.

But… there is still that business about how the TVs always agree whenever they’re tuned into the same channel. So now let’s explore its ramifications by introducing some new characters: the Broadcaster and the Nielsen Men (one on each coast).

I’ll make no starting assumptions about what information the Broadcaster has access to; for example, they may or may not be able to construct a consistent TV guide. As for the NY and LA Nielsen Men, each has access to precisely whatever information The Broadcaster has, plus the channel selection and displayed program at their location.

Now, the really interesting thing is, at least one of two things must hold:
A) The Broadcaster sometimes has information correlated with the viewers’ channel selections [so that, for example, there is a way for The Broadcaster to sometimes make predictions as to who will pick which channel, and be correct more than 1/9 of the time when he makes a prediction]
and/or
B) One of the Nielsen men on one coast sometimes has more knowledge about the other coast than The Broadcaster has [so that, for example, there is a way for the Nielsen man on one coast to sometimes confidently rule out a particular channel-genre combination on the other coast, even though The Broadcaster could not rule it out]

Why is this? Well, the negation of B) essentially states that whenever The Broadcaster can rule out “X happening in NY simultaneously with Y happening in LA”, The Broadcaster can in fact furthermore rule out at least one of “X happening in NY” or “Y happening in LA” period. Accordingly, since The Broadcaster can always rule out the possibility of “NY watches a comedy on Channel C and LA watches a drama and channel C” and similarly rule out “NY watches a drama on Channel C and LA watches a comedy on channel C”, one of four things must happen for B) to fail: either The Broadcaster can rule out that NY watches channel C at all, or can rule out that LA watches channel C at all, or can rule out that anyone watches a comedy on channel C, or can rule out that anyone watches a drama on channel C. In the first two cases, The Broadcaster has nontrivial knowledge about channel selections, and thus A) holds. If the first two cases never happen, then one of the latter two cases always happens, for each channel, which is enough for The Broadcaster to construct a TV guide guaranteed to be consistent with each viewers’ experience. But as we saw above, any TV guide exhibits correlation with the viewers’ channel selections, and thus in this case, A) holds as well. So, no matter what, either A) or B) holds.

Well, fine, either A) or B) holds, no matter who The Broadcaster is or what information they have access to. But now, the final punchline: let’s suppose The Broadcaster is in a position to know all and only those facts about the world dealing with events in spacetime which both the NY and LA viewer would have had time to be affected by by light-speed transmission when making their channel selection.

Then what we’ve just shown is this: Either The Broadcaster has the ability to predict the future to some degree [this is case A)] or one coast has access to knowledge about the other coast beyond simply what it can deduce from those events both coasts have time to be affected by by light-speed transmission [this is case B)]. Either one of these is a kind of non-local correlation; that, in a nutshell, is quantum entanglement.

Incidentally, though either of these can be viewed as some sort of faster-than-light correlation, B) cannot be used to actually communicate messages faster than light. For the correlation in B) is simply between what viewers see on their TV; but the viewers themselves needn’t (and indeed presumably don’t) have any influence over what’s displayed on the TV. It’s as though they have coordinated random number generators; they can ensure they get the same message, but they can’t pick what the message is. This is interesting, but it can’t be used to communicate anything from the one to the other.

15

In the classic setup of the experiment, the screen detects the electron hitting it (measuring it), but the slits have no detectors. Therefore, we know only two things about the system:

  1. that an electron was released at the start
  2. wave/interference patterns were detected on the screen.

Since 2 would require that the electron go through both slits simultaneously, the experimenters say “Let’s put detectors in the slits to confirm that the electron splits and goes through both slits.”

Now, we know three things because of the extra detectors:

  1. that an electron was released at the start
  2. that an electron went through one of the slits
  3. than an electron hit the screen

But… adding the detectors to the slits means that we will never see the wave/interference pattern that we got in the first experiment. To see that, we have to remove the detectors at the slits.

For the second half of your question - what’s important is not that the waveform interacts with the walls or slits, but whether we can measure that. Remember that at this scale, the process of measuring affects the measured entity. Putting a thermometer in your mouth reads an accurate body temperature because you weigh so much more than the thermometer. But if you use a thermometer to measure the temperature of a raindrop, you’ve significantly changed the raindrop’s temperature before you get a reading. At best, you can infer the drop’s temperature prior to the reading. The process of measuring is not a passive activity at a quantum scale.

I don’t even know how people measure which slit the electron goes through. But, clearly, whatever mechanism is being used to measure this changes the electron’s state - you always see particle-like behavior and never the wave-like behavior. We simply don’t have any measuring devices that can produce waveform interference on the screen AND see which slit it went through.

16

The usual two-particle Bell/EPR experiment requires a probabilistic what-if argument to derive the entanglement paradox, but in experiments of a “GHZ” class two pairs of entangled pairs are created, and (by blurring time coherence until it’s as large as half a picoseond?) one particle from each pair are sometimes indistinguishable. This leads to three-particle entanglement, and the EPR paradox is derivable without need for probabilistic argument.

Disclaimer: I definitely do not know what I’m talking about. I hope a physicist intervenes and describes such GHZ entanglements better.

17

Thanks for your answer. It helps a little but still leaves me wondering how the electron knows it has been measured.

If we set up the 2 slits with detectors, but didn’t look at the “readout” of those detectors, would it still count as being “measured” and eliminate the interference pattern behind the slits?

18

The “measurement” is the interaction with the detector. This causes the wavefunction to collapse and the particle’s position to be localized to one of the two slits. Whether the operator of the experiment is staring at the detector readout or passed out drunk on the floor has nothing to do with it.

19

What happens if you put a detector in one slit but not in the other?

20

That’s still enough to destroy the interference.