# Singlet state like |e>= |+> |-> - |-> |+>

1. Nov 16, 2009

### shakespeare86

In a singlet state like
|e>= |+> |-> - |-> |+>

if we take the two particles far apart and measure the spin of the first particle S1 first, we get the answer +1 or -1 with the same probability.
This means that if we perform many measurements of S1 over many equal states |e> we get the +1 half the times.
If we later measure S2, no matter how far particle 2 is, we get -1 if we got first +1 and we get +1 if we got first -1.
Sakuray, in his book, says that it's ok if we think that the second measurement S2 is performed on the same state |e> and so it has just to confirm the first measurement S1.

Is it true that no matter how they are far we get such a correlation of the spins?

The second one is:

I see what Sakuray mean. But if S1 and S2 are measured at the same time what does it happen?
If the measurements are still correlated, how have we to justify this?

Sorry for the long introduction.
Thanks.

2. Nov 16, 2009

### DrChinese

Re: Entaglement

1. Distance, per se is not a factor as long as the state otherwise remains intact. Entangled photons, for example, have been experimentally observed over distances of 10+ kilomters.

2. There is no observable difference in outcome regardless of the order of observation.

3. Nov 16, 2009

### dmtr

4. Nov 16, 2009

### shakespeare86

Re: Entaglement

Hi.
I didn't get the answer to the second question.
Did you mean it's not really possible to measure S1 and S2 at the very same time?

5. Nov 16, 2009

### dmtr

Re: Entaglement

The order of observations does not matter. Use the measurement as entanglement approach.

6. Nov 16, 2009

### shakespeare86

Re: Entaglement

Sorry my stupidity :(
But I don't understand.

It's ok that the order of observations does not matter.
But I asked what's the correct interpretation of the correlation of spins if the two measurements are done at the same time.

What I mean is:

if the two measurements aren't done at the same time (no matter the order), quantum mechanics orthodox interpretation of the correlation of spins is that the second measurement simply confirm the first measurement.

Now, if the two measurements are at the same time I can't apply this interpretation.

7. Nov 16, 2009

### dmtr

Re: Entaglement

The quantum mechanics orthodox interpretation also suggests to stay clear of the interpretation issues and stick to the math. There are some obvious advantages in this approach, for instance you won't get stuck in the deep philosophical questions and would be able to do the math.

8. Nov 16, 2009

### DrChinese

Re: Entaglement

If they could be done simultaneously (which is questionable even in principle for a couple of reasons), they would confirm each other. Any way you look at it, the information from the 2 measurements is redundant.

9. Nov 16, 2009

### dmtr

Re: Entaglement

Any particular reasons why the measurements couldn't be done simultaneously?

10. Nov 16, 2009

### DrChinese

Re: Entaglement

I can think of 2:

a) You would need a reference frame in which they are simultaneous. Maybe that would be when they are at rest to each other, but clearly other observers might not agree on the simultaneity.

b) Assuming a) wasn't a factor: What time delta would you need? Zero? A planck time interval? As we approach that interval, it will become very difficult to determine the order of the measurements. How are you ever going to be sure they were exactly simultaneous? And that is not even considering issues of the actual measurement device itself, which are substantial.

11. Nov 16, 2009

### shakespeare86

Re: Entaglement

Finding a frame where the measurements are simultaneously taken is not a problem.
It's the one fixed with the point where the entangled state is created. Call it O.
When S1 and S2 are measured, the second photon is out of the light cone of the first, but experimentalists in these points could send message to a O, that would know about the correlation even in the space separation case.

Anyway the only good reason i can see for not worry about the simultaneity is maybe the practical impossibility to perform such a measurement; so the question should be not a physical question.

12. Nov 16, 2009

### dmtr

Re: Entaglement

a) A reference frame at rest, a single observer.
b) Zero. Yes, but these are merely practical difficulties.

I might be wrong, but I don't see any rules in any QM interpretation that explicitly prohibit simultaneous measurements that are compatible or yield the same information.

13. Nov 17, 2009

### Demystifier

Re: Entaglement

The variable which is measured in encoded in the total wave function, or more precisely in the entanglement between the measured system and the measuring apparatus. Since the total system (measured system + apparatus) cannot have two or more different wave functions at the same time, only one variable can be measured at once.

And it does not depend on the interpretation.

14. Nov 17, 2009

### shakespeare86

Re: Entaglement

yes, of course there is not a rule that explicitly prohibits simultaneous measurements.
And this is the reason why I made my question in the first post.
Anyway there are practical difficulties.

They are not "mere practical difficulties" since physics is an experimental subject, so maybe, the answer to my second question is that my second question is out of the the things we can ask to Nature, since we just can't measure S1 and S2 simultaneously.
Even a little difference of time, make my second question useless.
Bye

15. Nov 17, 2009

### Demystifier

Re: Entaglement

Yes there is, see my post #13 above.

16. Nov 17, 2009

### Demystifier

Re: Entaglement

Dmtr and shakespeare, please take my apologies! I have not realized that you are talking about simultaneous measurement of mutually COMMUTING observables. They, of course, can be measured at the same time.

17. Nov 17, 2009

### Demystifier

Re: Entaglement

Yes it is.

Standard QM does not say what happens. If you want to know what happens, you must adopt some hidden variable interpretation of QM, like the Bohmian interpretation.

18. Nov 17, 2009

### shakespeare86

Re: Entaglement

don't worry ;)

19. Nov 17, 2009

### limarodessa

Re: Entaglement

It seems to me that hidden variables had not been entered by the Bohmian interpretation, but they had been entered by John Stewart Bell:

http://en.wikipedia.org/wiki/John_Stewart_Bell

However, probably I am mistaken or I incorrectly understood you.

Besides, I prefer to view Hugh Everett's interpretation, instead of Bohmian interpretation.

http://en.wikipedia.org/wiki/Hugh_Everett_III

Also, dear participants and visitors of a forum, I ask that you excused me - my English is bad. I am from Ukraine.

Last edited: Nov 17, 2009
20. Nov 17, 2009

### DrChinese

Re: Entaglement

Welcome to PhysicsForums, limarodessa!