# Quantum blended with a little SR

1. Aug 30, 2004

### Tom McCurdy

Is this a paradox between QM and SR:

If two particles say electrons are in the same quantum state then no matter what the distance if one "flips" then the other one does the same thing, because they are tricked into thinking they are right next to each other, however SR strictly implies nothing can go faster than c so whose right.

2. Aug 31, 2004

### Chronos

Both. No information is transferred faster than the speed of light.

3. Aug 31, 2004

### Gonzolo

Here is how I see the situation. Someone correct me if I am wrong.

Suppose a beam of photon is polarized. Now split it in two and send one to Mars, keeping the other beam on earth. By measuring the polarity of the one on earth, you instantly know what polarity is the one on Mars.

The same could be said of two unmarked bottle of beers from the same 6-pack. If one of the bottles from the pack is sent to Mars, you still can determine what it is by tasting the ones you kept. The important thing is that you know they are from the same 6-pack. (for photons, you know they are in the same state initially.)

Last edited by a moderator: Aug 31, 2004
4. Aug 31, 2004

### ZapperZ

Staff Emeritus
I'm not sure if you're trying to illustrate quantum entanglement here in your examples, but this illustrates why this is an important but subtle difference between quantum entanglement AND classical correlation. What you described is classical correlation due to conservation of momentum (either linear or angular). Let me explain...

Say you have an object with a zero angular momentum. At some time, it fragments into two pieces that fly apart in opposite directions. Now, no matter how far apart that object is, the moment I measure the angular momentum of one object, I immediately determine the angular momentum of the other object, ya? This is straightforward classical correlation.

But is this the same as the quantum entanglement as illustrated in the EPR-type experiment? No, it isn't, and the differences are subtle but very important. In the classical case, the angular momentum of both objects are already established - we just don't know it yet till we measure it. In the QM case, the spin state are still in a superposition! And I don't need to repeat the fact that superposition is REAL and has a distinct effect on commuting and non-commuting observables. So in this case, the direction that YOU pick to measure the orientation of the spins CAN be a factor!

I highly recommend you read carefully this link which tries to show the difference between classical correlation and QM entanglement:

http://www.mathpages.com/home/kmath521/kmath521.htm

This also illustrates the fact that one cannot learn just ONE aspect of QM (such as just entanglement or just superposition), because various parts of it are tightly connected. You can't just read about entanglement without understanding what superposition is, because then you can't tell what is so "weird" about measuring two particles having opposite spins to each other.

Zz.

5. Aug 31, 2004

### pervect

Staff Emeritus
It takes a fair a amount more mathetmatics than has been used so far in this thread to even demonstrate the existence of the paradox.

See for instance

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html

for one example - it's a bit to complicated to type it all into a post.

Generally speaking, one can say that local, realistic theories are not compatible with quantum mechanics in light of the more rigorous arguments such as that presented above. The usual solution is to abandon realism . One way of doing this is commonly called "Many Worlds" - to oversimplify a whole bunch, having more than one reality is sufficient to defeat the arguments based on "realism", while keeping SR.

6. Sep 10, 2004

### DaveC426913

>The same could be said of two unmarked bottle of beers from the same 6-pack. If one of the bottles from the pack is sent to Mars, you still can determine what it is by tasting the ones you kept. The important thing is that you know they are from the same 6-pack. (for photons, you know they are in the same state initially.)

From on layperson to another, let me see if I can expand the analogy the show the difference. (Caveat: I *think* I've got this right, loosely within the limits of the analogy.)

The two photons are not in the same state, they are in opposite states. But they don't become one of those states until they're measured.

The two beer bottles you pull out are from a pack of "ale-lager" - special beer that is neither ale or lager until you open it, at which time, it becomes one or the other. BUT, if you take *two* bottles, they will not be the same - i.e if the first one you open is ale, the other one *will* be lager.

You fire one off to Mars. You measure the one here on Earth - it becomes lager when you open it. Spookily, the one on Mars *will* be ale. But if the one you opened here on Earth was ale instead, then the one on Mars will be *lager*.

The two beers cooperate one what they end up being, but they don't make that decision until *after* they're too far apart.

The element missing from the descriptions of the quantum experiments is where they point out that the photons *do*not*have* an angular momentum *at*all* (not just unknown, it can be proven that they don't *have* it) until it is actually measured. By the time it is measured the one on Mars is too far away to be affected. Once you factor that in, it becomes spooky.

Last edited: Sep 10, 2004