3 ms·

Your example has the problem of having a 'hidden' variable; the assignment of sock to foot. When you put on your socks, you assign a sock to a foot. So, when yo

by esarbe 10y ago

Your example has the problem of having a 'hidden' variable; the assignment of sock to foot. When you put on your socks, you assign a sock to a foot. So, when you later look, this determines the outcome, in this case the color of your socks. This is not the case with the classical Copenhagen interpretation of QM - there are no hidden variables. I.e., the assignment of sock to foot happens at the moment when you look at them. In the meanwhile, you've been - metaphorically speaking - in a superposition of all possible states of wearing socks. Now, in order to explain this phenomenon, do you need faster-than-light travel of your left sock's color to your right sock at any point? Yes. More specifically you need non-locality, because you expect both feet to have socks of the same color. Now either this is a hidden variable, or the two socks have to coordinate their color at some point in time. Hidden variable theories have been proven not to be applicable. That leaves some way of coordination. Which requires non-locality.

codethief 10y ago
There are a few errors in your argument: 1) "Hidden variable theories have been proven not to be applicable." This is flat out wrong. Bohmian mechanics is a deterministic hidden-variable theory of quantum mechanics which can do without a probabilistic interpretation of quantum mechanics by giving up locality. The choice is really between giving up locality or determinism. But you don't have to give up both and the Copenhagen interpretation certainly does not give up both. 2) There is no hidden variable in my example. A hidden variable, by definition, is a variable that is inaccessible to measurements. Moreover, my example doesn't depend on the "feet" at all and would work perfectly well without them. That being said, I think what you're actually referring to is that you already choose a certain color when you put your socks on, i.e. the socks' color is not uncertain even if you decide to not look at them until later. True but this is why half of my comment is discussing exactly this point. I admit, though, that I'm being a bit vague there, so here goes another example: Let's say a friend of yours blindfolds you and flips a coin to determine whether to give you a pair of blue socks or a pair of red socks. He subsequently hands you a pair of the respective color and you put them on and decide not to look at them until later. From your point of view, the chances of your left sock being red/blue is 50% each. However, no matter the outcome of your measurement of looking at your left sock, you can be sure that if you look at the color of your right sock afterwards, its color will always be the same as your left sock's one. The two results are correlated. Now, I hope you won't argue that this is still not quantum mechanics because in QM a sock can be multiple colors at the same time whereas classically/in my example they cannot and will always have a certain color, no matter our (lack of) knowledge. This is exactly the point. If I could explain away quantum mechanics through a classical example like this we wouldn't need a non-local or non-deterministic model of our world. But Bell's inequality tells us otherwise. Anyway, what my example does demonstrate is that even for measurements whose outcome is probabilistic, correlations between the results (or "coordination" as you call it) can perfectly well be explained through prior arrangement, i.e. an arrangement at a point in space and time that lies in the past light-cone of both measuring events. So no faster-than-light traveling is needed. Now, of course this is not the most rigorous argument one can make. For a more rigorous one please refer to the C* algebras approach to quantum mechanics where "locality" can be defined a bit more precisely and regular quantum mechanics indeed turns out to be a theory respecting locality.

by esarbe 10y ago

codethief 10y ago

There are a few errors in your argument: 1) "Hidden variable theories have been proven not to be applicable." This is flat out wrong. Bohmian mechanics is a deterministic hidden-variable theory of quantum mechanics which can do without a probabilistic interpretation of quantum mechanics by giving up locality. The choice is really between giving up locality or determinism. But you don't have to give up both and the Copenhagen interpretation certainly does not give up both. 2) There is no hidden variable in my example. A hidden variable, by definition, is a variable that is inaccessible to measurements. Moreover, my example doesn't depend on the "feet" at all and would work perfectly well without them. That being said, I think what you're actually referring to is that you already choose a certain color when you put your socks on, i.e. the socks' color is not uncertain even if you decide to not look at them until later. True but this is why half of my comment is discussing exactly this point. I admit, though, that I'm being a bit vague there, so here goes another example: Let's say a friend of yours blindfolds you and flips a coin to determine whether to give you a pair of blue socks or a pair of red socks. He subsequently hands you a pair of the respective color and you put them on and decide not to look at them until later. From your point of view, the chances of your left sock being red/blue is 50% each. However, no matter the outcome of your measurement of looking at your left sock, you can be sure that if you look at the color of your right sock afterwards, its color will always be the same as your left sock's one. The two results are correlated. Now, I hope you won't argue that this is still not quantum mechanics because in QM a sock can be multiple colors at the same time whereas classically/in my example they cannot and will always have a certain color, no matter our (lack of) knowledge. This is exactly the point. If I could explain away quantum mechanics through a classical example like this we wouldn't need a non-local or non-deterministic model of our world. But Bell's inequality tells us otherwise. Anyway, what my example does demonstrate is that even for measurements whose outcome is probabilistic, correlations between the results (or "coordination" as you call it) can perfectly well be explained through prior arrangement, i.e. an arrangement at a point in space and time that lies in the past light-cone of both measuring events. So no faster-than-light traveling is needed. Now, of course this is not the most rigorous argument one can make. For a more rigorous one please refer to the C* algebras approach to quantum mechanics where "locality" can be defined a bit more precisely and regular quantum mechanics indeed turns out to be a theory respecting locality.