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I'm just an armchair physicist, but I thought we had already established that in quantum mechanics conservation laws only hold on average and not on a per run b

I'm just an armchair physicist, but I thought we had already established that in quantum mechanics conservation laws only hold on average and not on a per run basis. In https://news.ycombinator.com/item?id=24762436 https://news.ycombinator.com/item?id=24762436, @HackOfAllTrades notes that angular momentum is not preserved on a per run basis. In a Mermin Device a pair of entangled spin particles is set to two Stern-Gerlach experiments. The two particles has net (spin) angular momentum of 0 because that's was the net angular momentum of starting material. But if you measure the angular momentum of the two particles in two non-parallel directions, and if we also require that the only answers you are allowed to get are +hbar/2 or -hbar/2, then the sum of the angular momentum you get by adding +/-hbar/2 times one direction plus +/-hbar/2 times a different direction can never be 0.

tooltower 4y ago
But couldn't the missing angular momentum still be imparted onto the measurement device? I.e. maybe our Stern-Gerlach apparatus will start spinning ever so slightly if they were floating in space?
kgwgk 4y ago
What does starting with an entangled pair add to that argument? You could say simply that if you have prepared a (half) spin state |z+> the angular momentum along the x axis is zero but if you measure the spin along the x axis you will find a non-zero value.
- prof-dr-ir 4y ago
  This is not correct. The expectation value of the angular momentum along the x-axis might be zero, but the state itself simply does not have a definite angular momentum. I like your example because it clearly shows the subtlety that the original comment by rssoconnor also misses. Energy, momentum, and angular momentum absolutely are conserved quantities. But if you prepare your initial state such that it does not have a definite value of these quantities then you cannot with certainty predict the measured value, either.
  - kgwgk 4y ago
    Good point. Anyway, the original example reduces to this. After the first measurement [it doesn’t really matter which one is considered as first] we have a couple of complementary states +/- for the measured axis but it’s not well defined for other directions and in general a second measurement will break the symmetry.
  - JBits 4y ago
    What makes these quantities conserved in QM/QFT?

tooltower 4y ago

But couldn't the missing angular momentum still be imparted onto the measurement device? I.e. maybe our Stern-Gerlach apparatus will start spinning ever so slightly if they were floating in space?

kgwgk 4y ago

What does starting with an entangled pair add to that argument? You could say simply that if you have prepared a (half) spin state |z+> the angular momentum along the x axis is zero but if you measure the spin along the x axis you will find a non-zero value.

prof-dr-ir 4y ago
This is not correct. The expectation value of the angular momentum along the x-axis might be zero, but the state itself simply does not have a definite angular momentum. I like your example because it clearly shows the subtlety that the original comment by rssoconnor also misses. Energy, momentum, and angular momentum absolutely are conserved quantities. But if you prepare your initial state such that it does not have a definite value of these quantities then you cannot with certainty predict the measured value, either.
- kgwgk 4y ago
  Good point. Anyway, the original example reduces to this. After the first measurement [it doesn’t really matter which one is considered as first] we have a couple of complementary states +/- for the measured axis but it’s not well defined for other directions and in general a second measurement will break the symmetry.
- JBits 4y ago
  What makes these quantities conserved in QM/QFT?