Is there still a collapse problem after decoherence?

[Heidi]

Hi Pf,
I take the case of Alice and Bob in the EPR experiment. Here Bob does not measure spin projections but make a Young's double slit experiment. What Alice does on her side will not be known by Bob. She can decide to let her particles go freely to the left (in the environment of Bob).
Bob will see no interference. he cans suppose two things:
1) the which path information is known by Alice but he ignores the result so he is in a classical case of a probability problem , no more in quantum problem with ampkllitudes.
2) Bob knows what is decoherence , and how to use a reduced diagonal density matrix after decoherence.
in the two cases nothing can explain why the particle follow one path or the other. But is it still a collapse problem? we are now in the case where there is a lottery in Tokyo and that you read the results later in London. Would you talk about collapse problem.

 

[anuttarasammyak]

take the case of Alice and Bob in the EPR experiment. Here Bob does not measure spin projections but make a Young's double slit experiment. What Alice does on her side will not be known by Bob. She can decide to let her particles go freely to the left (in the environment of Bob).
Bob will see no interference.

How many photons participate in your young's double experiment ? Bob may not be able to judge there is interference or not by a single photon experiment. If many photon participates Bob observes that the setting is not Young slit but one slit.

 

[Heidi]

Two slits and a sufficient number of particles (Bob receives them one by one) to see if there are interferences.

 

[anuttarasammyak]

Thanks for clarification. I think Bob observing the pattern judges that only one of two slits is open each time. He observes a mixed state.

 

[Heidi]

How could he think like that? he has a device with two open slits.

 

[anuttarasammyak]

Oh I thought she and he shares a single double-slit and only she can operate the slits to open close.
You say each he and she has own double-slit. Double double-slit is too much complicated to me. Her slit door operation should effect his observation but not simple to analyze. For her incoming light is plane wave beam but for him light source is single source of two cases. I think photon interference takes place by his second slit even after her operation though pattern differs from the case of her no operation.

[EDIT]
Say $A_1,A_2$ are Alice's slits and $B_1,B_2$ are Bob's
If Alice does not do anything Bob observes superposition of light path
$$A_1B_1+A_1B_2+A_2B_1+A_2B_2$$
where $A_1B_2$ means probability amplitude of path along $A_1$ and $B_2$ or so.
If Alice open only $A_1$ Bob observes superposition
$$A_1B_1+A_1B_2$$
Difference is like that.

 

[DrChinese]

Just a reminder: neither Alice nor Bob will see interference while they are entangled. This is a peculiarly of entanglement. So the double slits on either side tell nothing useful.

 

[Heidi]

Heureux de vous lire DrChinois,
My question was about the classicality of the situation of Bob. he has to add probabilities. is it worth to talk about collapse then. No one talks about that in a lottery.