Unintended observations, how do we do with it?

[sweet springs]

I am wondering about QM observation in terms of , in Penrose way I call, the unitary process (U) and the reduction (R) of states. R occurs for any intended physical observation. Does R occur also in unintended situation? For examples

- We make a fog chamber and observe the white streak lines that show positions of charged particles. R occurs there. In natural fog in mountains area, do white streak line appear?

- We can calculate probability of transisition of the states in time interval: R(0) →U→ R(t).
Do we have to worry about unintented R during the process : R(0) →U→R→U→ R(t), R(0) →U→R→U→R→ R(t) or so take place and disturb our calculation?

 

[DaveC426913]

Yes.
The term observation in QM is not limited to what we usually consider observation. It doesn't even have to be by a person, or even a living thing.

 

[sweet springs]

Thanks. R occurs for every case in human sensing. More than that R occurs in some situation where human or living things may not be involved in. I would like to know the whole situation and how R occurs, e.g. decisive or probabilistic, that will be required in technological applications like designing quantum computers.
Best.

 

[atyy]

Whether R occurs or not is subjective in quantum mechanics, because R occurs only after a measurement has been made. A measurement occurs when there is a definite macroscopic or classical record, and must be put in "from outside" the theory. The measurement need not be done personally by the experimentalist, but it requires the experimentalist to delegate an instrument as a "classical measuring apparatus". This is the "Heisenberg cut" that is present in Copenhagen-style interpretations.

This is widely considered unsatisfactory, and is called the measurement problem. It is solved in limited situations by theories like Bohmian Mechanics or physical wave function collapse theories like GRW or CSL. Approaches like Many-Worlds are also very interesting attempts at solving it.

http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf
http://arxiv.org/abs/quant-ph/0209123
http://arxiv.org/abs/0712.0149

 

[sweet springs]

Thanks. Beyond interpretation, we will need technology to keep the states in U and not unintended R to occur, I suppose. Best.

 

[atyy]

Thanks. Beyond interpretation, we will need technology to keep the states in U and not unintended R to occur, I suppose. Best.

One only needs collapse if successive observations of observables M followed by N are made and one needs to calculate the joint probability p(M,N). If only one observation is made, then one doesn't care about the wave function after the first observation. Also, if one ignores the result from the first observation M, and only calculates the probability of results from the second observation N, then one only has p(N), not p(M,N) to calculate, and collapse is not needed.

So if the observation is not made, or the observation results are discarded, one can model the wave function by unitary evolution - in a larger Hilbert space.

http://arxiv.org/abs/1110.6815 gives the state after a measurement is made and the result is recorded as postulate II.4, while the state after a measurement is made and the result is not recorded as postulate II.5. Postulate II.5 can be obtained by summing over all the results in II.4, which makes sense since we could have recorded the results and then discarded them. However, Postulate II.5 can also be obtained by unitary evolution in a larger Hilbert space, and then restricting one's attention to a subsystem via the reduced density matrix formalism, as is done in decoherence. It is for this reason that decoherence is said to produce apparent collapse.

 

[sweet springs]

Thanks. I will challenge to read the paper to know more about decoherence. Best.