The TSVF interpretation of quantum mechanics

[Linkey]

I have found an information about the interpretation based on the two-state vector formalism (TSVF). I will try to retell in my own words what I saw, but I apologize in advance for not understanding many of the said.

It is usually considered that the wave function "collapses after measurement", i.e. the collapse goes from the past to the future. However, in fact, we can just as well consider that the measurement collapses the WF from the future to the past (i.e. firstly a unitary evolution goes from the future to the past, then a jump due to measurement, etc.).

The idea of weak measurements is based on the fact that you can simultaneously use two wave functions - the one from the past to the future and the one from the future to the past. This is called TSVF.

If you take TSVF and throw out the collapse, i.e. threat it as the MWI, but with two WFs, then you get an interesting thing. From these two WFs, we can make a matrix similar to the density matrix, and this matrix will have closed dynamics and obey the von Neumann equation.

So, if the usual density matrix simply becomes diagonal as a result of decoherence, then the density matrix of two WFs becomes not only diagonal, but also with only one 1 value on the diagonal. Thus, in this interpretation, it turns out that neither the collapse of the WF nor the existence of many universes is needed.

We can interpret this as follows: if we take two MWI trees, one branching into the future, the other into the past (this depends on the initial and final conditions), superimposed them on each other, as a result, one branch is coincided and this is the actual universe.

This looks a bit like the transactional interpretation, but I believe the TSVF interpretation is better, since it has determinism, while the transactional interpretation does not.

The idea of TSVF interpretation can be formulated as follows: after preparation and before measurement of the system, there is an intermediate state, and it is determined not only by the initial controlled actions of the experimenter, but also by the final result of the measurement.

What I have written above is a retelling of posts on the Internet forums, and I must say that I myself understand little here. As far as I understand, the TSVF interpretation combines the advantages of the Copenhahen and MW interpretations: it supports the determinism, and at the same time there are no multiple universes like in the MWI. Please help me understand more on this subject, and in particular I have a question - what is the density matrix?

[studiot]

3 hours ago, Linkey said:

and in particular I have a question - what is the density matrix?

Before launching ito some technical mathematics, let me ask you a question.

 

How much do you know about matrices and complex numbers in general ?

 

The density matrix is best studied in the first instance in connection with a very simple two state system (usually the spin states ).

It can then be generalised to many pure states and what are called mixed states.

Essentially the DM is a matric of real numeric coefficients with some rather special properties that applies to a system with finite number of states.

It falls down for the potentially infinite count of states of Many Worlds.

[Linkey]

1 hour ago, studiot said:

How much do you know about matrices and complex numbers in general ?

Slightly more than a common person with high education. I know how to diagonalize a matrix with Jacobi algorithm, I know what how does a multiplication of two complex number look like (the "angles" are summed up).

Edited December 3 by Linkey

[studiot]

Since you are studying  Physics, may I introduce you to this little book, whcih will answer all your questions and more.

When working with a subject, even one I know well, I like to keep two (sorts of) books on the subject.

A very basic book that explains things, including the maths, but is not too big and encyclopaedic.

A treatise type book that works out all the special cases, wrinkles and details for when I need to delve deeply at a particular part of the subject.

 

Susskind has written 3 titles  covering much of Physics using of the first type of book and this is the one you need.

It contains the whys and wherefores of quantum calculations, including useful tables of results, for entanglement, density matrices and compares with classical analogues, discussing the difference between quantum and classical versions.