# Quantum Measurement Problem (2 and half pages)

Question # 40138 | 8 months ago |
---|

$10 |
---|

**Second Paper**

Describe the quantum *measurement problem*. Then describe in detail the interpretation of quantum theory that you find most plausible. Describe what this interpretation says is *real*. Then describe how this interpretation attempts to solve the measurement problem. That is:

I. What does this interpretation say about the nature of physical reality? Is the *quantum state* as described by the *state function* a real physical process or field in space-time, or is it merely a convenient fiction, or what? Are quantum particles such as quarks, electrons, photons, and atoms real? Is there a separate *macroscopic reality*; or is *macroscopic reality* reducible to (or entirely made up out of) the *quantum reality*; or is there no *quantum reality*, but rather, is the quantum state function just a useful tool for making predictions about *macroscopic reality* (and is the *macroscopic reality* the only thing that's real)? On the account you are describing, is the *mind* a necessary part of the physics -- e.g. is it needed to “collapse” an indefinite quantum state (i.e. to *collapse the wave function*) into a new state that has (for a brief moment) definite values for such physical quantities as the position or momentum for particles?

II. How does the interpretation attempt to resolve the measurement problem? In particular, which of the following claims does the interpretation hold on to, and which claims does it give up -- and what does the account say in place of the claim(s) it gives up:

1. Descriptive Completeness: Each physical system is in a physical state that (at least in principle) is completely describable by a state-description of the kind that quantum theory presently employs.

2. State Description Evolution: Quantum state-descriptions only evolve in the way specified by the usual dynamics of quantum theory (i.e., according to dynamical equations of the same general sort presently employed by quantum theory -- i.e., linear dynamical equations like the Schrodinger equation).

3. Definite Measurement Outcomes: The measurement of each physical system results in a specific (“observable”) outcome, which can be accurately registered by the measuring device. The measurement outcome is always of a type that the state-description of the system *says* is one of the possible outcomes. Furthermore, large collections of systems that each begin in the same kind of physical state (and so are described by identical state-descriptions), result in the various types of possible outcomes in percentages that correspond to the probabilities specified by their state-descriptions.

Your discussion should describe what the interpretation says about what happens in at least one of the following situations:

A. the two-slit experiment;

B. the EPR experiment (e.g. the version in terms of spin correlations, or polarization correlations);

C. the potential barrier experiment described by Squires (pp. 12-17, or p.28 and pp. 46-50).

What weaknesses or problems does this interpretation face? Are the details of this interpretation already fully worked out? What part of this account might physicists need to develop in more detail (as “new physics”) in order to have a complete the theory of how physical reality works?

===============================================================================

Students often have trouble getting a paper started. The next page suggests one way you could begin this paper. Feel free to adapt it as you see fit.

**What Quantum Theory says about Physical Reality**

Is there a physical world, and if there is, what is it like? In other words, what is the nature of physical reality? Although this may seem like an overly philosophical question that physics need not address, our best current scientific theory about the basic stuff that makes up the physical world, quantum theory, seems to force scientists to take this question seriously. Even the scientific founders of quantum theory were driven to address this issue.

There is no quantum world ... only an abstract quantum description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature. (Niels Bohr)

This quote from Bohr may look like an attempt to avoid engaging in “metaphysical speculation”. But it does state a view about the nature of physical reality. So, it seems that no one who takes physics seriously as an attempt to give an account of *what the world is like* can avoid such issues.

In this paper I will discuss one view about what quantum theory says about the nature of physical reality. This view is commonly called “the ... xxx ... interpretation”. I will explain what this view says about the nature of the physical world, and what it says about the way in which quantum theory represents that physical reality. In particular I will describe how this view tries to resolve the quantum measurement problem.

Before proceeding, let me first provide an overview of the *quantum measurement problem*. The *measurement problem* derives from the fact that the following three claims are inconsistent, and any consistent account of the quantum world must give up one of them.

1. Descriptive Completeness: Each physical system in the universe is in a physical state that (at least in principle) is completely describable by a state-description of the kind that quantum theory presently employs.

2. State Description Evolution: Quantum state-descriptions only evolve in the way specified by the usual dynamics of quantum theory (i.e., according to dynamical equations of the same general sort presently employed by quantum theory -- i.e., linear dynamical equations like the Schrodinger equation).

3. Definite Measurement Outcomes: The measurement of each physical system results in a specific (“observable”) outcome, which can be accurately registered by the measuring device. The measurement outcome is always of a type that the state-description of the system *says* is one of the possible outcomes. Furthermore, large collections of systems that each begin in the same kind of physical state (and so are described by identical state-descriptions), result in the various types of possible outcomes in percentages that correspond to the probabilities specified by their state-descriptions.

To see that these three claims are inconsistent, consider a quantum system Q that is to be measured by interacting with a purely physical measuring device M. For simplicity, consider a case where, when system Q is measured by device M, system Q may only have one of two outcome states, Q1 or Q2. The measuring device M may indicate these outcome states by giving a “pointer reading” M1 when state Q1 is the measured outcome, and by giving a “pointer reading” M2 when state Q2 is the measured outcome. Now, according to claim 1 above the system Q and measuring device M are both completely describable by *quantum state descriptions* (also sometimes called quantum *wave functions*). Let’s indicate these *descriptions* of systems Q and M by the notation ‘|Q>’ and ‘|M>’, respectively. According to claim 2 above the joint quantum *state description* of Q and M must evolve from an initial quantum *state description* |Qinitial>|Mready>, which describes the state of joint system consisting of Q and M before the measurement interaction occurs, to a resulting quantum state description |Q1>|M1> + |Q2>|M2>, which describes the state of joint system consisting of Q and M after the measurement interaction occurs. However, this resulting quantum state description represents a superposition of the two possible outcomes states, (Q1 and M1) and (Q2 and M2). The problem is that being in such a superposition of states means that the system Q and the measuring device M are not in either of the definite outcome states (Q1 and M1) or (Q2 and M2), but are only is a combined configuration (called a *superposition*) of the possibilities of these two outcome states. More generally, the quantum evolution of a quantum system Q and a physical measuring device M as described by conditions 1 and 2 never evolves into any one of the possible definite outcome states. Rather, such a quantum state, |Qinitial>|Mready>, can only evolve into a superposition (a combined configuration) of the various possible outcome states. However, when we actually “look” at the measuring device, we are always able to observe a definite outcome state. Claim 3 above simply says that when we make such an observation of the measuring device, what we observe accurately reflects what the state of the world really is. The measuring device and the quantum system it measures really have evolved into one of the specific definite quantum states, either into state (Q1 and M1) or into state (Q2 and M2) in our example. However, we just saw that claims 1 and 2 deny that this can happen – they say that only a superposition (a combined configuration of form |Q1>|M1> + |Q2>|M2>) of the various possible outcome states will happen. So claim 3 is inconsistent with claims 1 and 2. In other words, the above three claims are jointly inconsistent. At least one of them must be wrong. Thus, any consistent interpretation of quantum theory must give up at least one of these three claims. This is *the measurement problem*.

I’ll now describe the ...xxx... interpretation of quantum theory, and discuss how it attempts to resolve the quantum measurement problem.