# Pilot wave theory

1. Jul 8, 2015

### Scheuerf

When people talk about qm you often hear about superposition and uncertainty. But if I'm correct pilot wave theory which is an interpretation of qm doesn't require those things. If we don't know which interpretation of qm is correct, why is it that it is taught as if things like superposition are a necessary part of qm?

2. Jul 8, 2015

### The_Duck

The pilot wave theory is in principle deterministic, but in practice experimental results remain unpredictable because we can't determine where the true state lies inside the pilot wave.

The pilot wave theory in principle eliminates superposition of states, but the weird physical effects of superposition still occur because the full wave function is still there, as the pilot wave.

We teach QM using a very naive Copenhagen-like interpretation because people have to learn the math of QM before they can think usefully about interpretations.

3. Jul 8, 2015

### bhobba

Just to expand on what the Duck said all superpoaition is, is a reflection of the vector space structure of so called pure states. Its part of the formalism of QM and is unavoidable - so every interpretation has it. Its meaning is what changes with different interpretations and in the pilot wave theory it doesn't have a fundamental status.

Thanks
Bill

4. Jul 9, 2015

### atyy

In classical probability theory, we can imagine that the system is in a definite state, but we don't know which. Technically, we say the state space is a convex set that is a simplex.

In the usual Copenhagen-style quantum theory, because of the vector space structure and superposition, we cannot uniquely assign a definite state about which we are uncertain. Technically, we say the state space is a convex set which is not a simplex.

However, we can embed the theory into a larger theory using additional variables so that the state space of the larger theory is a simplex, so that we recover classical probability. This is what the pilot wave theory does.

5. Jul 9, 2015

### ShayanJ

If I'm not mistaken, this means that the Kochen-Specker theorem applies to pilot wave theory(which is more commonly called Bohmian mechanics, right? Are they different things?). So again we are left with a theory which is in a way "absurd". It seems to me we can't escape the conclusion that nature is really absurd, either in a Copenhagen way or in a KS way. So even Bohmian mechanics can't make QM more intuitive, which was one of the goals of such theories in the first place.

6. Jul 9, 2015

### atyy

Copenhagen is pretty intuitive, so I don't know what you are talking about :P

The aim of Bohmian Mechanics is to solve the measurement problem. In Copenhagen, an observer us needed to place the classical/quantum cut, choose the preferred basis and decide when an observation is made. We cannot put the observer into the physics. But if we believe that the observer obeys the laws of physics, then QM is incomplete. So what are the possible completions? It is no different from studying string theory as a possible completion of quantum GR.

7. Jul 9, 2015

### Demystifier

What do you mean by that? It looks quite different to me.

8. Jul 9, 2015

### ShayanJ

I meant the departure from the way of thinking in classical physics. Otherwise I know what you mean by Copenhagen being intuitive ;).
Yeah, surely one of the main aims of any interpretation is to solve the measurement problem, but hidden variable theories have the extra (historical) aim of reducing the departure from the classical way of thinking. Of course this aim has diminished considerably from the first years of such theories but I think we should forget about it completely and focus on solving the measurement problem.
I'm not aware of the current status of the experimental search for Bohmian trajectories but is it really that they are as hard as string theory in terms of finding a way to observe them?

9. Jul 9, 2015

### atyy

Well, that should be hard as long as quantum mechanics holds. In Bohmian Mechanics the quantum prediction is due to a condition called "quantum equilibrium", which can be thought of as analogous to "thermal equilibrium" in statistical mechanics. Since in statistical mechanics, we also believe that the ensembles are not real, but instead the theory is only emergent due to the special condition of thermal equilibrium, then the reality underlying statistical mechanics is revealed by nonequlibrium phenomena described by Newton's laws. So one would have to look for violations of QM to hope to find evidence for Bohmian trajectories.

Like string theory, this is hard as long as we cannot observe deviations from our current "standard model". However, string theory has possible but unlikely scenarios in which we observe low-energy stringy phenomena http://resonaances.blogspot.com/2015/06/on-lhc-diboson-excess.html, and there are some suggestions that if we are lucky we might be able to observe Bohmian phenomena http://arxiv.org/abs/1306.1579.

More generally, there is research about experiments that might detect violations of QM and test other theories that attempt to solve the measurement problem such as CSL: http://arxiv.org/abs/1402.5421, http://arxiv.org/abs/1410.0270.

10. Jul 9, 2015

### atyy

Both BM and string theory are motivated by arguments that there is probably new physics, even though there is no observable violation of current theories.

11. Jul 10, 2015

### Staff: Mentor

A number of off-topic posts have been removed. Please, everyone, try to stay on-topic... A thread on pilot wave theories is not the place to raise talk about macroscopic measurements.

Last edited: Jul 10, 2015
12. Jul 10, 2015

### stevendaryl

Staff Emeritus
There are definitely things that are weird about Bohmian mechanics, but I don't think the KS theorem has much bite. The KS theorem says that there can't be a deterministic explanation of all variables (represented by all the possible observables, or Hermitian operators, in QM) in which those variables are intrinsic properties of the system. But in Bohmian mechanics, none of those variables are real, except for position. Observables such as spin are not intrinsic properties of a particle, but instead are artifacts of the interaction between the particle and measurement devices.

That's a more complicated view of observable, but there is nothing absurd about it.