Pilot Wave theory

“A freely moving body follows a trajectory that is orthogonal
to the surfaces of an associated guiding wave.” - De Broglie

Quantum mechanics, the study of how particles behave at very small scales, is an extremely successful theory. But the interpretation of the mathematics has always been difficult, because it’s very unintuitive. For example, it says that particles do not have any definite position, but instead exist in a cloud of probability, until it interacts with something that forces it to be in one place.

Pilot wave theory is an alternative explanation, that claims to lead to the same mathematics, but with a more concrete explanation.

This tree is an attempt to explain pilot wave theory in rudimentary terms, going into deeper and more rigorous terms when necessary.

Droplet analogy

To begin with, it’s best to start with a larger physical system that shows similar properties to the pilot wave theory.

We will then map the parts of this analogous system to the quantum scale.

Q1 : What is the guiding wave “made of”?

i.e. What is Ψ?

We start with a number of “silly” questions, because it’s the only way to achieving a deep understanding. This is the first, though possibly unanswerable at the moment.

• Is it subjective or objective?
• Does it merely represent information or does it describe an observer-independent reality?
• If it is objective, does it represent a concrete material sort of reality, or does it somehow have an entirely different and perhaps novel nature?
• What’s going on with the collapse?

There is very little agreement about the answers to these questions, but we can all agree that the following crudely-expressed possibilities must be correct: [Goldstein]

• The wave function is everything.
• The wave function is something (but not everything).
• The wave function is nothing.

Mike Towler - Cambridge Lecture 1

Ψ is information?

If Ψ had a real, objective, and concrete reality, how might we detect it?

Q2 : Does this mean that the guiding wave must take into account the entire universe?

(mysticism aside: we are talking about causality and non-locality, not mystical “oneness”)

In very simple terms, this non-locality is no different from that present in standard QM. (but need to expand on this further)

Q3 : Is there an equivalent to “drop bounces” in PW Theory?

References & Resources

(Unsorted)

• Pilot wave theory, Bohmian metaphysics,
  and the foundations of quantum mechanics
  • Mike Towler, Cavendish Lab, University of Cambridge
• “In the framework of the de Broglie–Bohm theory, the quantum potential is a term within the Schrödinger equation which acts to guide the movement of quantum particles.”
  • http://en.wikipedia.org/wiki/Quantum_potential
• “Strictly speaking, pilot-wave theory is not really an ‘interpretation’ of anything, but a mathematical formulation of quantum mechanics with essentially the same status as Feynman’s path-integral method.”
  • http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html

Other alternatives to Copenhagen interpretation

1. Ensemble interpretation, or statistical interpretation
2. Participatory Anthropic Principle (PAP)
3. Consistent histories
4. Objective collapse theories (GRW etc.)
5. Many worlds
6. Stochastic mechanics
7. The decoherence approach
8. Many minds
9. Quantum logic
10. Transactional interpretation
11. Relational quantum mechanics
12. Modal interpretations of quantum theory
13. Incomplete measurements
14. Pilot-wave interpretation (a.k.a. Bohmian mechanics, de Broglie-Bohm
    interpretation, causal interpretation, ontological interpretation, hidden variables)

(from Mike Towler - Cambridge Lecture 1)

Meta Notes

To contribute:

If you want to be able to add your own notes & questions, send me a quick email and I’ll add you: first.lastname@gmail.com.

• Adriano Ferrari

A Caveat

This has all the elements of “science drama”: A crazy theory, a simple explanation ignored for decades, brute authority overridding the mild mannered theorist, and the comeback of the underdog alternative theory that made sense all along.

And so we must be careful to separate the facts from the drama that’s giving this theory a resurgence, at least in popular media (WIRED article, Through the Wormhole episode, etc…)

If you are interested in the history of “Why nobody likes Pilot Wave Theory?”, have a look at Mike Towler’s lecture