Continuum Limit of Bell's Jump Process

Mentor: Professor Roderich Tumulka

Background and Motivation

Quantum Mechanics has been around for more than eighty years; it enjoys unprecidented and astounding accuracy in the prediction of the outcome of experiments. Despite this, it is notoriously difficult for beginners to assimilate because of the associated picture- one often talks about “particles”, even though strictly speaking there are no positions and no real particles in the theory. Often it is stated or implied that a fundamental particle picture is inconsistent and a field theory is the only sensible option. Still it seems inadvisable to break from the language of particles, as after learning the theory experts are not mislead by the familiar notion of a particle. Fortunately, there is a particle theory for (more or less) every field theory as shown here by Detlef Dürr, Sheldon Goldstein, Roderich Tumulka, and Nino Zanghì. The notion of physical particles need not be abandoned and talk of particles can be justified. This summer's work will focus on an aspect of the relationship between two highly successful particle theories: Bell's Jump Process and Bohmian Mechanics. Specifically, to work toward showing that Bohmian Mechanics is the continuum limit of Bell's Jump Process.

Week 1

Introductory presentation , theorem formulations.

Week 2

Proving auxillary theorems, writing the proofs up.

Week 3

Tweaking auxillary theorems, writing it up.

Week 4

Proving tweaked auxillary theorems, writing it up.

Week 5

Working on the main result formulation.

Week 6

Reworking the auxillary theorems to a more immediately useable form.

Week 7

Reworking the auxillary theorems to a more immediately useable form, closing presentation .

Week 8

Writing up the proofs of the auxillary theorems, proving the main theorem.

References

[1] Bell, J.S.: Beables for quantum field theory, Phys. Rep. 137, 49-54 (1986). Reprinted in [2], p. 173.

[2] Bell, J.S.: Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press (1987)

[3] Billingsley, P.: Probability and Measure. New York: Wiley & Sons (1979).

[4] Bohm, D.: A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables, I, Phys. Rev. 85, 166-179 (1952). Bohm, D.: A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables, II, Phys. Rev. 85, 180-193 (1952)

[5] Dürr, D., Goldstein, S., Zanghì N.: Quantum Equilibrium and the Origin of Absolute Uncertainty, J. Stat. Phys. 67, 843-907 (1992)

[6] Dürr, D., Goldstein, S., Taylor, J., Tumulka, R., Zanghì N.: Bell-Type Quantum Field Theories, J. Phys. A: Math. Gen. 38 R1-R43 and quant- ph/0407116

[7] Dürr, D., Teufel, S.: Bohmian Mechanics: The Physics and Mathematics of Quantum Theory, Heidelberg: Springer-Verlag Berlin (2009)

[8] Dürr, D., Goldstein, S., Taylor, J., Tumulka, R., Zanghì N.: Bohmian Mechanics and Quantum Field Theory, Phys. Rev. Lett. 93, (2004) 090402 and quant-ph/0303156v2

[9] Vink, J.C.: Quantum mechanics in terms of discrete beables, Phys. Rev. A 48, 1808-1818 (1993)