Abstract

It is argued that gravity should cause a breakdown of quantum mechanics, at low energies, accessible to table-top experiments. It is then shown that one can formulate a theory of quantum gravity in which gravitational correlations exist between worldline or worldsheet paths, for the particle or field of interest. Using a generalized equivalence principle, one can give a unique form for the correlators, yielding a theory with no adjustable parameters. A key feature of the theory is the ‘bunching’ of quantum trajectories caused by the gravitational correlations—this is not a decoherence or a ‘collapse’ mechanism. This bunching causes a breakdown of the superposition principle for large masses, with a very rapid crossover to classical behaviour at an energy scale which depends on the physical structure of the object. Formal details, and applications of the theory, are kept to a minimum in this paper; but we show how physical quantities can be calculated, and give a detailed discussion of the dynamics of a single particle.

Highlights

  • In 1957 Feynman remarked1 that there were was an apparent conflict between Quantum Mechanics (QM) and General Relativity (GR), if one cared to extrapolate QM superpositions to the macroscopic scale; and various authors have since refined and extended the discussion of this conflict2–9

  • We see that the main punchline here is that it is possible to devise an internally consistent theory in which the breakdown of QM is caused by gravitational correlations

  • The theory is consistent with Einstein GR at energies which certainly cover lab scales - we expect it to be consistent with GR for massive bodies, up the energies currently tested in astrophysics

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Summary

INTRODUCTION

In 1957 Feynman remarked that there were was an apparent conflict between Quantum Mechanics (QM) and General Relativity (GR), if one cared to extrapolate QM superpositions to the macroscopic scale; and various authors have since refined and extended the discussion of this conflict. There is a growing belief that QM should eventually fail, this time at macroscopic scales - this is because of the well-known paradoxes associated with the application of the superposition principle at these scales This belief is still rejected by most physicists, who prefer to modify our ideas about the macroscopic world to agree with QM, and to assume that GR must break down when it conflicts with QM. Some of the formalism is described, to show how CWL theory differs from standard low-energy quantum gravity, and how it can lead to experimental predictions This is an interesting time for laboratory work on this topic - several papers have proposed experiments, and there is some optimism that they may be able to test alternative theories.

Internal Problems within General Relativity and Quantum Theory
Quantizing Gravity
Problems quantizing Gravity in the Low-energy regime
EPR experiment with 2 entangled Masses
Previous work
Uncertainty Principle arguments
Stochastic Collapse approaches
Non-linear Schrodinger equations
Desiderata for a New Theory
Essential Features of QM
Essential Features of GR
DERIVATION OF THE CORRELATED WORLDLINE THEORY
Rationale for the CWL Theory
A Generalized Equivalence Principle
Formal Postulates of the CWL Theory
The first two Postulates
Postulate 3: the Role of Gravity
CORRELATED WORLDLINE THEORY
Sums over Correlated Rings
Correlated Rings Sums for higher propagators
Structure of Correlators
Structure of Propagators
Single Particle at low velocity
Measurements in ordinary QM
Measurements in CWL theory
CONCLUDING REMARKS
Full Text
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