The Gravity-Quantum Interface

T. P. Singh !!

Graduate Students: !Shreya Banerjee, Sayantani Bera, Srimanta Banerjee

Plan of the talk

1. The quantum measurement problem !

!

2. Some aspects of inflationary cosmology !

!

3. Alternatives to Dark Energy and Dark Matter

1. The Quantum Measurement Problem

Quantum theory is extremely successful, and agrees with every known experiment. However, there is one observational fact [collapse of the wave-function] the theory does not seem to be able to explain.

i~@ @t

= H

______________________________

i~@ @t

= H + ...|{z}

1. The Quantum Measurement Problem

1. The Quantum Measurement Problem

1. The Quantum Measurement Problem

1. The Quantum Measurement Problem

1. The Quantum Measurement Problem

One possible resolution: the Schrodinger equation is approximate. !

!

We have been exploring this approach to the quantum measurement problem.

Constraints on the modified equation!

• Should have a nonlinear part, which breaks superposition.

• The nonlinear part should be stochastic, so as to allow random outcomes, and avoid faster than light-signalling.

• The nonlinear terms should be anti-Hermitean, if they have to cause collapse.

• The nonlinear equation should be such that the Born probability rule is recovered.

• There should be an amplification mechanism, so that the nonlinearity is negligible for microscopic systems. All the experimental predictions of quantum theory must be recovered.

Continuous Spontaneous Collapse

• A modified Schrodinger equation:

d t =

� i

~Hdt+p�(q � hqit)dWt �

�

2(q � hqit)2dt

� t

• Nonlinear, stochastic, gives Born probability rule

Ref. : Bassi et al., Reviews of Modern Physics, 85, 471 (2013) arxiv: 1204.4325 !

Work Being Done HereWe explore: !1. If the modifications are being caused by gravity. (Bera et al. 2014, Sharma and TPS 2014)

2. If CSL can be derived from an underlying fundamental theory such as trace dynamics, and if it relates to the problem of time in quantum theory. (Lochan et al. 2012, TPS 2012) !3. Experimental tests, such as Anomalous Brownian Motion (Bera et al. 2015) !

Anomalous Brownian Motion•The stochastic hits in CSL predict a very tiny violation of momentum and energy conservation. !

• Momentum violation results in an anomalous Brownian motion of a quantum particle subject to these hits. !

•The estimated displacement of a micron sized sphere is of the order of its size, over a few seconds. !

•This is in principle detectable at a pressure of about 10�11

Torr and temperature few Kelvin: ordinary Brownian motion and thermal effects are sufficiently suppressed.

• Testing superposition: interferometry and optomechanics

• CSL induced spectral line broadening

• Heating of ultra-cold atoms

• Anomalous Brownian motion

• Constraints from known laboratory physics

• Constraints from astrophysics and cosmology

Putting bounds on the collapse strength �

Micro-world !

Superposition holds !

➔104 nucleons

Macro-world

Superposition does not hold

⬅ 1018 nucleons

Meso-world !

!

?? !

What could be happening here?

2. Some aspects of inflationary cosmology

2. Some aspects of inflationary cosmology

• The hypothesised epoch of inflation in the early universe is the source of quantum density perturbations which lead to structure in the universe.

• How do the quantum density perturbations become classical? We try to understand this using the CSL model. !(Suratna Das et al. 2013, Shreya Banerjee et al. 2014)

3. Alternatives to dark energy and dark matter

3. Alternatives to dark energy and dark matter

• Modified gravity as a common explanation for galactic rotation curves and cosmic acceleration !• We have been examining a model of fourth order gravity, which appears reasonably successful in this regard. !(P. Mishra and TPS 2012, 2013; Shreya Banerjee et al. 2015)

Future Directions

• Modified quantum theory: fundamental origins and experimental tests. !• The quantum to classical transition in inflation !• Understanding the origin of dark energy, and the nature of dark matter !• The possible role of torsion in gravity and quantum theory. !• Modified quantum theory, quantum gravity, and noncommutative geometry