From quantum foundations to quantum gravity

SCEST21: Schrodinger's Cat, and Einstein's Space-time, in the 21st Century

A blogspot for discussing the connection between quantum foundations and quantum gravity

Managed by: Tejinder Pal Singh, Physicist, Tata Institute of Fundamental Research, Mumbai

If you are a professional researcher / student researching on these topics, and would like to post an article here with you as author, you are welcome to do so. Please e-mail your write-up to tpsingh@tifr.res.in and it will be uploaded here.


Keywords: Quantum foundations; Quantum gravity; Schrodinger's cat; Spontaneous collapse theory

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November 22, 2019

From quantum foundations to quantum gravity

Tejinder Singh

Quantum theory was invented to explain experimental data which could not be explained by Newton’s mechanics. There is no such clear-cut compelling observational evidence to suggest that gravity must be quantised. It could be said that the classical general theory of relativity agrees with every experiment / observation carried out till date. It may or may not turn out to be the case that understanding dark energy, cosmological constant, dark matter, require us to unify quantum and gravity. It may or may not turn out to be the case that the gravitational singularities that arise in general relativity require us to quantise the theory.

However, there are reasons within quantum (field) theory which compel us to consider a non-classical description of space-time and of space-time geometry. Quantum theory needs a time parameter, so as to describe the evolution of quantum systems. This time parameter is a part of a classical space-time, whose geometry is determined by classical bodies according to the laws of general relativity. But classical bodies are a limiting case of quantum systems. It should be possible to describe the dynamics of a quantum system without having any dependence [direct or indirect] on classical bodies. And yet, in the absence of classical bodies [i.e. if all matter were quantum], one cannot have a classical space-time geometry, nor a classical space-time manifold. This is a consequence of the so-called Einstein hole argument, which you can learn more about, from say this video: The problem of time in quantum theory [https://www.youtube.com/watch?v=fGdOTokept8]

Thus, we must have a formulation of quantum theory which does not depend on classical space-time. This will be our sought for quantum theory of gravity. We do not quantise gravity or space-time. Rather, we remove space-time from quantum (field) theory.

Can this goal be achieved by applying the rules of quantum theory to a classical theory of gravity? The answer is no. Firstly, the quantum rules are written down assuming classical time to exist. How then can we apply these rules to quantise the very time parameter whose classical existence was in the first place assumed, for writing these rules? There is no guarantee that this [admittedly illogical] step will lead us to the correct theory. 

But secondly, there is an even more serious reason for the answer to be no. A classical theory of gravity does not permit superposition of space-time geometries: such superpositions are never observed, just as a chair is never observed in more than one place at the same time. On the other hand, a quantum gravity theory resulting from quantising classical gravity will naturally admit superpositions of geometries. And the theory will predict a superposition of geometries even when the bodies producing these geometries become large and classical. Same way as quantum theory predicts that a chair can be here and there at the same time. This is the Schrodinger cat paradox in the context of spacetime geometries. In the language of the previous post, such a quantum gravity theory is not the cover of classical general relativity.

To recover classical general relativity from quantum gravity, the sought for quantum gravity theory must admit a spontaneous collapse of superposed geometries, precisely in the spirit of the GRWP theory discussed in the previous post. Let us name such quantum gravity, which admits spontaneous collapse of geometry, as spontaneous quantum gravity. From here it is easy to reason that the absence of macroscopic position superpositions in the classical world  is a consequence of spontaneous quantum gravity. Classical space emerges from quantum gravity, and moreover for classical space to exist, macroscopic bodies must be classical (not quantum). Thus the GRWP theory is a consequence of quantum gravity. This is readily seen in another way. Imagine a situation in which no quantum object has yet undergone spontaneous collapse: then there is only quantum matter and quantum space-time - the domain of quantum gravity. It follows that GRWP must arise from quantum gravity. Hence the name spontaneous quantum gravity.

Spontaneous quantum gravity [SQG] is the cover for classical general relativity, same way as GRWP is cover for Newton’s mechanics. SQG is falsifiable, because it predicts spontaneous collapse, and the latter is falsifiable. Recall that in GRWP, spontaneous collapse is proposed in an ad hoc manner. But in SQG, spontaneous collapse is not ad hoc. It is a consequence of the structure and dynamics of the theory.

One could well ask, quantum (field) theories of other interactions, such as QED, are not covers of their classical counterparts, such as Maxwell’s electrodynamics. Yet, why is QED such a successful theory, even though it does not explain the absence of superpositions in the classical electro-magnetic world? The answer is that QED is not a quantum theory of spacetime. It is the quantum theory of a field which lives on spacetime, and of the electric charges which produce these fields. Quantum gravity has to explain how classical space emerges, and since classical space is tied to absence of position superpositions in macroscopic bodies, quantum gravity has to explain why macroscopic bodies are classical. Once the position of macroscopic bodies is localised, their mass is localised, and their electric charge is localised too, and hence the associated electromagnetic fields are classical. Electromagnetic fields live on classical space-time, and require space-time to pre-exist. Space-time does not live on a classical electromagnetic field! Hence the buck stops with gravity.

We saw in the previous post that GRWP theory is the cover for Newton’s mechanics, and for small systems GRWP reduces to quantum theory, because the rate of spontaneous localisation is negligible for small systems. In the present post we see that spontaneous quantum gravity is the cover for classical general relativity, and for small objects it reduces to …? Reduces to what? We expect it to reduce to quantum gravity, because now the rate of spontaneous collapse of geometries is negligible, where by quantum gravity we mean quantisation of classical general relativity. [Incidentally, when we talk of rate of collapse of superposed space-time geometries, how is rate defined? What is this time parameter which keeps the rate? We will take up this deep question subsequently]. Thus, in all likelihood, we expect that the limit of SQG for small objects is related to loop quantum gravity. So we can say:

GRWP theory = Quantum theory + Spontaneous collapse 

SQG = Quantum gravity + Spontaneous collapse

The GRWP theory already exists and is well defined and is being tested in the laboratory. How do we mathematically formulate spontaneous quantum gravity? We will take this up in a forthcoming post.