Why can't quantum mechanics explain gravity? - by Viktor T. Toth - Quora Question Review

This document contains a review of the answer by Viktor T. Toth on the question in Quora: "Why can't quantum mechanics explain gravity?"
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• The text in italics is copied from the article.
  
• Immediate followed by some comments
  

Contents

• 1. Answer Review Viktor T. Toth

Reflection

• Reflection 1 - Question Review

1. Answer Review Viktor T. Toth

First of all, allow me to explain what known physics can do, before I explain where the problems lie.

Contrary to what you may occasionally hear, "we can do quantum field theory on the curved spacetime background of general relativity.

What does that mean: "we can do"

The theory has some striking consequences, not the least of which is that the notion of a “particle” becomes observer-dependent, and depending on the circumstances, where some observers see particle content, other observers see nothing. (The technical background is that once spacetime is curved, there is no privileged flat Minkowski-background, and the so-called Fourier-decomposition of a field, which is what gives rise to the field quanta that we recognize as particles, is different in different accelerating reference frames.)

Why defining two types of observers?

It is also possible to introduce quantum matter as a source of gravitation, but only in a rather inelegant way. Quantum matter is represented mathematically using quantities that do not behave as numbers.

This raises the question if there is a physical difference betweem matter and quantum matter? Is the Earth matter or Quantum matter?

Spacetime, on the other hand, is characterized by numbers. To make the equations work, quantum matter is represented instead by an average of sorts, the so-called “expectation value”. This allows us to have an equation with numbers on both sides. This is called semiclassical gravity. It may be an approximation, a kludge, but semiclassical gravity accurately describes all regimes accessible to us through experiment or astronomical observation. This means, unfortunately, that Nature offers no hints as to how we can go beyond this level of description.

This whole paragraph is not clear.

What we would like to have is more than an ad hoc semiclassical equation, but a proper quantum field theory of gravitation or equivalent. The problem with gravitation starts with its coupling constant, Newton’s constant of gravitation. This is a dimensioned constant, that is, it has units attached. In units preferred by particle physicists, the gravitational constant has units of length squared or units of inverse mass squared. It is known that a theory with such a coupling constant is not renormalizable: that is, the usual technique of removing the infinities that arise in a quantum field theory and produce consistently finite results do not work for gravitation.

This whole paragraph is not clear.

This is a problem that so far found no satisfactory resolution. Semiclassical gravity works but it is inelegant. For a while, there was hope that in gravitation the unwanted infinities cancel out each other anyway but that has not been the case. Many different approaches have since been tried, ranging from novel approaches to quantizing gravity to not quantizing gravity at all. Ultimately, I think the real problem is that beyond semiclassical gravity, Nature offered no hints so far. Much as we’d like to think that we are smart enough to figure out things on our own, that has never been the case: Physics is dead without data.

This whole paragraph is not clear.

So that, then, is my answer to this question: Quantum physics so far failed when it comes to gravity because we never found a way to measure the quantum effects of gravity, and thus we’re trying to solve a riddle without any clues.

3.

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