Why do physicists believe that a mathematically consistent model that unites quantum mechanics and general relativity exists?It is a good question, and obviously hit a nerve. I have written a FQXi essay on this topic, and many blog postings. Today's theoretical physicists are preoccupied with the belief that there is some inconsistency between quantum mechanics and relativity that must be resolved, especially for black holes.
If mathematics breaks down when applied to black holes, why do scientists believe that mathematics can describe black holes? Perhaps the search for the mathematics that unites quantum mechanics and general relativity is pointless. Mathematics is a useful tool for modelling the universe in many ways, but maybe black holes are exceptional entities that can't be modeled by mathematics. Is it possible that the interior of black holes are so alien to our known universe and so different that current mathematical models/abstractions simply do not apply.
In fact there is no inconsistency as a physical problem. Quantum mechanics has been made fully consistent with relativity and gravity for all observable scales. To get a problem, you have to assume that all the mass of an electron is concentrated in a point, reject QFT renormalization, and look for the electron's event horizon. Of course, the electron is not really a point particle.
What annoys Motl is that well-known Berkeley professor Richard Muller does not subscribe to the string theory religion on this question:
It is almost a physics religion to believe that relativity can ultimately be combined with quantum physics. There is no evidence for this other than the fact that all the other forces of physics have been "unified". It is possible that relativity is different; that it is geometric and not quantum mechanical. But most physicists think that will not be the case, in large part because quantum physics has been so successful in the past. That's why they are looking to unify them. But it is worthwhile to recognize that this is based on hope, not on any firm physics or mathematics reason. ...He is right. Motl answers:
Much of the enthusiasm for string theory is that it addresses this [renormalization] problem, while introducing many more (extra dimensions, huge numbers of parameters, etc). Personally, given the problems of string theory, I am not optimistic that it will be with us 20 years from now.
Well, the person who wrote this question is a layman who obviously doesn't understand what the words "mathematics" and "science" mean. Mathematics can't "fail" as a description of Nature because mathematics is, pretty much by definition, the language of the most accurate and reliable description of anything. ...Math is all about deducing consequences from axioms. Physics is all about explaining the natural world. The study of quantum gravity is neither.
Dr Muller clearly stands next to the most insane pro-religion nuts who say that theoretical physics is just another religion – one that only tries to compete with The Church of Jesus Christ of Latter-day Saints.
When our leading theoretical physicists focus on questions with no possible observable consequences, then it is like discussion of theological issues.
Physicist Sabine Hossenfelder attempts to answer these questions:
1. Why do some physicists think our universe may be a hologram?To summarize, our physics elites believe we are in a hologram, but there is no rigorous math for this, and no observable consquences.
2. Why is it interesting that our universe might be a hologram?
3. Where are we in the holographic universe?
4. How well does this duality work?
5. Does this have something to do with Stephen Hawking's recent proposal for how to solve the black hole information loss problem?
Sometimes physics is determined by a boundary value problem, and the boundary to the universe can be considered the set of black hole event horizons. So maybe we are all determined by black hole boundaries. Sound profound? No, it is just a stupid idea to use some mathematical trickery to confuse you.
Update: Motl attacks another Muller answer on black holes.