I've been reading a lot of physics books over the past year, and almost all authors assert that "unifying" quantum mechanics and general relativity is one of the major "challenges" of physics. Also over the past couple of hours I researched this issue further to see if I could easily find a answer, but I couldn't. My question is:
Why is it important for Quantum Mechanics and General Relativity to be unified?
Most physicists say that QM and GTR don't contradict each other.

As far as I know QM governs the very small, and GTR governs the very large, so what would we gain by "unifying" them?

Any answers would be great!

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The first principle is that you must not fool yourself - and you are the easiest person to fool.
~~~ Richard Feynman ~~~
There is no harm in doubt and skepticism, for it is through these that new discoveries are made.
~~~ Richard Feynman ~~~

The GUT.

The basic goal is to understand the universe, as a whole, to be able to explain it. But also to be able to influence it.
Quantum Mechanics may bring us Amazing computers and FTL (maybe). Same can be said for Relativity.

But if the Understandings are not United- if there is a gap- if they aren't bridged- then basically we must be misunderstanding. Because the very existence of both demonstrates that they are Unified- it's our understanding of them that is not unified.
Until we unify it in our descriptions- then we are lacking in understanding.

The two biggest answers I can give you are cosmology and black holes (see below).



While they don't really contradict each other, they aren't compatible. The biggest incompatibility is that in QM, the Electro-Weak and Color are forces that are mediated by the exchange of particles. In GR, gravity is an effect of the geometry of spacetime, it's not a force.

GR is a classical theory. There are no discreet quantities in GR. As a matter of fact, GR uses the idea of the manifold of differential geometry to model spacetime. This has to be smooth and continuous for GR to work. QM, requires discreet components In addition, being classical, the idea of the uncertainty principle in not part of GR. GR equations can't determine the warping of spacetime, when a particle's position is uncertain.


Let's go back to those two answers. What you may not know, is that very small can also mean a very large energy. For cosmology, QM and GR an still compatible all the way back to approximately 10^-43 sec. after the Big Bang. A time of very high energy. Earlier than that time, infinities start turning up in the GR equations that render the GR equations useless. We simply can't say anything about any time earlier than that.

With black holes, we have the very small. As a star collapses to a black hole, there is nothing we know of that can stop the collapse to a singularity at the center of a black hole. All the mass of the star compressed down to a single point. Again, the GR equations become undefined at this point (we end up dividing by zero).

In both cases, the unification of QM and GR into a Quantum Theory of Gravity, holds out hope of solving both of those problems. Now, one of the problems of trying to combine these is that the pertubative methods that are used in QM to get rid of the infinities (google renormalization) do not work if you try to do a straight conversion of GR into a Quantum theory with a force.

Hope this helped.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

The Grand Unifying Theory (or GUT) possibly the first step to The Theory of Everything (or TOE) would allow thoughts and discoveries along new lines. The lesser potential is to harness the forces, it would be preferable work with the forces of nature as they are intended to be used. Then the next steps toward the TOE is understanding consciousness, reality and finally our place in the universe.

It is a tall order and many have tried. Perhaps there is something that we are not seeing yet or do not recognize for what it is.

The saddest thing about such a discovery would be the basic human desire to profit from it selfishly or seek power and abuse such knowledge. One could only hope such a discovery would find those with the wisdom to moderate their initial greed and look for the long term benefit of all creatures.

Michael.

Thanks spratleyj and Tensor for a great question and a great answer. I was also one of the many people who 'knew' the two were incompatible, but not even as much of an answer to why as Tensor just gave.

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Forming opinions as we speak

Thanks for the responses, I think Tensor explained it very well... one follow up question: Would this "unification" require "new" physics? or would it just be a way of "combining" GTR and QM?

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The first principle is that you must not fool yourself - and you are the easiest person to fool.
~~~ Richard Feynman ~~~
There is no harm in doubt and skepticism, for it is through these that new discoveries are made.
~~~ Richard Feynman ~~~

Depends on what you mean by new physics. The main problem in making GR work like a strait QM theory is that the force carrier (You've probably heard of the hypothetical "graviton") would be a massless, spin 2 particle. Massless, because it works over an infinite distance (much like a photon, the force carrier for the QED) and spin 2, because gravity is only attractive (spin 2 particles are only attractive. the photon is spin 1 which allows attraction and repulsion). The problem as I said, is that our current methods of renormalization don't work with spin 2 particles. I we could find new mathematical techniques to renormalize spin 2 particles, then no, new physics would be needed.

On the other hand, String theory is new physics. Another possibility that you may not have heard of is Loop Quantum Gravity, also new physics. This is an attempt to quantify the manifold of GR. Physically, this would mean, spacetime, instead of the being continuous, as in GR, would be discreet quantities, subject to uncertainty and superposition, as requried by a quantum theory. Both are nonpertubative.

One of the main differences is that String theory (more correctly Superstring Theory) is background dependent) and LQG is Background independent. Background dependent means that the background is seen to be fixed and unchanging. GR is background independent as spacetime (represented the manifold) changes or is dynamic, depending on the energy within spacetime. LQG recaptures this independence.

Both theories, can produce the Black Hole entropy equations of GR. LQG can't produce, as of yet, any of the equations of GR in the semiclassical limit. One exciting thing about String theory is that String theory itself is not internally self-consistent, unless the equations of GR are satisfied within the theory. Neither has produced any prediction that differs from GR.

None of the above make either theory "right". But, there is enough there to keep investigating, for now.

I thought I caught in one of your posts that you were in your teens. You may want to read a bit on all this. I would recomment "QED The Strange Theory of Light and Matter" by Richard Feynman, "Spacetime Physics" by Taylor and Wheeler (this is a college textbook, but you seem to be able to handle most of it). "The Theory of Almost Everything:The Standard Model, the Unsung Triumph of Modern Physics" by Robert Oerter, The Elegant Universe" by Brian Greene and Black Holes and Time Warps: Einstein's Outrageous Legacy" by Kip Thorne. These books will give you a good feel for current thought in Relativity (both Special and General), the Standard Model of Particle Physics and some information the the attempt to get to a GUT and to find a Quantum Gravity Theory.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

I've always found it intriguing that this figure is less than one order of magnitude from Planck time, 5.39 × 10⁻⁴⁴ s. Given that it's just "approximately," statistically, we could say that it's equivalent (or nearly so) to Planck time...

And if it were equivalent... ?

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I am Mugs, of the Alien clan of Usa, Nordamerica, a Terran, of Sol. Human.

Whoever says "perception is reality" is daft. It's merely an abstraction, and often not a very good one.

Yes, I'm 15... again thanks for the helpful post I've already read a couple of those books... I'm currently finishing up Black Holes and Time Warps, which I have found to be very interesting and well written... I try to read what ever I can get for free (either online, or from the library), but I'll eventually purchase some books, thanks for the suggestions.

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The first principle is that you must not fool yourself - and you are the easiest person to fool.
~~~ Richard Feynman ~~~
There is no harm in doubt and skepticism, for it is through these that new discoveries are made.
~~~ Richard Feynman ~~~

Tensor. Good recommendations for reading. I'll strongly suggest "Mirror Asymmetry and Time Reversed Worlds" by Martin Gardner, and "The Neutrino" by Isaac Asimov, too, for a rookie. Good introduction to group theories, and particle physics. pete

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A third rate theory forbids
A second rate theory explains after the fact
A first rate theory predicts...A. Lomonosov

Those are good too Pete, and he may want to look into those two after he gets through mine(or before, I'm not picky). They cover their particular subjects much more in depth. Mine were based on trying to cover as much territory in as few books as possible, for his particular question.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.