Quantum Mechanics vs. Relativity?

Detailed Answer (Summary at the end if you don't want to read it):

Great question, and lots of good responses. I want to point something out: general relativity is well tested, but not to the precision and accuracy of quantum mechanics. Many physicists prefer the quantum view of the universe over the general relativistic view in the sense that one is "more right" than the other. Feynman, for example, didn't like GR all that much from what I hear. But a lot of the black hole jocks (Hawking, Penrose, etc.) are fueling the idea that QFT (Quantum Field Theory - the successor of QM that takes into account Special Relativity but can't handle GR) has some flaws in light of recent discoveries in the theoretical work of blackhole physics. When applying QFT to Black Holes (which are heavily based on GR), they come up with results that indicate some issues with QFT. The QFT guys disagree.

So when Hawking says "both" theories are wrong, he's coming at it from a very biased, but most likely correct, point of view. Keep that in mind.

Black holes represent the limits of GR - as matter becomes more and more dense inside a blackhole (and even in Neutron stars), the energy density gets high enough that QFT is needed to really understand the physics. A blackhole in GR is explained as a singularity - the highly dense matter of the BH shrinks to a infinitesimally small point. Einstein and others didn't like this, of course, because it represents a mathematical "infinity" which are usually considered not physical. So black hole physicists deal with the Event Horizon of the blackhole, not the singularity. This is where QFT comes in. The correct theory of the universe should explain what happens as the star collapses to a black hole's singularity. Does something stop the collapse or does a true singularity really exist in nature?

Now QFT treats the forces of nature as an exchange of particles. Two electrons "feel each other" because they keep sending photons back and forth. Furthermore, the vaccuum of space is constantly "bubbling" with virtual particles that come into and out of existance according to the Uncertainty Principle. As a particle moves in space, it's interacting with this "bubbling brew" of particles. GR, on the other hand, treats space as a very smooth medium that warps and bends as particles with mass/energy pass through it.

Since gravity is caused by this curvature, quantizing gravity to treat it with QFT causes some bad mathematical results - namely infinities. It is, technically speaking, a non-renormalizable theory. That translates into: they can't find a way to ignore the bad results. Furthermore, no one can explain why gravity is so much weaker than the other forces. Think about it, every massive particle has gravity, but it takes entire planet-size masses for gravity to become important. That's not the case with the other forces. As physicists are trying to unify all the forces into one theory/force, gravity being so much weaker makes things a lot harder. It's also the hardest to test on the small scale for the same reason.

Summary:

OK, all that long explanation boils down to this: no one has succeeded in quantizing gravity because when they apply the same "techniques" to gravity as they did to the other interactions of nature, the Math yells at them and gives them results that go to infinity. This is the case with the other interactions, but those smart theorists found a way to eliminate the infinities which doesn't work with gravity. It has to do with how space is so "rough" on the small scale (in the sense that particles keep popping in and out, thus causing gravity to fluctuate). Also gravity is so much weaker than the other forces that it is hard to unify it with them (extra dimensions might solve this).

Quantum Mechanics Vs General Relativity

RE:

Quantum Mechanics vs. Relativity?

I have recently reread "A Brief History of Time" by Stephen Hawking and in the book, he states that quantum mechanics and relativity are contradictory to each other and therefore cannot both be correct. I realize that at present physics lacks a unified theory that incorporates both but in...

The fundamental problem between the two is that relativity assumes that space and time can be infinitely divided -- that there is no "fundamental unit" of space or time. Quantum mechanics assumes (but does not prove) the opposite -- that space and time do have a fundamental unit (i.e., there must be a minimum "quantity" of space and time). In most cases only one of the theories needs to be used to make predictions. However, there are cases where both need to be applied, and that's where the problems arise, because they don't play well together. Most physicists assume that singularities do not really exist; however, they need a more complete theory (string theory, perhaps) to make them go away.

Both can't be correct is a strong statement to make. The problem lies in the fact that relativity is known to work very well in a grand scale like the scale of stars and galaxies and quantum mechanics works in the scale of atoms and electrons. But when one tries to use them in different scales one gets contradictory results. That probably means we need to adjust them to work in all scales but no one has yet figured out how.

you can say both are very accurate within their own scale, quantum mechanics is very accurate in things that are really really small and relativity in things very very big... thats probably a very simple but understandable way to say it.

What Hawkins probably wants to say is that there is no one unified theory we can apply to any physical system regardless of its scale

Scale. It is not surprising that he would say they contradictory to each other. There are big differences in realms of atoms and molecules (where quantum mechanics is used) and stars and galaxies (where relativity comes into play).

He is pushing it by saying both cannot be correct. Quantum mechanics takes into account electrostatic charge and EMF generation which are very important in very Small systems. Relativity takes into account the relationship between mass and gravity which does not seem to be required for very Small systems, but is very important in very Large systems.

His statement is more like these cannot both be correct if applied to the wrong scale. The exact crossover is in the field of miniature black holes which have very high mass and yet very small size.

you recently answered my question on "expansion of the universe". thanks. you recommended " a brief history of time" ( read it when it came out ). i recommend to you " 3 roads to quantum gravity" or " the trouble with physics" both by Lee Smolin.

the above books address your question thoroughly with the latest understanding.

to answer your question, ( and i am NOT a person with limited understanding of physics ! ) , current physics is in a stagnant period and a great new idea must come forward now to move ahead.

your question is THE central dogma in physics today. the next great physicist ( forget about Hawking ) will be the ONE who unifies gravity with quantum physics.

i firmly believe radical NEW ideas will have to be accepted BUT that eventually, this new understanding will be based in a framework of einsteinian relativity with a "quantum" component. ( as opposed to string theory ). you can read Brian Greene's "Elegant Universe" for a look at string theory.

you are a great student of science in asking this bold question. i hope you explore more of it ! ( and please communicate with me if you like ! [ email same as tag ]

:)

Both represent two different regions of matter behaviur. One represent the macro behaviur and the other micro behaviur. We have very limited mathematical capablities. So we have theories that are valid in some region and no unified theory to combine all of them.

You have peaked my interest to re-read Hawking's book. I love this stuff.

Paradox is the two edge sword of reality; will it ever be unified?? Multi-verse (vs. the universe), black holes, that energy can be both a particle & a wave at the same time depending on how it is measured, etc. is amazing. I love it!

THANKS for your thinking........... :-)