How do quantum mechanics (physics) and general relativity contradict each other?

Question

please answer with examples or something i can understand. I'm new at physics.

Answer 1

The quantum theory of gravity is non-renormalizable, a fancy word which means it breaks down at really small distance scales / high energy levels.  The theory we have today must be only an effective theory that works at low energies and large distances.  String theory is an attempt to come up with underlying theory that explains both coherently.  The problem is that it isn't terribly good at predicting phenomena at energies we can achieve experimentally.

I guess I sort of restated what Eri said.  What oldpilot says is true, but the problem is a little deeper than that.

Scythian--of course non-relativistic QM is inconsistent with relativity.  Unless you're an undergrad in introductory QM, I wouldn't call the Schrodinger equation the centerpiece of quantum mechanics.  The relativistic equations (Klein-Gordon, Dirac, Proca) fix the trivial problems you mention.  The problems with relativistic gravity go deeper, however.  It sort of lies in the fact that the theory is non-linear.  Gravity couples to energy, including gravitational energy.  So the loop diagrams get out of control and lead to infinities that can't be renormalized.

Bio-freak--I wouldn't sweat too much over the GR model and the idea that bending space-time is somehow fundamental to gravity.  QFT can reproduce (at the macroscopic, low-energy limit) the same results without resorting to a warping time and space.  That probably will never be as useful computationally as the traditional approach to GR, but it's probably more reflective of the underlying reality at short distances and high energies.

Answer 2

They don't.  General Relativity discribes the macro world.  Quantum Mechanics discribes the micro world.  The micro world is lumpy and probibilalistic.  When things get big enough to be p[art of the macro world the lumps average out and things "look" smooth."  The difference is the scale at which observations are made.  

Got to PBS.org and look for "The Elegant Universe"  it is about 6 hours of vedio that ties this all together

Answer 3

In quantum mechanics, you can have a superposition, which means that a system can be in two (or more) states at once.  One possible superposition that can be attained is a spatial superposition, where an object can be in two (or more) locations at once, let's call them locations A and B.  From relativity, we know that an object with mass will bend space-time.  So if you think of the object in location A, there will be a space-time associated with that object in that location.  If you now consider the object in location B, there will be a space-time associated with this location as well.  So a spatial superposition requires a superposition of space-times as well.  But one thing that relativity requires is that there to be a single space-time.  Therefore, there can not be two space-times between which you can have a superposition.  This is a conflict between the two theories.

Answer 4

The centerpiece of quantum mechanics is the Schrodinger wave equation, which is a differential equation operating on state functions.  Position state functions, for example, are decomposable into deBroglie waves of varying wavelengths.  In order for the well-oiled mathematical machinery of all of this to work, the pure momentum deBroglie waves cannot truly be relativistic waves, that is, where E² = (pc)² + (mc²)².  They have to be "Newtonian" deBroglie waves where E = p²/2m.  If relativistic deBroglie waves are used, then we end up not with the Schrodinger wave equation, but with the Klein-Gordon equation, which presents all kinds of dificulties, such as that probability is not conserved for single particle systems. The KG equation is more fruitful when used in relativistic quantum field theory, where there is better harmony between QM and SR.

ADDENDUM:  (Ω)Mistress Bekki, thanks for pointing out that the Asker's question may be addressed to the current state of quantum theory, not undergrad quantum mechanics.  He did say that he was "new" to physics, and when taking undegrad quantum mechanics, it is almost never pointed out that the texts on QM are pulling a fast one in claiming that there's any harmony at all between QM and SR.  I thought it would be worth pointing that out, so that the Asker wouldn't be confused about that.  As for the larger question of harmonizing QM with GR, well, that's still an unresolved matter, isn't it?  Quantum Loop Gravity seems ahead in this race in resolving it, but it's not a done fact.  I don't think we even have the mathematical apparatus yet to resolve this issue, we are still trying to make a radio using only gears and pulleys, so to speak.

Answer 5

Quantum mechanics works very well on small scales (photons, particle, hydrogen atom).  General relativity works very well on large scales (everything bigger).  But when you try to use one to predict the other, you run into a problem - quantum mechanics works using probabilities, but when you try to use general relativity in there you get infinities in your equations.  Since probabilities go from 0 to 1, that's a problem.  It can be solved be adding more dimensions (ala string theory) but has not yet been tested experimentally.