How do relativity and quantum mechanics contradict each other?

[mrspeedybob]

I didn't think this question really belonged in either sub-section so I put it here. I hope that's OK. I've always heard that they contradict each other but I've never understood how. What predictions do they make differently?

[zhermes]

The biggest issue is that the Schrodinger equation (the fundamental equation of QM) is not lorentz-invariant. This means that the equations of QM are different for two observers moving at a relative velocity to one another---which is clearly unacceptable for relativity.

Additionally, QM always maintains a conserved particle number. From relativity we learn that E=\gamma mc^2, and thus whenever the energy of a system (e.g. a pair of photons) is greater than the rest mass energy of another particle-pair (e.g. electron-positron pair), we can expect some probability of particle creation.

[Dr Lots-o'watts]

What about the Dirac equation? What is it missing to reconcile the two?
http://en.wikipedia.org/wiki/Dirac_equation

[snackster17]

some one told me yesterday that massive particles indeed can reach the speed of light, is this true?

[Dr Lots-o'watts]

some one told me yesterday that massive particles indeed can reach the speed of light, is this true?

99.99...% the speed of light and as many "9"'s you can afford, but never 100% the speed of light.

Now frankly, it does make sense that anything massive could never go as fast as something that is not.

[zhermes]

What about the Dirac equation? What is it missing to reconcile the two?
http://en.wikipedia.org/wiki/Dirac_equation
I'm pretty sure the dirac equation is fully relativistic.

The Dirac equation is still missing other features... e.g. remember it only applies to spin-1/2 particles, and its still not a field theory---so again, it has issues with varying particle number.