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Engage the warp drive , Mr. Sulu... cosmic speed limit may have been broken! Engage the warp drive , Mr. Sulu... cosmic speed limit may have been broken!

02-28-2012 , 04:30 PM
Quote:
Originally Posted by Aaron W.
If not, is there a non-technical (or not overly technical) explanation as to the nature of the incompatibility?
One comment that I've heard on this before is that QM treats time and space differently. Space shows up as an observable (a hermitian operator); time shows up as a parameter characterizing the group of time evolution operators. Writing this out, though, it occurs to me that you'd think this would already be a problem in the context of special relativity, which quantum field theory can handle.
Engage the warp drive , Mr. Sulu... cosmic speed limit may have been broken! Quote
02-28-2012 , 06:53 PM
Eh. QM sort of breaks the letter of special relatively as it's taught to undergrads in that it does allow for some types of faster-than-light travel. It doesn't break the spirit of special relatively in that it obeys the Lorentz transforms without appearing to actually violate causality.

I was referring to the mess related to quantum gravity. The oversimplified explanation is "General relativity describes gravity as a smooth curvature in spacetime, with gravitational attraction applying a continuous force. QM explains the other forces as the quantized exchange of force particles in a fuzzy but flat spacetime, a world in which the idea of a continuous force doesn't really make sense."

In reality, some of that isn't necessarily a problem. E.g., curved spacetime and flat spacetime might just be different models and mathematics that lead to the same results. The problem of a continuous force in quantum mechanics is much more serious. It gets messier still because attempts to model gravity in a more quantum-style way (whose success would imply that GR is an imperfect theory, though a very good approximation) have so far failed.

(Note: I have almost no sense at all for what string theory is. Maybe they've come up with a potential solution to this problem. Maybe they're also just writing some physics papers about a universe that doesn't exist with math that nobody's figured out how to do anything with.)

Last edited by NoahSD; 02-28-2012 at 07:08 PM.
Engage the warp drive , Mr. Sulu... cosmic speed limit may have been broken! Quote
02-28-2012 , 07:10 PM
The instant way to see a problem is through the field equations of General Relativity if i tried to bypass formalism and other Quantum Field Theory ideas to offer a crude argument (better illustrated later by first studying Quantum Electrodynamic for example
http://en.wikipedia.org/wiki/Quantum_electrodynamics
where Special Relativity and QM work well together up to a point, but forced to move away from classical electromagnetism concepts in order to address questions that Quantum theory renders sensible ie you no longer deal with forces and point particles and perfectly known trajectories etc).


http://en.wikipedia.org/wiki/Einstein_field_equations

You try in them (field equations) to relate the geometry of spacetime (Riemann Tensor) with the energy momentum (stress) tensor. In other words the distribution of matter and energy defines the geometry.

http://en.wikipedia.org/wiki/Stress%...3energy_tensor

The source of the field ie particles are of quantum nature eventually yet this treatment insists on dealing with them as perfectly localizable sources that their position and momentum are perfectly known at the same time (eg see how GR solves the Kepler problem of Sun -Earth using a point source for Sun). The source is treated as having the kind of objective reality that the metric desires but the particles as quantum objects fail to behave in that manner. So instantly the field equations cannot be quantum mechanically consistent.

Try to write down a stress tensor for say an electron when we know its described by a wave function and can be only seen as a probability cloud. The metric geometry doesnt have a probabilistic nature but the sources do!


Read also other ways to visualize the problem here;

http://en.wikipedia.org/wiki/Planck_scale


From a Quantum field theory perspective Renormalization fails when you try to quantize gravity.

http://en.wikipedia.org/wiki/Renormalization

http://en.wikipedia.org/wiki/Third_quantization
Engage the warp drive , Mr. Sulu... cosmic speed limit may have been broken! Quote
02-28-2012 , 07:19 PM
^^^ Yeah, except it's even messier than that because you can think "Well, the continuity and exactness of GR might be approximate just like classical E+M", but then you run into the problem that attempts to quantize gravity completely fail at high energies. In other words, the problem isn'tt simply that GR isn't a quantized theory, it's that we've failed to come up with any decent quantized theory of graviry.

I should stop talking before I put my foot in my mouth, though... assuming I haven't already.
Engage the warp drive , Mr. Sulu... cosmic speed limit may have been broken! Quote
02-28-2012 , 09:41 PM
Quote:
Originally Posted by Aaron W.
If not, is there a non-technical (or not overly technical) explanation as to the nature of the incompatibility?
I wouldn't call this non technical, but hopefully it's not overly technical either.

http://golem.ph.utexas.edu/~distler/...es/000639.html
Engage the warp drive , Mr. Sulu... cosmic speed limit may have been broken! Quote
02-29-2012 , 07:04 PM
Quote:
Originally Posted by NoahSD
^^^ Yeah, except it's even messier than that because you can think "Well, the continuity and exactness of GR might be approximate just like classical E+M", but then you run into the problem that attempts to quantize gravity completely fail at high energies. In other words, the problem isn'tt simply that GR isn't a quantized theory, it's that we've failed to come up with any decent quantized theory of graviry.
Instead of quantizing graviry, why can’t we ontologize quantiviry? Oh yeah,
“If we can't disprove Bohm we must all agree to ignore him.” – Robert Oppenheimer
Engage the warp drive , Mr. Sulu... cosmic speed limit may have been broken! Quote

      
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