Joined: June 2006
|You might want to read Penrose's The Road to Reality.|
Penrose provides hypothetical geometries that could have been "real". Using complex numbers for dimensional quantities isn't a problem. Actually, not using complex numbers makes things unrealistic. Otherwise, you end of trying to segment things artificially in an attempt to avoid negative square roots (like you did above). Complex numbers are no more artificial than irrational numbers.
What you added was meaningless. When events are space-like, they are not causally connected, so you don't interpret the result the same way. I chose to use an actual General Relativity text, in this case Sean Carroll's Spacetime and Geometry which is based on the work of Thorne, Weinberg, Taylor, Wheeler, Hawking, Ellis, and Nash. There are actually different schools of thought on which convention to use, but the negative one is added to the metric, not the actual vector. If you want to classify imaginary numbers above as space-like separation that's fine, but you're arguing a convention, nothing more.
|BTW, if you are suggesting their is no interial frame of reference, how do you explain the Twin Paradox? The problem looks the same to both Twins. Each twin is standing still in his/her frame of reference and the other twin is the one moving. Why are the results different?|
I never made such a claim, merely that relativity was built up from electrodynamics as a way of satisfying Maxwell's equations in moving reference frames. No point was being made, just wanted to share some of his words. The twin paradox represents and equivalence in space-time. In this case dL^2 must be the same for both the traveling twin and the stationary twin. In the earth's frame of reference (with the speed of light set to 1):
by definition x,y,z=0, let's say 1 year passes and the brother travels 0.5 light years, the observer will see
L^2 = t^2 - x^2-y^2-z^2 = 1^2 - 0.5^2 -> L = 0.75 light-years
How much time has passed in his frame?
L^2 = t^2-x^2-y^2-z^2 -> 0.75^2 = t^2 -> t = 0.75 years
Time passed for stationary: 1 year. Time for traveling: 0.75 years.
|Say that three times fast. Better yet, say it in terms the listening audience can understand.|
I think they may figure out you aren't saying anything that contradicts what I said.
My point was that even though things like collapsing the wave function seem to violate relativity, they don't. You still need to compare the results, which will subject to the rules of space-time. I wasn't really trying to contradict, mainly to point out the practicality of so-called faster than light communication.
|This makes the entire universe (space and time) one large wavefunction in Minkowskian geometry.|
Quite. The structure of our universe was built up from density and tensor perturbations (quantum effects), much of that information can be found in things like the CMB. However, the unfortunate result from QM shows that as you increase the energy level, you revert to a classical state, in which case the wavefunction really becomes indistinguishable from a classical description.
|Hearing no objections from my last comment (I waited a whole five minutes), I will presume everyone understands and agrees that quantum effects are interconnected both in space and time.|
Unless you start talking about inflationary epochs, in which regions of the universe became causally disconnected as it expanded. I recommend Peacock's Physical Cosmology or Peeble's Inflationary Cosmology for more information.