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Complex trjectories?

  1. Nov 6, 2003 #1
    in fact you can e that any solution of the schroedinguer equation can be put in the form F=expi/hbar(S+hbar/iLn[R] where R is the real number formed by setting R=F*.F so this implies the relationship
    Pq[F>=Pc+hbar/igra[R][R> for any R so we would have the equality
    Pq= quantum operator asociated to momentum
    Pc=classic momentum
    hbar= planck,s h/2pi

    Pq=Pc+hbar/igra[R] so with this i conclude that:
    a)particles have trajectories in the complex plane
    b)the trajectories are given by extremizing the lagrangian
    L=L0+V+hbar/igra[R]/[R], with L0 the free lagrangian V the potential

    What do you think?.
     
  2. jcsd
  3. Nov 6, 2003 #2

    Njorl

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    I didn't check your math, so I don't know if what you did is valid. The question of complex velocities has arisen before. It brings up an interesting possibility. There really is no ban on superluminal velocities. The "impossibility" is movement at the speed of light. It has always been assumed that superluminal velocities are also banned because an object would need to accelerate through c to get to them. But if we allow complex velocities, one could accelerate "around" c to go superluminal.

    Njorl
     
  4. Nov 6, 2003 #3
    If there is no ban on super-liminal velocities, would a particle be constrained to either super-liminal, or sub liminal velocity. Or could it tunnel across the light barrier ? It cannot cross the light barrier because it needs infinite mass or infinite accelleration.

    If subatomic particles were travelling at above light speed, then at sqrt(2)c their mass would be j, compared to 1 at v=0. In fact we should consider their mass/energy to be a vector with angle 0, and their mass/energy above light speed to be a vector with angle pi/2.

    Would we oberve the mass/energy of a super-liminal particle as the length of its mass vector, or would be unable to observe it ?

    Actually such a particle would have complex mass, travel a complex distance, take a complex amount of time (actually from Einstein's equation I don't get negative time which is what I grew up beleiving) but it would travel at a real velocity which happens to be above c, between two points in real time space.
     
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