The velocity of photons is isotropic property in vacuum, while in fermions it's affected by the uncertainty principle. How can we understand this conflict. If there is a velocity transformation between a fermion and a classical observer. Do you think it will be real or imaginary?
and If there is a velocity transformation between a photon and a classical observer do you think it will be real or imaginary? with the reason please.
Thanks to all;
Dear Christian Baumgarten
The classical observer if observes electron can't say exactly what it's velocity is, if he/ she try to measure it, it will certainly change the value of this velocity. in photons the matter is different you don't have to measure them in vacuum to know their velocity. If you apply the LT in describing the velocity of an electron relative to a classical observer this will contradict quantum mechanics, because the real transformations suppose to give a precise result, while if we have an imaginary one this will be more consistent with quantum mechanics which usually prefers the complex form.
The velocity of photons in vacuum is the same in any inertial frame, as an expression of relativistic invariance. The velocity of massive fermions doesn't have this property for the same reason: only massless excitations have this property. The uncertainty principle as such is relevant for non-relativistic quantum mechanics but doesn't prohibit the existence of momentum eigenstates, which, for free, massive, particles, would be velocity eigenstates. However massless particles, such a the photon, don't make sense in this non-relativistic approximation.
In the context of relativistic quantum mechanics, i.e. quantum field theory, massless particles, whether bosons or fermions, travel at the speed of light in vacuum.
Dear Prof. Stam
Thank you, but I'm asking about transformations of velocities for classical observers relative to elementary particles, if there is such one, do you expect it to be real or imaginary, for photons and fermions?
Massless particles, whether bosons or fermions, travel at the speed of light in vacuum-the sentence quoted was chopped in a way that makes it *wrong*: bosons or fermions DON'T travel at the speed of light in vacuum; MASSLESS particles, whether bosons or fermions, travel at the speed of light in vacuum.
And the reason is the energy-momentum relation E=|p|c, which holds for massless particles.
It doesn't matter what the observers are: the Lorentz transformations from one inertial frame to another don't depend on the spin of the particle. More precisely, the spin components will transform appropriately and the statement that a particle is a boson or a fermion depends on the corresponding Casimir of the Poincaré group, which is invariant, just like the mass.
Dear Christian,
Thank you for your interest.
I will explain the points in the same order as follows:
a. the non classical observer is any elementary particle that we want to accomplish the transformation of position and time between it and any classical observer.
b. The complex LT which are intended to accomplish transformations between elementary particles and classical observers are in the following reference:
https://www.researchgate.net/publication/259996539_Solving_the_instantaneous_response_paradox_of_entangled_particles_using_the_time_of_events_theory
c. Even if you have a precise value of position and momentum at the same time (which is forbidden by uncertainty principle) the transformations suppose not to return a precise value because the classical observer itself is moving and its movement is related to elementary particle's movement by a complex relation.
wish it becomes clear now.
regards
Sadeem
Article Solving the instantaneous response paradox of entangled part...
Dear Christian,
a. I think there is no harm in assuming that, on reverse this may give a real advantage to understand how particle observe each other and how they observe our measurement. I prefer using these concepts if we really want to understand what's going on in between these particles. Otherwise we have no choice just to deal with measurements and the result from them, but this is not enough to understand what's really happened in each phenomenon.
b.Ok,
c. You can consider it as a claim which is based on the new theory assumptions. In this theory there is a difference between time dilation that yielded from the relative movement of two observers one of them at rest and the other with velocity v, and the time dilation that yielded from the movement of two observers one with velocity v1 and the other v2, but the relative velocity is v. This difference only appears at velocities near the speed of light, while in conventional velocities its not recognizable.
regards,
Sadeem
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