Based on college sophomore-level knowledge, we developed [1] a description of special relativity (SR) that applies to accelerated, and arbitrary, motion.
This discussion considers, although not regularly offered at sophomore-level, that general relativity (GR) gives a better basis in undergraduate courses, and can be derived using [1].
This is useful because GR underlies much of the contemporary understanding of modern physics, including the big bang, pulsars, quasars, and gravitational waves.
As shown in [1], the laws of SR are just often simpler when they work in-between inertial frames, as originally stated.
[1] Preprint Special Relativity Applied to Arbitrary Motion
Eres pariente del otro Gerk? Si, bajo aceleracion constante se puede resolver un problema en SR que va de velocidad cero hasta c
A mi tambien me interesa problemas de Sturm Liouville, mas bien en contexto cuantico.
Manten tu creatividad, un saludo, Juan
Ola Juan,
Without a c? Probably. On this group, yes. Yes, but arbitrary motion is also possible -- it is in the paper.
The Sturm-Liouville problems provide a good intuition for quantum systems. However, they do not seem to work well with relativistic quantum mechanics, and I am interested in solutions there. Do you know any?
Thank you, Edgardo V. Gerck
Edgardo
From speed 0 up to c, the upper limit, when mass diverges.
Well the reason SL would not work for relativistic is clear. The structure of the Dirac equation is quite different, you
would have to start from something much closer to Dirac, with its matrices and 4 spinor. That is relativistic QM.
The SL structure is basically Schrodinger like.
Felices fiestas, Juan
Juan,
Arbitrary motion is within c, the speed of light. Length contraction or time dilation does not cease to exist just because the acceleration changes. In the paper, I gave an example, well-known, of a particle with changing acceleration in the lab frame, but the formalism of SR can handle that in intrinsic coordinates in a closed expression (integrable). This is shown in Fig. 1, and discussed later in the paper.
Yes, the reason SL would not work is clear. However, would it be possible to extend it piecewise? For example, one can add SR to a Newtonian representation, through a continuous infinity of hypothetical momentarily comoving inertial observers (as referenced in the paper). Could this offer, mutatis mutandis, a connection from SR to SL to Dirac? Adding a family of continuous, infinite, momentarily comoving, SL?
Feliz 2019, Edgardo
Edgardo
SR is still a clasical theory, nothing to do with the quantum. So if you want to do the quantum relativistically,
you go to the Dirac equation, which has proven to be Lorenz invariant also. You have to consult books on relativistic quantum
theory, or that have a chapter dedicated to it. Basically it comes from a linear form, which when squared reproduces the Einstein equation for energy in operator form, you have to read about it. It has negative energy levels, spin comes out naturally, antiparticles have some explanation. It is still the best, without going into still unsettled quantum field theory.
What I did with SR, is in the dynamic form, involving the relativistic form of momentum, so I dont even realize if length or time is
altered. I just added a force ma, where a is a parameter, not the actual resulting aceleration, except at low speeds. The model did give me a speed approaching c. I suppose if all the dynamics is done properly, then maybe the length and time are adjusted as you say, piece wise. As you probably know force is a bit controversial in SR.
The easiest path to turn Dirac into somthing more general would be to assume a weight function multiplying the wave function, on the right hand side,
in the time independent form. You start with some of the well known solutions of the Dirac equation, and you try to generalize it a bit. First you have to study these solutions, which are in the books.
Saludos Juan
One of the many failures of modern physics is that sophomores may not have a notion of the concepts of modern physics. That is, the fundamentals are made so complex that few have a true notion of the concepts (job security I suppose). Without such notion, confusion reigns. The goal should be to make models able to be comprehended by the sophomore.
John,
Thank you. That's why the principles are shown and discussed in the paper, extensively. I also provided examples. It's important to avoid belief, either way, but the basis is on experiments.
This discussion is now closed. RG is unsuitable for physics discussions, for lack of moderator and presence of cabals. I can be reached by PM.
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