There’s no problem with solving the Klein-Gordon Equation. It’s just that some of the solutions have a form for which [math]H\Psi=i\frac{d\Psi}{dt}=E\Psi[/math] with arbitrarily large negative values of [math]E[/math]. If we were to try to interpret the solution as a quantum wavefunction this would correspond to having no lower bound on the energy – which is physically unstable.
Category: Quora Answers
Is special relativistic time dilation a real effect or just an illusion? Given two inertial frames each observer finds that the clock of the other runs slower than that observer’s own clock. So who is right?
This is a pretty good answer except that I wouldn’t say either of them is right if they think that their perception of relative slowness represents something that is objectively true for all observers.
Time dilation is a real effect on the perceptions of observers (with regard to the rates at which one another’s clocks are ticking). Neither of them is “right” if they think there is any real sense in which the other’s clock is objectively slower. But neither of them is wrong about how it appears to them, so it’s not really an illusion any more than the fact that if they are looking at one another then their ideas of the “forward” direction are opposite to one another. What turns out to be more of an illusion is the sense we all have that there is some absolute standard of time which determines which of two spatially separated events occurs before the other.
Are the electric and magnetic fields always perpendicular to each other?
Not always. The rate of change of either is perpendicular to the other, but there is no such general relation between the actual values. In fact for static fields it is easy to make them parallel – as, in the picture below, at the centre of a current carrying loop with positive and negative charges above and below:
If magnetism is the relativistic effect on the electric field, how does someone explain magnetic fields generated by a particle’s spin? Also, how does someone explain light as both fields propagating perpendicularly if they are ‘the same thing’?
The only situation in which magnetism could be considered to be just the relativistic effect on the electric field is one in which there is an inertial frame in which all charges are stationary. In any situation with relatively moving charges there is a magnetic field in every frame, and it is only the way in which the splitting of the combined electromagnetic field varies between observers that is a relativistic effect. In particular, a current loop always produces a magnetic field in every reference frame and the situation for electron spin is analogous (though not quite the same because it’s a pure quantum effect and not really due to actually moving charges).
In the absence of any static fields, the electric and magnetic fields are perpendicular to one another but for light waves they both propagate in the same direction.