Is the Lorentz Transform the Complete Picture?

[marlowgs]

Einstein wasn't wrong but could there be more to the picture than his version of special relativity? You can see what I'm talking about if you rewrite the Lorentz transformation gamma factor in the form of the Pythagorean theorem: c*c=v*v + c*c/g/g. The complex quantity ~c = v + i*c/g clearly includes the gamma factor as its magnitude but also includes a phase component. The real component is the observed velocity. For photons the observed real component is c so there is no imaginary component. For photons in free space, electric and magnetic waves are in phase. Particles of matter contain a real and imaginary component. Thus from the complex representation, one can surmise that matter is made of electric and magnetic waves that are out of phase (by 90 degrees for particles at rest).

 

Multiply both sides by m*c and you get a complex energy ~E = p*c + i*Eo. The real component is the transmitted energy (not kinetic) and the imaginary component is the stored (rest) energy. Divide both sides by Plank's constant and you get a complex frequency ~f = p*c/h + i*fo. The real component gives the DeBroglie wavelength h/p. This is the wave that creates the interference pattern of particles of matter passing through a slit.

 

With this complex representation the origin of matter waves is explained. Also the equivalence of matter and energy is no mystery because they are made of the same thing - electric and magnetic waves. Only the phase distinguishes the two.

[Perturbation]

Complex energies, momenta etc. of real particles don't make any sense physically and are just as undesirable as negative energies. Wave nature is well explained by quantum mechanics without having to resort to complex energies etc. That's an odd looking form of the Lorentz transformation for a boost.

 

As for the Lorentz group [imath]SO^{\uparrow}_+(1, 3)[/imath], it's not the full picture, as it doesn't include translations, only rotations and boosts. The full symmetry group is the Poincare [imath]\cal{P}[/imath].

[marlowgs]

That is only the gamma factor of the Lorentz transformation. And the imaginary component makes quite a lot of physical sense. It is a 90 degree shift between electric and magnetic waves. One sees this same thing in alternating current circuits. The reactive components (inductors and capacitors) store energy by a 90 degree shift between voltage (electric field) and current (magnetic field).

[Perturbation]

By saying "let's introduce some difference in phase" doesn't allow one to conclude that matter consists of out of phase magnetic and electric waves. If they were, it would be noticable. Any wave-form can be described by a complex number. And in that complex number you're saying that c, the speed of light, is a complex number with Re©=v. Furthermore, playing with the gamma factor doesn't change anything about the particle itself, the gamma factor is derived from the geometry of Minkowski space-time.

 

The duality of matter is described well enough with QM.

[ydoaPs]

where did the alternating current stuff come from?

[Klaynos]

where did the alternating current stuff come from?

 

An example of the physicall meaningness of complex numbers...

[marlowgs]

The phase difference is noticeable. Because the observed velocity of the imaginary component is zero (a particle of matter at rest), we see the waves frozen in time. The phase difference of the electric wave is seen as charge – one polarity leading the magnetic wave by 90 degrees and the other lagging by 90. This is why charge produces a static electric field. The phase of the magnetic wave is seen as spin – again the two polarities differing by 180 degrees. And this is why spin produces a static magnetic field.

 

Any pair of waves can be described by a complex number – so why not electric and magnetic waves?

 

The complex speed of light (~c) has a constant magnitude of c. Photon particles travelling in free space have an imaginary component equal to zero (no rest mass).

 

The phase component is lost in the geometry of Minkowski space-time and only magnitude is described.

 

QM does a good job but there are still many unanswered questions, not the least of which is unification.

[Perturbation]

The phase difference is noticeable. Because the observed velocity of the imaginary component is zero (a particle of matter at rest)' date=' we see the waves frozen in time. The phase difference of the electric wave is seen as charge – one polarity leading the magnetic wave by 90 degrees and the other lagging by 90. This is why charge produces a static electric field. The phase of the magnetic wave is seen as spin – again the two polarities differing by 180 degrees. And this is why spin produces a static magnetic field.

 

Any pair of waves can be described by a complex number – so why not electric and magnetic waves?

 

The complex speed of light (~c) has a constant magnitude of c. Photon particles travelling in free space have an imaginary component equal to zero (no rest mass).

 

The phase component is lost in the geometry of Minkowski space-time and only magnitude is described.

 

QM does a good job but there are still many unanswered questions, not the least of which is unification.[/quote']

 

Oh well, if any plane waves can be described by a complex number then we can call this plane wave electromagnetic rather than, say, a water wave. No, we cannot. Electromagnetic waves consist of two orthogonal waves which obey Maxwell's equations. Just because you've rearranged the gamma factor of SR doesn't mean you can conclude that matter is just a wave. The gamma factor does not in any way relate the nature of matter, as I said it's derived from the geometry of Minkowski space-time and brings new implications for the nature of relative interital motion. Again if matter were an electromagnetic wave it would be noticable in the same way that photons are: electromagnetic waves behave completely differently to the "matter-waves" (spin, statistics etc. etc.).

 

If your complex speed of light is "lost in the geometry" then there's no way to verify your assertion and your claim is pretty redundant. Really all your [imath]c=v+i\frac{c}{\gamma}[/imath] is saying is that the speed of light is complex, not matter itself, and there's also no reason why v shouldn't be the imaginary part, as we get the same modulus for c either way.

 

Phase isn't the imaginary part of a complex number anyway, it's the angle subtended from the line joining the origin to the complex number with the real axis in the Argand plane.

 

The problem of unification in physics lies in reconciling general relativity with the standard model. Here we're dealing with special relativity and the transformation group associated with boosts and rotations on the tangent space of a globally flat manifold, not the pseudo-Riemannian manifold whose curvature is, in general, non-zero that one operates on in general relativity, and where the Lorentz group is not globally applicable. It's very easy to incoporate special relativity in quantum theory, all I'd have to do is write down some Lorentz invariant field equation/Lagrangian, such as the Dirac or Klein-Gordon equations. Since relativistic quantum mechanics and field theory are well established divisions of particle physics there's no reason to deny them the title of an accurate model because we haven't been able to formulate GR at Planck scales when we're discussing special relativity.

[Perturbation]

You're equation for energy, and thus the de' Broglie wavelength, won't work for light, as you've multiplied it by [imath]m_0\gamma[/imath] and [imath]m_0=0[/imath] for real photons.

[marlowgs]

I don’t see where I multiplied by m0*g. The imaginary component of light energy is zero because mo = 0, but I’m saying that de Broglie waves come from the real component. So a light particle will produce an interference pattern just like the real component of a moving particle of matter. A photon is simply a particle with no rest mass and it works fine in my equation for energy.

 

As for your previous post, if you don’t like the gamma factor, start with the equation for energy: E^2 = (pc)^2+Eo^2 or its mass equivalent: m^2 = (p/c)^2 +mo^2. The fact that this represents a right triangle is a hint that complex numbers may be involved. I chose the imaginary component to be Eo because it looks like stored energy, just like one sees in the energy stored in a capacitors or inductors. And I chose pc to represent the real part because it represents transmitted energy (the energy of a photon with momentum p) because it looks like the radiating energy of a resistor. Minkowski space-time is derived only from the observation of the speed of particles of light and matter. But the speed of particles only represents the real part of a possible complex quantity. In an imaginary space-time one would expect to see the oscillation and transmission of the imaginary component of a complex energy. In fact it should look just like light. In our real space-time, defined by the motion of particles, the imaginary component should appear differently. The two properties of matter (the possible imaginary component) that look most like electric and magnetic waves are charge and spin. The question of how we would observe this imaginary space-time is still open. I’m guessing that the imaginary time component occupies all of real time and appears frozen to us. The imaginary space component (beyond the wavelength of the energy) would occupy all of real space and its amplitude would appear to obey the inverse square law. A frozen electric wave gives you a static electric field and a frozen magnetic wave gives you a static magnetic field. Add the frozen waves using the inverse square decline in amplitude and you get the electric and magnetic force without resorting to exchange of virtual photons.

 

What could be more beautiful than a universe that consists of only electromagnetic waves and their interactions? I think it will take more than 10 dimensions of space and time to undo the mistakes of previous work we now take as religious canon.

[Perturbation]

Damn it, stupid accidental post.

[marlowgs]

If you need more evidence, just look at the combination of matter and antimatter. As I said, the electric waves would be 180 degrees out of phase between the two charges (one +90 from the magnetic wave and the other -90). If you combined the two, you would get zero for the imaginary component (stored energy of matter). But the energy can't be lost so it must be converted to the real energy of light. In the opposite process of pair production you start with a photon that passes by a heavy particle (such as a proton) and you get a matter/antimatter pair (such as an electron and positron). This indicates that matter is in some way made from electric and magnetic waves. The simples way to do this is to shift the phase.