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by Bruce Linnell |
Concept behind the Lorentz Transformation: How do you make it so that EVERYONE passing through the origin of the light-cone is at the CENTER of the lightcone?
Obviously, not every line passing from the bottom to top of the light-cone is at the center horizontally. But you can chop the light-cone at a different angle, so that they are at the center of the light-cone.
It may seem odd that two different observers coming through the same point would have such different perspectives of simultaneity.
But look how strange three-dimensional rotation is:
See how quickly up and down, left and right, and forward and backward are changed. Notice how the apparent angles go from 0 degrees to 180 degrees. Notice how the lengths of the lines seem to grow and contract.
The Lorentz Transformation does the same thing with a few constraints and differences. Whereas, with rotation, left becomes forward, and forward becomes down, etc. The future and past axes are different. You cannot move the future-past axis to lie in any of the up-down-left-right-forward-backward planes. That is, you cannot make a space-like "interval" into a time-like interval, or vice versa.
A similarity between rotation and Lorentz Transformation is that they both require an ORIGIN. You get mightily different results depending on what point you point of rotation, or your fulcrum. Namely, in these animations, if I used a different origin, the transformations would swing the image right off the screen!
I guess I could try to name all the similarities and differences between rotation and lorentz transformation. But really, they aren't that much alike, except for a few superficial mathematical similarities. Or are they very alike, because of the striking mathematical similarities? That is a matter of opinion, of course.
But what is NOT opinion?
That photons act as both particles (interacting with single particles) and waves (having measurable wavelength λ). That photons (travel in/occupy) that boundary between space and time. That photons do not experience either time nor space; but rather photons are a direct interaction between the source and destination particles.
Somewhere in that divide between time and space, I feel like there's an important question, begging to be asked, and if it could be phrased just right, the answer would come along shortly.
But what is that question? Does it have something to do with deBroglie matter waves? Diffraction? Magnetism? Bell's Theorem? Quantum mechanics?
I don't know.