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Huummm… Noether's Theorem doesn't really relate position and momentum, or time and energy. It simply states that every differentiable symmetry ( time and translation )of the action ( integral over time of the Lagrangian ) has a conserved current ( energy and momentum ). I'd put it down to coincidence. But if someone can show a relation, I'd be very interested in hearing about it. ( good question, Strange )

It is also not made of wood. What does that have to do with anything? You asked if "speed is directly proportional to transparency".

That's the Sagnac effect. As seen in a Mach-Zehnder interferometer or laser gyroscope, among other places.

You have to separate the inherent behavior from our ability to perceive. The eye's response has limitations, which is why we perceive a series of still images as motion (i.e. it's why we can appreciate movies) So you need to distinguish "People can't see it" (i.e. invisible to the naked eye) from "it can't be seen/detected" (and can sometimes be applied to specific wavelengths/frequencies of EM radiation, e.g. "invisible to radar") Are atoms invisible, just because they're small? Depends on which definition you use.

Yes. So maybe I am asking why those specific pairs are related via Fourier transforms. No, there isn't. Which is interesting.

Local would have to be a lot smaller than that, eg. "measured at the center of the centrifuge" might work. If you're moving fast enough for it to not be negligible, and you send light in a path around the edge of the centrifuge, then an observer moving around the centrifuge will measure that light will take more time to make a round trip (from observer back to observer) in the direction the observer is going, and less than usual in the opposite direction. Both path lengths are measured to be the same in either direction. You can confirm the timing in the "outside" inertial frame: by the time the light has made a full circle in the outside frame, the observer has moved on from its original position, and light must make more than a full circle when sent in the same direction the observer is moving, and less in the opposite direction. However, this is not really a valid measure of the speed of light. You could call it the "coordinate speed" of light, and it's been argued on these forums that it's a meaningless measure. I'd say it'd be like making individual measurements in different momentary inertial frames of the revolving observer; you can get similar invalid measures of the speed of light if you switch between inertial frames in SR without properly accounting for the switch.

Yes to the first but on the second (which affects the first) instead of the y axis replace the y axis with ct. Your Lorentz transforms being two frames of importance is the x and x prime and ct and ct primed. Here is a primer https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.physics.umanitoba.ca/~tosborn/EM_7590_Web_Page/Resource%20Materials/Lorentz%20transformation.pdf&ved=2ahUKEwihsuGZ_rrkAhURip4KHYFJCgoQFjAOegQIAhAB&usg=AOvVaw2q6445SkfrxpQV8FkQ34jD This one is handy as it includes the Minkowskii diagram showing the hyperbolic rotation.

E=mc^2 The energy content of an object at rest is proportional to its mass. An object can also have KE (or energy associated with its motion) which is not part of the rest energy. Yes No. Mass and energy are properties. Everything has energy. Many things have mass. It is a property, not a substance. Not virtual I would say that it’s a property of time-translation symmetry, but that is probably too pedantic in this level of discussion.

No, transparency of everyday objects such as fan blades is not affected by velocity relative an observer I think it can be explained like this: Lets say that the fan blades cover 50% of the circular area of the fan. 50% is openings between blades. Start the fan and let it rotate fast so that eyes cannot track the movement of the blades, it looks like a blur. Now think of how eyes works. Simply the eyes register photons and by averaging over many photons an image is created and interpreted by the brain*. Noe look from below the fan towards ceiling. Since the fan blades are spinning fast the photons coming from the fan blades and also from the ceiling between fan blades. Since the blades are 50% of the area there is approximately 50% photons from fan blades and 50% photons from ceiling reaching the eyes of the observer. Result would be that brain interprets photons as coming from something like a half-transparent disc. For a fan with a color similar to ceiling and thinner blades the fan could look almost invisible or almost fully transparent. *) very simplified, hopefully correct enough for the context

Please upload the math, too.

Nonsense.