Johnny5

I have recently become interested in inertial guidance systems, specifically I want to know the physics of how they work. Assume I know nothing and go from there. Thank you

Special relativity does not say that the speed of light is constant. Einstien got his idea that the speed of light is constant from classical Maxwellian electrodynamics. He then wrote that the speed of light is c, in all reference frames in which the laws of classical electrodynamics are true. He and others presumed that those frames were inertial frames. The actual answer is that they are true in the frames in which the experiments that measured [math] \epsilon_0 [/math] and [math] \mu_0 [/math] were carried out, namely the gravitational rest frame of the earth. Recall: [math] c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} [/math] [math] \epsilon_0 [/math] is the permittivity of free space [math] \mu_0 [/math] is the permeability of free space The units of c are that of a speed, specifically the speed of a wave in Maxwell's theory.

No I derived it years ago using the galilean transformations, but I forgot what I did. I was hoping someone here might have done the same thing, or have a different argument, reaching the same formula. Regards PS The argument went something like this. Start with the sine function: y = sin x The maximum amplitude is 1. Now, let the amplitude be arbitrary: [math] y = A_0 sin x [/math] Now, fix your attention on a point on the wave, at x = 90 degrees=pi/2 radians sin (90 degrees) = 1 A0 sin (90) = A0 So the coordinates of the point on the wave are: (x,y) = (pi/2,A0) Now, the wave is supposed to travel in the direction of increasing coordinates, so that this point on the waveform must have some velocity v, in that direction. Work fowards from here. Has anyone ever seen this derivation?

How in the world do you reach the conclusion that this becomes very apparent when v approaches c? Where are you getting the idea that if something is moving in your rest frame with speed v, and you push it with force F in the direction of motion and give it acceleration a1, that the same force applied perpendicular to v would give it an acceleration a2, which is different from a1. Are you using relativistic mass? Regards PS Did you draw the inference from experiments using particle accelerators? Could there be a drag force at work? I have many more questions.

Your statement is incorrect. The fundamental postulate of the theory of special relativity is that in any inertial reference frame, the speed of a photon must be measured to be exactly 299792458 meters per second. It does not postulate that the speed of light in ANY frame is 299792458 m/s.

Prove your statement please. Regards

Where on earth did you come up with that??? In a photonic frame, a photon's speed is zero by fiat. But, where did you get the idea that photons travel at c in all frames? That's just wrong. Regards

Isn't this incorrect, as you just said? And I have a few questions about weight, now that you bring it up. Is my weight on earth, the same kind of thing as when I am in a spaceship being accelerated? I mean on the earth, there is a force F upon me, and on the ship there is a force F, upon me. The origins of the force upon me are different. In the one case, my body is in a nonzero gravitational field, and in the other case, my body is in a zero gravitational field. So if weight is strictly caused by gravity, then is it correct to write W=mA, where A is the absolute acceleration of the spaceship? Or to ask the question succinctly, are gravitational and inertial mass equivalent? Regards

Start with the definition of rest frame, and go from there. You will see that photon's must have rest frames. Regards

That link doesn't say it, but on page 36 it talks about an alternative to BCS theory. I will find a link for you that does give the BCS prediction for the limit. Regards Here's an argument which shows that BSC theory incorrectly predicts penetration depth: IOP article on penetration depth

Your answer to A is incorrect. Your answer to B depends upon whether or not photons can be accelerated in their frame does it not? Or to come at the question from another angle, according to the principle of equivalence, the inertial mass of a photon is equivalent to its gravitational mass, its gravitational mass is nonzero, which means that its inertial mass is nonzero. Would you mind deriving the formula for total quantum mechanical energy for me in a simpler way, then maybe we can get this right. Regards

Of course photons have rest frames, and if m0=0 then for a photon you will get E=pc, but as I said, photons do have rest frames. Regards

For one I really don't like that derivation, isn't there a simpler one? Next, you just blatantly say that it is only true for photons, but if the formula for total energy is reference frame independent, then it applies to all particles even photons, so that even for a photon we have: [math] E^2 = (pc)^2 + (m_0c^2)^2 [/math] Where m0 is rest mass of a photon, in the rest frame of a photon. So if the rest mass of a photon isn't zero, then isn't your formula E=hf is wrong for photons? Regards

Will the answer depend upon whether or not the object I push in a vacuum is spinning? Regards

Can you explain why you claim both? Thank you

That sounds like an excellent answer. Let me ask you something, why did you exclude gravity? Thanks

Can you derive the formula for total energy of a free particle for me, using the 'spatiotemporal' Laplacian, because I agree, I do think there's an error somewhere. Thanks

I have a question about derivatives. Is there any step in the definition of a differential of time,dt, which mathematically stipulates that the flow of time is unidirectional, or does the mathematics of the "unidirectionality of time" have to come from the thermodynamical concept of entropy? Thank you

Is it possible to derive the formula for a traveling wave using classical Newtonian mechanics? Here is the formula I want to derive: [math] A(x,t) = A_0 sin(kx-\omega t ) [/math] Thank you

I want to know whether or not the universe has a center of mass. Is there any experimental fact that dictates that the universe must have one? Thank you