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A question about a sign convention that leads to a lot of confusion. This is not the only instance multiple sign conventions in Science. In this case it is a result of History. Thermodynamics was originally developed by physical scientists and engineers. They were concerned with making machines (steam engines) for the industrial revolution. Steam engines are heat engines. That is they thought in terms of input (heat in the form of fuel) and output (work). Both of these were thought of as 'naturally being' positive quantities. So they wrote their version of the Law of Conservation of Energy (The First Law of Thermodynamics) as ΔU = q - w. Chemists came to the scene from a different point of view. They wanted all forms of energy to have the same sign, whichever side of the conservation appearance they appeared so they could present the equation as a sum on both sides of the equation. So they wrote their equation as ΔU = q + w. By then it was also realised that, although all the terms are energies, there is a difference between ΔU , which is a state variable of the system, and q and w which are exchange variables of the energies crossing the system boundary. So they tidied up by stating that all energies crossing the boundary from the system to the surroundings are negative and all energies passing from the surroundings to the system are positive. Now they could add them up, move them about in equations and between equations in other parts of Science in a consistent manner. It is an improved system But it shows the importance of knowing the sign convention in use and the equations that go with it. This last remark also applies to other such instances of multiple conventions such as those in Electricity, Elasticity and elsewhere.

This graph is the refractive index for water. The function of refraction index is not as simply dependent on wavelength as you are suggesting. The shape of the curve depends on the medium material, among other things. I hadn't considered dispersion before this conversation, and I appreciate your input, but I've already said that the function of refractive index by wavelength through spacetime could simply be a constant (i.e. not dependent on wavelength at all). The Einstein Lens could be proof of this. If you aren't satisfied with this response that's OK, but I'm not sure any further commentary on this topic is constructive. This can't be true. Instead of peaks and troughs, imagine tennis balls. Observer A hits a ball down towards B every second, and numbers them. If observer B is receiving these tennis balls at a higher frequency than 1 per second (from A's perspective) then he would be receiving tennis balls not even served yet. We rectify this by allowing A to claim that the frequency is the same but the wavelength (i.e. distance between tennis balls) is shorter for B -- and it would literally look like that to A because hitting tennis balls into a field of dilated time is like hitting them into a puddle of syrup. The frequency remains constant, but the wavelength shortens. (Wavelength) * (frequency) = (c) locally, and (wavelength at B from A's perspective) * (frequency at B from A's perspective) = (c at B from A's perspective) which means that light is moving more slowly at B from A's perspective. I did my best to explain my perspective on cavity interactions. If you think we still harbor a difference of opinion then I would agree that further discussion isn't going to be meaningful. Thanks though, Joigus. With these objections, it makes me question the function of gamma and GR time dilation in general. Is it only useful relative to two points in spacetime? Is time dilation represented in the field equations? Can we derive even derive a complete, universally valid time dilation field in GR?

This post made me think of 'Alice in Wonderland', then my next thought after reading on your mentioning his plans future plans, I thought "Curiouser and curiouser!".

GR uses the Levi-Civita connection, so there is no torsion. Also, if there were any vector fields involved, then those would be 4-vectors, not 3-vectors; and two separate vector fields still do not capture the necessary degrees of freedom. The field equations - like all physical quantities in GR - need to be covariant, so no, you can’t make any kind of explicit reference to an observer. One could also think of it in terms of gravitational radiation fields. These fields extend to infinity, and wave fronts in free space propagate at the speed of light; furthermore you have two distinct polarisation modes. In terms of field quanta, this automatically implies massless spin-2 bosons - which, mathematically speaking, can only “couple” to rank-2 tensors. So this is the lowest rank object that is needed to fully capture all relevant degrees of freedom of gravity.

Quadrillion in some countries is 10^24. The same issue as with billion and milliard. The same word but different meaning depending where you are living.

...and after all he's done for Fox News....ingrates!

Because they're chemists. Whaddaya gonna do?

Ah, got it. Thanks. You being a fluids guy may have this paper open up to you more than most. It seems to be a hard sell. -W I mean a dimensional manifold is a little more complex than the space needs. It's a simple 4-D space. -W Ghideon, It's plain to see you have read my paper carefully, thank you. Thank you for enlightening me on the big bang, i researched it since then and understand your position. As far as the big bang goes, my theory only needs a lot of energy to be released in a small amount of time. This will form up to a blast wave. The speed of sound is sqrt(k/rho). In ether, this results in the speed of light. No, but the Big Bang is part of the ether model. Conflict with established theory is what every reasonably skeptical observer should consider. -W I have researched the Big Bang and apologize to everyone who took exception at my calling it an event. I'm fine with expansion from a hot, dense state. This forms up into a blast wave. -W

Certainly. But you still have to prove they're pink! We can't just accept your word for everything.