Your derivation looks very amateurish - like someone’s first foray to electrodynamics. A creationist class with this will make it apparent that creationist physicists are subpar. I am sure that this is not your intent.

Also, don’t dodge this point, the paper you linked in that thread:

Did not find anisotropy in the speed of light. In contrary, it found no signal that could be detected by their instruments, which leads to the upper limits that they published (as if there is a signal larger than this limit, their instruments would be able to detect it). This is clear if you read the paper.

Your derivation looks very amateurish - like someone’s first foray to electrodynamics.

Ok, so I’m an amateur, that’s fair. My intent was to describe the invariance accurately from something some of them may know already, and even then, not every one has even an undergrad semester of electrodynamics, so even a step down for you would be several steps up for others. It’s certainly a nice way to get a refresher on the meaning of the symbols of Maxwell’s equations.

Did not find anisotropy in the speed of light. In contrary, it found no signal that could be detected by their instruments, which leads to the upper limits that they published (as if there is a signal larger than this limit, their instruments would be able to detect it). This is clear if you read the paper.

Cahill interpreted it differently. I put it on the table because that’s how Cahill read it, and I provided Cahill’s commentary on that and other experiments. Cahill was probably saying the results were UN-witting, as well as other experiments.

Cahill is a known crackpot, and completely biased on this matter. I don’t care about second hand interpretation of the result (especially from a biased crackpot) when we have the first hand account: Show me where in the original paper that there is a detection of the anisotropy.

I this is how Cahill interpreted it graphically (with experiment in question by Kircher in the topmost and bottom most panels reflected by the blue line, which looks like the original graph in Kircher’s paper):

Michelson-type Interferometers with Fresnel drag can be re-interpreted to give similar results according to Cahill. Up until I encountered these dissident views, I was unacquainted with Fresnel drag, even though it is a well established phenomenon. Most Michelson-type interferometers were operated in a vacuum and thus removed the Fresnel drag – a rather important thing in detecting the aether.

I know what Cahill wrote. This does not suffice. Where is the data analysis section? What are the systematics?

Just saying that the data is in phase with each other are not enough, especially as the period is 24 hours. Do you not know that, because of the 24 hour period of the Earth’s rotation, there are many daily systematics aside from preferred frame effects?

Regardless, is this paper the one you mean when you said:

If so then this claim is wrong, as even Cahill thinks that the Krisher paper alone is not enough to show an anomaly, but only when it is combined with the other experiments.

Edit: @stcordova, I have to go to mass, so any reply will be delayed. You’re saved by the bell (literally) this time.

On second thought, that actually is a good feature since a freshman who can find partial derivatives and state partial derivatives with the chain rule can, if he is determined enough, do exactly the derivation I did. The fundamental pillar of SR then becomes accessible. “Amateurish” is a prejudicial word, I prefer, “accessible” as it describes why I liked that approach. No need to be so disdainful of teaching things at an elementary level.

As far as you derogatory remark that it was silly, a professor of physics thought it was a good exercise for his students to do that very derivation 12 years ago. I merely had to reconstruct it again as I had heretofore forgotten how to do it. I found it very edifying to go through that exercise myself.

I’m sorry for being derogatory, on second reading, it’s a very harsh thing to say.

What I am more concerned with is this: you claim that you can justify a non-standard interpretation of the Lorentz transformation, yet are very amateurish with the standard interpretation. When we want to modify something, it is important to first master what we want to modify. This is also coupled with your misunderstandings of equations such as, and I quote from your other posts:

\LARGE v(t) = \int {a(t)}

the way you write it doesn’t even have any mathematical meaning…

Your last post on the twin paradox also shows that you don’t even grasp the basics of special relativity, yet try to use it to justify preferred frame effects.

You mean the indefinite integral rather than the definite integral? I could throw in a dummy variable and then insert the limits of the integral.

If that’s the fix I need, then I thank you for your comment. That made it worth my while then to post it here.

you can justify a non-standard interpretation of the Lorentz transformation

That was more in line with the interpretation by Lorentz himself in his Lorentz Ether Theory (LET). I’m not exactly re-inventing the wheel, just resurrecting what was suggested by the author of the transformations that are, ironically, still at the heart of Einstein’s version of relativity.

At issue is whether there can be experimental test that distinguishes Loretz-SR from Einstein-SR, and I think something entailing speed of light in a di-electric medium like air or glass where there is Fresnel dragging will be a deciding factor. In fact, Fresnel dragging wasn’t even mentioned in my intro Electro Dynamics book by Hayt. I have the Griffiths book somewhere packed away and I have to look at it. Michelson-Interferometers that have Frenel dragging apparently show the anomaly that favor’s Lorents.

An important experiment, that Lorentz analyzed and provided his own Fresnel dragging formula is the Fizeau experiment:

The Michelson-Morely experiment with air inside the interferometer had small amounts of Fresnel dragging. The versions of this experiment were by Michelson-Morely themselves and Dayton Miller. When analyzed in light of the Fresnel dragging, we see the appropriate fright shifts.

Your last post on the twin paradox also shows that you don’t even grasp the basics of special relativity, yet try to use it to justify preferred frame effects.

One clock accumulates less ticks than another. That is experimentally verified. Extending the thought experiment a little farther will show there is a V_ref = 0.

It is clear that your preferred frame theory is different from Lorent’s original ether theory. Hendrik Lorentz’s theory, by construction, has no observable prediction that is distinct from special relativity. You are making modifications upon Lorentz’s original theory.

Newtonian mechanics has an infinite number of preferred frames , called inertial frames.

Newtonian mechanics, and by extension, special relativity, do have an infinite number of preferred frames, the non-inertial frames. This is distinct from “preferred frame” effects, which specifically refers to having a preferred non-inertial frame.

The fact that non-inertial frames are preferred in SR is not news. This is the cause of the asymmetry in the twin paradox, one frame is inertial, while the other isn’t. This is covered in any basic special relativity textbooks.

Ok, a student exercise thought experiment involving Base Space station with two spacecraft (Turtle and Rabbit). We launch the space craft in opposite directions and accelerate them to 86.66% the speed of light relative to the Base Space station and coast along for a while, then they return to the space station. And (with some adjustment due to acceleration and GR) effects, we find the clocks on Turtle and Rabbit have fewer ticks than the clock on the Base Space station. Do you have a problem with that? We record the number tick difference between the Base Station, Turtle and Rabbit.

Now we will replicate the experiment with the only variation that the Base Station before launching the rockets will itself be accelerated to 86.66% the speed of light in the direction that Rabbit will eventually be launched. When Base Station accelerates to it’s terminal velocity (relative to where it started) at 86.66% the speed of light, I expect one would get the same result comparing ticks with Rabbit against Base Station, but what about ticks of Turtle vs. Base Station?

I’m afraid this is not well explained in text because two frames that are unacelerated relative to each other during the experiment are considered inertial in the treatment of elementary explanations!

The history of acceleration of one frame relative to another is not usually stated in elementary treatments. The two frames are treated as inertial.

In the limit of infinite acceleration (which for ease, is usually what is presented in introductory textbooks), Rabbit (the moving twin) only becomes non-inertial at one point: the turning point. This is enough to break the symmetry in the twin paradox.

But regarding these supposed intertial frames, how then do we deal with the supposed clocks in Supernova decay curves. Supernova at High Z supposedly evolve slower relative to our clock. Do their clocks really slow down or is that an illusion? I mean if we had an observer in this High Z supernova looking at us in our vicinity, would they think supernova near us had slower clocks. Assume the answer is yes, that means both clocks slowed down? That seems a logical contradiction.

Having high z supernova breaks the degeneracy, as the time dilation due to cosmological redshift is a GR (gravitational) effect that is non-symmetric. In other words, the frame of the high-z supernova is not inertial and cannot be treated with special relativity.

It is due to the expansion of space. This expansion is a GR (gravitational) effect, and is what makes the frame of the high-z supernova non-inertial. In the picture with Hubble velocity, the velocity changes with distance, so there is acceleration, making the frame moving with Hubble velocity non-inertial.