KJW

So why is the paper entitled On the electrodynamics of moving bodies ? And why is page 1 of the paper all about Maxwell, electrodynamics and what the paper is going to do with them (which he subsequently does) ? And why is his concluding technical statement "These three relationships are a complete expression for the laws according to which, by the theory here advanced, the electron must move." ? That was more than a hundred years ago. Relativity has moved on since Einstein. The concept of spacetime didn't even exist at the time of Einstein's paper on Special Relativity... that was Minkowski's innovation. And it was an important innovation because without it there would be no General Relativity. Relativity, both Special and especially General, is about spacetime, regardless of historical development.

Relativity is not about electromagnetism, it is about spacetime.

vp = λ f Are you sure about that? After all, differences in phase are observable without contradicting gauge invariance. I see two meanings to "wave" in QM. Firstly, there is "wave" as in "wavefunction", a general term referring to any waveform. But there is also "wave" as in "wave-particle duality" which I see as referring specifically to a sinusoidal waveform. In other words, a particle with definite momentum, and therefore definite wavelength. But also definite energy, and therefore definite frequency. Phase velocity might not be meaningful for all wavefunctions, but that does not make it meaningless for all wavefunctions.

vp = λ f I don't know about that. Earlier, I mentioned time crystals, the time-based analogue of ordinary crystals, but nobody seemed to have noticed. This at least allows frequency to be measured in principle even if not currently in practice.

Is this some form of holography? I tend to agree with this. But ultimately, I was simply justifying the statement that phase velocity can be obtained from the measurements of wavelength and frequency.

It's definitely from x-ray crystallography. Note that only the carbon atoms are showing because hydrogen atoms are rather insensitive to x-rays. Neutron diffraction would be better if one needs to explore bonding to hydrogen atoms.

I don't think so. And? Yes, I did. The velocities of the two frames are relative to the third frame. Perhaps I should have simply said the velocity relative to the third frame of the second frame is equal and opposite that of the first frame. Why would I?

Correct. Although I haven't seen an electron density map of hexamethylbenzene before, I have seen electron density maps of other compounds, so I did know what I was looking at with your picture. Hmmm, perhaps I spoke too soon. The direct image from x-ray crystallography is an arrangement of spots of various intensities. A Fourier transformation of these intensities yields a Patterson function (a convolution of the electron density with its inverse) due to the "phase problem". So how does one obtain a photographic plate image of the electron density? Specifically, what is performing the Fourier transformation? In particular, how is the "phase problem" being solved? I didn't use those as examples as I'm not very knowledgeable of those fields.

There are two inertial frames of reference in which there is no acceleration. The acceleration in going from one inertial frame to the other inertial frame does not count. Otherwise, it would be one non-inertial frame of reference.

I did substantiate my claim. I said:

As I said, I'm familiar with chemistry.

I'm familiar with chemistry. That's why I chose an example from chemistry. It seems to me that you don't understand the point I'm making.

No, I don't have a diagram. I actually don't see the difficulty.

The same could be said about any quantum wavefunction because we are in fact talking about the quantum wavefunction of a free non-zero mass particle.

I don't think it would be too difficult to arrange the frames of reference and the rod orientations to give the same length contraction, thereby establishing that the rod is the same length in both frames of reference. The simplest would be for the rod to be oriented parallel to the change in velocity in both frames of reference, and for the third frame of reference to be collinear to the other two frames of reference.

One could measure the clock and the rod in both frames of reference from a third frame of reference relative to which the two frames of reference have equal speeds.

How is the above a direct measurement of electron density? I've already indicated above that x-ray crystallography is not a direct measurement of molecular structure. Producing a detailed image of the electron density of a molecule is not the same as being a direct measurement. That's exactly my point. If a direct measurement is unavailable, then an indirect measurement based on sound principles is acceptable. Thus, although the phase of a De Broglie wave cannot be measured, the phase velocity of a De Broglie wave can be indirectly measured by measuring the wavelength and frequency of the wave.

No, you have misunderstood what I said. If in some inertial frame of reference, I have a clock that ticks away seconds and a rod that is one meter long, and I accelerate to some other inertial frame of reference, then the clock will still tick away seconds and the rod will still be one meter long. This is the principle of relativity in action and neither time dilation nor length contraction would make sense without it.

A lot of science is based on indirect measurements based on some theory. For example, in chemistry, do we really have direct knowledge of chemical structure? Perhaps the most direct measurement of a molecule's structure is through x-ray crystallography, but even that involves the theory of x-ray diffraction along with dealing with Fourier transforms.

I don't know if the frequency is currently measurable, but in principle at least, one could use time crystals.

Or alternatively, by measuring the frequency and wavelength by some form of diffraction experiment.

When I quote a post that quotes a post, I do not get the quote within the quote, only what the poster of the post I quoted wrote. But I've seen other people have quotes within quotes. How?

How do I create multiple quotes from the same post? And how do I quote within a quote? More generally, how do I view the codes within a post (rather than a WYSIWYG view of a post)?

You need to recheck this.

No, λf does not equal the group velocity. vg = dω/dk whereas λf = ω/k = vp.