CarlB
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JesseM said:Are you assuming the 4th spatial dimension is a compact one? If not, why do we seem to have only 3 degrees of movement? And if so, then is the "preferred reference frame" the same as the one where the diameter is maximized?
Different people treat the proper time dimension differently. I treat it as compact for the reasons you give.
Instead of the diameter of the compact dimension, if I'm going to talk about measurements along the hidden dimension I prefer to measure its circumference. Otherwise you have to define an embedding space or some such. Unfortunately, as with other ether theories, there is no way for us to measure distances in the hidden dimension, so there is no way for us to determine the preferred reference frame (at least with normal matter and light).
What I'm trying to say here is that the death of the preferred reference frame and ether was not from Einstein's showing that it was unneeded. In fact, a preferred reference frame / ether had never been needed in that no one ever had any idea where such a frame existed. They were needed only as a philosophical item in that it could not otherwise be imagined how vibrations could move through a vacuum.
Instead, the death thrust to the preferred reference frame / ether was the requirement that vibrations in it (i.e. light) satisfy the Lorentz transformations for different reference frames. This is a very special symmetry. But if that symmetry arises naturally from a hidden dimension, then the philosophical support for the preference frame / ether returns.
I wrote up a very short and simple 2 page paper on the phase velocity of de Broglie waves and the "proper time geometry", which is what I call Euclidean relativity that may give a better idea of why one naturally thinks of a preferred reference frame when using Euclidean relativity, but does not when using special relativity:
http://brannenworks.com/a_phase.pdf
The paper looks ugly in some versions of acrobat but it prints cleanly. It's not my current thinking on the subject, but it does give a suggestion of how QM and Euclidean relativity interact.
I should note that I wrote the above before I appreciated how many other people were working in the area, so there aren't nearly enough references included. Euclidean relativity is so natural that many authors, myself included, came upon it without knowing that others had already discovered it. The newer (and better) papers deal with general relativity, but my own interest is in elementary particles and fields. So naturally, I came to Euclidean relativity through an exploration of standard model particle symmetries.
Carl