Excellent analysis.

Good analysis.

Dear Karl,

I also analyzed the dimensional hurdle at the elementary particles level, so I will quote your text as I go and insert my comments, because you touch so many aspects of the problem in your short synthesis, that I know I would get lost into needless side issues if I try to cook up a single comment to all of this.

" We note that a slow-moving particle will have total energy (sans any potential energy) of E = mc^2/2 + mc^2/2 + mv^2/2"

Ok, but this is the traditional formulation grounded on classical mechanics and even on Special relativity, the mv2/2 representing the momentum energy.

Due to a discovery made by Paul Marmet in 2003, there is however reason to believe that the total energy of the particle would rather be:

E = mc2 + mv2 (double the energy of mv2/2, the other half going into relativistic mass increment at any velocity - asymptotically limited to c - Ref: equations (2) to (13) in this paper: https://doi.org/10.4236/jmp.2018.95067).

"Let us suppose that all energy of the particle is kinetic or potential energy."

"Potential" energy is an old concept that dates back to Newton's time, before electromagnetism was discovered and at least sufficiently well understood to develop useful devices such as the electric motor. From this new perspective, the concept of "potential energy" is not required to explain observed processes. So, I myself would simply formulate this statement as:

"Let us suppose that all energy of the particle is kinetic"

"The above equation suggests that the particle is also moving at c along two dimensions unknown to us."

Absolutely. There is the possibility of two such dimensions, two spaces actually perpendicular to each other and to normal space, from the electromagnetic perspective, both perpendicular to the direction of motion of the particle in normal space, one in which the internal transversely oscillating electromagnetic energy making up the rest mass of the electron reaches c as its energy is transversely moving towards maximum presence in one of these dimensions, and the other one as it reaches c again as it swings back transversely in this other dimension. Also described further on in the same paper.

"There is no known requirement that these dimensions obey special (or general) relativity,"

Absolute agreement, again.

"... or that their fundamental constants are the same as those in our familiar dimensions."

There is no known requirement either that they could not be the same as those of our familiar dimensions. So from the Occam's razor perspective, I would keep the more simple alternative, that is, that "if" there are such other dimensions, I think that their fundamental constants would be the same as those in our familiar dimensions.

"The kinetic energy from this motion yields the "rest mass" internal energy of the particle."

More complex to comment, but I would rather formulate this as:

"The kinetic energy from their motion yields their momentum energy plus the energy of their relativistic mass increase, while the kinetic energy that makes up their rest mass remains stable."

"Such a situation would mean two things. Mass all by itself is not energy. And there are additional dimensions."

From the perspective I concluded to, mass would be made of kinetic energy oscillating transversely with respect to normal space, within these additional dimensions that you suspect of existing.

"Starting from here, modified as may be necessary, could this be made to work (ie, to be compatible with) our existing physics?"

The answer is yes, and it actually is compatible with the set of existing electromagnetic equations.

"Energy then is always ultimately action or potential for action, not "internal." "New" interactions may exist in the two new dimensions."

You are so close to what I concluded. From my perspective:

"Energy is always ultimately action, that is, kinetic energy always in motion even within massive elementary particles and also as momentum energy or free moving energy".

And yes, these "new interactions" may exist in these two new dimensions (or spaces).

Best Regards, André

André Michaud Thanks very much for your interesting, quality response. Do you know of others here who have involved themselves with the same question?

Karl