I am working on the multi-dimensional spacetime. I realized that we can describe and expand the relation between the energy, mass and momentum of the particles from one dimensional spacetime and create their relationship formula in the higher dimensional spacetime. I realized that dimensional analysis is not valid in this method. I didn't find any source for discussing on the dimensional analysis when some terms of the equation belongs to n-dimensional spacetime and other terms are belong to the m-dimensional spacetime. For instance, does the unit of the measurement of the energy of the a one-dimensional particle is equal to the unit of the measurement of the three-dimensional particle?. these are my preprint paper and equations that not supported by dimensional spacetime.
These Preprints are under review, I don't know that could I use natural system of units for overcoming consistency.
Preprint Is Einstein's special relativity wrong?
Preprint Is it possible to obtain multi-dimensional energy-momentum e...
Preprint Introducing new equation for total energy, potential energy,...
Dear Bahram,
However many dimensions-spaces geometries you are considering, the unit of measurement of energy must be identical for consistency to be maintained, either joules (or ergs) or electronvolts (eV).
For an example of vector structure for the Maxwell equations compliant expanded trispatial geometry, you will see in the following paper how they are deployed in the trispatial LC equations of this model:
Michaud A (2017) The Last Challenge of Modern Physics. J Phys Math 8: 217. doi: 10.4172/2090-0902.1000217
https://www.gsjournal.net/Science-Journals/Research%20Papers-Unification%20Theories/Download/6877
Best Regards, André
Dear Bahram,
You can use the Planck units.
Here is an example of how I use them based on the maximum and minimum that the universe marks:
Preprint ENERGIA FOTÓN, APROXIMACIÓN GRAVEDAD UNIVERSAL DE NEWTON Y L...
The dimensional analysis is always one of the simplest methods to check the accuracy of derived physical quantities in terms of the fundamental ones by applying the principle of homogeneity in the dimensional formulae;
It is always valid if and only if the parametric dependencies of physical variables are restricted as per the SI predictions
Guys, I have prepared one section in these articles and have discussed about the dimensional analysis in the 4th dimension (time dimension) in the Minkowski spacetime, Also I have expanded it in the n dimensional spacetime.
Preprint Comparing multi-dimensional energy-momentum equation and rel...
and
Preprint How quantum of the mass, k box, and photon make light and matter?
in the time dimension [v]=1
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