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ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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The Importance of Newtonian KE and P on Special Relativity

Authors: Ruggeri, Francesco R.;

The Importance of Newtonian KE and P on Special Relativity

Abstract

Special relativity is often thought of as arising as a math transform linked to Maxwell’s electromagnetic equations, or through Einstein’s thought experiments using light and the invariance of frames moving at constant speeds relative to each other. Here, we argue that even though Newton’s equations seem to be largely focused on the notion of momentum, which is a vector, the second law dp/dt = F leads to a scalar (under rotation), namely p dot p /2m which is not simply p dot p. In other words, we argue that Newton’s notion of both a p (vector) and p dot p /2m (scalar under rotations) as describing a free particle state actually leads to special relativity. In other words, a single object, either p or p dot p /2m is not sufficient for describing a free particle. We note that an object at rest is also described by a number mo and p=0. For a particle moving at a very low v, the state is still mo to first approximation even though there is mov and .5movv. As a result, we suggest that Newton’s idea of a vector p and scalar .5movv describing a state actually be extended to a particle at rest, and that one must consider mof(v/b)bb and mov h(v/b) where f and h are unknown functions. One may see that a constant b must be introduced and b should have the same value as seen from any constantly moving frame, i.e. should represent a particle with mo=0. We use the idea of a scalar under rotation and a vector as describing a state as characterizing a free particle state. We note that for the rest state p=0 and so one only mobb. This means that one may introduce a linear, i.e. matrix transformation, because mobb, mov and .5movv are all linear in the factor mo. We suggest that given the presence of b, which has velocity units, it must be a constant and have the same value as seen in all frames. This, we argue, implies that a clock in a rest frame cannot have the same period as one in a moving frame. As a result, we suggest that special relativity follow from Newton’s idea of characterizing a free particle state by a dual, mo, .5movv and p vector and that one may obtain special relativity from this idea alone because it requires the introduction of a speed b which is the same as seen in all frames moving at constraint v.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green