four-position product needs to be changed

Hi guys,

I took me some time but I finally found some fresh idea what we could do to link field phenomena with space-time definition.

I wait for reviewer comments for the article, but - as always - I would be glad to discuss my idea with you.

First part of my article below

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To simplyfy calculations we assume c=1.

In Special Relativity four-position gives proper-time as product of

(1)

Taking proper-time derivative on above one gets

(2)

One may easy show, that present four-position product definition excludes any filed existence, no matter how we define field!

From (1) one may easy derive

(3)

thus one may easy transform (2) to

(4)

From above using easy calculations one may get

(5)

where is perpendicular component of velocity.

Therefore for radial move () we get

(6)

Substituting above to (2) one gets

(7)

One may easy calculate taking proper-time derivative on above, that for such , time component of four-acceleration vanishes

(8)

Since time component of four-acceleration vanishes only if there is lack of acceleration (resultant acceleration vanishes) so we have just proved that present four-position product definition excludes any acceleration for radial move.

But it is known, that e.g. for radial move of charged particles acceleration exists... And the same time, no matter how we define field, present four-position product definition excludes acceleration for radial move.

It is crucial to understand, that even if one artificially adds a field to Lagrangian, present four-position product definition excludes radial acceleration by definition.

So we need to change somehow four-position product in Special Relativity to ensure possibility of the field presence.

In the next post I propose some solution.