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Suppose, in frame $A$, two particles are present at $t=0$, at locations $x=1$, and $x=2$. Let's call these 'existence states of particles' to be events 1 and 2 respectively. We say that a force exists between the two events causing exchange of momentum between them.

In Galilean relativity, if we look at the same events from a frame $B$, the particles would still be found at $t=0$ at some locations, and a force will be between them.

In special relativity, if we look at the same events from a frame $B$, they would be found to exist at different times. So the two events can no longer exert force on each other, as they don't exist at the same time. So a force exists between the two events in frame $A$ but not in frame $B$.

I was thinking, is this where the idea of a Four-Force come into the picture? Does the concept of Four-Force resolve this issue? If so, how?

G. Smith
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Ryder Rude
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  • A particle that comes into existence and then vanishes is non-physical. So any conclusions you might reach using a theory designed to describe physical phenomena is certainly meaningless. – garyp Sep 01 '20 at 03:57
  • @garyp I didn't mean for the particles to vanish afterwards. They do exist. But still no force is present between the events 1 and 2 when viewed from frame $B$ (as, in frame $B$, the events 1 and 2 no longer exist at the same time) – Ryder Rude Sep 01 '20 at 04:01
  • Forces don’t exist between events; they exist between particles. The notion that the force vanishes in another frame because “they exist at different times” is completely wrong. Four-forces have nothing to do with it. – G. Smith Sep 01 '20 at 04:21
  • It might help to imagine a specific force, namely the electromagnetic force between two point charges. Their fields don’t disappear when you change frames, so neither do the forces each exerts on the other. – G. Smith Sep 01 '20 at 04:21
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    Possibly of interest Moving charge in different frames of reference – mmesser314 Sep 01 '20 at 04:35
  • @G.Smith So then the force vector between Events 1&2 in frame $A$ has no "transformed-version" in frame $B$. This is what makes me suspect that 'force' is not a physical entity but merely a mathematical construct to explain the evolution of particles over time. In the force interpretation, the two events are directly interacting in frame $A$ but not interacting in frame $B$. – Ryder Rude Sep 01 '20 at 05:03
  • @G.Smith I agree that some force is still present between the particles even after we switch frames. But the "same" force vector does not carry over to frame $B$. The interaction between events 1&2 only exists in frame $A$ – Ryder Rude Sep 01 '20 at 05:08
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    Please reread my first comment. You are thinking about this in the wrong way. You are describing a “personal theory”, not mainstream physics, and personal theories are off-topic. – G. Smith Sep 01 '20 at 05:10
  • @G.Smith I guess the solution is to think in terms of fields instead. In frame $B$, there exists a transformed version of the force field due to event 1. It's just that the same force field no longer interacts with event 2 when we look at things from frame $B$. Do you agree with this? This interpretation solidifies the theory that fields cause forces, and that fields are more fundamental than forces. – Ryder Rude Sep 01 '20 at 05:21
  • Whether a transformed field is “the same field” or “a different field” is a meaningless philosophical distinction for me. The field exists in all frames, and can be calculated in any frame. – G. Smith Sep 01 '20 at 16:12

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