# Time dilation of fast moving object that are not relative?

I meant to say fast moving "objects" in the title, my bad... my title kind of sucks

https://en.wikipedia.org/wiki/Relativistic_electromagnetism#The_field_of_a_moving_point_charge

That section is basically what my questions are about. I want to know generally about the overall forces. Two protons in the LHC moving the same direction will not experience much repulsion difference relative to their own perspective, but from our perspective outside the LHC their repulsion should weaken? The repulsion of two protons without electrons I mean.

But two protons colliding in the LHC going opposite directions. Because their speeds are not relative, they would have increased repulsion? I can't understand the wikipedia article that well. I think it's saying the increased repulsion would be from the sides as they pass each other (assuming they didn't collide)?

ok, one more question about, voltage and current, that i guess kind of has to do with time dilation. If you took a beam of fast moving electrons, could that create a voltage for a wire or something near by right? I mean of course a wire with current would create a voltage, but would it also work for a beam of electrons in a vacuum? How come electrons are supposed to repulse other electrons, but a voltage creates a current? thanks

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2021 Award
Two protons in the LHC moving together feel an electrostatic repulsive force in their frames. When you transform this force to the Lab frame, it is weaker, because of time dilation.

In the Lab frame, these protons still have their electrostatic repulsion, but they also create a current, which is attractive, and substantially reduces the attraction. You get exactly the same force in this frame through this analysis as you did in the preceding paragraph.

godzenon
Two protons in the LHC moving together feel an electrostatic repulsive force in their frames. When you transform this force to the Lab frame, it is weaker, because of time dilation.

In the Lab frame, these protons still have their electrostatic repulsion, but they also create a current, which is attractive, and substantially reduces the attraction. You get exactly the same force in this frame through this analysis as you did in the preceding paragraph.

Staff Emeritus
2021 Award