If time moves slower the faster you go. Doesn't that mean that the gravity experienced will be lower too?

Question

Disclaimer: I still don't understand the theory of general relativity. I'm completely ignorant.

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I was watching the movie Interstellar yesterday and saw their interpretation of time dilation, I also watched the Lightyear movie which is about the same. Those movies got me interested in this supposed phenomenon.

These movies got me thinking about when I took my physics classes and I thought of the following:

x = position t = time v = speed

v = Δx/Δt

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and if

a = acceleration

a = Δv/Δt

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m = mass a = acceleration

f = force

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My point:

Since gravity is a force and time moves slower, all of the previously mentioned equations depend on time. Wouldn't the forces, including the gravity experienced, be less the faster you move?

Please comment on whether or not I am correct and Why.

Answer 1

You don't need GR to get an intuitive feel for what is going on.

Imagine you are sitting on the Earth experiencing the acceleration and force of gravity to be what Newton predicts. Now I fly past the Earth (at a distance where the Earth's gravitational effect on me is negligible) at say 0.8c. Using the equations of SR, I see the transverse force acting on you as reduced by a factor of gamma (60%) and see the transverse acceleration reduced by a factor of gamma squared, so I see things falling on the Earth as falling in slow motion. You on the other hand experience no change in the force of gravity on the Earth simply because I have flown past. The force of gravity as measured in a gravitational field by a local stationary observer is always the Newtonian expectation even near black holes in GR.

Now relativity is symmetrical, so if we take the point of view that my spaceship is stationary and the Earth is moving, then the results are exactly the same. You experience no change in force on the surface of the Earth.

This is why moving bodies do not collapse into black holes due to apparent increase in relativistic mass when they are moving relative to the observer. The local transverse force of gravity as measured by me flying by: $$ F = (m \gamma) \ (g \gamma^{-2}) = m g \gamma^{-1}$$ where $g$ is the acceleration of gravity and $\gamma$ is the gamma factor. You see no change in the gravitational force on Earth and I see a reduced force when flying by, so there is no chance of Earth becoming a black hole.

For similar reasons, while I see you as time dilated as I fly by, your local perception of time passing is always normal in GR or SR.