I Confused about time dilation -- motion vs energy

[mr John wheeler]

TL;DR Summary

Why relativity treat velocity and energy separately for time dilation

Hey, I’ve been trying to understand time dilation, and I think I might be mixing some concepts.

If you’re moving very close to the speed of light (say 0.99999c), your clock slows. If you then enter a strong gravitational field, that also slows clocks. From your point of view, would that mean time almost comes to a stop?

That made me wonder: maybe it isn’t motion itself that directly causes time dilation. Motion just produces kinetic energy — and in GR, it’s energy that curves spacetime and affects how clocks tick.

I tried to check this idea with GPS satellites:

• Their clocks tick faster by about +45 μs/day because they are higher in Earth’s gravitational potential.
• SR predicts their motion slows them by about –7 μs/day.
• Together, that gives the well-known +38 μs/day correction.

But if I instead take their kinetic energy and put it into a GR time-dilation style calculation, I get about +35 μs/day, which is very close to the engineering correction. That made me wonder if an “energy-based” view works just as well as the usual “motion-based” one.

Planets also crossed my mind: yes, they have much more total kinetic energy than a human moving near light speed, but in GR what matters is energy density and stress, not just the bulk KE. Locally, a human could even have higher energy density.

I’m not trying to propose a new theory — I’m sure I’m misunderstanding something.
My question is: is there a formal reason relativity treats velocity-based time dilation separately from an energy-based interpretation?

Thanks for any clarity

 

[Nugatory]

If you’re moving very close to the speed of light (say 0.99999c), your clock slows.

That is not what time dilation means.

Consider that right now you are moving at that speed relative to a cosmic ray particle wandering through the solar system - but is your time slowed down? No of course not, time is passing for you at the rate of one second per second just as you expect.

We have a bunch of older threads explaining how time dilation really works, and you will want to work through some of them to understand what is going on. And be aware that despite the confusing use of the same words. gravitational time dilation is a completely different phenomenon that the kinematic time dilation in the quoted text.

 

[phinds]

TL;DR Summary: Why relativity treat velocity and energy separately for time dilation

If you’re moving very close to the speed of light (say 0.99999c), your clock slows

That is not what time dilation means.

This is a VERY common misconception, promoted by incorrect statements in almost every pop-science presentation you'll ever see/read/hear.

 

[Dale]

TL;DR Summary: Why relativity treat velocity and energy separately for time dilation

That made me wonder if an “energy-based” view works just as well as the usual “motion-based” one.

No. As you mentioned, you can put 5 J of KE into an electron and get a huge amount of time dilation. The same 5 J of KE into a planet produces essentially no time dilation.

but in GR what matters is energy density and stress

This also doesn’t work. I can increase the energy density by many means, such as thermal, chemical, or mechanical. These will all result in negligible time dilation, they are not equivalent to the same amount of energy as KE.

 

[Ibix]

My question is: is there a formal reason relativity treats velocity-based time dilation separately from an energy-based interpretation?

There isn't really an "energy-based interpretation". You frequently do see gravitational time dilation and kinematic time dilation treated separately, but it's only possible to do that in some kinds of spacetime (called "stationary" spacetimes), and then it's only really useful if you accept some global definitions of time (which you can choose not to do).

More generally, all time dilation-like phenomena can be understood by realising that the elapsed time for a clock is a measure of the "distance" it travels through spacetime. A flock of clocks that are mutually at rest travel on (loosely speaking) parallel lines. Kinematic time dilation happens because a clock moving relative to them is moving at an "angle" to them, so travelling one unit of time at an angle doesn't leave them at the same event clocks in the flock. Gravitational time dilation happens because spacetime is curved, and you get effects similar to walking 1m along a line of latitude near the pole and near the equator - one travels about 60° round the Earth, the other practically nothing.

The energy of the clock has nothing to do with this. Apart from anything else, its energy depends on who is observing it.

 

[PeroK]

You’re right. I oversimplified when I said “your clock slows.” I understand that, from your perspective, time always ticks at 1 second per second. Time dilation only appears when comparing different frames. I wrote it that way to keep the post brief.

What I really wanted to ask is this: since general relativity says spacetime curvature comes from energy and momentum, can the kinetic energy from motion be seen as a cause of kinematic time dilation too? I checked this idea with the GPS satellite example. The energy-based approach provided nearly the same correction as the standard split of SR and GR. Thank u for your attention , really value your clarification

The energy and momentum of a clock depends on its mass. The measured time dilation does not.

 

[Nugatory]

can the kinetic energy from motion be seen as a cause of kinematic time dilation too?

It cannot, because time dilation is independent of the energies and momenta involved.
This is to be expected because time dilation is implied by the relativity of simultaneity, which depends only on the relative velocities but not on the energy and momentum. The calculations that lead to the time dilation formula are done in a completely flat no-curvature spacetime.

 

[Sagittarius A-Star]

and in GR, it’s energy that curves spacetime and affects how clocks tick.

As others mentioned, that's wrong.
The following explanation in a local scenario shows, that "gravitational" time-dilation happens also in flat spacetime.

Source:
Book "Relativity - Special, General and Cosmological", Second Edition, chapter 1.16 "Gravitational frequency shift and light bending" of W. Rindler
https://www.amazon.com/-/de/dp/0198567324?tag=pfamazon01-20