Time Dilation and/or Kinetic energy the same/different?

[Noja888]

Greetings All! (first post). I have been trying to find some data/experiment that validates Time Dilation for me. I am not trying to de-bunk Relativity but seeking to validate a key point to further my own thought experiments. Take into account these next two statements (that I assume to be true) and let me know if I am missing something.

On the case of Muon decay being an example of Time Dilation...
Question(?) Does the Kinetic Energy gained by Muons allowing them to reach sea level (and not decaying in our atmosphere) a result of Time Dilation or the Kinetic Energy gained due to its velocity grants more energy to the Muon - making it decay slower?

On the case of clocks in motion moving slower to a stationary one (such as GPS satellites)...
Question(?) Because of more velocity is more mass would this be that the "gears" of the moving clock has more mass due to velocity - making it run slower because there would be more energy needed to make it run at the same rate as the stationary clock that does not have as much mass (because it is not in motion relative to the moving clock)

Could someone explain why it is time dilation and not Kinetic energy displayed? Is there other experiments that confirm? Not sure what I am missing here. Any insight or a link to info would be great. -ThanksNoah

 

[dx]

The kinetic energy is simply a number that is used in analyzing problems in dynamics. It has no role in the time dilation of a single clock. Say a clock is set to explode when it reads 1 second. If you are in a frame in which the clock is at rest, then it will explode when your clock reads 1second. But if you are in a frame in which the clock is moving, it will not explode when your clock reads 1second. When your clock reads 1 second, the moving bomb clock only reads √(1 - v²) seconds. In your frame, it takes 1/√(1 - v²) seconds for the bomb clock to explode.

 

[fhisicsstudnt]

Interesting thought. In the experiment where Cesium clocks were flown around the world one might say they didn't technically measure "time". A HF transition is a release of energy. Two cesium clocks have identical energies E0 and are losing energy at the same rate dE due to HF transitions when "at rest" then one clock is flown away and back. The flying clock must gain some energy E1 while in transit. They cannot, then, both lose energy at the same rate without violating energy conservation. The moving clock will have to undergo fewer HF transitions to maintain energy conservation.

 

[pervect]

Not really true, since the cesium atom is used to define the second. But more importantly, if you trace the development of clocks, you'll see good clocks getting smaller and smaller - to avoid, for instance, the effects of motion. Look at the development of the naval chonometer, for instance. The first attempts were huge ungainly beasts - but they had a fatal problem, one that was ultimately solved by making them smaller. ((See the TV show "Longitude" for what I'm talking about if you're not familiar with the history.))

The ultimate development of this has been to use some of the smallest possible bodies in nature, atoms, as clocks. Furthermore, since atoms are all identical, you don't have any problem with manufacturing variations, that you do with other, larger, time-keeping pieces.

It's true that atoms vibrating involves energy - but so do all dynamical processes. Quartz crystals vibrating also have energy. Everything has energy. But it's not reallly useful to conflate (confuse and combine) energy with time - they are separate concepts that should be kept separate.

 

[Noja888]

Thanks dx - That makes much more sense than the examples I gave in the start of this thread. (visual thinker here - learning the math as I go - my machining background tells me there is a use of inverse time here in your explanation - I will enjoy figuring this out).

Also thanks pervect for the comment - I was not trying to conflate energy and time - just that the examples of "field tested" time dilation I was reading about seemed explainable in a mechanical sense (classical/sorta-Newtonian i guess), or that there was a correlation.

Let me get a bit more of the "relativity math" under my belt and so I can see/explain this to myself a bit better. I have a good knowledge of algebra,geom,trig etc. but putting it all together at these higher levels is a bit tricky - Newtons' stuff is easy compared to this. Thanks for the help!