Time Dilation: Does Total Speed Matter?

[LM542]

When a spaceship accelerates to 1.000 kmh, the effect of time dilation is tiny. But what happens if this spaceship accelerates in an inertial frame whose
total speed is much slower or whose time goes much faster, will the time dilation effect be the same?

If the spaceship travels in a inertial frame that has a speed of 1.000.000 kmh an additional speed of 1.000 kmh is just 0,1 of the total speed.
But if the speed of the inertial frame is 1.000 and the spaceship travels with an additional speed of 1.000 kmh, that doubles the total speed. Will the time dilation be the same?

I think that time dilation is:
Total speed of the observer through the total speed of the spaceship

So in the first example,
1.000.000
/
1.001.000
=
0,999 (that is how much time goes by in the spaceship)For the second example
1000
/
2000
=
0,5 (that is how much time goes by in the spaceship)Wouldn't it be possible based of the amount of time dilation to determine how fast the Earth is moving?

 

[rootone]

How fast the Earth is moving relative to what?
You need to specify that for the question to make sense.

 

[Ibix]

I'm afraid that time dilation doesn't work quite like that, so the answer to your last question is "no".

Time dilation is an effect measured between two objects in relative motion. It isn't something that one object can measure in itself. The clocks on your spaceship will always tick at one second per second. However, if you watch my spaceship passing by your spaceship you will see my clocks ticking slowly - and me moving, thinking and reacting equally slowly, so you will be unsurprised that I see nothing unusual about my clocks. I can watch your spaceship too, and I will also see your clocks ticking slowly and you moving slowly so, again, I will be unsurprised that you don't notice anything odd.

This all adds up to the result that (as long as you aren't accelerating) you can't deduce a velocity just by looking at your clocks. They will always look normal to you and everyone else's will always look slow. This is because there is no absolute sense in which one can say something "is not moving". You always have to say "is not moving relative to..." - that's why it's called relativity theory. This even applies on Earth - when we say we aren't moving, we really mean "...relative to the surface of the Earth".

 

[phinds]

In addition to what Ibex said (and rootone's pointing out the relativity of motion), think about this: you, right now as you are reading this are MASSIVELY time dilated relative to an "accelerated" particle at CERN and you are mildly time dilated relative to an asteroid speeding towards (or away from) Earth, and you are not time dilated at all relative to your chair. Do you feel any dilation? Do you feel an infinite number of different time dilations all at the same time?