B Time Dilation & Relativity: Explained for Beginners

[Mattv]

Good morning

I'm a total beginner in physics, but I recently started to read books and watch videos about cool physics stuff, like relativity.

I heard that the closer to the speed of light you travel, the "slower" time passes for you. I'm talking about the fact that clocks in GPS satellites are late after some time.

So I don't really understand why, but I can assume that "time goes slower when you move faster". But I learned at school that speed is relative, and a spaceship moving at X speed is the same as the ship being immobile and the Earth (and the rest) going at X speed in the opposite direction.

In that case, why is the satellite clock late compared to the Earth ? And why isn't the Earth clocks late compared to the satellite ?

Thanks guys !

 

[PeroK]

Good morning

I'm a total beginner in physics, but I recently started to read books and watch videos about cool physics stuff, like relativity.

I heard that the closer to the speed of light you travel, the "slower" time passes for you. I'm talking about the fact that clocks in GPS satellites are late after some time.

So I don't really understand why, but I can assume that "time goes slower when you move faster". But I learned at school that speed is relative, and a spaceship moving at X speed is the same as the ship being immobile and the Earth (and the rest) going at X speed in the opposite direction.

In that case, why is the satellite clock late compared to the Earth ? And why isn't the Earth clocks late compared to the satellite ?

Thanks guys !

"Time goes slower when you move faster" is not an accurate way to describe time dilation. All inertial (constant velocity) motion is relative, so there is never any sense in which something is absolutely moving and time is moving slower. Instead, velocity-based time dilation is a symmetric reciprocal effect of measuring time between two reference frames in relative inertial motion.

The motion of a satellite round the Earth is not inertial. The satellite is orbiting the Earth in a circular orbit, which implies centripetal acceleration. In this case the symmetry is broken and there is a sense in which the satellite clock is running relatively slower than an Earth clock.

The scenario is complicated because there is also gravitational time dilation, which makes the satellite clocks run slightly faster than Earth clocks. But, when you put the two together you get slightly slower ageing for a satellite.

 

[Ibix]

There are several related effects here.

If we both move inertially (i.e. at constant speed on a straight line) and in the absence of gravity, then your clock will tick slowly as measured by me and my clock will tick slowly as measured by you. This is the symmetric time dilation effect you appear to be expecting.

However the situation with the satellite is more complicated - it's moving in a circle. We can compare its clock readings to our own each time it passes overhead, and we do indeed find that in those circumstances the clocks on the satellite tick slower as measured by us and our clocks tick faster as measured by the satellite. This situation is further complicated by the presence of gravity which has a time dilation effect too - clocks higher up tick faster than clocks lower down.

A simpler scenario to study would be the Twin Paradox, which is essentially the same thing but without involving gravity. The underlying explanation for all of it is that a clock measures the "length" (actually called interval, because it's not quite the same as length) of its path (called a "worldline") through spacetime. And if two clocks meet up once and meet up again they could have followed worldlines of different "length", in which case they'll show different elapsed times. Inertial motion in the absence of gravity is a special case - we can only meet up once because we can't turn around without moving non-inertially. It turns out that the "both see the other's clock tick slow" effect is due to different ways of defining how to compare clocks that aren't in the same place.

 

[anuttarasammyak]

In the special theory of relativity synchronicity of different places is not absolute one as it is in our daily lives e.g. London and New York shares the same moment and same TV news. When they are away and in relative motion, his AT THE SAME TIME and her AT THE SAME TIME are different. One can interpret other's AT THE SAME TIME is not his/her own so no confusion take place.

Please find attached my hand drawing. There two rockets pass by the Earth. The three do not share AT THE SAME TIME any more when they are apart. The clocks tick NORMAL, SLOW or VERY SLOW by relative speed.

 

[Dale]

In that case, why is the satellite clock late compared to the Earth ? And why isn't the Earth clocks late compared to the satellite ?

Others have mentioned the technical aspects, but I would also like to mention a practical aspect: nobody lives on the satellite. From a practical standpoint we don’t care about the reference frame of the satellite. We certainly could calculate it, but doing so wouldn’t help someone navigate which is the purpose of the GPS system.

 

[anuttarasammyak]

nobody lives on the satellite.

Wikipedia time dilation
"For example, at the ISS time goes slower, lagging 0.007 seconds behind for every six months."

ref. https://upload.wikimedia.org/wikipe...n.png/360px-Daily_satellite_time_dilation.png

 

[kent davidge]

In the special theory of relativity synchronicity of different places is not absolute one as it is in our daily lives e.g. London and New York shares the same moment and same TV news. When they are away and in relative motion, his AT THE SAME TIME and her AT THE SAME TIME are different. One can interpret other's AT THE SAME TIME is not his/her own so no confusion take place.

Please find attached my hand drawing. There two rockets pass by the Earth and the three do not share AT THE SAME TIME any more when they are apart.

In your sketch, I think you had it the other way: the Earth is moving very slowly, and the rocket is moving slowly. That's because the velocity as seen by the "moving rocket" in its own frame is $(v_e+v_r)/(1+v_ev_r/c^2)$ where $v_e$ is Earth's velocity and $v_r$ is the other rock's velocity, both measured by the rocket at "rest". And these two velocitites got the same sign. So the Earth is moving slower than the other rocket.

For reference, http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/einvel.html

 

[jbriggs444]

In your sketch, I think you had it the other way: the Earth is moving very slowly, and the rocket is moving slowly.

I think that you have misunderstood what @anuttarasammyak was attempting to depict. The drawing was not trying to depict relative rates of motion but rather relative rates of time passage -- time dilation.

The scenario had a rightward moving rocket, a leftward moving rocket and the earth.

From the rest frame of the leftward moving rocket, the Earth is moving rapidly rightward and the other rocket is moving even more rapidly rightward. Accordingly, from this frame, time is passing slowly on the Earth and even more slowly on the other rocket.

From the rest frame of the Earth, one rocket is moving rapidly rightward and the other rapidly leftward. Accordingly, from this frame, time is passing slowly for both.

From the rest frame of the rightward moving rocket, the Earth is moving rapidly leftward and the other rocket is moving even more rapidly leftward. Accordingly, from this frame, time is passing slowly on the Earth and even more slowly on the other rocket.

The key take-away is that everyone calculates everyone else's clocks to be running slowly. Time dilation is symmetric.

That is all that the drawing depicts. It is purely qualitative. There was no attempt to be quantitative and invoke the relativistic velocity addition formula. There was no attempt to include the relativity of simultaneity -- the "leading clocks lag" rule. There was no attempt to account for gravitational time dilation. Nor was there any attempt to adopt "the" non-inertial frame of an clock being accelerated in a circular orbit [or of an inertial clock in a ballistic orbit in curved space-time].

 

[Mattv]

Well thanks a lot for your answers I didn't expect that much haha, that helped a lot
Special shout-out for the hand-drawn pic

Do you know any good book about that topic that doesn't need too much theoretical knowledge ? I'd like to go further than YouTube videos

 

[PeroK]

Well thanks a lot for your answers I didn't expect that much haha, that helped a lot
Special shout-out for the hand-drawn pic

Do you know any good book about that topic that doesn't need too much theoretical knowledge ? I'd like to go further than YouTube videos

You could try this:

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf

 

[Ibix]

Do you know any good book about that topic that doesn't need too much theoretical knowledge ? I'd like to go further than YouTube videos

Former Mentor here, Ben Crowell, wrote a fairly easy-to-read non-mathematical treatment of relativity - Relativity for Poets - which can be downloaded from www.lightandmatter.com. For a proper textbook, there's also a Special Relativity text there - I haven't read it, but liked both the Relativity for Poets and his General Relativity text. Otherwise, PeroK is fond of Morin which he's already linked. I quite like Taylor and Wheeler's Spacetime Physics, the first chapter of which is also freely available online from E.F. Taylor's website.