Visualizing Time Dilation

[Music] welcome back to science clique today time dilation time is an essential concept for describing our world the passing of time allows us to quantify the evolution and the movement of objects at first glance one might think that time is absolute with a single clock for the whole universe at the beginning of the 20th century a discovery drastically rocked our previous understanding relativity time is no longer absolute it is relative each object has its own time its own clock and two initially synchronized clocks that follow different paths through space can meet again and indicate different times in 1971 an experiment was carried out using atomic clocks aboard two airplanes after traveling around the earth in opposite directions the two initially synchronized clocks showed a difference the contents of the first plane clock passengers and everything else it contained appeared to have aged 300 nanoseconds less a small difference nonetheless detectable by these very precise clocks how do we explain this phenomenon how can it be that one of the two clocks had aged less than the other has time dilated has it passed more slowly to understand this phenomenon intuitively it will be useful to first consider a situation that seems completely unrelated we simply imagine a meadow on which person a walks straight ahead at a steady pace counting her steps a measures the distance she travels across the plane on this meadow there are two trees and a is oriented such that on the 20th step she passes both trees at the same time now a second person b is also moving straight ahead but not in the same direction from his point of view b does not pass both trees at the same time he first passes the tree on the right then the tree on the left for a the passing of the two trees is simultaneous but for b it occurs at different times the order of passage depends on the direction in which one is moving let us imagine that a observes the footsteps left by b from her point of view a does not perceive the direction of these tracks she only observes that they seem closer together as if b had marked shorter steps likewise for b the trace is left by a seem contracted [Music] in reality a and b walk at the same pace the tracks are identically spaced it is just a question of perspective due to different orientations finally imagine that a and b walk in the same direction but that this time the ground is not flat b has to walk across a hill again for a the tracks left by b appear to be contracted as if they were shorter and once again it is just a question of perspective the steps are equally spaced but they are oriented differently along the slope of the hill and thus for a they seem shorter to sum up when two people compare their footsteps they can observe shorter steps appearing to be contracted either if the directions are different or if the surface is curved this contraction is however only an effect of perspective in reality the two individuals always walk at the same pace [Music] now let's go back to our initial problem according to relativity objects in the universe move across a surface called space-time it is a fairly complex four-dimensional surface but to simplify we can imagine it as two-dimensional just like the meadow in our example in space-time all objects move and as they progress along their trajectories the clocks of each object tick the time they carry passes as they move forward the time carried by an object is therefore equivalent to the footprints in the meadow the seconds that pass on our clocks measure the distance we travel through space-time it is very important to understand that all objects whether it is a human an apple a star or an atom all move at the same rate within one second they always travel the same distance about three hundred thousand kilometers through space-time but not all in the same direction each observer carries two axes one they call time tangent to their trajectory and along which they're clock ticks and another axis perpendicular to time which they call space an object that moves in the same direction as us seems to be stationary the object is still moving through space-time but on the axis we call space it does not change position conversely if the object moves along a direction different from ours it appears to us to be in motion its position varies on the axis we call space this is called speed the speed between two objects is the angle between their trajectories as in the meadow if we imagine two events that occur at the same time for us [Music] these two events can occur out of sync for someone else who would be oriented differently simultaneity is relative be careful this is not just an optical illusion but really a difference in perspective the two observers have different definitions of what they call time and space their axes are not the same hence these different perceptions [Music] as in the meadow if we observe an object in motion compared to us we perceive its time axis from a different perspective as if it were ticking at a different pace in reality the times of the two objects tick at the same rate but in different directions it is this effect we call time dilation we understand that this is not really a dilation the ticking of time has not changed it is simply a matter of perspective imagine a set of twins that is separated with one remaining on earth and the other making a round trip at high speed through space since the paths don't have the same length through space time at their reunion the twins are no longer the same age in the experiment with the airplanes the explanation is similar the two planes separate follow different trajectories through space-time and it turns out that one of these trajectories is longer than the other in terms of distance through space-time the clocks have not traveled the same distance and therefore do not measure the same durations [Music] finally if space-time is curved which is the case around a massive body like earth we will also perceive a kind of time dilation the seconds seem to tick at different rates for objects at different altitudes twins who separate live at different altitudes then reunite will not have traveled the same distance through space-time and therefore one of the twins will have aged more than the other in the extreme situation which the slope would be vertical an object moving there would seem frozen in time from the outside a situation analogous to the horizon of a black hole [Music] to conclude the analogy of the meadow gives us a good geometric intuition of what we call time in relativity objects all move along a surface space-time and each have their own time and space axes such that when they are oriented differently the durations and distances they measure are different the analogy however has its limits it is not perfectly equivalent to relativity in particular in the meadow the footprints appear to be contracted while in relativity the time of a moving object seems to be dilated another difference in the plane it is possible to turn around you can go back on your steps but in space-time even though objects can accelerate as much as they want change direction their trajectories are restricted within a cone the peculiar geometry of space-time prevents them from turning backwards in this weird geometry the pythagorean theorem no longer holds this trajectory is shorter than this one and there is a kind of speed limit the speed of light we call this laurentian geometry [Music] you

Channel: ScienceClic English

Views: 180,156

Rating: 4.917541 out of 5

Keywords:

Id: 5qQheJn-FHc

Length: 11min 5sec (665 seconds)

Published: Tue Mar 23 2021

Reddit Comments

[u/vorkazos]

This explained it more clearly and concisely than anything else I've ever seen about it.

YMMV

[u/Joanet18]

Thanks, that was really cool!

[u/dirtylostboy]

Never stop making these videos.

[u/Zambeezi]

Love your videos! The first one I watched was on visualizing the flow of space-time, and I've been hooked since then!

[u/23569072358345672]

Oh geez. I shouldn’t have watched that, I only started my degree this year and this raised more questions than I thought I had...

[u/thankdestroyer]

So we can think that all things (human, atom, star etc) have the same budget that they can invest either on time or travel through space. Since we are not traveling as fast as light, we invest mostly on time and time flows really quick for us where it stops for light since light invests all its' budget to speed. How close is my analogy to be true? (English is not my native language. So sorry for any kind of mistakes).

Edit: I forgot to mention how well prepared the video is. Thanks for sharing.

[u/ta0questi]

Sorry , I didn’t hear what kind of geometry it is, at the very end. Can someone spell it?

Edit to say I enjoyed this even though I’m not very educated in math or physics.

[u/MetricVeil]

Loved it. Very simple and clear images and explanations. :)

[u/Even_Impression2644]

Brilliant!