A Glimpse of Time

Need more time in your daily life? I know I do…
How do we define “time”? By the little arms on our watches? Or by the digits displayed on our clocks?

We know that “time” can vary from clock to clock. Some are purposely set to be couple minutes ahead, and some just run slow because of the inaccuracy of the clockwork. How do we know which clock is absolutely accurate and is the one that we should be setting all our clocks and watches to? Does an absolutely accurate clock even exist in this world?

note: this post is a continuation of a previous post A Glimpse of History

In 1905, Albert Einstein also pondered about the concept of time in his famous paper “On the Electrodynamics of Moving Bodies” [1]. Not only did he question the simultaneity of any events, he also questioned if the interval of time moves at the same rate depending on if we’re moving or stationary. All of this led to his famous theory of special relativity, which I’m sure we have all heard the term before.

The short version is: Time moves slower at faster speed of travel.

If you’re still interested, the long version is…

Einstein started with the assumption that light emitted or bouncing off a object will travel at a constant speed c regardless of whether the object is stationary or moving at any velocity. Einstein made this assumption based on a thought experiment [2] (note: this thought experiment is explained with a quoted explanation in [2]). This assumption was later shown to be true with theoretical calculation in his 1905 paper [1].

The concept of special relativity is quite difficult to explain/understand, but I’ll try to explain it using a simple example. The basic concept of this example is borrowed from [2] but further modified and illustrated with my beginner-ish animation skills.

Imagine we have a kid on a platform, kicking a little red ball at a wall. He kicks it in a straight line. The ball bounces back in a straight line to his feet.

Scenario 1

If we observed this event with a camera mounted above the platform, we will see:

             

The path of the ball as captured by the camera will be a straight line to the wall and a straight line back, shown above on the right.

Scenario 2

What if the platform is now moving at a unknown speed, but we will continue to watch from a camera mounted above the platform that is moving with the platform. We will then see:

             

The path of the ball as observed by us will be a straight line there and a straight line back, as shown above on the right. Exactly the same as if the platform and the camera were both stationary. This is because the camera and the platform is in the same frame of inertia.

Scenario 3

What if the platform is moving, but our camera is in a stationary position relative to the ground instead of the platform. We will then see:

            

The path of the ball as captured by the camera will be different from the second case. In fact, if we traced the path of the ball as captured by the camera we will find that the path of the ball is actually longer than in scenario 2 above. However in scenario 3, the ball is actually observed to be travelling faster as well along the triangular path (at higher velocity) because of the extra inertia given to the ball by the movement of the platform.

From this we can see that, the same event captured from the ground (in a stationary position like in scenario 3) and captured from the platform (in the same inertia frame as the event as in scenario 2) will make us perceive the event differently, i.e. the ball travels faster and farther in scenario 2.

Actually, it can be shown mathematically that the extra inertia given to the ball from the moving platform (when observed on the ground) cancels out the longer observed path travelled (when observed on the ground), so the two event should take the same length of time to occur to a person on the platform and to a person on the ground.

Now from a deeper physics perspective…

Image the ball is now a photon (i.e. a packet of light). But unlike the ball, the moving platform cannot give a photon extra inertia because of our initial assumption that light travels at the speed c regardless of the velocity of the object. So regardless if the platform is moving or not, the photon will travel at c when observed on either the platform or on the ground.

So what does this all mean?

If we are observers on the ground (i.e. Scenario 3), the photon will take more time to travel the longer path than if we are observers on the moving platform (i.e. Scenario 2). But it’s the exact same event, we are simply looking at it from two different perspectives. How can we perceive the travel of the photon (i.e. path length) to be different from one perspective to the other?

Einstein explained the difference occurs because time travels slower when measured from a moving object compared to a stationary object. For example in the case shown above, the camera mounted on the platform may record that the event took 10 seconds to occur. But on the ground we would see that it took 10.2 seconds to occur.

So, 10 seconds as perceived on the moving platform = 10.2 seconds as perceived on the ground

This would mean that it takes longer for a “second” to occur on the moving platform than it is perceived from the ground. So which perception of time is correct? The answer is neither.

That’s the gist of Special Relativity, the interval of time is relative and not absolute. It depends on the relative difference in speed of the observers.

To boggle your mind some more, remember that the Earth is moving around the sun at phenomenal speed. The sun and the solar system also move at phenomenal speeds around the center of our galaxy, and so on. So there is no such thing as stationary, we are simply stationary with respect to the Earth because we are in the same inertia frame as Earth.

By the way, I actually exaggerated in the above equation. In order to have a 0.2 second difference in the two cases, the platform must be travelling at 0.197c, which is equal to 212,673,664.6 km/hr–which is unrealistically fast.

In everyday life, we barely notice the difference in the interval of time (i.e. the “length” of a second), because the speed we travel at (even on a jet) is so much slower than the speed of light. However, this difference in time increases  exponentially as the velocity of the observer reaches closer to the speed of light.

Einstein’s Special Relative theory spurred the famous twin paradox. Imagine a set of twins that is separated at birth, one grows up on earth while the other grows up on a rocket ship that is constantly traveling near the speed of light, let say 0.99c. When they meet again, the twin that grew up on earth is 80 years old, while the twin that’s been travelling near the speed of light this whole time is only about 11 years old!

So if you want to stay younger, then you better start building an engine that can let you travel near the speed of light…

—————–
[1]* A. Einstein. (1905). On the Electrodynamics of Moving Bodies. [Online] Available: http://www.fourmilab.ch/etexts/einstein/specrel/www/

*Originally in German titled “Zur Elektrodynamik bewegter Körper”. Annalen der Physik17, pp. 891. 

[2] D.M. Harrison. (1999). The Special Theory of Relativity [Online]. Available: http://www.upscale.utoronto.ca/PVB/Harrison/SpecRel/SpecRel.html#Constancy

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One response to “A Glimpse of Time

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