Physics
Intuition Behind Time Dilation
Einstein published his paper on Special Theory of Relativity in 1905. It completely changed our notion of Space, Time, Mass and Energy. The conclusions of Special Relativity are :
1. Constancy of Light Speed: Speed of light is not relative to your speed of motion. i.e. even if you run at close to speed of light parallel to a beam of light, this light will still race ahead of you at the speed of light.
2. Relativity of Time (or) Time Dilation: Time slows down the faster you move or the more gravity you experience.
3. Length contraction: Space itself contracts along the length as you move faster.
4. Relativity of Mass: Observed Mass of an object increases with its speed of motion.
5. Relativity of Simultaneity: i.e. there is no Universal “Present Moment”
6. Energy — Mass Equivalence: Energy and Mass are 2 sides of the same coin, i.e. E=MC²
These conclusions are mind boggling and counter intuitive to every human experience isn’t it? And yet, Einstein got the Nobel prize for a “relatively” modest discovery of photo electric effect that he published in 1905 as well. It makes you look at Nobel prize committee and go “duh”.
In this blog, I will just focus on the intuition behind Time Dilation. Special Relativity is really derived from two fundamental laws of Physics which are deemed irrefutable , so far. 1. Maxwell’s Electromagnetic Theory and 2. Newtonian Relativity.
Maxwell’s equations on Electromagnetism essentially concluded that Visible Light ( i.e. all the colors from Violet to Red in the rainbow spectrum) is also an electromagnetic wave and thereby can travel in vacuum. How does he conclude this? Well, there’s loads of math. But, in simple terms, he was able to calculate that speed of propagation of electromagnetic waves using his equations. And every time he calculated, he came up with a number which was almost the same as the speed of light, i.e. ~ 186,000 miles per second. Hence, the conclusion that light is an electromagnetic wave. Until Maxwell’s discovery, physicists believed that light travelled in this invisible medium called “Ether” which was spread everywhere in the universe.
The second postulate is from Newton’s Relativity which basically states that Newton’s laws of motion are the same in all inertial frames of reference. What does that mumbo jumbo mean? Imagine you are standing stationary in the ground and your friend is travelling in a fast train past you at 100 miles per hour (mph). You are both in different inertial frames of reference. However, as long as the train is travelling at constant speed, the Laws of motion are the same for you and your friend. In fact it is impossible to detect who is actually moving in this scenario. Your friend would be equally correct in stating that he is stationary, while you, the train track and the rest of the world is zooming past the train in the opposite direction. You might argue that the train is burning fuel and hence it is moving. However, bear in mind that we are only dealing with a special case of Constant Velocity motion (hence the term “Special” in Special Theory of Relativity). Assuming the train experiences 0 friction, it can keep travelling in Constant Velocity forever without any fuel. The most obvious example of Newtonian Relativity is the fact that we are all hurtling through space at a speed of 67000 mph, around the Sun. However, we really cannot tell that we are moving.
Einstein realized that when you put Maxwell’s discovery about light and Newtonian relativity together, the conclusions of Special Theory of relativity were inevitable. Let’s try to deduce Special Relativity ourselves, intuitively, using a couple of thought experiments. No Math, I promise. Let’s evaluate whether there is any scenario wherein Newtonian relativity is breached. i.e. Is there any way of proving that it is in fact the train that is moving, and not you?
Imagine playing tennis inside this Constant Velocity train versus outside. The tennis ball (and everything else inside the train) will follow the same laws of motion both inside the train and outside. The players inside the train do not have to exert any more force on the ball compared to the players outside, assuming of course that the train is travelling at constant speed and ride is perfectly smooth. So, we cannot really conclude whether the train is actually moving.
Now imagine the train is travelling East at 100mph past you, while you are standing outside on the ground. Your friend who is travelling in the train, stands in front of the train and throws the tennis ball outside towards East, at a speed of 100mph. What will be the speed of the tennis ball? Well, it is relative, right. You will observe the ball to be moving at 200mph ( i.e. 100 mph due to its inertia while in the train + 100 mph due to force exerted by your friend). Inertia should be 0 while at rest and hence you will be right in claiming that the Train is in fact moving.
However, now imagine you throwing a tennis ball in the Westerly direction at 100mph. Your friend claims that you and rest of the world are already moving west at 100mph. Hence, he will observe the ball to be moving at 200mph away from him (i.e. 100 mph due to inertia + 100 mph due to force exerted by you). Yet again, it is impossible to detect who is moving at a Constant Velocity.
In fact , any matter or particle you throw out of the train will already have intertia and experience air resistance. But, wait a minute. What about light? Light does not have any rest mass. Therefore, no inertia nor air resistance. And, according to Maxwell’s theory, light is an electromagnetic wave. It does not require a medium to travel.
Now imagine your friend in a space ship travelling in outer space at the Speed of Light © . You are floating at a stationary point in outer space, far enough to observe the space ship’s journey. Again, you claim that he is moving while he claims that you and rest of space is moving behind him at the Speed of Light. This time, instead of throwing a tennis ball, lets imagine the space ships turns on its overhead light and you turn on your flash light simultaneously.
Now, given that your friend is also flying at the Speed of Light, you can argue that from your friend’s perspective the light beam is frozen ( bear in mind.. light has no inertia), i.e. speed of light beam = 0mph from his perspective. However, your light beam will appear to move away from you at the speed of light. “Aha”…you might exclaim, at the thought of winning the argument with your friend over who is actually moving. Clearly the apparent speed of light is different for you and your friend. Does this thought experiment really mean that you can detect Space ship is moving and not you, thereby breaching Newtonian Relativity?
Not so fast, says Einstein. According to Maxwell’s theory , there is no such thing as Electromagnetic Wave at 0 mph or “frozen”. Since light is an electromagnetic wave, it cannot be at rest. Besides, Newtonian Relativity was viewed as unbreachable as well. If neither of these theories can be at fault, then the only possible conclusion is that your friend’s light beam is actually moving away from him at the speed of light as well., i.e. Speed of Light will always be the same constant for observers in every Inertial frame of reference.
Now, wait… how is that possible? We just observed in the above experiment that Speed of light was 186,000 miles per second for you and 0 miles per second for him. Let’s understand this with some numbers.
Let’s say your friend’s space ship was moving at 90% the speed of light. So, if the light beam covered some 186,000 miles in 1 second , the space ship has covered 90% of that distance, ie. 167400 miles in that time You might argue that Speed of light from his perspective is = Distance Covered / Time , which is 18,600 miles per second. How can this be equal to 186,000 miles per second? Einstein concludes that the only explanation is that denominator ( Time) is smaller and Numerator (Distance) is larger, from your friend’s perspective. Einstein gives you Time Dilation and Length Contraction. When 1 second has elapsed in your clock, only about 0.43 seconds elapsed on his clock, based on the Time Dilation formula derived by Einstein in Special Relativity. Likewise, while the distance between the space ship and the light from your perspective is 18600 miles, it is longer from his perspective because the entire space along the direction of travel appears contracted to him.
You might be thinking this is a bit too simplistic to be logic behind special relativity. But, a similar thought experiment is what led Einstein to conclude that Time is relative to speed.
