Special Theory of Relativity Part 3 - Time dilation and Length Contraction
In the previous blogs, we spoke about various details and ideologies of the Special Theory of Relativity. In this blog, we'll discuss some very important and mind blowing concepts and implications of The Special Theory of Relativity that changed our perception of the universe and modern physics drastically.
Time Dilation:
The phenomenon due to which an object moving at very very high speeds (close to the speed of light), experiences the slowing down of time is called time dilation.
Einstein's work was heavily influenced by the work of the two most iconic physicists of his time - the laws of motion proposed by Isaac Newton, and the laws of electromagnetism by James Clerk Maxwell. Newton's laws of motion said that motion is no absolute and it's relative. Hence, you must add a phrase like 'with respect to' when speaking of motion. This gave rise to relative motion that Newton considered to be universal.
Maxwell, on the other hand, said that the speed of electromagnetic radiation,i.e., the speed of light is a constant quantity from all points of view.
However, Maxwell's notions seemed to be incompatible with Newton's relative motion. If Newton's laws were truly universal, why is the speed of light an exception? This presented Einstein with a daunting dilemma. Einstein had to make a difficult decision, either Newton's laws of motion were incomplete or the speed of light is not a constant.
Einstein concluded that both of these could co-exist with a slight tweak in Newton's laws. He concluded that time itself should slow down with increase in velocities such that the magnitudes of both the speed of light and the time remained same. He called this puzzling phenomena time dilation and this gave rise to the theory of special relativity.
Newton believed that time moved unflinchingly in the same direction. Einstein on the other hand just discovered that time can bend and varies and is not absolute.For its malleability, time deserved a dimension. Einstein believed that together they made up the fabric on which the mundane events of the universe occurred, commonly called the space time continuum, which we will discuss later.
Here's an example to further concretise out understanding of time dilation (Fig 1 below).
Let's say there are 2 people - Jack and Jill. Jack is on the ground and from his frame of reference there are 2 synchronised clocks - C1 and C2 with the distance of a million miles or 6 light seconds between them.
Jill is in a spaceship with a clock C' which is synchronised to C1. Her spaceship travels at 0.6c, where c is the speed of light, parallel to the line C1C2.
Both Jack and Jill record the time taken for Jill to cover the distance. From Jack's point of view, Jill takes 10 seconds to cover the distance, further enforced by the formula - time = distance by speed, and in this case distance is 6 light seconds and her speed is 0.6c. Hence, common sense says that she will take 10 seconds. On the contrary, on Jill's clock the time shown is 8 seconds.(fig. 2)
This is time dilation. The closer your speed is to the speed of light, the slower time passes by. Note that there are various mathematical equations called the Lorentz transformations that are used to calculate the time dilation factor but are way beyond the scope of this blog.
Length Contraction:
Here's an example to further concretise out understanding of time dilation (Fig 1 below).
Let's say there are 2 people - Jack and Jill. Jack is on the ground and from his frame of reference there are 2 synchronised clocks - C1 and C2 with the distance of a million miles or 6 light seconds between them.
Jill is in a spaceship with a clock C' which is synchronised to C1. Her spaceship travels at 0.6c, where c is the speed of light, parallel to the line C1C2.
Figure 1 Copyright : University of Virginia physics
Both Jack and Jill record the time taken for Jill to cover the distance. From Jack's point of view, Jill takes 10 seconds to cover the distance, further enforced by the formula - time = distance by speed, and in this case distance is 6 light seconds and her speed is 0.6c. Hence, common sense says that she will take 10 seconds. On the contrary, on Jill's clock the time shown is 8 seconds.(fig. 2)
Figure 2 Copyright : University of Virginia physics
Length Contraction:
Time dilation may seem like the weirdest thing you've heard of. But, there's still plenty more to get through with this theory. As it happens, it's not just time that is relative, even length is relative. Just like how time itself slows down at high speeds, length too contracts at high speeds.
The phenomenon due to which a moving object's length is shorter than its actual length when at rest is called length contraction.
Remember that these effects of time dilation and length contraction can't be experienced distinctly in our day to day lives like when you're driving your car on a highway. Only at substantial fractions of the speed of light can these be observed clearly.
To understand this bizarre effect let's talk about the pole in the barn paradox (Fig 3).
There's a pole of length 20 m and a barn with two doors on either side 10 m apart. If the pole moves at about 90% the speed of light toward the barn and both doors are open, for a split second the pole would fit in the barn and both doors could be closed. This is because of length contraction. Remember that this is from a person outside the barn's point of view.
On the contrary, a person who's sitting on the pole would not concur with the person outside the barn. From his point of view, the barn would have shrunk and the barn doors were not open at the same time. Remember, for the person who's on the pole, the barn would be moving towards him at 0.9c.
On the contrary, a person who's sitting on the pole would not concur with the person outside the barn. From his point of view, the barn would have shrunk and the barn doors were not open at the same time. Remember, for the person who's on the pole, the barn would be moving towards him at 0.9c.
Figure 3
Copyright - hyperphysics
As weird as these effects sound, their existence and effect is very much true. Remember that I am not discussing the Lorentz transformation that are pretty important for the study of time dilation and length contraction but are based on complicated math and beyond the scope of this blog.
There you have it, two very puzzling effects of the Special theory of Relativity. In the final blog we'll summarise all the key concepts of relativity as well as matter energy equivalence or universally known as E = mc^2.
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Very nice writrup Pranav...
ReplyDeletethank you
DeleteSuperb Pranav, thanks for teaching time dilation and length contraction. Does it mean that any object of finite length will never be able to move faster than the absolute velocity of light in vacuum because of time and length dilation ?
ReplyDeleteActually chikappa, an object cannot reach the speed of light because, as it reaches the speed of light, its mass increases gradually and the energy required to accelerate it further will increase too. When the object reaches the speed of light, its mass in turn becomes infinite and hence, the energy required will also become infinite, which is impossible making the speed of light the universal speed limit.
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