Special Relativity
Overview
In the year 1905, while working as a patent clerk in Switzerland, Albert Einstein published four papers which upended the world of physics. One of the papers was on special theory of relativity.
By special relativity paper, Einstein put forward the following radical ideas about the nature of the universe.
- Time and space are not absolute; they are relative depending on the motion of the observer.
- Duration and simultaneity are relative too. There is no way to state that two events are really simultaneous from two different referential frames which are moving relative to another.
- Time dilates in a moving reference frame from the perspective of an observer on the other reference frame.
- Relativistic mass of a moving body increases with speed.
- Mass and energy are equivalent. (E=mc2)
- Speed of light is constant regardless of the speed of the emitting source.
- There is no need for ether or absolute rest to explain the propagation of light.
These ideas, no doubt, sound perplexing. We are trying to explain these concepts in simple terms.
Keep reading.
Why is it 'Special'?
Why it is ‘special’ relativity? What is the significance of the word special? It is special because it applies only to a special situation. A situation in which observers are moving at constant speed relative to one another, and the observers are moving uniformly in a straight line.
In order to understand how Einstein arrived at these revolutionary ideas in special relativity, we need to briefly review what was going on in the world of physics from Galileo’s time till the end of 19th century.
Precursors
Though the special relativity was certainly the brainchild of Einstein, all the required components of special relativity existed before 1905.
In the 17th century, Galileo was the first to put forward the idea of the principle of relativity. He stated that the laws of physics were the same whether we are at rest or moving at constant speed in a straight line.
In the 19th century, James Maxwell (mathematical physicist from Scotland), while trying to unify electricity and magnetism, predicted the existence of electromagnetic waves propagating with a constant speed. He also concluded that light was indeed an electromagnetic wave.
At that time, scientists (wrongly) believed that electromagnetic waves (light) required a medium to propagate like sound waves. They called that medium ‘ether’ which was thought to be at absolute rest with strange elastic properties. In 1887 Michelson-Morley (US physicists) conducted an experiment to detect ether. Their experiment did not return results as expected. Though the experiment was a failure, they received Nobel prize for their work because the negative result was a turning point. The negative result paved the way for Einstein’s special theory of relativity.
In an attempt to explain the negative result of Michelson-Morley experiment, Hendrik Lorentz (Dutch physicist, 1853-1912) put forward the idea of length contraction, in the direction of motion, based on a new transformation rule which is now known as Lorentz transformation. Though Einstein used the mathematical tools and concepts of Lorentz, Einstein was the one who put all the pieces of the puzzle together and interpreted the physical significance of all the concepts.
Though Jules Henri Poincaré (French mathematician, 1854-1912) questioned the absolute nature of time, he (Lorentz too) was not able to abandon the idea of absolute rest, nor ether.
Now, let us look into what special relativity teaches us.
Postulates
While others hesitated to abandon the Newtonian concepts such as absolute space and absolute time, Einstein abandoned them and uncovered the true nature of space and time.
Einstein strongly believed that Galileo’s relativity principle not only applied to mechanical motions but also to electromagnetic waves (light). For Einstein, the significance of Michaelson-Morley experimental results was a strong proof for his belief.
By thought experiments and deduction, Einstein arrived at the following two postulates in special theory of relativity.
First postulate:
It is known as the principle of relativity. The first postulate asserts that the laws of physics are the same for two observers moving at a constant speed (in a straight line) relative to one another.
Second postulate:
Known as the light postulate, it says that light travels with constant velocity, and it is independent of the state of motion of the emitting body.
Space and Time are relative
The consequence of the second postulate is startling. It implies that time and space are NOT absolute. Meaning that they are relative to the motion of the observer.
But for Newton, space and time are absolute. They are universal, and they exist independent of matter and energy. Space is a fixed backdrop. Time is universal. A common universal clock exists.
However, for Einstein space and time are not absolute. They are relative to the motion of the observer. But spacetime is invariant. Spacetime is an integral part of matter. It does not exist in the absence of matter or energy.
So, according to special relativity, a serious correction is needed in the Newtonian way of thinking.
Moving clock And
Time Dilation
As mentioned above, according to special relativity time is not absolute. It is relative to the observer’s relative motion. In addition, time dilates in a moving reference frame from the perspective of another reference frame which is at rest relative to the first frame. What exactly is time dilatation? Let us illustrate it by a thought experiment.
Consider that you are sitting inside a train which is moving with a constant speed of ‘u’ in a straight line. Assume that you have a ‘light’ clock apparatus with you inside the train.
The light-clock works this way: A flash of light starts from the bottom, and it travels to the top where it gets reflected and goes down. When it reaches the bottom, you hear a ‘click’. Assume that the time, light takes, to complete one round trip is T1. So, you will hear a click sound for every T1 time interval.
Therefore,
Now assume that your friend, who is standing on the platform, observes the light-clock inside the train. As he watches, the train is moving with a velocity ‘u’. So, how does the path of the light beam appear to your friend who is standing on the platform? It appears to take the path as shown in the figure below.
From the point of view of the standing person on the platform, the light beam travels along the path “H” which is greater than the vertical distance of ‘L’, as ‘H’ is the hypotenuse. If ‘t2’ is the time that your friend sees it takes to complete one trip, then ‘T2’ can be computed this way:
According to the 2nd postulate, the speed of light is constant independent of reference reframe. Since H is greater than L, T2 must be greater than T1.
What does that mean? It means that the light-clock, inside the speeding train, runs slow from the perspective of your friend who is standing on the platform. This is known as time dilation.
Time Dilation is real
Time dilation, that we discussed above in a moving reference frame which is moving relative to another reference frame, is real. It is not just a perception from the other reference frame.
Here are some real-world scenarios where the time dilation is observed.
As you may know, the GPS systems rely on multiple satellites which are orbiting at high-speed relative to the Earth. The GPS system adjusts for time dilation of the clocks in the satellites to figure out the actual location of your car on the Earth.
Another example of time dilation is from the behavior of muons (a subatomic particle) which are produced at the top of Earth’s atmosphere because of bombardment of cosmic rays from deep space. We know that muons’ mean life is only 2 micro-seconds. So, when it travels at 75% of speed of light, it should integrate within 456 meters. But how does it travel so many kilometers through atmosphere to reach the surface of the Earth? Travelling close to speed of light, the time dilation is the reason muons are able to reach the Earth. From the point of a muon, it lives for only 2 micro-seconds. However, from our perspective it lives much longer and hence travels a longer distance to reach the surface of Earth.
Simultaneity is relative too
In addition, Einstein showed that simultaneity is relative too. There is no way of asserting two events to be simultaneous from two reference frames that are moving relative to one another.
To understand this, let us perform another thought experiment as discussed by Einstein. Consider a long train which is moving at the speed of ‘u’. Assume that you are standing on the embankment at the point M, and your friend is sitting inside the train.
Suppose that two lightnings strike at points A and B on the ground and assume that you happen to stand (on the embankment) exactly in the middle of these two points A and B. You can say that the two lightning strikes are simultaneous if the light-beams from the two lightning strikes arrive at M at the same time.
Now the question is how do they appear to your friend who is inside the train? Assume that he happens to be at the point of Mt which is also the mid-point of A and B. Do lightning strikes appear simultaneous to him too? The answer is no. Since he is in a moving train which is moving toward the point B, the light from point B reaches him first and the light from the point A reaches him a little later. So, he obviously will say that the events (lightning strikes) are not simultaneous.
The bottom line is that events that are simultaneous in one reference frame is not simultaneous from the other reference frame that is moving with respect to the first reference frame.
Hence, Einstein’s concluded that simultaneity was relative too.
Relativistic mass
We know that mass is responsible for inertia. We need more force to move a more massive body than a lighter body. Right?
Special relativity shows that the total mass of a body is not only from the rest mass but also consists of relativistic mass which depends on the speed of that moving body.
According to Newton’s second law:
The law states that the resultant acceleration of a body is directly proportional to the force acting on it. More the force more the acceleration. When we carefully look at the equation, you can notice that there is no upper limit to acceleration (and therefore no upper limit to velocity) when we impart a force continuously on a body.
However, according to Einstein’s special relativity, speed of light is the maximum speed anything can reach. Nothing can move faster than speed of light. According to Einstein, the relativistic mass increases with speed.
This is given by the equation:
When we substitute mass ‘m’ in equation (3) from equation (4), the force required to increase the speed of a body to ‘c’ (light’s speed) gets to infinity. So, the key point is we can never ever make a body (with mass) attain the speed of light, let alone make it move faster than light.
Mass-Energy equivalence
From the eqn.4 above, applying binomial theorem and simple mathematical manipulations, Einstein was able to arrive at the famous equation.
Since the speed of light is high (300 million meters per sec), when the mass is totally converted to energy, the energy released is extremely enormous.
Our Sun is a good example of the power of Eqn.5.
In its core, our Sun burns 600 million tons of hydrogen every second, producing 596 million tons of helium. The missing 4 tons of mass becomes pure energy. Using equation 5, when we compute the energy released by the missing mass, we get an astronomical number: 360 septillion watts (360 followed by 24 zeros!). Just to put a context to this enormity, this is equivalent to 4 million years of electricity usage by the entire world. What powers the Sun is this incredible amount of energy released, every second, from the nuclear fusion process in the core.
References
- Einstein – His life and Universe by Walter Isaacson
- Six not-easy-topics by Richard Feynman
- https://en.wikipedia.org/wiki/Hendrik_Lorentz