The theory of relativity is popular among people, not as much as Einstein himself but still popular than his any other theory. May be Einstein’s relativity is the most popular theory in the world. Despite the term being so popular, its understanding is limited to a group of physicists only. I’ll try to explain it as simply as I can.
“Everything should be made as simple as possible but not simpler.” – Albert Einstein
The theory of relativity simplified
The theory of relativity describes how the state of our observation changes our view of the Universe. It explains the effect of relative motion between the observer and the observed in spacetime, for a force-free system (non-accelerating). Finally, it interprets motion under the influence of gravitation (force), describing the gravitation geometrically. It sounds difficult but not for so long.
There are two theories of relativity as follows.
Special theory of relativity (STR)
STR was proposed by Einstein in 1905. It has two postulates.
1. The physical laws are invariant in all non-accelerating frames of reference (The physical laws do not change relatively in uniform motion)
Imagine yourself waiting for the bus sitting at the bus stand. If you flip a coin perpendicularly, it falls on your hand. As you catch the bus and it starts moving at the constant speed (not accelerating), you are in motion with respect to the observer outside the bus sitting at the bus stand (one frame of reference) but you are at rest with respect to the passenger sitting next to you (another frame of reference). Again if you flip the coin perpendicularly, it falls on your hand as before.
No matter you are in a constantly moving bus or just sitting at rest in a bus stand, the laws of physics that apply to you and your surrounding is same; here the laws are applied to coin you flipped, so it falls on your hand likewise. The laws do not change relative to the motion. Another thing we can conclude is motion is a relative term, since you were in motion viewing from outside (one frame of reference) and at rest viewing from inside (another frame of reference) of the bus.
This is because, on the bus, the whole system (you, people inside the bus, driver, seats, the coin, everything associated with the bus) is moving with the speed of the bus. So relative to the coin, you are at rest as before and the coin acts as before. Hence, the physical laws do not vary in the inertial (non-accelerating) frame of reference.
Now let’s look at a larger picture. The rotational speed at the equator of our Earth is 1,674.4 km/hr (1040.5 mph), its speed around the Sun is 107,208 km/hr (66,616 mph) and its speed along with Solar system around Galactic centre of our Galaxy is 828,000 km/hr (514,509.4 mph). Everything in this universe is in motion. This constant motion has no effect in physical laws, this is the theme of relativity. The physical laws are the same since neither Earth nor our solar system is accelerating.
2. The speed of light in a vacuum is constant in all frames of reference.
This is much fun. If you are traveling at the speed of 2 m/s and your friend is traveling away parallel to you at 3 m/s away, you will see your friend traveling at the speed of 5 m/s ( 2 m/s + 3 m/s ).
What if you were traveling with a speed 100 thousand km/s and you switched on a torch towards the direction opposite to your motion? Will you see the photon (particle of light) emitted from the torch traveling at 400 thousand km/s (100 thousand km/s + 300 thousand km/s = 400 thousand km/s)?
So here is the crazy part! According to Einstein, you’ll still see it traveling at the speed of light i.e 300 thousand km/s no matter how fast you are moving. Light has a constant speed of 300 thousand km/s in vacuum whatever may be the speed of the observer. Instead of the change in the speed of light due to relative motion, the spacetime changes!
As we use these two postulates and do a little math, we can prove that your clock slows down (time dilation), mass increases and length contracts as your speed increases. So mass, length and time are relative i.e the change in speed can bring about change in these quantities. (time dilation/length contraction)
The variable form of time introduced the concept of negative time (past) and positive time (future). Finally, time became the fourth dimension including the other three spatial dimensions (along length, breadth, and height in a rectangular coordinate) used to define the position of a matter in the spacetime continuum.
The variability of time is proved by muon decay experiment while the variability of mass has aided the accuracy of measurement in particle physics experiments.
The General Theory of Relativity (GTR)
GTR, proposed in 1915, is a generalization of STR in non – inertial (accelerating) frame of reference. Force comes with the presence of acceleration and hence it describes the action of force in the spacetime continuum.
This theory was the manifestation of equivalence principle due to which if you accelerate in space on a spaceship with acceleration 9.8 m/s^2, you will feel the same force as if you are on Earth since the gravitation of Earth provides same acceleration. This implies that your inertial mass will be equal to gravitational mass. This means the experience of force on an object does not depend upon the shape of the object exerting force.
The spacetime appears flat in inertial and curved in non – inertial frame of reference. Flat here means the change of one with respect to other is uniform and curved means the change is non – uniform. So, the force is expressed as a curve in spacetime as in the figure below. These curvatures of spacetime are called Geodesics, it is flat in the inertial region and curved in non – inertial region.
The orbital path of planets is the projection of the four-dimensional geodesics in three-dimensional space. Also, small regions of the curved geodesics are like flat geodesics, so force does not seem to appear in such small regions.
GTR is rather geometric and mathematical. It has been verified by phenomena such as bending of light while passing massive objects, the precession of orbits of mercury, etc.
The theory of relativity is just amazing. Can you simply believe that we can get massive as our speed increases and Gravitation is due to the curvature of spacetime? You have to, the truth cannot be much finer than this!
“The magic of this theory will hardly fail to impose itself on anybody who has truly understood it.” – Albert Einstein