The equation E=mc2, is arguably one of most famous equations of physics that has revolutionized the entire way we perceive reality. Before the equation was discovered, the universe was thought to have been composed of two distinct entities – matter and energy. But that notion had changed ever since the equation was discovered; these two entities are not very different from each. They are interchangeable. But how does this equation or even relativity affect us in everyday life? It is easy to consider relativity as rocket science that despite its mathematical correctness and accuracy, fails to sell itself, as far as its use in everyday lives are concerned. One cannot be further from truth to even think so. If not for Einstein’s theory of relativity, GPS systems would have failed to exist and as a consequence, the wheels of technological progress would have slowed down to a great extent and Google Maps would be been only a figment of our collective imaginations.
So, what is relativity?
It is the study of how relative motion between observer and the observed change various physical phenomenon such as mass, gravity, time.
As an introductory article, we are going to deal with two such theories that will set a foundation for advanced sub-topics in the next article:-
- Everything is relative
The effect of relativity is not limited to an apparatus in a lab or entities in a fixed set of condition. It is applicable to the entire universe and that means – the sun, moon, earth – pretty much, everything one could think of! It says that every measurable phenomenon has a frame of reference.
Let us understand this through contradiction.
Consider an example of a man inside a bus moving north, as he observes the trees outside his window. Is the person sitting on a moving bus, in motion?
This question can be answered in several ways with the answers being both, yes and no. Yes, when compared to the tree outside that the bus just passed by. No, when compared to his seat. But how can an object be both in motion, and not at the same time?
Now that we have established that the bus is moving relative to the tree outside, the tree must be static. Right?………………………………………..
Wrong! General theory of relativity tells us that in the system where the man in moving bus and tree exists, the same situation can be interpreted in either way and that both of the following interpretations holds true:-
- The tree is moving south relative to the bus
- The bus is moving north relative to the tree.
Thus, to answer the above question more accurately, would be to say – depends on the observer!
If we were to perform mathematical operation and write equations of motions based on the above two cases, the results obtained would be different from one another. But why, is it so?
The example of tree and moving man doesn’t seem to quite satisfy us. Our prior experience with such commonplace objects sort of makes us biased and tricks us into thinking that somehow, even if slightly, the second case must be a better answer, if not the correct answer and for that, we must come up with a better example in ideal condition where both the observer and the observed are identical.
The above example has to be modified in the following ways:-
- Consider the man on the train to have no prior experience whatsoever with trees or trains. The motion of a train, or the static nature of a trees is not lodged deeply into his habit of thought .
- For an ideal condition, we shall assume that the world outside the train has nothing, but only trees.
- Also, the movement of the train is perfectly smooth, friction-less and doesn’t jerk or make any local movements, apart from translation along the tracks.
- The train doesn’t accelerate or decelerate, just moves with a constant velocity .
- Instead of the directly viewing the window, the observer is made to look outside his window. Under the following conditions, is there any way for the observer to tell with absolute certainty, that it is he, who is in motion and not the other-way?
Well, there isn’t – because he has no prior experience with neither trees, nor trains. Moreover, he doesn’t experience any force not even the occasional tremors and jerk.
Even if one were to ignore motion, and explain relativity with the aid of measuring length, we could sufficiently explain the larger idea it tries to convey, if not the one question. Let us consider the sentence – “a man is six feet tall”. In saying so, we are essentially assuming that the definition of feet is known to us. Without its proper definition, the words “six feet” makes no sense.
The sentence – “John weighs 100 kloons”, makes no sense, because it begs the following questions – “What is a kloon? What is its relation to the known units of mass?”
Thus, in saying that “a man is 6 feet tall”, we are saying that he is 6 times of what is considered as a foot. Thus, even lengths are measured in relative terms and needs a basis. If this seems a bit too overwhelming you can consider the third example.
Consider the scenario of you, reading this or any other article on the internet. The most common solution to view web pages whose length exceed the size of your screen(smartphone, tablets and desktops) is the scroll button on your right. As you scroll down, one cannot determine with certainty that the view of your screen that is moving down, or it the document that is moving up. Both these scenarios serve the exact same purpose i.e. displaying information outside the view port through movement, but if we were to consider only one of the answers as correct, it would be simply our interpretation and nothing more. This is what relativity tries to convey. Without a frame of reference, nothing can be defined. In this case, movement of page occurs relative to the view and that is what matters, as far as calculations are concerned.
The elaborated theory of having a prior experience versus not having one i.e. the second example, can easily be considered trivial in the sense, it might seem as a painful elaboration of the obvious to the intelligentsia. By virtue of “having no experience”, they cannot ask the question whether it is “true” or not, because truth can only be associated with phenomenon observed, and the mathematics doesn’t not limit itself only to observed phenomena. (It deals with abstract topics such as imaginary numbers and the concept of infinity that has barely anything to do with reality.)
- Everything is relative
Now that we have discussed, what relativity is, let us discuss what frame of reference is.
A frame of reference in simple terms is the basis point from which measurements are taken. Previously, in the example of “a man is six feet tall”, we have discussed the importance of the definition of “foot” for “six feet” to make sense. Similarly, when we take measurements, the point corresponding to the zero marker serves as the reference point and the entire scale its frame of reference.
In the three examples, we have failed to explicitly mention what the frame of reference. To find out something is moving or not, we must define what is static in the system which we shall consider the zero marker. In the second example, everything, inside the train (which is our chosen reference frame), is static with respect to him. But, from the tree (consider a man sitting on the tree), he can observe the train moving along with the man . Both these theories are true, because their reference frames are different, and hence they do not violate each others equation of motion.Thus, we can conclude that the concept of motion(and lack of it) is purely subjective and can only be “relative” to the frame of reference, chosen.
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This is the first part of a 3 part series: