...Continued from Part 2
This could be hard to explain. Its definitely not as easy as explaining why the conversion between meters and feet is ‘3.3’. But I will try my best. Remember, the equation E=MC2 is a part of Einstein's work on his ‘Theory of Relativity’ and ‘C’ was a term pivotal to that theory. Einstein was particularly fascinated by Light, its speed, its properties. During his work on Theory of Relativity, it dawned upon him that C - the ‘Speed of Light’ (or an electromagnetic radiation) in vacuum has to be constant in all frames of reference (The fundamental basis of Theory of Relativity)
- The first assumption in his theory of relativity was that C, the speed of Light in vacuum, was always constant for observers in all frames of reference. So me, standing on earth (one frame of reference) and you travelling in a rocket at around 15-20 times speed of sound (second frame of reference), or our friend travelling at half the speed of light (third frame of reference) – all will measure the value of C to be the same (approximately 300,000 km/s).
- The second assumption was that laws of motion should apply the same way to all systems travelling at constant speed ‘relative’ to each. So if you are travelling at half the speed of light and I am at rest on earth, you can say that you are at rest in your spaceship and earth is travelling at half the speed of light. So we are travelling at constant speed ‘relative’ to each other and both can apply the laws of physics (for example Newton’s laws of motion) the same way in our own systems.
So C is the only thing that remains constant in all frames of references, the only thing that is ‘absolute’ with an ‘absolute’ value of 300000 km/s. Everything else is ‘relative’. For laws of motion to hold in all frames of reference (which measure C to be the same) – Time, Distance, Mass, Energy - have to adjust in order to maintain the constantness of C. Einstein proposed that, for a system moving at constant speed with respect to a system at rest – ‘Time’ would slow down, ‘Distance’ would be compressed, ‘Mass’ and ‘Energy’ would increase (with respect to the same terms measured in a system at rest). The “extent” by which time, distance, energy, mass differ in two systems moving ‘relative’ to each other – is determined by formulas - all of which contain the term ‘C2’.
For example assume that system is moving at a speed of 'V' m/s. Then as per equations of theory of relativity, the slowed-down time (t') of that system with respect to time (t) measured in system at rest is:
t' = t (1-V2/C2)½
So as an example assume that you are travelling at 60 % the speed of light from point A to B, and I am at rest. If ‘I’ measure 10 minutes in my watch as your travel time from A to B in my frame of reference, then ‘I’ would measure 8 minutes (80 % of 10) in your watch which is operating in a system that is moving relative to my system at 60 % the speed of light. That means ‘time’ in your frame of reference, has slowed down, as observed from my frame of reference.
Based on the same principle, In order to keep C (Speed = distance/time) constant for both frames – distance (or length) must also reduce in value (compress). So if the spacecraft in which you are travelling is actually 10 meters long, I would see it compressed to 8 meters from my frame of reference (applying the same equation for distance). But you in your own frame of reference would measure yourself as 10 meters. Confused? The point is that time and distance that I measure in your system, are different than what I measure in my system.
It’s not important that you understand how Einstein arrived at these equations. What is important is the role played by the term ‘C2’. Apply the same logic to Energy. Yes you guessed it right. The difference between energies of the two systems moving relative to each other at constant speed must be having term ‘C2’ involved somewhere. Einstein figured out that when objects emit energy in form of heat, sound, light etc (or decay and emit radiations) they were actually losing mass. The form of energy being emitted was not important. So for purpose of calculation of this equation, Einstein considered a system where a body emitted light (radiation):
From frame of Reference of Object at Rest:
"Energy of an Object before emission = Energy of that object after emission + Energy emitted"
Then he applied the same equation for the frame of Reference that was moving with respect to object at Rest.
"Energy of a moving Object before emission = Energy of that moving object after emission + Energy emitted by moving object"
Then he compared the observations in the two systems for calculation of the emitted energy and arrived at a conclusion that - when a body emits energy 'K', its mass diminishes by an amount = K/C2. This means the mass of the object depicts how much energy it contains.
This explanation is surely a very short excerpt. But the gist is that Einstein formulated E=MC2 as part of Theory of Relativity where the term ‘C’ plays a pivotal role. The equation was proved decades later in 1938 when German scientists successfully carried out fission of uranium for the first time and found that the energy released during the fission due to loss of mass was exactly in line with this equation (A Swedish physicist named Lise Meitner was the one to prove this).
Even today most of the mankind doesn’t see what terrific revelation is hidden in this equation, but Einstein visualized it more than a century ago. What a revolutionary and mind-blowing concept it has been.
Authored by: Mandar Garge
9 comments:
It indeed is a mind-blowing theory. I had always heard about the fascinating implications of relativity (you win time when you near speed of light etc.) but never understood how it could really transpire. You have very nicely explained this and that too using minimal help of equations. Very cool!
Was an interesting read mandar. I think I understand this concept a little now. Just one suggestion - something popped out right way..when describing the value of C you jump between units a lot, i.e. in some places you say km/sec, in other places you say mps. The user could benefit if you adopted a consistent metric system. Looking forward to more of your work.
Nivedita,
Thanks for your comments.
Pradeep,
Thanks for your suggestion. I have made a few changes to try using consistent metric units whereever possible.
It's really a nice post (all the three parts). It will be great if you could write a post on historical background of these concepts :)
I also would like to mention one correction. All the three parts talk of "Special theory of Relativity" published in 1905. This theory works in zero gravity space.
In Part3, the example of "earth" as first frame of reference should be avoided as it is affected gravity.
Pankaj,
Thanks for your comment. You are correct. I have especially talked about objects and bodies moving relative to each other at 'constant' velocity - which is what 'Special Theory of Reativity' talks about.
The earth reference is just used as an easy-to-understand example to indicate how relativity comes into picture. The effects of gravity are ignored for the purpose of explanation :)
ka mandar ka? itkey varsha shiklo bas zhala ki :d
Examples are very interesting and helps to understand. I see this article as home work before going to watch "Interstellar".
Mandar,
An explanation in terms of energy does make the argument more intuitive.
However, somewhere in the thought-train, I would include two points:
(i) the entire explanation is limited only to the frames that travel at constant velocities. For instance, one frame is attached to the earth, and another to a space-ship which is traveling at a constant velocity. The moment the spaceship accelerates (e.g. if it turns around in a semi-circular path so as to return to the earth and complete the twin paradox), the analysis based on SR fails.
(ii) SR is just a consequence of the Maxwellian---i.e., the classical---electrodynamics. Not many people get that. SR is not at all as revolutionary as it is made out to be, in the pop. sci.- (and even text-) books.
(iii) Since SR is essentially electrodynamic in nature, its conclusions cannot be directly applied to charge-less bodies, or the forms of energy that are regarded in the contexts of charge-less bodies. What that means for your description here is this: You need to tell your reader that SR still holds, mainly because Maxwellian electrodynamics is more comprehensive in scope and therefore more fundamental, than the Newtonian mechanics (i.e. the mechanics of the charge-less classical bodies). But before we can regard SR to hold even for energy losses via Newtonian (charge-less) routes such as heat and sound, they are first to be seen as the net consequences of certain more microscopic mechanisms which are Maxwellian electrodynamical in nature. For instance, heat is random motion of molecules, and it diffuses (or in general spreads) from hotter to colder regions only through certain statistically preferential directions in the motions of molecules. This directionality arises out of the electrodynamical forces between those molecules. Thus, since heat and sound (and other energy loss mechanisms) are electrodynamic, therefore, SR applies---provided the spaceship is traveling at a constant velocity w.r.t. an earth which is regarded as stationary.
OK. Enough is enough.
--Ajit
[E&OE]
Very succinct explanation of a complex theory whose practical aspects are quite difficult to visualize and grasp...I really enjoyed trying your 3 posts... Wish it was there when I was grappling with trying to fathom this challenging subject in college ;)
_ MandarK
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