Susanta Dutta
Imagine Albert Einstein shouting at the pilot, "Damn, there goes my image again! How many times I told you not to fly at the speed of light when I am shaving!"
Let the story of one of the all time greats begin.
Albert Einstein was born in Ulm, Germany (14.03.1879), just like rest of us.
Europe was in political turmoil. Jews were getting the blame of financial crisis.... Many emigrated to America.
Albert's father, Hermann, and uncle, Jacob, shifted to Munich and started manufacturing dynamos, electric instruments and arc lights. They could not sustain competing with giants like Siemens and Halske.
Albert proved to be a slow, dreamy child. His closest friend, then, was his sister, Maja, who was two year younger. He was admitted to a school, having military discipline. It was a Catholic school, where Albert was the only Jew. To him, teachers in elementary school, appeared to be like sergeants and lieutenants.
Compass was the first scientific gadget, his father introduced to him. It fascinated Albert! How does it always point the same way? How does it float by magnetism?
Albert liked his uncle, Jake (Jacob), who introduced him to Maths. Jacob used to say, "Algebra is a merry science...When the animal we are hunting, cannot be caught, we temporarily call it X...and continue to hunt until it is caght."
Albert's mother, Paulin Koch, introduced him to violin and literature.
It was a Jewish custom in South Germany to invite a poor Jew to dinner on Thursdays. Max Talmey, a medical student in Munich, used to attend invitations to Einsteins'. Talmey brought some 'popular science' best-sellers for Albert. These books were of great public interest in science. Max also introduced to him Geometry and then Calculus.
Albert was dreaming to be a theoretical Physicist. He had a good time in Aurau with his Physics teacher, August Tuschmid. Finally, he opted teaching as his profession after graduation in 1896.
Albert, like most beginning Physics students, particularly admired the ability of Mechanics to explain the behavior of gases. But it was the Physics of electricity and the electrodynamics of Faraday, Maxwell and Hertz that most attracted his attention.
Faraday, to him, was the most accomplished 'experimental Physicist' of the 19 th Century.
Maxwell's equations showed that, electric and magnetic forces should move through empty space at exactly the speed of light. Albert made a note of this.
Optics into the theory of electromagnetism, with its relation to the speed of light, was like a revelation to Albert. He wanted to understand what is going on when light spreads out from place to place. He wondered what would happen to light if he would be moving right along with it, at the speed of light. Make a note: This was his first step towards his theory of relativity!
Suppose, one moves at the speed of light, holding a mirror in front. Light from himself could not catch up to the mirror !!! He can't see himself in the mirror !!
With other eminent scientists of that century in 'Olympia Academy', he chewed over the puzzle of riding on light particle. Finally the concept of ether, in space, was rejected.
'Principle of relativity' was first experimented by Galileo in 17 century. He stated," All steady motion is relative and cannot be detected without reference to an outside point." This was again under review by these scientists of Academy.
You cannot say an aircraft moving, when you are sitting inside and the aero plane cruising at a uniform velocity. But a person, looking from the terrace of your school building, would say that, you along with the aircraft, are moving with a velocity. This is relative to each other from two different references.
In 'Annaler der Physik', Albert expressed :
- Galileo's principle of relativity stands good for light as well as ordinary motion...
- Everyone should always observe the same velocity for light, which is independent of the state of motion of the emitting or receiving body.
Now, Albert had to show:
- How everyone can see the same speed of light, c...
- What happens when you try to get an object to move faster than the speed, c.
He stated that, the concept of time, length and mass must be changed when simultaneous events, from different reference frames, are measured.
Classical mechanics of Newton says:
- Time interval between events, is independent of motion of the observer...
- Space or length is independent of the motion of the observer.
But Albert says: 1. Space and time are relative and do depend on the motion of the observer.
Newton : "Space and time intervals are absolute and speed of light is relative.
Einstein: "The speed of light is absolute and space and time are relative.
Now, recap the Pythagorean theorem: c2=a2+ b2.. ...Albert would use this shortly...
Though Plato geometrized the ancient world, to Albert Einstein in reality, Mathematics is only a language to describe sizes, quantities and relationship between measurable things. And that was exactly how Einstein used Maths...to express the relationship between time and space of an event with respect to different reference.
Let us make it simpler.
X'Y': a moving frame, S' and XY a stationary frame, S
Let, S' frame is given a velocity, v with respect to S frame. (Fig 1)
observers in two reference, viz., S' and S. Here, Albert bounces Lorentz' transformation to express the different experience of two
x= (xvt)/(1-v2/c2)1/2
y' = y
r =(t vx/c2)/(1-v2/c2) 1/2
Stationary observer, looking at moving clock from S, hears more time elapse than stationary clock in S'... Albert said," Moving clock runs slower than stationary clock !"
Don't have a nervous break down! Go slowly....
v = velocity of moving frame
c= speed of light
t' = time between clicks in moving frame
t = time between clicks in stationary frame
t'=2L/c
t= 2h/c or, h=ct/2
L= ct'/2
d/2= vt/2
Now, Albert used 1500 year old Pythagorean Theorem :
- h2=L2+(d/2)2
- (ct/2)2=(vt/2)2+(ct'/2)2 (from Fig 2)
- t=t/(1-v2/c2).
This is too complicated! Try out on an astronaut in a rocket, moving at 8/10 th speed of light (c). The astronaut returns after 3 days in his rocket clock.
- t' time elapsed in rocket clock = 3 days
- V= speed of the rocket = 0.8 c
- So, we get the time elapse on an earth clock, t=3/(1 (0.8c)2/c2)1/2 =3/ (0.36)1/2 =3/0.6= 5 days. Hence, when a clock moves, it runs slower.
Ridiculous!!
Speed of light, c=d/t= constant. So space traversed, d, and time elapsed, t, must change relatively to maintain c as constant.
Okay, don't get worried. Among physicists there is a saying, "You never really understand a new theory. You just get used to it.'
Now, coming back to our classic formula applied on an electron in a moving frame,
- a = F/m, where a = acceleration imparted to the electron of mass, m, by the force, F. The electron is moving with the frame S' at velocity, v.
Here what happens :
- The electron goes faster because of the force. But....
- In the moving frame, S', where the electron is at rest, the "time" over which the force acts, get smaller and smaller compared to the time in stationary frame, S... (Remember, moving clock runs slower!) So ???...
- In the moving frame, where the electron is at rest, the force acts for a shorter and shorter time, as the electron tends to a speed of light.
Albert states a new equation: a = (F/m). (1-v2/c2)32.... (A) against
conventional a = F/m... Here, when v=c, a=0...
So, even if you keep on pushing, the electron does not pick up any speed.
What does this mean? It means, an electron at nearly the speed of light, gets heavier!
Wait a minute. We can put in work, W= F. d, but the body doesn't pick up speed. Why?
From equation (A), Albert changed the conventional equation W= m v2/2 to
- W = mc2/(1 v2/c2)1/2 mc2, where E= mc2/(1 v2/c2) 1/2 is the energy of the electron.
- So, E=W+mc2.... (B)
Now just wonder...if energy goes into giving a body inertia, then inertia must contain energy. That means dead weight has energy??? Crazy!!!
Albert answers: If W = 0,ie, no work, then still the electron has an energy, Then equation (B) changes to:
E=mc2 the most famous equation of the 20 th century.
What does this equation really signify?
The Big Al says, " Mass of a body is a measure of its energy content."
Energy = Inertia x (speed of light)2
Albert's argument is not a proof because you cannot prove a definition. Neither did he say how to get this energy out, in the first place. But this magical equation lead to the tragic fate of Hiroshima and Nagasaki during the World War II.
Later, after the A-bomb was dropped, Einstein said, "If I knew they were going to do this, I would have become a shoe-maker."
In 1921, when he was awarded the Nobel Prize on Physics, he was already in his own world of new exploration trying to relate gravity with electricity... (Remember, compass was the first scientific gadget, which fascinated him!)... Noble prize money practically had no impact on Albert's searching mind. He made a unique statement with conviction," I can't believe God plays dice....Unlimited competition leads to crippling of social consciousness of individuals."
2,99,800,000 m/s !!!