topics: |  physics | relativity | science

combines the wonderful essays from the books Mr Tompkins in Wonderland and Mr Tompkins explores the atom.

1. City speed limit

[Mr T dozes off while attending a lecture by a professor on the theory of relativity.]

When he opened his eyes again, he found himself sitting not on a lecture room bench but on one of the benches installed by the city for the convenience of passengers waiting for a bus. It was a beautiful old city with medieval college buildings lining the street.

He suspected that he must be dreaming but to his surprise there was nothing unusual happening around him; even a policeman standing on the opposite corner looked as policemen usually do. The hands of the big clock on the tower down the street were pointing to five o'clock and the streets were nearly empty.

A single cyclist was coming slowly down the street and, as he approached, Mr Tompkins's eyes opened wide with astonishment. For the bicycle and the young man on it were unbelievably shortened in the direction of the motion, as if seen through a cylindrical lens.

 
    the bicycle was unbelieveably shortened in direction of motion

Then Mr Tompkins felt very proud because he could understand what was
happening to the cyclist - it was simply the contraction of moving bodies,
about which he had just heard.

[in his dream, he has entered a world where the speed of light is less.
speeding bicycles seem far shorter.

And then Mr Tompkins lifts a bike and starts to pedal... he doesn't become
shorter, but the world becomes narrower in his direction of
motion.]


     the windows of the shops began to look like narrow slits, and the
     policeman on the corner became the thinnest man he had ever seen.

"By Jove!" exclaimed Mr Tompkins excitedly, "I see the trick now.  This is
where the word relativity comes in.  Everything that moves relative to me
looks shorter for me, whoever works the pedals!"

[although half an hour has passed by the wall clock, it seems much
less and is only 5:05 on his watch.]

A young man chastizes him for not knowing these things - "What's the matter
with you, anyway? Did you fall down from the moon?"

	   The young man was evidently a native, and
	   had been accustomed to this state of things
	   even before he had learned to walk. p.6

2 The Professor's lecture on relativity which caused Mr. Tompkins's dream

	starts with newton's view of space, from Principia:

	   Absolute space, in its own nature, without regard to anything
	   external, remains always similar and immovable ...
	   Absolute, true and mathematical time, of itself, and from its own
	   nature flows equably without regard to anything external. [Principia]

  	and goes on to describe the process by which contradictions appeared
	in this view, with Michelson's experiments on the absoluteness of the
	speed of light.  and how einsteins eqn of velocity computation
	restricts velocity.

The contradiction in adding velocities

is it not possible to construct a super-light velocity by
adding several smaller velocities which can be physically attained?

For example, we could consider a very fast-moving train, say, with three
quarters the velocity of light and a tramp running along the roofs of the
carriages also with three-quarters of the velocity of light.

According to the theorem of addition the total velocity should be one and a
half times that of light, and the running tramp should be able to overtake
the beam of light from a signal lamp.

However, since the constancy of the velocity of light is an experimental
fact, the resulting velocity in our case must be smaller than we expect—it
cannot surpass the critical value c; and thus we come to the conclusion that,
for smaller velocities also, the classical theorem of addition must be wrong.

[here the tramp running on the roof of a train at 3/4c, while the train is
moving at 3/4c, has a speed of (v1+v2) / (1+v1v2/c²), which implies the
resulting velocity is 24/25 c, still less than vel of light.

Leads on to demolishing the notion of simultaneity (can only exist in a
local frame).

   When you say, ‘The explosion in the mines near Cape town happened at
   exactly the same moment as the ham and eggs were being served in your
   London apartment,’ you think you know what you mean.

   I am going to show you, however, that you do not, and that, strictly
   speaking, this statement has no exact meaning.

   Asks us to compare:

	   Two events in diff places considered simultaneous from ref frame A
	   will be separated by a definite time interval in ref frame B

   and now compare:
	   Two events in diff times at same place in ref frame A will be
	   separated by a definite space time interval in ref frame B

   which can well happen - e.g. two events on a moving train.  But this is
   completely symmetric to the earlier statement.  Einstein's insight
   consisted in noting this symmetry and building the space-time continuum
   on it.  goes on to the equations for shortening of space [length mult by
   sqrt (1 - (v/c)²)], and expanding of time [time mult by 1/sqrt above].

6. Cosmic opera

   	a number of poems that describe the nature of the universe - an opera
	about the big bang theory, complete with music scores, and a famous poem
	on the big debates between the big bang theory (Gamow's view) vs the
	entrenched opinion on the univ being in a steady state, written
	by George Gamow with his wife Barbara Gamow (some opine that
	it was mostly Barbara).  It outlines the debate with the
	steady-staters (Fred Hoyle, Hermann Bondi, Thomas Gold).  Ryle is the
	radio astronomer Martin Ryle, who computed the density in the far
	reaches of the universe.

  	   "Your years of toil,"
	   Said Ryle to Hoyle,
		"Are wasted years, believe me.
           The steady state
	   Is out of date.
		Unless my eyes deceive me,

           My telescope
	   Has dashed your hope;
		Your tenets are refuted.
           Let me be terse:
	   Our universe
		Grows daily more diluted!"

           Said Hoyle, "You quote
	   Lemaître, I note,
		And Gamow. Well, forget them!
    	   That errant gang
	   And their Big Bang—
		Why aid them and abet them?

	   You see, my friend,
	   It has no end
		And there was no beginning,
           As Bondi, Gold,
	   And I will hold
		Until our hair is thinning!"

	   "Not so!" cried Ryle
	   With rising bile
		And straining at the tether;
	   "_Far galaxies
	   Are, as one sees,
	        More tightly packed together!_"

	   "You make me boil!"
	   Exploded Hoyle,
		His statement rearranging;
           "_New matter's born
	   Each night and morn.
	        The picture is unchanging!_

	   "Come off it, Hoyle!
	   I aim to foil
		You yet" (The fun commences)
	   "And in a while"
	   Continued Ryle,
		"I'll bring you to your senses!"

Contents

     Preface
     Introduction
1    City Speed Limit  				       	       1
2    The Professor's Lecture on Relativity which caused Mr
     Tompkins's dream   				       	       9
3    Mr Tompkins takes a holiday 				       19
4    The Professor's Lecture on Curved Space, Gravity and
     the Universe 						       31
5    The Pulsating Universe 					       44
6    Cosmic Opera 						       55
7    Quantum Billiards   				       	       65
8    Quantum Jungles 					       	       85
9    Maxwell's Demon 					       	       95
10   The Gay Tribe of Electrons 				       112
10½  A Part of the Previous Lecture which Mr Tompkins slept
     through 						       	       128
12   Inside the Nucleus 					       136
13   The Woodcarver 						       149
14   Holes in Nothing   				       	       166
15   Mr Tompkins Tastes a Japanese Meal 			       177
	   a very lucid explanation of "strong interaction"
	   forces, which are caused by mesons jumping back and
	   forth between the particles in contact.  theory due to
	   Hidekei Yukawa, which is the Japanese connection.

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