OF MOVING BODIES
By A. Einstein
June 30, 1905
In his magnum opus, “On the Electrodynamics of Moving Bodies”, Einstein endeavored to reconcile Newton’s Mechanics with Electrodynamics. He got more than he bargained for.
His fundamental postulate is:
…[L]ight is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.
Comment:
This postulate has now been on the books for 104 years. It has yet to be verified by observation or experiment. No paper on this subject that I have seen measures velocities. The reports deal with interference and resonance and the results have been shown to be compatible with Einstein’s postulate. They are also compatible with the Ritz theory.
He starts with a “ Definition of Simultaneity”:
We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. I
comment.
“Time” is not a collection of instants; nor can I agree that:
all our judgments in which time plays a part are always judgments of simultaneous events.
This argument dates back to Aristotle. Time is a continuum. The criterion for a continuum is that the partitions have shared boundaries. “Now” is not an interval but the shared boundary between past and future, and you can not define time as a sequence of “Nows”
The {argument} is that already given above, to the effect that the flying arrow is at rest, which result follows from the assumption that time is composed of moments: if this assumption is not granted, the conclusion will not follow. (Aristotle, discussing Zeno’s “Arrow Paradox”)
By analogy: Points are the shared boundaries of line partitions but you cannot create a line by a sequence of points. Two points cannot be adjacent.
Next he deals with “The Relativity of Lengths and Times”:
The following reflexions are based on the principle of relativity and on the principle of the constancy of the velocity of light. These two principles we define as follows:--
1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.
: Comment
True, the laws are the same but the picture of the events may depend on the choice of reference. Following is a relativistic description of a hit and run: “I was sitting peacefully at the wheel of my car, when a pedestrian approached me at high speed, hit my car and continued in under it.”
2. Any ray of light moves in the ``stationary'' system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.
He concludes that a moving body is shortened along the axis of the velocity :
l’ = l √(1 - v2/c2)A rigid body which, measured in a state of rest, has the form of a sphere, therefore has in a state of motion--viewed from the stationary system--the form of an ellipsoid of revolution with the axes
Thus, whereas the Y and Z dimensions of the sphere (and therefore of every rigid body of no matter what form) do not appear modified by the motion, the X dimension appears shortened in the ratio sqrt{1-v2/c2}, i.e. the greater the value of v, the greater the shortening. For v=c all moving objects--viewed from the ``stationary'' system--shrivel up into plane figures.
And on the moving body time is dilated:
comment
“I can’t believe that” said Alice.
“Can’t you?” the Queen said in a pitying tone.
“Try again: draw a long breath, and shut your eyes.
Alice laughed. “There’s no use trying,” she said: “one can’t believe impossible things”
“I daresay you haven’t had much practice,” said the Queen.
“When I was your age, I always did it for half an hour a day.
Why, sometimes I have believed as much as six impossible things before breakfast .”
“Can’t you?” the Queen said in a pitying tone.
“Try again: draw a long breath, and shut your eyes.
Alice laughed. “There’s no use trying,” she said: “one can’t believe impossible things”
“I daresay you haven’t had much practice,” said the Queen.
“When I was your age, I always did it for half an hour a day.
Why, sometimes I have believed as much as six impossible things before breakfast .”
It is not clear to me whether he considers the shortening of the rods and the expansion of time as real or perceived. He is not consistent. Either way, it leads to contradictions that are not easily resolved.
On balance, I believe he considers the results as real, as when he describes the shape of the electron changing from a sphere to an ellipsoid being flattened in the direction of the motion, even to the shape of a disc when moving at the “speed of light”.
Textbooks do not equivocate. The contraction and the time dilation are real. Even Feynman uses the muon example as proof of the time dilation.
I might be convinced that rods shorten when they move. But, given the relativity principle (it is irrelevant which system we consider “at rest”), the rod should also shorten when I move. That is harder to accept,
Also, since there is no absolute, only relative motion, an observer riding on the rod would declare that it is the time in the “stationary” system that is dilated.
The Ritz hypothesis is free of these paradoxes. The muon paradox, e.g. disappears when you remove the speed limit.
I shall repeat Einstein’s rod experiment, analyzed in accordance with the Ritz hypothesis
Premises:
Photons (electromagnetic quanta), are emitted with velocity ‘c’ relative to the source, regardless of their energy content and the motion of the source. In an empty space their speed and content remain constant “forever” .
Electromagnetic velocity vectors abide by standard rules of vector calculus.
Consider two Cartesian reference systems; their respective axes are parallel; one system has its origin located somewhere on the y-axis of the other. Both systems are originally at rest.
Name them for convenience system ‘p’ and ‘q’.
A rigid rod is embedded in the x-axis of system ‘p’, its length ‘l’ given by the distance between two markers on the axis.
A light source is located at the end close to the origin (a), of the rod, a mirror at the far end (b). A photon is emitted along the length (ab) of the rod, reflected by the mirror and returned. Imagine a stop watch able to record the elapsed time (t) between the two events at ‘a’.
The speed of light would be c = t/2ab. (We find that our ‘c’ is Maxwell’s constant.)
Now let the rod move with speed positive ‘v’, staying in the
x-axis, and repeat the experiment.
According to Ritz, the photon should now move with speed
c+v. At time ‘t/2’ it has moved a distance (t /2)(c+v). overshooting the length of the rod . But the rod is rigid, the mirror has moved along with it. On the return trip the speed of the photon is (c-v). At time ‘t/2’ it has moved the distance (t /2)(c-v)., where it is met by the source, The total time elapsed, between the two events at ‘a’, is still ‘t’, The transit time between front and back is not affected by the motion of the rod.
This result will be the same if he rod is moved out of the axis and allowed to roam free but with a constant, linear velocity. Vector notation would result in different values for vector c+v in each reference system but all inertial systems, regardless of relative speed and orientation would record the same transit time. In this sense the “speed of light” is constant but not in the sense that all systems would operate with the same absolute numbers
Contrast this with Einstein’s results:
The moving rod running parallel to the x-axis will be shortened to a length l’
l’ = l √(1 - v2/c2)
Let system ‘q’ now move in uniform translation relative to system ‘p’, with speed ‘v’ in the opposite direction of the motion of the rod. In system ‘q’. The recorded length of the rod l’’ is l’’ = l √(1 - 4v2/c2)
If the shortening is real, who is right?
The issue, however, is not whether or not the relativity theories are correct. The question is: are they necessary?
No comments:
Post a Comment