Let me start by saying that I have always admired Einstein.
He has been one of my idols since I was a boy. However…
In Einstein's book Relativity in the chapter on the
Lorentz Transformation, he gives us these formulas as the transforms:
x' = (x-vt)/sqr(1-(v2-c2))
y' = y
z' = z
t' = t-(v/c2)
∙x .
sqr(1-(v2-c2))
He then says:
If in place of the law of transmission of light we had
taken as our basis the tacit assumptions of the older mechanics as to the
absolute character of times and lengths, then instead of the above we should have
obtained the following equations:
x' = x-vt
y' = y
z' = z
t' = t
This system of equations is often termed the "Galilei
transformation."
It is unlikely that Galileo Galilei (1564-1642) had anything
to do with those. He had no need of any transforms because to him, and up to
Sir Isaac Newton (1642-1727) the whole universe had only one set of coordinates
as far as they were concerned.
On page 115 (the derivation of the Lorentz transforms) he
states "We require to find x' and t' when x and t are given." This makes it
clear that we are solving for x' in the first formula of each set.
Now let's examine the first of the latter set of formulas
with a thought experiment. We are standing beside the train track watching the
train come from our left side as it moves to our right side. When the front of
the train is right in front of us, we start our stop watch. After 10 seconds we
signal to a friend who is running along side the train to mark the spot where
the front of the train is then. We measure it off to be 100 feet from the spot
we were standing. The variable x is the position of the train in the x axis.
Where we were standing was beside the zero point. We call the velocity of the
train when going from left to right positive, and consistently we call positions
on the right to be positive, and left ones to be negative. The train has moved
+100 feet in 10 seconds, so it's velocity is +10 feet per second.
Now let's use the formula to calculate it: x' = x-vt =
0-(10*10) = 0-100 = -100 feet. Suddenly, from the formula, the train has moved
200 feet to the left instantly, surpassing the speed of light!
(humor). It is obvious that the correct formula is x'
= x+vt, which would give the correct result. This is high school level physics.
Is this Einstein's biggest mistake?
Einstein goes on to say on page 33:
"The Galilei transformation can be obtained from the
Lorentz transformation by substituting an infinitely large value for the
velocity of light c in the latter transformation."
Since the latter ones do not contain c, he must have meant
the former ones. That's 2 mistakes on 1 page. I wonder how many others there
are. Let's see if his statement is right otherwise. Substituting our values
with infinity for c we get:
x' = (x-vt)/sqr(1-(v2-c2)) =
(0-100)/sqr(1-(102-∞2))
Since infinity can't be squared (it's already infinite), the
formula can't be solved precisely so let's use a high arbitrary number of 1
trillion + 100 for ∞2. We will ignore the 10^2 which is insignificant. Now we need to take the square root of -1
trillion. Negative numbers have no square roots, so we still can't solve it
(but I bet one of you is going to do it). I can't wait to see your solution.
Let us just say for arguments sake that the square root was -1 million. Now we
divide -100 by -1 million and we get +.0001. Had we used +1 million for the denominator
we would get -.0001. Neither answer is anywhere close to -100 as Einstein
promised.
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Einstein's Biggest Mistake?
Re: Einstein's Biggest Mistake?
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