In Einstein’s book(adsbygoogle = window.adsbygoogle || []).push({}); Relativity – the special and the general Theory(authorized translation by Robert W. Lawson, University of Sheffield) in chapter XI (the Lorentz Transformation), he gives us these formulas as the transforms:

x’ = (x-vt)/sqr(1-(v^2/c^2))

y’ = y

z’ = z

t’ = t-(v/c^2)∙x / sqr(1-(v^2/c^2))

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.”

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 alongside 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 its 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 (the wrong answer).

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 greatest mistake?

The same bad formulas are shown in the appendix I (Simple derivation of the Lorentz Transformations) on page 118.

Any thoughts on this? Could this mistake have infected later math?

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# B Einstein’s Greatest Mistake?

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