this is jeff’s job here, but in short, we know the wavelength of ionized hydrogen and other elements, so we measure shifts from the standard values very accurately.

cheers,
t.

Here’s the book I have: http://www.amazon.com/Relativity-Special-General-Albert-Einstein/dp/0517884410

In the back it shows his derivation of the Lorentz Transformation, pretty cool.

That IS pretty interesting, It’s amazing how things change as we figure out new things.

Nick

I VERY WARMLY (hotly) suggest “SPACETIME PHYSICS” by Taylor and Wheeler. The analogy, both formal and fertile (useful in describing reality), between ordinary (circular) trigonometric functions and hyperbolic “trigonometric” functions is easy and every student should know it. But most do not.

In particular a physics student should know it. He would appreciate how the simple trigonometric law of “addition of slope” can be seen to be related to the law of “addition of velocity”. This is discussed in great detail for several pages in SPACETIME PHYSICS because the book is elementary (but not easy). The final sensation is that if one assumes knowledge of hyperbolic functions then the connection between euclidean rotational transformations and psuedo-eucliean space-time (lorentz) trasformations can truely be made in just one or two lines maximum, and the law of addition of velocities is immediate.

Ah the power of mathematics!!! People react to its power in two different ways. Some get excited and breathless when they see how great physics concepts, made at great expense in terms of experimental and cognitive effort, can be expressed elegantly and very succinctly. Others, mainly professional mathematicians and an annoying number of theoretical “physicists”, do not appreciate real Physics because they see the “physics” as trivial.

Nick,
Looking at Einstein’s 1905 paper, it’s interesting that he deliberately takes a complicated approach to deriving the Lorentz transformation. In a footnote he even refers to a short cut, but one which would not have so clearly shown the compatibility between the principle of relativity and the constancy of the velocity of light.
Of course, once he gets the Lorentz transformation, his derivation of the addition of velocities just relies on a neat application of Pythagoras’s theorem. He also points out that it is an example of how Lorentz transformations form part of a group (what we now call the Poincare group, the foundation of quantum field theory) – little did he realise at the time just how significant this group property would become!.
It’s interesting to compare this with his neat derivation of the addition of velocities in his book “The meaning of relativity” written seventeen years later. Once he introduces spatial rotations as a special example of a Lorentz transformation, he derives the addition of velocities in just one line!

By the way as I have a very bad memory I decided to check on the web and indeed the book where I found Mermin’s derivation was NOT written by him!
Here it is
http://www.cambridge.org/uk/popsci/catalogue/0521435323/

By the way as I have a bad memory I decided it best to look on the web. Indeed the book where I found Mermin’ derivation is NOT by Mermin.
Here it is
http://www.cambridge.org/uk/popsci/catalogue/0521435323/

Good stuff! I just got Einstein’s book “Relativity” and now I’m even more excited to read it.

Nick

Isn’t this true only if the speed of light can exceed c as in variable speed of light [VSL].

If MAX(speed of light)=c, then c+v=c, for any magnitude of v.

I did not add anything. I think I even used his notation. I suggested to Tommaso to post it as EVERY physics colleague I asked, and many teach (that is why I asked), did not know it. My students like it very much as they find the reasoning easy to follow and can all pin-point to the role of Einstein’s dictum. The spin-off discussions (Newton’s limit; special cases such as u=c and v=c; … make them interested to know more. Only at this point do I mention briefly Lorentz trasformations as it allows me to recap on Galileo trasformations and the Newton way of adding velocities. I’ve asked the demonstration several times in oral exams because I think it is a healthy excercise to reason out the kinematics from the simple space-time diagram.

I anyone wishes to have the *.ppt file and/or the *.doc files just send me an email (goffredov@yahoo.it)