Question: I am developing a new derivation of the [Lorentz transformation](http://en.wikipedia.org/wiki/Lorentz_transformation) which I think and hope is more attractive to students than those I have seen in currently available texts. I am carefully defining and discussing the important concepts of homogeneity and isotropy of space.

My question is this: am I justified in assuming that a transformation between inertial reference frames cannot reverse handedness? I understand that parity is not conserved in all particle interactions, but my question concerns two relatively moving observers. Can one of them distinguish that the other has adopted the oppositely handed coordinate frame? References would be appreciated.

Answer: 
There is no such mechanism. The probability for a photon to pass through a polarizer at an angle $\theta$ is $\cos^2(\theta)$, regardless of what has happened before, and regardless of how many photons "at once" try to pass through it. As [Bell's theorem](http://en.wikipedia.org/wiki/Bell%27s_theorem) tells us, the quantum world is really random (or non-local).
If that happened, we would be able to detect it by looking at correlations between successive photons' "decisions."

That is, suppose you represent each pair of consecutive photons (1 and 2, 2 and 3, 3 and 4, etc.) with $+1$ if they both made the same "decision" or $-1$ if one went through the polarizer and the other didn't. Take the average of these numbers for all pairs and call it $C$. If a run of photons making the same decision changed the probability for the following photons, $C$ would be greater than zero. In reality, it comes out to zero, meaning that each photon doesn't change its behavior depending on what the one before it did. So we have clear experimental evidence that this modification of probabilities doesn't happen.