Understanding Discrete Reversal of Time Direction

[Aziza]

In my book it says that the Lorentz group O(3,1) includes 'discrete reversals of the time direction'.

What on Earth does this mean?

So I get that time reversal is making time go backward instead of forward, but what is the word 'discrete' doing there?


Thanks in advance!

 

[PeterDonis]

I get that time reversal is making time go backward instead of forward, but what is the word 'discrete' doing there?

Because time is either reversed or it's not; there's no continuous group of transformations that reverse time a little bit, then a little bit more, etc. There's just one single transformation that reverses time.

 

[WannabeNewton]

$t\rightarrow -t$. It's discrete simply because it is not in the connected component of the identity. In other words you cannot reach the time reversal by a continuous series of infinitesimal Lorentz transformations (rotations + boosts) starting from the identity. If you're familiar with QM then time reversal symmetry corresponds to an anti-unitary representation of the Lorentz group.

 

[Aziza]

Ohh ok yes that makes perfect sense, Thanks!:D