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

 

[sardar]

I can explain the concept of discrete reversal of time direction in the context of the Lorentz group O(3,1). This group is a mathematical framework that describes the symmetries of space and time in special relativity. It includes transformations that preserve the laws of physics, such as rotations and boosts, but it also includes discrete transformations, which are changes that occur in distinct steps rather than continuously.

In this case, the discrete reversal of time direction refers to a specific transformation in the Lorentz group that changes the direction of time in a discrete manner. This means that instead of smoothly transitioning from one moment to the next, time would jump in distinct steps in the opposite direction. This concept is important in certain areas of physics, such as particle physics, where the behavior of particles can be affected by the direction of time.

The term "discrete" in this context simply means that the reversal of time direction occurs in specific and distinct steps, rather than continuously. This is in contrast to a continuous reversal, where time would smoothly and continuously flow in the opposite direction.

Overall, the inclusion of discrete reversals of time direction in the Lorentz group highlights the complex and multifaceted nature of space and time in modern physics. It also demonstrates the importance of considering all possible transformations in our understanding of the laws of the universe.