Understanding Discrete Reversal of Time Direction

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Discussion Overview

The discussion centers on the concept of discrete reversals of the time direction within the context of the Lorentz group O(3,1). Participants explore the meaning of 'discrete' in relation to time reversal, particularly in the framework of physics and transformations.

Discussion Character

  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions the meaning of 'discrete' in the context of time reversal, noting that time can either be reversed or not.
  • Another participant explains that time reversal is considered discrete because it cannot be achieved through a continuous series of transformations starting from the identity.
  • A further contribution mentions that time reversal symmetry corresponds to an anti-unitary representation of the Lorentz group, linking it to quantum mechanics.

Areas of Agreement / Disagreement

Participants generally agree on the interpretation of time reversal as a discrete transformation, but the discussion does not resolve all nuances regarding its implications or connections to other concepts.

Contextual Notes

Some assumptions about the familiarity with quantum mechanics and the Lorentz group are present, which may limit understanding for those less versed in these areas.

Aziza
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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!
 
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Aziza said:
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.
 
##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.
 
Ohh ok yes that makes perfect sense, Thanks!:D
 

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