Time Travel and Quantum Mechanics

What is time?

• time is what clocks measure

  • measure time objectively, therefore does not help our subjective definition of time

• $t$ - just like another quantitative variable (period of time, not absolute)

• fourth dimension

• these describe properties of it, not its implications or how it works

  • implications are generally determined through intuition

• sense of time is inherent to all humans - every human has memory and some idea that time is observable through changes in space

  • computers have memory, do they have a concept of time?

Therefore, we have:

1. Subjective time

• presumably everyone experiences this notion of time
• has the property of lapsing (time approaches $\infty$)

2. Physical time

• represented by $t$
• objective
• quantitative (period, not absolute)

All paradoxes arise from the fact that time lapses / flows - we are basing time on subjective time, not physical time

Concepts of time in physics

Thermodynamic time arrow

• second law of thermodynamics:
• total entropy cannot decrease over time (randomness of particles)
• Hence, time has a specific direction (approaching infinite entropy)
• This can be modelled as $t=e$. If $e$ cannot be subtracted from, $t$ can only go one way.
• entropy is an irreversible process
• therefore, time travel backwards is impossible

Block time

• time is fourth dimension - all dimensions are related
• universe exists as a whole, in four dimensions, just like a chair can exist in three dimensions (plus time)
• you cannot isolate one value in one of the three dimensions and define it by itself - it would be ridiculous to say that a point ($x=2,y=1,z=3$) can exist if y and z are not defined
• therefore, past and future must also exist as a relation of four values ($x,y,z,t$)

2. Are the past and future real?
   By using the present as a proxy for the past or future, we can simulate them, effectively nesting times inside times (a simpler idea of a time machine - normal time machines lose the idea of the present).

3. Do events that occurred in the past / future exist?

What is the physical prompt to change to a different time?

Grandfather paradox

• Grandfather is not necessary - could be the suicide paradox
• Mathematical status - 1 bit (dead or alive):
  • $x=$ existence at 2 yrs, $y=$ existence at 20 yrs
  • $0=$ dead, $1=$ alive
• $x=1$ (alive - assumed because you must exist in the first instance)

(case 1) if $x=1$, then $y=1$ (assuming you don’t die between) $\therefore x = y$
(case 2) if $y=1$, then $x=0$ (because you killed yourself)
This is not a contradiction - it simply states that $x=0 \lor 1$ (one or zero)

$\therefore$ both situations can exist (superposition) - suggesting multiple universe theory

• Implies a link to quantum mechanics: dead or alive, or between (superposition):
• $1 \over 2$ probability of killing grandfather/self (two parallel realities - Murphy’s law)

Many worlds interpretation

• different branches of superposition are different universes. Perception jumps between universes.
• time can be defined only by the physical state of things at the time - this is the only way it can be derived. therefore, by changing the physical state, you are creating a new "time (or timeline)