philosophy / time-travel.mdon commit [spec] minor clarifications to calculus section of sac notes (065aae3)
   1# Time Travel and Quantum Mechanics
   2
   3## What is time?
   4- time is what clocks measure
   5  - measure time objectively, therefore does not help our subjective definition of time
   6
   7- $t$ - just like another quantitative variable (period of time, not absolute)
   8
   9
  10- fourth dimension
  11
  12- these describe properties of it, not its implications or how it works
  13  - implications are generally determined through intuition
  14
  15
  16- sense of time is inherent to all humans - every human has memory and some idea that time is observable through changes in space
  17
  18  - computers have memory, do they have a concept of time?
  19
  20Therefore, we have:
  21
  22**1. Subjective time**
  23- presumably everyone experiences this notion of time
  24- has the property of lapsing (time approaches $\infty$)
  25
  26**2. Physical time**
  27- represented by $t$
  28- objective
  29- quantitative (period, not absolute)
  30
  31> All paradoxes arise from the fact that time lapses / flows - we are basing time on subjective time, not physical time
  32
  33## Concepts of time in physics
  34
  35### Thermodynamic time arrow
  36- second law of thermodynamics:
  37- total entropy cannot decrease over time (randomness of particles)
  38- Hence, time has a specific direction (approaching infinite entropy)
  39- This can be modelled as $t=e$. If $e$ cannot be subtracted from, $t$ can only go one way.
  40- entropy is an irreversible process
  41- therefore, time travel backwards is impossible
  42
  43### Block time
  44- time is fourth dimension - all dimensions are related
  45- universe exists as a whole, in four dimensions, just like a chair can exist in three dimensions (plus time)
  46- 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
  47- therefore, past and future must also exist as a relation of four values ($x,y,z,t$)
  48
  49
  502. Are the past and future real?
  51By 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).
  52
  533. Do events that occurred in the past / future exist?
  54
  55> What is the physical prompt to change to a different time?
  56
  57## Grandfather paradox
  58
  59- Grandfather is not necessary - could be the suicide paradox
  60- Mathematical status - 1 bit (dead or alive):
  61  - $x=$ existence at 2 yrs, $y=$ existence at 20 yrs
  62  - $0=$ dead, $1=$ alive
  63- $x=1$ (alive - assumed because you must exist in the first instance)
  64
  65
  66**(case 1)** if $x=1$, then $y=1$ (assuming you don't die between) $\therefore x = y$  
  67**(case 2)** if $y=1$, then $x=0$ (because you killed yourself)
  68This is not a contradiction - it simply states that $x=0 \lor 1$ (one *or* zero)
  69
  70**$\therefore$ both situations can exist (superposition) - suggesting multiple universe theory**
  71
  72- Implies a link to quantum mechanics: dead or alive, or between (superposition):
  73- $1 \over 2$ probability of killing grandfather/self (two parallel realities  - Murphy's law)
  74
  75
  76### Many worlds interpretation
  77
  78- different branches of superposition are different universes. Perception jumps between universes.
  79- 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)