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-# 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)

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-  </head>
-  <body class='markdown-preview'><h1>Time Travel and Quantum Mechanics</h1>
-<h2>What is time?</h2>
-<ul>
-<li>
-<p>time is what clocks measure</p>
-<ul>
-<li>measure time objectively, therefore does not help our subjective definition of time</li>
-</ul>
-</li>
-<li>
-<p><span class="math"><script type="math/tex">t</script></span> - just like another quantitative variable (period of time, not absolute)</p>
-</li>
-</ul>
-<ul>
-<li>
-<p>fourth dimension</p>
-</li>
-<li>
-<p>these describe properties of it, not its implications or how it works</p>
-<ul>
-<li>implications are generally determined through intuition</li>
-</ul>
-</li>
-</ul>
-<ul>
-<li>
-<p>sense of time is inherent to all humans - every human has memory and some idea that time is observable through changes in space</p>
-<ul>
-<li>computers have memory, do they have a concept of time?</li>
-</ul>
-</li>
-</ul>
-<p>Therefore, we have:</p>
-<p><strong>1. Subjective time</strong></p>
-<ul>
-<li>presumably everyone experiences this notion of time</li>
-<li>has the property of lapsing (time approaches <span class="math"><script type="math/tex">\infty</script></span>)</li>
-</ul>
-<p><strong>2. Physical time</strong></p>
-<ul>
-<li>represented by <span class="math"><script type="math/tex">t</script></span></li>
-<li>objective</li>
-<li>quantitative (period, not absolute)</li>
-</ul>
-<blockquote>
-<p>All paradoxes arise from the fact that time lapses / flows - we are basing time on subjective time, not physical time</p>
-</blockquote>
-<h2>Concepts of time in physics</h2>
-<h3>Thermodynamic time arrow</h3>
-<ul>
-<li>second law of thermodynamics:</li>
-<li>total entropy cannot decrease over time (randomness of particles)</li>
-<li>Hence, time has a specific direction (approaching infinite entropy)</li>
-<li>This can be modelled as <span class="math"><script type="math/tex">t=e</script></span>. If <span class="math"><script type="math/tex">e</script></span> cannot be subtracted from, <span class="math"><script type="math/tex">t</script></span> can only go one way.</li>
-<li>entropy is an irreversible process</li>
-<li>therefore, time travel backwards is impossible</li>
-</ul>
-<h3>Block time</h3>
-<ul>
-<li>time is fourth dimension - all dimensions are related</li>
-<li>universe exists as a whole, in four dimensions, just like a chair can exist in three dimensions (plus time)</li>
-<li>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 (<span class="math"><script type="math/tex">x=2,y=1,z=3</script></span>) can exist if y and z are not defined</li>
-<li>therefore, past and future must also exist as a relation of four values (<span class="math"><script type="math/tex">x,y,z,t</script></span>)</li>
-</ul>
-<ol start="2">
-<li>
-<p>Are the past and future real?<br>
-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).</p>
-</li>
-<li>
-<p>Do events that occurred in the past / future exist?</p>
-</li>
-</ol>
-<blockquote>
-<p>What is the physical prompt to change to a different time?</p>
-</blockquote>
-<h2>Grandfather paradox</h2>
-<ul>
-<li>Grandfather is not necessary - could be the suicide paradox</li>
-<li>Mathematical status - 1 bit (dead or alive):
-<ul>
-<li><span class="math"><script type="math/tex">x=</script></span> existence at 2 yrs, <span class="math"><script type="math/tex">y=</script></span> existence at 20 yrs</li>
-<li><span class="math"><script type="math/tex">0=</script></span> dead, <span class="math"><script type="math/tex">1=</script></span> alive</li>
-</ul>
-</li>
-<li><span class="math"><script type="math/tex">x=1</script></span> (alive - assumed because you must exist in the first instance)</li>
-</ul>
-<p><strong>(case 1)</strong> if <span class="math"><script type="math/tex">x=1</script></span>, then <span class="math"><script type="math/tex">y=1</script></span> (assuming you don’t die between) <span class="math"><script type="math/tex">\therefore x = y</script></span><br>
-<strong>(case 2)</strong> if <span class="math"><script type="math/tex">y=1</script></span>, then <span class="math"><script type="math/tex">x=0</script></span> (because you killed yourself)<br>
-This is not a contradiction - it simply states that <span class="math"><script type="math/tex">x=0 \lor 1</script></span> (one <em>or</em> zero)</p>
-<p><strong><span class="math"><script type="math/tex">\therefore</script></span> both situations can exist (superposition) - suggesting multiple universe theory</strong></p>
-<ul>
-<li>Implies a link to quantum mechanics: dead or alive, or between (superposition):</li>
-<li><span class="math"><script type="math/tex">1 \over 2</script></span> probability of killing grandfather/self (two parallel realities  - Murphy’s law)</li>
-</ul>
-<h3>Many worlds interpretation</h3>
-<ul>
-<li>different branches of superposition are different universes. Perception jumps between universes.</li>
-<li>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 &quot;time (or timeline)</li>
-</ul></body>
-</html>

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+# 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)