Thanks for all the feedback... I've decided to take your advise and try and get a paper published! So here is an exclusive preview!

Infinite Time
----------------

Date: March 2019

Abstract
-----------

With infinite time, we can divide the possible models for the origin universe into deterministic ('Can’t get something from nothing’) and non-deterministic ('Can get something from nothing’). We argue that both possible models lead to contradictions so therefore time must have a start.

Motivation
--------------

There are problems with prime mover / cosmological arguments:

- In the quantum era, cause and effect are under question [1]. Cosmological arguments rely heavily on cause and effect.
- The prime mover argument is inconsistent in that it uses cause and effect to trace back all motion to a single unmoved mover but then says that the unmoved mover is beyond cause and effect.

So there is a need for a cosmological argument that does not rely on cause and effect as an axiom.

Method
----------

With infinite time, we can break down the possible models of the origin of the universe into two:

1. Matter/energy is created - ‘Can get something from nothing’
2. Matter/energy has always existed - ‘Can’t get something from nothing’

If we can show that both models are impossible, we can conclude that time has a start.

Model 1 - 'Can get something from nothing' and 'Time is infinite'
-------------------------------------------------------------------------------------

If matter/energy is naturally created and time is infinite, we should have reached infinite matter/energy density by now which is clearly not the case. Notes:

1. The universe is expanding, but it cannot have been expanding forever because if we trace back in time, we would find a point in time when it was not expanding; at best the universe must be oscillating, so infinite matter density would still be reached.
2. If creation events are naturally occurring and time is infinite, we would expect an infinite number of Big Bangs. There is evidence of only one Big Bang.
3. If matter creation is not natural, that implies a creator. But such a creator must be outside time as discussed in footnote 1 below, so time would still have a start.

Model 2 - 'Can’t get something from nothing' and 'Time is infinite'
-------------------------------------------------------------------------------------

This is the model of matter/energy always existing (never created). Infinite existence within time, is it possible? Consider a particle or an entity that has existed forever:

1. In order for something to exist, it must start existing. But there is no time from which the particle/entity could start existing.

2. Certain innate attributes are permanent like eye colour for a being or mass for a particle. For an infinite particle/entity, there is no time at which these permanent attributes could have been established.

3. An infinite entity would have a memory. Everything it remembers would have happened a finite time ago. But some things are infinitely memorable (first sex etc…). Remembering the first of something would contradict its status as an infinite being - it would remember that it first had sex X years ago - meaning it must of had a finite life span after all.

4. The particle/entity has always experienced events (eg particle collisions). No matter how far we go back in time, the particle/entity experienced events. So it must have experienced some events greater than any number of years ago. Which is a contradiction - can’t be a number* and greater than any number at the same time.

By these considerations, infinite existence seems untenable.

*(Infinity is a concept not a number, proof: Infinity, if a number, would be a number X which is greater than all other numbers. But X+1>X).

Summary
------------

We have argued that both the following are impossible:

- ‘Infinite time’ and ‘can’t get something from nothing’
- ‘Infinite time’ and ‘can get something from nothing’

So the possibility space is exhausted and time must be finite.

Footnote 1: God
----------------------

This is an argument that if God exists, then time must have a start:

1. An eternal in time (presentist) God exists in a universe where time has no start.
2. Such a God has no start in time; no coming into being; so cannot logically exist
3. Or if the God had a start point in time, there would be an empty stretch of time before him and nothing to cause his existence, which is also impossible
4. So God must be timeless
5. Implying time has a start

Footnote 2: Eternalism
------------------------------

Eternalism is the opposite view of presentism. It is the belief that past, present and future are all equally real. A proof via contradiction that Eternalism is true:

1. Assume only now exists (presentism)
2. So before the start of time there was nothing *
3. But creation ex nihilo / without time is impossible
4. So more than only now exists **

* If there is more than one time, this proof refers to the first or top level time (base reality).
** We know now exists and more than now exists. So at least one moment other than now must exist. But all moments are identical so they all must exist.

References
---------------

[1] Procopio, L. M. et al. Nature Commun. 6, 7913 (2015).