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Proof Eternalism is Correct

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devans99
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Joined: June 17th, 2018, 8:24 pm

Re: Proof Eternalism is Correct

Post by devans99 » November 28th, 2018, 1:35 pm

That was an early draft I posted. Hope below makes more sense!



Eternalism is the belief that past, present and future are equally real. It contrasts to Presentism; the belief that only now exists. In this paper we demonstrate that time has a start and further demonstrate that this implies Eternalism is true. That result would be in agreement with Einstein's special and general relativity.

Outline of proof

- Definitions
- Proof Time had a start
- Proof of Eternalism
- Lemma: Actual infinity does not exits
- Related Propositions

Definitions

We will be discussing infinity, so these two definitions of Aristotle [1] will come in useful:

Potenial Infinity
Characterised by a repeating process, such as repeatedly adding to a number. These processes increases towards infinity without ever actually reaching it.

Actual Infinity
The results of carrying out an iterative process forever. This is what most people think of when they say infinity; a non-finite number or quantity. Examples would be the actual existence of a completed infinite set or a physical property like length, mass taking on an infinite value.

Time
Time is fundamental to the universe. The speed of light speed limit (speed = distance / TIME) is obeyed by every particle in the universe and exists independently of change. To be a normally functioning universe, a speed limit is required. Else it's possible to accelerate objects to infinite velocity and thus straight out of the universe. So time is not emergent; it is fundamental to the universe.

If reality is somehow a simulation, the the arguments in this paper relate to ‘base reality’ time rather than system time.







Proof Time had a start

The counting paradox
- Say you meet an Eternal being in your Eternal universe
- You notice he is counting
- You ask and he says ‘I’ve always been counting’
- What number is he on?

It’s impossible to count to infinity so the being cannot be on that (no matter how many times you add one, you never reach infinity). If the being is on a finite number, then he is not eternal; he started counting a finite time ago.

This paradox highlights the nonsensical nature of anything eternal (in time). Such an entity has no temporal starting point so it’s impossible that it could exist.

The Measure Problem
This is a paradox of eternal time from Cosmology:

- Assume time is eternal.
- If it can happen it will happen.
- An infinite number of times.
- No matter how unlikely it was in the first place!
- So all things happen an infinite number of times.
- So all things are equally likely.
- Reductio ad absurdum.
- Time is not eternal

The solution to the paradox is to assume time is not infinite; it has a start

Proof time has a start

- Time is a series of moments. Take away one moment and the following moments are undefined/cannot exist. For example, take away Monday and the rest of the week does not exist. So there must be a starting moment; an anchor point for the whole time series or none of it exists.

- Imagine Eternity, it has no starting moment, so none of it can exist. Think of the initial starting positions of all the particles in the universe. If that was removed, what is left? Something completely undefined. So eternity is rather like negative infinity; the start is undefined so the whole thing does not exist.

- If time did not have a start then an actual infinity of time has passed so far which is impossible

- Imagine an eternal being; he would have no start in time so could never exist. Being is possible we therefore conclude Eternal is not (imagine if your moment of birth was removed somehow, would you still exist?)

- Intense gravity causes the passage of time to slow so time came to an almost stop at the Big Bang (strong candidate for start of time).

- A moment cannot of occurred infinity long ago, because there is no way for the effects of that moment to get to today (-oo + 1 = -oo), so all moments happened finitely long ago





Proof of Eternalism

Assume only now exists
So before the start of time there was nothing *
But creation ex nihilo / without time is impossible
So more than only now exists **

* If there is more than one time, this proof refers to the first or top level time.
** 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.

Alternative Proof

(top level) Time had a start
Can’t get something from nothing* so Something has always existed
But Something can’t have always existed in time (because time had a start)
Implies Time must have always existed
IE Eternalism

Nothing is no dimensions, mater or energy


Note that Eternalism is in agreement with the Theory of Relativity whereas Presentism is not.




Lemma: Actual Infinity does not Exist

Actual Infinity does not exist

In set theory, actual infinity is defined to exist via an axiom; nowhere in maths is the existence of actual infinity proven. Its non-existence is quite straightforward to prove.
Actual infinity, if it existed, would be a quantity greater than all other quantities, but:

There is no quantity X such that X > all other quantities because X +1 > X

Further, actual infinity does not follow common sense or mathematical rules:

oo + 1 = oo implies
1 = 0

Nothing in the real world can you add to whilst it remains unchanged. This logical absurdity implies infinity is not a mathematical quantity.

Materialistic Argument
- How exactly is Actual Infinity and the materialistic world view comparable?
- For example, can a physical quantity larger than any other possible physical quantity exist?

Geometrical Construction
- It is impossible to construct a line segment with the property that it is longer than all other line segments

Is there an Actual Infinity of points on a Line Segment?

- Consider the points on a line segment length 1.
- Does the interval contain an actual infinity of points?
- No.
- Points have length zero
- So the length of the interval 1 divided by the length of a point 0 equals UNDEFINED.

The real number line

The situation is similar when we examine the real numbers:

- Consider the Numbers on the real number line.
- For example between 0 and 1.
- Does the interval contain an actual infinity of numbers?
- No.
- Numbers have length zero
- they are just logical labels on a line
- So the length of the interval 1 divided by the length of a number 0 equals UNDEFINED.


The non-existence of actual infinity implies negative actual infinity does not exist. Negative actual infinity has the same structure as past eternal (in time):

{ …, 2015, 2016, 2017, 2018 }
{ …, -4, -3, -2, -1 }

IE past eternal (in time) is impossible.






Related Propositions

Time Has An End
If Eternalism and Finitism are both true, then time must have an end.

The Universe is Finite
The universe is expanding so it cannot be infinite in space else there would be nowhere to expand to. Infinity is the problem: it's larger than any possible thing. Yet we require it to expand; implying it was not larger than any possible thing
The universe started with the Big Bang 14 Billion years ago and has been expanding since then; it must have a finite radius
Time has an end, so with the speed of light limit, the universe can only ever reach a finite size.
The 2nd Law of Thermodynamics says if the universe has been around for ever then it should be in thermodynamic equilibrium by now. But the universe is not in thermodynamic equilibrium. So time must of had a start. Or to put it another way: If time did not have a start, and infinite amount of time has past, so we must have reached the big freeze. But we have not reached the big freeze, so a finite amount of time has past since the beginning of the universe, so time had a start.

Time is Circular

There is only one place in the universe to get all the matter and energy for the Big Bang; the Big Crunch has it in precisely the right quantity. IE time is probably circular (with a single set of time co-ordinates). This leads to a very simple model of the universe:

Everything has existed always (timelessly)
Everything is finite in time and space
Start of time is the Big Bang
End of time is the big crunch
Time is probably circular

We note that the expansion rate of the universe has slowed in the past (the end of cosmic inflation) and also that the universe is still very young; so the expansion of the universe could turn into contraction at a later time.

The state of the universe at the Big Bang and Big Crunch should be identical with all matter/energy packed into a single discrete space-time cell.

We also note that energy is conserved and there is nowhere for the energy to go at the end of time apart from back to the start of time.

If the time is not circular, it leaves a puzzle as to where all the matter and energy goes at the end of time - it should be conserved in this universe.

If time is circular and finite then it implies Eternalism. The start/end point of time is somewhat arbitrary but the big bang/big crunch seem most appropriate.

That every moment of time requires a preceding moment also suggests time is circular.
Space and Time are Discrete

Is it reasonable to regard the position of particles as information about the volume of space containing the particles? If yes, then there seems to be a simple argument for space being discrete:

- Assume space is continuous
- Implies particles have infinite positional precision. We might not be able to measure with infinite precision; but the underlying system is continuous so possesses infinite precision
- So there is an infinite amount of information in a spacial volume of 1 cubic unit
- And there is also an infinite amount of information in a spacial volume of 10000 cubic units
- Both infinities are the same kind and have the same cardinality
- But this is a logical contradiction, there must be more information in the larger volume.
- So there must be a false assumption in the argument; space must be discrete

A similar argument applies for time.

Paradoxes Solved
A paradox is indicative of an underlying logic error. In all the following cases, the logic error is the assumption that Actual Infinity occurs:

- Galileo's paradox is solved: There are less squares than numbers because not all numbers are squares. Yet each number has a square so the number of numbers and squares must be the same. He is trying to compare two actually infinite sets, IE comparing two undefined things. A set definition is not complete until all its members are iterated.
- Hilbert’s infinite hotel paradox is solved; such a hotel cannot exist.
- Cantor's Paradox: ‘The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.’ The set of all sets is an ACTUAL INFINITY so not a completely described set. You cannot soundly reason with it. Leads to the paradox.
- Zeno’s paradoxes are solved. Time and space are discrete (separate proof)


The Anthropic principle
The Weak Anthropic explains the universe must be compatible with life for us to be here. It does not explain why the universe is compatible with life
The Strong Anthropic explains that the existence of multiple universes with different properties account for our existence. But other universes are statistically likely to be like this one (Life supporting) so the SAP does not explain why the multiverse is fined-tuned for life.


Quantum Fluctuations and Infinite Time

Could a Quantum Fluctuation have occurred infinity long ago?
No because there is no way for the effects of the Quantum Fluctuation to get to today (-oo + 1 = -oo)
IE There is no way to get from -oo to today, thats the definition of infinity
So all Quantum Fluctuations occurred finitely long ago.
So there must be a finite total number of Quantum Fluctuations
So ‘if it can happen, it will happen’ does not apply
So Quantum Fluctuations did not cause the Big Bang

Same argument for random particle collisions.



Summary

The universe is:

- Finite in Space and Time
- Eternal outside of time
- Probably circular in the time dimension

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