Seen, Heard, Said

Axiom’s are a rather interesting thing and it seems that Quinn McGinnis has been rather intrigued with them the last few weeks. Quinn sent me a link to a site that proves that 2+2=4. Here’s what the site basically says:

Peano’s Axioms

1. Zero is a number.
2. If a is a number, the successor of a is a number.
3. zero is not the successor of a number.
4. Two numbers of which the successors are equal are themselves equal.
5. (induction axiom.) If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.

and the definition of addition

Let a, b be numbers, we define (the successor of a) if ;
and if

Existence and definition of 1, 2, 3, and 4

By axioms 1 and 2, since 0 is a number then the succesor of 0 is a number, lets call it 0′
By axiom 3, 0′ is different from 0
so, 0′ is a new number, lets call it 1
by axiom 2 the succesor of 1 is a number, lets call it 1′
by axiom 3, 1′ is different from 0
axiom 4 implies that 1′ is different from 1 (Do you see why?)
so, 1′ is a new number, lets call it 2

Idem 3=2′ and 4=3′ and 1,2,3,4 are different numbers

Theorem: 2+2=4

Since 2 =1′ then by definition 2+2=(2+1)’
Now, 2+1=2’=3 , then 2+2=(2+1)’=3’=4

Q.E.D. (quod erat demonstrandum, which was to be demonstrated)

This all leads to today. Quinn sent out another email purporting to prove the existance of God. The site makes some good points, however, there is one issue I took disagreement with:

#3. Whatever has the possibility of non existence, yet exists, has been caused to exist.

1. Something cannot bring itself into existence since it must exist to bring itself into existence which is illogical.

At first glance, some of you may be screaming Law of Thermodynamics, Andrew! I assure you, there is a way. And thus I sent out the following email:

The proof is slightly wrong. God can only exist if the universe continues to expand and does not contract back on itself. The reason for this lies in the laws of thermodynamics. Currently, matter and anti-matter is created and destroyed randomly throughout the universe. The laws of thermodynamics allows this to happen because the net energy created from this reaction is still zero. There is no cause for the matter and anti-matter to be created, it just is. If the universe eventually contracts back on itself, the net energy is zero and thusly doesn’t need an outside force to have created it originally. However, if the universe is expanding and never contracts back on itself, then the net energy of the universe is a positive number and therefore requires something to have created it, that something being God.

Quinn had some issues with it:

Sereral parts of your email don’t make sense to me.

You said:
“God can only exist if the universe continues to expand and does not contract back on itself.”
This is wrong. God could easily create a universe that expanded and contracted back on itself. Just because you can think of something that doesn’t require God to make it doesn’t mean that God doesn’t exist.

“There is no cause for the matter and anti-matter to be created, it just is.”
Really? How do you defend this?

“If the universe eventually contracts back on itself, the net energy is zero and thusly doesn’t need an outside force to have created it originally.”

This doesn’t seem to follow. I don’t know what energy conservation has to do with things being created or not being created.

Also, you haven’t really addressed the basic claim that the website made. Even if you have a universe that expands and contracts back, there still can’t be an infinite regression of causes! It has to start somewhere with an “uncaused” thing. Do you have an argument against that?

I responded:

1) My mistake, Let me restate that: God can exists if the universe contracts back on itself. God must exists if the universe continues to expand (which it currently is, by the way).

2) From “A Brief History of Time,” pages 105-106, by Stephen Hawking:

“How is it possible that a black hole appears to emit particles when we know that nothing can escape from within its event horizon? The answer quantum theory tells us, is that the particles do not come from within the black hole, but from the ’empty’ space just outside the black hole’s event horizon! We can understand this in the following way: what we think of as ’empty’ space cannot be completely empty because that would mean that all the fields, such as the gravitational and electromagnetic fields, would have to be exactly zero. However, the value of a field and its rate of change with time are like the position and velocity of a particle: the uncertainty principle implies that the more accurately one knows one of these quantities, the less accurately one can know the other. So in empty space the field cannot be fixed at exactly zero, because then it would have both a precise value (zero) and a precise rate of change (also zero). There must be a certain minimum amount of uncertainty, or quantum fluctuations, in the value of the field. One can think of these fluctuations as pairs of particles of light or gravity that appear together at some time, move apart, and then come together again and annihilate each other. These particles are virtual particles like the particles that carry the gravitational force of the sun: unlike real particles, they cannot be observed directly with a particle detector. However, their indirect effects, such as small changes in the energy of electron orbits in atoms, can be measured and agree with the theoretical predictions to a remarkable degree of accuracy. The uncertainty principle also predicts that there will be similar virtual pairs of matter particles, such as electrons or quarks. In this case, however, one member of the pair will be a particle and the other an antiparticle (the antiparticles of light and gravity are the same as the particles).

Because energy cannot be created out of nothing, one of the partners in a particle/antiparticle pair will have positive energy, and the other partner negative energy. The one with negative energy is condemned to be a short-lived virtual particle because real particles always have positive energy in normal situations. It must therefore seek out its partner and annihilate with it. However, a real particle close to a massive body has less energy than if it were far away, because it would take energy to lift it far away against the gravitational attraction of the body. Normally, the energy of the particle is still positive, but the gravitational field inside a black hole is so strong that even a real particle can have negative energy there. It is therefore possible, if a black hole is present, for the virtual particle with negative energy to fall into the black hole and become a real particle or antiparticle. In this case it no longer has to annihilate with its partner. Its forsaken partner may fall into the black hole as well. Or, having positive energy, it might also escape from the vicinity of the black hole as a real particle or antiparticle. To an observer at a distance, it will appear to have been emitted from the black hole. The smaller the black hole, the shorter the distance the particle with negative energy will have to go before it becomes a real particle, and thus the greater the rate of emission, and the apparent temperature, of the black hole.”

3) The point is this: many people are familiar with the axiom that energy (which also includes matter via E=mc^2) cannot be created or destroyed. In reality, this is not entirely true. What is should say is that in net reaction of an event, you must have as much energy as you started with. However, during that reaction, an infinite amount of energy can be created and destroyed. If we were to look at the universe as a single reaction: if the universe were to collapse back in on itself, the net energy would be zero.

4) This ties points 2 and 3 together. If the universe eventually does collapse back on itself, it is possible for the universe to have been a causeless event because the net energy change is still zero.

Jeff Staples chimed in, questioning:

If that proof of God’s existence will convince someone to enter into
a relationship with the personal and ultimate reality, then go ahead
and give it to them. But I have two suggestions. First, God can’t
be proved to exist or to not exist. Second, He doesn’t need you or
me to defend the fact that He is the I AM. God can handle himself.

-Jeff

Quinn responded to both Jeff and myself:

Ferg-
You said:
“If the universe eventually does collapse back on itself, it is possible for the universe to have been a causeless event because the net energy change is still zero.”

I don’t see how that follows.

Jeff-
You said:
“First, God can’t be proved to exist or to not exist.”
Would you please explain the flaw in the cosmology theory, then? I’m not convinced by Ferg’s explanation.

You also said:
“Second, He doesn’t need you or me to defend the fact that He is the I AM.”
Of course. I don’t think I ever implied anything against this notion.

Anyhow, my question still remains. Without an infinite regression of causes, how do you explain the existence of the universe?

Ferg, I know you’re trying to explain your point of view to me, but I’m having trouble putting it all together. Would you summarize it in a straightforward manner?

I will say that I can sometime be confusing. I often skip around in my head and don’t mention that to people I am talking with (or emailing in this case). So I spent the better part of two hours researching and typing up the following response which is currently my offical stance:

For this to work, I’m going to get a little technoblable, but I’m going to try and make it easy to understand. The First Law of Thermodynamics states that “Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another.” (Source: http://www.emc.maricopa.edu/faculty/farabee/BIOBK/BioBookEner1.html).

The first part (“Energy can be changed from one form to another”) is derived from Einstein’s E=MC², where E is energy measured in joules, M is matter measured in kilograms, and C is the speed of light (a constant, hence the C) (Source: http://en.wikipedia.org/wiki/E%3Dmc%B2). The whole point of this first part is to relate energy and matter so that they are indistinguishable.

The second part (“…but it cannot be created or destroyed”) is slightly misleading, especially when you start talking about quantum mechanics. The Heisenberg Uncertainty Principle states that “you cannot possibly know both [location and velocity]…with total precision. Moreover, the more precisely you know one, the less precisely you know the other. And although we have described this for electrons, the ideas directly apply to all constituents of nature.” (Source: Elegant Universe, The. By Brian Greene. Page 114). So when you observe what you believe to be completely empty space, it is not actually empty because that would violate the Uncertainty Principle: “what we think of as “empty” space cannot be completely empty because that would mean that all the fields, such as the gravitational and electromagnetic fields, would have to be exactly zero. However, the value of a field and its rate of change with time are like the position and velocity of a particle: the uncertainty principle implies that the more accurately one knows one of these quantities, the less accurately one can know the other. So in empty space the field cannot be fixed at exactly zero, because then it would have both a precise value (zero) and a precise rate of change (also zero).

There must be a certain minimum amount of uncertainty, or quantum fluctuations, in the value of the field. One can think of these fluctuations as pairs of particles of light or gravity that appear together at some time, move apart, and then come together again and annihilate each other. These particles are virtual particles like the particles that carry the gravitational force of the sun: unlike real particles, they cannot be observed directly with a particle detector. However, their indirect effects, such as small changes in the energy of electron orbits in atoms, can be measured and agree with the theoretical predictions to a remarkable degree of accuracy. The uncertainty principle also predicts that there will be similar virtual pairs of matter particles, such as electrons or quarks. In this case, however, one member of the pair will be a particle and the other an antiparticle (the antiparticles of light and gravity are the same as the particles).” (Source: “A Brief History of Time,” pages 105-106, by Stephen Hawking).

What has just been said here is that, at least on very small scales in our known universe, particles (whether they be matter, electrons, gluons, weak gauge bosons, quarks, etc, etc) can spontaneously and without cause be created, so long as the appropriate anti-particle is created to maintain net zero change in energy. For example, let’s say it take 100 joules of energy to create an electron and it’s anti-particle, the positron. We now owe the universe 100 joules of energy. Because the electron and positron are created with such proximity to each other, they usually instantly annihilate, creating pure energy. 100 joules of pure energy to be precise. I said usually because sometime a particle or its anti-particle will be sucked into a black hole, but that’s a really a different topic. Brian Greene has a great analogy that should make this clearer: “[I]magine that you are completely destitute and suddenly learn that a distant relative has passed on in a far-off land, leaving you a tremendous fortune to claim. The only problem is that you don’t have the money to buy a place ticket to get their. You explain the situation to your friends: if only they will allow you to surmount the barrier between you and your new fortune by temporarily lending you the money for a ticket, you can pay them back handsomely when you return. But no one has the money to lend. you remember, though, that an old friend of yours works for an airline company and you implore him with the same request. Again, he cannot afford to lend you the money but he does offer you a solution. The accounting system of the airline is such that if you wire the ticket payment within 24 hours of arrival at your destination, no one will ever know that it was not paid for prior to departure. In this way, you are able to claim your inheritance.” (Source: “The Elegant Universe,” page 115.) It is this quantum accounting that I am now going to use to explain why God has to exist if the universe fails to collapse.

Assuming the universe doesn’t collapse on itself and continues to expand forever (Note: staying the exact same size is not an option, the universe must either be expanding or collapsing), time will have no end (at least in the way we define time). Because time will be open ended on one side (i.e. is has defined beginning, but no defined end [i.e. infinity]), the amount of energy in the universe must be greater than zero. This does not jive with our previous assertion because matter is was created but will not be destroyed. Only God has the power to do that.

However, if time does collapse back on itself, time will have a defined beginning and end and therefore is in agreement with our assertions about conservation of energy. In this scenario, God is neither confirmed nor denied to exist.

That took forever to write…did any of it make sense?

That is where the conversation has left off for now. I think it’s a really interesting debate and that is why I chose to post it. Feel free to chime in using comments. Any further developments will also be posted in the comments deptartment.