In the beginning, there was order, a very hot singularity, but as time progressed the universe expanded and cooled--and became more disorderly. Scientists predict a "big freeze." It's all due to entropy. As you read this blog, entropy continues. Why? That's what we will explore below. First, let's define the variables we will use:
We begin with the partition function, which has the Boltzmann factor, an exponent with a thermodynamic beta power over the base e:
If we want to determine the probabilities of the energies in a system, we make sure the probabilities add up to 1, so we normalize the partition function by dividing it by itself (Z):
However, if we want to model the universe's evolution, we need to make a slight change to the partition function. Instead of using the thermodynamic beta, we use its reciprocal. We also change the i index to a time (t) index:
Also, we want the universe's total energy to be conserved. We know dark energy is increasing and radiation energy is decreasing, so we put together an energy-conservation equation:
At equation 5, notice how an increase in the universe's volume (V) reduces the radiation energy (Er) but increases the dark energy (pV). Multiply the two energies, add a little dark and baryonic matter, and take the square root and we get a constant energy (E).
We define temperature as follows:
As volume (V) increases, the universe's temperature decreases. Equation 7 below gives us the probability of the temperature at a given time t:
A high temperature has a low probability. A low temperature has a high probability. So there is a high probability the universe's temperature will continue to decrease, and a low probability the temperature will increase. Thus, an expanding universe has a higher probability.
Now, let's take a look at entropy. We define it as follows:
We see that entropy increases as temperature decreases--so it has the same probability as temperature:
So why does entropy happen? Greater entropy has a higher probability than lower entropy. We can also say that reverse entropy is possible but less probable. A good example is the one Tyson discussed in the above video. There are pockets of order caused by star energy, so life is possible.
Was the universe once a singularity? If so, did it have infinite gravity? What forces overcame infinite gravity so our universe could expand to its current size? We can get some answers from Einstein's field equations.
Equation 1 below is the typical textbook rendition of the field equations. At equation 2, on the left side, I changed a plus sign to a minus sign. The third term contains the cosmological constant and shall represent spacetime expansion which is the opposite of gravity, so a minus sign is placed in front of it. We shall treat gravity as positive and expansion as negative.
Normally the first two terms on left side are huge compared to the third term, so the left side of the equation has a positive value. Albeit, something surprising happens if we reduce the universe's radius (r) and hold all other values constant. To make this more obvious, let's change up the variables a bit:
We now reduce the radius to zero:
Equation 13 above shows we derive infinite negative pressure or expansion pressure--and no gravity to hold it back! How is that possible? Well, if we start with the assumption that there was infinite gravity, we are stuck trying to find a force that overcame it. On the other hand, if there was infinite outward pressure and no gravity, it's pretty obvious why the universe grew to its present size.
Gravity must have emerged from the rapid expansion that resulted from so much pressure. To have gravity, there needs to be more than just a point of spacetime. The first two terms of the field equations show that there must be a difference of spacetime curvature between two points in space. In other words, there needs to be more than one reference frame. If the universe was just a single point, there was only one reference frame. Because they represent the same point of spacetime, the first term has a value of infinity, the second term also has a value of infinity. Infinity - infinity = zero spacetime curvature. As soon as there was some distance between, say, point A and point B, gravity emerged.
But then the question becomes, "What caused the infinite pressure at a single point?" The answer is nothing. If the infinite pressure was the beginning, nothing happened before it; there was no time or space. A "cause" is an event, and an event is a function of time and space. So, in the beginning there was infinite outward pressure from a single point ...
Is time eternal? Or is it finite? If time is eternal, then an infinite amount of time has passed. Thus, there will be no future. If there is a future, then there is more time left. Thus, an infinite amount of time has not passed. Time is then finite; it had a beginning.
So how did time begin? For that matter, how did the universe begin? Where did energy, matter and space come from? Did something come from nothing? If we decide that nothing caused something, what does that mean? It could mean that time, space, etc. arose from the great void and black abyss of nothingness, or it could mean that these things always existed--and were, therefore, caused by nothing; i.e., had no cause.
Is your head spinning yet?
Let's assume, for starters, that time had a beginning, where time (t) equaled zero. The equation below reveals something interesting. To have zero time requires infinite energy:
Unfortunately our universe does not have infinite energy. Furthermore, it's a non-sequitur that there would be any energy if there was no time. Energy can't exist for any period of time without time.
There's also Heisenberg's Uncertainty Principle to consider.
As you can see, if time was ever zero, the Uncertainty Principle was violated. Without time, there was clearly no momentum or motion. Today we have momentum, so momentum was not always conserved. If nothing existed (if and when there was no time) then the current energy and mass were not always conserved either. Then again, why would any laws of physics exist in the "great nothing abyss"?
If time was at zero the challenge before us is to figure out how everything emerged out of nothing. If we start with nothing, the concept of "cause and effect" is useless. We're back to the nothing-caused-something paradox discussed above.
If we start with something, "cause and effect" remains intact, but if we regress far enough into the past, we find nothing again--or we have the infinite-time paradox (also discussed above).
We must also consider relativity. Photons, for example, experience zero time, so zero time is possible if there is another reference frame where time progresses. The equations below show that time (t') can be zero as long as time (t) is greater than zero. The syntax t'/t means time (t') per time (t)--e.g. zero time (t') lasted for a period of time (t) seconds.
In the beginning there was no time for a period of zero seconds. In other words, a state of no time can't exist without time. Yet there was a beginning? A big bang? What caused it? Well, nothing. If something caused it, then we are not at the beginning. We need to move back in time another step or more.
There are several theorists who have proposed various models that allegedly explain how time, space and everything else emerged. But their models consist of shapes, objects, dimensions and other devices that are all functions of time and space. Their reasoning is circular. A geometric object can't cause time or space, since the geometric object requires time and space (and the imagination of the physicist who created it) to exist.
What if time is both eternal and finite? Relativity suggests this could be the case. We know that as the universe expands, its energy density decreases and its time rate increases. If we reverse the process, go back in time, the rate of time would decrease. It would slow to a crawl as we get closer and closer to the beginning.
Imagine you're wearing a watch that gives the time (t') illustrated above. If you start at the beginning and wait approximately 13.8 billion years, you experience the entire span of time. For you, the total time is finite.
Now imagine you're wearing a watch that gives the time (t). Recall the concept of the limit you find in elementary calculus texts. Imagine taking a string and cutting it in half, then cutting one of the halves in half. Repeat this process an infinite number of times. You find you get closer and closer to a zero length, but you never reach it.
Time (t) is an eternity, since a full 6.9 billion years passes for every fraction of that time (t')--and there are an infinite number of those fractions of (t').
So here's the scoop: Whether time is finite or eternal depends on which time you are looking at. Historical time (t') gives us a finite amount of time. But if we use current time (t), the universe's beginning was an infinite number of years ago. We can say that momentum and energy have always been conserved. We can say Heisenberg's Uncertainty Principle is eternal. We can say these things because the beginning of time is a limit that can never be reached. Yet, we have a future because time (t') is finite. So go ahead and eat the cake because we can have it too.
So what about space? Why did space expand? Well, I think it had no choice:
You see, space (x) is light speed (c) times time (t). If time grows, so must space. The first equation above shows what would happen if this were not the case. If time (t) grew and space (x) did not, energy would not be conserved and light speed would be less than c.
According to Phys.org "[t]he universe may have existed forever, according to a new model that applies quantum correction terms to complement Einstein's theory of general relativity."
(Click here to read the article by phys.org.)
The universe-existed-forever hypothesis has been thoroughly debunked. I am amazed someone dusted it off and is trying to resurrect it. If the universe existed forever, then anything that is probable has happened already, since an infinite amount of time has passed, but wait! Infinity is not a finite number and it is improper to treat it as such. By its very nature, infinity never ends, so infinite time cannot pass, and the universe has not existed forever.
Even if we were to entertain the notion that the past could somehow stretch back to infinity, then it took an infinite amount of time to get to this moment, but infinity never ends, so this moment isn't here yet. But wait! It is here--so much for the universe-existed-forever hypothesis.
Here is another amusing gem from the article: "These terms keep the universe at a finite size, and therefore give it an infinite age. " Uh oh! I guess there's no Hubble constant or red shift. But wait! There is. The evidence shows the universe is expanding. The "terms" don't trump the evidence.
"Anti-matter looks like matter going backwards in time," is a quote I've been hearing lately. Here's a question that popped into my head: What does matter going back in time look like? The typical response is it looks like a rewinding video. However, if matter truly goes back in time it would simply vanish or would exist in the past, not the present or future. It would be unobservable. All we can see is it going in the opposite direction in forward time.
Case and point: positrons have been experimentally trapped for as long as 16 minutes. How is that possible if they go back in time? To exist for 16 minutes, they have to go forward in time for 16 minutes. If you ask me, anti-matter looks like matter with an opposite charge--FULL STOP.
Anti-time does not take you to the past, but rather, it makes the past possible. If there was no anti-time there would be nothing to cancel the current moment in time. The moments would pile up. You would not only be living in the present moment, but all your past moments as well. All your memories would be all too real. Hopefully, for your sake, they are good memories.
To demonstrate how anti-time works, let's start with a time-moment represented by an arrow:
The plus sign indicates that it is a positive, forward time-moment. The time-line arrow to the right is how we normally think of time: just a straight line going up in this instance. Now let's add a second time-moment and see what happens:
The first time-moment is canceled by an anti-time-moment (arrow pointing down). That leaves us with the present moment. We get a similar result when another time-moment is added:
But why isn't there an anti-time arrow to cancel the current time-moment? Well, at the beginning of time, there was no past, so time could only go forward, but once it went forward a little, there was some room to go back and still room to go forward--so we get a forward arrow followed by a backward arrow and another forward arrow, etc. As a result, we get time that has a forward bias.
This is a pretty bizarre theory! Can it be tested? Sure. Ask yourself, "Is history history or is it still happening?" If history is history, obviously something is cancelling those time-moments that would otherwise pile up. In mathematics we use a minus sign to cancel a plus sign, so it stands to reason that -time cancels +time leaving us only with the present.
Around the time of the Big Bang there was, according to one theory, unequal amounts of matter and anti-matter. When matter met anti-matter, they annihilated each other, albeit a little bit of matter was left over--that matter is the matter of our universe. Below is a Feynman diagram illustrating the process of matter-anti-matter creation and destruction.
According the above diagram, a particle (+A) and an anti-particle (-A) destroy each other and produce a boson (B). The boson then goes on to produce another +A/-A pair. This is all done in time (+t) and minus time (-t). (Anti-particles allegedly have anti-time.)
To my knowledge, the above theory has yet to be experimentally verified. It would be great if some scientist could show that a photon, for example, could produce an electron without the positron. That would surely establish why our universe is predominately matter.
The next best thing is to demonstrate that an anti-particle always comes with a particle, but in spite this, a universe could still end up with mostly matter or anti-matter. That is what we are going to demonstrate below.
(Note: What we call matter could very well be anti-matter. However, we are biased and like to think positive--so we label what we have "matter" and its opposite "anti-matter.")
Let's kick things off with a diagram of two electrically charged plates. Let's pretend the positively charged plate is matter and the negatively charged plate is anti-matter. The arrows represent the field lines. Let's also assume the plates are identical in every way except for the charge--this will be analogous to equal amounts of matter and anti-matter.
The arrows originating from the positive plate point away from the source. One arrow goes up and another goes down and through the negative plate:
The arrows originating from the negative plate behave in the opposite fashion:
Now let's add the arrows. Arrows pointing in opposite directions shall cancel each other. Arrows pointing in the same direction shall enhance each other.
Well would you look at that! The arrows didn't cancel each other out completely. We end up with two left over. So it is possible to start with equal amounts of opposite charge, put them together and not end up with zero. However, what if we had a second pair of plates that are reversed?
As you can see the arrows left over are pointing in the opposite direction. If we add those arrows to our original left-over arrows, we get zero.
So whether we get zero or left-over arrows depends on whether we have an odd or even number of plate pairs. An odd number will always give us left-over arrows. Even-numbered pairs will sometimes give us left-over arrows and sometimes not.
We could ask, what is the probability we will get an odd or even number of pairs? I'd say .50 is a reasonable estimate. (P1(a) stands for probability of getting an odd or even number of pairs. The "a" stands for annihilation.)
Let's assume our luck is bad and there are two pairs of plates. What is the probability (P2(a)) that the left-over arrows will be opposite and cancel each other?
How about .50? Finally, what is the total probability (P(a)) that we will end up with zero arrows? What is the probability (P(!a)) we will have something left over when matter and anti-matter annihilate each other?
It should be obvious our universe had at least a .75 (or 75%) chance of having some matter (anti-matter) left over. The odds improve when bigger numbers are crunched. For example, four pairs of plates have a .375 probability of cancelling each other out and yielding zero. That raises the chance of left-over matter to .78 (or 78%) (1- (.5 * .375)= .81; [.81+.75]/2=.78).
