Featured Post

Was the Speed of Gravity Successfully Measured?

ABSTRACT: This paper shows mathematically and experimentally why it is highly unlikely that the speed of gravity was successfully measured....

Monday, March 12, 2018

Why Entropy Happens

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.

2 comments:

  1. All of these assertions are based on the Big Bang model, one in which all that the Universe is, was there at the beginning in one form or another. I say that the Universe exists only in the ever present, and its existence is caused solely by a continuing creative expansion of invisible absolute space from within each component or "space bubble" of the Universe. This is all that there is! These bubbles expand randomly and in quantum steps causing all of the properties of the Universe: time passage, energy, gravity, inertia, electromagnetic forces, matter ... The bubbles invisibly expand at a rate that defines the speed of light, hence all actions are bound by this limitation. http://papazstuff4u.blogspot.com/2018/01/the-universe-is-just-bubbles.html

    ReplyDelete
  2. Question:
    What was more in order, the Singularity before the Big Bang and a few hundred thousand years afterwards, or what we have today? It seems to be that because of Thermodynamics we have reverse Entropy going on in the case of Universal Expansion.

    By the way, for what it's worth, and in my humble opinion, I say the Big Bang never happened and I have a little summary narrative I wrote about it before I start messing with the math, if you are interested.

    ReplyDelete