In order to explain
the evidence of an expanding universe, many physicists have resorted to the
idea that there is such a thing as dark energy. This line of
reasoning is typical of most of the physicists I know and have worked with over
the years. When data doesn’t fit with existing theory, add in a new term to
help the data and the theory fit together. Even Einstein tried to add a
“cosmological constant” to his theory of general relativity in order to create
a stationary universe, so it’s understandable that today’s physicists might
want to follow in Einstein’s steps and chose a difference value for the “cosmological
constant” in order to explain the expansion of the universe. But just because Einstein
made up a term in his equation doesn’t mean that this is correct. What’s
interesting is that most physicists would rather add a term to an existing
equation (and keep the underlying reductionism and determinism of their
equations), then to resort to incorporating a non-reductionist concept like
entropy. Note that entropy is a non-reductionist concept because it’s not a
property of a particle or a property of space itself, it’s about the relationship
between particles. And “increasing entropy” is also a non-deterministic concept
if we lived in a deterministic universe, the entropy would be constant.

Until recently, most physicists
were not willing to use the existing concept entropy to explain the expansion
of the universe. To many physicists, entropy is a ‘non-entity’ and not really a
fundamental concept (in the same way that determinists believe that ethics or
free will is a non-entity.) These physicists believe in a reductionist and
deterministic world-view in which there is no difference between forward and
backwards time. For them, entropy is just due to ‘course graining’ and is not
really fundamental. It’s just something we’ve made up because we don’t know the
position and velocity of all particles in the universe. Deep down, they believe
that if we knew the position and velocity of all of the fundamental particles
and if we knew the forces of nature, then we could calculate the forward and
backwards trajectory of those particles. As you are probably aware by now, I am
not a determinist and I am not a reductionist, even though I am absolutely
fascinated by the fundamental particles and forces of nature.

So, I was pleasantly
surprised to find a paper written in the last few years, in which physicists
prove that the acceleration of the universe can be solely explained by the
increase in entropy inside of the universe. The goal of this post will be to
describe the problems with the concept of dark energy, and to explain how an
increase in entropy is the valid way of explaining the expansion of the
universe. The goal of this post is to refute the claims of determinism (as I’ve
done in prior posts but pointing out that the weak nuclear force is time asymmetric.)
The goal of the next post will be to refute reductionism (using a difference
line of argument than Plato did two thousand years ago.)

Before continuing, I’d
like to point out the fact that when I use the term “energy” in this post, I do
not mean our common usage of the term “energy” (in which we really mean “exergy,”
or the potential to do useful work. Examples of exergy are the electrical
exergy of charged particles at high voltage (compared with the voltage of the
Earth), the thermal exergy of a hot body (compared with the temperature of the
Earth), the mechanical exergy of a compressed gas (compared with the pressure
of the Earth's atmosphere), or the chemical exergy of a molecule at high
concentration (compared with that molecules concentration in the Earth’s environment.)
In this post, when I use the term “energy”, I mean the physicist's definition
of energy, i.e. the total kinetic and potential energy of a system with respect
to the vacuum energy of empty space.

Using Noether’s
theorem and the assumption of time translation symmetry of the laws of physics,
one can prove that the total energy of the universe is a constant. And since
Einstein proved in 1905 that the conversion factor between mass and energy is simply the speed of
light squared ( E=mc

^{2 }), then both the mass and the energy of the universe is a constant. In other words, energy is mass, and mass is energy, and both are conserved. The only difference is that mass has units of kilograms and energy has units of kg*(m/s)^{2}.Anything with mass has energy and anything with energy has mass. For example, a photon has zero "rest-mass" but has a mass exactly equal to its energy divided by the speed of light squared. The same is true for thermal energy in the form of phonons. When thermal energy is transferred through a steel bar (i.e. when one side is keep hot and one side is kept cold), phonons travel through the steel. These phonons carry energy, mass, as well as momentum. So, let's take the case of a hot gas confined inside of a steel cubic box. The gas will cool over time due to heat transfer through the steel box because we are assuming that the temperature outside of the box is less than the temperate inside of the box. This means that energy and mass are transferred from the gas to the outside environment. (The reason that momentum is not transferred in this case is that the box is perfectly symmetric...whereas in the steel bar case, there was an axis of asymmetry.) So, if mass is being transferred through the box to the environment, where did it come from and where did it go?

The answer is that as the gas inside of the box cools, the gas losses mass exactly equal to Q/c

^{2}, where Q is the heat transferred through the steel box. Likewise, the gases in the environment gain mass equal to Q/c

^{2}. In other words, all forms of energy (including the kinetic energy of gases) have an associated mass equal to E/c

^{2}. And this is what we mean by conservation of energy or conservation of mass. The amount of energy and mass in the universe is not changing. Energy can change forms and can change locations, but the total amount of energy remains the same. (Note: when we commonly say 'energy consumption' we mean 'exergy consumption.' Exergy is not constant over time. You can find out more about exergy here.)

So, if Einstein already proven over hundred years ago that energy and mass are the same thing (except for the conversion factor that relates the units of energy to the units of mass), why do are some physicists talking about dark energy as a form of energy that has no mass? The answer is that many physicists have mistakenly put their faith into the “cosmological constant”, have failed to really appreciate the beauty of entropy, and have forgotten that you can’t invent the concept of a dark energy that has no mass without throwing out Einstein’s relationship between mass and energy, E=mc

^{2}.

But to be fair, I'll summarize their arguments for dark energy. First, the universe started in the big bang. This is a location of high density/energy in a small location. Second, we appear to live in a world in which the universe has expanded from this small location of the Big Bang. Third, the rate of expansion appears to be increasing. Fourth, if gravitational energy is a purely attractive force, then the mass in the universe would tend to pull the universe together, rather than accelerate it further apart. Fifth, when Einstein created the theory of general relativity he added a dark-energy term in order to yield a universe that was stationary (i.e. not growing or shrinking.) So, it’s understandable how physicist might use Einstein’s concept of the “cosmological constant” (i.e. dark energy of the vacuum) to try to explain the expansion of the universe.

This seems fine and dandy, but to believe the above line of argument, you have to throw out Einstein's equation that mass and energy are the same things, just measured in different units. So, you can't postulate dark energy without postulating dark mass. You can't postulate a "mass-free energy." It's a silly as postulating a "velocity-free momentum." All energy has mass, and all energy moving a certain velocity has momentum. All forms of energy attract other forms of energy. The reason that all of the energy of the universe is not one big clump is that there is such a thing as entropy. As stated before, entropy is a non-reductionist concept because entropy is a property of a system. And as we will see in this post and in the next post, a system can have a purpose even when the particles in the system obey laws of nature that show and exhibit no purpose. (But that’s for the next post, in which I’ll discuss Plato’s theory of forms and his refutation of reductionism and determinism.)

So, if you can't
postulate dark energy as the answer to
the question: why is the universe accelerating? You have to postulate
something different.

Well, that's exactly what a group of physicists (Easson, Frampton, and Smoot) did recently in a paper you can find here (http://arxiv.org/abs/1002.4278 and http://arxiv.org/pdf/1003.1528v3.pdf). These physicists calculated the acceleration of
the universe due to the increase in entropy within the finite volume of the
universe, and showed that you don't need to invoke a dark massless-energy. The expansion of the
universe is simply due to the fact that the entropy of the universe is
increasing. While gravity tends to pulls things together, we know that things
don't always stay together. For example, slowly over time, the amount of hydrogen
in the Earth's atmosphere has been disappearing. The reason is that hydrogen is
lighter than N2/O2 (less mass) and at the same temperature (kinetic energy.)
Hydrogen molecules have a greater chance of obtaining enough energy to escape
the earth's gravitational energy.

As when studying the thermodynamics of the universe, we can state the following: the total energy is constant and the entropy will increase in time. Using Stephen Hawking theorem that the entropy of a blackhole is equal to the surface area of the blackhole and assuming that the same equation is valid for our universe as a whole, then this means that when the entropy increases inside of the universe, there must be a corresponding increase in the surface area of the universe. Below is a quote from the Easson, Frampton, and Smoot paper:

In other words, you don’t have to invent a new concept like mass-less dark energy (which of course violated Einstein’s E=mc2) in order to explain the expansion of the universe. Instead, you just need to recognize that there is “arrow of time” and that entropy increases. You can measure how much the entropy of the universe has increased by measuring the surface area of the universe. The two are related by a proportionality constant.

Well, that's exactly what a group of physicists (Easson, Frampton, and Smoot) did recently in a paper you can find here (http://arxiv.org/abs/1002.

As when studying the thermodynamics of the universe, we can state the following: the total energy is constant and the entropy will increase in time. Using Stephen Hawking theorem that the entropy of a blackhole is equal to the surface area of the blackhole and assuming that the same equation is valid for our universe as a whole, then this means that when the entropy increases inside of the universe, there must be a corresponding increase in the surface area of the universe. Below is a quote from the Easson, Frampton, and Smoot paper:

*"To accommodate the observed accelerated expansion of the universe, one popular idea is to invoke a driving term in the Friedmann-Lematre equation of dark energy which must then comprise 70% of the present cosmological energy density. We propose an alternative interpretation which takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there. Dark energy is thereby obviated and the acceleration is due to an entropic force naturally arising from the information storage on the horizon surface screen. We consider an additional quantitative approach inspired by surface terms in general relativity and show that this leads to the entropic accelerating universe."*In other words, you don’t have to invent a new concept like mass-less dark energy (which of course violated Einstein’s E=mc2) in order to explain the expansion of the universe. Instead, you just need to recognize that there is “arrow of time” and that entropy increases. You can measure how much the entropy of the universe has increased by measuring the surface area of the universe. The two are related by a proportionality constant.

Even more, there is no way to predict the future and how much entropy
will be generated by irreversible processes. The universe is not deterministic,
as Laplace and many others have thought. The weak nuclear force is not time
reflection symmetric, and this allows the entropy of the universe to increase. There
is no way to predict the amount of entropy generation either. There is not
set of equations that can be used to calculate the rate of entropy production, so
not even the largest computer can predict the rate of entropy generation in the
future, and hence no person or computer or rational agent can predict the future
of the universe and for that matter predict the surface area of the universe in
the future.

Later in life, Einstein called his cosmological constant
the “biggest blunder of his life.” I hope that most physicists soon realize
that dark energy is a major blunder, and that the acceleration of the universe
is evidence that the entropy of the universe is increasing with time, and hence
evidence that entropy is a real concept and irreversible entropy generation is
a real phenomena.

As discussed earlier in this post, in my next post I’ll expand on Plato’s
refutation of determinism & reductionism and show how there is an
underlying digital (i.e. countable) structure within our seemingly analog (i.e.
continuous & deterministic) universe. That digital structure is related to
the symmetry relations between particles and can only grow with time. (I don’t
mean digital in the sense of 0,1’s like in the Matrix. I mean that there is a
countable structure of symmetries and that this underlying structure increases
with time.) Life forms help grow that underlying digital structure of symmetry
relations when they self-replicate. The self-replicating digital life forms can’t
violate the analog laws of the universe, but at the same time, these digital structures
could self-replicate even if placed on a different substrate than our own
universe.

But that’s a story for the next post.

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