Monday, October 29, 2012

The Oscillating Universe

Consider that there are two universal principles governing the fate of the universe: one, energy is conserved; two, the total energy is zero. Then as energy is perpetually undergoing a conversion between the potential energy of Dark Energy and kinetic energy of matter, the expansion and contraction of the universe would be a result of that interplay. There would be no Big Bang, no Big Crunch and no Big Rip, and no need for extra dimensions. In a way, Dirac’s sea of negative energy would be vindicated. It also could account why the universe is populated with matter and not anti-matter.

Potential Energy (P.E.), is encoded in Dark Energy, and Kinetic Energy (K.E.) is encoded in ordinary matter ( baryonic + dark). Dark Energy generates a repulsive force, and matter, an attractive force.

The total energy of the universe is zero: − E + E = 0

1st phase: At the beginning of this phase, the potential energy of Dark Energy is at its maximum, while the kinetic energy of matter is at its minimum. As the potential energy of Dark Energy decreases, the kinetic energy of matter increases. What we see is a universe with galaxies moving away from each other. Also, temperature decreases (Cosmic background Radiation). When this phase of the cycle has been exhausted, the potential energy is at its minimum, and kinetic energy is at its maximum.

2nd phase: The kinetic energy of matter decreases ( the universe is decelerating), until its reaches a minimum, after which the universe reverses course, and follows a similar pattern during the 3rd and 4th phases.

Entropy: this is a reversible and adiabatic process

→ dS = 0.

Temperature: In the 1st phase, the universe is hot, its temperature is high. There are two distinct functions for Dark Energy: it acts as a repulsive force, and it acts like a heat reservoir. As its potential energy is converted to the kinetic energy of matter, the universe accelerates. But due to the repulsive force of Dark Energy, it also expands, which has the net effect of cooling it down, (heat flows from matter to Dark Energy).

− E + ∆E → 0 (from maximum negative to minimum)

Note: there are two processes of the energy exchange, ∆E, and we shouldn’t confuse them.

(a) Potential energy is being converted to kinetic energy (acceleration):

For Dark Energy:
a decrease in potential energy,(|P.E.|− ∆E)

For matter:
an increase in kinetic energy, {K.E. + ∆E}

The net result is at any given time:
(|P.E.| − ∆E) + { K.E. + ∆E} = |P.E.| + K.E.

Energy is conserved.

(b) Heat is flowing from matter to Dark Energy (cooling):

For Dark Energy:
an increase in heat, (− E + ∆E)

For matter:
a decrease in heat,{E − ∆E}

But at any given time, the net result is:
(− E + ∆E) + {E − ∆E} = 0

What we see in the 1st phase is that galaxies are accelerating and moving away, and temperatures are going down.

In the 2nd phase, the process occurs in reverse. Initially, the potential energy of Dark Energy has been exhausted. The kinetic energy of matter, after reaching its maximum, is now being converted to the potential energy of Dark Energy.

For the potential energy: 0 + ∆E → |P.E.|
For the kinetic energy: E − ∆E → 0

As the kinetic energy is decreasing, the universe decelerates, and the attraction of gravity dominates, forcing the galaxies to contract.

During that 2nd phase, heat flows from Dark Energy ( it becomes more and more negative) to matter, and the matter in the universe gets hotter and hotter.

What is seen in the universe is that galaxies are moving closer, and temperatures are going up.

In this model, there is no Big Bang, no Big Crunch and no Big Rip, and there’s no need for extra dimensions.

Transition period (T): This is the short period of time when the universe reverses course in direction: the temperature is so high that particles are completely decoupled. However were you an electron, assuming an electron can survive such extreme temperatures, you would see a period in which every thing has been pulled apart and rapidly moving closer to each other( the ending of 4th phase of the old cycle) and soon afterwards, particles starting to rapidly move away, the temperature going down by a very large factor, allowing for recombination (the beginning of 1st phase of the new cycle).

Inflation: This is a result from the thinking that there is a singularity () and from that point, one sees a greater expansion than what really happened – which was really a short period of rapid contraction followed soon after by a short period of rapid expansion. This has a net effect of making the universe to appear as if expanding exponentially.

Counter-intuition: You would think that as the energy flows out from matter to Dark Energy (during the 1st phase, for instance), the matter in the universe would slow down. Instead, its kinetic energy is increasing ( potential is converted to kinetic), therefore it is accelerating. Because of the repulsive force, galaxies are moving away, the net effect is that the universe cools off. What we have is that energy, through the interplay between an attractive and a repulsive force, is doing an oscillation through its conversion. Energy is conserved. At the same time, while heat is exchanged,the total energy is zero, and. What can be measured -- the expansion (contraction), the cooling (heating) of the universe -- is a result of these two laws.

Final notes:

(i) Dark Energy had been previously discovered twice. First in Einstein’s General Theory of Relativity, it was called the Cosmological Constant. It was initially used as a factor to stabilize the universe. Unknown to Einstein, the universe would be discovered by Hubble a decade later to be expanding. It was also discovered by Dirac, which is no surprise, as one takes the Einstein energy equation, quantize it and you get the Klein-Gordon equation. Dirac saw in that equation the asymmetry between time and space, and took the square root of it. The pay off was that the spin is encoded into that equation. But also, to prevent energy from sliding into infinite negative energy levels, which would have nixed the idea of a ground state and undermined Quantum Mechanics, Dirac came up with the idea of a sea of negative energy which is fully occupied. And with that, he correctly reasoned that one could borrow from that sea and create anti-matter, a prediction which was confirmed shortly after with the discovery of the positron. But at the times, no one knew what to do with this sea of negative energy. And now, we know better. In this model, the very nature of Dark Energy is potential energy on a global scale. But locally, it can also be seen as anti-matter, but only under the right circumstances. The existence of anti-matter is brief, and this accounts why the universe is populated by matter and not anti-matter.

(ii) Historically, the flaw in a perpetual motion of an oscillating universe resided in the 2nd law of thermodynamics which said that an increasing entropy would eventually bring it to rest. In this model, the total change in entropy is always zero. This is restated as: the total energy of the universe is always zero, which is a stronger statement – the popular version being, “there are no free lunches.” That the change in entropy can be zero had already been discovered in reversible, adiabatic systems. However, since most of the systems we observed are typically irreversible in nature, the second law has been mostly stated with the notion that the entropy always increases, often leaving aside that it can be non-increasing. It turns out that Dark Energy is exactly the means needed by which this process can that place.

iii) Locally, the Higgs field gives matter its mass, providing matter with the central character in the evolution of the universe. Globally, the universe is the stage on which this kinetic energy of matter is seen. While Dark Energy fills the vacuum, it is the field that provides potential energy on a global scale for the universe to oscillate without collapsing into a singularity.

Sunday, August 26, 2012

Why our present theories collapse at Planck scale

Suppose we want to probe the Planck scale. To do that we would need a particle of a certain mass m.

According to quantum physics, for every particle, there is a wavelenth associated with it.

(1) λ = ℏ/mc

According to General Relativity, at Schwarzschild radius, when the mass collapses to a black hole:

(2) r = 2mG/c2

Equating (1) and (2), and solving for m, we get,

mBlack Hole = (ℏ c/2G)½

But the Planck mass is mpl = (ℏ c/G)½

We can see that mBlack Hole < mpl. In probing the Planck scale, the probing particle will have a mass that will precipitate its collapse into a black hole before it even attempts to probe the Planck scale.

The implication is that unless there is a theory that can circumvent QM + GR, we can know absolutely nothing of what is taking place at Planck scale, as if Nature has shut its doors to our inquisitive curiosity.