Sunday, September 30, 2012

Time Travel is Impossible

This post is a continuation and a summary of the previous post (What does the Universe looks like?)

There's a lot of hype around time travel into the past or into the future using blackholes or wormholes. But's its just hype created by a lot of people who want to sell you their books. The goal of this post is to summary my previous post and to highlight those aspects of the previous post that show why time travel is impossible (as depicted in sci-movies or as discussed by astrophysicts such as Richard Gott or Kip Thorne.)

Here's a short summary:
(1) We live on a wrinkled 3D surface of a 4D sphere.
(2) The 2nd Law of Thermodynamics states that there is no way to give a particle enough energy such that it has enough mass/energy to curve space-time enough to go back to the Big Bang.
(3) Time travel is impossible. Even if you give a particle enough energy such that it is locally further back in time than its surrounding environment, as soon as you de-accelerate the particle back to normal speeds, the particle goes back to being at the same radius (time) as its surrounding environment.
(4) When you account for acceleration and de-acceleration (i.e. General Relativity), the Twin-Paradoxes and the idea of Time Travel go away completely. Therefore, when we teach Special Relativity to students in the class room, it's important to simultaneously time some of the basics of General Relativity.
(5) In the long-run, growing life is the best and fastest way to generate entropy and to expand the radius and surface area of the universe. Culture grows, music expands, art thrives, and mathematics dazzles while we expand life from Earth to other planets. It's a win-win situation for everybody. We live into an unknown future, with only the past as a rough guide on how best to grow life and expand the universe.

Here's the longer summary of the previous post:

Wednesday, September 26, 2012

What does the universe look like?

Our universe is a wrinkled 3D surface on a 4D sphere. To image what this looks like, start by thinking about the wrinkled 2D surface of the 3D spherical earth, but realize that this is only an analogy of what a 3D surface looks like on a 4D sphere. Just as the Earth is not a perfect 3D sphere, the universe is not a perfect 4 dimensional sphere. On Earth, there are valleys and mountains. Likewise, the surface of the 4D sphere is wrinkled due to the inhomogenity of mass/energy. As Einstein showed, the 3D surface of the 4D sphere is curved at different points on the surface depending on the amount of mass/energy. The 3D surface curves into the 4th dimension (time). The time dimension is the radius of the 4D sphere. For example, the Sun's mass/energy causes the change in the curvature of the 3D surface, and it creates a small valley about which the planets can orbit around in ellipses.

On average, the mass/energy causes the universe to take the shape of a 4D sphere but near locations of large amounts of energy/mass, the 3D surface curves more than the average curvature...this is like a valley caused by an impact crater which has more curvature than the average curvature of the Earth's surface. The location of the center of the large clump of energy/mass is lower than the surrounding environment. What I mean by lower is nearly the same as what we mean by lower on Earth. Here, lower means closer to the center of the Earth. In the 4D sphere, lower means closer to the center of the 4D sphere. And since the radius from the center of the sphere to location of the energy/mass is what we mean by 'time', the center of energetic/massive clumps of particles is actually further back in time. Around us, the clumps of mass/energy are like tiny valleys, but there are locations like blackholes in which the well is so deep that particles that fall into the well are so far back in time that they can't travel fast enough to catch back up to our present time near the surface of the 4D sphere. Since we live on a 3D surface, there is no edge to the universe. In any direction you look, all you see more galaxies. And if you look really far away in any direction, all you see is photons from the aftermath of the Big Bang.

Stated again, the universe as a wrinkled 3D surface on a 4D sphere, and the size of the wrinkles is proportional to the amount of mass/energy (and momentum/shear to be precise) at any location. But that's not it. The universe is actually getting larger. The Earth is not getting larger, but one can think about the increasing 2D surface of an inflating balloon to get a feel for this inflation. Points on the surface of the balloon are getting further apart. The evidence we have for this is the red-shift in photons from distant galaxies. The further away the galaxy is, the more the photons increase in wavelength. It's like the fabric of space itself has increased during the time that it took to travel from the galaxy in the past to our galaxy in the present. Space itself has increased over time...but this is redundant statement because the total  surface area of sphere obviously increases as the radius from the center of the sphere to its surface increases. Time is the radius of the 4D sphere (the radius is not the same at all locations.) On average, the radius is increasing, but locally, the radius can decrease (such as for a blackhole.)

The question is: why is the radius of the universe expanding on average? Einstein's theory of general relativity can tell you about how space-time is curved by mass/energy, but it doesn't specify the actual shape of the universe, and it doesn't specify whether the surface area will increase, remain the same or decrease. It's just an equation, not a solution. So, in other words, the answer to the question of why the universe is expanding is still not completely known, but here is my best guess based off of the evidence available presently about the universe:

Sunday, September 16, 2012

Disproving a Heat Death to the Universe

There have been the claims by lots of famous chemists and physicists that there will be an eventual “Heat Death of the Universe.” In fact, the whole idea of a heat death of the universe has generated an entire philosophy of life called the Thermodynamic Imperative. In a previous posts, I've pointed out that there is an irrational fear in parts of our society regarding entropy production. One way of stating the Thermodynamic Imperative is the following: "Waste not useful potential energy." I couldn't agree more with this statement. I think that we should be using useful potential energy to help grow life. The problem is that there are some people in the scientific-environmental community (such as Nicholas Georgescu-Roegen) who have taken the Thermodynamic Imperative to the extreme and have taken it to mean that we should minimize the production of entropy at all costs and we should do this by promoting a philosophy of de-growth. Before I delve into the problems with the philosophy of de-growth, I'd like to go back to one of the original statements regarding the heat death of the universe.

In 1862, Lord Kelvin (William Thomson) wrote the following regarding the implications of the second law of thermodynamics:

"The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. But it is impossible to conceive a limit to the extent of matter in the universe; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and hence into heat, than to a single finite mechanism, running down like a clock, and stopping forever."

So, even from the beginning, Lord Kelvin was aware of the implication of the second law of thermodynamics, but was smart enough to realize that whether we reach a heat death depends entirely on whether the universe is finite and whether it is growing in size. Lord Kelvin was spot on when he stated that science points to "endless progress" (emphasize is mine.)

If the universe were finite in size, then the idea of a heat death to the universe makes sense. However, if the size of the universe were to increase as entropy increases, then there would never be a true heat death. The average energy density in the universe would decrease, but the universe could continue to increase in entropy because there would continue to be the capability to do useful work because there would still be gradients in temperature and chemical composition.

Thursday, September 13, 2012

Fallacy of Government Stimulus

Here's the simplest line of reasoning why goventment stimulus doesn't work:

(1) The economy grows when power plants self-replicate. The higher the rate of return on work invested (IRR), the faster the growth rate of the economy.

(2) Power plants that can self-replicate with large 'unsubisidized rates of return on work invested' don't need a government stimulus to self-replicate (by definition).

(3) Government stimulus comes from (a) borrowing from today's investors by promising future direct taxes to pay off the loans, or (b) indirect taxes on present investors (by printing what the Federal Reserve is doing right now.) The direct or indirect taxes lower the inflation-adjusted growth rate of those power plants that can self-replicate because some of the project's profits go to paying taxes (both directly and indirectly) rather than re-investing the money into self-replicating power plants.

(4) Some of the government money goes to projects that are barely self-replicating (only with the government assistance) and some of the money goes to projects that are not self-replicating (even with the government money.) Either way, the government ends up picking projects with lower 'unsubisidized' rates of return on investment than would an individual or a company. (Note that individuals and companies aren't perfect at knowing where to invest, but on average throughout history, individuals and companies choose projects with higher rates of return on investment than do government agencies. This is true across the globe. It's true in the U.S., E.U., China, and Japan. Higher average growth rates occur when the government makes less decisions on where to invest.)

(5) There is friction associated with the act of taking money from one project and giving it to another project. The friction (i.e. money that goes to pay the salary of tax collectors and government bureacrats) consumes useful work, which means: not only is the government picking projects with lower 'unsubsidized' rates of return on investment, but the very act of picking projects with government agencies requires taxing self-replicating power plants to pay for the government agencies. It's like a double tax on self-replicating power plants: a tax to subisidize the un-self-replicating project and a tax to pay the government tax collectors and government bureaucrats to choose what project to subsidize.

(6) Therefore, government 'stimulus' lowers the growth rate of the economy by taking money from projects and power plants that are self-replicating and giving the money to projects that are marginally self-replicating or that are not self-replicating. Money is transferred from power plants with large positive values of rate of return on investment to projects with marginal or negative 'unsubsidized' rates of return on investment. Since the growth rate of the economy is a weighted average of the growth rate of each of the individual projects, when governments take money from projects with large growth rates and give the money to projects with low to negative growth rates, the overall weight average growth rate of the economy is less than if the government did not take money from the projects that naturally have high growth rates.

The conclusion, therefore, is the following: let individuals and companies decide where they want to invest their money. Let the government focus on what it's supposed to be doing according to the constitution and the updated bill of rights.

Saturday, September 8, 2012

You have a digital self-replicating soul

My goal in this post is the summarize the key points of a previous post so that the main points of that post don't get lost in the arguments for the main points. If you follow the main points below, you'll get a glimpse of how ethics is real and quantifiable in the digital world, but not real in the analog world.

1)  We live in an overlapping analog-digital world. By analog world, I mean the four laws of physics and the particles in the universe. By digital world, I mean the countable, finite symmetries within the equations of motion for the particles.

2) In the digital world, there are self-replicating structures (like you and me.) There are also non-self-replicating digital structures, such as Bénard convection cells.

3) The essence of the digital world is the symmetries of the differential equations of motion of particles. The number of symmetries in the differential equations is not constant (for systems without irreversibility.) The language of the digital world is the language of symmetry groups (both Lie and finite groups.) The alphabet of the digital world is the 'simple groups.' (These are the most basic groups upon which you can build larger groups...analogous to the prime numbers for the positive integers.)

4) The presence of self-replicating digital structures in the digital world is due in part to Gödel's Incompleteness Theorem. The mathematics of simple groups is incomplete. Certain symmetry groups contain within themselves the information to create copies of symmetry groups (and hence grow the number of symmetries.) In other words, there is an inherent feedback loop between the differential equations and their symmetries that allows for self-replication of certain structures.  [Note that there is still a wide open field of research, and I hope that more mathematicians start studying the interplay between  Gödel's Incompleteness Theorem and the self-replication of symmetry groups.]

5) Growth of symmetries (either by self-replicating or non-self-replicating structures) is only possible because of the weak nuclear force. If it weren't for the weak nuclear force, we would be living in a reversible world (because the gravitational, electromagnetic and strong nuclear forces are time reversal symmetric.) In a reversible universe, there is no future and there is no past. In a reversible world, there are no gradients in pressure, temperature, chemical potential or voltage. If you would like to imagine what a reversible world looks like, watch videos of superfluid helium, superconductivity, or just look out at the stars in the night sky. The photons from other stars are bosons and they don't interact via the weak nuclear force. They stay nearly exactly the same as they travel across the universe because photons can't interact via the weak nuclear force. The same is true for superfluid helium and electrons in superconductors. Electrons pair together in superconductors and form boson states in which they can't interact with each other via the weak nuclear force, and the system becomes nearly perfectly reversible (i.e. no irreversibly and no ability to maintain voltage gradients.) The fact (that we have gradients in temperature, pressure, voltage and chemical potential in systems that can interact via the weak nuclear force and that we don't have gradients in temperature, pressure, voltage and chemical potential in systems that can't interact via the weak nuclear force) implies that we live in a mostly irreversible world. (You can find examples of reversibility only when you eliminate the weak nuclear force or when the system reaches equilibrium...such as the spherically-symmetric distribution of neutrinos in galaxies. But of the universe is still far-from-equilibrium, i.e. far-from-being perfectly symmetric.)

6) When you only look at the analog world, then Hume is correct to say that you can't derive 'ought'  from 'is.' If you only look at the analog world, there is no meaning. Ethics, beauty, morality, the good are only apparent when you look at the digital world. Moral actions are those actions that helps life to self-replicate as quickly as possible and that do not harm or prevent other life forms from being able to self-replicate.

7) Language is only possible because language is taking part in the digital world. Plato first made this argument over two thousand years ago. (Note that any digital action shows up in the analog world. The analog world is like a computer and the digital world is like a self-replicating program. There is both a digital and an analog aspect to software. There is the software and then there is the physical copy of it on certain computers.) If there were no digital world, language would not be possible. Language is possible because of our shared underlying use of the alphabet of the digital world (the simple symmetry groups.) Human languages and other languages of conscious beings depends crucially on the underlying 'machine code' of simple symmetry groups, just as higher-levels codes like java depend on lower level 'machine codes,' amd these 'machine codes' ultimately depend on the underlying 'simple symmetry groups.' We don't see the simple groups when we communicate with speech just as we don't see the underlying machine codes when we read a blog post, but the 'simple groups' are underlying our ability to communicate.

8) The symmetry group of the present universe contains the symmetry group of the universe of the past as a subgroup. Growth of new symmetry groups does not destroy the symmetry groups of the past. This is why it's important not to confuse DNA structures with the underlying symmetry group structures that allow for self-replicating structures. DNA information can be destroyed, but the underlying symmetry groups that allow for self-replicating systems (which contain DNA, proteins, cell walls, feedback loops, etc...) can't be destroyed. (Note: this doesn't mean that murder can ever be considered to be ethical. What I'm saying here is that there is an imprint of the past on the future in the fact that the symmetry group of the future contains the symmetry group of the past as a subgroup.)

9) The symmetry group of the universe only increases (as seen by the expanding of the surface area of the universe.) The future symmetry group of the universe can't be calculated. Just as in Gödel's Incompleteness Theorem (i.e. there are true statements in number theory that can't be proven), there are true future states of the universe that we can't prove to be true. There is no real way to predict the future, which is why we must maintain a certain level of humility and this is why all conscious life forms have basic rights. Conscious lifeforms must be free to self-replicate in ways that don't injure, steal from, or kill other conscious lifeforms from being able to self-replicate. You can't justify murder on the grounds of growing life elsewhere in the universe because there is an inherent inability to predict the future of the universe. As society grows, hopefully we will be able to add to the list of conscious lifeforms that are guaranteed certain basic rights to life, liberty and the pursuit of self-replication.

9) In summary, you have a digital self-replicating soul. You are a digital free-agent. You can't perfectly predict the future outcome of your actions, but you have stored memory, and can draw upon history, science, engineering, art, and literature to help estimate the outcome of any action. Moral actions are those actions that are taken freely and purposely help grow life. Immoral actions are those actions that are taken freely and purposely to destroy life or to waste stored useful energy (exergy.)

Tuesday, September 4, 2012

Are neutrinos the main component of dark matter? (Most likely yes)

There is a large debate right now in the physics community about whether neutrinos are the main component of the dark matter of the universe. And the idea that neutrinos can explain dark matter is starting to pick up in the physics community. The first goal of this post is to discuss experimental evidence that points to neutrinos as the main source of the dark matter in the universe. This is also called the Neutrino Minimal Standard Model. The second goal of the post is to discuss why this would have any relevance to anybody’s day-to-day life.

I’m going to start this post with a recently developed picture by other researchers of the mass/energy distribution of dark matter in a spiral galaxy. This picture was generated using data from the spiral galaxy NGC 4216. The dark matter is represented by a blue glow (even though it really does not emit photons…it really is dark.)