Evolution of the Universe

Has the Universe always been around? If not, how did it begin? There were two theories about the evolution of the Universe to describe these two ideas: the Steady State Model and the Big Bang Model.


The Steady State Model tells us that the universe has always been around and will always be around. It just is. The Steady State Theory was championed by Fred Hoyle. The idea is that even though the Universe is expanding, as demonstrated by Edwin Hubble and the Hubble law, in order to see the universe as homogeneous, galaxies must be continuously created in the empty space between existing galaxies. In other words, matter must be continuously created and based on Einstein mass-energy equivalency, energy must also be continuously created. The theory requires that the universe looks the same in all directions at all times. This is referred to as the Perfect Cosmological Principle - the Universe looks the same in all places at all times. If we were able to see the universe 5 billion years ago or 10 billion years ago, or even 50 billion years in the future, the universe would look the same. However, we can actually observe the universe from 10  billion years ago and 5 billion years ago and can see that the universe does not look the same as it does today. The universe appears more crowded (i.e. denser) in the past than today. So what does this tell us?


The Big Bang Model is the theory that the Universe began about 14 billion years ago (the age of the Unverse is under debate with the prevailing idea that the Universe is about 13.8 billion years old, give or take a few hundred million years) with a sudden explosion of matter, energy, and space into nothing. Note, that the Big Bang does not say that matter and energy exploded into space, but that the singularity that started the Universe included space with the matter and energy. This means that all the matter and energy that exists in the Universe now equals the matter and energy at the beginning and that the amount of matter and energy will be the same in the distant future. This also tells us that as the Universe expands, the distance between galaxies will also increase which is what is observed. The Big Bang Theory was actually coined sarcastically by Fred Hoyle who as mentioned above was an advocate for the Steady State Theory. The Big Bang Theory tells us that while the Universe may change with time, it does not change with space and is a feature of the Cosmological Principle. We will talk more about the Big Bang Theory in the next post.

Special Relativity

Previously, we briefly discussed General Relativity and how it expands Newtonian Mechanics to include the interaction between mass and space(time). Today, we are going to talk a little bit about Special Relativity in that what happens to physics when we approach velocities near the speed of light.

There are two postulates that Albert Einstein proposed make up Special Relativity.

1.      All Laws of Physics are invariant in all inertial systems - basically, the laws of physics must remain the same for all reference frames that are not accelerating.

2.      The speed of light in a vacuum is the same for all observers, regardless of the motion of the observers. In other words, the speed of light, c, is the same for a stationary person and a person moving at any speed, up to the speed of light (which is impossible).

One of the amazing things about Special Relativity is the idea of time dilation. It means that for any body travelling at any speed, time is not constant. To a stationary observer, it would appear that the clock for the moving object slows down, but for the observer in motion, the clock of the stationary person speeds up. In both cases, each observer sees the clock in his or her reference frame as moving normally. How does this work?

We have to use math to show this. There is an equation that describes how time is relative using the Lorentz transformation:

Where  is the time for the moving observer,  is the time for the stationary observer, and  is the Lorentz factor given by , where v is speed of the moving observer and c is the speed of light (3x10⁸ m/s). Since v is always less than the speed of light, is always greater than one, therefore Δt’ > Δt. For the stationary observer, the clock of the moving person is slow, while for the moving observer, the stationary person has a fast clock. For velocities much smaller than the speed of light, γ is virtually 1 and the times are equivalent. However, we have seen for objects moving near the speed of light (particles with little mass), this actually holds true. An example is a muon. A stationary muon would decay in only 2.2 μsec; however, when a muon is travelling near the speed of light will last much longer than 2.2 μsec (to a stationary observer).

Another strange feature of special relativity is the idea of length contraction. In other words, a moving object will appear shorter than it would be if it were stationary.

Where Δx’ is the length of the moving object and Δx is the length of the stationary object. This again leads to another strange phenomenon: relativity of simultaneity.

Relativity of simultaneity means that something that happens simultaneously in one inertial frame is not necessarily simultaneous in another. The best example given is called the ladder paradox.

Imagine a ladder and a barn. The ladder is just a little bit longer than the length of the barn. Now imagine that the ladder is moving at a relativistic speed. Someone in the barn reference frame will see the ladder shorter than its stationary length, and can close doors at both ends with ladder inside simultaneously. However, to keep the ladder from crashing through the end door, the doors must open up again. For the ladder, however, it sees the end door close first, then the front door close secondly, with the end door opening up before the ladder reaches it. The ladder does not see both doors closed at the same time.

A third phenomenon of special relativity is the idea of infinite mass. For a moving mass, Δm’=γΔm. As v approaches c, you can see that γ nears infinity (v/c approaches 1 and the denominator in the Lorentz factor approaches 0). This is why nothing can reach the speed of light as its mass will become infinite, which leads to another famous equation: E=mc², the energy-mass equivalency. This means in order to accelerate a mass to the speed of light, the amount of energy required goes to infinity.

General Relativity

General Relativity is a theory of gravity that was developed by Albert Einstein between 1907 and 1915. It is actually an expansion of Newtonian gravity by adding a component to Isaac Newton's theory: spacetime.


Isaac Newton's Law of Universal Gravitation only showed how two masses interacted with each other. It is given by this equation:

The force of gravity between two masses, M and m, is the product of a constant, G, and their masses divided by their separation squared. For a couple of centuries, this worked. But when careful examinations of Mercury were made, this equation did not really fit the observations. That's when Einstein made his revelation.

MASS CURVES SPACETIME

What does this mean? For thousands of years, everyone thought of space as having three dimensions: length, width, and depth; and those three dimensions were flat. But Einstein showed mathematically that there are actually four dimensions, the fourth being time. But the more important thing is that mass can affect the flatness of space.

Imagine a sheet of rubber. You stretch it out flat. Now, on that sheet, place a marble. Where the marble lies, there is a small depression. Take the marble away, and replace it with a bowling ball. The depression is much bigger. This is like spacetime. The higher the mass, the deeper the depression in spacetime.

From Astronomy Today

As shown, the higher the concentration of mass, the larger the curvature. Around the Earth, the depression is small compared to the Sun's depression. Around a larger star, like Rigel, the depression is enormous.

This curvature helps explain why the equinoxes precess, why orbitals are elliptical, and why objects move faster the closer they are to the body they orbit. This theory was proven when observing Mercury's orbit and why it's perihelion precessed. It also was proven by Sir Arthur Eddington when he observed a star behind the Sun during a solar eclipse, which will be explained next.

Neutrinos as Dark Matter

I've discussed neutrinos before, way back in June, but we can also look at neutrinos as a form of dark matter. As previously mentioned, neutrinos are highly non-interactive as it would take a block of lead an eighth of a light-year wide to stop just one neutrino. However, they are abundant as they are a product of the fusion going on in the cores of stars.
We also know that neutrinos come in six different flavors, depending on the associated lepton (electron, positron, muon, anti-muon, tau particle, and anti-tau particle) and that when they interact, they can change flavors.
But remember, that neutrinos have virtually no mass, though they are not massless. Since there are so many stars and have been billions of stars in our own galaxy creating neutrinos every time fusion occurs, there must be a lot of neutrinos existing in our galaxy, as well as other galaxies. A lot of something that has little mass ends up having a huge mass. Therefore neutrinos are probably another component of dark matter.
Again, the hard part to confirm that neutrinos make up dark matter is (1) that they are nearly massless, so any gravity they impart is small, and (2) they virtually do not react with matter. So although there is a lot of neutrinos out there, they are hard to detect.