Assorted Links I

Instead of writing an article today, I have decided to list a few of my favorite websites:

Any decent physics listing has to start with the serious stuff. Physics is one of the few industries in which all work is available for free on the internet. The main collection of research is the Arxiv. But there are other groups have indexed the arxiv and other collections, making for easier searching for papers through SPIRES and important reviews of different subjects are given at the Net Advance of Physics. Existing bounds on new physics and the most precise values of physical constants are provided by the Particle Data Group. For all mathematics questions, the Mathworld site provides an amazingly extensive source of information.

There are also a number of interesting newsletters/blogs on modern physics. John Baez's site lists very interesting topics in mathematics and mathematical physics, while the Cosmic Variance blog provides coverage of general physics topics

Those are my favorite websites. I will be adding more as I find them, and I would encourage anyone with a physics website to add it as a comment. (However 'alternate physics' sites will be removed unless they are really good and really interesting)

The Eternal Universe?

I started thinking about the birth of the Universe today. Anyone who would actually read this probably already knows about the standard Big Bang explanation - but I will repeat it anyways.

Einstein's theory of relativity, and numerous observations of distant galaxies, have shown that the universe itself is expanding. A common misconception is that there was an explosion inside of the Universe and that space remains fixed while the stars and galaxies fly apart. The reality is that space itself is expanding (one way to understand this is to draw some stars on a balloon and then inflate it. The stars are not moving relative to the balloon, and yet the distance between them is increasing).
Of course if something is always expanding, it must have started out very small. And in fact the predictions of the Big Bang model have been accurately measured to be accurate - as far back as a fraction of a second after the Big Bang. But there is one problem - at the moment of the Big Bang none of the existing theories of physics are valid. And that means we cannot say what happened before the Big Bang.
In fact, the generally accepted theory is that time started with the Big Bang, so we cannot even probably discuss 'before' the Big Bang. Many people are uncomfortable with time having a beginning - if something happened then something else must have caused it right?

The first option is that the Universe might stop expanding at some point and start contracting again. It would continue to get smaller (and hotter - start the 'End Cosmic Warming' protest!) until it crunched into either a single point or a very tiny miniverse (the Big Crunch). And then that tiny Universe would explode out again in a new Big Bang and create new stars and galaxies. In this model the Universe can continue expanding and contracting eternally with no start or end of time.
The model has an important problem though. Each reborn Universe must be more disorganized than the previous one. So if the Universe has been doing this eternally in the past, stars and galaxies should not even be forming - there is just too much entropy!

But there is another option! We could be one Universe in a giant Multiverse, in which Universes are constantly being created and destroyed. The Multiverse could exist forever without introducing problems.

Yet another option is that there are two Universes that collide occasionally (the Ekpyrotic Universe). Each time they collide they create a Big Bang in each Universe, then they separate and each evolves for billions of years on its own. During the evolution the Universe expands so much that the 'disorder' it contains gets dilluted until it is almost non-existent. Then the Universes collide again and the process repeats. Just like the Multiverse, this process can continue forever with no problems!

So perhaps the Universe is older than we think...

Simply Relativity, Cosmic Coincidences, & A Mathematical Mystery

After several busy weeks of travel and actual work, I finally have returned to this blog. Since I haven't posted in a while, I will post three at once...

1. I will start with a link to my webpages on the Bondi k-calculus. For a lot of people, the special theory of relativity is a complete mystery, with assumptions that the theory is just speculation or that it requires mathematics so complicated that no ordinary person could hope to understant it . This is not true.
The Bondi k-calculus is a very simple method of looking at special relativity, and requires no math past grade school. It is also accurate - many advanced mathematics and physics courses in university teach this method.

Having said all that, it is also true that there are possible violations of the theory of relativity. At the end of this posting I will give two of the possibilities that are currently being explored.

2. The Cosmic Coincidence. This mystery is well known by physicists, but it is not well known among the general public.
As we understand it, everything in the universe fits into three categories. There are photons, which form light and radio waves and x-rays. There is matter, both the ordinary stuff of stars and planets as well as an unknown form of dark matter. And there is dark energy, a mysterious substance that fills the entire universe causing it to expand.
Now comes the problem. The density of photons decreases with the fourth power of the size of the universe, matter density decreases with the third power of the size of the universe, and dark energy (probably) stays constant. Since the universe is rapidly growing, and has been for 14 billion years, that means the three densities must be radically different.
Wrong! Dark energy and matter densities are about 2 to 1, while photons are maybe a factor of 10 less dense. In the future matter and photons densities will drop to almost zero. In the past they were billions of times larger than the dark energy density.
So why do we happen to live at the one point in history at which the three values are almost equal?

3. Now for something completely different. A mathematical mystery! (This result was published last year in a paper by Sondow, and has been summarized as part of John Baez's weekly posting )

The result is simply three formulae that give the values of pi , the natural exponent e, and Euler's constant γ.

       2  1/1      22   1/2     23 × 4  1/3       24 × 44    1/4
e =  ( - )     ( ----- )     ( ------- )     ( ------------ )     ...
     1         1 × 3          1 × 33          1 × 36 × 5

π     2  1/2      22    1/2^2      23 × 4   1/2^3          24 × 44      1/2^4
- = ( - )     ( ------ )       ( --------- )           ( ------------- )     ...
2     1         1 × 3              1 × 33                  1 × 36 × 5

 γ     2  1/2     22   1/3     23 × 4   1/4      24 × 44    1/5
e  = ( - )     ( ----- )     ( ------- )     ( ----------- )     ...
     1         1 × 3         1 × 33           1 × 36 × 5

Three completely different fundamental mathematical constants, with three nearly identical formula!


Answers to part 1:
What are the exceptions to relativity? There could be several, but these two are popular in the literature right now.
- Einstein assumes that all light travels at the 'speed of light' with no possible variation. In reality, it is possible that high energy light (x-rays, γ-rays) might travel at a different speed than mid-energy light (visible light) and than low energy light (radio waves, microwaves). This would introduce some changes to the theory, although experiments looking for this effect require the speed difference to be miniscule.
- The theory of relativity also assumes empty space, or at the least that there is just bits of stuff in an empty background. But the Higgs mechanism which provides masses for all matter requires space to be filled with a form of vacuum energy, so this assumption is not true. While the Higgs mechanism does not affect relativity, it is possible that there is a related mechanism (sometimes called the Bumblebee model) in which the particles are spinning, and their contribution to the vacuum energy (which would require the spins to align like in a magnet) would include a preferred direction along the common axis of their spin. Again, experiments require this effect to be tiny.