Friday, July 31, 2009

Wind Robots

I found out about this two years ago but I still think Theo Jansen is the man.

video

Wednesday, July 15, 2009

Not math/physics related but still cool:
wiki wiki

Tuesday, July 14, 2009

Mirror Matter

Imagine a universe like ours only all particles are replaced with antiparticles, left and right are reversed, and the direction of motion for all particles is reversed. Don't think too hard; such a universe would be indistinguishable from ours by the laws of physics. The same would be true if we left out the last condition. That is, life would be exactly the same for people who were our mirror images and were made out of antimatter.

If the laws of physics are unchanged under all three laws, and under only the first two, it must also be true that they are unchanged under the third condition only (Perform all three operations, then perform the first two). This means that a universe in which all is the same except for the direction of motion (i.e. the direction of time) is identical to ours. Einstein's special relativity implies such observers, which can best be shown through representation in Minkowski spacetime. Minkowski spacetime is a four dimensional manifold in dimensions, x,y,z, and ct where c is the speed of light. In the image below, as is commonly done, the dimension z is omitted so we can visualize the manifold. The speed of light determines the boundaries.
For an event at (0,0,0), any observer in our universe is represented by a point in the upper cone. For all observers whose spacetime coordinates fall in the lower cone, time is reversed.

Such transformations demonstrate the symmetry of our universe. For anything to be symmetrical, you must be able to exchange the (two) parts without changing anything. Upon the observation that subatomic particles called neutrinos only spin left, a theory of mirror matter was formed, by which every particle has a mirror "twin" that spins in the opposite direction, restoring the symmetry. Such particles would be invisible to us, as our photons (light particles) all spin in one direction, allowing us to see only half of the predicted particles.

Although these particles would be invisible to us and have little to no effect on our universe, they would be affected by gravity (the weakest force, but the only force that is not exchanged through particles, by modern physics). But if that's the case, how could we still not know whether mirror matter actually exists? Many people believe that "dark matter," hypothetical matter that is undetectable by its emitted radiation but effects visible matter via gravity, is in fact mirror matter. Dark matter is postulated to explain missing mass in our galaxies, and may account for more than half of the matter in our universe. Observations of the rotational speeds and temperature distribution of galaxies strongly suggest dark matter's existence.

Just to be clear, there is no "mirror universe," mirror matter would exist in our space-time. In fact, Robert Foot also suggests in his book "Shadowlands: Quest for Mirror Matter in the Universe" that meteorites of mirror matter may collide with our Earth, causing catastrophic events, that seem unexplained. He gives an explosion in Siberia in 1908 as an example, among 6 others. Also, he claims that it is likely that many planets which we perceive as starless, are in fact rotating stars composed of mirror matter.

Perhaps the most interesting thing about mirror matter is that if mirror matter does exist, it is likely that time is reversed for such matter. Meaning left and right would be reversed, and so would time. And although there is no mirror universe, mirror matter should have the same physics as observed matter. This is a result of the fact that our laws are unchanged by the direction of time as long as everything in the system stays consistent. And in fact, reversing time does change the spin from left to right. If a neutrino were coming towards you, it would be spinning left (clockwise), meaning if it were moving away from you, as if the event had been rewound like a VHS, it would appear to be spinning counterclockwise.

Presuming symmetry has led to several discoveries in physics. Consequently several types of matter have been proposed to preserve symmetry:

1. Antimatter
  • A new form of matter necessary to make Einstein's theory of relativity consistent with the quantum mechanical theory of the electron.
  • Predicted by Dirac who noticed that the mathematical description of the electron would only exhibit Lorentz symmetry (the four dimensional rotational symmetry of space-time) if such matter existed.
  • Particles have the same masses as their corresponding anti-particles.
  • Has been experimentally verified.

2. Supersymmetric partner particles
  • Necessary for String theory to accurately describe our universe.
  • Particles have the same mass as their superpartners, although broken symmetry causes the mass of superpartners to be so high that these particles could only be seen at very high energies.
  • Particles also have the same charge as their superpartners.
  • One superpartner is a fermion (a particle with half integer spin, which as far as we know is always a matter particle) and the other is a boson (a particle with integer spin, typically a force carrying particle).
  • Has not been experimentally verified but may be in the next decade using the Large Hadron Collider.

3. Mirror Matter
  • Developed to preserve symmetry despite the fact that most fundamental particles are left-handed.
  • Mirror particles interact with ordinary particles via gravity only.
  • Has not been experimentally verified but poses as an interesting solution to what dark matter is.

My question: Is the theory of mirror matter inconsistent with String theory by which the force of gravity is in fact carried by a particle, the graviton? Can both theories be correct? If not, what is more likely: that gravity is in fact the only force not carried by a particle, or that our universe despite possessing many symmetries is overwhelmingly unbalanced in favor of left-handed particles?

Foot says "The prospect that the most natural symmetry imaginable -- mirror symmetry-- is not a symmetry of nature, while every other obvious symmetry such as rotational symmetry and translational symmetry are indeed symmetries seems rather surprising to say the least." Then again it also seems surprising that all of the fundamental forces besides gravity can be unified.

Foot can't seem to promote his own theory without undermining supersymmetry and String theory. But I like both.

Thursday, July 9, 2009

Hypercubes

I've been planning a "mirror matter" post for a while now but it's so fun to research that I haven't had the discipline to write about it. Hopefully I'll get around to it soon.

In the meantime, I've been reading "Surfing Through Hyperspace" by Clifford Pickover. It might be the strangest book I've ever read, but it does pose some very interesting questions. The book deals with understanding higher dimensions through a second-person narrative science fiction story interspersed with more technical explanations. There is an emphasis on 4-dimensional beings and what it would be like to interact with them. We would only see 3-dimensional blobs changing in size. But a 4-dimensional being looking at us would be able to see everything; they would be able to look at us inside and out all at once. A 4-dimensional being would be much like a god: able to see and hear everything at once; would be incapable of being seen; and it would have miraculous powers, like the ability to remove a tumor without making a single incision. I found it interesting that immediately after, Pickover pointed out that a 4-d being could also impregnate a virgin.

Later on, he discusses hypercubes: 4-dimensional cubes. I've seen pictures of 4-dimensional cubes projected into 2-dimensions. I used to draw them all the time when I was bored in class.
But he also gives beautiful images of 5-d, 6-d, 7-d, and 8-d cubes projected into two dimensions, that I've actually never seen before.

A 5-dimensional cube:
A 6-dimensional cube:
A 7-dimensional cube:
and, an 8-d cube:
What I found even more interesting was a graph he gave of the volume of a radius 2 sphere as a function of dimension.
The x-axis corresponds to the number of dimensions of the sphere, and the y-axis, to the volume of the sphere. The peaks occur at different places depending on the radius of the sphere.

Thursday, July 2, 2009

Wiki Wednesday

Every week I remember to, I plan on sharing a cool wikipedia page, cause there are so many.