I have started a new project on Kickstarter, to spread models of the Universe. You've seen globes and models of the Moon, planets and solar system. For the cost of a latte, you will have a downloadable model of the entire Universe sitting on your desktop! The model also includes the stars and constellations of the hemisphere. Any proceeds will go toward publication costs and registration at an international conference I'm invited to. Check it out and tell all your friends!
Showing posts with label cosmology. Show all posts
Showing posts with label cosmology. Show all posts
Saturday, March 24, 2012
Tuesday, March 13, 2012
Happy 3.14!
Albert Einstein's birthday is easy for mathematicians to remember, March 14 or 3.14! The Einstein-de Sitter Universe has a "critical" density of (6 $\pi$G t^2)^(-1), a density that keeps it from collapsing or expanding without bounds. Scientists long wondered why the density is exactly this, invoking strange ideas like "inflation" to explain it.
A cosmology where GM=tc^3 actually predicts that the "critical" density is in fact the stable density. If the Universe were less than this density, matter would be created via pair production until this density were reached. For a 4-dimensional spherical Universe of mass M, initial density is just (2 $\pi$^2 G t^2)^(-1). Difference between initial and final density is the difference between 3 and $\pi$ or 4.507034%. The density of baryonic matter that has been measured by the WMAP spacecraft may be precisely predicted from pure math.
Ancient Greek mathematicians first thought that the ratio between a circle's circumference and diameter was exactly 3, then later wondered why it should be an irrational number like 3.14. Fortunately $\pi$ does not equal 3, or the matter that we are made of would not exist!
Monday, October 24, 2011
The Capitol Dome
The entrance to our hotel in Washington is in sight of the Capitol Dome. Something is universal about the spherical shape. Domes have been part of human architecture for thousands of years. The architecture of our bodies is full spherical cells. Moons, planets, stars and even raindrops form spherical shapes. Many great thinkers have thought that the Universe itself is spherical.
Blaise Pascal, one of the great mathematicians of all time, thought the Universe was spherical. "Nature is an infinite sphere of which the center is everywhere and the circumference nowhere," wrote Pascal. Edgar Allen Poe, who lived near here in Baltimore, also thought the Universe was spherical. The spherical Universe was subject of Poe's EUREKA, a prose about cosmology. Among all his great works of poetry and fiction, Poe was most proud of the little-known EUREKA.
Most prescient, Poe suggested that this spherical universe expanded from a tiny point! "From the one particld. as a center, let us suppose to be irradiated spherically--in all directions--to immeasurable but still to definite distances in the previously vacant space." 75 years later Alexander Friedmann, who was a big Poe fan, also predicted an expanding Universe.
Einstein realized that if the Universe contained enough mass, gravity would bend it into a sphere of four dimensions. He also realized that gravity would also cause the sphere to collapse, unless it were already expanding. Einstein then added a repulsive "cosmological constant" to prevent collapse. Later, when Edwin Hubble's observations showed that the Universe was expanding, Einstein considered the CC his greatest blunder.
Today it is fashionable for cosmologists to say that our Universe is flat, like the Earth. If you question cosmologists, they will first ignore you but then admit that on the large scale it must be spherical. If the Universe expanded from a tiny point, it is topologically impossible for it to be flat. The exponential expansion called inflation would have expanded the sphere so much that it would appear flat to our observations. On the largest scales, the Universe must still be spherical.
The beauty of the Capitol dome reminds us that the spherical shape is universal. Applied to the Universe, great thinkers like Pascal, Einstein and Poe considered our Space/Time to be spherical. Edgar Allen Poe made amazing predictions like an expanding universe. Einstein first proposed a cosmological constant, then considered it a great blunder. Though it is fashionable to say the universe is flat, fashions change with time.
We finish the meeting with a banquet at the Rayburn Senate Office building, close to the Capitol. As the spherical Sun disappears behind the curve of a spherical Earth, we are reminded how universal the sphere is.
Sunday, July 31, 2011
Higgs To Be Confirmed, Or Not
A headline in Christian Science Monitor confidently states:
The God Particle Existence To Be Confirmed by 2012
This refers to the elusive Higgs Boson, whose existence is predicted by the Standard Model of particle physics. The term "God Particle" was coined by physicist Leon Lederman in the 1990's while seeking funding for the Superconducting Supercollider. When that project was cancelled by the Clinton administration, it was a huge setback for US science. Physicists had to find work in other fields, like cosmology.
Since SSC was cancelled, the Large Hadron Collider has been built in Europe. Though the headline predicts a discovery, so far LHC has found no Higgs. The phase space it could inhabit has grown smaller. By 2012 LHC may have found no Higgs at all.
In big ticket projects, there is a great danger of overconfidence. Scientists must justify their funding by predicting what they will discover. Gravity Probe B was designed to find evidence of relativistic frame dragging. Though the data proved difficult to separate fr noise, Grav Probe 's operators concluded that they had confirmed relativity. There is great pressure to skew the results toward a preselected discovery.
Since the SSC was cancelled, many physicists moved into studies of the Universe. In the late 1990's they claimed discovery of a repulsive "dark energy" causing the universe to accelerate. Following the habits of Physics, they developed a "standard model" for cosmology. Results of other experiments, such as WMAP, were interpreted as confirming the model. As in the Higgs search, there is great danger of overconfidence. Future experiments may confirm that "standard models" are wrong.
The God Particle Existence To Be Confirmed by 2012
This refers to the elusive Higgs Boson, whose existence is predicted by the Standard Model of particle physics. The term "God Particle" was coined by physicist Leon Lederman in the 1990's while seeking funding for the Superconducting Supercollider. When that project was cancelled by the Clinton administration, it was a huge setback for US science. Physicists had to find work in other fields, like cosmology.
Since SSC was cancelled, the Large Hadron Collider has been built in Europe. Though the headline predicts a discovery, so far LHC has found no Higgs. The phase space it could inhabit has grown smaller. By 2012 LHC may have found no Higgs at all.
In big ticket projects, there is a great danger of overconfidence. Scientists must justify their funding by predicting what they will discover. Gravity Probe B was designed to find evidence of relativistic frame dragging. Though the data proved difficult to separate fr noise, Grav Probe 's operators concluded that they had confirmed relativity. There is great pressure to skew the results toward a preselected discovery.
Since the SSC was cancelled, many physicists moved into studies of the Universe. In the late 1990's they claimed discovery of a repulsive "dark energy" causing the universe to accelerate. Following the habits of Physics, they developed a "standard model" for cosmology. Results of other experiments, such as WMAP, were interpreted as confirming the model. As in the Higgs search, there is great danger of overconfidence. Future experiments may confirm that "standard models" are wrong.
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