Friday, April 30, 2004
Tuesday, April 27, 2004
Amazing huge surf movies - got the link from futurehi which I'm thinking about writing for.
I also found a great mathematical physics blog by John Baez.
I also found a great mathematical physics blog by John Baez.
Sunday, April 25, 2004
I really like this picture of a forest dragon that Allison took in Australia.
So, getting back to the Lee Smolin visit. OK, he builds on the idea that collapsing black holes could have Bojowald bounces through the singularity, thus seeding baby universe big bangs, furthermore if the fundamental constants change slightly at each bounce, then those universes that have conditions best suited to produce more black holes will dominate the counting, and you would expect to find yourself in a universe with physical constants at least close to a local maximum for producing as many black holes as possible. Indeed it appears we do - one indicater is the masses of neutron stars - the lower the upper bound the better, and all observed so far do have the low value of 1.4 solar masses. Also the nuclear chemistry in stars leads to heavy element production in large stars, which is good for both life and black hole production...
That said, Lee didn't really push his theory very hard - because the fine details aren't there yet at all. For instance, in string theory the physics is determined by the geometry of the compactification of the higher dimensions. This geometry would melt at each bounce, so it's not clear in what manner it recrystallizes afterwards, and whether it would likely be similar to the previous compactification (good for evolutionary cosmology), or completely random (bad - and seems more likely...).
So, getting back to the Lee Smolin visit. OK, he builds on the idea that collapsing black holes could have Bojowald bounces through the singularity, thus seeding baby universe big bangs, furthermore if the fundamental constants change slightly at each bounce, then those universes that have conditions best suited to produce more black holes will dominate the counting, and you would expect to find yourself in a universe with physical constants at least close to a local maximum for producing as many black holes as possible. Indeed it appears we do - one indicater is the masses of neutron stars - the lower the upper bound the better, and all observed so far do have the low value of 1.4 solar masses. Also the nuclear chemistry in stars leads to heavy element production in large stars, which is good for both life and black hole production...
That said, Lee didn't really push his theory very hard - because the fine details aren't there yet at all. For instance, in string theory the physics is determined by the geometry of the compactification of the higher dimensions. This geometry would melt at each bounce, so it's not clear in what manner it recrystallizes afterwards, and whether it would likely be similar to the previous compactification (good for evolutionary cosmology), or completely random (bad - and seems more likely...).
Thursday, April 22, 2004
Mothers Against Boomerangs! - my parents should bring me one back from Australia. Also want to try posting pictures see how this goes:
Seems to work well!
More good news - I got the Space Grant! And I also got into the Gmail beta! Woot!
More thoughts on physics to come - i.e. Lee Smolin's talk on Monday...
Seems to work well!
More good news - I got the Space Grant! And I also got into the Gmail beta! Woot!
More thoughts on physics to come - i.e. Lee Smolin's talk on Monday...
Saturday, April 17, 2004
I think it's about new right now too, or getting close. The APOD picture for Saturday got to me - we really have been up there and walked around on it. We need to return.
Hmmm, this Fermi energy thing has me thinking about black hole singularities... With Quantum Loop gravity it is concievable that you could avoid the mathematical singularities from classical General Relativity by having discrete nodes in space, perhaps then all the particles that fall into a black hole would be compressed together in a volume a couple Planck lengths long - but then what about the fermi energy due to the exclusion principle? - it would be vastly larger than the original mass.... More later...
Not surprisingly my 1 kg holographic-principle-breaking neutron black hole doesn't work - for a cold dense Fermi gas, the Fermi energy is hbar^2/mass*(6pi^2/v)^2/3, where v is the reciprocal of the number density v=V/N where V is the volume and N the number of particles. For a kilograms worth of neutrons squeezed down almost to its schwarzchild radius (10^-27 meter), the Fermi energy for the quarks becomes an absurd 700 trillion kilograms. Thus the combined weight of the now ultra-relativistic quarks would be about that of the Milky Way.
Here's a cool math site - integers are laid out on a line with even spacing, and the line is spun to form a spiral, and there are emergent lines with high prime densities...
Tuesday, April 13, 2004
Smash Hit Tom from Plastic pointed me to this cool link which gives simple numerical results for collisions of asteroids with the earth. Needs to be a 3-D hydrodynamic code though, so you could make a movie of the results...
Trying out the new feature on BoingBoing that links to blogs that link to stories on BoingBoing, which I often do. Since linking to the actual news item on BB that states this is just too damn meta, I'll link to the next link which is some amusing pictures Cory took of a graveyard in England.
Monday, April 12, 2004
This Link shows the most recently updated pictures to livejournal blogs - can be really funny and occasionally NSFW.
More on the holographic principle and black holes from a conversation with Tobin Fricke on Live Journal.
There is a theory going around - the holographic principle - that the amount of information that can be stored in a region goes as the surface area of the region (let's just say a sphere) and NOT the volume. For instance this meshes with black hole thermodynamics - the temperature is related to the mass (inversely - a black hole's Hawking radiation has an average wavelength the size of the black hole, so a solar mass black hole would emit 1.5 kilometer radio waves - i.e. it would be much colder than the current microwave background) and thus to the surface area of the event horizon. Another derivation is given by UNC's own Jack Ng and Hank Van Dam - gr-qc/0403057 - check it out, it's an easy read. Thus my instinct when presented with something like this is to try and break it - and since the volume grows much faster than the surface area it seems like you should take a giant volume and then cram as much matter (and thus info) inside it as possible. The problem is that a black hole's radius grows that much quicker - the event horizon is linear in mass: R=2M (G=c=1). Thus very large black holes have very low average densities - indeed as I found (trivial really), current intergalactic densities give a black hole radius of about the radius of the visible universe. So to break the volume/area thing you actually want to go to small volumes or else you'll form black holes immediately. Let's see, the earth has a mass of about 10^25 kg, which is 10^52 protons, and a Schwarzchild radius of about 1cm, and Lplanck = 10^-33 cm, so there are 10^66 Planck lengths squared on an Earth sized black holes - no good. Hold on, matter at nuclear densities also won't work no matter how small, but taken at schwarzchild radius density... OK 1 kg of neutrons is ~10^27 particles, with a RBH~10^-27 meter = 10^7*Lplanck, so there are ~ 10^15 possible bits on the horizon according to the holographic principle, but 1 bit/neutron would bit 10^27 bits! You can beat it at tiny volumes! I'm going to have to look at this more, but the densities here are much higher than nuclear density - not that this would stop a theorist! Thanks for getting me back onto this Tobin! I'll see if the details pan out... For one thing it would be a quark-gluon plasma, not neutrons - but I don't think the binding energy mass would increase much - only gets big when you try to separate them. Ah, but they are fermions - degeneracy pressure would push the temperature and energy way up - have to check it out.
Oh yeah, and we're not in a black hole because there must be matter beyond our visible horizon at 13.7 billion light years - can tell that because from measuring the CMB radiation we know space is very flat. If it was a vacuum outside, our visible universe would collapse to a singularity in time T=pi/2*(3/(8*pi*G*rho))^1/2, rho~10*10^30*10^11*10^11/(10^10*10^16)^3=10^-25kg/m^3, so T=2*10^17 seconds, which, I'll be damned, is about the age of the universe. But then the metric for a collapsing ball of dust is the same as the Freidmann-Robertson-Walker metric, so maybe I shouldn't be surprised. Huh. So the evolution of the universe forward from the big bang really is very similar to a black hole collapse. Lee Smolin has the idea that collapsing black holes seed new baby universes - then if the physical constants can change at each singularity the system will evolve towards universes that have physical constants most favorable to the formation of lots of new black holes - these will dominate the counting. That's looking even clearer to me now. I can't wait to talk to Lee on Monday, he's coming to give a colloquia. I need to really go back and look at Martin Bojowald's singularity evolution code...
There is a theory going around - the holographic principle - that the amount of information that can be stored in a region goes as the surface area of the region (let's just say a sphere) and NOT the volume. For instance this meshes with black hole thermodynamics - the temperature is related to the mass (inversely - a black hole's Hawking radiation has an average wavelength the size of the black hole, so a solar mass black hole would emit 1.5 kilometer radio waves - i.e. it would be much colder than the current microwave background) and thus to the surface area of the event horizon. Another derivation is given by UNC's own Jack Ng and Hank Van Dam - gr-qc/0403057 - check it out, it's an easy read. Thus my instinct when presented with something like this is to try and break it - and since the volume grows much faster than the surface area it seems like you should take a giant volume and then cram as much matter (and thus info) inside it as possible. The problem is that a black hole's radius grows that much quicker - the event horizon is linear in mass: R=2M (G=c=1). Thus very large black holes have very low average densities - indeed as I found (trivial really), current intergalactic densities give a black hole radius of about the radius of the visible universe. So to break the volume/area thing you actually want to go to small volumes or else you'll form black holes immediately. Let's see, the earth has a mass of about 10^25 kg, which is 10^52 protons, and a Schwarzchild radius of about 1cm, and Lplanck = 10^-33 cm, so there are 10^66 Planck lengths squared on an Earth sized black holes - no good. Hold on, matter at nuclear densities also won't work no matter how small, but taken at schwarzchild radius density... OK 1 kg of neutrons is ~10^27 particles, with a RBH~10^-27 meter = 10^7*Lplanck, so there are ~ 10^15 possible bits on the horizon according to the holographic principle, but 1 bit/neutron would bit 10^27 bits! You can beat it at tiny volumes! I'm going to have to look at this more, but the densities here are much higher than nuclear density - not that this would stop a theorist! Thanks for getting me back onto this Tobin! I'll see if the details pan out... For one thing it would be a quark-gluon plasma, not neutrons - but I don't think the binding energy mass would increase much - only gets big when you try to separate them. Ah, but they are fermions - degeneracy pressure would push the temperature and energy way up - have to check it out.
Oh yeah, and we're not in a black hole because there must be matter beyond our visible horizon at 13.7 billion light years - can tell that because from measuring the CMB radiation we know space is very flat. If it was a vacuum outside, our visible universe would collapse to a singularity in time T=pi/2*(3/(8*pi*G*rho))^1/2, rho~10*10^30*10^11*10^11/(10^10*10^16)^3=10^-25kg/m^3, so T=2*10^17 seconds, which, I'll be damned, is about the age of the universe. But then the metric for a collapsing ball of dust is the same as the Freidmann-Robertson-Walker metric, so maybe I shouldn't be surprised. Huh. So the evolution of the universe forward from the big bang really is very similar to a black hole collapse. Lee Smolin has the idea that collapsing black holes seed new baby universes - then if the physical constants can change at each singularity the system will evolve towards universes that have physical constants most favorable to the formation of lots of new black holes - these will dominate the counting. That's looking even clearer to me now. I can't wait to talk to Lee on Monday, he's coming to give a colloquia. I need to really go back and look at Martin Bojowald's singularity evolution code...
Posted this over at LiveJournal on the connection between General Relativity and gravitons.
Yeah, gravitons and Classical GR are somewhat disjoint. In GR you can assume weak feilds (chap 18 in Gravitation, or MTW as we call it), i.e. guv=nuv+huv where g is the metric (u,v indices) n is the metric for flat space - Minkowskian - and h is a pertubation on n, with |h|<<|n|. You can then get various things out of h, like Newtonian gravity (laplacian psi = rho...) and then post-newtonian effects (precession of Mercury's orbit, gravitational redshifting and time dilation - and hopefully frame dragging will be detected shortly with Gravity probe B). Using a 'Lorentz' gauge, you can also get box(h)=T, i.e. the wave equation. So in the weak field limit you can think of h as a separate field on top of a flat background, and you quantize just h (creation and annhilation operators for quanta of h with certain momentum), and this spin 2 field is the graviton, all of this following the standard prescription of quantum field theory for QED and so on. Note in string theory also you have this spin-2 h field on top of a fixed background metric. So String theory will not be the final theory, we'll probably also need to unite it with quantum loop gravity for the strong field limit, although this is probably premature since we can't even extract the minkowski spacetime limit from quantum loop gravity yet! Not to mention classical GR needs it's strong field limit tested also, which hopefully will be done with LIGO and LISA, and it may well not hold up. Lots of people are also trying to modify GR due to dark matter and dark energy - mostly dark energy I think because gravitational lensing makes it fairly clear there are smooth galactic scale lumps of matter out there.
Yeah, gravitons and Classical GR are somewhat disjoint. In GR you can assume weak feilds (chap 18 in Gravitation, or MTW as we call it), i.e. guv=nuv+huv where g is the metric (u,v indices) n is the metric for flat space - Minkowskian - and h is a pertubation on n, with |h|<<|n|. You can then get various things out of h, like Newtonian gravity (laplacian psi = rho...) and then post-newtonian effects (precession of Mercury's orbit, gravitational redshifting and time dilation - and hopefully frame dragging will be detected shortly with Gravity probe B). Using a 'Lorentz' gauge, you can also get box(h)=T, i.e. the wave equation. So in the weak field limit you can think of h as a separate field on top of a flat background, and you quantize just h (creation and annhilation operators for quanta of h with certain momentum), and this spin 2 field is the graviton, all of this following the standard prescription of quantum field theory for QED and so on. Note in string theory also you have this spin-2 h field on top of a fixed background metric. So String theory will not be the final theory, we'll probably also need to unite it with quantum loop gravity for the strong field limit, although this is probably premature since we can't even extract the minkowski spacetime limit from quantum loop gravity yet! Not to mention classical GR needs it's strong field limit tested also, which hopefully will be done with LIGO and LISA, and it may well not hold up. Lots of people are also trying to modify GR due to dark matter and dark energy - mostly dark energy I think because gravitational lensing makes it fairly clear there are smooth galactic scale lumps of matter out there.
Amusing collection of perpetual motion devices, and some very good stereogram illusions too.
Thursday, April 01, 2004
