Sad to say it took me this long to find out that the National Ignition Facility came online in march this year!!!

http://www.wired.com/science/discoveries/news/2009/05/gallery_nif?currentPage=1

the pictures are amazingly cool looking and they are expected to finally be able to get more energy out than they put in with this one!!! In case you are wondering I checked on ITER too and they are not expecting to switch on until 2018. Makes you wonder if icf isn't the future of fusion after all.

## Tuesday, June 30, 2009

### blowing up Jupiter again

Because it has been so very long since the last time I discussed the blowing up of Jupiter on this blog I figure it is time again. Furthermore I really think it would be very healthy for me to try to make a blog post every day. Up to this point I have always been serious about the ways that one might employ in order to blow up poor Jupiter but now I think it is time to put the constraint of serious aside. I think I am going to start posting methods of blowing up Jupiter that just don't make any practical sense. For instance we could try to turn jupiter into a black hole by shooting a single extremely highly energetic proton into its atmosphere. If the proton had the kind of energy of say 10^45 J then the first particle it hit would cause a collapse into a positively miniscule black hole hurtling towards the planet giving off insanely high energy hawking radiation in every direction this black hole would probably evaporate but the high energy radiation coming out from the black hole would cause a huge pressure wave which would itself spawn multiple black holes in the pressure wave and the whole planet would become a huge explosion. Unfortunately the formation of all these tiny black holes would probably ensure that instead of collapsing into a black hole afterwards the planet would just explode and completely destroy the solar system and very probably any other system within say a few hundred light years. Jupiter is a loss then but the shockwave could very possibly cause the collapse of hundreds or thousands of stars into black holes. Admittedly this doesn't seem very appealing but it is just such a pretty picture, sending one particle into a planet to make a apocalyptic explosion.

### The weight of light continued

The previous weight of light blog piece was inspired by thinking about how big the mass of the cosmic background radiation is. As per my previous post an individual photon does not have mass but a collection of photons generally will. At any rate since the cmb is isotropically distributed that means it has a net zero linear momentum and so we can find its rest mass by the simple application of the E = mc^2 law. The cmb is basically a perfect blackbody distribution so we can use the relation u = 8pi^5t^4/(15h^3c^3) Where t is the temperature in joules. Since the cmb has a temperature of about 2.7 kelvin that translates to 3.7 x 10^-23 joules. That yields an energy density of about 4 x 10^-14 J/m^3 a quick google search provides a radius for the universe at roughly 78 billion light years. A light year = 9.4605284 × 10^15 meters so we get a volume of 4/3*Pi*r^3 = 4/3*Pi*(78000000000*9.4605 x 10^15)^3 = 1.6 x 10^81 m^3 So multiplying the two gives a value for the total energy content of the cmb which is 6.4 X 10^67 J. Translating this into Kg we get m = 7.1 x 10^50 Kg.

The mass density of visible matter in the universe is estimated at 3 x 10^-28 kg/m^3 so the total mass of the visible matter using the above given value for the volume of the visible universe gives a mass of 4.8 x 10^53 Kg. So the cosmic background radiation weighs in at about a thousandth of the mass of visible matter in the universe but still a not insignificant contribution to the overall mass. Anyway I thought it would be fun to post t3h calculation.

The mass density of visible matter in the universe is estimated at 3 x 10^-28 kg/m^3 so the total mass of the visible matter using the above given value for the volume of the visible universe gives a mass of 4.8 x 10^53 Kg. So the cosmic background radiation weighs in at about a thousandth of the mass of visible matter in the universe but still a not insignificant contribution to the overall mass. Anyway I thought it would be fun to post t3h calculation.

### We Won!!!!

I can't believe I forgot to put up a post about this. We won the pacman competition our team came out on top over berkeley and I didn't have to take the final in AI. I'd write a more detailed story but its late and I am going to bed.

## Monday, June 29, 2009

### The weight of light

It is a fairly commonly known fact that the photon has no mass. While this is true for a single photon it is not necessarily true for collections of photons. Lets take a step back for a moment and say what we mean when we say "rest mass". In both Newtonian dynamics and relativity the energy of an object is a function only of its velocity. In Newtonian dynamics the zero for the energy scale is determined arbitrarily and only changes in energy have meaning. In other words it doesn't matter whether you say a baseball going 2m/s has an energy of 4 joules or -10 joules all that matters is that when the ball goes from 2m/s to 4m/s the energy of the ball goes from 4 to 16 or from -10 to 2. Once a zero was picked for the energy scale you could talk about changes in energy and that was all that mattered. Relativity changed all that because in relativity there is a more absolute meaning to energy. I don't remember the derivation but the end of the story is that the equation E^2 = (pc)^2 + (mc^2)^2 holds. Here p is momentum m is mass E is energy and of course c it goes without saying is the speed of light. Solving this equation for mass you get m = c^-2 * sqrt(E^2 - (pc)^2) Just like for any other particle light obeys the relation p = h/L where L is its wavelength. Also E = hf and f = 1/T = c/L so

E = hc/L plugging this in to the first equation we get that m = c^-2*sqrt((hc/L)^2 - (h/L * c)^2 = 0 and all is well. So you might think that the mass of a system of 2 photons would also be massless 0 + 0 = 0 right? Well... maybe and maybe not. A single photon had no mass because it just so happened that for a photon E = pc so E^2 - (pc)^2 = 0. But when you consider a system of 2 photons while its energy is just the sum of the energies of the two particles the momentum of the system is the vector sum of the two momenta. So if you have two photons of the same wavelength moving exactly opposite of each other then you get 0 momentum for the system. Now you find that the system of 2 photons does indeed have mass!! m = 2*h/(cL).

So here is the big idea I want to know what happens when two photons traveling perfectly parallel to one another with one in front of the other by a little distance hit a mirror. At first they are traveling with each other so their momenta add and we have a system with 0 mass. But after the first photon hits the mirror and gets reflected we now have a system with mass because now their momenta cancel. This is where an awesome experimental setup comes into play. The LIGO setup is built in order to be an incredibly sensitive instrument for the direct detection of gravity waves. This is done by making a gigantic perfectly tuned michelson inferometer. You watch the fringe on the inferometer and look for changes. Theoretically if there are no gravity waves there shouldn't be any changes to the fringe but of course because the thing is so damn sensitive it actually picks up vibrations from people walking around a mile away and stuff like that. Fortunately the changes in the fringe from local vibration and what you would see from a gravity wave are different. Now the thing is that we still haven't detected a gravity wave with the LIGO. So here is the deal why not try and make a gravity wave right smack on top of the damn thing? The idea is to shove an extra little laser pulse on top of the continuous beam already circulating in the inferometer. every time the laser pulse passes we add a little bit to it. The laser pulse would have to be extremely brief and extremely powerful in order for it to make a measurable g-wave. I don't really have the necessary knowledge to know exactly how powerful it would have to be to be detectable but as the wave began to hit a mirror its mass would increase to a peak as half the pulse has been reflected and then go back to zero as the rest of it got reflected. The mass generated by the pulse even at its peak would be absolutely minute but it would go from 0 to full mass in the tiniest fraction of a second. I don't know if that violence would be enough to make a measurable gravity wave either. The point is it is a totally freaking awesome idea. Use the device built to detect gravity waves to make them!!!!

To put things in perspective the gravity wave would be extremely extremely weak. Even assuming we could get the total energy in the burst to be somewhere around the order of a petajoule the mass generated by the pulse would be about a ten thousandth of a gram. So a bounce event at one of the mirrors would be something like a mote of dust appearing and vanishing in the tiniest fraction of a second. Now on top of the absolutely tiny mass we are faced with an additional 11 orders of magnitude or so coming from the gravitational constant. So even a petawatt burst would probably not be enough.

Actually I just realized that I've been ignoring the fact that the momentum from the light being reflected goes into the mirror so when you consider the mirror and photons as a system the total rest mass is unchanged. so the whole idea is dead in the water. Still though it was an interesting thought.

E = hc/L plugging this in to the first equation we get that m = c^-2*sqrt((hc/L)^2 - (h/L * c)^2 = 0 and all is well. So you might think that the mass of a system of 2 photons would also be massless 0 + 0 = 0 right? Well... maybe and maybe not. A single photon had no mass because it just so happened that for a photon E = pc so E^2 - (pc)^2 = 0. But when you consider a system of 2 photons while its energy is just the sum of the energies of the two particles the momentum of the system is the vector sum of the two momenta. So if you have two photons of the same wavelength moving exactly opposite of each other then you get 0 momentum for the system. Now you find that the system of 2 photons does indeed have mass!! m = 2*h/(cL).

So here is the big idea I want to know what happens when two photons traveling perfectly parallel to one another with one in front of the other by a little distance hit a mirror. At first they are traveling with each other so their momenta add and we have a system with 0 mass. But after the first photon hits the mirror and gets reflected we now have a system with mass because now their momenta cancel. This is where an awesome experimental setup comes into play. The LIGO setup is built in order to be an incredibly sensitive instrument for the direct detection of gravity waves. This is done by making a gigantic perfectly tuned michelson inferometer. You watch the fringe on the inferometer and look for changes. Theoretically if there are no gravity waves there shouldn't be any changes to the fringe but of course because the thing is so damn sensitive it actually picks up vibrations from people walking around a mile away and stuff like that. Fortunately the changes in the fringe from local vibration and what you would see from a gravity wave are different. Now the thing is that we still haven't detected a gravity wave with the LIGO. So here is the deal why not try and make a gravity wave right smack on top of the damn thing? The idea is to shove an extra little laser pulse on top of the continuous beam already circulating in the inferometer. every time the laser pulse passes we add a little bit to it. The laser pulse would have to be extremely brief and extremely powerful in order for it to make a measurable g-wave. I don't really have the necessary knowledge to know exactly how powerful it would have to be to be detectable but as the wave began to hit a mirror its mass would increase to a peak as half the pulse has been reflected and then go back to zero as the rest of it got reflected. The mass generated by the pulse even at its peak would be absolutely minute but it would go from 0 to full mass in the tiniest fraction of a second. I don't know if that violence would be enough to make a measurable gravity wave either. The point is it is a totally freaking awesome idea. Use the device built to detect gravity waves to make them!!!!

To put things in perspective the gravity wave would be extremely extremely weak. Even assuming we could get the total energy in the burst to be somewhere around the order of a petajoule the mass generated by the pulse would be about a ten thousandth of a gram. So a bounce event at one of the mirrors would be something like a mote of dust appearing and vanishing in the tiniest fraction of a second. Now on top of the absolutely tiny mass we are faced with an additional 11 orders of magnitude or so coming from the gravitational constant. So even a petawatt burst would probably not be enough.

Actually I just realized that I've been ignoring the fact that the momentum from the light being reflected goes into the mirror so when you consider the mirror and photons as a system the total rest mass is unchanged. so the whole idea is dead in the water. Still though it was an interesting thought.

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