 # George Jones

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## Everything posted by George Jones

1. The LIGO detectors respond to amplitude, not intensity. This means that the sensitivity the detectors falls as 1/r, not 1/r^2. I have attached an interesting (but somewhat technical) discussion of this. GW Detection.pdf
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• 2. The developments in decoherence over the last have few decades have been tremendously important and enlightening, but for me (and my limited understanding), these developments haven't reduced quantum weirdness to zero. The way I understand it, decoherence takes a quantum state to a statistical mixture of classical states, but it doesn't say how a particular classical state is chosen from the classical mixture. Also (more technically), during decoherence, a quantum superposition evolves into a diagonal density matrix, but different classical mixtures correspond to the same diagonal density matrix.
3. Here is a visual simulation of this merger:
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• 4. You're right, I also should have considered (spatial) momentum. This prohibits a single heavier free particle at rest from decaying into a single lighter free particle in motion. Standard quantum field theory together with the standard model of elementary particles explains how a protons can change into neutrons. Just as maths allows changing A = B + C + D into A - C = B + D, physics allows the electron to be "taken to the other side" in the above process. When this is done, the electron becomes an antimatter electron (positron) "on the other side" (the equivalent of C changing to -C in the maths example). Then, proton + anti-neutrino -> neutron + positron when the anti-neutrino is energetic enough. This is the inverse beta decay to which Andrew referred above.
5. In a certain of units, the mass of a proton is 938.3, and the mass of a neutron is 939.6. (Which units?). Consider neutron -> proton in a reference frame in which the neutron is at rest. In relativity, there can be transformations between energy and mass, so this process can conserve mass/energy if the proton is moving, and hence has mass and kinetic energy. This process does not conserve electric charge, as the total electric charge on the left side of the above process is zero, while the electric charge on the right is +1. Try neutron -> proton + electron Now, mass/energy and electric charge can be the same on both sides of this process, i.e., can be conserved. There is still a problem, though. Lepton number is different on the two sides of the process. A lepton is a particle that does not feel the strong nuclear force, and that has a certain type of spin. Since both neutrons and protons feel the strong nuclear force, they are not leptons, and they both have lepton number zero. An electron is a lepton, because it does feel the strong nuclear force, and it has the right type of spin. The lepton number of an electron is plus one. Consequently, the lepton number on the left is 0, while lepton number on the right side of the process is 0 + 1 =1. Try neutron -> proton + electron + anti-neutrino A neutrino is also a lepton with lepton number +1, so an anti-neutrino has lepton number -1. Now mass/energy, electric charge, and lepton number are all conserved, i.e., are the same on both sides of the process.
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• 6. Since a proton has less mass than a neutron, a free proton, on its own, cannot decay into a neutron. A free neutron, can, however, decay into a proton. Let's do this case first. After that, proton into a neutron.
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• 7. What is the mass of a proton? What is the mass of a neutron?
8. As some others already have said, the Big Bang singularity is not a point. A small, good, non-technical (but still difficult) book on singular spacetimes is "The Edge of Infinity" by Paul Davies. Speaking very loosely
9. Welcome to SGL! Back in 2005-2006, I lived in Brandon for a year.
10. I don't know Stephen Hawking, but I did go out on a glacier with him.
11. I posted the results of a full GR evaluation above, i.e.,
12. See also the post and discussion at cosmologist Peter Coles' blog, https://telescoper.wordpress.com/2016/10/26/a-non-accelerating-universe/ including comments by Nobel laureate Brian Schmidt.
13. What is Newton's version of Kepler's third law?
15. The weight felt by the hovering astronaut is W = WN * sqrt( 1 + (Rs) / h ) , where Rs = 2 * G* M / c^2 is the Schwarzschild radiaus, WN =G * M * m /(Rs + h)^2 is the astronaut's Newtonian weight, and h is the height above the Schwarzschild radius.
16. Imagine that that an astronaut uses a powerful rocket to hover at constant height (here, 1000 km) above the black hole. Then, the astronaut will have an (apparent) weight. Newtonian gravity works well for the solar mass black hole, but it looks like Newtonian gravity is off by several orders of magnitude for the large black hole, and Einstein's gravity must be used to find the weight in this case. Still, the weight of the astronaut hovering above the large black hole seems to be much, much smaller than the weight of the astronaut hovering above the solar mass black hole. I have to go shovel 10 cm of snow off the driveway, but I hope to post a little math later.
17. Since the 1000 km height is larger than the Schwarzschild radius of the Sun, but smaller than the Schwarzschild radius of the billion solar mass object, this is not easy to predict with arguments like: this goes like this, and that goes like that, and therefore the answer scales as ... I have derived an expression on my board (probably with mistakes), but I haven't run the numbers. Anyone interested in seeing the math?
18. Piero, as an elaboration on the post by Dave S, you might try the "Characteristics" section of https://en.wikipedia.org/wiki/Proxima_Centauri
19. Actually, the only (standard model) type of universe that has a Hubble constant that is constant in time is a universe that not only has accelerating expansion, but that has exponentially accelerating expansion. The different studies use different methods to measure the parameters of standard models of the universe. Once these parameters are measured, they can be used to calculate a value for what the Hubble parameter is right now. The different methods produce different values for the cosmological parameters, and thus calculate different values for the present Hubble parameter.
20. For my attempt (probably quite confusing) at giving a concrete example of this, see
21. Now that I have run the numbers, I think that you are right, there are more Big Bang neutrinos in us than solar neutrinos. Each cubic centimetre of us contains 112 x 3 = 336 Big Bang neutrinos. For comparison to solar neutrinos, I had to do a bit of a calculation. According to https://en.wikipedia.org/wiki/Solar_neutrino 7 x 1010 solar neutrinos stream through each square centimeter every second (at the Earth). Dividing this number by the speed (in cm per second) of the solar neutrinos (very nearly the speed of light) gives the number of solar neutrinos per cubic centimetre (maths motivation at bottom), (7 x 1010) / (3 x 1010) = 2.3 solar neutrinos per cubic centimetre. No, my intuition was wrong. Thanks. Technical Motivation Because the Earth is so far away from the Sun, at the Earth, solar neutrinos all move in (almost) the same direction. Imagine a cube that is 1 cm on each side. Start with an empty cube that is oriented so that all neutrinos stream in through one face (a square centimeter). Neutrinos start to stream out the opposite face after the time T that it takes a neutrino to cross the one centimeter distance between the front and back faces. After this time T, the ciube is "full", because if we wait any longer, neutrinos will start to stream out the back face. Time T is distance (1 cm) divided by speed ((3 x 1010 cm/s). The number of neutrinos in the cube (1 cubic centimetre) is time T multiplied by 7 x 1010 solar neutrinos per square centimetre per second.
22. At any instant, we have in us about 20 or 30 million neutrinos that were produced shortly after the Big Bang.
23. Short answer: Nuclear reactions produce neutrinos, and nuclear fusion in the Sun produces almost all the neutrinos that stream through us. If we know the rate of nuclear reactions in the Sun (that, e.g., produces the observed energy output of the Sun), and we know the distance from the Sun to the Earth, we can calculate the number of solar neutrinos that stream through us.
24. A galaxy that supposedly consists almost entirely (99.99%) of dark matter has been discovered. http://www.wired.co.uk/article/dark-matter-galaxy-dragonfly-44 https://www.newscientist.com/article/2102584-ghost-galaxy-is-99-99-per-cent-dark-matter-with-almost-no-stars/
25. also, the Gimli Glider! http://blogs.wsj.com/speakeasy/2013/07/23/gimli-glider-pilot-recalls-landing-without-engines-30-years-ago/ https://en.wikipedia.org/wiki/Gimli_Glider
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