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    An initial to general state problem (QM Help)

    Ok, working on it a bit more I think I figured it out (amazing what taking a break for dinner may do). So I have the unnormalized eigenvectors. If I normalize them I should wind up with: \left|s_1\right> = \frac{1}{\sqrt2}\left(\begin{array}{c}0\\1\\-1\end{array}\right)...
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    An initial to general state problem (QM Help)

    1. A 3 level system starts at time t = 0 in the state \left|\psi_0\right> = \frac{1}{\sqrt2} \left(\begin{array}{cc}1\\1\\0\end{array}\right) The Hamiltonian is H = 3\left(\begin{array}{ccc}1&0&0\\0&1&1\\0&1&1\end{array}\right) If \hbar = 1 find the state \left|\psi_t\right> of the...
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    Multiple Integral question

    It has been a long while since I've done any multiple integral stuff and I must say this question posed to me has me stumped, even though I suspect it is trivial. 1. Find the volume of the of the region bounded by the first octant and x+z=3 and y+5z=15 I figure since it is in the first...
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    Apophis Strikes Earth: Odds still 1 in 45,000

    Indeed! I'd say the odds are less than 1 in 45,000 that that would happen.
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    Apophis Strikes Earth: Odds still 1 in 45,000

    This is sort of in response to an article Ivan posted in the locked Apophis thread: [Broken] The above is the url from Ivan. Below are urls to the contrary
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    My idea for Space Travel

    Well if I recall there was the idea of a gravitational tractor of sorts. You place a massive object with propulsion near the sun and slowly set it off in the direction you wish for it to go. The object moves and due to gravity the sun moves with it. This of course is incredibly slow and takes...
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    Black Hole Evaporation

    This is just like that other thread! :) As a black hole evaporates it gets hotter and hotter and radiates more and more until at roughly the planck size it just evaporates away (hence the name of the process) into a shower of high energy photons and other particles.
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    How does black hole evaporation end?

    That is why I am skeptical there will be enough energy!
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    How does black hole evaporation end?

    Might being the operative word. I'm a bit skeptical the energies will be sufficiently high enough to test black hole evaporation.
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    No magnetic fields?

    The problem per se arises when you define A as a gradient of some scalar. This would be incompatible with Ampere's law mainly because the curl of a gradient is always zero. So in this case you are specifically setting B = 0 from the start essentially.
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    Can virtual particles appear ANYWHERE?

    I would beg to differ. The evidence comes from the calculations. I suppose if you wish to get technical I will parse my language and say it provides indirect evidence since by their nature virtual particles cannot be directly observed. However, as I was taught, they arise from some of the...
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    How does black hole evaporation end?

    From what I recall the black hole continues to shrink until it reaches an effective radius on par with the planck length, at which point, as the name evaporation implies, it just 'explodes' into a lot of energy via photons and leptons, and it does this because I suppose as you said, it becomes...
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    Can virtual particles appear ANYWHERE?

    Yes, the Casimir effect provides good evidence that virtual particles do in fact occur.
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    Proof That the Universe is Electrically Neutral

    Just out of curiosity what sources are there for this, and just what do you mean by a slight imbalance? i.e how slight? 1 part per quintillion?
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    Why our time dimension is about to become space-like

    Huh, that is weird. Just when you think you've heard everything! It is an interesting idea but unless there is someway to actually test and verify it is correct it is just a curious exercise :tongue2:
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    Gaping hole found in universe is a link to the teams pre-print for their accepted paper.
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    Supernova 7000 ly away

    I should hope it corroborates. As an issue, if Eta were a binary system, then when one of the partners went supernova it would be a lot less bright than what it would be in the above examples.
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    Black Holes

    As the medium becomes denser then in general yes, the effective speed of light decreases. For example light travels fastest in a vacuum, slower in air and slower still in water. And correct, light is just an electromagnetic wave. What makes it special to us is we can see a sliver of the...
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    Gliese 581 d

    They all could be right due to a few things. When you calculate the density via M/V you are basically assuming a constant density throughout the entire planet, but usually that is a decent for a very rough approximation. I notice the article you mention is lacking citations on both the...
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    Supernova 7000 ly away

    Yes, I stand corrected on that error (two too many zeros :yuck: )
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    Black Holes

    As has been stated, your assumption is incorrect. If you look at general relativity, gravity is a manifestation of the curvature of spacetime. Light, or photons, travel along null geodesics, which are essentially a generalization of straight lines in curved space. So if a photon is traveling...
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    Supernova 7000 ly away

    Yes, but are you not forgetting to take into account several aspects when you say this: a)Extinction effects that block out a lot of light from the galactic core b)Even though we can see towards the core, that still isn't the full galaxy. At any rate, Chronos is pretty much right. At...
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    I got a physicist for Christmas!

    But they aren't scientists!! Even though I'm a physicist I still wished for a mathematician :cry: Getting an economist...follows the following equation: Economist \equiv rock
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    E = mc^2

    Actually if memory serves correctly the proper equation for it is: E_0 = m_0 c^2 E_k = \gamma m_0 c^2 \gamma = \frac{1}{\sqrt{1 - v^2/c^2}} E_t = E_0 + E_k To get really general: E^2 = p^2c^2 + m^2_0 c^4
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    I got a physicist for Christmas!

    All I got for Christmas was an economist :frown:
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    Fascinating Time-Travel Paradox

    Probably from General Relativity. As far as I know, there isn't a thing in the laws of physics that expressly prohibits it. However it may be very improbable.
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    A card game

    I got into a debate with some people I know here at university and no consensus was reached. For this hypothetical situation, there are four players playing cards. So there are 52 cards, and 4 hands. All the cards are dealt out into four equal piles of 13. What are the chances, that the...
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    Quick question travelling at c

    From the photon's point of view? I'd have to say no time at all. From a photon's point of view time might as well not exist.
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    Neutrinos back into the picture?

    Yes, that is a method for detecting neutrinos. Bravo. I'll touch on the reactor bit in the next quote. And you are still wrong about absorption/emission. If the sun were to absorp neutrinos such that it wouldn't explode, then that means all neutrinos frome very direction will push with...
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    Neutrinos back into the picture?

    That site implies that there would be one side of the earth that is going to be such that people will not have gravity as strong as the other. Again, I am still waiting for a good answer as to how neutrinos, which interact via the weak force, can in any way do something with a photon. Not only...