Jesse, somehow our conversation has bifurcated into 2 quite different topics, environmental concerns and fundamental physics, today I'll just talk about the physics.
On Sun, Mar 16, 2014 at 8:05 PM, Jesse Mazer <laserma...@gmail.com> wrote: > I already addressed your confusion about the implications of black hole > entropy in detail in my post at > https://groups.google.com/d/msg/everything-list/hJ9bNWqoAzI/QTrL0CopHJ8Jwhich > you never replied to. > And I never responded to it because it was incoherent, I give the following exchange as a example: John: "If there are 2 different states of the universe that could have produced things as they are now then there is no way to decide between them and history is unknowable (just as it is in the Game of Life) and the laws of physics are not reversible. Jesse: "You think in classical statistical mechanics there can't be 2 different ways to get to a given *macrostate*??? If so you are badly confused." And I'm the one who is supposed to be confused??? There is not one drop of Quantum Mechanics or probability in the Game of Life, it is 100% classical mechanics, and yet there CAN be 2 or more ways to get to a given macrostate. It's 100% deterministic so if I show you a Game of Life pattern you can calculate what it's future evolution will be (there doesn't seem to be anything analogous to chaos in the Game) but you can't figure out it's history was, or at least not a unique history. >> Today the deepest understanding of entropy comes from the study of Black >> Holes. From: >> >> http://www.phy.olemiss.edu/~luca/Topics/bh/entropy_origin.html >> >> "S [entropy ] is the log of the number of quantum mechanically distinct >> ways that the black hole could have been made, or information lost in the >> creation of the black hole" >> > > > Are you suggesting that this new "deep" understanding invalidates the > older understanding of entropy as the number of microstates for a given > macrostate, the one you yourself quoted in your last post? > I am saying that Kip Thorn, one of the world's best physicists, wrote on page 446 of his book "A Black Hole's entropy is the logarithm of the number of ways that the hole could have been made". And I'm saying that in classical physics a state can produce only one future state, but any given state can have been produced in more than one way, therefore the number of microstates in a Black Hole must equal to k times the number of states that made it where k is some constant integer. Therefore if Entropy is proportional to the logarithm of the number of microstates in a system then according to the laws of logarithms Entropy MUST also be proportional to the logarithm of the number of ways the system could have been produced. > Assuming the unitary nature of quantum mechanics is preserved so that > information is not "lost" when things fall in [into a Black Hole] > That is quite a assumption, today it's one of the greatest controversies in physics and nobody knows if that assumption is valid; see Leonard Susskind's book "The Black Hole Wars". > the number of quantum microstates that any macrostate can have NOW must > be the same as the number of initial quantum microstates in the PAST which > would have led to the current macrostate, so the number of "distinct ways > it [the current macrostate] could have been made" would be exactly the same > as the number of "distinct quantum microstates it could be in now" > So why in hell do you say Entropy is proportional to the logarithm of the number of microstates something can be in and still have the same macrostate, but it is not proportional to the logarithm of the number of ways the thing could have been produced? > > in practice, I think almost any real-world experiment you could do in an > elevator in free fall in deep space wouldn't show any divergence from the > predictions of special relativity that would be measurable by modern > equipment. > Not true. As far back as 1963 it was noticed that clocks tick slower on the first floor of the physics building at MIT than they do on the second floor, Special Relativity had no explanation for this but General Relativity did, clocks on the first floor were closer to the center of the Earth than those on the second floor and thus were in a stronger gravitational field and thus ticked slower. And today the standard GPS receiver in your car must synchronize it's internal clock with the clocks in 3 or more navigation satellites, to do this it must take into account some pretty exotic things; for example, the satellite is moving very fast so due to Special Relativity the satellite's clock will LOSE 7210 nanoseconds a day, but the satellite's clock is in a weaker gravitational field than the clock in your car because it is further from the Earth's center, so due to GENERAL RELATIVITY the clock will GAIN 45850 nanoseconds a day. Taking these 2 factors into account the satellite's clocks gains 45850 -7210 = 38,640 nanoseconds a day relative to the clock in your car. If your car GPS receiver did not take this correction into account your indicated position would drift by 6 miles each and every day, but it knows about General Relativity so it doesn't drift at all and can find its position to within a few inches. >> And by the way, according to General Relativity in addition to mass and >> energy pressure and tension can curve spacetime too. >> > > > That's true, although I would think ultimately the pressure and tension > at each point could be derived from knowledge of the mass and energy at > every point, > I once thought that too but it turns out not to be the case. Yes something under pressure (or tension) does contain more energy than something not being compressed and that does bend spacetime, but in addition to that there is a additional contribution made by pressure itself. > I'm not saying you're wrong that curvature does not depend on the > observer, of course I agree with that. I'm saying you're wrong that in the > SR case where curvature due to mass/ene/pressure/tension is negligible, > spacetime would still be curved by acceleration. > Special Relativity says nothing about gravity curving something and Einstein never even mentioned spacetime. It was a year after Einstein's 1905 Special Relativity papers came out that Hermann Minkowski introduced the idea of Spacetime, and at first Einstein didn't like Minkowski's paper at all and said it clarified nothing and was needlessly mathematical, although he soon changed his mind and embraced spacetime with a vengeance, and after working so hard it nearly killed him ten years later he discovered General Relativity. > the angle formed by 3 lasers is NOT a valid way of measuring spacetime > curvature. > Bullshit. From http://en.wikibooks.org/wiki/General_Relativity/Curvature Einstein's brilliance was to suggest that although gravity manifests itself as a force, it is in fact a result of the geometry of spacetime itself. He suggested that matter causes spacetime to curve positively. The sun, for instance warps spacetime, and it is this warping of geometry to which the planets react and not directly to the sun itself. *This is a central tenet of the General theory of Relativity*. This local curvature can be described in mathematical terms using tensor calculus, an incredibly elegant tool which provides consistent results, regardless of the chosen frame of reference." "This predicts that if a giant triangle was to be constructed around the sun, the angles at its vertices would in fact add up to more than 180o. This is easy to imagine if one thinks of the sun as warping geometry, causing the triangle to have "wonky" sides. However it is *incredibly*important to note that these lines are in fact the *straightest lines possible* (*geodesics*) in this warped geometry. These predictions can be tested, and have been to a very high degree of accuracy." > > Do you understand the difference between the coordinate-invariant > curvature of 4D SPACETIME, > Yes. Do you understand it takes TIME for a Laser beam to travel from one point to another? > In physics straight lines are defined as the path that light takes >> > > > In general "straight lines" in spacetime are defined as geodesics, > And light always takes a geodesic path in spacetime. So if spacetime is curved then triangles formed by light beams don't have 180 degrees. > Do you understand the difference between the coordinate-invariant > curvature of 4D SPACETIME, > Yes. Do you understand it takes TIME for a Laser beam to travel from one point to another and thus the number of degrees a triangle formed by light beams has involves FOUR dimensions? >> In physics straight lines are defined as the path that light takes >> > > > In general "straight lines" in spacetime are defined as geodesics, > And light always takes a geodesic path in spacetime. So if spacetime is curved then triangles formed by light beams don't have 180 degrees. > >> But it you don't like light beams and triangles for some reason then >> how do you determine if spacetime is curved or not? What's your technique? >> > > > The curvature of spacetime as a whole is defined by a metric which tells > you the proper time along any arbitrary timelike path and the proper > distance along any arbitrary spacelike path. > That's nice but I didn't ask for a definition, I asked for a technique. I repeat, If you don't like light beams and triangles for some reason then how do you determine if spacetime is curved or not? Please be as clear and specific as I have been. > Curvature can also be defined at a point using a "curvature tensor" > That's nice but I didn't ask for a definition, I asked for a technique. I repeat, If you don't like light beams and triangles for some reason then how do you determine if spacetime is curved or not? Please be as clear and specific as I have been. >> For a inertial observer or any other sort of observer for that matter, >> what part of "measure the 3 angles of a triangle and add them up" doesn't >> make sense? >> > > > For one thing it isn't measuring spacetime curvature (4-curvature), at > best it's a way of measuring spatial curvature (3-curvature). > Apparently you say that because you think Laser beams move at infinite speed so the time dimension is zero. I think light moves fast but not infinitely fast so that dimension is not zero. > Long story short, if you have lasers attached the the wall of an > accelerating elevator, this particular setup of lasers might count as a > valid way of measuring spatial curvature in *some* coordinate system, but > [...] > There are no "buts" about it, if one observer says there are not 180 degrees in a triangle then all of them do. 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