On Sat, Mar 22, 2014 at 6:41 PM, Jesse Mazer <laserma...@gmail.com> wrote:
> So, you admit you were wrong to object to my statement "even with > reversible laws there is more than one way to get into a given MACROstate"? > No, sometimes that would be true but because of chaos it wouldn't always be. For 2 things to be in the same macrostate small changes to the microstate must make no difference the way the things behave at the largest scale, but some systems are inherently chaotic and any change at all in them can cause a huge macro change in behavior. Some things like a box full of gas have almost no chaos and that's why the equations of thermodynamics work. Some systems like planetary motion have only a modest amount of chaos, and some systems like global weather patterns have lots and lots of chaos. > A "microstate" can be used to refer to the exact physical state of any > system, so even if the most exact possible description of a black hole told > you nothing but its mass, charge and angular momentum, you could still call > that a microstate. > Or you could call it a macrostate. If physics is not unitary (and it almost certainly is unitary) and a Black Hole really can be completely described by just 3 numbers (2 really because the charge is almost always zero) then the entire macrostate\microstate distinction starts to break down. > > It is true that if physics is non-unitary then black hole entropy could > not be defined in terms of its microstates, but that's what I already said, > that in this case there would be two different types of entropy, one for > black holes and one for everything else. > But it would remain true that if X is proportional to the logarithm of the number of microstates in a system then according to the laws of logarithms X MUST also be proportional to the logarithm of the number of ways the system could have been produced. > >>The physical laws in the Game of Life are not unitary, so a large block >> of dead cells would be equivalent to a Black Hole in our universe if the >> laws of physics were not unitary. In both cases it would be gibberish to >> talk about the microstates of a block of dead cells or of a Black Hole >> because they would have none, they would only have a macrostate. >> > > > Why would it be gibberish? The "microstate" would have the same meaning > for a block of dead cells as it would for a block with a mix of live and > dead cells, > Now that I think about it in a block that has a mixture of live and dead cells in the Game of Life I know what a microstate would mean but I'm not quite sure what a macrostate would mean. It's supposed to mean behaving the same at the largest scale even though small changes have been made, but very small changes can dramatically effect a pattern's macro behavior, some patterns die completely and will fade away to nothing, some will start to oscillate and never die, and some finite patterns will generate a infinite (not just very large but infinite) number of additional live cells. > > if macrostates are defined in terms of the ratio of live to dead cells > [...] > I think that would be such a crude measure as to be useless. The smallest known Game of Life pattern that is capable of infinite growth has only 36 live cells, but kill just one of those 36 cells or move just one of the cells one space to the right (or left or up or down) and the pattern no longer has that capability to produce infinity. The difference between finite and infinite is about as macro as you can get, so do you really want to say any 36 cell pattern has the same macrostate? > > Of course I agree the physics in our universe is almost certainly > unitary, but this whole debate about entropy got started when you suggested > the second law of thermodynamics was possible to deduce from logic alone, > Yes, even if we knew none of the fundamental laws of physics from logic alone we could deduce that there are more disordered states than ordered ones, if in addition we assume that in the distant past the universe was in a much more ordered state (please note this doesn't necessarily mean more complex) than it is now you could then deduce that something very much like the second law of thermodynamics must exist. This is unlike the first law of thermodynamics, we believe in that not because the contrary to it is illogical but simply because we've never observed it being violated and using induction we infer that we never will. > >> you've got it backwards. If the fundamental laws of physics were >> non-reversible then it would be easy to see how time could have a preferred >> direction and easy to understand why the second law of thermodynamics is >> true. >> > > > It would be easy to see why time would have a preferred direction but > this wouldn't necessarily be the direction of increasing entropy, > Huh? I don't know what you can say about time's dimension except that entropy increases and the universe expands when you move along it in one direction and entropy decreases and the universe contracts when you move along it in the opposite direction. > > you agree it's possible to have an observer that moves inertially from > top to bottom of the accelerating elevator in deep space, with no external > forces from the elevator or anything else acting on him as he travels? > Yes. > > would you also agree that if this observer had a laser emitter at rest > relative to himself, and he measured its path using his own inertial rest > frame, he would find that the laser's path was a perfectly straight line in > this coordinate system? > Yes and we've been over this before, there is no contradiction everybody agrees. You would say that a triangle formed by your lasers contained exactly 180 degrees and your friend in the accelerating elevator looking at your triangle would agree with you, it has 180 degrees. And when your friend forms his own triangle he says it does NOT have 180 degrees, and when you look at his triangle you agree with him, it doesn't have 180 degrees. > > So you are claiming that in spite of the fact that special relativity > applies here, all observers inside the elevator would still agree spacetime > is curved? > No, both you and your friend agree that your triangle was NOT drawn in curved spacetime. > >> unless you're talking about Neutron Stars the contribution caused by >> pressure is far too small to be important (it's trivial even in White Dwarf >> stars) and unless you're talking about Inflation Theory you never have to >> worry about tension. >> > > > The Misner/Thorne/Wheeler textbook I linked to indicates that there is > an exact mathematical relationship between the spacetime curvature and the > mass/energy density > Yes. What is your point? > > Of course even if one understand the Milne model to be a valid solution > to the equations of GR, it isn't an accurate cosmological description of > the real universe since the average energy density of our universe differs > non-negligibly from zero > Nor can Milne explain the cosmic frequency of abundance of hydrogen, deuterium, Helium-3, Helium-4, Lithium-6 and Lithium-7 as the Big Bang theory can. Nor can it explain the Cosmic Microwave Background Radiation much less it's polarization as Big Bang\Inflation theory can as we discovered just last week. I'm really being too kind because Milne can't explain anything at all except a universe with nothing in it. For this reason nobody is very interested in the Milne model anymore, > > I assumed that when you said "please show me a place where 3D space is > curved but 4D space-time is not" you were expressing skepticism that such a > thing is *theoretically* possible > You assumed wrong. Lots of things can be mathematically modeled in a logically consistent way, but that doesn't necessarily mean they have the slightest thing to do with the way the world actually works; you can only decide that through observation. As I clearly said I already know lots and lots of places to point my telescope at to observe gravitational lensing, those are places where spacetime is strongly curved, but I wanted you to give me the sidereal coordinates I can point my telescope to so I can observe "the Milne model" or anywhere else where 3D space is flat but 4d spacetime is curved (hell, I'll settle for the reverse, a place where 4D spacetime is flat but 3D space is curved), You are unable to supply me with such coordinates. > > Do you agree that the Milne model [...] > Enough already, I don't give a damn about the Milne model because it's transcendentally dull ! It's a trivial case, a universe with absolutely nothing in it. Zero Zilch nada goose egg. So it's true I couldn't perform my triangle test there, first of all because I'm something so I couldn't be in the Milne universe, and second because there would be no light to form the triangle, not one single photon. > >> Isn't it obvious? In General Relativity all of the field equations that >> include time as a variable also include space variables or variables that >> can be deconstructed into space, like speed, acceleration, momentum and >> energy. >> > > > I still don't see how this is relevant to the discussion, > It's relevant because if a universe has matter in it (ours does and some think that fact is rather important) and if 3D space is curved but 4D spacetime is flat (or the other way around) then one of Einstein's field equations must describe how matter filled space can be curved without making use of the time variable or properties that can be deconstructed into time , like speed, acceleration, momentum, and energy. But there is no such field equation. > > unless you are claiming that this implies that in general relativity > should be theoretically impossible to have a spacetime where the > 4-curvature is zero but the simultaneity surfaces are chosen in such a way > that 3-curvature is nonzero, > Do you even know what 3-curvature means? Do you imagine that something like the surface of a basketball is an example of 3-curvature? It isn't, that's 2-curvature, I don't believe anybody can visualize 3-curvature so when dealing with that we must rely on the mathematics. > >>I am saying that the shortest path (geodesic if you want to get fancy) >> between any two events (points in 4D spacetime if you want to get even >> fancier) is always the path that light takes. >> > > > So you are talking about actual spacetime path taken by the light, > rather than the spatial component of the path? > There you go again acting as if space can be completely segregated from time when in reality neither space nor time makes sense without the other. Remember Minkowski's words: "Henceforth space by itself and time by itself are doomed to fade away into mere shadows and only a kind of union of the two will preserve a independent reality." > > But your explanation doesn't address the specific question we were > discussing, namely whether you understand that when they say "the universe > is flat" > It means that astronomers know the maximum linear size that lumps in the Cosmic Microwave Background Radiation (CMBR) should have, 380,000 light years, and they know how long it took for light from those lumps to reach us, 13.8 billion years. So if the 4D spacetime of the universe is flat and triangles still have 180 degrees then they can use Euclid to figure out what the angular size those lumps should have, and the answer is about one degree of arc. So they then go to their telescopes and measure what the size of the arc actually is, and they find it's about one degree. So they can conclude that Euclid was right and triangles really do have 180 degrees and the universe at the largest scale is flat, or nearly so. > > they are referring specifically to the 3-curvature, not the 4-curvature. > Jesse, If time were not a variable in this , if light moved at infinite speed we would not be seeing what we are seeing now, in fact we would not be seeing the CMBR at all, the electromagnetic waves from the Big Bang would be long gone. > > I suspect you just haven't thought through your views very carefully > (you've stated plenty of standard conclusions that I doubt you understand > the detailed mathematical derivations of, like the conclusion that light > always follows a geodesic path even in curved spacetime). > An event has a position and a time, and a geodesic in space time is just the shortest path between 2 events; so saying that light always follows a geodesic even in curved spacetime is just another way of saying that nothing can travel faster than light even near and massive star where spacetime is strongly curved. And that's why such stars produces gravitational lensing. Light follows a geodesic when it goes through glass too, and light travels slower through glass than it does through air, so when light is reflected off an object and passes through glass curved like a lens the path to the focus is always a geodesic, the path the ray of light takes is not the shortest path as measured by a tape measure (it's not straight but bent toward the center of the lens) but it takes the shortest path in 4d spacetime,;or to say it more simply, light always takes the quickest path not the shortest between 2 events. So both gravitational lenses and glass lenses work for exactly the same reason, light ALWAYS follows a geodesic in spacetime no matter what. > > What's "vague and muddled" is summing this up with the imprecise phrase > "always agree on the distance between them in spacetime" > There is nothing vague or muddled about the distance between 2 events in spacetime, it's just a number and it's not even difficult to calculate, I did it in my High school physics class when I was 16. And all observers will agree on what that number is. Minkowski's formula to find this straight line distance (geodesic) in spacetime between two events is very similar to and no more complicated than Pythagoras's formula to find the hypotenuse, the only difference is we subtract and not add the squared time difference from the squared distance difference, and then take the square root of the result. Observers in different reference frames will disagree about the time between 2 events and they will disagree about where the 2 events happened but when any observer use Minkowski's formula they will not get something vague and muddled they will get a simple number, just one number. And all observers no matter how radically different their reference frame may be will get exactly the same number. > > deciding for yourself that since the sum of angles in a triangle sounds > kinda sorta like a type of "distance in spacetime" to your ears, that it > must be something all observers agree on too (even though you have never > ever heard a physicist claim this about the sum of angles of a triangle > explicitly). > >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." > >>I've run across this sort of thing before when somebody is losing an >> argument, they keep demanding definitions for everything I say. >> >> > > I'm not asking for a verbal definition of the word "angle", but rather > some details on the *physical procedure* to determine the angle > I've heard that there is a new high tech tool called a "protractor". > > If you do agree that the angle depends on the velocity of the observer > measuring it, then you should be able to see the rather obvious fact that > "measure the angle the lasers make at the event of their crossing" is a > physically ill-defined instruction if you don't specify the velocity of the > observer making the measurement > What on earth are you talking about? This has nothing to do with theory, this is a empirical observation and a protractor will work just fine for measuring angles regardless of the theory. 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