Jesse Mazer <[email protected]> wrote: > 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 >
First you say "Macrostates are defined only in terms of a set of *present* microstates" and then you give a quote (which as usual you have absolutely no understanding of but could nevertheless still find by searching with Google with a few simple keywords) that said " Standard references define macrostates either as sets of microstates, i.e. subsets of phase space, with given values of a small number of macroscopic observables". Well, all game of life patterns that contain 36 live cells is a subset, and 36 is a small number, and one element in that set will grow to infinity and the others will not, and the process of growing to infinity is certainly macroscopic and observable. So I repeat my question, do you really want to say that only the number of live cells is important not their position, so all 36 cell Game of Life patterns have the same macrostate? > > the definition of a macrostate says nothing whatsoever about *future* > behavior. > If so then the entire concept of macrostate would be a pretty damn useless idea. > >> 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. >> > > > Not if it's non-reversible, no. > YES! In non-reversible physics like the Game of Life 2,3, 4 or k different patterns could have produced the pattern you're looking at now. So however you wish to define "microstate" if X is proportional to the logarithm of the number of microstates in that pattern then it is also proportional to k times the logarithm of the number of microstates in that pattern because k is a constant. So 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 finite game of life example, with macrostates defined in terms of > the ratio of dead to live cells, > Nobody knows if our universe is a cellular automation or not but it's pretty clear it's not a finite cellular automation. And even if it were why is that definition more useful that others? Why is the number of cells more important that the position of those cells? Remember, one 36 cell pattern produced infinity, the others do not. > > But "macrostate" does not mean "the same at the largest scale even > though small changes have been made", that's a definition you just made up > that has little to do with how physicists define it. > BULLSHIT! > > If you don't believe me that the basic definition of what constitutes a > valid "macrostate" in statistical mechanics can be any choice of > macroscopic observable regardless of considerations like whether > knowledge of the observable allows you to predict future behavior, see for > example http://arxiv.org/pdf/cond-mat/0303625v1.pdf which says: > I'll tell you exactly what it says, it says: "The set of macrostates forms the unique maximal partition of phasespace which 1) is consistent with our observations (a subjective fact about our ability to observe the system) and 2) obeys a Markov process" And a system obeys a Markov process if it is non-reversible and you can make PREDICTIONS about the FUTURE state of the system based only on the present state of the system. It also says "Macrostates arrived at in this way are provably optimal statistical predictors of the future values of our observables." So wave goodbye to your previous ideas about macrostates. And that my dear Jesse is the problem in giving lengthy quotes found by Googling keywords that you have no understanding of. > > the definition of Boltzmann entropy in terms of the log of the number of > microstates associated with a macrostate does not say that the parameter > that determine the macrostate must be a "useful" > Oh for christ sake! A scientist has an idea, he writes a paper about this idea, but if he doesn't specifically say "I think this idea is worth a damn" therefore we must conclude he doesn't think his idea is worth a damn. > > 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. > >> 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. >> >> > > But in the coordinate system of the accelerated observer moving with the > elevator the paths of the lasers wouldn't even be straight lines > Yes, and elevator man's triangle wouldn't have 180 degrees. > the light beam travels in a straight line as seen by an inertial observer Yes, and inertial man's triangle would have 180 degrees. > > I thought this phenomenon of laser beams looking curved in an > accelerating frame was where you were getting the notion that the > accelerating observer judges spacetime to be curved. > It is. > > By "friend forms his own triangle" do you just mean he's using a laser > emitter that's accelerating along with the elevator? > Yes. > > But do you understand that a photon will travel in a straight line once > it leaves the emitter, as measured in an inertial frame, > The accelerating man places his laser pointer against the left wall of the elevator absolutely parallel with the floor and exactly 3 feet above it; he then sees a spot of light on the right side of the elevator only 2 feet above the floor. The non-accelerating man will see the same thing. >>both you and your friend agree that your triangle was NOT drawn in curved >> spacetime. >> > > > But you just said "when your friend forms his own triangle he says it > does NOT have 180 degrees, > Yes. > > and when you look at his triangle you agree with him > Yes. Suppose you're in a inertial frame and have constructed an equilateral triangle and you are confident that all 3 angles have exactly 60 degrees. I fly by in my spaceship parallel to one of the sides of your triangle at nearly the speed of light. To me distances will look contracted but only in the direction of my travel, so I will not see a equilateral triangle, one side of the triangle, the one I'm flying parallel to, will look shorter than the other 2 sides, and 2 of the angles will be more than 60 degrees but the third angle would be a good deal less than 60 degrees, but the sum of the 3 would still be 180. > > so are you saying the presence of triangles whose angles add to 180 does > not suffice to show that spacetime is curved > No, if it ads up to 180 it's sufficient to show that spacetime is NOT curved, or at least not curved in that direction. If you measured 3 perpendicular triangles and got 180 for all 3 you'd know that spacetime was NOT curved in any direction. > >> 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. >> > > > this indicates that the curvature of spacetime can be determined exactly > from knowledge of how the scalar energy density varies from one point to > another in space and time, there is no need for separate information about > pressure/tension even if they are huge, > Mass\energy density is not enough if you want to know exactly how much a object will curve spacetime, you also need to know the pressure and tension. However if you knew the mass and energy and MOMENTUM of every particle that makes up an object you could theoretically (but probably not practically) calculate now much pressure, or its negative tension, that he entire object was experiencing > > I have no idea what you mean by "acting as if space can be completely > segregated from time". > I know you don't and that's exactly the problem. You don't know what you mean when you talk glibly about 3D space being curved but 4D spacetime remaining flat as a pancake. There is simply no way that mass or energy or pressure or tension can warp space and leave time unaffected. > > So you are talking about actual spacetime path taken by the light, > rather than the spatial component of the path? > A light ray may or may not take the shortest path as measured by a tape measure but light ALWAYS takes the shortest (straightest) path in spacetime, in other words light always chooses to take the quickest path to get from point A to point B. That's why gravitational lenses work, and why glass lenses work too. > > In relativity one can foliate a 4D spacetime into a series of 3D > hypersurfaces, and quantify the 3-curvature of a given hypersurface, which > would include the notion of "spatial geodesics" in that 3D hypersurface, > (the locally shortest paths that *lie entirely within that hypersurface*), > distinct from spacelike geodesics through the spacetime (which need not be > confined to any one of the hypersurfaces we have chosen). In any given > coordinate system one can project the spatial component of a light > worldline onto a given 3D simultaneity surface of constant coordinate time > (what I was calling the "shadow" of the worldline on that 3D simultaneity > surface). For example, say in this coordinate system the light ray's path > can be parametrized by a parameter p with functions for the worldline's > spatial and time coordinates as a function of p, x(p), y(p), z(p), and > t(p), such that for any specific value of p the corresponding x,y,z,t will > be a point on the light ray's worldline. Then if we have a simultaneity > surface of constant time coordinate t=T0, the spatial projection of the > light ray's worldline onto this simultaneity surface would be the spacelike > path given by x(p), y(p), z(p) and t=T0. If you use the FRLW coordinate > system in the FRLW spacetime, the projecting the spatial component of a > light worldline onto a simultaneity surface always results in a spatial > geodesic within that hypersurface > WOW, Google really is wonderful! You found lots and lots of nifty buzzwords, but I don't have a clue what the hell all that bafflegab means. Do you? > > When physicists talk about using the angles of a triangle to measure > curvature, they are talking about measuring 3-curvature > I know you say you do but I still strongly suspect you don't understand what 3-curvature means, much less 4-curvature. > >> 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. >> > > > But no one who claims that observational evidence suggests that the > universe is "flat" is saying "the 4D spacetime of the universe is flat" > No Jessie, everybody who claims that sort of observational evidence INSISTS that means the 4D spacetime of the universe is flat. > >> 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. >> > > > Huh? Geodesics have nothing specifically to do with speed > They do if you're talking about a geodesic in 4D spacetime because speed is about how the position of something in 3D space changes with another dimension, time; that's why it's called spacetime. A straight line is the shortest path between 2 points in a flat plane and a geodesic is just a generalization of the concept of a straight line that works in a space in any number of dimensions no matter how strongly it is curved. So the geodesic between 2 events in 4D spacetime is the path between those events that is the shortest, and that is the path that is the quickest; and this is the path that light always takes regardless of if the spacetime is flat or curved. The idea that light always takes not necessarily he shortest path but the path of least time is not new, it's just Fermat's principle and was discovered 400 years ago and has been used to design lenses ever since. > > rather they are saying the spacetime is closely approximated by the FLRW > model with Omega=1 > Stop the pretense, we both know you found the phrase "FLRW model" with a Google search and have no idea what its all about. > > I don't see how "saying that light always follows a geodesic even in > curved spacetime is just another way of saying that nothing can travel > faster than light". > I know you don't see that, and that tells me you don't understand what spacetime means. > > and a theoretical "tachyon" that had one as its worldline would be > moving faster than light. > In the very unlikely event that a tachyon is ever found almost everything in physics would need to change, including the statement that light always follows a geodesic in spacetime, but I think it will be a very long time if ever before any caveats to it are required. > > such geodesics are well-defined > Dragons are well-defined too! I don't give a damn if it's well-defined if it doesn't exist, this is physics not mathematics. > > nowhere does the above quote say that all observers agree on the sum of > angles in a triangle, or that the sum of angles in a triangle can be > considered a form of "distance in spacetime". > The sum of angles in a triangle can be considered a form of distance in spacetime?? That's news to me. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
