On Thu, Mar 20, 2014 at 6:00 PM, Jesse Mazer <[email protected]> wrote:
>>Chaos theory tells us that even in classical physics a change in a micro >> state can soon lead to a change in the macro state. And if it's a >> reversible theory then there are NOT 2 different states of the universe >> that could have produced things as they are now. >> > > > Are you claiming that if the underlying micro-physics is reversible, > then it's impossible for there to be two different past states that would > lead to the present MACROstate? > Then 2 different states of the universe could still lead to the PRESENT macrostate, but depending on if the system is chaos sensitive or not (not everything is, a cylinder of gas isn't) it might not lead to the macrostate after next. >> The fact remains that if Entropy is proportional to the logarithm of > the number of microstates something can be in and still have the same > macrostate then it's also proportional to the logarithm of the number of > ways the thing could have been produced and still have the same macrostate. > > Only if physics is unitary, which is an open question in black hole > physics. > Then Entropy is NOT proportional to the logarithm of the number of microstates something can be in and still have the same macrostate because a Black Hole would have no microstates. > >> Bekenstein DERIVED that the entropy of a Black Hole was proportional >> to it's 2D surface area, to just define it that way without any arguments >> showing how it was consistent with physics previous use of the word >> "entropy" would have been imbecilic, and Jacob Bekenstein is not an >> imbecile. >> > > > As I already explained, what he showed was that IF you define "black > hole entropy" by the specific equation he gave, and IF black holes also > have a specific temperature defined by another equation, then the known > laws of classical thermodynamics will be preserved in the presence of black > holes. > And that is just another way of saying Bekenstein DERIVED that the entropy of a Black Hole was proportional to it's 2D surface area. > But this is not the same as "deriving" either of these things, > Why the hell not? I suspect you're insisting on this not because you have a strong opinion on the matter but simply because you've developed a reflex to contradict anything I say. If I say white you must say black. https://www.youtube.com/watch?v=kQFKtI6gn9Y >> Regardless of what English word you call it if X is proportional to >> the logarithm of the number of microstates something can be in and still >> have the same macrostate then X is also proportional to the logarithm of >> the number of ways the thing could have been produced and still have the >> same macrostate. >> > > > Only if physics is unitary > No such qualification is necessary because if physics is not unitary then X is NOT proportional to the logarithm of the number of microstates something can be in because if that something is a Black Hole then it has no microstates. And today almost all physicists think physics is unitary, even Stephen Hawking now thinks so and he was among the last holdouts. > Do you deny that the number of microstates something can presently be in > could be different from the number of past microstates that could have led > to the present macrostate > I never denied that. if the very concept of microstates is still meaningful (that is to say if physics is unitary) then I can't say it better than what I said on March 18: "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 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." > in the Game of Life on a finite grid > Then it's not the Game of Life. Let's not needlessly complicate things and stick to the original. > if you define macrostates in terms of the ratio of black (live) to white > (dead) cells, then the macrostate with ratio 0:100 has only one PRESENT > microstate it could be in (since every single cell must be white to have > that ratio), but lots of past microstates that could have led to it. > 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. So if you want to talk about Entropy you can only talk about the ways something could get made; however you should keep in mind that unlike the Game of Live the physics in our universe is almost certainly unitary. > Remember, this whole debate about entropy got started because I pointed > out that it's logically possible the second law of thermodynamics wouldn't > work if we lived in a universe where the fundamental laws were > non-reversible, I know and that's nuts, 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. But as near as we can tell the fundamental laws of physics ARE REVERSIBLE, and yet time DOES have a preferred direction and the second law of thermodynamics DOES work. The answer to the puzzle must be that the state of a system doesn't just depend on the laws of physics, it also depends on initial conditions, the universe must have started out in a very very low Entropy state. Because of this physicists could have predicted the existence of the Big Bang 200 years ago when primitive steam engines were being made and we were first learning about thermodynamics, but unfortunately they did not. > Aren't you claiming that the acceleration of the elevator alone is enough > to lead to the conclusion that spacetime is curved? > Yes. And if you were accelerating in deep space at 1g or just sitting on the surface of Earth straight lines (light) would bend in exactly the same way. > Wouldn't you therefore say this would still remain true in the case of an > elevator accelerating in deep space, > Yes, and you can introduce the concept of Spacetime to explain what is going on but because gravity is not involved it would not be necessary and such needless erudition would just introduce unneeded mathematical compilations. General Relativity can certainly be used in a case like that but it would be overkill, for such a simple situation Special Relativity would be better suited. > >> something under tension also has more energy than something not being >> pulled apart and this does indeed mean the increase in mass\energy causes >> more gravitational attraction BUT there is another component to consider. >> According to General Relativity another result of this tension is a >> gravitational REPULSION not attraction. This effect isn't talked about as >> much as the component made by pressure because we've seen objects under >> astronomical amounts of pressure such as a Neutron Star, and if you want to >> understand the geology of a Neutron Star the additional gravitational >> attraction caused by the pressure becomes important, but up to now we've >> never seen a object undergoing comparable amounts of tension. > > > > Not sure why you think the fact that general relativity says tension > causes repulsion would invalidate my guess that the tension itself can be > derived from knowledge of all the potentials at each point. > Take 2 equal solid masses and then add a equal amount of potential energy to both of them, but do it by putting one under pressure and the other under tension. Both masses and their internal potential energy will produce a gravitational attraction (curve Spacetime) but the one under pressure will curve it more because the one under tension will have an additional small gravitational repulsion factor that counteracts a very small part of the gravitational attraction caused by the mass itself and the additional potential energy. > I would also note that the convention of talking about "mass/energy" > curving space and spacetime, without separately referring to > pressure/tension, is one that I picked up from reading things written by > physicists, > That's because 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. > >> Please show me a place where 3D space is curved but 4D space-time is >> not and explain how such a thing could come to be. >> > > > it's the Milne model > In what galaxy can I find that? The Milne model was an old 1930s cosmological model that involved Special Relativity not General, in fact was a rival theory to Einstein's. Unlike General Relativity Milne's theory had the rather important disadvantage of being unable to describe matter, and because the predictions made by that model are not consistent with more recent observations there is no direction I can point my telescope in and observe "the Milne model" and see a place where 3D space is curved but 4D space-time is not. Is mathematics powerful enough to produce a system that is logically consistent but inconsistent with General Relativity where time is unaffected by curved 3D space? Yes absolutely. Is the universe such a system? Observations say no. > >> As Herman Minkowski, Einstein's old mathematics teacher and the man >> who invented the very concept of spacetime said in the last sentence of his >> famous paper, the one Einstein at first didn't like and then became its >> greatest champion: >> >> "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". >> > > > How is that quote supposed to be relevant? > 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. > Of course 4-curvature is more fundamental physically than 3-curvature > since 4-curvature is coordinate-invariant whereas 3-curvature depends on > your choice of simultaneity convention > Yes, your space is a combination of my space and my time and vice versa. > > but that doesn't mean 3-curvature isn't well-defined. > 3-curvature is perfectly well defined but we're no better at visualizing it than 4-curvature and must rely on the mathematics to work out the consequences. > Are you saying that no matter how we foliate a 4D spacetime into a series > of 3D hypersurfaces, spatial geodesics within each surface will always > correspond to the path that light takes? > 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. > >>> obviously they think that light paths tell us something about the >>> curvature of 3D spacelike surfaces in the 4D spacetime, >>> >> >>> >> >> And obviously the number of degrees a triangle formed by those light >> paths tells us something about the curvature of 4D spacetime. You're so >> confused you've forgotten what side you're arguing on. > > > > No, it really doesn't. If observers at rest in the Milne coordinate > system [...] > Nobody cares about Milne anymore! It was a fair fight but Einstein ended up beating Milne more than half a century ago. > my point that measuring the internal angles of a triangle is a way to > measure the curvature of 3D space, *not* the curvature of 4D spacetime, > We've found lots and lots of places where 4D Spacetime is curved, we can tell by the gravitational lensing, but I ask again for you to show me where I can point my telescope so I can observe curved 3D space but flat 4D spacetime. I can easily make up a large table showing the azimuth and elevation positions I can place my telescope at and observe curved spacetime, but I need your help to make a comparable table so I can observe curved 3D space but flat 4D spacetime. > >> Show me a place in the universe where 3D space is flat but 4D spacetime >> is not. >> > > > Um, that's the whole idea of a "flat" FRLW universe where Omega, the > ratio of the actual density to the "critical" density, is equal to 1 (i.e. > the density is exactly equal to the 'critical' value). > That's all very nice, but show me a place in the universe where 3D space is flat but 4D spacetime is not. > > Since you seem to have read some popular articles about cosmology and > such I imagine you've come across the concept of a "flat" universe before, > what did you think it meant? > Astronomers have recently found that on the largest scales the universe is flat or nearly so, and on Feb 21 I explained what that means and how they found out about it: Astronomers proved that, although there are certainly local variations, on the very largest scale the universe is in general flat. They did this by looking at the Cosmic Microwave Background Radiation (CMBR), it is the most distant and oldest thing we have ever seen and was formed just 380,000 years after the Big Bang, so if we look at a map of that background radiation the largest structure we could see on it would be 380,000 light years across, spots larger than this wouldn't have had enough time to form because nothing, not even gravity can move faster than light, a larger lump wouldn't even have enough time to know it was a lump. So how large would a object 13.8 billion light years away appear to us if it's size was 380,000 light years across? The answer is one degree of arc, but ONLY if the universe is flat. If it's not flat and parallel lines converge or diverge then the image of the largest structures we can see in the CMBR could appear to be larger or smaller than one degree depending on how the image was distorted, and that would depend on if the universe is positively or negatively curved. But we see no distortion at all, in this way the WMAP and Planck satellite proved that the universe is in general flat, or at least isn't curved much, over a distance of 13.8 billion light years if the universe curves at all it is less than one part in 100,000. > > You've provided wall to wall links and tons of quoted verbiage, but I >> don't think you understand any of it. Prove me wrong, not with yet another >> link (I know how to use Google too), but with an explanation in your own >> words on how you would perform a experiment to determine if your local >> spacetime is curved. I have given a clear explanation on how I would do it, >> but you don't like how I did it so I want to know how you would. >> > > > I don't know the details of how the five-point curvature detector > device works > I see. It is my policy not to include lengthy quotes even if they seem to support my position if I don't clearly understand what they're talking about because it could turn out they're not as supportable to my position as strongly as I thought they were. >> Different observers might disagree about the distance between 2 events >> in space or the distance between them in time but they will always agree on >> the distance between them in spacetime. >> > > > More vague and muddled verbal arguments > Vague and muddled my ass! It's clear as a bell and one of the core concepts in General Relativity. This is relativity 101 and you're muddled already? >>> could you please also address the question I asked about whether you >>> understand that an observer could be within the volume of an accelerating >>> observer yet himself qualify as an inertial observer, >>> >> >> >> I already did, everybody agrees on how many degrees the triangle has >> so everybody agrees if the space the triangle is drawn in is curved or not. >> > > > Not an answer to my question, which was not about triangles or whether > space was curved. Just asking whether an observer inside the elevator can > qualify as "inertial"--yes or no? > Obviously NO, the elevator is accelerating so it can't be inertial. And strictly speaking you sitting at home right now are not a inertial observer either because you are in a gravitational field, but if we're comparing your observations to that of somebody on a Neutron Star you're close enough to inertial for a good approximation of such a thing. > >>> How would you define the angle at a single EVENT of two lasers >>> meeting? >>> >>> >> >> An event is a point is spacetime, so mount 3 lasers that fire in 2 >> directions 180 degrees apart at any 3 points, the point in spacetime where >> the photons from the lasers intersect forms the vertices of the triangle >> you're measuring. >> > > > I didn't ask how to define the triangle, but rather how to define the > angle. > I've run across this sort of thing before when somebody is losing an argument, they keep demanding definitions for everything I say. And any definition I give will be made of words, and they will then demand a definition of at least one of those words, and so it goes. Nevertheless I will do as you request but first you must define define. 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.
