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Natural Science Forum / Physics / General Physics / June 2008Time symmetric physical laws
Now, there is an idea I've nodded my head at a long time. But when it comes down to it, I'm not sure I could give an axiomatic definition (i.e., something a little more rigorous than "looks the same when you run it backwards, whatever that means). Would anybody care to try? What is the generic form of a "physical law"? Does the idea "time symmetric" even make sense when we consider relativity? > Now, there is an idea I've nodded my head at a long time. But when it > comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 4 lines] > law"? Does the idea "time symmetric" even make sense when we consider > relativity? Feynman Diagrams... run the time in either direction... nature does it! >> Now, there is an idea I've nodded my head at a long time. But when >> it comes down to it, I'm not sure I could give an axiomatic [quoted text clipped - 7 lines] > Feynman Diagrams... run the time in either direction... nature > does it! LOL Nature runs backwards? LOL Wow. I would love to see the world that flowers appear back on the stem from backwards time blowing winds and then grow back into the ground naturally. That would be a wild world. I have seen it on video.. but that was.... video. It is magic! unlike Nature. :) LOL  SignatureJames M Driscoll Jr Spaceman >> Now, there is an idea I've nodded my head at a long time. But when it >> comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 7 lines] > Feynman Diagrams... run the time in either direction... nature > does it! Hey Sammy, would you explain how "Feynman Diagrams" fit "time symmetric" into "relativity"? Please use math or logic steps so folks can see how you integrate the continuous and the discrete. SignatureTom Potter http://www.geocities.com/tdp1001/index.html http://notsocrazyideas.blogspot.com http://tdp1001.wiki.zoho.com http://groups.msn.com/PotterPhotos >> Feynman Diagrams... run the time in either direction... nature >> does it! > > Hey Sammy, > would you explain how "Feynman Diagrams" have a read Potter: http://en.wikipedia.org/wiki/Feynman_diagram http://en.wikipedia.org/wiki/Arrow_of_time#The_quantum_arrow_of_time > fit "time symmetric" into "relativity"? Perhaps, Potter, you meant "time asymmetry". > Please use math or logic steps Before we get into the nitty-gritty, Potter, do a bit of self education and pose a proper question. > so folks can see how you integrate the continuous and the discrete. > Now, there is an idea I've nodded my head at a long time. But when it > comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 4 lines] > law"? Does the idea "time symmetric" even make sense when we consider > relativity? If you mean reversal of time, no, Relativity can only go to the "stopped time" limit ifthat at all since you can't even get a "clock" to such speeds yet. :) Of course in reality you are not even going to slow "time" itself as a universal thinking of such and you will only be able to slow action-reaction such as what occurs as the clocks problem in time dilation. (the clock malfunction) It simply loses its normal action-reaction rate and slows the clock hands.. And other things that are based upon the same things :decay rate and such will so the same, could call them slowing down in action-reaction rate. But time marches on and no other clock cares about such a action-reaction rate change of that frame so time itself never slowed at all. :) SignatureJames M Driscoll Jr Spaceman :) | Now, there is an idea I've nodded my head at a long time. But when it | comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 4 lines] | law"? Does the idea "time symmetric" even make sense when we consider | relativity? Your crank ideas look the same when run backwards or forwards. The "generic" 1 a: relating to or characteristic of a whole group or class : general b: being or having a nonproprietary name <generic drugs> c: having no particularly distinctive quality or application <generic restaurants>2: relating to or having the rank of a biological genus (a peculiar American term) form of a physical law is "effect follows cause" and is a clear example of not being time symmetric. > Now, there is an idea I've nodded my head at a long time. But when it > comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 4 lines] > law"? Does the idea "time symmetric" even make sense when we consider > relativity? This is the Arrow of Time problem. The laws governing interactions don't themselves specify a time direction; in principle any given interaction can run forwards or backwards and conserver energy, monentum, mass, etc. As Sam mentions, any Feynman diagram is equally valid "running" it in either time direction. And it seems that individual particle interactions are pretty blase about the direction of time. It's more complicated systems that start to "look funny" when run backwards, and for some reason Nature seems to prefer to have time run in one direction, driving an entropy increase. > > Now, there is an idea I've nodded my head at a long time. But when it > > comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 9 lines] > in principle any given interaction can run forwards or > backwards and conserver energy, monentum, mass, etc. Yes, I know the words on that level. What I am realizing is that I couldn't specify what that means in terms of some abstract formulation of physical law. E.g. Let F(x,y,z,t) = 0 be our "law". Is this an adequate form? How do we specify that it "looks the same run forwards or backwards"? > As Sam mentions, any Feynman diagram is equally valid > "running" it in either time direction. And it seems [quoted text clipped - 4 lines] > prefer to have time run in one direction, driving > an entropy increase. As I said, I claim I follow you on that level. I was looking for the next level of abstraction. >>> Now, there is an idea I've nodded my head at a long time. But when >>> it comes down to it, I'm not sure I could give an axiomatic [quoted text clipped - 17 lines] > E.g. Let F(x,y,z,t) = 0 be our "law". Is this an adequate form? How > do we specify that it "looks the same run forwards or backwards"? Do positive and negative values of t both give real solutions? How about for the differentiated version for positive and negative changes in time (Dt's)? >> As Sam mentions, any Feynman diagram is equally valid >> "running" it in either time direction. And it seems [quoted text clipped - 7 lines] > As I said, I claim I follow you on that level. I was looking for the > next level of abstraction. > "EdwardGreen" <spamspamsp...@netzero.com> wrote in message > [quoted text clipped - 29 lines] > solutions? How about for the differentiated version > for positive and negative changes in time (Dt's)? Is it as simple as "invariant in form under the change of variables t' = - t? >> "EdwardGreen" <spamspamsp...@netzero.com> wrote in message >>> E.g. Let F(x,y,z,t) = 0 be our "law". Is this an adequate form? >>> How do we specify that it "looks the same run forwards or [quoted text clipped - 6 lines] > Is it as simple as "invariant in form under the change of variables t' > = - t? Perhaps. I'd have to think about that. > Is it as simple as "invariant in form under the change of variables > t = - t? Yes, at least for Lagrangian systems ... Time is isotropic if the Lagrangian is unchanged under a time reversal (t replaced by -t). In that case the equations of motion are also unchanged, and if a given motion is possible in a system, then so is the reverse motion (that is, the motion in which the system passes the same states in the reverse order). In classical mechanics, the usual form of the Lagrangian, L = T - U, guarantees time isotropy. See Landau-Lifshitz, Mechanics, page 8-9. /mel > > Is it as simple as "invariant in form under the change of variables > > t = - t? [quoted text clipped - 11 lines] > L = T - U, guarantees time isotropy. > See Landau-Lifshitz, Mechanics, page 8-9. Empty motion picture film can welded sealed about its periphery. Penetrating port and pipe centered in and normal to one broad face, welded in. Pentrating port and pipe tangent to its edge, welded in. Fill with water. Pump water in the middle and out the edge - no problem. Pump water in the edge and out the middle - no flow. There is your absolute arrow of time - conservation of angular momentum. No appeal to microscopic reversiblity will compromise it. SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 > EdwardGreenwrote: > [quoted text clipped - 13 lines] > L = T - U, guarantees time isotropy. > See Landau-Lifshitz, Mechanics, page 8-9. Now I'm really going to try your patience: is that a passive or active change of variables? E.g. (I'll be neutral whether this represents a possible L) Let F = sin(kx - wt) If we symbolically replace t with -t, we have (active) F' = sin(kx + wt) OTOH, if we write the original F in terms of t' = -t, (passive) we have F = sin(kx + wt') Hmm... the final form is the same (in this case, not invariant under the transformation, however). Is that always true? I can't think of a counterexample right now, or a proof either. > > EdwardGreenwrote: > [quoted text clipped - 34 lines] > > I can't think of a counterexample right now, or a proof either D'uh. OK... I will answer my own question (1) It's a passive transformation. (2) Of course letting t -> -t and letting t -> -t' give the same form in t and t', respsectively (give me a "stoopid" please, Uncle Al). So it doesn't matter that much whether we correctly interpret it as a passive transformation, or not. Speaking of Uncle Al... angular momentum establishes the arrow of time? Interesting (== no way I agree with that, but a bold ansatz :-). >>> EdwardGreenwrote: >>> > Is it as simple as "invariant in form under the change of variables >>> > t = - t? [quoted text clipped - 19 lines] >> >> F' = sin(kx + wt) ... that's how I see it. [...] > Speaking of Uncle Al... angular momentum establishes the arrow of > time? Interesting (== no way I agree with that, but a bold > ansatz :-). Let's consider an example in classical mechanics: A particle which moves in the central force field F_ = -kr_, has constant angular momentum r_ x mv_ about the force center O. Assuming that |r_ x mv_| > 0, this means that the particle moves in the plane through O perpendicular to the (r_ x mv_)-vector. Making that plane the xy-plane, we get the Lagrangian L = T - U = (m/2)[x'^2 + y'^2] - (k/2)[x^2 + y^2]. The equations of motion (the Euler-Lagrange eqs), mx'' + kx = 0, my'' + ky = 0, are easy to solve. With w = sqrt(k/m), and suitable initial conditions [(x,y) = (a,0) and (x',y') = (0,u) at t = 0] we get the (origin-centred) elliptical trajectory x = a cos(wt), y = (u/w)sin(wt). Now, if we make the time reversal t -> -t, we see from these equations that the trajectory is traversed in the reverse order. What about angular momentum then? t -> -t implies a velocity flip, v_ = (x',y') -> (-x',-y') = -v_ ... and, consequently, an angular momentum flip! /mel > Now, there is an idea I've nodded my head at a long time. But when it > comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 4 lines] > law"? Does the idea "time symmetric" even make sense when we consider > relativity? Time is asymmtric. It slows down from acceleration. It is Slow physics with the math of Gamma. Mitch Raemsch > Now, there is an idea I've nodded my head at a long time. But when it > comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 4 lines] > law"? Does the idea "time symmetric" even make sense when we consider > relativity? A physical law is a generalization of empirical observations expressed in some precise, concise language, generally some math or computer language. "time symmetric" only exists in isolated systems, during periods when no quanta of action are being added or removed from the system. If you add or remove action from a system you change it's natural frequency ( frequency = energy / action ) and you cannot assume the system is "time symmetric" as you have to account for the times at which the action in the system changes, and how much the action changes. SignatureTom Potter http://www.geocities.com/tdp1001/index.html http://notsocrazyideas.blogspot.com http://tdp1001.wiki.zoho.com http://groups.msn.com/PotterPhotos >> Now, there is an idea I've nodded my head at a long time. But when it >> comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 8 lines] > expressed in some precise, concise language, > generally some math or computer language. "Computer Language"? Surely Potter, you must realize that computers merely do calculations. They are of no value unless properly programed to carry out some specific task. And then one must pay attention... Garbage in.. garbage out. >>> Now, there is an idea I've nodded my head at a long time. But when it >>> comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 14 lines] > task. And then one must pay attention... Garbage in.. > garbage out. Surely Sammy , you must realize that "A physical law is a generalization of empirical observations" and that "physical laws" can be "expressed in many precise, concise languages", such as Algebra, geometry, tensors, MatLab, Pascal, BASIC, Java, etc. I suggest that if you get yourself a copy of MatLab, and play with the "expression" of Planck's Radiation Law that you can find at the URL below, that you will come to understand the fact that physical laws can be "expressed" in many languages. http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=1619&ob jectType=file SignatureTom Potter http://www.geocities.com/tdp1001/index.html http://notsocrazyideas.blogspot.com http://tdp1001.wiki.zoho.com http://groups.msn.com/PotterPhotos > Now, there is an idea I've nodded my head at a long time. But when it > comes down to it, I'm not sure I could give an axiomatic definition [quoted text clipped - 4 lines] > law"? Does the idea "time symmetric" even make sense when we consider > relativity? Time is 100% asymmetric despite microscopic reversibility - Feynman's sprinkler. Conservation of angular momentum is an absolute arrow of time. Entropy is a weak arrow of time as it statistically depends on the Large Numbers theorem. SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 |
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