Hopefully! When the volume of space is large, there is not much difference between the SD Hamiltonian and the GR Hamiltonian (they converge to the same thing). That might help. Glad to hear your interested in these ideas.
Sean.
ps. I don't know why the last post came up as "anonymous"... I should have been logged in. Sorry about that.
I would like you to read my essay "Billy Pilgrim Blues". I cover the same issues as your essay, but in a very different way. Please honestly tell me what you think.
You're right that we are tackling similar issues from a very different perspective.
In our proposal, there might be a way to relate time, as a renormalization group flow time, to a measure of complexity. This could indeed be a kind of entropy of configurations. However, I believe this is quite different from the kind of relationship you are suggesting.
I don't agree with your statement that "entropy is needed to define time". Your pendulum example is misleading because clocks don't have to be cyclic. In Julian Barbour 2009 essay: The nature of time, he describes a relational notion of time that is perfectly well defined without a notion of entropy. This is what astronomers use to define time. So I don't understand your argument.
Best,
Sean.
Sean,
Thank you for your comments and taking the time to read my essay.
Clocks do not have to be cyclic. I used the example of a perfect cyclic timepiece to isolate time from all other factors. The Earth spins on its axis and the stars move in relationship to each other, but the Earth is different each day and the stars burn a little of their store of hydrogen each momentum. Entropy is very much a part of Astronomy. At the quantum scale, when enthopy change is harder to come by, postion relationships between indivual particles are uncertain. Please show me a way to mark time that does not change enthopy.
All the best,
Jeff
You need to define entropy more precisely. In particular, if you're talking about thermodynamic entropy then this is not even defined for systems outside of thermodynamics equilibrium. Surely you are not suggesting that time is not defined for systems (such as the sun and humans) far from equilibrium?
Dear Sean,
I'd like to remark only that
1. Einstein the physicist was agree to simplify mathematics, in particular, he used the 3-dimensional simplified version of the Pythagorean theorem in the form x2 y2 z2 = t2 ( i.e in a rectanglular box, the square of the space diagonal is equal to the sum of squares of the three sides ). Purely mathematically, however, it is not correct, because it is valid only for even x and y ( for example 3,4,12,13, etc ). But Einstein equation IS NOT valid for positive odd x and y, actually ( please, see Pythagorean Quadruple and Euler Brick problems, and my FQXi essay also )
2. On time. Mathematically speaking, Einstein's time is an attempt to introduce a new kind of complex number of the type ( x x' x'' yi ) as a kind of displacement. Thus,it could be difficult ( beyond popular science ) to deduce taking time theory seriously from this sort of attempt. The minus sign has important sense here, because it is a part of complex number algebra.
Entropy still exists for systems out of equilibrium, it is just a far more difficult calculation to find the value of the change in entropy for non-equilibrium systems. Humans and the Sun still obey the second law of thermodynamics.
In macroscopic systems the entropy change is clearly defined (but sometime hard to calculate). At the very small scale (atomic scale) the change in entropy can be undefined.
Dear Sean Gryb,
"an experiment by Michelson and Morley ... measured the speed of light to be
independent of how an observer was moving". Isn't the speed of a wave in general independent of how its source as well as its many possible observers are moving?
Eckard
You claim: "Entropy still exists for systems out of equilibrium".
I'm sorry but that is simply not true. The sun has negative specific heat and that's allowed because the 2nd law simply doesn't apply. It only applies for isolated systems in equilibrium. Check any textbook.
Sounds waves don't have this property. Their speed measured by some observer depends on the speed of the source and the observer relative to the medium of propagation (like the air).
Sean,
You wrote: "Sounds waves don't have this property. Their speed measured by some observer depends on the speed of the source..."
Are you sure? An undergraduate would fail the exam for this.
Pentcho Valev
Sean & Flavio
Speed of sound depends on speed of source!? I've just picked myself up off the floor, and am still wondering if you're serious! Sure the detected absorbed wavelength thus the frequency depends on the source speed.
I agree there is also a case of course where the observer/detector is in the same frame as the source, and the speed is calculated by using coordinated clocks, but in this case we have to ask speed wrt what, so we need a background frame, and then the calculated speed would be inverse to the source speed (with no Doppler shift on detection. I struggle to think you considered this case as, simply, nobody does. Can you explain?
Nicely written and argued essay all round with some interesting views. Well done for getting to the top, hold on for the sleigh ride!
I agree with your point that; "The measurement problem results from the fact that quantum mechanics is a framework more like statistical physics than classical mechanics." And have offered a solution to this via a mechanism in my own essay, which I hope you will read.
I look forward to your comments.
Best wishes
Peter
They definitely have. The speed of sound in air refers to the medium air and has a constant value c that is determined by the medium: about 330 m/s dependent on temperature, humidity, etc. but NOT by the observer.
There is no acceptable reason why this should not hold for electromagnetic waves including light too. There was such reason, and indeed it led first to FitzGerald's and Lorentz's idea of length contraction and later to Einstein's special theory of relativity. Yes, I refer to the failure to explain the null-result of the experiment by Michelson and Morley (MMX). Relativity does not rest on solid ground.
All five Figs. of my essay are compellingly putting basic assumptions in question. Fig. 5 refers to the MMX. Pentcho Valev who favors emission theory calls me an etherist. I would rather say, I merely agree with those who found out that the MMX was wrongly expected to measure the so called aether wind. All of the many implications deserve reconsideration. This will most likely also put the basis of your essay in question. I am sorry for that.
Eckard
With relativity I meant Einstein's relativity. Galileo was definitely correct.
Eckard
Oops, how did the word "source" get in there?! (I'm tired...)
Of course their speed through the medium is constant. All I was trying to say is that if you are moving wrt to that medium, you will have to add your motion relative to this. Hope there is no more confusion!
Sean meant that "the speed of soundwaves depends on the speed of the observer relative to the medium of propagation".
"source" was a slip of course.
I'm reading your essay with interest...
All the best,
Flavio
The speed of the sound/light waves, relative to the observer, varies with the speed of the observer, doesn't it? Is Sidney Redner right?
http://physics.bu.edu/~redner/211-sp06/class19/class19_doppler.html
Professor Sidney Redner: "The Doppler effect is the shift in frequency of a wave that occurs when the wave source, or the detector of the wave, is moving. Applications of the Doppler effect range from medical tests using ultrasound to radar detectors and astronomy (with electromagnetic waves). (...) We will focus on sound waves in describing the Doppler effect, but it works for other waves too. (...) Let's say you, the observer, now move toward the source with velocity vO. You encounter more waves per unit time than you did before. Relative to you, the waves travel at a higher speed: v'=v+vO. The frequency of the waves you detect is higher, and is given by: f'=v'/(lambda)=(v+vO)/(lambda)."
Pentcho Valev pvalev@yahoo.com
Sean, Flavio,
It may be a very moot point wrt light as well, as you're hopefully finding in my essay.
As the source of sound is NOT also the detector the only way to get a relative speed is by calculation, of c over the flight distance.
Of course it's exactly the same with light when calculated with that same data. That's where the paradox is, because that gives c + v, yet the detector at the end of that flight path, but in the same frame as the emitter, measures 'frequency' (a derivative of effective wavelength on detection) and finds the speed at c/n wrt his lens, not c + v!!
I should say that's where the paradox 'was'. I believe it has now gone using DFM dynamic logic. Because all detectors are made of matter, and all matter is a medium, then all detectors MUST find c/n, because light MUST change speed on arrival to the new local c comply with the constant refractive index n and SR in all frames. (It works the same in a vacuum with scattering off diffuse plasma).
That may need you to lie down with your eyes shut and think through a few dozen times. I've failed abysmally to falsify the model, and found all the apparent issues with it evaporate like the SR paradoxes. Except the human factor of course, as few can overcome it's unfamiliarity. Working at Perimeter may just allow you to not reject it before full testing (I have a stack of test data).
I look forward to your comments or questions (and maybe the look on Lee's face when it's explained to him).
Thanks, and best wishes
Peter
Pentcho.
Correct but incomplete. Like saying; 'music is the variation in sound made by instruments'. It misses the critical mechanism of 'HOW'.
My post below of 20.01 was in answer to Flavio's message above. The fluctuation must have crossed the media boundary (refractive plane) and be propagating within the detector medium BEFORE it reaches any brain cells or sensors.
Old assumption, including Einstein's, was, let's say; 'incomplete'. You might well of course equally say 'wrong'.
Peter
Dear Sean Gryb,
Except for the missing negation you were correct when you wrote "depends on the speed of the source and the observer". Actually, the speed of a wave relates to the medium, neither to its source nor to observers.
This undisputed for sound fact contradicts to Einstein's relativity as well as to the emission theories that are here advocated by Pentcho and by Peter.
The key question is the interpretation of MMX. I am not the first one who understood that the unexpected null-result was actually to be expected. I merely discovered how the outcome of the MMX can be made compellingly plausible and quantitatively confirmed by Feist's experiment.
Please do not lazily ignore these arguments.
I know there are further arguments that putatively confirm either Lorentz or Einstein; in particular Maxwell's equations are not covariant.
Phipps Jr. already revealed that Maxwell's equations were adapted to the (wrong) interpretation of MMX.
Eckard