Hello,
I agree that the second postulate is non-intuitive and difficult to reconcile with the Newtonian picture that seems so natural at terrestrial speeds. However the essay is less about the validity of the postulate and more about a what-if scenario where we relax the classical picture of smooth worldlines between events. By examining how a simple digital clock works under these circumstances one can see interesting connections to quantum mechanics.
Hi Armin,
thanks for the comments. I agree there are definite similarities with the ideas you suggest. I shall read your work on QM and relativity with interest!
Hello Helmut,
thanks for the comments. I look forward to reading your paper.
Hello Jayakar,
thanks for the link.
Hi Constantinos,
thanks for the comment. I would be very interested to see the second law used to consider the picture of events as having finite duration vs events as a 'points'. I will read the chapter with interest.
Dear Garnet,
Thanks for your interest in my Chapter (and my essay). There is much in it and can be a little confusing upon the first reading to unravel the results. But specifically on your stated interest of 'my take' on the Second Law. Let me give you a little guidance on how this comes about.
One of the many results to come out of my derivation of Planck's formula for blackbody radiation is a direct proportionality between entropy and time. The actual result is as follows: ΔS = kνΔt , where k is Boltzmann's constant and ν is frequency (or 'rate of evolution' is more closer to the 'truth'). From this, it is obvious to me that the Second Law is not really about 'entropy' (though it can be thought that way) but really about 'physical time'. Thus, the Second Law can be restated to say, "every physical event takes some positive duration of time to occur'". It is curious to me why there is no Basic Law in physics pertaining to probably the most fundamental of all physical quantities; "physical times" associated with physical events. I like to suggest the Second Law is just that Law of Nature.
With this understanding, many mysteries in Physics and Cosmology clear up. Foremost, the misuse of Spacetime to represent physical events.
Best regards,
Constantinos
Dear Garnet,
Your idea is very interesting. It is a mystery that matter has a frequency but its amplitude has only a probabilistic meaning. I share the same idea of a clockwork in a particle. In fact, I have used a similar idea but assuming the particle has a vibration of time rate in my essay and is able to obtain the properties of a particle field. I am reading other papers in the contest but your paper is one that I read a number of times. Our approach seems to have many common points. I hope we can continue to communicate even in the future to get your feedback and ideas.
To better understand your idea, I have two questions:
1. The Compton clock has 4 states. The clock rotates around these states with spatial displacement. Since it has spatial displacement, will the clock run slower than the clock in an inertial frame? From relativity, the particle should be running along a time-like geodesic and has the same time rate of an outside inertial frame.
2. The states of the clock is real. However, the overall phase of the matter wave is unobservable. The phase can be shifted without changing the probability density. Can the field generated by the Compton clock have the same property?
Sincerely,
Hou Ying Yau
Hello Yau,
thanks for the comments. Please send me an email if you would like more discussion.
In answer to the first question, the 'moving clock will run slow'. This feature is controlled by the fixed spacetime area between audible events. It is actually the fact that the invariant is an area, that leads to wave propagation and the uncertainty principle in the 'chessboard' limit.
The phase of Compton's clock in the chessboard limit is similar to what one would expect in quantum mechanics as the model faithfully produces the Dirac propagator. However, although the model hints at measurement features, there is as yet no immediate implication of the Born postulate. One could simply invoke it, but the hope is that it will ultimately follow through a statistical argument.
Dear Garnet,
You have written a very interesting and relevant essay. I have a few questions:
1. Do the causal dymanical triangulations people know about your work? I notice that you referenced the paper by Ambjorn, Jurkiewicz, and Loll.
2. Two different possible "methods of quantization" are confusing me. Following your discussion of continuous spacetime as an infinite mass limit (up to the middle of page 5), one might reasonably think about "classical discrete spacetimes" built from the Alexandrov-type "areas," somewhat in the spirit of CDT. One could then "sum over geometries" to get a quantum theory. Alternatively, you mention the chessboard model with stochastic edge lengths and Feynman sums over a particular spacetime. I am not sure how much of your discussion in this particular paper is intended to apply to SR only, and how much should be expected to generalize.
3. On a related note, I am trying to compare the type and amount of local information you use with the corresponding approaches in CDT and causal sets. It seems that you have a local scale (via the clock), local dimension, and local orientation?
4. I note from your bio that you study statistical structure underlying quantum theory. The only classical statistical structure I see here is the stochastic edge length. Does such structure play any other role in your view of fundamental spacetime?
5. Near the beginning of your essay, you express the opinion (with which I wholeheartedly agree) that the real numbers are not real (i.e., physical), but that they are convenient for calculus, etc. Now it seems to me that the taking the continuum for granted can have very serious effects that have nothing to do with harmless interpolation. For instance, the whole of quantum field theory is based on the representation theory of the Poincare group, which falls apart once you shed the continuum. I think that you and others are very right to keep the fiction of the continuum front and center.
By the way, if you want to know the motivation for my questions about emergent spacetime, you may read my essay here: On the Foundational Assumptions of Modern Physics.
Take care,
Ben Dribus
Dear Garnet,
Your model has very interesting features using 4 states for the internal clock that lead to some familar properties of Dirac propagator. The model that I developed in my essay has fluctuations in time rate which can produce the quantum field for a zero spin particle. It also has properties that I hope can resolve some fundamental questions for non-locality. The future step will be to extend it to 1/2 spin particle field. It seems our approaches have some common points that may supplement each other to get the Dirac field. I hope I can get your feedback on my essay.
Sincerely,
Hou Yau
Hi Ben,
thanks for your comments and questions. To save space, I use your numbering system below.
1) I am not sure, but in general I think the relevant binary relation is not symmetric.;-)
2) Up to the middle of page 5, the infinite frequency limit has been taken as in Fig. 3a. The result is Equation (7). The lowest order approximation of this clock is (6) and because it is translation invariant, the resulting 't' could well represent Newton's absolute time.
(7) as it stands, as you suggest, has a form of quantization in it. The quantization however just scales the unit vectors of the `spacetime' for which the 'clock' is a representative time-keeper. In taking the limit we see a link between the initial finite areas of the Compton clock, and the infinite frequency limit that shrinks those areas to zero while filling in the events on the t-axis. This leads to Minkowski spacetime with its odd signature, but by shrinking the areas to zero we have supressed quantum propagation.
The second limit is more interesting because by building in a Poisson process for events, infinite frequency is allowed, but the probabilistic weight favours a mean finite area between events. The result is the chessboard model that gives the Dirac propagator! By allowing the finite area, the multiple-history picture of the path-integral survivies and it is this that gives wave propagation. The fact that wave propagation survives in this limit and not the original is I think the most interesting feature of this sketch. It shows that SR is conventionally classical because it starts in the continuum in such a way that quantum propagation is surpressed. If you back away from the continuum, as per this clock, you see spacetime as an infinite mass limit and Dirac propagation as continuum limit in which mass is kept finite.
I do expect this picture to generalize. The above calculation shows that relatiity and quantum mechanics are siblings rather than marriage partners. We should be looking for the parent from which they emerge, and to do that we may have to forgo the initial convenience of the calculus.
(3) Yes on all counts. The scale is determined by event frequency (ultimately mass). The local dimension that characterizes clock frequency is two (spacetime area), and the oriented area (in the sense of geometric algebra) is what is averaged by the stochastic process in the chessboard limit.
(4) My background in stat mech colours my view of both relativity and quantum mechanics. In the sketch, I only mention the Poisson process that, when added to the clock, gives the chessboard model. However structural similarities between, for example, the diffusion and Schroedinger equations and the telegraph and Dirac equations are, to me, too direct to be a coincidence. The classical equations emerge from an underlying statistical mechanics, and as a result the partial derivatives involved are an approximation valid on restricted scales. I would expect the same to be true for our 'fundamental' quantum equations too.
(5) I agree. Scale dependence is common in macroscopic physics and I suspect that to resolve some of our foundational problems we shall have to be more circumspect about the continuum.
Dear Garnet,
Thanks for the detailed reply! By the way, have you studied Sorkin's classical sequential growth for causal sets at all? The reason I ask is because this is a stochastic model which is as "primitive as possible," and I wonder how it compares to your view of an underlying statistical structure. I don't agree with all of Sorkin's postulates, but my own ideas are fairly close to his in spirit; in particular, theories like CDT assume a lot of structure that I would prefer to try to explain. Take care,
Ben
I agree with Pencho. It is not about intuition, it is about logic. I disagree with Pencho in that the situation requires the "ballistic interpretation." Whereas a pulse of light seems to act like a particle in that it has a beginning and an end, and if emitted from a coherent collimated laser, stays relatively compact as it radiates, a strobe flash radiates in a hemispheric pattern, any given observer only intercepting a portion thereof. The wave interpretation has more going for it.
See: A Challenge to Quantized Absorption by Experiment and Theory
See also my essay: A Logical Analysis of Albert Einstein's Mirror-Light-Clock Gedankin
Hello Garnet,
Your essay was an interesting and fun read for me. A lot of the content resonates with me, as well, and I touch on fractal spacetime and other related topics in my own contest essay 'Cherished Assumptions and the Progress of Physics.' You make excellent use of equations and diagrams to render technical aspects of your model accessible in a non-intimidating way. I'm trying to get through a large number of essays right now, but I may have some questions or comments a bit later.
Thanks for some enjoyable reading. That's a nice clock you have.
Regards,
Jonathan
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process.
I wanted to mention;
I particularly liked the opening of your essay, Garnet, in analogy of Korzybski's 'the word is not the thing, the map is not the territory...' I do hope to get back and comment further, but in the meanwhile - good luck.
All the Best,
Jonathan
dear Garnet,
exellent essay. R. Guy Grantham has told me about your work. Actually we both describe particles as reference clocks, see my essay http://fqxi.org/community/forum/topic/1519 or my publications on arxiv. You deserve a hugh rate.
Best regards,
Donatello
Hi Jonathan,
thanks for the kind comments. I look forward to reading your essay.
Hi Donatello,
Thanks for the comments! I shall read your articles with interest.
Best wishes,
Garnet
Dear Garnet!
Sorry could not read your essay before, during rating.
1. I also love the geography, moved in my life in different places more than 70 times, but I think that we need not geography, and a new deep ontology. We must remember that as well as mathematics and physics, including basic theories of physics-QM and GR - is operational theory, not ontologically grounded. They work in some parts of the whole world. Mathematics - science also not ontologically grounded. So now the main problem of fundamental physics - the problem of FOUNDATION KNOWLEDGE. And for that we need a new ontological revolution. We need a new conceptual ontological revolution to "grab" (understand) the desired structure of space-time.
2. Archaeology can also be an assistant in order to know how a person ("Protogeometr" - Edmund Husserl "Getting geometry") and learned the triunity of absolute forms of existence of matter.
3. Your drawings are great, but they do not overcome linear thinking. It is therefore necessary to take only three of the state vector - an equilateral triangle, as a representative of the Logos and the triunity of absolute forms of existence of matter, and analyze its invariants.
4. Many physicists want to "kill time". But to «kill time» is to kill the "memory." There is only one way: a new model of the universe is a model of an ETERNAL UNIVERSE. Here mathematics (especially geometry) comes to the fore as the language of nature.
Sincerely, Vladimir
