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The Nature of Time Essay Contest
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The Nature of Time by Julian Barbour
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Julian Barbour wrote on Dec. 1, 2008 @ 14:20 GMT
Essay AbstractA review of some basic facts of classical dynamics shows that time, or precisely duration, is redundant as a fundamental concept. Duration and the behaviour of clocks emerge from a timeless law that governs change.
Author BioAfter completing a PhD in theoretical physics, I became an independent researcher. I wished to study fundamental issues and avoid the publish-or-perish syndrome. For forty years I have worked on the nature of time and motion and have published numerous papers (details on my website platonia.com). I have written two books: The Discovery of Dynamics and The End of Time. I was also the joint editor of the conference proceedings Mach's Principle: From Newton's Bucket to Quantum Gravity. I have recently been made a Visiting Professor in Physics at the University of Oxford.
Download Essay PDF File
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Dr. E (The Real McCoy) wrote on Dec. 2, 2008 @ 04:49 GMT
Thanks for the paper!
I also greatly enjoyed your book: THE END OF TIME.
Loved your quote: "As Ernst Mach said (1883) [3]: It is utterly beyond our power to measure the changes of things by time ... time is an abstraction at which we arrive by means of the changes of things; made because we are not restricted to any one de¯nite measure, all being interconnected. Einstein, an...
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Thanks for the paper!
I also greatly enjoyed your book: THE END OF TIME.
Loved your quote: "As Ernst Mach said (1883) [3]: It is utterly beyond our power to measure the changes of things by time ... time is an abstraction at which we arrive by means of the changes of things; made because we are not restricted to any one de¯nite measure, all being interconnected. Einstein, an admirer, quoted this passage in his obituary of Mach, calling it a gem. Oddly, Einstein never directly attempted a Machian theory of time, but in fact such a theory of `time without time' sits hidden within the mathematics of his general theory of relativity [4], the foundation of modern classical physics."
Mach uses that word "change" twice, and yet it does not seem that change was ever woven into Einstein's and Minkowski's spacetime, until now.
Finally we have been liberated from frozen time and the block universe, with a simple postulate and equation--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, or dx4/dt=ic.
This naturally implies x4 = ict, and thus all of relativity may naturally be derived from this postualte and equation of Moving Dimensions Theory.
Give me a 4D universe where
x1=x
x2=y
x3=z
and
x4=ict
And all of relativity will naturally arise--all because of a fundamental invariant--dx4/dt=ic--the fourth dimension is expanding relative to the three spatial dimensions.
Now a great thing about this hitherto unsung universal invariant--the expansion of the fourth dimension--is that as an invariant, it can also easily account for the slowing of light and time by gravity, as well as the gravitational redshift, as is done in the attached paper.
For the first time in the history of relativity, change has been woven into the fundamental fabric of spacetime with dx4/dt=ic.
Loved the Shakespeare quote too (from one of his sonnets), which tells us that change does indeed need to be woven into the fundamental fabric of spacetime, which is exactly what Moving Dimensions Theory does:
When forty winters shall besiege thy brow,
And dig deep trenches in thy beauty's ¯eld,
Thy youth's proud livery, so gazed on now,
Will be a tattered weed of small worth held.
Wheeler oft quoted Shakespeare. Modern physicists could benefit infinitely from a more classical liberal arts education--there's something about that heroic spirit, which underlies the advancement of art and science, that our academies are failing to teach these days.
I think you will enjoy my paper: Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken :
http://fqxi.org/community/forum/topic/238
"In his 1912 Manuscript on Relativity, Einstein never stated that time is the fourth dimension, but rather he wrote x4 = ict. The fourth dimension is not time, but ict. Despite this, prominent physicists have oft equated time and the fourth dimension, leading to un-resolvable paradoxes and confusion regarding time’s physical nature, as physicists mistakenly projected properties of the three spatial dimensions onto a time dimension, resulting in curious concepts including frozen time and block universes in which the past and future are omni-present, thusly denying free will, while implying the possibility of time travel into the past, which visitors from the future have yet to verify. Beginning with the postulate that time is an emergent phenomenon resulting from a fourth dimension expanding relative to the three spatial dimensions at the rate of c, diverse phenomena from relativity, quantum mechanics, and statistical mechanics are accounted for. Time dilation, the equivalence of mass and energy, nonlocality, wave-particle duality, and entropy are shown to arise from a common, deeper physical reality expressed with dx4/dt=ic. This postulate and equation, from which Einstein’s relativity is derived, presents a fundamental model accounting for the emergence of time, the constant velocity of light, the fact that the maximum velocity is c, and the fact that c is independent of the velocity of the source, as photons are but matter surfing a fourth expanding dimension. In general relativity, Einstein showed that the dimensions themselves could bend, curve, and move. The present theory extends this principle, postulating that the fourth dimension is moving independently of the three spatial dimensions, distributing locality and fathering time. This physical model underlies and accounts for time in quantum mechanics, relativity, and statistical mechanics, as well as entropy, the universe’s expansion, and time’s arrows."
Thanks for the paper & all the best,
Dr. E (The Real McCoy)
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attachments:
12_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf
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Dimi Chakalov wrote on Dec. 2, 2008 @ 05:20 GMT
Julian Barbour is again trying to suggest that (quote) "time should be banished" (end of quote), but the simple proof against his hypothesis is the fact that his brain is working.
Namely, no living brain can operate in a "block universe", because it will have to function as a Turing machine installed in some IGUS, and the perpetual "encoding of information", by any conceivable "code", will lead to decreasing of the entropy of the "hard drive", until the poor Turing machine develops severe structural damages and breaks down with a stroke.
Please check out the essay
'Quantum Mechanics 101'.
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Cristi Stoica wrote on Dec. 2, 2008 @ 09:53 GMT
Dear Dimi,
A Turing machine can be viewed as a succession of states, and the relation (transition, in a temporal view) between states is governed by the physical laws. Any Turing Machine can be embedded in a block universe, exactly as any algorithm can be stored on a storage device. You are right that the entropy is the enemy of such a machine, but nobody claims that our brains will live forever (although Tipler seems to overcome this problem).
Cristi Stoica
“Flowing with a Frozen River”,
http://fqxi.org/community/forum/topic/322
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Cristi Stoica wrote on Dec. 2, 2008 @ 10:24 GMT
Dear Dr. Barbour,
Contrary to the common impression, that the Newtonian Mechanics provides too little room for a more profound analysis of time, your essay proves the contrary. Thank you for this beautiful exposure.
Cristi Stoica
“Flowing with a Frozen River”,
http://fqxi.org/community/forum/topic/322
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Peter Lynds wrote on Dec. 3, 2008 @ 00:56 GMT
Dear Julian,
As with your recent talk at the Perimeter Institute on the same subject, I enjoyed your essay. I also very much agree with you that duration/interval does not exist and is merely an out-flow of motion. I have a question though. Do you still believe that instants and instantaneous magnitudes exist? If you perhaps do, and I get the impression from reading your essay that this is the case, I think that your view about time has some issues. Firstly, as they would constitute the building blocks of time, if one assumes the existence of instants (and instantaneous magnitudes), one also necessarily assumes the existence of time. Secondly, to deny the existence of interval, and yet hold onto instants, is not consistent, as, by definition, an interval is simply a duration bounded by two instants; as long as the instants are still there, the interval will be too. Indeed, if such instants existed, it can be shown that they would render change, motion, and as such, the idea of a clock, impossible.
Best wishes
Peter
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Chi Ming Hung wrote on Dec. 3, 2008 @ 01:44 GMT
Peter, not that I'm trying to answer for Julian, but I believe that the existence of instants does not necessarily have to entail the existence of intervening durations/intervals. In fact I argued in my essay that one can have a perfectly consistent theory of Time and Becoming where only instants (or moments of Becoming) are real, while the supposedly continuous happenings (e.g. the evolution of the wave function) in between instants are just mathematical artifacts. Let me give an example of how one might define intervals/durations in a theory with only instants:
Consider a certain number of cycles of a certain stable regularly recurring process, say 9192631770 cycles of the process corresponding to the radiation from the transition between the two hyperfine levels of the ground state of the Caesium 133 atom. We DEFINE this to be our unit of Time (it's the actual definition of a second). All other "intervels/durations" of Time are then measured with respect to this process. e.g. if two instants of certain events coincide with the 10th and 11th cycles of the photon process above, then we say the duration/interval between the two instants is 1/9192631770 second. That doesn't mean that anything real has to happen or exist in this duration/interval, because we can define change as simply the discrete transition from the state at one instant to the state at the next instant, WITHOUT ANYTHING HAPPENING IN BETWEEN. There's nothing wrong with such a theory of change, and in fact it seems to me that quantum mechanics demands such a theory of change.
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Ken Sasaki. wrote on Dec. 3, 2008 @ 04:42 GMT
Dear Chi Ming:
You say, “That doesn't mean that anything real has to happen or exist in this duration/interval, because we can define change as simply the discrete transition from the state at one instant to the state at the next instant, WITHOUT ANYTHING HAPPENING IN BETWEEN.” But you can then do away with any concept, such as velocity, or length, or energy, because you don’t know anything about it, if you are not observing it. There isn’t anything wrong with this, but is it especially useful? You make an assumption, regardless of whether you choose to believe that something is in between, or not.
Commenting more generally:
It seems to me that there is no physics in the choice between time emerging from relations between events and relations between events reflecting an underlying time. If time must be eliminated to explain observations, then there will be physics; but this was not demonstrated in the essay, even if you assume (see the end of the essay) a finite universe and no black holes.
In the end (again, see the end of the essay), the argument comes down to Occam’s razor. There is no problem with arguments based on Occam’s Razor, I have used it myself; and, in the end, it is often necessary. But is anything really simplified by eliminating time? I don’t think so; because you are not only left with events, but also an ordering of them. And what does time do? It orders events. Even if you eliminate time, you must keep the ordering. The replacement of the concept of time, with some other conceptual ordering does not get you anything; even if you want to call it purely abstract, it is just time, by another name.
Or, with different semantics: Either you have time plus events producing an emergent order, or events plus an order producing an emergent time – there is a difference, but not a simplification; so Occam’s Razor cannot choose.
Finally, note that there is another essay, arguing for time but no space, at:
http://fqxi.org/data/essay-contest-files/Markopoulou_Spac
eDNE.pdf
I think that you can define away space, just as easily as you can define away time; but, again, I see no physics in it (yet).
Take care,
Ken.
http://fqxi.org/data/essay-contest-files/Sasaki._TD
oT.pdf
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Ken Sasaki. wrote on Dec. 3, 2008 @ 04:53 GMT
I forgot to add, to my initial comments, that this essay did a really great job of presenting some very interesting material.
Ken.
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Peter Lynds wrote on Dec. 3, 2008 @ 05:14 GMT
Dear Chi Ming Hung,
Thanks. I would recommend having a look at my essay for an explanation of what is I think is wrong with that idea.
Best wishes
Peter
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Chi Ming Hung wrote on Dec. 3, 2008 @ 23:06 GMT
Ken,
I disagree that there's no physics if we "define away time". First of all, I'm not advocating the elimination of Time like some in the quantum gravity camp (and Julian) are advocating. The idea I'm trying to put across is that we should eliminate the Time **CONTINUUM** as something unphysical, because there's no need for it except as a mathematical convenience.
And this is not just a matter of convention either, because by treating Time as though it's a physical continuum, physicists are led to the inevitable paradoxes between continuous unitary evolution between measurements, and discontinuous non-unitary transitions during measurements. And to make matters worse, most physicists seem to think that the UNOBSERVABLE continuous evolution of the wave function is the true physics while the OBSERVABLE quantum jumps are the aberrations that needed to be explained away (e.g. using decoherence). This seems most illogical to me.
I think we can all learn a lesson from how things are done in the early days of Quantum Mechanics, when Heisenberg and company were trying to work out Matrix Mechanics in order to explain the correlations between observables (and only observables) like the frequencies of light from atomic spectra and their relative intensities, with a minimum of mathematical assumptions. It's true that even Heisenberg and company assumed the time continuum and wrote exp(-iwt) for a process of frequency w (omega), but my point is that we should keep the physically unobservable mathematical assumptions in our theories to a minimum and recognize that's what they are: just mathematical assumptions. In fact I think Quantum Mechanics would have developed very differently (and much more logically) had Heisenberg and company gone all the way with their philosophy and eliminated even the unobservable exp(-iwt) from their equations...
And you're right that if we eliminated the Time continuum, then all we're left with are just instants and their orders. But that's all we need! My contention is that modern physics (esp. Quantum Mechanics and General Relativity) can be recast into physics about only instants and their orders, and when this is done, we can gain deeper insights into physics that have been hidden from us by the unphysical Time continuum.
And I think that's not very far from Julian's ideas...
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Ken Sasaki. wrote on Dec. 4, 2008 @ 01:03 GMT
Dear Chi Ming:
Thank you for your comments.
You state, “And this is not just a matter of convention either, because by treating Time as though it's a physical continuum, physicists are led to the inevitable paradoxes between continuous unitary evolution between measurements, and discontinuous non-unitary transitions during measurements.” You also state that you find certain attempts, to reconcile the continuous with the discontinuous, to be “most illogical”.
I don’t think that discretizing time is necessarily objectionable; but I think that there should be a real reason, based on observation. I do object to the idea that there is any utility in abandoning the concept of time entirely. In addition, I agree that there are certainly discontinuities in QM; and, if time must be discretized, to prevent a paradox, then doing so is mandatory. But is there really a paradox, as you say – a logical contradiction – in continuous time evolution, with discontinuities at certain interactions; or is it just something that seems odd? If there is a logical contradiction, can you please explain it to me?
Consider also that, while there are situations that observably demonstrate discontinuity (EPR and other entanglement situations; many worlds not withstanding), most situations do not. Note also that “collapse of the wave function” is peculiar to certain interpretations of QM, but not all. If you are going to discretize time, to make everything look like wave-function collapse, then you are, in effect, choosing certain interpretations, over others; and to do this, you should have an observation that supports those interpretations, over the others. Can you please tell me if you have such an observation?
Take care,
Ken.
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Chi Ming Hung wrote on Dec. 4, 2008 @ 02:11 GMT
Ken,
you seemed to have misunderstood me when I said:
"And to make matters worse, most physicists seem to think that the UNOBSERVABLE continuous evolution of the wave function is the true physics while the OBSERVABLE quantum jumps are the aberrations that needed to be explained away (e.g. using decoherence). This seems most illogical to me."
What's illogical a priori is not that we may have a theory with "continuous time evolution, with discontinuities at certain interactions", but rather that physicists are treating the **UNOBSERVABLE** part of the wave function evolution as true physics, while treating the **OBSERVABLE** quantum jumps as aberrations. To me, it should be the other way round, treating observable phenomena as true physics, while relegating the unobservable part of physics as mere mathematical convenience.
As for the reality of quantum jumps or wave function collapses, I suppose many physicists are still unwilling to accept it because it contradicts what they believe to be the true physics behind quantum mechanics, namely the continuous and unitary evolution of the wave function. I guess what I prefer to call reality is not something that lives in a Platonic world of mathematical ideals, but rather what I see with my own eyes (and with the help of instruments): I see always a world of definite states, never fuzzy quantum superpositions. You asked me for evidence of my "interpretation" over others, that's what I submit.
But let me ask you for evidence to the contrary: Please show me any physical evidence of a wave function that evolves continuously in time. I don't think you can, because BY DEFINITION, it's unobservable! The best you can do is to point out experiments (e.g. interference and entanglement experiments) that INDIRECTLY implies the existence of a wave function that evolves continuously in time, but that's all. You never see a ghostly ether-like wave leisurely traversing space and time, all you ever see are dots and discrete events in your screens and instruments.
I'm not arguing against the utility of using a mathematical wave function that evolves continuously in time, what I'm arguing against is to take this mathematical convenience too seriously and think that it is physical reality.
The development of 20th century physics has taught us that what's not directly observable should not be treated as real. Such is the case for the ether, the absolute time of Newton, and a list of other ideas. My contention is simply that the Time continuum and the denizens that evolve in it should join the list and be recognized as what they are: mathematical conveniences, not physical realities.
(P.S. I should apologize to Julian for hogging the forum for his essay. I think we should continue this discussion in our essays' forums...)
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Mark Stuckey wrote on Dec. 4, 2008 @ 21:39 GMT
Dear Julian,
I appreciate your attempt to provide "an equation of time," thereby demoting time from its otherwise fundamental status. I've a question concerning this proposal that I'm hoping you will answer.
In order to use your definition, I need to unambiguously identify entities in different configurations, e.g., THAT planet in configuration 2 is Mars and it is the SAME planet I called Mars in configuration 1. I need this identification process articulated so I can measure the delta d’s, for example. How do you define this identification process without bringing time in the back door? Isn't this identification process precisely the basis of "trans-temporal identification?"
Thanks,
Mark
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Chris Clyde wrote on Dec. 5, 2008 @ 13:00 GMT
Dr. Julian
I am impressed with your handling of the "Big Picture".
The way I understand your proposal is, to answer Mark Stuckey above, yes time comes in the back door as the sidereal choice necessary to make eq. (3) a relational, quantitative measure. Then time is led right back out the front door when its utility is exhausted in finding the principle of least action it defines in the motion observed.
I found your analogy of the synchronous relation of arcs swept out by the tips of hands of different clocks very enlightening.
It seems both you and Carlo Rovelli propose time should emerge From and As the kinematics of observable (local) variables via the principle of general relativity.
i.e. "extremal curves" are not absolute but locally finite.
Your ideas on time can apply with equal efficiency to mass and space, for once you have set mechanics "fully adrift" in the relativistic sea, all three dimensions emerge in a similar way. Your "extremal curve" is a physical constant, an observable that is defined by its dynamical equivalent observed in the constancy of the speed of light. The kinematics expressed by the principle of least action arise from the dynamics that define the three fundamental dimensions as different aspects of the same thing.
Although my essay won't win or place in this competition and few will even realize what I've said, I am very grateful for your work here as both you and Carlo have offered methodology to my madness. The model I've presented is so far adrift in general relativistic scope, no one would dare jump aboard without the compass you have designed.
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Chris Kennedy wrote on Dec. 5, 2008 @ 18:15 GMT
Dr. Barbour,
Terrific essay. My questions are:
If the universe can tell perfect time and could be considered the perfect clock, how would that assumption be affected if it is determined that there is no absoulte age of the universe? If I am living on a far away galaxy accelerating at a much faster velocity than ours - then (assuming I take enough vitamins to live through the whole process) how old do I think the universe is from my perspective? Or, how old is the universe to me if I am near a black hole or better yet - If a very long time ago I watched the big bang from a safe distance (where my gravity and velocity would be very different compared to being "inside" the universe) how old would I think the universe is right now? Who would be correct?
Take care,
CJ
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anon wrote on Dec. 9, 2008 @ 00:27 GMT
"Duration" is not physical. It can't be found in the heavens. It has meaning only in the presence of an observer.
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Lawrence B. Crowell wrote on Dec. 12, 2008 @ 00:54 GMT
Hi,
I thought your paper was fun. The ending was good.
I will say right off that I think the issue of whether time exists or not is irrelevant, even though time has some mysterious elements to it. I do think it is something which is operational with respect to the universe, and not something which the universe operates according to. I found your section one relative timess,in particular on page 7 with the ratio of times for two solar systems interesting. My paper #370 illustrates how time is a scaling principle. I illustrate a program for a renormalization group system for energy (or its conjugate time) on different scales. Your classical mechanical example at its kernel is I argue for.
cheers,
Lawrence B. Crowell
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Anonymous wrote on Dec. 16, 2008 @ 00:53 GMT
Dr. Barbour:
Your paper was interesting for me to read, as it arrives at the same conclusions as mine, although clearly in a much more rigorous way.
After all that we have learned from science in the last few centuries, one might think that we would have learned to separate physical reality from what our senses perceive. Clearly, though, there are few that are ready to take that step.
James Tyson
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Dimi Chakalov wrote on Dec. 19, 2008 @ 21:20 GMT
Dear colleagues,
I'm afraid there is no sense in posting our comments and questions here, because Julian Barbour lives in a different world, and just doesn't care.
Dimi Chakalov
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anon wrote on Dec. 20, 2008 @ 23:39 GMT
Isn't that the point? We all live in different worlds.
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amrit wrote on Dec. 23, 2008 @ 16:10 GMT
Dear friends,
we live all in the same world and all in his/her individual mind.
The spirit of science is to build up a model of the SAME world that we all agree on it.
Regarding time I do not agree with the Julian that motion and time are ilusions...According to my research time is a coordinate f motion...
yours amrit
attachments:
2_In_The_Theory_of_Relativity_Time_is_a_Coordinate_of_Motion__Sorli_2009.pdf
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amrit wrote on Dec. 28, 2008 @ 15:25 GMT
Eleven steps to right understanding of time
1. Motion of objects and particles do not happen in time, it happens in space only.
2. Time is what we measure with clocks: with clocks we measure duration and numerical order of massive objects and elementary particles motion into space.
3. As a “fourth” coordinate of space-time time is a “coordinate of motion”, it describes motion of massive bodies and particles into space.
4. Space-time is a math model only; space-time does not exist as a physical reality.
5. In a model of space-time we describe motion of objects and particles into space.
6. Space itself is atemporal.
7. Humans experience atemporal space as a present moment.
8. Past and future exists only in the mind; physical past and future do not exist.
9. Time as a coordinate of motion in atemporal space exists only when we measure it.
10. Time as a “coordinate of motion” is not elementary physical quantity as energy matter, space and motion are.
11. Universe is an atemporal phenomenon.
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Narendra Nath wrote on Dec. 30, 2008 @ 11:25 GMT
Both space and time are concepts formulated to relate the physical phenomena, all of these show some kind of motion.
Motions may be conceptualized otherwise. A new set of concepts may then emerge. Such concepts are checked by the correctness of theories based on them. Let us have alternate concepts to space and time that cover the entire range of physical phenomena. Merely if quantum gravity needs to be invoked to understand the behavior of black holes, does not mean that gravity has to be quantum in nature or even the quantum mechanics provides the only way to understand the phenomena at micro-level. Alternate explanations may emerge in the future, as Einstein himself indicated that he was not particularly happy with the probabilistic nature of quantum mechanics. Carrying one's own bandwagon all the time can be quite distressing for any individual! Openness and unbiased approach appears to be best to follow in the growth of any science worth the name.
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Julian Barbour wrote on Dec. 30, 2008 @ 16:48 GMT
Apologies for not responding to the postings until now. I would like to assure Dimi Chakalov that I do live in the same world and do care. However, personal circumstances make it difficult for me to keep up with things in the way I would like. Let me now answer some of the postings.
1. Peter Lynds, Dec. 2nd. In my view, instants have no magnitude. I liken them to snapshots. The basis of all my work about motion and time is that it is the difference between such snapshots that counts. The difference is found by a process called best matching, as I explained in my book The End of Time and in the papers cited on my website platonia.com. The best-matched difference between two nearly indentical 'snapshots' then measures the duration between them. The magnitude is 'between' the snapshots, not in them.
2. Ken Sasaki on Dec. 3rd. Your comments about Occam's razor are certainly correct as far as classical physics is concerned. However, quantum theories of the universe with and without time are likely to be very different and have correspondingly different observable predictions. Unfortunately, we have no such theory as yet with or without time. If my work does have value, I believe it will be for the hints that it may give about how to create a quantum theory of the universe.
3. Mark Stuckey, Dec. 4. Your comment is very well made and was the main reason why Bertotti and I introduced the idea of best matching in order to develop a theory of fields in which permanent identity cannot be postulated. This leads to comparison of complete field configurations. There is a PDF file of my 1982 paper with Bertotti on my website platonia.com if you or anyone else are interested. In my essay I thought it was reasonable to take the short cut; I am confident that the whole theory can go through without "bringing time in the back door".
4. Chris Kennedy, Dec. 4. I described how duration arises only for a Newtonian-type situation. Something similar but much more sophisticated happens in general relativity. It may be that in the scenarios that you describe my way of accounting for the appearance of time fails, as I acknowledged briefly at the end of my essay.
5. anon, Dec. 9. I agree that we only learn about duration through our observations, but I am a realist and make the working assumption that there is a real universe 'out there'. I am not sure whether you are advocating solipsism.
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anon wrote on Dec. 31, 2008 @ 17:09 GMT
Julian, "solipsistic" only as to "duration" which seems to have no meaning apart from the psychological
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Peter Lynds wrote on Jan. 1, 2009 @ 00:18 GMT
Dear Julian,
Thanks for your reply. Can you see though that by asserting/assuming the existence of zero duration instants (the regular definition of an instant), snap-shots (another name for an instant), and nows (the present tense version of an instant), you are also asserting/assuming the existence of time? The same applies to assuming the existence of instantaneous magnitudes, such as velocity, momentum etc. Given that instants would constitute the building blocks of time, it is analogous to saying that water doesn't exist, but that water molecules (or ice-cubes) do (and in relation to instantaneous magnitudes, that things can also be frozen in such ice-cubes). The only difference is that instants have zero size, but this not effect the validity of the analogy.
If one accepts the existence of instants and instantaneous magnitudes, as well as this assuming the existence of time, one must also deny motion and change, which is violently at odds with observation, and I think, reason too. I realise that you do not believe in change and motion, and indeed, neither does one who accepts the standard interpretation of the block universe, so this need not signal a problem, but this leaves one unable to imply any continuity, including even the "sense" of it for an observer. In your work, you argue that there are countless zero duration instants/snap-shots underlying the universe. You argue that such instants are unrelated to each other and they do not progress from one to the next. The problem with this is that it renders it impossible for even a "sense" of succession or continuity to arise. In order for an observer to think that he observes things moving, there must be a succession of these instants for him. Because your model says that such a succession is not possible, even his perception of motion and change is impossible. Indeed, he is unable to even think. Again, this is violently at odds with observation.
If one denies the existence the instants, instantaneous magnitudes, space-time points etc, however, motion and change suddenly become possible, the problems and paradoxes disappear, and this is still completely compatible with relativity and the lack of absolute simultaneity. That is, one gets an evolving block universe (with all times shown by a clock sharing equal footing) that is completely timeless.
Best wishes
Peter
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Julian Barbour wrote on Jan. 7, 2009 @ 17:55 GMT
In response to the last two posts, I am afraid the one from anon is too enigmatic for me to understand. With regard to your comments Peter, I agree that they seem reasonable on the basis of our conscious experiences, but direct experience has often proved a hindrance to advance in science. Galileo made this point with tremendous skill. As a theoretical physicist, I come to a position that does seem almost impossible to believe on the basis of direct experience, but I recognize that my theoretical model must contain structure correlated with experience. I believe that my idea of 'snapshot-within-snapshot' time capsules as presented in my The End of Time meets this minimum requirement and puts me very close to Boltzmann's position. I freely admit that at the end I must rely on the unknown way in which structure in the brain can lead to conscious experience.
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Peter Lynds wrote on Jan. 9, 2009 @ 02:25 GMT
Dear Julian,
Thanks for your thoughtful comments. I'm somewhat hesitant to say this, as I appreciate the manner of your replies, and I don't at all want to be confrontative (hopefully you won't take the following as such), but you seem reluctant to acknowledge my point that to assert/assume the existence of instants and instantaneous magnitudes, one also asserts/assumes the existence of time. In relation to instants (and instantaneous magnitudes), and although from reading your book, I already know at least part of the answer to this question, can I ask what the basis of your belief in them is?
I agree that direct experience has often proved a hindrance to advance in science. I think Galileo and Copernican vs. Ptolemaic theory, Mach's criticism of Boltzmann, the speed of light being frame independent, or our perception of time flowing, are all really good examples of this. I feel the issue of change/motion being illusionary is somewhat different, however, because, with the exception of what I see as being incorrect assumptions, I think pretty much everything, not only experience, but reason, physical intuition, the need to avoid paradox, etc, points against it too. Indeed, as I think motion and change are the actual basis of physics, without them, I don't see how one can even talk of physics. Of course, physicists who deny motion/change because of their interpretation of gr or qm and the related formalism, still write papers and do physics, but they also still assume change whenever they talk of evolution or accept and work with variable magnitudes or values (i.e. constantly). I find this situation – seeming apathetic acceptance of an overtly contradictory position – somewhat bizarre. Your proposal is obviously immune from this criticism, as there is no assumption of continuity there at all. I'm unable to see though how a changeless physical universe can give rise to the perception of change for physically based observers.
Best wishes
Peter
post approved
John Merryman wrote on Jan. 10, 2009 @ 00:07 GMT
Peter,
It poses some interesting conceptual analysis of the thought processes involved that the search for the immutable and unchanging laws of the universe have resulted in the conclusion that the universe is immutable and unchanging. That the dynamic which so overwhelms the physical reality in which we find ourselves is supposedly just an illusion. Is physics static, or is it just the institution of physics which is static?
I agree that time is linearity of motion, not the basis for motion. I also think it is quantized by intervals of non-linear motion, be it quantum fluctuations or geologic earthquakes. Complexity Theory offers some logical support.
post approved
Dr. E (The Real McCoy) wrote on Jan. 10, 2009 @ 20:53 GMT
Hello All,
I am rather amazed and perplexed to read statements such as, "I agree that direct experience has often proved a hindrance to advance in science."
This is like George Bush's recent statement that to save the free market, he had to abandon free market principles.
Physics, and the quest for *physical* reality rooted in the senses and *physical* models has ever...
view entire post
Hello All,
I am rather amazed and perplexed to read statements such as, "I agree that direct experience has often proved a hindrance to advance in science."
This is like George Bush's recent statement that to save the free market, he had to abandon free market principles.
Physics, and the quest for *physical* reality rooted in the senses and *physical* models has ever advanced physics.
Do not take my word for it, but listen to those greats far greater than I.
"Gradually the conviction gained recognition that all knowledge about things is exclusively a working-over of the raw material furnished by the senses. ... Galileo and Hume first upheld this principle with full clarity and decisiveness." --(Albert Einstein, Ideas and Opinions)
"But before mankind could be ripe for a science which takes in the whole of reality, a second fundamental truth was needed, which only became common property among philosophers with the advent of Kepler and Galileo. Pure logical thinking cannot yield us any knowledge of the empirical world; all knowledge of reality starts form experience and ends in it. Propositions arrived at by purely logical means are completely empty as regards reality. Because Galileo saw this, and particularly because he drummed it into the scientific world, he is the father of modern physics -- indeed, of modern science altogether." --Albert Einstein, Ideas and Opinions
"I have hardly ever known a mathematician who was capable of reasoning."--Plato
The above quote is hanging in the Boston Museum of Science, and it seems to agree with Albert Einstein, Galileo, and Max Born:
http://www.ilfilosofo.com/blog/2008/04/12/plato-mathema
tician-quote/
"I personally like to regard a probability wave as a real thing, certainly as more than a tool for mathematical calculations. ... how could we rely on probability predictions if we do not refer to something real and objective? (Max Born on Quantum Theory)"
Max Born wrote, "All great discoveries in experimental physics have been made due to the intuition of men who made free use of models which for them were not products of the imagination but representations of real things."
To reject *physical* intuition and replace it with the nonsensical block universe MDT does away with seems to go exactly against the spirit by which physics has ever advanced, according to Galileo, Einstein, and other noble physicists.
It seems a preposterous conclusion that quantum mechanics, which works so very well, must be thrown out and reformulated for something which MDT shows there is no need for--the block universe.
"In the long run my observations have convinced me that some men, reasoning preposterously, first establish some conclusion in their minds which, either because of its being their own or because of their having received it from some person who has their entire confidence, impresses them so deeply that one finds it impossible ever to get it out of their heads. Such arguments in support of their fixed idea ... gain their instant acceptance and applause. On the other hand whatever is brought forward against it, however ingenious and conclusive, they receive with disdain or with hot rage - if indeed it does not make them ill. Beside themselves with passion, some of them would not be backward even about scheming to suppress and silence their adversaries. I have had some experience of this myself. ... No good can come of dealing with such people, especially to the extent that their company may be not only unpleasant but dangerous."--(Galileo Galilei)
"my dear Kepler, what do you think of the foremost philosophers of this University? In spite of my oft-repeated efforts and invitations, they have refused, with the obstinacy of a glutted adder, to look at the planets or Moon or my telescope." --Galileo Galilei
We must forver keep physical reality in the front and center, along with logic and reason and *physical* intuition--otherwise progress in physics will grind to a halt, as it has for the past thirty years.
Math can be very pretty, but Einstein reminds us that physicists ought pursue *physics,* founded in a physical reality--“Mathematics are well and good but nature keeps dragging us around by the nose.”"
"It is anomalous to replace the four-dimensional continuum by a five-dimensional one and then subsequently to tie up artificially one of those five dimensions in order to account for the fact that it does not manifest itself." –Einstein to Paul Ehrenfest. Just think what Einstein would have said about entire parallel universes we cannot see!
With an heroic spirit, MDT takes us back to origin of modern physics--to the original papers on relativity and QM, and it humbles itself upon that mountaintop. And when it comes on down, off the shoulders of relativity and QM's giants, MDT presents us with a fundamental view of reality that conforms to all experimental evidence, while not only resolving the paradoxes of the non-locality of the EPR effect and seemingly frozen time in Godel’s block universe, but also unifying the resolution of both physical curiosities within a simple physical postulate--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic. In a sense, this is the first theory to predict QM's nonlocality and entanglement, by postulating that the fourth dimension is inherently nonlocal via its expansion--an empirical fact that the timeless, ageless, nonlocal photon agrees with, as the photon surfs the fourth expanding dimension. And not only does MDT predict this, but it also provides a *physical* model for entropy and time and all its arrows and assymetries throughout all realms. And finally, all of relativity may be derived from MDT's simple postulate, as it is in my paper--the fourth dimension is expanding relative to the three spatial dimensions--dx4/dt = ic. A postulate and an equation representing a novel *physical* feature of our universe--a fourth expanding dimension--and the natural, subsequent prediction of all of relativity, qm's nonlocality, entropy, time's arrows and assymetries in all realms, and quantum entanglement.
"I don't believe in mathematics."-- Quoted in Carl Seelig. Albert Einstein.
Do not worry about your difficulties in mathematics, I assure you that mine are greater. --Einstein
Geometry is not true, it is advantageous. --Jules H. Poincare
In Disturbing the Universe, Freeman Dyson writes, "Dick [Richard Feynman] fought back against my skepticism, arguing that Einstein had failed because he stopped thinking in concrete physical images and became a manipulator of equations. I had to admit that was true. The great discoveries of Einstein's earlier years were all based on direct physical intuition. Einstein's later unified theories failed because they were only sets of equations without physical meaning. Dick's sum-over-histories theory was in the spirit of the young Einstein, not of the old Einsetin. It was solidly rooted in physical reality." --Freeman Dyson
Smolin writes in TTWP that Bohr was not a Feynman “shut up and calculate” physicist, and from the above Dyson quote, it appears that Feynam wasn't either:
“Mara Beller, a historian who has studied his [Bohr's] work in detail, points out tha there was not a single calculation in his research notebooks, which were all verbal argumen and pictures.” --Smolin's The Trouble With Physics
In Dark Matters, Dr. Percy Seymour writes, "Albert Einstein was a great admirer of Newton, Farady, and Maxwell. In his office he had framed copies of portrtais of these scientists. He had this to say about Farady and Maxwell, in "Maxwell's Influence on the Development of the Concept of Physical Reality": "The greatest change in the axiamatic basis of physics--in other words, of our conception of the structure--since Newton laid the foundation of theoretical physics was brought about by Faraday's and Maxwell's work on electromagenetic phenomena" --p. 33-34, DARK MATTERS
In his book Einstein, Banesh Hoffman tells us: "Meanwhile, however, the English experimenter Michael Farady was making outstanding experimental discoveries in electricity and magnetism. Being largely self-taught and lacking mathemtical facility, he could not interpret his results in the manner of Ampere. And this was fortunate, since it led to a revolution in science. . . Ampere and others had conentrated their attention on the visible hardware--magnets, current-carrying wires, and the like--and on the numbers of centimeters separating the pieces of hardware. In so doing they were following the action-at-a-distance tradition that had devloped from teh enormous success of the Newtonian system of mechanics and law of gravitation. . .But Faraday regarded the hardware as secondary. For him the important physical events took place in the surrounding space--the filed. This, in his mind, he filled with tentacles that by their pulls and thrusts and motions gave rise to the electromagnetic effects observed. Although he could thus interpret his electromagnetic experiments with excellent precision and surprising simplicity, most physicists adept at methematics thought his concepts mathematically naive."--BANESH HOFFMAN, EINSTEIN
It is interesting that Einstein introduced relativity as a principle--as a primary law not deduced from anything else.
Well, I guess I was dumb enough to even ask, "why relativity?"
And I found the answer in a more fundamental invariance--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic. Change is fundamentally embedded in space-time. And not only can all of relativity be derived from this, but suddenly we have a *physical* model for entropy, time and its arrows and assymetries in all realms, free will, and quantum nonlocality and entanglement.
Best,
Dr. E (The Real McCoy)
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post approved
John Matthewson wrote on Jan. 20, 2009 @ 19:02 GMT
What is the principle of least action in a four dimensional manifold? For surely we need to extend Barbour's 3D analysis in the light of temporal double slit experiments.
See Horwitz 2005 On the Significance of a Recent Experiment
Demonstrating Quantum Interference in Time
(http://arxiv.org/abs/quant-ph/0507044 ).
post approved
Dr. E (The Real McCoy) wrote on Feb. 15, 2009 @ 18:53 GMT
Hello Julian! Hope all is well! I was wondering what your take might be on Lee Smolin's most recent comments-- reflecting his epic change of mind--that time is indeed now real.
It is great that Lee is coming around and seeing time as a *physically* real entity. MDT goes a step further in seeing time as a *physically* real entity that emerges because of a more fundamental, universal,...
view entire post
Hello Julian! Hope all is well! I was wondering what your take might be on Lee Smolin's most recent comments-- reflecting his epic change of mind--that time is indeed now real.
It is great that Lee is coming around and seeing time as a *physically* real entity. MDT goes a step further in seeing time as a *physically* real entity that emerges because of a more fundamental, universal, hitherto unsung *physical* invariant--the fourth dimension is expanding relative to the three spatial dimensions at c:
In January 2009 Smolin wrote at The Edge, "THE LIBERATION OF TIME
I would like to describe a change in viewpoint, which I believe will alter how we think about everything from the most abstract questions on the nature of truth to the most concrete questions in our daily lives. This change comes from the deepest and most difficult problems facing contemporary science: those having to do with the nature of time." --http://www.edge.org/q2009/q09_9.html
On Thu Jan 25, 2007 11:07 am, I used the word "liberate" in writing, "MDT unfreezes time, liberating us all with free will-the free will to move beyond ST & LQG, which are not inextricably locked into the fixed future of the block universe as Brain Green and Paul Davies would have you suppose. Neither the future nor the past exists. Motion is inherent in the underlying four-dimensional space-time geometry, as the fourth dimension is expanding relative to the three spatial dimensions. Einstein noted that all objects are moving through space-time at the velocity c. This never changes. An object stationary in the three spatial dimensions is translating through the fourth dimension at the rate of c. An object stationary in the fourth dimension-a photon-is translating through the three spatial dimensions at the rate of c. Hence it is obvious that the fourth dimension is expanding relative to the three spatial dimensions. String Theory's greatest contribution to physics has been the utter rejection of the obvious, the denial of common sense, and the institutionalization of thousands of mediocrities to ignore or shout-down any physics that might get in the way of their vast commercial industries which must trump truth-their salaries, benefits, and science-fiction books. Indeed, ST gives full license to make one's ignorance one's arrogance, and thus it is the breeding ground for those with ambitions overshadowing their talents." --http://www.groupsrv.com/science/about204630.html
In January 2009, Smolin writes "There is also no past. The past only lives as part of the present, to the extent that it gives us evidence of past events. And the future is not yet real, which means that it is open and full of possibilities, only a small set of which will be realized. Nor, on this view, is there any possibility of other universes. All that exists must be part of this universe, which we find ourselves in, at this moment."
--http://www.edge.org/q2009/q09_9.html
In January, 2007, I wrote, "Neither the future nor the past exists. Motion is inherent in the underlying four-dimensional space-time geometry, as the fourth dimension is expanding relative to the three spatial dimensions. Einstein noted that all objects are moving through space-time at the velocity c. This never changes. An object stationary in the three spatial dimensions is translating through the fourth dimension at the rate of c. An object stationary in the fourth dimension-a photon-is translating through the three spatial dimensions at the rate of c. Hence it is obvious that the fourth dimension is expanding relative to the three spatial dimensions. "
All of this was posted in an amazon.com forum on 11/13/2006 for Lee's Book: The Trouble With Physics: The Rise of String Theory, The Fall of Science, and What comes Next:
http://www.amazon.com/Lee-Smolins-Great-Book-Dimensions
/forum/Fx1FYSVRZO4ARYG/Tx3BGVHQPRMS4OD/1
/ref=cm_cd_dp_tft_tp
?%
5Fencoding=UTF8&s=books&asin=061891868X&store=books
"Lee Smolin's Great Book : A Dialogue with Lee Smolin / Moving Dimensions Theory"
Over the years I have shared several emails with Lee, Including this one from 9/26/07--I have yet to hear back, but now that he thinks time is real, perhaps he might find some :):
to lsmolin@perimeterinstitute.ca
date Wed, Sep 26, 2007 at 11:56 AM
subject Hello Lee: The Curious Nature of the Photon, Einstein's Annus Mirabilis, and Moving Dimensions Theory
Hello Lee,
Hope all is well with you--just bought a second copy of TTWP to read while in the server room, recovering some lost data. :) Loved it even more the second time around.
If you ever get a moment, would be grateful for any comments on MDT.
Keep up the great work!
Elliot
INTRODUCTION TO MDT
As the hallmark of Moving Dimensions Theory is a simple postulate reflecting an underlying physical reality, let us begin with the simple postulate:
The fourth dimension is expanding relative to the three spatial dimensions.
That is it. This postulate underlies relativity--length contraction, time dilation, and the equivalence of mass and energy. It underlies quantum mechanics--wave interference, tunneling, entanglement. It underlies statistical mechanics--entropy and time's arrow.
The great power of Moving Dimensions Theory is that the simple postulate, representing an underlying physical reality, explains curious physical phenomena in every realm-from relativity, to quantum mechanics, to statistical mechanics. MDT accounts for quantum entanglement and relativistic length contraction. It accounts for entropy and action-at-a-distance. MDT unifies all of time's arrows, and it shows that all the curious dualities-wave/particle, space/time, and mass/energy, derive from the same source. MDT resolves both the paradox of Godel's block universe/block time and the Einstein, Rosen, and Podolsky paradox.
MDT--a simple sentence brought forth by a single individual--is what physics ought to be all about--descriptions of physical reality that unify and explain physical phenomena with simple, concise underlying physical models. And, as MDT predicts relativistic length contraction, entanglement, the constant velocity of light, and wave interference, it is one of the best-tested theories of all time, in addition to being a most fundamental theory regarding the emergent nature of time.
The Curious Nature of the Photon, Einstein's Annus Mirabilis,
and Moving Dimensions Theory
As the contemplation of the photon lead to both quantum mechanics and relativity, let us also begin the presentation of Moving Dimensions Theory by contemplating the photon. Einstein's revolutionary 1905 papers included one devoted to the photoelectric effect—which considered the quantized nature of the photon—and a paper devoted to the electrodynamics of moving bodies—which considered electromagnetic radiation, relativity, and the wave properties of the photon as embodied by Maxwell's Equations. Another 1905 paper discussed statistical mechanics in the form of Brownian Motion, and Einstein's final three-page paper that year commented on the equivalence of mass and energy, as denoted with his famous equation, E=mc 2. Moving Dimensions Theory underlies and unifies all of Einstein's 1905 papers with its simple postulate—the fourth dimension is expanding relative to the three spatial dimensions.
Consider the emission of a photon in free space. One second later, the photon has equal probability of being found anywhere upon a sphere with a radius of 186,000 miles, as the velocity of light, c, is 186,000 miles per second. If we covered the surface of said sphere with detectors, one, and only one, would click. And the photon, although having traveled 186,000 miles through space, will not have aged one iota, for time stops at the speed of light. The photon will have traveled 186,000 miles through the three spatial dimensions, and yet it will not have moved one iota in the fourth dimension. And there lies our first clue to moving dimensions theory. For how can a photon propagate 186,000 in the three spatial dimensions, and yet not budge an inch in the fourth dimension, unless that fourth dimension is expanding, right along with it? Ergo, the fourth dimension is expanding relative to the three spatial dimensions. A photon, as we shall see time and again, is matter surfing the fourth expanding dimension.
Consider two interacting photons that are directed to propagate in opposite directions, as in experiments conceived by Bell and conducted by Aspect et al. One second later, each photon's polarization is measured at detectors separated by 372,000 miles. According to the laws of quantum mechanics and numerous supporting experiments, the measurement at one detector instantaneously affects the measurement at the second detector. It is as if the photons are yet side-by-side for all intents and purposes. This "spooky action-at-a-distance," as Einstein called it, is not so spooky in the context of Moving Dimensions Theory, for MDT states that although separated by 372,000 miles, the photons are yet in the exact same place in the fourth dimension, as the fourth dimension is expanding relative to the three spatial dimensions. So it is that quantum phenomena on the photonic level, as well as relativistic phenomena on the photonic level, are both accounted for with simple elegance via MDT: the fourth dimension is expanding relative to the three spatial dimensions.
Another paper Einstein penned in 1905 was devoted to Brownian motion and statistical mechanics. Drop a thimbleful of food coloring in a pool. The laws of statistical mechanics dictate that there is a high probability that the coloring will spread throughout the entire pool, and never again reassemble in a localized region. That all systems tend towards random disorder is a fundamental law of physics and condition of physical reality, and this too can be accounted for by Moving Dimensions Theory. As the fundamental motion of the universe is the expansion of the fourth dimension relative to the three spatial dimensions, two photons originating from a common origin will harbor a vast probability of being found at great distances from one another one second later—distances far greater than the distance that separates them at their emission. This is because each one has an equal probability of being found anywhere upon the surface of a spherically-symmetric wave front of probability, corresponding to the wave front of the fourth expanding dimension. Recall our system of detectors placed everywhere upon the surface of a sphere with a radius of 186,000 miles—each photon has an equal chance of being found at any detector after one second after they were emitted at a common origin, and chances are that the detectors will be farther apart than the distance of zero that defines the separation between photon's common origin. Hence entropy. Entropy arises because the fourth dimension is expanding relative to the three spatial dimensions. All particles undergoing thermal vibrations interact with photons, and all photons reside in the fourth expanding dimension, dragging all of entirety into random disorder.
Yet another paper published by Einstein in his "Miraculous Year" (annus mirabilis), was devoted to the equivalence of mass and energy. Think about the fascinating physical reality implied by Einstein's most famous equation—E=mc2. A kilogram of gold or lead or feathers sitting on a desktop is the same thing as 9x10 16 joules of energy—an exorbitant amount of energy—enough to power, or to destroy, a major city. How is it that a stationary mass possesses such a great energy? It is because the mass, which is stationary in the three spatial dimensions, is yet propagating through the fourth dimension at the rate of c. This is because the fourth dimension is expanding relative to the three spatial dimensions. Matter surfing the fourth expanding dimension appears at photons. Furthermore, as noted earlier, the photons will propagate at the rate of c through the three spatial dimensions, and yet they will never age—they will stay in a fixed place in the fourth expanding dimension. The primary invariant is c—all matter and/or photons—be it propagating through space or time, or some combination thereof, always, always moves at the rate of c. To be stationary in the three spatial dimensions means to propagate at the rate of c through the fourth dimension. To be stationary in the fourth dimension means to propagate at the rate of c through the three spatial dimensions. Ergo the fourth dimension is expanding at the rate of c relative to the three spatial dimensions. Most objects share motion between space and time, but the overall velocity of propagation through space-time is fixed at c— this primary invariance can never change, and this reality arises because of the deeper physical reality of Moving Dimensions Theory.
And so it is that Moving Dimensions Theory underlies and unifies the papers Einstein Published during his Annus Mirabilis—his "miraculous year." I highly recommend Harvard University Press's Einstein 1905: The Standard of Greatness by John S. Rigden, about wcich Publisher's Weekly writes,
"The year 2005 will be the centenary of Einstein's annus mirabilis, when he published the five papers that marked him as one of the greatest scientists of all time. Washington University professor Rigden (Hydrogen: The Essential Element) sits readers down in front of his white board and explains what Einstein said in each of these papers, what was significant in them and how the scientific community reacted (not very well, in most cases—for a while). Einstein started off with a bang: in March he proposed that light was not a continuous wave, but was made up of particles. In April he finished what became his dissertation, on how to determine the size of molecules in a liquid (that may not sound very exciting, but this is one of Einstein's most cited papers). In May he wrote his paper on Brownian motion, and then in June came the summit of his achievements that year: the paper proposing his principles of relativity and the consistency of the speed of light (commonly known as the Special Theory of Relativity). Finally, almost as an afterthought, in September came the three-page paper that unleashed his now-famous equation, e=mc2, upon an unsuspecting world. Rigden writes with a rare felicity, free of jargon and with everyday metaphors that Einstein himself would no doubt have appreciated."
I encourage everyone to read Einstein's and Bohr's and Heisenberg's and Dirac's original papers, and contrast their majestic elegance, eloquence, reason, and logic to the snarky death threats and crackpot indexes manufactured by today's "best and brightest," and the accompanying silence from their established elders—the founders of string theory's oppressive regime and hand-waving, reason-subjugating, PBS miniseries. The future book on Moving Dimensions Theory will look back to the giants of yesteryear with deep honor and reverence, so that tomorrow's physics might advance in the spirit of simple Truth and Beauty. Every effort will be maintained to demonstrate that true physics is marked by grace and simplicity, as opposed to obfuscation and bullying. Moving Dimensions Theory is an idea whose time has come, and ideas are bulletproof.
The fourth dimension is expanding relative to the three spatial dimensions. Moving Dimensions Theory accounts for the aetherless aether.
This simple postulate offers a physical model underlying and unifiying:
RELATIVITY:
1) length contraction
2) time dilation
3) the equivalence of mass and energy
4) the constant velocity of light
5) the independence of the speed of light from the velocity of the source
QUANTUMN MECHANICS
1) action at a distance
2) wave-particle duality
3) interference phenomena
4) EPR paradox
THERMODYNAMICS
1) Time's arrow
2) Entropy
STRING THEORY'S MANY DIMENSIONS / KALUZA/KLEIN THEORY
1) a fourth expanding dimension can be interepreted as many dimensions, each time it expands
THE UNITY OF THE DUALITIES
1) wave/particle duality
2) time/space duality
3) energy/mass duality
4) E/B duality
GENERAL RELATIVITY
1) Gravitational redshift
2) Gravity waves
3) Gravitation attraction
THE SPACE-TIME BACKGROUND
1) quantum foam
2) the smearing of space and time at small distances
3) Hawking's imaginary time
PARADOXES
1) MDT explains away Godel's Block Universe
2) MDT unfreezes time
3) Resolves Zeno's Paradox
ONE GETS ALL OF THIS FROM A SIMPLE POSTULATE:
The fourth dimension is expanding relative to the three spatial dimensions in a spherically symmetric manner, in units of the Planck length, at the rate of c.
--dr. e's email to lsmolin@perimeterinstitute.ca
date Wed, Sep 26, 2007 at 11:56 AM
subject Hello Lee: The Curious Nature of the Photon, Einstein's Annus Mirabilis, and Moving Dimensions Theory)
I also sent other emails regarding Moving Dimensions Theory, including one sent on 4/19/07 which was cc'd to a dozen other physicists.
Lee writes at The Edge, "The view that time is real and truth is situated within the moment further implies that there is no timeless arbiter of meaning, and no transcendent or absolute source of values or ethics. Meaning, values and ethics are all things that we humans project into the world. Without us, they don’t exist."
Yes--while time is real, I will yet agree with Einstein over Lee--Einstein writes, "Yes, we have to divide up our time like that, between our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever."
Yes--I will have to stick with dx4/dt=ic from here on out to eternity, just as Ludwig von Boltzman has s=klogw on his tombstone and Max Born has xp-px=ih on his.
Best,
Dr. E (The Real McCoy)
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attachments:
retina2.jpg,
1_2_wheeler_recommendation_mcgucken_medium2.jpg
post approved
Zephir wrote on Mar. 9, 2009 @ 15:44 GMT
AWT uses a geometric definition of spatialized time. This definition explains, why time has an arrow, the physical meaning of dual time arrow, concept of many time dimensions etc.
http://aetherwavetheory.blogspot.com/2008/09/aether-and-
definition-of-time.html
post approved
Georgina Parry wrote on Mar. 10, 2009 @ 01:51 GMT
Lee Smolin had better jump back on the fence.In my humble opinion.
Einstein is quoted as having said....."But the development of physics has shown that at any given moment, out of all conceivable constructions, a single one has always proved itself decidedly superior to all the rest."
MDT is nice in that a simple solution resolves such a lot.
I am pleased if it really will open up the minds of scientists to alternative frameworks of explanation.
Rather than the 4th dimension expanding, I would prefer to explain this as all of the matter of the universe changing position along the 4th dimension as potential energy decreases.This change in position along the 4th dimension (if it is visualised as spatial)or change in potential energy(if it is considered in energetic terms only) being equivalent to c measured in 3D vector space.The advantage of this model is that it enables explanation of objective reality without time, but time and relativity to be an emergent phenomena due to the changing position along the 4th dimension, which is change in potential energy.
So there are two separate realities. One, objective reality,in which there is no time and one in which there is time. The latter is subjective reality in which all observations are made and science is conducted.Time is therefore both real and not real depending on the reality under consideration.
The fence is the best place to sit in this situation because any other position on the reality of time would not be taking into account both realities and the Prime Reality Interface that separates them.
post approved
DonLimuti (www.zenophysics.com) wrote on Mar. 11, 2009 @ 07:02 GMT
Congratulations on your well-deserved winning of the essay contest.
Don l.
post approved
amrit wrote on Mar. 12, 2009 @ 20:26 GMT
What Barbour says in a very complex way can be postulated in three points:
1. universe is timeless (atemporal)
2. with clocks we measure duration of material change in timeless universe
3. time is a mind model in which humans experience stream of material change
yours amrit
attachments:
4_ETERNITY_IS_NOW_Sorli_2009.pdf
post approved
wanjohi wrote on Mar. 26, 2009 @ 17:21 GMT
Barbour's universe, if timeless, is also endless(infinite).It is non-existent or imaginary. Before we banish time-keeping in an everlasting bliss, stern science demands some accountability: How can death and radio-active decay be explained away in such an eternal set-up?
The 'astronomers in a crow's nest taking snapshots from above the solar system' is theoretically and experimentally impossible, because such a vantage point is outside the universe; but not outside Barbour's universe, so he should try to prove his point by initially sending a satellite there!
The long and short of my opinion is that Barbour confuses a mathematical universe,where everthing is beautiful and perfect, with a physical universe which is ugly and imperfect. He eliminates the unpleasant duration but that also removes physicality itself.
post approved
johan masreliez wrote on Apr. 3, 2009 @ 23:51 GMT
Dear Dr. Barbour,
It is very likely that it is premature to abandon the progression of time as a physical process. Perhaps our difficulty to understand it merely indicates missing physics.
As human beings we have always felt the need to confine our existence to a limited place in space and time. Maybe this is in order to avoid confronting our smallness in comparison to the immense vastness of the universe. But, gradually over the millenniums we have become aware that the world is much larger than we ever thought. And, now our last holdout will fall; we will come to realize that there is no beginning or end of time.
However, to make eternal existence possible, a dynamic process must exist that makes time progress, and is capable of energizing the world forever. The expansion of both space and time could do this, and the resulting cosmos would agree with all our observations. Furthermore, it would mean the existence of dimensions ‘beyond space and time’ given by vibrating metrics of spacetime, which could make the missing connection between general relativity and quantum mechanics. It would also explain the origin of Inertia. However, this new insight would require revision of physics going all the way back to Galileo, leaving most modern theories of the universe on the ash-heap of history.
The expansion of both time and space would in effect be an expansion in scale, which would not change Einstein’s field equations of General Relativity (GR). Consequently this process, which also might constitute the essence of the progression of time, may proceed ‘beyond’ the four dimensions of spacetime.
It is a physical process that cannot be modeled by current physics.
But, it may be modeled by a semi-discrete process whereby the cosmos expands in short time intervals terminated by discrete scale adjustments. The resulting Scale Expanding Cosmos (SEC) theory agrees with all observations. With this new model there is no missing dark energy and no accelerating expansion. And, as already mentioned, this new Dynamic Incremental Scale Transition (DIST) process could also explain the progression of time.
Therefore, it appears that our current inability to explain the progression of time merely indicates that we do not yet know enough. As usually is the case, what we do not know may appear mysterious and unexplainable.
Best regards,
Johan Masreliez
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johan masreliez wrote on Apr. 3, 2009 @ 23:54 GMT
The attached paper was published in Physica Scripta.
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Imre von Soos wrote on Apr. 12, 2009 @ 09:58 GMT
Greetings,
The concept dimension is defined as a measurable extent of any kind. Spatial and temporal dimensions exist only as the spatial and temporal demarcating relationships of events. They have no physical substance, but form parts of physical reality. Neither can be perceived as such: only the objects and events that fill them can be perceived and their respective relationships...
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Greetings,
The concept dimension is defined as a measurable extent of any kind. Spatial and temporal dimensions exist only as the spatial and temporal demarcating relationships of events. They have no physical substance, but form parts of physical reality. Neither can be perceived as such: only the objects and events that fill them can be perceived and their respective relationships established.
Their extent can only be defined in relation to the events they delimit. All being relative to each other, there exist neither absolute spatial or temporal reference frames, nor absolute spatial or temporal units of measurement.
Dimensions do not move or flow or expand as such: phenomena are moving within them, according to the harmonies that characterise the particular universal level to which they belong. Spatial and temporal sequences are sensed and determined by the elements existing and acting within that space-time continuum.
It is a basically flawed way of thinking that attempts to eliminate a fundamental, sine qua non physical reality, like the dimension of time, because its absence would produce more favourable mathematical equations underlying an otherwise shaky theory.
Not less defective is to – instead of using mathematics to express thought-processes – manipulate mathematical assumptions in the trust of the "unreasonable effectiveness of mathematics" and in the hope that one of the trials will come up with a right solution. Like in the Watson/Skinnerian Behaviouralism, results are met by "getting them by manipulation, shifting them about until a new pattern is hit upon", a procedure "controlled entirely by contingencies of reinforcement".
"I take the positivist viewpoint – wrote Stephen Hawking – that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation." Behold the 'positivist' viewpoint of a very negativist sceptic, with destructive effects not only as a scientific approach in research and theorising, but, through its untruthful scientific attitude towards reality, also as a false and corruptive life-philosophy.
I have dropped in on the paper of Dr. Julian Barbour, because he has a good spectrum of comments and because his statement that "the quantum universe is static. Nothing happens; there is being but no becoming" has touched a home note.
According to my cosmovision, expressed in my book Living Universe, ""Being" is the absolute, inherent and transcendent Life-Ground, Underlying Principle, of Summa Existence. Nothing can precede it, because "Non-being", the absence of "Being", is a contradiction in terms: a concept demanding a subject, the subject the concept is referring to is a "Being" by conceptualisation. As Space and Time are dimensions referring to spatial and chronological relationships of events, local references to position and precedence, and have no purpose to exist by themselves, without a content, they could not have preceded "Being", nor could "Being" be contained in, or be a function of Space and Time, because "Being" is timeless. Thus "Being" exists as an atemporal present, without beginning and end, without it ever having to have been created or appeared out of "Non-Being". As Being is the fount of all Becoming, it is a causa sui.
Being represents Life, Mind and Consciousness. Without life, mind and consciousness there can be neither being nor becoming. Knowing Itself as Being, and knowing Itself as the creator and the created, It is the source of all differentiated life, mind and consciousness; all harmony, wisdom and power. It is the oneness, universality, timelessness, changelessness, formlessness, boundlessness, within and out of which space-time, form, individuality, diversity, temporality and transformation – becoming – transpire: the infinite expresses itself through the finite. It is here where creating, being created and the created – the Creator (Natura naturans) and Creation (Natura naturata) – are one.
Pure Being is pastless and futureless: It simply IS. Being is static and contains – and thus transcends – all Becoming, represented by – materialised into – substance, accident and mode – structure, event and process. Becoming is dynamic, manifested in the harmonious movement, change, and the spatial, chronological and causal relationship and order of energy and matter, while matter itself is not a conglomeration of "things", but consists of by its Underlying Principle ordered "processes" in interwoven and interdependent harmonic system-relationships of energy-quantums.
Space and time are contained by "Being" as conceptual conditions and dimensional constituting fundamentals of Becoming. Only through the existence of the dimensions of Space and Time – representing an inseparable, four-dimensional space-time continuum – may exist movement, change, and spatial, chronological and causal order. Thus all Becoming is space- and time-dependent. Inversely, without movement and change there exists only a static state without content, devoid of space, time, matter, and energy, which are thus co-emergent, co-existent, interdependent, interacting and co-evolving constituents of a dynamic universal process. Neither space nor time "flows" or "moves", or "expands": matter and its movements are interacting within and with space-time according to their constitution, dynamically readjusting each other's geometries and qualities.
Creation, movement, change, causality, physical, chemical and biological processes are dynamic phenomena, constituent elements of Becoming. Their dynamic systems and dynamic rules – the laws of physics, chemistry, biology, of the summa Cosmos – are not rigid predetermined, pre-existing rules, according to which the self-created and self-evolving content of the Universe must work, but are also co-emergent, co-existent and co-evolving integral constituents of it, keeping within the harmonious relationship of the All.
The Summa Universe, being the intrinsic Self of each and all It contains, is self-configuring structure, substance and event in a constant dynamic and harmonious process, being thus the subject, instrument and object of Its own creation through all Its individuated selves, each of which becomes thus also the subject, instrument and object of its own, particular creation and sustention. "Self-configuring" implies thought out, intelligent process, the Intelligent Self-Creation, Self-Sustention and Self-Evolution of the Universe in dynamic equilibrium.
I am a fraction of the ultimate "I" and am inherent and am transcending my manifested physical body, as that ultimate Universal "I" is inherent and is transcending the manifested Universe.
"My body functions as a pure mechanism according to the Laws of Nature," – wrote Erwin Schroedinger – "Yet I know, by incontrovertible direct experience, that I am directing its motions, of which I foresee the effects, that may be fateful and all-important, in which case I feel and take full responsibility for them. Therefore I – I in the widest meaning of the word, that is to say, every conscious mind that has ever said or felt 'I' – am the person, if any, who controls the 'motion of the atoms' according to the Laws of Nature."
Best regards,
Imre von Soos
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Frank Martin DiMeglio wrote on Aug. 1, 2009 @ 03:44 GMT
Hello Julian and readers:
Importantly, time is dependent upon the integrated extensiveness of being and experience (including space and thought).
Here are some basics regarding the fundamental nature of being, experience, and time:
Since the self has extensiveness of being and experience (in and with time) in conjunction with the integrated and natural extensiveness of sensory experience, we spend less time dreaming (and sleeping) than waking. The integrated extensiveness of being and experience go hand in hand. Consistent with this, the integrated extensiveness of the being and experience of the Common Chimpanzee is understood to be in the middle (or between) that of our waking and dream experience. Accordingly, the Common Chimpanzees live two-thirds as long as we do (in captivity, of course). In comparison to the Common Chimpanzee, we are understood as being more conscious in conjunction with experience that is (on balance) more unconscious; and this is evident in our waking and dream experiences.
Dreams are an emotional experience that occur during the one third of our lives that we spend sleeping, because emotion is one part (or one third) of feeling, emotion, and thought. Consistent with this, both feeling and thought are proportionately reduced in the dream. Thoughts and emotions are differentiated feelings. Dreams are essential for thoughtful and emotional balance, integration, comprehensiveness, consistency, and resiliency. Indeed, emotion that is comprehensive and balanced advances consciousness. If the self did not represent, form, and experience a comprehensive approximation of experience in general, we would be incapable of growth and of becoming other than we are.
It can be seen that in comparison to the Common Chimpanzee, the self does represent, form, and experience a comprehensive approximation of experience IN GENERAL.
This is, indeed, not only a great truth, but it is also a new description/understanding of experience in general.
Your comments and questions are very welcome.
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Frank Martin DiMeglio wrote on Aug. 30, 2009 @ 02:49 GMT
FQXi participants:
Some important facts/truth regarding time:
Time is ultimately dependent upon the integrated extensiveness of being, experience (and space), and thought. You can see how this applies to photons in relation to time -- consider how the words "integrated extensiveness" apply.
Dreams improve upon memory and understanding by increasing (or adding to) the...
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FQXi participants:
Some important facts/truth regarding time:
Time is ultimately dependent upon the integrated extensiveness of being, experience (and space), and thought. You can see how this applies to photons in relation to time -- consider how the words "integrated extensiveness" apply.
Dreams improve upon memory and understanding by increasing (or adding to) the integrated extensiveness of being and experience (including thought) in and with time.(This effect is clearly evident in the works of genius, and also with the past/present/future extensiveness and superior predictability regarding the thoughts of genius.)
Since the self has extensiveness of being and experience (in and with time) in conjunction with the integrated and natural extensiveness of sensory experience, we spend less time dreaming (and sleeping) than waking. The integrated extensiveness of being and experience go hand-in-hand.
The natural and integrated extensiveness of being and experience go hand-in-hand -- and, in and with time as well.
Dreams are an emotional experience that occur during the one third of our lives that we spend sleeping, because emotion is one part (or one third) of feeling, emotion, and thought. Consistent with this, both feeling and thought are proportionately reduced in the dream. Thoughts and emotions are differentiated feelings. Dreams are essential for thoughtful and emotional balance, integration, comprehensiveness, consistency, and resiliency. Indeed, emotion that is comprehensive and balanced advances consciousness. If the self did not represent, form, and experience a comprehensive approximation of experience in general, we would be incapable of growth and of becoming other than we are.
Thought involves a relative reduction in the range and extensiveness of feeling. In keeping with this, dreams make thought more like sensory experience in general. Accordingly, both thought and also the range and extensiveness of feeling are proportionately reduced in the dream. (This reduction in the range and extensiveness of feeling during dreams is consistent with the fact that the experience of smell very rarely occurs therein.) Since there is a proportionate reduction of both thought and feeling during dreams, the experience of the body is generally (or significantly) lacking; for thought is fundamentally rendered more like sensory experience in general. Thoughts and emotions are differentiated feelings. By involving the mid-range of feeling between thought and sense, dreams make thought more like sensory experience in general. The reduction in the range and extensiveness of feeling during dreams is why there is less memory and thought therein.
Also, the unification of Maxwell's theory of light and Einstein's theory of gravity -- that is proven by the addition of a fourth spatial dimension -- demonstrates that this one third relation (i.e., three to one ratio) holds for BOTH space and time. Note the three to one relation of space dimensions to time in Einstein's theory; and note, as well, the three to one ratio (one third) of space dimensions in relation to said unification with the fourth spatial dimension.
Accordingly, I have shown that the extension of BOTH time AND space in the dream is consistent with this one third. Moreover, this is all consistent with the fact that the dream is the fundamental union of gravity and electromagnetism/light.
See:
The Dream Fundamentally Balances and Unifies Gravity and Electromagnetism
http://radicalacademy.com/studentrefphilfmd1
3.htm
Time has an important place in physics.
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0=v.i. wrote on Sep. 4, 2009 @ 09:49 GMT
In 1D x^2=(ct)^2 or dx/dt=c as well as dx4/dt=ic (if we cinsider c a constant).
Why MDT consinders that only x4 is expanding by time?
dx4/dx=i this means that x4 is moving relative to x by i (and not by c).
I feel that c=kt (k=costant) that means dx/dt =2k and dx4/dx=2ik.
In this case all "patial" dimensions are expanding by a factor of k and x4 by ik.
(synpan.blogspot.com)
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Buz Craft wrote on Sep. 13, 2009 @ 14:40 GMT
Congrats Julian! Please remember this old East Texas rancher's conclusion: TIME IS TEMPERATURE!
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Charles Z. wrote on Oct. 13, 2009 @ 03:41 GMT
A photon, though travelling through space for 12 billion years, experiences no advance in time, because at the speed of light at which it moves time slows down to zero. This photon is and always has been in an actual state of timelessness.
Time must therefore be a real attribute of any object which moves slower than this photon.
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Michael wrote on May. 4, 2010 @ 09:08 GMT
This argument about time reminds me of Zeno's paradox -Achilles who runs ten times faster than a tortoise in a race of pre-determined length Achilles gives the tortoise one hundred yards start Achilles completes the hundred and the tortoise is ten yards ahead, Achilles completes the ten yards and the tortoise is 1 yard ahead -ad infinitum does this mean that Achilles will take infinitely smaller distances to catch the tortoise? never doing so? Obviously not.. Using the correct equation including the time taken for Achilles to cover the pre-determined distance at 1 yard per second and the tortoise at 1 yard per ten seconds we can calculate precisely where and when Achilles will pass the tortoise and the difference in time between Achilles finish and the Tortoise.. My question Is Julian Barbour a latter day Zeno?
Michael
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John wrote on May. 26, 2010 @ 13:32 GMT
It is ironic that this essay won just as the existence of time was being demonstrated by experiments (the first in 2005):
Attosecond double-slit experiment
Authors: F. Lindner, M. G. Schaetzel, H. Walther, A. Baltuska, E. Goulielmakis, F. Krausz, D. B. Milosevic, D. Bauer, W. Becker, G. G. Paulus
http://arxiv.org/abs/quant-ph/0503165
(which has been confirmed and repeated by several labs in several different ways)
But since then there have been few attempts to produce a new relativistic quantum theory. This is bizarre when, as Ashmead says, the area of study is an "experiment factory". Here are a few background articles that have come out since the first of these double slit experiments:
Overview: Quantum Time
by John Ashmead http://arxiv.org/abs/1005.0789
On the significance of a recent experiment demonstrating quantum interference in time
Authors: Lawrence P. Horwitz
http://arxiv.org/abs/quant-ph/0507044
Kryukov's excellent papers on the subject http://depts.uwc.edu/math/faculty/kryukov/index.html
This area of study will be the big one in a decade or two. Come on physicists, get your fingers out, I dont want to wait 20 years!
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Patrick replied on Jul. 27, 2010 @ 22:33 GMT
Ironic, indeed.
This essay won because it seems to be one of the better written entrants. Barbour uses clear, easy language and develops his material in a very logical fashion (unlike other more difficult essays), but his central argument is incorrect. He relies on proving that one can have a "timeless" equation to quantify time-like phenomena. In his attempt, he uses V and E, ignoring the obvious fact that V embeds Newton's G which has dimensions which include time and that E embeds c, also requiring the dimension of time. Hence, his "timeless" equation is nothing more than a mathematical tautology.
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Kan wrote on Jul. 8, 2010 @ 08:52 GMT
Dr Barbour,
I have read your article The Nature of Time and some other pieces on your website and watched the video. I find them very interesting because I am interested in the subject as well and have done some thinking about it sometime ago.
If one has the privilege to observe the Universe from the outside, there seems to be a simple way to define (or...
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Dr Barbour,
I have read your article The Nature of Time and some other pieces on your website and watched the video. I find them very interesting because I am interested in the subject as well and have done some thinking about it sometime ago.
If one has the privilege to observe the Universe from the outside, there seems to be a simple way to define (or construct) a "Time" (duration) as "the change in the state of a dynamical system".
Consider a CLOSED Dynamical System, S, whose state is described by the state function, F.
F has n allowed "values": F1, F2,... Fi,..., Fj,..., Fk,... Fn, where i, j, k,.. n are positive integers.
Then one can define (or construct) Time (or Time increment/Time interval), dt, as follows:
Suppose the state function F of S initially has value Fi, and then it changes to Fj (written as
Fi --> Fj), then a certain time increment, dt, is said to have ELAPSED; where dt = 0 if i = j,
and dt is non-zero if i is different from j, for ANY values of i and j from 1 to n.
So, there is a "dt" associated with each "-->".
This notion of Time is applied over the entire S and may, therefore, be called the "Universal Time" (or Global Time) for S. Whether a Time (or Time increment) defined this way can be applied UNMODIFIED to portions of S is not yet clear.
A "Time" (Time increment) defined in this way is, at most, a DERIVED physical quantity, instead of being a "fundamental physical quantity" as we were taught at school and it has the following properties:
1) If S does not exist, then Time (or time increment), dt, does not exist.
2) Time is quantized, instead of being a continuum.
3) If F changes in sequence given by "Fi --> Fj --> Fk", then the 2 "dt's"
(associated with the 2 "-->") are perceived as being equal in magnitude since
in reality only Fi, Fj and Fk, but not something in-between, that are observable (can be detected) in the physical world. It is not conceivable that the "in-between's", which cannot be detected, can be of different magnitudes. But we are quite sure that the "in-between's", "dt's", do exist because their end-points exist.
4) If F changes in sequence given by "Fi --> Fk --> Fj", where i, j and k all have different values, for example, then the 2 "dt's" are taken as having the same sign (direction). This follows naturally from the way "dt" is defined above since the 2 "dt's" are defined in exactly the SAME manner, if one has a positive (or negative) sign, so does the other.
Following the above, if F changes in sequence given by "Fi --> Fk --> Fj --> Fi", we should perceive S having RETURNED to its "earlier" state of Fi, instead of perceiving Time having gone backwards.
Time is, therefore, unidirectional.
5) Consider the set f = {F1, F2,... Fi,..., Fj,..., Fk,... Fn} and g1, g2 are subsets of f, say,
g1 = {F1, F2,..., Fi} -- g1 has i elements
g2 = {Fj,..., Fk} -- g2 has (k - j + 1) elements
That is g1 is a macrostate contains i microstates {F1, F2,...Fi}
and g2 is a macrostate contains (k - j +1) microstates {Fj,... Fk}
Then the relative amount of "Time" S being in macrostates g1 and g2 are
in the ratio of i to (k - j + 1). This, as I remember, is one of the basic assumptions in Statistical Mechanics.
6) If R is a subsystem of S, one might expect the "Time increment" in S be "more finely quantized" than that in R.
7) If R1 and R2 are both subsystems of S, following from (6), ot should be possible to find out the relationship of the "Time increments" in R1 and in R2 by relating each to the "Universal Time" of S.
Since "Time" can be shown to be a "derived physical quantity", there is reason to believe that Space too is a "derived physical quantity", and, likewise, it should be possible to define (construct) a notion of Space by thought/argument alone. The same might also be true for Matter (inertia mass).
But I could not get any further than this-- Not being able to find a convincing way to define Space-- and consequently stopped pursuing the subject.
Recent reading of the article Is Time an Illusion in Scientific American and further browsing of your website re-ignites my interest on this subject and I am thinking about Space and Matter and might have some preliminary leads on them.
Kan
SSHK
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