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What's Ultimately Possible in Physics?
Spring 2009
Special Thanks to Bruce & Astrid McWilliams
read/discuss • winners
The Nature of Time
Spring 2008
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FQXi FORUM
September 2, 2010
CATEGORY:
The Nature of Time Essay Contest
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TOPIC: What Makes Time Special by Craig Adam Callender [refresh]
TOPIC: What Makes Time Special by Craig Adam Callender [refresh]
Essay Abstract
What is the difference between time and space? This paper proposes a novel answer: the temporal direction is that direction on the manifold of events in which our best theories can tell the strongest, most informative “stories.” Put another way, time is that direction in which our theories can obtain as much determinism as possible. I make two arguments. The first is a general one based on an empiricist theory of laws. I argue that according to this theory time is distinguished as the direction of informative strength. The second argument is a more specific illustration of the first: understanding informative strength as having a well-posed Cauchy problem, I show that for a wide class of equations (i.e., second-order linear partial differential equations) the desire for strength does indeed distinguish the temporal direction. Not only that, but the argument rigorously connects three otherwise mysterious connections among temporal features to one another.
Author Bio
Craig Callender is Professor of Philosophy at the University of California, San Diego. He works in the foundations of physics, especially on statistical mechanics, the interpretation of quantum mechanics, and topics in quantum gravity. Much of his work focuses on the nature of time in modern physics. He has published extensively in philosophy and physics journals. In addition, he has edited two books "Philosophy Meets Physics at the Planck Scale" (CUP) and "Time, Reality and Experience" (CUP), and authored the popular science book "Introducing Time" (Icon/Totem).
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What is the difference between time and space? This paper proposes a novel answer: the temporal direction is that direction on the manifold of events in which our best theories can tell the strongest, most informative “stories.” Put another way, time is that direction in which our theories can obtain as much determinism as possible. I make two arguments. The first is a general one based on an empiricist theory of laws. I argue that according to this theory time is distinguished as the direction of informative strength. The second argument is a more specific illustration of the first: understanding informative strength as having a well-posed Cauchy problem, I show that for a wide class of equations (i.e., second-order linear partial differential equations) the desire for strength does indeed distinguish the temporal direction. Not only that, but the argument rigorously connects three otherwise mysterious connections among temporal features to one another.
Author Bio
Craig Callender is Professor of Philosophy at the University of California, San Diego. He works in the foundations of physics, especially on statistical mechanics, the interpretation of quantum mechanics, and topics in quantum gravity. Much of his work focuses on the nature of time in modern physics. He has published extensively in philosophy and physics journals. In addition, he has edited two books "Philosophy Meets Physics at the Planck Scale" (CUP) and "Time, Reality and Experience" (CUP), and authored the popular science book "Introducing Time" (Icon/Totem).
Download Essay PDF File
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Nice paper, Craig. I was struck by your segue between events and PDEs, however, on page 7, as reminiscent of quantum mechanics, while ultimately your argument depends on an argument about PDEs. Given your preference for an empiricist approach, I feel that you don't adequately justify a transition from epistemological issues of what we can measure to what seems to be an ontology of classical fields. To be specific, if we can observe only discrete events, an empiricist has some trouble in justifying even trajectories unless the events are Perfectly Correlated, even more in justifying the existence of (classical) fields as the cause of the events.
Personally, I justify fields pragmatically, as a useful and empirically effective class of models, not as a necessary explanation for events, so I'm curious to know if you're willing to step out of empiricism as far as a model-building methodology of Physics, which I take to be a constructive way to address the post-empiricist critique (you say you favor "versions with an empiricist slant", which is a perfectly nuanced statement except for its lack of commitment to a specific methodology).
Because your approach is so technical, for example in its invocation of the Cauchy problem for PDEs, I feel that it may not be robust to being reformulated in terms of quantum theory. A PDE approach to a /fluctuating/ field theory is immediately problematic, even if it's classical, because a field theory (loosely speaking) becomes not differentiable as soon as we introduce any kind of fluctuations.
Hamiltonian or Lagrangian formalisms for quantum theory clearly have trouble dealing with multiple time-like dimensions of space-time, so we would have to construct a more purely algebraic formalism for quantum or random fields; such a mathematics seems possible, at least for random fields, in which case I suppose we would have to accept that our 1-dimensional time would be contingent (the last part of this may well be incomprehensible unless you look at my "Lie fields revisited", Arxiv:0704.3420, J. Math. Phys. 48, 122302(2007), sorry, though my FQXi paper might be enough to get the idea).
post approved
Personally, I justify fields pragmatically, as a useful and empirically effective class of models, not as a necessary explanation for events, so I'm curious to know if you're willing to step out of empiricism as far as a model-building methodology of Physics, which I take to be a constructive way to address the post-empiricist critique (you say you favor "versions with an empiricist slant", which is a perfectly nuanced statement except for its lack of commitment to a specific methodology).
Because your approach is so technical, for example in its invocation of the Cauchy problem for PDEs, I feel that it may not be robust to being reformulated in terms of quantum theory. A PDE approach to a /fluctuating/ field theory is immediately problematic, even if it's classical, because a field theory (loosely speaking) becomes not differentiable as soon as we introduce any kind of fluctuations.
Hamiltonian or Lagrangian formalisms for quantum theory clearly have trouble dealing with multiple time-like dimensions of space-time, so we would have to construct a more purely algebraic formalism for quantum or random fields; such a mathematics seems possible, at least for random fields, in which case I suppose we would have to accept that our 1-dimensional time would be contingent (the last part of this may well be incomprehensible unless you look at my "Lie fields revisited", Arxiv:0704.3420, J. Math. Phys. 48, 122302(2007), sorry, though my FQXi paper might be enough to get the idea).
post approved
Love your paper Craig! Thanks so much for it!
You write, "What is the difference between time and space? This question, once a central one in metaphysics, has not been treated kindly by recent history. By joining together space and time into spacetime Minkowski sapped some of the spirit out of this project."
The secret, Craig, is to go back to the scene of the crime. Neither...
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You write, "What is the difference between time and space? This question, once a central one in metaphysics, has not been treated kindly by recent history. By joining together space and time into spacetime Minkowski sapped some of the spirit out of this project."
The secret, Craig, is to go back to the scene of the crime. Neither...
view entire post
post approved
Dear Prof. Callendar,
i can't claim to be terribly good at advanced math, but have the impression that what you have done here with your hyperbolas is to re-discover the light cone.
going out on a limb a bit and predicting that the angle of the asymptotes of your hyperbolas will consistently be 45º.
whether or no my empirically intuitive impressions of what you have done prove correct, the relationships described in your paper are very interesting.
re:
"Theories of laws of nature come in many forms, but I've always favored versions with an empiricist slant. Empiricist theories seek to explain the laws given the distribution of actual or observed facts, rather than going the other way round and explaining why the facts are what they are in virtue of the laws."
i've noticed that there appears to be a third category: explaining what the laws are by virtue of other laws.
:-)
thank you,
matt kolasinski
post approved
i can't claim to be terribly good at advanced math, but have the impression that what you have done here with your hyperbolas is to re-discover the light cone.
going out on a limb a bit and predicting that the angle of the asymptotes of your hyperbolas will consistently be 45º.
whether or no my empirically intuitive impressions of what you have done prove correct, the relationships described in your paper are very interesting.
re:
"Theories of laws of nature come in many forms, but I've always favored versions with an empiricist slant. Empiricist theories seek to explain the laws given the distribution of actual or observed facts, rather than going the other way round and explaining why the facts are what they are in virtue of the laws."
i've noticed that there appears to be a third category: explaining what the laws are by virtue of other laws.
:-)
thank you,
matt kolasinski
post approved
Dear Craig,
it is fascinating to see a presentation that emphsizes faith in time as a concept. Both space and time do help describe the phenomenon observed in our Universe. However, i see that spacetime/get joined as the forth dimension through the involvement of the velocity of light and its constancy. It does present problems if the value of c is changing. Some exptal evidence exisits that the velocity of light coming from a 12 billion old source is small degree higher than what we take as constant today. In my own essay, while discussing the first billion years of universe after Big Bang, i propose that the turmoil of those times may well demand significantly higher value of c . Besides, even the relative strengths of the four physical force/fields may well have varied from their currently taken relative values.
Similarly, the relation, E = mc^2, may need a relook too! Thus, the philosophical consequences arise that may affect the currently established physics!
Another interesting point that some authors here have discussed extensively concern the non-physical entity called ' consciousness ' as a possible creator of every thing physical, beginning from Big Bang, as it always exist independent of time. Your thoughts/ideas on htese aspects will be valuable.
post approved
it is fascinating to see a presentation that emphsizes faith in time as a concept. Both space and time do help describe the phenomenon observed in our Universe. However, i see that spacetime/get joined as the forth dimension through the involvement of the velocity of light and its constancy. It does present problems if the value of c is changing. Some exptal evidence exisits that the velocity of light coming from a 12 billion old source is small degree higher than what we take as constant today. In my own essay, while discussing the first billion years of universe after Big Bang, i propose that the turmoil of those times may well demand significantly higher value of c . Besides, even the relative strengths of the four physical force/fields may well have varied from their currently taken relative values.
Similarly, the relation, E = mc^2, may need a relook too! Thus, the philosophical consequences arise that may affect the currently established physics!
Another interesting point that some authors here have discussed extensively concern the non-physical entity called ' consciousness ' as a possible creator of every thing physical, beginning from Big Bang, as it always exist independent of time. Your thoughts/ideas on htese aspects will be valuable.
post approved
Dear Craig,
I liked your ideas of time as the great informer, and the comparison you make between space and time.
Perhaps the connection between information and Cauchy problem can be made stronger. One question: when you propose a criterion for selecting the time among other directions in spacetime, do you refer at selecting a particular direction, or a class of directions that can play the role of time?
Best wishes,
Cristi Stoica
“Flowing with a Frozen River”,
http://fqxi.org/community/forum/topic/322
post approved
I liked your ideas of time as the great informer, and the comparison you make between space and time.
Perhaps the connection between information and Cauchy problem can be made stronger. One question: when you propose a criterion for selecting the time among other directions in spacetime, do you refer at selecting a particular direction, or a class of directions that can play the role of time?
Best wishes,
Cristi Stoica
“Flowing with a Frozen River”,
http://fqxi.org/community/forum/topic/322
post approved
Dear Craig,
I want to tell you how proud the family is of you and how woefully ignorant we are about physics. But, you are not only brilliant but a nice person too.
Your proud Dad's cousin,
John Young
post approved
I want to tell you how proud the family is of you and how woefully ignorant we are about physics. But, you are not only brilliant but a nice person too.
Your proud Dad's cousin,
John Young
post approved
There is a justifiable connection between space dimensions and inertia/motion. On the other hand, there is similar connection between time and energy content. This gets reflected in the two uncertainty relations as the two respective conjugate parameters. As motion is the significant character in the physical universe, we apparently need both space and time as concepts to describe motion and the implicit energy source that gives rise to it is needed too!
Unless alternates to such concepts are evolved, one need to continue to believe till better conceptual picture emerges. The same may as well be true about Quantum Mechanics as explanation for tye motions in the micro-world or for that matter in explaining the anamolous behavior of black holes with intense density of matter/radiation. An alternate explanation can always be on the cards, as the human mind ia capable of reaching the ultimate limits of cosmic knowledge.
post approved
Unless alternates to such concepts are evolved, one need to continue to believe till better conceptual picture emerges. The same may as well be true about Quantum Mechanics as explanation for tye motions in the micro-world or for that matter in explaining the anamolous behavior of black holes with intense density of matter/radiation. An alternate explanation can always be on the cards, as the human mind ia capable of reaching the ultimate limits of cosmic knowledge.
post approved
I enjoyed the clarity of your paper. The thesis of your paper is that hyperbolic DE's pose well formed Cauchy data. On this I would agree. There appears to be a converse problem however. Elliptic DE's, four dimensional Laplacian heat or diffusion equations for gauge terms have well behaved moduli spaces. Hyperbolic spacetimes obey the Lorentz group which are modulo Z_2 SU(1,1)xSU(2) as the product of a 3-rotational group and a hyperbolic group of transformations which define boosts. The transformation of the (A_+, A_-, A_3), by the hyperbolic g = e^{-ze_3) results in a nonHausdorf condition on the moduli.
This seems to lead to a curious situation. Hyperbolic Des have well defined Cauchy data, but a moduli space which has an irregular topology such as Zariski. Conversely an elliptic DEs on an open domain do not have well defined Cauchy problems, but a well defined Hausdorff moduli space.
A Hausdorff space obeys a Cauchy convergence condition, so that a sequence of connection terms will converge in a separable manner. However, in general we do not have well defined Cauchy data (same name but different concepts here) for hyperbolic DEs or gauge connections.
cheers,
L. C.
post approved
This seems to lead to a curious situation. Hyperbolic Des have well defined Cauchy data, but a moduli space which has an irregular topology such as Zariski. Conversely an elliptic DEs on an open domain do not have well defined Cauchy problems, but a well defined Hausdorff moduli space.
A Hausdorff space obeys a Cauchy convergence condition, so that a sequence of connection terms will converge in a separable manner. However, in general we do not have well defined Cauchy data (same name but different concepts here) for hyperbolic DEs or gauge connections.
cheers,
L. C.
post approved
It seems to me that the curvatures in space and time may be varying both ways as per the demands of the universe evolution. It may also be true that the Big Bang singularity may not be the sole reason fot the Universe we see. Other alternatives like expanding/contracting and /or matter/antimatter pre=existing universes had a role too. Also, at some stage the changing curvatures in space and time may not be coordinated togather, as per the theory of relativity demands on space/time! Unless, accurate comological data becomes available from far into space, the accuracy and precision may remain in uncertainties!
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post approved
Time is an accounting of the relative motions in space of bodies without which neither time nor space can be understood. Or, time is a system of accounting for the relative motion of bodies in space. And how we keep "score" is by means of human - invented clocks and calendars. See: http://www.relativitycalculator.com/John_Harrison.shtml and http://www.relativitycalculator.com/plato_cave.shtml
Don Saar, drdonzi@crocker.com, Relativity Calculator, www.relativitycalculator.com
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Don Saar, drdonzi@crocker.com, Relativity Calculator, www.relativitycalculator.com
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Flawed relativistic theories aside, time need not flow in a single direction or even flow at all. To assume that WYSIWYG applies to the universe seems a little absurd to me. We perceive time to be linear because that is how we are wired. There is no unified theory because not only are we missing pieces of the puzzle we can't even imagine what the picture actually looks like.
Human perception is limited by what the brain can absorb, our perceptions of time may be the result of one of those limitations.
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Human perception is limited by what the brain can absorb, our perceptions of time may be the result of one of those limitations.
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Dear Craig,
I've just read your excellent paper in Scientific American. I am far from fundamental physics, but the idea of timeless universe resonated with my own thoughts. Since our observed world undergoes constant changes at all scales, it seems to be natural to assume that we need at least 4 dimensions to describe it; whether you call the extra dimension “time” or something else, it doesn't matter. Yet this 4-th dimension is so different from the other 3 coordinates and so dependent on often random interactions between various objects constituting the universe that it is very tempting to accept that time is imaginary and it makes sense only within subsystems, while the universe as a whole lacks this "artificial" property.
Yet, astrophysics theories claim that not only individual components of the universe have been changing since the big bang. The space itself went through "inflation" and continues to expand “over time”. It's hard to get how this concept can be consistent with the timeless universe model.
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I've just read your excellent paper in Scientific American. I am far from fundamental physics, but the idea of timeless universe resonated with my own thoughts. Since our observed world undergoes constant changes at all scales, it seems to be natural to assume that we need at least 4 dimensions to describe it; whether you call the extra dimension “time” or something else, it doesn't matter. Yet this 4-th dimension is so different from the other 3 coordinates and so dependent on often random interactions between various objects constituting the universe that it is very tempting to accept that time is imaginary and it makes sense only within subsystems, while the universe as a whole lacks this "artificial" property.
Yet, astrophysics theories claim that not only individual components of the universe have been changing since the big bang. The space itself went through "inflation" and continues to expand “over time”. It's hard to get how this concept can be consistent with the timeless universe model.
report post as inappropriate
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