What Makes Time Special by Craig Adam Callender

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).

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 Einstein nor Minkowski ever stated that time is the fourth dimension, but rather they wrote x4=ict. And t and ict are very different entities.

You will find that this resolves the dilemmas you enumerate in your paper--your astute perceptions of the fundamental differences between time and space--with "the dimensionality" of time and "metrical difference" of time, and the facty that "we have relatively free mobility in the spatial directions but not the temporal ones," as you note on p. 2 of your paper.

x4, the fourth dimension, is moving relative to the three spatial dimensions, given by dx4/dt=ic. The fourth dimension is expanding relative to the three spatial dimensions, manifesting itself as a spherically-symmetric wavefront of probability expanding at c in our three spatial dimensions--distributing locality and fathering time. t is but an emergent parameter we see measured on our clocks and watches, which rely on the propagation of photons, which are but matter surfing the fourth expanding dimension. I cover all this in my paper:

http://fqxi.org/community/forum/topic/238

All of relativity may be naturally derived from dx4/dt=ic.

Or approach Moving Dimensions Theory this way:

1. Relativity tells us that the ageless, timeless photon remains in the exact same place in the fourth dimension.

2. Quantum Mechanics tells us that a photon's motion is described by a probabilistic spherically-symmetric wavefront that exapnds at c.

Ergo the fourth dimension must be described by a probabilistic spherically-symmetric wavefront that exapnds at c.

The only way to stay stationary in the fourth dimension is upon a sperically-symmetric wavefront expanding at c. Ergo the fourth dimension is expanding at c, relative to the three spatial dimenions.

And finally change is woven into the fundamental fabric of spacetime, and we are given a physical mechanism for quantum mechanics' nonlocality and entanglement, as well as entropy and relativity, and time and all its arrows across all realms.

And too, all of realtivity may be derived from MDT's deeper prinicple. It could all be put on a t-shirt:

Consider a 4D universe x1, x2, x3, x4 wherein x4 is expanding relative to the three spatial dimenions: dx4/dt=ic. Ergo relativity and E=mc^2.

A longer treatment of this is given in my paper, where I use Moving Dimension's Theory hitherto unsung fundamental universal invariant: dx4/dt=ic, to provide a deeper motivation for Einstein and Minkowski substituting ict for x4.

Einsetin eventually concluded that x4=ict, becuase he started with his principle of relativity, and thus x4 had to be ict.

The *reason* our universe obeys Einstein's relativity is that we reside in a 4D universe wherein the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic.

Einstein's Relativity may be derived from dx4/dt= ic, which represents a more fundamental invariance of this universe--the fourth dimension is expanding relative to the three spatial dimensions. Einstein introduced relativity as a principle--as a law of nature not deduced from anything else, and well, I guess I was dumb enough to 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.

And not only can all of relativity be derived from this, but suddenly we are liberated from the block universe and time and progress in theoretical physics are unfrozen. And change is seen in a most fundamental equation that weaves change into the very fabric of space-time, where it needs to be, as change pervades every realm of physics and all acts of *physical* measurement. And suddenly we have a *physical* model for entropy, time and its arrows and assymetries in all realms, free will, and quantum mechanics' nonlocality, entanglement, and wave-particle duality. The fourth expanding dimension distributes locality, fathering time. MDT accounts for the constant speed of light c--both its independence of the source and its independence of the velocity of the observer, while establishing c as the fastest, slowest, and only velocity for all entities and objects moving through space-time, as well as the maximum velocity that anything is measured to move. And suddenly we see a physical basis for the dualities--for space/time, wave/matter, and energy/mass or E=mc^2. Energy and mass are the same thing--it's just that energy is mass caught upon the fourth expanding dimension, and thus it surfs along at "c."

Well, I would call all of this a massive unification--all based on a simple *physical* model and equation. I imagine this is just the tip of the iceberg of everything implied by this new physical model--this hitherto unsung fundmanental invariant of the universe--the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt=ic.

Love your words! "At a time when researchers in quantum

gravity regularly propose speculative theories with no time at all, a better understanding of time in physics is all the more important--even if only to see what is lost by its absence."

Yes--too many physicists these days set out to explain what they do not understand by denying its existence, and so you get antitheories in which foundational questions regarding foundational aspects of the universe are considered rude and illegal. This supreme lack of humility, and snarky arrogance, is why theoretical physics has ground to a halt over the past thirty years.

Hopefully the dialogue generated in FQXI's brave, new format and forum will help physics advance beyond the nihilistic, postmodern, aging antitheory regimes, which have evloved to place the bottom line and handwaving groupthink over the higher ideals, logic, and reason. For physics is only ever advanced by pursuing the higher ideals--the immortal *physical* truth--over temporary titles, tenure, honors, and awards.

Best,

Dr. E (The Real McCoy)

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

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.

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

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

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.

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.

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!

moving dimension theory

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

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.

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.

I believe the "If/then" statement(the most powerful equation in the universe)necessitates some sort of time continuum< Craig. But I really enjoyed your artical...

Time and Space

Space is an intrinsic attribute of the existent entities which comprise our reality, time is not. Time should not be reified as if it is another physical dimension of our reality. All existent entities undergo change, and our concept of time is a function of our experience of that change. By putting similar entities in different situations, its value can be altered, but that is a function of the observation process (which we are able to quantify anyway). It is not an inherent characteristic of time, which only has one value. However, utilising time as a measuring tool helps in everyday life and in articulating scientific observations. As always, contemplations about what happens 'beyond' our existence might be fascinating, but are irrelevant metaphysical considerations when developing objective understanding.

© Paul Reed

April 2011

Connections

The binding of existence

This is a story, built upon knowledge, intuition, and speculation. In the end, it is built upon some known theoretically successfully tested truths, and some unknowns conveyed in a formula that I consider trumps any objections - as we ponder the scope of existence. First we know of existence, by way of our self-awareness, coupled with scientific knowledge. Second by way of the unknowns i.e., "Infinity", that must incongruously play with us (self-aware-finite creatures), in some connected manner.

This Second irascibly indefinable thing called "Infinity", simply stumps our "finite" minds every time, when we attempt to figure out its mathematical infinities. As it must. As if it did not stump our efforts to understand it, it would become defined, and anything defined, is "Finite.". So we have an absolute conundrum that operates our existence. But we are still connected, in a union, both finite and infinite, through the known attributes we have scientifically tested to be true. As without "Infinity", there can be no "Finite." And remember Infinity, has no bounds, no time, no space, no beginning and no end.

This is plainly contrary to finite logic, but Infinity simply is contrary. Always has been. And always will be. But it is also the very milk of our very finite existences... We are Connected... Our actions matter, as I will soon explain - in summary.

INFINITY: Irascible and fundamentally a necessary fickle fact. An argument that no mathematics or thought equation can defend against... To challenge this premise is to supersede infinity's very nature. It will never ever happen.

Therefore we are circumscribed to live within, the physics - largely of Newtonian and Einstein's mathematics. I would caution to note: that these finite mathematics are subject to change that currently work fairly well for our finite existence as we mathematically calculate how to penetrate and maneuver the Stars, or add 2 plus 2 to equal 4. But they do not work to unravel Quantum Mechanics (in total), and the cache of oddities, such as "Superposition's", whereby subatomic particles are in several places at one time, until they are interrupted by measurement. Or do these current finite mathematics explain "Entanglement", which allows for two subatomic elements to be millions of miles apart, however if one changes its state of "spin" or "electrical" charge the other particle millions of miles away responds instantly. Yes, this violates the concept of the speed of light as the fasted method of action in the Universe.

As Einstein called "Entanglement" Spooky, but none the less real. This seemingly violates the speed of light. But hold on, the Speed of Light travels, Entanglement implies "Connection". Or what is known as Local action.

Space is the key to this thought equation. Since space is "Infinite" to the "Finite" Observer. Space in this context is also in union with waves - as well as particles. However waves may connect all things instantly, just as waves may allow for "Superposition's."

The answer is simply that: This makes us both Local and Non-Local at the same time. Waves and or theoretical "Strings" perhaps in some union - connect our space and possibly time in ways we do not fully comprehend. If true, our infinite extended connections are observed from a finite realm only. It might be important to note here: That simply no distance is allowed in an Infinite realm, as infinity is immune to classification, therefore it is all things and no things at the same time. Make sense? It usually should not, as finite logic has a difficult time with this both intuitively and implicitly mathematically. Make sense yet?

Probably not, as this means that "Everything is Nothing and Nothing is Everything." Hence there are no real "infinites" to calculate in an Infinite realm. But this last statement is a clear oxymoron, as it should be, as infinity does not have mathematics or anything defined based in or of it. As this would imply a finite realm. It is simply infinite, and does not apply to our finite realm of mathematics.

Mathematics is purely the purview of the finite.

When I said there are really no infinities in the infinite realm. I meant it. But to us, within the finite realm or finite conscious state, as observers, Infinities are what - infinity, space and time are made of. Once again, the ultimate and infinite conundrum. However, how does this allow for the stuff of existence, such as "us", or cars, and trees and so on to exist? Well we do need infinity to have a finite realm, as I said.

That is the puzzle? That must never be answered technically, nor can it, again from a finite perspective or finite observer. This mind trap we are caught in trying to view infinity - would seem to drive one mad to think that Infinity, Space and Time have no beginning or an end.

But get use to it.

Infinity is indelible. Terms like "time" and "space" are non-words to describe Infinity correctly, as Infinity never had a beginning or an end. The space and time word terms we use within the realm of Infinities definition, or lack thereof, could not and do not exist. Unlike the finite world, which has an Alpha and Omega. (Dust to Dust, Evolution, and Space to move to, and a length of Time that life gives us to observe.

And - That is that...

We are here by way of connections of an indefinable Infinity, which has always been, and will always be. Make no mistake about it. This will provide us and others forever to give sentiency a journey to discover anew. New science from physics to health, coupled with new modes of life, new cultures to come. Save an Asteroid impacting the Earth, or a Super-Volcano taking us to our end of time as sentient beings. But others will arise, no doubt by way of times finite arrow.

The finite with a beginning and end is necessary, to find hope. Just imagine living for eternity without end. That proposition, would invoke a person to lose goals, have no new hopes, and actually impart a crazy madness of hopelessness. As you would be in the ultimate Trap, or Jail forever, if self-aware. What would be the point? One would ask themselves... And therefore, Life and Death, are necessary.

Dust to Dust and then perhaps? Take your best shot at a faithful guess! The options are many, the realities may be few. No one really knows. No one...

Plainly beyond us, the Infinite and Finite will ebb and flow, and new existences will arise through an endless connection to everything for all time...

Essential Points:

1. The Science is: That Infinity is incomprehensible to any complete understanding and, the Finite is limited to understanding all things, perhaps itself and certainly infinity. The connection between the finite and the infinite operate as if Everything is Nothing and Nothing is Everything... Have fun with that analogy! As for me, it holds true, as it confirms to me that cognitive logic eventually meets the illogic of Infinity. This lets us clearly know we will never actually know honestly and truthfully the great questions of life: As to know "ALL" or "Truth" would be to actually define a place and a time, which can only be finite. And that would defy the rules of Infinity, which cannot be technically ever defined. Otherwise it is no longer infinite; it would then become as a mere canvas with parameters. And Infinity is incomprehensible. End of Story - Yesterday, Today and Tomorrow... In other words Forever!

2. The Moral is: That Legacies matter. Build a good one. The Butterfly Effect is always on... And that is what really matters.

All the best in our journey's, Russ Otter

www.otterthink.blogspot.com