Posted on 08/01/2005 10:58:13 AM PDT by wallcrawlr
For me, time is a dimension and apart from timelessness – physical reality is not merely three spatial dimensions evolving over (absolute) time. Moreover, there may be more than three spatial dimensions and more than one temporal dimension.
In the void, the null, which precedes the beginning in all cosmology there is no time, no space, no matter/energy, no corporeals, no causality, no order, no information. It is a difficult concept, but it is the context in which "all that there is" (heaven and earth, spiritual and physical) is cast.
The order that arises from that chaos is mathematical per se and may be manifest many times over in “reality”. Thus A=A is a mathematical statement of identity which applies to all instances of A - whether spiritual or physical. Likewise A=pi times the radius of a circle squared is a mathematical statement of identity regardless of instance on any geometric plane.
The math is universal. Further, it exists with a metaphysical quality:
Mathematics does play, however, also a more sovereign role in physics. This was already implied in the statement, made when discussing the role of applied mathematics, that the laws of nature must have been formulated in the language of mathematics to be an object for the use of applied mathematics. The statement that the laws of nature are written in the language of mathematics was properly made three hundred years ago;[8 It is attributed to Galileo] it is now more true than ever before. In order to show the importance which mathematical concepts possess in the formulation of the laws of physics, let us recall, as an example, the axioms of quantum mechanics as formulated, explicitly, by the great physicist, Dirac. There are two basic concepts in quantum mechanics: states and observables. The states are vectors in Hilbert space, the observables self-adjoint operators on these vectors. The possible values of the observations are the characteristic values of the operators but we had better stop here lest we engage in a listing of the mathematical concepts developed in the theory of linear operators.
It is true, of course, that physics chooses certain mathematical concepts for the formulation of the laws of nature, and surely only a fraction of all mathematical concepts is used in physics. It is true also that the concepts which were chosen were not selected arbitrarily from a listing of mathematical terms but were developed, in many if not most cases, independently by the physicist and recognized then as having been conceived before by the mathematician. It is not true, however, as is so often stated, that this had to happen because mathematics uses the simplest possible concepts and these were bound to occur in any formalism. As we saw before, the concepts of mathematics are not chosen for their conceptual simplicity even sequences of pairs of numbers are far from being the simplest concepts but for their amenability to clever manipulations and to striking, brilliant arguments. Let us not forget that the Hilbert space of quantum mechanics is the complex Hilbert space, with a Hermitean scalar product. Surely to the unpreoccupied mind, complex numbers are far from natural or simple and they cannot be suggested by physical observations. Furthermore, the use of complex numbers is in this case not a calculational trick of applied mathematics but comes close to being a necessity in the formulation of the laws of quantum mechanics. Finally, it now begins to appear that not only complex numbers but so-called analytic functions are destined to play a decisive role in the formulation of quantum theory. I am referring to the rapidly developing theory of dispersion relations.
It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind's capacity to divine them. The observation which comes closest to an explanation for the mathematical concepts' cropping up in physics which I know is Einstein's statement that the only physical theories which we are willing to accept are the beautiful ones. It stands to argue that the concepts of mathematics, which invite the exercise of so much wit, have the quality of beauty. However, Einstein's observation can at best explain properties of theories which we are willing to believe and has no reference to the intrinsic accuracy of the theory. We shall, therefore, turn to this latter question.
Order out of chaos is the theme of Genesis 1 – it is built into the Hebrew language itself: evening is chaos, morning is order. The word “kind” speaks to the ordering of life by generation of heritable traits. The Hebrew language is also mathematical.
And, of course, the “guide” to the system is Jesus Christ Himself. (Col 1, John 1, Hebrews 1:3). To me, it is no wonder that He is called the Living Word of God (Rev 19), the Logos (John 1):
One does wonder about the "unreasonable effectiveness of math" in allowing us to probe and "see" what cannot be directly observed within our four physical dimensions.
Bertrand Russell once skeptically (it seems) remarked that physics "is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover."
That last comment is particularly interesting to me. It suggests physics can only deal with a "reduction" of the physical world, and implies recognition that there are properties of the physical world that are not "mathematical." It isn't clear to me what Russell meant by this remark. I could interpret it to mean that he recognizes that science is limited to its side of the "cartesian split," and that the other side quite legitimately has its own work to do. So to speak. But I really don't want to put words in Russell's mouth here....
I certainly agree with you that methodological materialism wipes out of existence all geometric physics and information science. Yet I'm increasingly fascinated by Wesson's 5D with 2T (geometric) model as it might apply to Bell's experiment.
I'm still thinking that one through.... Anyhoot, thank you so Alamo-Girl, for your excellent essay/posts!
Beautifully stated, Alamo-Girl! It's also the theme of Plato's creation myth.
It seems spunkets may not want to see this. I think perhaps he has conflated the representation (physical science) with the thing of which it is a representation. But this can only be a reduction, or partial view, of an utterly ungraspable Whole.
Or so it seems to me, for whatever that's worth....
Thank you so much for the link from Wigner, noting "Einstein's statement that the only physical theories which we are willing to accept are the beautiful ones. It stands to argue that the concepts of mathematics, which invite the exercise of so much wit, have the quality of beauty. However, Einstein's observation can at best explain properties of theories which we are willing to believe and has no reference to the intrinsic accuracy of the theory."
How can mathematics be understood to be only implicit or "embodied" in physical nature if mathematical theories can be volitional objects for man, without regard to whether any particular theory is intrinsically accurate?
Thank you, Alamo-Girl, for your outstanding essay/post!
Sometimes I wonder if scientists who begin with a presupposition of naturalism aren’t somewhat like the person who comes into a movie already in progress. How can there be understanding without cosmology?
And I also greatly appreciate your raising Plato’s cosmogony of chaos to order. His concept of forms (or universals) lies at the heart of many differences around here and among the disciplines of science and math.
Thank you also for that interesting quote from Russell. It does indeed suggest that there is more than the strictly mathematical in “all that there is”. If he meant the division between what science can address and what it cannot – then I would suggest we ought to compare it with Bohr’s. I do have a tendency to reduce the boundary between science/math and theology/philosophy to “meaning” - one can theorize and test/observe how the physical realm “is” but the other must address why it is.
I look forward to your thoughts on Wesson’s 5D/2T v. non-locality!
Jeepers, you’ve given me a weekend’s worth of meditations. Thank you!
Thank you so much for your encouragements, Alamo-Girl! All I can say is, "ouch, my head hurts!" :^) Russell especially can have that effect on one....
Seems to me there's more to the "all that there is" than meets the eye. You know how much I love Plato. Plato had to develop a whole "new language" to even speak of these things that don't ever meet the eye, but which we humans experience anyway (e.g., qualia, thought, feelings, emotions, susceptibility to beauty, truth, et al.). That was the language of the myth.
Today, the word "myth" means something false or a superstitious belief. But Voegelin reminds us that, for Plato, "the myth remains the legitimate expression of the fundamental movements of the soul."
I'm writing away this afternoon on "Timothy." Things seem to be going well; but you will have the opportunity to make your own judgment about that, pretty soon.... I truly hope you will be most severe and critical when the time comes!
Hugs, dear sister! Thank you so much for writing!
Hey!
Hit the Road, Jack!
And as a columnist friend of mine once remarked: "The only good thing about the devastation of a nuclear war would be that so many people deserve it."
"I think perhaps he has conflated the representation (physical science) with the thing of which it is a representation. But this can only be a reduction, or partial view, of an utterly ungraspable Whole. Or so it seems to me, for whatever that's worth...
Nah, the particles and waves and eqs. are not the reality. They are mental contstructs used to know and understand it.
"I'm increasingly fascinated by Wesson's 5D with 2T (geometric) model as it might apply to Bell's experiment.
" it is mathematically reasonable that rather than 1080 particles in 4 dimensions, what we "observe" may actually as little as a single particle in a 5th spatial dimension with 2 temporal dimensions, multiply imaged 1080 times. (Wesson)
"...Wesson’s 5D/2T v. non-locality!
The experiments have already been done. Superluninal comm is impossible and there are no hidden variables. You're in 4d, everything you see(your observations) is in 4d.
Wesson's space-time-mass theory is ~equal to higher 10/11d compactified string theory- brane theory. Wesson's is a 5d theory. In it a 4d spacetime hyperspace exists on a 5d manifold. ie. a 4d on a brane well. The 5th d is either timelike, or space like. It's not compacted and you don't see it. The 5th d is the normal to the 4d hypersurface.
The 5d space is Ricci flat and "looks" empty. That's where that, "looks like a single particle on the 5th" comes from. It's not really a single particle.
I would guess that 5th coord. is spacelike for 2 reasons. It doesn't make sense for the normal to this hyperspace to represent time. In interactions with the mass that exists within the 4d hyperspace, because of the 5th, c is the limiting comm signal between here and the vacuum(IMO, the "flat", the "particle" of 5d). Also, hypothetical hspace interactions would have some "c". I think proper time(t2) for this 4d hyperspace is simply linear in this model. That's really another t, but it's not needed, because there's no dynamics.
Thank you so much for the great insights on Plato. Indeed, the word "myth" has morphed over the years to mean something unseemly. Nevertheless, great literature down the ages has inspired people both to understanding and wisdom.
Sorry, forgot to ping you too.
I've suggested before (some where in the FR archives) that one cannot have 2-dimensional time; 1 or 3 is possible but not 2 (or 4 or 5 or 6; 7 is posible.)
One problem with two (or any higher dimensional) time is that the geometry is no longer hyperbolic; experiment seems to show that the universe is hyperbolic. (Someone pointed this out to me last spring.)
Another problem (of my own making) is algebraic. If one does the Minkowsky thing with two dimensional time, one gets three space dimensions (x,y,z for example) and two time dimensions which are imaginary Sqrt(-1)*t and Sqrt(-1)*u (using "u" as the another time dimension.) The two Sqrt(-1)s cannot be the same else the two dimensions could not be told apart; thus one really has (using i**2=-1 and introducing j**2=-1) so that the coordinates of an event are (x,y,z,it,iu). However when taking the metric in the presence of mater leads to terms in it*ju and thus requiring i*j to exist; it cannot be 1 or -1 (as was pointed out by Hamilton in the 1840s) and thus we need ij=k so that there is a third time coordinate. So we really need (x,y,z,it,ju,kv) with i**2=j**2=k**2=-1 and ij=k. This allows a consistent algebra. The geometry isn't hyperbolic though and the metric need not be symmetric.
I should point out that even with 2 or more dimensional time; causality isn't a problem. The definition of a light-cone still applies. Things with space-like separation cannot be causally (causa efficiens, of course) connected.
THE FIRST ENTANGLEMENT OF THREE PHOTONS has been experimentally demonstrated by researchers at the University of Innsbruck (contact Harald Weinfurter, harald.weinfurter@uibk.ac.at, 011-43-512-507-6316). Individually, an entangled particle has properties (such as momentum) that are indeterminate and undefined until the particle is measured or otherwise disturbed. Measuring one entangled particle, however, defines its properties and seems to influence the properties of its partner or partners instantaneously, even if they are light years apart. In the present experiment, sending individual photons through a special crystal sometimes converted a photon into two pairs of entangled photons. After detecting a "trigger" photon, and interfering two of the three others in a beamsplitter, it became impossible to determine which photon came from which entangled pair. As a result, the respective properties of the three remaining photons were indeterminate, which is one way of saying that they were entangled (the first such observation for three physically separated particles). The researchers deduced that this entangled state is the long-coveted GHZ state proposed by physicists Daniel Greenberger, Michael Horne, and Anton Zeilinger in the late 1980s. In addition to facilitating more advanced forms of quantum cryptography, the GHZ state will help provide a nonstatistical test of the foundations of quantum mechanics. Albert Einstein, troubled by some implications of quantum science, believed that any rational description of nature is incomplete unless it is both a local and realistic theory: "realism" refers to the idea that a particle has properties that exist even before they are measured, and "locality" means that measuring one particle cannot affect the properties of another, physically separated particle faster than the speed of light. But quantum mechanics states that realism, locality--or both--must be violated. Previous experiments have provided highly convincing evidence against local realism, but these "Bell's inequalities" tests require the measurement of many pairs of entangled photons to build up a body of statistical evidence against the idea. In contrast, studying a single set of properties in the GHZ particles (not yet reported) could verify the predictions of quantum mechanics while contradicting those of local realism. (Bouwmeester et al., Physical Review Letters, 15 Feb.)
I’d appreciate your explaining how you see quantum entanglement involved in P.S. Wesson’s 5 Dimension/2 Time Theory!
Concerning Wesson’s theory you oberved:
I would guess that 5th coord. is spacelike for 2 reasons. It doesn't make sense for the normal to this hyperspace to represent time. In interactions with the mass that exists within the 4d hyperspace, because of the 5th, c is the limiting comm signal between here and the vacuum(IMO, the "flat", the "particle" of 5d). Also, hypothetical hspace interactions would have some "c". I think proper time(t2) for this 4d hyperspace is simply linear in this model. That's really another t, but it's not needed, because there's no dynamics.
Doctor Stochastic, I'd appreciate your comments on the above - he addresses the Minkowski gauge and curvature points in the body. The violation of physical causality was raised by Cumrun Vafa's f-theory. Somewhere I have a bookmark to an interesting debate between Vafa and Tegmark on that very point. I'll see if I can find it for the Lurkers.
Wesson's 5D/2T model calls for both an additional spatial dimension and an additional temporal dimension and for dynamics. The particles actually exist in the 5th spatial dimension and may be multiply imaged in 4D. The abstract reads:
In what follows, we wish to extend what has been noted above and derive several new results in two-time 5D relativity that are remarkable.
In Wesson's theory, or the equivalent, std 4d(x3,ct) remains whether the 5th is spacelike, or timelike. 4d must remain to fit the observations. The 5th d is the normal to the local 4d h-space, so that the 5d space remains Ricci flat. A Minkowski equiv construction/calc with that, regardless of the 5th being timelike, or spacelike, is impossible. The fifth only appears to unite EM, gravity and account for most of the particles in the std model. This 5d construction results in mass appearing in the 4d space, unites EM and gravity and accounts for most of the particles in the std model with limits of... => It's ~10/11d string theory, w, or w/o supersym. I think 26d is required to account for all the particles. Some fermions are missing with 10/11d. I'm not that familiar with all the variations here, details and various equivalences and consequences of any change of details. One at a time here.
It's all relative. Right now, bedtime. Reality is closing down fast...
My definition for reality would be what actually exists. I can say that physical reality, supports the non physical reality that only exists in the mind-the representations. All I can do to describe both is to use representations, math, mental images and words.
But I wanted to let y'all know I haven't been able to find the Tegmark/Vafa debate about 2T violating physical causality in F-Theory.
I did however find Itzhak Bars who has been following the 2T subject rather closely and wanted to clue y'all in on a interesting chart he prepared: 2T Physics
I'll try to catch up with y'all tomorrow!
I'll pass.
" the second timelike coordinate is related to the (inertial) rest mass of a particle in both induced-matter and membrane theory."
The process of getting that mass and such processesthat are considered in QED cause me to think the d is spacelike, because x/c has always been used and observed as the limiting time. Lorentz invariance. I'd guess they'd never see Higg's particles in upcoming experiments if the d is timelike.
The Higgs field/boson, which has not yet been made or observed – is necessary to the Standard Model. If not found, another explanation is needed. But even if found, the Higgs only explains 5% of the critical density of the universe (ordinary matter). Hence, the search is on for supersymmetry.
Moreover, the 5D theories consistently propose that matter of all kinds in 4D is a manifestation of higher dimensional dynamics.
At any rate, the Higgs alone will not do the trick - nor even with superparticles do we have a complete explanation; therefore, the investigation continues for a geometric solution to understand mass. It's like peeling an onion, each layer tells us more.
For Lurkers, a recent Freeper discussion on The Mysteries of Mass
Concerning investigations into the possibility of violating Lorentz invariance, Lurkers might want to keep tabs on Kostelecky and Mewes. There's always someone picking at the paradigms in physics. That is one of the great things about the discipline, IMHO!
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