Professor Victor Stenger spoke on his book “God: the Failed Hypothesis” this Wednesday.  His topic is ambitious and usually considered to be out of bounds in academic physics.  He broke the partition between physics and metaphysics.  But even so, he finessed some of the fundamental questions, and did not want to debate questions off of his outline.  Of course, I am willing to stray well away from the outline, and some other students of physics might not object.

So it is only on the implicit questions that I could criticize his talk, meaning of course that it explicitly presented a number of important insights.

He explained to an amateur audience that Newtonian physics has been superseded by a more recent doctrine that offers even less support for intervention by an activist or theist god.

(You might think that the Newtonian view also discourages animistic thinking, but Newton was very much the theist.  He intensely believed that God was both a puppet master and a mathematical designer.  So his empirical approach, that followed from his belief, to the mathematics of physics beat out the a-priori reasoning of the Enlightenment philosophers.  A-priori mathematics was nowhere near ready for the task at that time, but it demands another look now.)

Unlike Newton, Stenger cited the absence of intervention by God in Newtonian affairs as empirical evidence for his nonexistence.

Then Stenger pointed out with clarity that the data supporting quantum mechanics destroys the notion of a watchmaker god.  Whatever God would have done at the startup of the watch is actually a continuing activity.  But he did not claim the highest level of persuasion against faith for this point.

He added the point of his original calculation of the hot chaos at the big bang.  It concurs with the current assertion of Stephen Hawking on the absence of a singularity.  Supposedly designed interventions by God at that point are lost in the randomness by definition of thermodynamics.  Causal traces of a previous universe are lost in the indeterminacy of quantum tunneling.  And he asserted that the thermodynamic reversal of time between two mirror universes anchored at the common locus of chaos would confuse theologians.  But every type of event horizon marks off a disjuncture in the direction of time.

I do not recall that Stenger made a sufficiently big fuss about the point that a watchmaker god with ongoing activity would not be hiding behind the uncertainty principle.  He leaves that for his book in press.  The point is that there is no mechanism for hidden causes, such as a watchmaker, when the mechanism of causality has itself failed, due to exceeding the limits of its mathematical premises.  (The major, independent and sufficient premise is the existence of a spacetime metric.  Thermodynamics is another partially independent but sufficient premise.)

Stenger did not distinguish strongly between a watchmaker god and a cosmic designer and rule maker, and he mentioned but did not refute the purely metaphysical god of Plato and Spinoza.  I argue in the spirit of Spinoza that design and rule making are necessarily causal activities, but that the necessary premises for causality can not be relied on in the context of general metaphysics.  A cosmic designer is not a coherent hypothesis, even though it is implicit dogma that is embedded in the anti-intellectual empiricism that is fiercely enforced on many occasions, even in academic departments of physics.

Or alternatively, you can take Stenger’s implicit belief, which he did not mention and would have not discussed.  But he writes in the summary for his book now in press that, “The laws of physics were not handed down from above but are human inventions.”.  This also supports the conventional opposition to mathematical rigor and to the investigation of a-priori mathematics.

So I protest that the human brain is not a sufficient mechanism to impose mathematical order on the universe.  There would be no theorem out there to even support the reliable and continued existence of a physics department.  But there is a perspective on a-priori mathematics that seems capable of picking out the important theorems.

http://www.colorado.edu/philosophy/vstenger/dice.html
http://slashdot.org/~mburns/journal/

—
Michael J. Burns

Hypnos referred me to http://www.amazon.com/Geometry-Topology-Physics-Graduate-Student/dp/0750306068/ref=si3_rdr_bb_product , an advanced graduate text.  It’s saving grace is that the table of contents lists a single page sub-sub-section on the Bianchi identity - “The boundary of a boundary is zero.”.  The Amazon search of contents shows no mention of the phrases, “general covariance” and “geometric object”.  The Bianchi identity, the non existence of preferred coordinate systems, and the primary existence of curved spacetime are all fundamental to understanding physics, even for advanced graduate students..

I can say again that a cultural malaise is responsible for the neglect of ideas that are actually key.

—
Michael J. Burns

If you attend a lecture on physics, then be sure to doubt the tired metaphor of a bowling ball distorting a membrane that is meant to illustrate Einstein’s idea of gravity.  The truth is that a stationary field of gravity does not curve space at all, since that sort of curvature only shows in “planes” that are more or less aligned with time.  (I fail to recall which one of the lectures made this error.)  Especially do not be confused by an appeal to gravity and centrifugal force in order to explain the very same.  And understand that spacial curvature by itself affects all moving trajectories in a way that does not match the ordinary understanding of gravity.

A proper understanding of the principle of general covariance and all of its corollaries allows you to calculate this by way of scale diagrams - very simply compared to other coordinate-based methods.  I think this is teachable, along with a major portion of classical physics, to motivated novices in three to five hours of dialog over diagrams drawn on a scratch pad.

I challenge you to diagram a perfect tachyon, infinitely fast, and verify that it is not deflected or slowed at all by stationary fields, nor does it deflect stationary objects.  Show that perfect tachyons repel each other unless their path is perpendicular - pure spacial curvature.  Show that time-like trajectories are decelerated by a perfect tachyon unless they are stationary or perpendicular to the purely spacial path of the tachyon.  You can do this with no strain if you truly understand general covariance.

—
Michael J. Burns

I should change out that word tachyon used in my previous post to the term tachyonic region, something not necessarily a point object.

Whether region or point. this represents a geometric object that is conserved in a path along its orientation by reason of the Bianchi identity. Space is dilated along its path (a spacial dilation or contraction is the definition of this type of object), so that there is a natural divergence of other parallel objects from it.

—
Michael J. Burns

The Cosmological Constant is a Big Problem.

David Garfinkle’s lecture on the empirical foundations of cosmology was apparently well appreciated, and it is deservedly so. His kind manner enhanced the evening.

But the standard opinion - sufficiently explained by him - of the cosmological constant defies mathematics as I understand it.

The standard opinion is that, as the universe expands, new space comes into being with a constant density of centers for blue shift already embedded in it.

Actually, this is my more rigorous characterization of the concept of the cosmological constant. The standard opinion is conflated; there is language about dark energy, which in turn is a thought about the correspondence of the apparent phenomenon to the ideas of mass and energy that occur in the separate mathematical system of mechanics. It is Einstein’s equation of gravity which translates between the two distinct systems of mathematics. Centers of blue shift on one side of that equation translate to instances of negative mass on the other side.

Mechanics is an ad hoc theory, which had no mathematical foundation until Einstein wrote his equation. The usual exposition is that gravity is explained by his equation. But gravity is a phenomenon of spacetime itself, which can be studied with blithe ignorance of mechanics.

Spacetime by itself has behavior which derives from the Bianchi identity, “The boundary of a boundary is zero”. The Bianchi identity is a theorem that follows from the existence of the metric. And, the metric represents a way for different observers to agree on the separation between two events.

So, when the Bianchi identity is used to prepare a geometric construction of the natural behavior of spacetime, then Einstein’s equation can be used to transfer this behavior to the realm of mechanics. One of the Bianchi identities of spacetime translates by this equation into the conservation laws of mechanics. The theory of mechanics now has a foundation.

The cosmological constant breaks this Bianchi identity. Understood from the spacetime side of Einstein’s equation, the cosmological constant mandates the continuing appearance of new centers of blue shift, contrary to the Bianchi identity which conserves the existing centers. Geometric constructions of the future and past from information about the present are allowed by the existence of the metric and the Bianchi identities. The cosmological constant destroys these constructions with the passing of every instant of time, requiring new constructs of history and the future for every instant.

On the side for mechanics, the cosmological constant undermines the conservation laws, the only foundation that mechanics ever had. New negative mass materializes in every instance of time.

—
Michael J. Burns

Let me correct an omission. There is always something more to learn.

The cosmological constant would also mandate the appearance for newly instantiated space of a particular density of new centers of spacial contraction. They are oriented in the three different major directions of space and coordinated in magnitude with the density of new centers of blue shift.

These additional components are still contrary to the Bianchi identity, which demands a value of zero, but there are still interesting hypothetical properties of a cosmological constant that can be discussed.

In flat spacetime, free of fields and matter, the rule of Planck relativity applies, so that the effects of the cosmological constant reduce to a shift in units of measurement over time. This reduces the value of the constant to a subjective matter of opinion. It is in a universe with instances of high curvature that the cosmological constant causes trouble.

On the side for mechanics of Einstein’s equation, the new centers of spacial contraction translate to negative tachyons in three directions, and the new centers of blue shift translate to negative mass. Pressure and radiation energy are insufficient interpretations because they yield the wrong proportion between different directions of time and space.

Suppose that dark energy is not a cosmological constant, and is also not the conserved amount of negative mass and negative tachyons that is allowed by the Bianchi identity. Then the proportions and density can differ in direction or over time, and the universe accumulates over time a preferred rest frame or spacial orientation.

Good metaphysics does allow for discussion of contraries, only not in a particular context of classical physics. Theories to replace classical spacetime should be consistent about leaving behind properties of spacetime, and of Newtonian space and time also, that are obsoleted in the new context.

Even in metaphysics, considering a possible refutation of spacetime might not make for sound philosophy. The collection of theories that might replace spacetime must entirely outclass spacetime in their collective elegance, otherwise the necessary absence of a cosmological censor, as first argued by Spinoza, allows spacetime to compete successfully for the attention of observers. The economical and distinct definition of spacetime, along with its richness of expression, eliminates the need for a censor to suppress the competitive mathematical systems.

—
Michael J. Burns

I beg for patience, so that I might post a revision of my previous argument on the cosmological constant.

The cosmological constant is a crisis for classical physics. It implies that, as the universe expands, new space comes into being with a constant density of centers for blue shift already embedded in it. The cosmological constant would also mandate the appearance for newly instantiated space of a particular density of new centers of spacial dilation. They are oriented in the three different major directions of space and coordinated in magnitude with the density of new centers of blue shift. (Sources of gravity are not always reducible to the effect of a single vector or 1-form at a given point.) All of these serve as sources of divergent curvature.

The standard opinion is conflated; there is language about dark energy, which in turn is a thought about the correspondence of the apparent phenomenon to the ideas of mass and energy that occur in the separate mathematical system of mechanics. It is Einstein’s equation of gravity which translates between the two distinct systems of mathematics.

On the side for mechanics of Einstein’s equation, the new centers of spacial dilation translate to positive tachyons in three directions, and the new centers of blue shift translate to negative mass. Negative pressure and negative radiation energy are insufficient interpretations because they yield the wrong proportion between different directions of time and space. Dark energy necessarily responds to gravity and loses its uniformity over time.

Mechanics is an ad hoc theory, which had no mathematical foundation until Einstein wrote his equation. The usual exposition is that gravity is explained by his equation. But gravity is a phenomenon of spacetime itself, which can be studied with blithe ignorance of mechanics.

Spacetime by itself has behavior which derives from the Bianchi identity, “The boundary of a boundary is zero”. The Bianchi identity used here is a theorem that follows from the existence of the metric. And the metric represents a way for different observers to agree on the separation between two events.

So, when the Bianchi identity is used to prepare a geometric construction of the natural behavior of spacetime, then Einstein’s equation can be used to transfer this behavior to the realm of mechanics. One of the Bianchi identities of spacetime translates by this equation into the conservation laws of mechanics. The theory of mechanics now has a foundation.

The cosmological constant breaks this Bianchi identity – in the absence of quantum interaction with higher dimensions. Which higher dimensions should then be grouped beside the classical, despite the logical barrier. Understood from the spacetime side of Einstein’s equation, the cosmological constant mandates the continuing appearance of new centers of blue shift and spacial dilation, contrary to the Bianchi identity which conserves the existing centers in the relativistic direction of their extension. Geometric constructions of the future and past (neglecting tachyons) from information about geometry near the present are allowed by the existence of the metric and the Bianchi identities. The cosmological constant destroys these constructions with the passing of every instant of time, requiring new constructs of history and the future for every instant.

Calculations of the evidence by Syksy Rasanen on the dispensability of the cosmological constant have priority here. Any amount of negative mass and positive tachyons that is necessitated by evidence could still be compliant with the conservation laws (on the side for mechanics of Einstein’s equation).

And it could still be so that the action of conserved blue shifted regions and tachyons fulfills the cooling and homogenizing functions postulated for inflation.

There are other interesting hypothetical properties of a cosmological constant that can be discussed.

In flat spacetime, free of fields and matter, the rule of Planck relativity applies, so that the effects of the cosmological constant reduce to a shift in units of measurement over time. This reduces the value of the constant to a subjective matter of opinion. It is in a universe with instances of high curvature that the cosmological constant causes trouble.

Suppose that dark energy is not a cosmological constant, and is also not the conserved amount of negative mass and positive tachyons that is allowed by the Bianchi identity. Then the proportions and density can differ in direction or over time, and the universe accumulates over time a preferred rest frame or spacial orientation. And it seems that Hawking radiation, and exchanges of mass and tachyons, into external diverging higher dimensions would eventually stop, if not decrease along with the net mass.

Good metaphysics does allow for discussion of contraries, only not in a particular context of classical physics. Theories to replace classical spacetime should be consistent about leaving behind properties of spacetime, and of Newtonian space and time also, that are obsoleted in the new context.

Even in metaphysics, considering a possible refutation of spacetime might not make for sound philosophy. The collection of theories that might replace spacetime must entirely outclass spacetime in their collective elegance, otherwise the necessary absence of a cosmological censor, as first argued by Spinoza, allows spacetime to compete successfully for the attention of observers. The economical and distinct definition of spacetime, along with its richness of expression, eliminates the need for a censor to suppress the competitive mathematical systems.

—
Michael J. Burns

Mr. Burns,

May I pose a question which may seem hopelessly naive and completely unrelated to your excellent presentation on Cosmological Constant?

Is a Black Hole (extreme gravity) considered to have any causal relationship with separate dimensions or is it more like a whirlpool in the ocean or even a flowing river (converging kinetic energies), which remains wholly connected to three dimensional space?

Your mention of extreme curved space brought to mind the extreme spacetime curvature in a black hole, similar to the extreme curvature of the water surface in a whirlpool.

With this question I am not trying to imply anything. It is just a search for clarification on the issue of additional dimensions and tunneling and my own mental visualizations, without benefit of in-depth knowledge of physics. Anything beyond four dimensions (itself a daunting visualization), let alone some 16 dimensions, are completely alien concepts to me and I am groping for handles to help me trying to understand these in their most rudimentary form/s.
If this would be a waste of your (valuable) time, I would appreciate a reference (by anyone) to some basic instructional materials on the subject.

I can put down some related thoughts. I especially endorse your attempt to visualize matters in general relativity. The academic priesthood will likely hate me for saying taboo things, for instance that scaled and sparse drawings are of the essence in general relativity, and that the arcanum of compensating errors usually taught as the content is actually misleading.

There is no necessary relation of a black hole to higher dimensions, but no prohibition either. This is not different from ordinary space. But there is a logical barrier at event horizons; if you want to get fancy, then a context dependent logic is required. A universalistic logic breaks down there, august authority to the contrary.

The problem is that observers on the far side of an event horizon, the cosmological horizon also, can not agree at all on the direction of time with us. This is a flat out logical disparity. Since logical consistency is at the heart of physics, all rational communication is prohibited. This same prohibition applies to tachyonic observers also, although tachyonic gravitational fields are entirely allowed. So tachyonic observers might have something informative to share with the victims of an event horizon.

Electrical charges work out naturally in good theory as partially tachyonic spacetime disturbances in one or more higher dimensions. The diagramming shows that the electrical charge of a tachyon is modified; in the extreme the distinction between positive and negative charge is lost.

A high school sophomore who is an enthusiast for geometry could reproduce the necessary diagrams to show all of this. But I am at a loss as to how to help you with your visualization project. Academics do not have the background to do this. I want students for an 11 to 21 hour tutorial, so that I can develop complete materials for comprehending this subject..

My “Bad Physics And How Not To Do It” paper is available for download, and it serves as an abstract for the tutorial. My “Hacking Physics” manuscript is there too. It is at a higher level of abstraction and at greater length.

http://kyoto.cool.ne.jp/mburns/downloadindex.html

—
Michael J. Burns

mburns - 26 October 2010 07:42 PM

I can put down some related thoughts. I especially endorse your attempt to visualize matters in general relativity. The academic priesthood will likely hate me for saying taboo things, for instance that scaled and sparse drawings are of the essence in general relativity, and that the arcanum of compensating errors usually taught as the content is actually misleading.

There is no necessary relation of a black hole to higher dimensions, but no prohibition either. This is not different from ordinary space. But there is a logical barrier at event horizons; if you want to get fancy, then a context dependent logic is required. A universalistic logic breaks down there, august authority to the contrary.

The problem is that observers on the far side of an event horizon, the cosmological horizon also, can not agree at all on the direction of time with us. This is a flat out logical disparity. Since logical consistency is at the heart of physics, all rational communication is prohibited. This same prohibition applies to tachyonic observers also, although tachyonic gravitational fields are entirely allowed. So tachyonic observers might have something informative to share with the victims of an event horizon.

Electrical charges work out naturally in good theory as partially tachyonic spacetime disturbances in one or more higher dimensions. The diagramming shows that the electrical charge of a tachyon is modified; in the extreme the distinction between positive and negative charge is lost.

A high school sophomore who is an enthusiast for geometry could reproduce the necessary diagrams to show all of this. But I am at a loss as to how to help you with your visualization project. Academics do not have the background to do this. I want students for an 11 to 21 hour tutorial, so that I can develop complete materials for comprehending this subject..

My “Bad Physics And How Not To Do It” paper is available for download, and it serves as an abstract for the tutorial. My “Hacking Physics” manuscript is there too. It is at a higher level of abstraction and at greater length.

http://kyoto.cool.ne.jp/mburns/downloadindex.html

—
Michael J. Burns

Thanks so very much for your indulgence. You have provided me with plenty material to keep me busy for a long time…

You are welcome!

—
Michael J. Burns

It’s past Dec. 15, and there is no word on the Higgs boson.

Professor Wiggins spoke here at Grand Rapids this year. In answer to a question, he opined that evidence regarding the Higgs boson would be announced by now. But there was data announced which instead weighed against a variant of string theory.

Neither the Higgs boson nor this variation of string theory - that postulates higher dimensions with larger extent than that needed to create charges - are well formed mathematically so far as I can see. I can wonder that this is work from Harvard and Maryland.

—
Michael J. Burns

I am indebted to Professor Furton of GVSU for presenting the Carl Sagan Day Lecture in Grand Rapids. It was presented in a gentle and friendly spirit.

He was also humble in his presentation of cosmological data and analysis. As I must be humble but only in part, since I am not a master of coordinate based calculations when the premises are unphysical, namely the cosmological constant. (But I am a master of diagrammatical solutions of curved space. Take my tutorial!) The lecture was an incentive for me to do more study.

None the less, I must comment on a bias in the discussion by physicists of cosmological data. Here is a link to supernova Ia data and analysis, which shows a very mild departure from empty and flat space - about 5%. This is a philosophically important comparison. Evolution of supernovae and accumulation of graphene dust (a nanotube form recently observed) might yet account for this small departure of 10% from the expected brightness.
http://www.astro.ucla.edu/~wright/sne_cosmology.html

Physicists habitually use Friedmann coordinates for discussion of cosmology. But a point mostly forgotten is that this coordinate system is highly noninertial and artificially curved. Such coordinates invoke fictitious acceleration. By the weak principle of equivalence, fictitious acceleration is the equivalent of fictitious gravity, and thereby the equivalent of fictitious sources of gravity. So declarations of cosmological constants and acceleration of the universe must be adjusted for this bias. (Analysis from data on the cosmological microwave background must also be adjusted.)

So the challenge for me is to analysis the data in inertial coordinates.

The cosmological constant breaks the principle of conservation from mechanics. It also violates the Bianchi identities from differential geometry. (Confusion here comes from another habitual error of physicists - using the wrong tensor rank, or diagram type, to represent physical objects.)

Lets speculate that spacetime is indeed flat, which is fairly close to the evidence. That would require a background source of negative gravity, which is conserved in agreement with the Bianchi identities, and which is sufficient to counterbalance the positive gravity from matter, radiation and dark matter. (Differential geometry has no prohibition on negative gravity.) By the evidence as taken in an inertial coordinate system, the universe fairly closely resembles one which is flying apart with neither acceleration nor deceleration.

The cosmological constant is not needed now, only a conserved background source of gravity. If anything, the universe is decelerating. A simple kinetic understanding of supernovae distances also indicates this deceleration if it is real.

Michael J. Burns

mburns
Lets speculate that spacetime is indeed flat

If I may be permitted to express a musing:
Intuitively I have always been enamored by the concept of a doughnut shaped cosmos, with spacetime occupying and expanding along the “flat” surface area. In such a configuration, the current universe would start at the very center (a cosmic white hole) expressed as a BB and expand in all directions along the surface area with an apparent acceleration of expansion, until it reached the equator where the surface area begins to contract again towards the center of the doughnut, perhaps eventually collapsing into a “cosmic black hole”, only to reappear through the white hole as a new reanimated universe.
To a layman (as myself) this would answer a lot of questions, i.e. infinity, multiple universes, without negating the string theory or other accepted theories of spacetime structure which allow for curvature, gravity, quantum, conservation, etc.
Would you indulge me with a simple answer if this could be possible or if such a concept has already been ruled out?

Your question comes from a powerful intuitive notion.

Within my competence to expound on Calabi-Yau space, extra dimensions within this universe - 6 to account for for 6 kinds of charge - do indeed form a kind of hyper doughnut; this is to achieve a kind of flatness in spite of the sharp curves required by the small classical size of charges. Physicists such as Michio Kaku are able to use this mathematics with sufficient insight to make the mathematical prediction of 6 extra dimensions.

The mathematical possibility of a hyperverse exists. The universe would be a spontaneous black hole in the hyperverse; the axis of time for the universe would, from the outside, seem to be pointing inward toward the center. Complex forms for a universe are allowed in the higher dimensions of the hyperverse; only one extra is needed to allow a torus. (Even in a hyperverse, only one direction is logically allowed for time, but the interior of black holes disagree on that direction by mathematical necessity. So communication to the hyperverse is disallowed by the same mathematical necessity.)

The big bang occurring in a hyperverse implies a very small conserved mass for the universe - a background of negative mass to balance the ordinary matter and radiation as well as dark matter. Flatness is strongly implied.

The empirical evidence for the accumulated curvature of the universe is 5% or less (a 10% slowing of speed); evolution of supernovae and the accumulation of dust could still account for the 10% shift in brightness. Discussions of a 71% cosmological constant are impelled by a gross mathematical error - the naive use of a noninertial coordinate system compounded by wrong tensor ranks and wrong algebraic manipulations. I would guess that the optical effects of a torus shape for the universe would be apparent very soon when they are looked for with the correct mathematics. A real equivalent to the mathematically wrong cosmological constant would imply a real acceleration of the universe; this is still an empirical long shot. The doughnut universe is that same long shot.

—
Michael J. Burns