Cosmologists need to check their work by using different coordinates. The Friedmann coordinates conventionally used are rife with fictitious potentials which interact nonlinearly with real sources of gravity. It is Cartesian coordinates alone that have no such effects. And hyperspherical coordinates are still orthogonal everywhere, so they have no off-diagonal fictitious potentials.

The whole point of coordinate systems other than Cartesian is to pretend that they are Cartesian themselves. To maintain this fiction without error, fictitious forces and their potentials must be inserted. The fictitious potentials then seem real and not different from ordinary gravity. They affect sources of gravity in the same way as real potentials.

When the correct fictitious potentials are inserted into the boundary conditions, then the Bianchi identities can be integrated on. This can be a graphical process when the correct tensor ranks are used.

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Michael J. Burns

The quality of CD player reproduction is on my mind today, as is the contribution of fictitious potentials to cosmology. Both questions are guarded (at sites like Wikipedia and arXiv) by the orthodox priesthoods that censor discussion for the sake, in the end, of their personal equanimity.

Practical digital to analog converters do not interpolate using the entire digital stream, so the relevant theorem fails to protect these converters from outputting substantial distortion. Aliased signals, albeit of reduced strength, occur around all of the frequencies that are a factor of the sampling frequency. In another context it would be called a Moire effect. I am sure that an artificial sound track could be made that sounds terrible when recorded and played back from an audio CD - shoutiness and quavering.

The fictitious effects, nonlinear on sources of gravity, by coordinate systems that are not a priori Cartesian are incorrectly ignored by academics in general relativity and cosmology. There may also be an effect on sources by the incorrect use of the second rank tensor as opposed to the fourth rank. The cosmological constant is also an artifact of confusion that is occasioned by use of the second rank.

Including the effect of fictitious and real forces on sources, use of covariant coordinates, adopting the exterior derivative, and representing the two Bianchi identities in the correct fourth and fifth ranks, are the practices needed to clarify cosmology. Then solutions can be understood graphically due to full compliance with the principle of general covariance.

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Michael J. Burns

http://blogs.scientificamerican.com/degrees-of-freedom/2011/11/06/the-cosmic-magnifying-lens/

I really think that this calculation by Dr. Castelvecchi of the magnification of the cosmic background radiation is spoiled by an artifact of Friedmann coordinates, that he takes as real instead of discounting it.

The actual magnification by spacial curvature is comparatively small. What does happen is that the big bang physically expands shards of the big bang, that then preserve sufficiently high temperature due to time dilation from their speed of recession. Which expanded shards are then perceived relatively undistorted in size by any gravitational optical effect.

Light, as a matter of definition in this circumstance, can not reverse course as drawn in his diagram; it seems to behave so in his diagram because Friedmann coordinates are not inertial. The data for supernovae Ia brightness is remarkably close to that expected in a flat and empty universe (a deviation of only about 5% in distance), so calculations using special relativity alone are useful as a first approximation and check point.

In addition, a proper calculation of kinetics (assuming the kinetic origin of the dimming, and not evolution of white dwarfs or an epoch of dust) shows deceleration of us as observers, not acceleration. This is so even when the magnification by convergent spacial curvature is accounted for, because acceleration effects dominate curvature effects in a homogeneous universe.

He then takes this coordinate artifact and attributes the cause to an increase of dark energy, which to me is a telling criticism of the concept of dark energy. A version of general relativity rigorously based on the Bianchi identities (rather than on a momentum tensor which does not include the fictitious effects of a noninertial coordinate system) forbids any version of dark energy that is not conserved.

But I am very interested, of course, in the real amount of spacial curvature. Flatness in Friedmann coordinates implies convergent spacial curvature and deceleration of the universe when inertial coordinates are used. In a universe that is inertially flat and does not decelerate, the graininess of the cosmic background radiation would be grown to a scale of 206 million light years today, as I calculate. Deceleration would cause a decrease in this scale.

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Michael J. Burns

I have been studying how to do cosmology with inertial coordinates, not the Friedmann coordinates that cause such dogmatic chaos.

For instance, kinetics in an inertial frame show extra supernovae Ia dimming with distance as evidence for slowing of expansion if anything. The departures from the expected dimming are 10%, and could have other causes. The Friedmann coordinates are noninertial to the point of changing the sign of the usual unwary calculation! Things not having a magic velocity are said to have cosmological acceleration by measure of Friedmann coordinates; the light signals from supernovae are included in this fictitious effect.

It is proclaimed that the typical distance scale of variation, from peak to valley, of the temperature in cosmic microwave background proves the flatness of space. But flatness within the Friedmann coordinates does not imply flatness in inertial coordinates. A flat and empty universe by inertial standards would possess negative curved space by measure of Friedmann coordinates.

This typical distance for variation in the background is extrapolated to a present size of 206 million light years, when an inertial or geodesic version of space is used. So, if this is also the typical spacing between superclusters and the middle of the adjacent voids, then space is indeed flat. But flatness in Friedmann coordinates implies positive spacial curvature in inertial. The positive curvature would magnify the variations in the cosmic background. And acceleration or deceleration trumps curvature with a stronger effect. So, if the spacing of superclusters is smaller today, then both counts imply deceleration of the universe.

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Michael J. Burns

The predictions by quantum mechanics of net vacuum energy and of slowing of ultrashort wave radiation by a quantum foam do not work out. This is because general relativity has theorems to the contrary. But why would those theorems win out? General relativity wins within the domain of its axioms, because a lockin theorem applies, namely the Bianchi identities that follow simply from the existence of the metric. It prevents the subject matter, spacetime, from experiencing alternatives to governance by the metric. Only where the metric can not be defended, on the small scale, can quantum mechanics overrule relativity with its theorems.

This dominance by relativity on large scales can even be nonlocal in the case of quantum foam. This foam can make as much mischief as it can in any small scale where the metric is not viable, but the theorems of general relativity intervene at some other location to require the opposite.

It is remarkable that a large scale effect of quantum mechanics does exist; the states of matter impelled by Bose and Fermi statistics are not overruled by relativity.

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Michael J. Burns

The daily upgrade broke booting on the new kernel; it forced booting with the next older kernel and required a "yum reinstall kernel" command for the latest kernel, 3.1.5-2.fc16.x86_64, to boot on my hardware - an AMD, Radeon, and Realtek equipped Toshiba T115D. Grubby reported a fatal error, no valid template found.

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Michael J. Burns

I understand now how Friedmann coordinates obscure thinking on cosmology. So an addition to my old meditation on superluminal philosophers is needed. Even though they are contemporary to us by definition, they actually are on the far side of the big bang. Before we imagine them at a suitable distance, we must think of evidence of the big bang being mathematically deducible at a closer distance. Reasoning that excludes communication with such philosophers is complemented by the argument that they are on the far side of the big bang.

The Friedmann, also known as comoving, coordinates are artificially curved, non inertial and non homogeneous. This is confusing to the unwary, and academics do get caught in the trap. Pontifications on the acceleration of the universe and on the cosmological constant are invalidated by this error.

And my worries about matter tunneling into the universe from outside are solved by this enlightenment. That eventuality is actually assignable to the big bang itself.

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Michael J. Burns

With today's update of Fedora 15, I no longer need to suspend my Toshiba 115D to enable the external sound output.

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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.

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Michael J. Burns

http://www.nytimes.com/2011/03/08/science/08fukuyama.html?pagewanted=all

âoeThe Origin of Political Orderâ, by Professor Francis Fukuyama, seems (to me) to make fundamental points. It is an ongoing struggle to suppress older methods of government: personal vengeance, nepotism, gangs, tribal war gods, graft, bribery and patronage.

http://www.rollingstone.com/politics/blogs/national-affairs/a-history-of-americas-eleven-nations-20111006

âoeAmerican Nationsâ, by Colin Woodard, identifies me as a citizen of Yankeedom, a secular puritan who sees government as a serious contributor to an ideal society. Maybe the nation competing for sovereignty over Grand Rapids is the Midlands, where emotional and intellectual detachment from government is the norm.

http://www.foreignpolicy.com/articles/2011/09/14/a_dictators_handbook_for_the_president?page=0,0

âoeThe Dictatorâ(TM)s Handbookâ, by Professors Bruce Bueno de Mesquita and Alastair Smith, expounds on the stability of systems other than democracies. President Obamaâ(TM)s inclusive coalition is a fairly fragile accident of history.

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Michael J. Burns

My Fedora 16 upgrade only allows my Gnome 3 login twice in an hour of trying. It is a legacy home directory originally from Fedora 14 and earlier, then switched to a uid and gid of 1000 from 500 before the upgrade. My XFCE login reports a dbus error. A new test account is allowed.

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Michael J. Burns

The new tight bunching of neutrinos, at 500 nanoseconds of separation, are a bit too close to be distinguished by uncalibrated Ethernet timers. The specification, as pointed out by AZSquib, is only plus or minus fifty parts per million. Before being reset by the master clock every six tenths of a second, these 100MHz timers could be off by 3000 ticks, or 30000 nanoseconds. Suppose that these timers are fifty times more accurate than the specification, then the maximum error could be 600 nanoseconds.

This consideration is a woeful omission in the error analysis by the original paper. Lets hope that the new results to be announced at the end of the month really are hashed.

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Michael J. Burns

I studied the published graphs of supernovae Ia brightness versus redshift. So I came to accept that the comparison curve on what is expected in an empty universe is correct. This certainly makes interpretation on the deviations easier. (In Wikipedia the dimming due to redshift is stated incorrectly, so my doubts were not unfounded.) See http://www.pha.jhu.edu/~bfalck/SeminarPres.html#adeptsim

One plausible interpretation is that a few groups of supernovae binned by their redshift are 10% more distant than expected. But simple kinetics interprets that as deceleration of the observer. Cruising away from the starting point at speed gets you more separation than accelerating to speed after the starting point. Slowing to speed after the starting point gets you yet more separation.

Could obscuration by dust, nanofiber carbon produced in mass ejection from stars and accretion disks, increase to 20% and then decline by dilution? Divergent spacial curvature would cause this 20% dimming, but why does that dimming reach a peak? The extended conservation theorems, from the Bianchi identities applied to superluminal sources of gravity, imply that divergent curvature must decrease with time. These Bianchi identities, when used with a hard-fought insight into geometry, rule out any nonconserved version of dark energy.

These supernovae intrinsically vary by 20% due simply to their ragged shape and random orientation. Aboriginal supernovae may be as much as 10% brighter due to their lack of heavy elements. Recent supernovae may be brighter due to their rapid spin and cooler temperature that delay detonation.

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Michael J. Burns

I have already written on the contradictions involved in electromagnetic radiation from a superluminal source. The best conclusion is that superluminal charges themselves should be defined as unobservable.

But superluminal sources of gravity are not contradictory in their effects, unlike superluminal sources of electromagnetic potential. And their gravitational radiation is shared in only one direction - the direction of travel of the superluminal source. (In higher dimensions, more directions for gravitational radiation are available for sharing. And in two dimensions gravitational radiation is not possible at all, because two dimensions plus time are required to produce it, and another dimension is required to propagate in.)

The questions are: Does this have anything to do with the number of dimensions we experience? And is there an additional uncertainty principle needed to prohibit the communication of contrary observations from a superluminal partner?

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Michael J. Burns

For this the kudos go to Scott Gray, publishing as AZSquib - see http://blog.vixra.org/2011/09/19/can-neutrinos-be-superluminal/#comment-11088 . It is regrettable that, as quickly as the problem was identified, it was not found sooner, before public attention was expended on the reported results. As discovered by AZSquib, standard issue Ethernet quartz crystals and circuits were used to timestamp event records. These were never calibrated, and their possible variation was not included in the error analysis. Neither the official specification nor the usual accuracy are sufficient for the task of measuring the speed of neutrinos. The experimenters used a master clock, but to no real effect.

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Michael J. Burns