Why Space has Three Dimensions

Why Space has Three Dimensions   – see Matthew Chalmers, New Sci 28 Sept 2013

That space is 3-D follows from electromagnetic and gravitational theory, both being experimentally validated and both free of quantum theory’s offence to views of reality (Chalmers, NS 28 Sept, p.34).

The reasons are surely much deeper than the inverse square ‘law’ (argument in the Box).

First, accelerated charges emit synchrotron radiation in a beam relative to the inertial reference frame of special relativity, of 3-space plus time.

Second, Einstein’s general relativity gives slightly different answers for light travel times (eg. Earth to Venus) for different accelerated frames – a unique answer comes by specializing to the inertial frame.

Einstein’s strong form of the “equivalence principle” led him astray, in that it took accelerated frames as equally valid, rejecting a unique space frame. His followers like Fock, Weinberg and Logunov have found good reasons for the inertial frame and thus for 3-space being real.

Seeing 3-space as real and higher dimension spaces as mathematical models, thus implies a weak form of the equivalence principle, applying locally, eg. in Einstein’s lift, but not in rotating planetary systems.

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Not only time is real, but space too!

Comment on “Time Reborn: from the crisis in physics to the future of the universe”

Time is real, okay! A time-sequence is essential for the causality principle. Good that Lee Smolin comes out against “laws of physics” that take time to be an illusion. We know the laws are man-made. As he writes, light-rays reach us only from the past, not the future, so the ‘laws’ should encompass this.

The time coordinate in Maxwell’s electromagnetic theory is different from the 3 space coordinates. The beauty of the 4-vector differential formulation, with ‘imaginary’ time the 4th coordinate, has led people astray.

The time-explicit formulation of light waves uses (Liénard-Wiechert) retarded potentials to form an integral over waves reaching each point from earlier times. This satisfies the Penrose criterion for a truly fundamental law being irreversible, unlike the differential equations of Maxwell.

If general relativity (GR) is to encompass gravity and electromagnetic fields, as is often claimed, it must be formulated so as to cover travelling waves. It cannot depict them as sources of energy-mass that distort the geometry of space.

There has been progress in reformulating GR, in identifying a real energy-momentum tensor (not the pseudo-tensor of Einstein) which describes fields and associated waves carrying real energy through space – not across space, as in theories of photons. Defining a real tensor requires, however, the choice of a preferred metric, ie. with coordinates for real space.

Some leading physicists of the mid-20th Century (Vlad Fock, Steven Weinberg) saw it as essential to define a real energy tensor in GR, and were ready to adopt real space coordinates. They were largely ignored by the abstract theorists, including Smolin. Time now for him to acknowledge both real time and real space!

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Higgs-like particle

Such was the hype in billing the CERN results that the science teams were forced to come up with something definite. And that has persisted despite scientists soon questioning the fundamentalist claims: the Higgs boson does not relate to the neutrino, gravity or ‘dark matter’ and could be a composite particle.

Now it’s downgraded to a “a Higgs-like particle”: the recent $3million Fundamental Physics Prize was awarded for discovering “a Higgs-like particle at CERN’s Large Hadron Collider”.

But the British media continues in ignorance, encouraged by the aging Peter Higgs and the award of a New Year “honour”. An interview reprinted from El Mundo reports the Higgs particle in mystical terms:

“In 1963 Higgs predicted the existence of a force-carrying particle, part of an invisible energy field that filled the vacuum throughout the observable universe. Without the field, or something like it, we would not be here. The field clings to the smallest fundamental particles and gives them mass. The field, which switched on moments after the big bang, allowed particles to come together and form all the atoms and molecules around today.”

Peter Higgs played this up, disclosing emotion over-riding science:

What was so overwhelming really was the response of the audience at Cern. It wasn’t like a scientific seminar, it was like the end of a football match when the home team has won, and that was what was overwhelming to me, to be a part of that …

So cocky is Higgs that he ventures to defend religious beliefs, arguing in the El Mundo interview, that science and religion were not incompatible. He attacked Richard Dawkins for ‘fundamentalism’, without appreciating how closely he fits the Dawkins cap:

The true scientist, however passionately he may ‘believe’, in evolution for example, knows exactly what would change his mind: evidence! The fundamentalist knows that nothing will.”

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Gravitational collapse without black holes

The contemporary notion of black holes originates in Oppenheimer and Snyder’s 1939 article “On Continued Gravitational Contraction” (Phys. Rev. 56:455, 1939).  Later Roger Penrose (Phys. Rev. Lett. 14:57, 1965)  showed that the O&S metric gave rise to trapped surfaces, ie. regions of space from which no light rays can escape, and proved that within such surfaces black-hole formation is inevitable. But what if their metric is faulty?

Trevor Marshall’s challenging article uses differential geometry to show that a simple modification of the O&S metric, fully consistent with General Relativity, enables all radial light rays originating in the interior escape to the exterior. There is no trapped surface and no black hole; on the contrary there is a stable end state with finite density, contained within a sphere of Schwarzschild radius, contracting ever more slowly on itself over infinite time.

Such solutions may be seen as counter-intuitive if, above a certain density, “no force can countervail against gravity”.  Indeed, they require gravity to be repulsive in the extreme high regime, where its energy density is comparable to mass densities.  It therefore fits intuitively with the field interpretation of gravity.  On the other hand, the purely geometric interpretation based on the extreme form of the ‘Equivalence Principle’ has no light-ray connectivity, so is not consistent with causality. Is that not counter-intuitive?

Trevor Marshall’s full paper is in the December issue of Astrophys. Space Sci. (2012) 342:329–332.  DOI 10.1007/s10509-012-1170-y

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Higgs science in turmoil

New Scientist shines some realism into the Higgs-hype in reporting (by Slezak and Grossman, 14 July) from some of the scientists involved

“…beginning of the end of the standard model” (Georg Weiglein)
Rates of decay into pairs of other particles are different from predicted (especially the decay into photon pair), so that the Higgs could be a composite (Alex Pomarol), not a fundamental particle after all.

Higgs doesn’t cover photons which, being mass-less, are supposed to slip unhindered through the Higgs field. It tells us nothing about the neutrino, perhaps also mass-less. Nor does it cover the majority of matter in the galaxy – “dark matter”.

Rather than the discovery of the Higgs being a keystone, they now say the standard model doesn’t include gravity and gravitons and quote Steven Weinberg “it’s crucial to keep looking for a more comprehensive theory”.

Lisa Grossman changed her tune from only one week earlier (Let the Higgs games begin, New Scientist, 7th July) when she claimed the ‘standard’ “model is one of the most successful in physics” and wrote than knowing the Higgs’ mass should give us a theory explaining the varied masses of ‘fundamental’ particles, dark matter and gravity. A severe affliction of hope trumping reason, as spawned ‘Higgsteria‘.


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Self-bending wave packets – a counter-example to the photon model

Self-bending light-beams are predicted in a new PRL paper called Nondiffracting Accelerating Wave Packets of Maxwell’s Equations (April 2012)

Previously ‘Airy’ wave packet solutions had been found and demonstrated experimentally, but diffraction for finite angles of bending tend to destroy them.  ‘Airy’ plasmons propagating at an air-conductor interface do show self-healing properties and bend while retaining a beam-like form to a distance of 10-20 μm.

The new non-diffracting solutions of Maxwell’s equations are much superior, propagating in vacuo in a 90 degree arc in just 35μm.  The  ‘photon’ model of light has no counterpart to these exact vector-solutions of the full Maxwell equations.  This adds to the examples of photon-failures described earlier.

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Black Holes and whacky physics on BBC’s Horizon

The Horizon programme’s Who’s afraid of a big black hole (BBC2 16 Feb. and BBC4 19 Feb. 2012) shows how badly so-called ‘leading physicists’ have departed from solid analytical physics.

This programme was a vehicle for physics-mystics; giving up on making their ideas and speculations consistent with normal physics, they opt for changing to some post-modern physics based on undefined theoretical concepts. “The collapse of physics as we know it claims Prof. Andrew Strominger. Black holes, string ‘theory’ and quantum extremism all get a look in. While speculation has a useful role in science, this popularisation doesn’t just belittle established physics, but turns into reactionary anti-physics, giving credibility to wacky statements antithetical to critical science.

These post-modern physicists try to claim the authority of Einstein, though Albert was in fact hostile to black holes and fundamentally critical of quantum mechanics.

The early part of the programme overplays an image of a river flooding over a waterfall, said to simulate space moving ever faster. Not even light can climb out, it states, but no mention is made of ever-slowing light speed on approach to the boundary ‘waterfall’. The analogy between black holes and waterfalls is most misleading and falls far short of Tegmark’s claim that it “lets us calculate all properties of black holes exactly”.

 Max Tegmark tells us Black Holes have existed in theorists’ minds and notebooks for almost a century, “most notably in the mind and notebook of Albert Einstein”. Yet Einstein denied they exist, and showed this in his 1939 paper – which Tegmark simply slates as ‘incomplete’.

Tegmark is evidently a believer in “gravity equals geometry”, giving no ground to critics of this. So he can ignore the maths of the Einstein equation and resort to elementary topology:

imagine that this piece of jelly is the space, then the presence of matter distorts the space.  All massive objects like stars and planets bend the space and time around them. Any object that passes through that warped space time will move as if being pulled by a force, and this is what we experience as gravity.  Anything very heavy and very small would create such a strong gravitational field that space and time would be bent and twisted to breaking point.”

 See how he slides from warped ‘space’ to warped ‘space-time’, making another questionable if common assumption that time and space dimensions are identical (even interchangeable).

His error is that equating gravity with geometry breaks down in strongly-varying gravity. Solving instead the Einstein equation for inward collapsing matter (as Oppenheimer-Snyder considered in parallel with Einstein in 1939) shows that matter collapses onto a shell (Marshall). This solution has no problem with collapse onto a point – Ramesh Narayan‘s talk about a “monster” singularity in the equation from which anything might emerge (as physics can’t predict) is flamboyant nonsense.

The assertion “gravity is not really pulling me down to the ground, it is space that is pushing me down” is not only counter-intuitive (a physicist’s delight) but also misrepresents Einstein’s equivalence principle, as that says nothing about cause. And Einstein’s formulation has limitations, eg. in strongly-varying gravity as above. 

We are told of the core-collapse supernova that left no visible core, yet the programme didn’t tell us of other instances where a remnant central core star is visible. We hear of orbit tracking of some 30 stars near the centre of our galaxy, with Reinhard Genzel claiming nothing fits this other than a black hole. Yet Genzel’s 1996 limit (http://dx.doi.org/10.1038/383415a0) was 100 times the size of the solar system and over 2 000 times the Schwarzschild radius for a mass of 4-million suns. The Schwarzschild radius (R*) denotes the strong (relativistic) gravity regime, so even a far larger partially-collapsed body would easily meet the bill. Eckert and Genzel’s “most probably occupied by a massive black hole” was a huge leap of faith that the journal Nature would normally exclude.

Subsequent studies in 2008 reduced Genzel’s limit from star tracking to 45AU, about 1000 R*, but he still claimed this to be the best evidence that ‘black holes’ exist. In the second edition of Black Holes in the Universe, Begelman & Rees incredibly claim it to be ‘definitive proof’, based on the density of the central mass (from the star orbits) being too high for a stellar cluster, but they do not consider the idealised dust star collapsed on a shell of order R*. The SgrA* radio source near or at the galactic centre is observed to be 6 R* or less, so still does not show the central object is as compact as R*.

Ramesh Narayan talks of other galaxies, in which ‘black holes’ are 1000x more massive and pedantically draws a Figure showing rough proportionality to the galaxy mass. But he doesn’t ask why should a ‘black hole’ which is disconnected from a galaxy follow any such relation. He then jumps to asserting that stellar mass ‘black holes’ are very numerous in every galaxy, everywhere, without evidence.

Andrew Strominger plays the leading anti-physics role: declaring physics is having a nervous breakdown – the collapse of physics as we know it – and asserting that ‘black holes’ are the next step to understanding the universe. It’s “quite likely”, he says, that quantum mechanics is needed to understand the ‘black hole’ singularity. Narayan at least admits that claims of ‘quantum gravity’ being the solution are simply semantics: “we don’t know, have no clues at all” it’s a “theory beyond understanding”.

We are told that black holes are formed from cores of massive stars “imploding all the way down to a point” and “totally mysterious”. The explanation does show the reasoning is inconclusive:   Doug Leonard believes he spotted a black hole when a massive explosion of a supernova signalled the death of a star. After two years he failed to find the central star (on early images) which had exploded as a supernova and disappeared. 

He fails to mention that in other supernova explosions, a central star often remains detectable, in radio waves if not the visible spectrum – so his belief that in the one case it had vanished into a black hole is unscientific.

Finally, after pontificating about the ‘shadow of the event horizon’ and about cracking the problem of quantum gravity, Shep Doeleman gives the game away:
 “It might seem as if it would be easier if things like black holes just went away, but then, where would the fun be?”

This is not serious but speculative non-science. Horizon does us a disservice with such promotion of extreme and ‘reactionary’ post-modern physics.

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