Wednesday, December 05, 2007

Night at the Museum


Even on sunny afternoons, one can find stars in a planetarium. A tour of New York's bright lights has included Times Square, the Christmas tree at Rockefeller Center, and Grand Central Terminal. American Museum of Natural History recently starred in NIGHT AT THE MUSEUM. The movie reminded us what an adventure this place is, for one could spend days here without seeing everything. Within the glass cube of its Rose Center for Earth and Space, a gigantic sphere marks Hayden Planetarium. The current show, COSMIC COLLISIONS, is narrated by Robert Redford and features breathtaking images of asteroids and meteors. Though New York lights drown out the stars, this place is a reminder of how Space can touch our lives.

The sphere's lower half is home to a circular Big Bang Theatre, with a show narrated by Maya Angelou. The winding exit ramp is a Big Bang Walkway with milestones of cosmic evolution marked along the tour. While "inflation" and "dark energy" are not on this guest list, Rose Center has at great expense built a model of our spherical Space/Time. Complementing this space are models of the planets, further reminders of the beauty of spheres.

We learn about the Greek Pythagoras via the straight sides of triangles, but he was also interested in spheres. He encouraged men and women to have many interests, making contributions to music and astronomy. As a musician, he is credited with the idea that “music of the spheres” described the planets. Reasoning that it was the most harmonious shape, he theorised that Earth was spherical. Today’s science seeks to explain the Universe from such principles.

To please his musician’s ear, Pythagoras sought a “cosmic harmony.” As a mathematician, Pythagoras was inspired to claim that “all is numbers,” meaning that everything in the world could be described by equations. This idea is the basis of modern physics. Pythagorean ideas began a quest that would last thousands of years, to find equations describing the Universe.

Everyone should own a book called "RELATIVITY: A Clear Explanation that Anyone Can Understand" by Albert Einstein. For about 6.95 US you will get a better view of the subject than any imitator book. In Chapter 31 Einstein dares to imagine the entire Universe. He tries to follow a Cosmological Principle that the Universe looks the same from all locations. Like Pythagoras, he reasons that the most harmonious shape is a sphere. Using General Relativity, Einstein predicts that enough mass will cause Space/Time to be curved into a sphere of 4 dimensions, of which our 3 dimensions are just the surface.

Einstein also realised that gravity would cause this spherical Space/Time to collapse, unless it were supported by some repulsive force. Taking the Cosmological Principle into 4 dimensions, he desired a Universe that looks the same at all times. Here Einstein made the blunder of introducing a "cosmological constant" to prevent the sphere from collapsing. Later Alexander Friedmann and Georges Lemaitre independently found solutions to Einstein equations indicating an expanding Universe. Edwin Hubble's observations of redshifts finally allowed Einstein to drop the cosmological constant

The simple expression R = ct predicts that the Universe expanded from a tiny point. When t was tiny, c was enormous and the Universe expanded like a Bang. Maya Angelou and a preponderance of evidence support the "Big Bang." According to one paradigm, faster-than-light inflation would have expanded the radius so much that its sphere would be to our perception flat. When pressed, even inflation theorists admit that on the largest scales the Universe must be spherical. It is not topologically possible for a tiny point to expand into flat Space. According to General Relativity, even the smallest mass will cause Space/Time to be curved.

Views of the Cosmic Microwave Background may also indicate a spherical Universe. By measuring distances between acoustic peaks, scientists hope to complete a triangle and determine curvature. When a changing speed of light is accounted for, the angles do not add up to 180 degrees and the triangle is not flat. Most telling, the scale of density fluctuations is nearly zero for angles greater than 60 degrees. Like a ship disappearing over Earth's horizon, the lack of large-angle fluctuations is smoking-gun evidence that the Universe is curved. Both lines of CMB data indicate that the curvature has radius R = ct.

According to fashion magazines, it was fashionable to believe that the Universe was flat, like the Earth. Large objects under the influence of gravity, even raindrops, tend to form spheres. The Universe is very, very large. The flat vs. sphere debate once raged about Earth, and everyone knows which side won. Even the work of mathematician Gregory Perelman and the Poincare Conjecture predict a spherical Space. The Universe model at American Museum of Natural History hints that the sphere will win again. The only missing ingredient is "GM=tc^3" written on the side.

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6 Comments:

Blogger Kea said...

I'm glad to see you are enjoying the sights. Maybe you could post about an interesting You Tube video, too.

10:28 AM  
Blogger nige said...

This is a nice post and has a lovely picture, Louise.

Einstein's assumption that spacetime gets literally curved - that geometry rather than particle interactions is the reality of the universe - is evidently a classical belief that dates back to Riemann. One thing I like about Smolin's 1996 book is the way he gives a graph of space (distance) versus time, draws a curve on it (acceleration) and then says that the curve is "curved spacetime". I think that makes curved spacetime very clear; it's a mathematical concept, a curved graph of the motion of a particle in space is really all that is scientifically defensible in what is meant by "curved spacetime".

What we know for certain is that a ray of light is deflected as if it has travelled along a curved geodesic when gravity acts on it.

That's a long way from proof that the vacuum has purely geometric properties, and it conflicts with the picture of the vacuum as a particle-filled entity (which existing successes of quantum field theory seems to suggest).

I used to collect quotations about Einstein's geometric problems and the issues various particle physicists had with them:

‘Looking back at the development of physics, we see that the ether, soon after its birth, became the enfant terrible of the family of physical substances. ... We shall say our space has the physical property of transmitting waves and so omit the use of a word we have decided to avoid. The omission of a word from our vocabulary is of course no remedy; the troubles are indeed much too profound to be solved in this way. Let us now write down the facts which have been sufficiently confirmed by experiment without bothering any more about the ‘e---r’ problem.’ – Albert Einstein and Leopold Infeld, Evolution of Physics, 1938, pp. 184-5. (This is a very political comment by them, and shows them acting in a very political - rather than purely scientific - light.)

‘The idealised physical reference object, which is implied in current quantum theory, is a fluid permeating all space like an aether.’ – Sir Arthur S. Eddington, MA, DSc, LLD, FRS, Relativity Theory of Protons and Electrons, Cambridge University Press, Cambridge, 1936, p. 180.

‘The Michelson-Morley experiment has thus failed to detect our motion through the aether, because the effect looked for – the delay of one of the light waves – is exactly compensated by an automatic contraction of the matter forming the apparatus.... The great stumbing-block for a philosophy which denies absolute space is the experimental detection of absolute rotation.’ – Professor A.S. Eddington (who confirmed Einstein’s general theory of relativity in 1919), MA, MSc, FRS, Space Time and Gravitation: An Outline of the General Relativity Theory, Cambridge University Press, Cambridge, 1921, pp. 20, 152.

‘Some distinguished physicists maintain that modern theories no longer require an aether... I think all they mean is that, since we never have to do with space and aether separately, we can make one word serve for both, and the word they prefer is ‘space’.’ – A.S. Eddington, ‘New Pathways in Science’, v2, p39, 1935.

‘... the source of the gravitational field can be taken to be a perfect fluid.... A fluid is a continuum that "flows" ... A perfect fluid is defined as one in which all antislipping forces are zero, and the only force between neighboring fluid elements is pressure.’ - Bernard Schutz, General Relativity, Cambridge University Press, 1986, pp89-90.

‘Popular accounts, and even astronomers, talk about expanding space. But how is it possible for space ... to expand? ... ‘Good question,’ says [Steven] Weinberg. ‘The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.’ [Martin] Rees agrees wholeheartedly. ‘Expanding space is a very unhelpful concept’.’ – New Scientist, 17 April 1993, pp32-3. (The volume of spacetime expands, but the fabric of spacetime, the gravitational field, flows around moving particles as the universe expands.)

‘All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs. The virtual fermions with charges opposite to the bare charge will be, on average, closer to the bare charge than those virtual particles of like sign. Thus, at large distances, we observe a reduced bare charge due to this screening effect.’ – I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.

‘It seems absurd to retain the name ‘vacuum’ for an entity so rich in physical properties, and the historical word ‘aether’ may fitly be retained.’ – Sir Edmund T. Whittaker, A History of the Theories of the Aether and Electricity, 2nd ed., v1, p. v, 1951.

‘It has been supposed that empty space has no physical properties but only geometrical properties. No such empty space without physical properties has ever been observed, and the assumption that it can exist is without justification. It is convenient to ignore the physical properties of space when discussing its geometrical properties, but this ought not to have resulted in the belief in the possibility of the existence of empty space having only geometrical properties... It has specific inductive capacity and magnetic permeability.’ - Professor H.A. Wilson, FRS, Modern Physics, Blackie & Son Ltd, London, 4th ed., 1959, p. 361.

As an example, in about 1996, I came up with a simple physical mechanism idea for getting solid predictions about gravity (out of a spacetime fabric) which went like this: there is evidence for a spacetime fabric of some sort, but there is no evidence that it gets compressed, or the opposite. It's associated with the vacuum properties in electromagnetism and the exchange of gravitons between masses presumably gives rise to the spacetime fabric which is approximated classically by general relativity.

The simplest model of the spacetime fabric which is possible is that it doesn't expand or contract, regardless of the motion of mass. This is quite similar to water (which is virtually incompressible).

Hence, with this simplest model for the vacuum's fabric, we immediately get checkable predictions: as the masses recedes from one another due to the expansion of the universe, voids between sub atomic particles are created which need to be filled by the spacetime fabric (gravitons, etc.). Around us, masses are receding radially. Hence, to prevent voids or a reduced presence of the spacetime fabric in the volume continuously being vacated behind moving fundamental particles, you need to have spacetime fabric moving inward, towards us, to take up those vacated spaces.

It's easy to do rigorous calculations of this. If fundamental particles of volume X recede from us at velocity v, the the simplest possible (incompressible) model of the spacetime fabric immediately predicts that a volume of spacetime fabric X is moving towards us at velocity v. In other words, there is an equal and opposite effect. This allows you to have a quantitative, predictive, mechanism for gravity because in the big bang, since the recession velocities we can see increase with distance away from us and hence vary with observable spacetime; this is equivalent to an acceleration of mass away from us. Thus, you get an effective outward force of the big bang F=ma, and equal inward force carried by "gravitons" (or whatever the spacetime fabric is) which allows you to get a mechanism for gravity which makes some easy calculations by correcting the Fatio/LeSage shadowing theory. I've done calculations on this basis which predict the strength of gravity and make various other predictions about cosmology which turned out to be correct (the main one being the prediction that the universe is not being slowed down by gravitation and that the Friedmann-Robertson-Walker metric predictions as of 1996 were wrong; it only I'd have known that I'd be ignored and a small cosmological constant would misleadingly be added to GR to misleadingly "fix" the problems, I'd also have been able to "predict" the size of the required cosmological constant two years ahead of its discovery).
This correction consists of applying it to "virtual" radiations such as gauge bosons like gravitons, not to the massive everyday particles that Fatio/LeSage assumed (which can't cause long-range fundamental forces: they would have the problems of scattering off one another and then ending up going into the shadows after an average of one mean free path, and killing the theory; they would also generate a lot of unobserved real heat radiation when scattering off one another and off masses in the vacuum).

However, despite virtual / exchange radiation (gauge bosons) being a real part of quantum field theory, the mathematical presumptions of most physicists is such that they don't allow simple calculations of the effects of this (predictions of the strength of gravity, etc.) to be taken seriously. This is not a matter of abandoning a theory, but of supplementing it with a simple mechanism which allows other predictions to me made and tested. The situation is now a lot less tolerant than it was even back in 1974, when the late Dr Lakatos wrote:

‘Scientists have thick skins. They do not abandon a theory merely because facts contradict it. They normally either invent some rescue hypothesis to explain what they then call a mere anomaly or, if they cannot explain the anomaly, they ignore it, and direct their attention to other problems. Note that scientists talk about anomalies, recalcitrant instances, not refutations. History of science, of course, is full of accounts of how crucial experiments allegedly killed theories. But such accounts are fabricated long after the theory had been abandoned. ... What really count are dramatic, unexpected, stunning predictions: a few of them are enough to tilt the balance; where theory lags behind the facts, we are dealing with miserable degenerating research programmes. Now, how do scientific revolutions come about? If we have two rival research programmes, and one is progressing while the other is degenerating, scientists tend to join the progressive programme. This is the rationale of scientific revolutions. ... Criticism is not a Popperian quick kill, by refutation. Important criticism is always constructive: there is no refutation without a better theory. Kuhn is wrong in thinking that scientific revolutions are sudden, irrational changes in vision. The history of science refutes both Popper and Kuhn: on close inspection both Popperian crucial experiments and Kuhnian revolutions turn out to be myths: what normally happens is that progressive research programmes replace degenerating ones.’ – Imre Lakatos, Science and Pseudo-Science, pages 96-102 of Godfrey Vesey (editor), Philosophy in the Open, Open University Press, Milton Keynes, 1974.

If he was writing today, maybe he would have to reverse a lot of that to account for the hype-type "success" of string theory ideas that fail to make definite (quantitative) checkable predictions, while alternatives are censored out completely.

No longer could Dr Lakatos claim that

"What really count are dramatic, unexpected, stunning predictions: a few of them are enough to tilt the balance; where theory lags behind the facts, we are dealing with miserable degenerating research programmes."

It's quite the opposite. The mainstream, dominated by string theorists like Jacques Distler and others at arXiv, can actually stop "silly" alternatives from going on to arXiv and being discussed.

What serious researcher is going to treat quantum field theory objectively and work on the simplest possible mechanisms for a spacetime continuum, when it will result in their censorship from arXiv, their inability to find any place in academia to study such ideas, and continuous hostility and ill-informed "ridicule" from physically ignorant string "theorists" who know a lot of very sophisticated maths and think that gives them the authority to act as "peer-reviewers" and censor stuff from journals that they refuse to first read?

1:03 PM  
Blogger nige said...

For an historically-based discussion of discontinuous versus continuous manifolds (i.e., quantum vacuum of QFT versus spacetime continuum of GR) see for example the Perimeter Institute PDF slides file:

http://www.perimeterinstitute.ca/pdf/files/975547d7-2d00-433a-b7e3-4a09145525ca.pdf

On page 43, this quotes a letter to Michele Besso from Albert Einstein in 1954, where Einstein writes:

"I consider it entirely possible that physics cannot be based upon the field concept, that is on continuous structures. Then nothing will remain of my whole castle in the air, including the theory of gravitation, but also nothing of the rest of contemporary physics."

Pages 44-46 quote 1954 letters from Einstein to David Bohm and H.S. Joachim which are similar to this. Page 47 then quotes Einstein's last words on the subject in 1954 (shortly before he died):

"One can give good reasons why reality cannot at all be represented by a continuous field. ... a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accordance with continuum theory ..."

1:40 PM  
Blogger L. Riofrio said...

For Kea: What video would you like? I will shortly be linking to the "this week in Space" reports.

For nige: Thanks, and I hop you keep at it. My experience is that good ideas can't be suppressed forever.

5:35 PM  
Blogger Kea said...

I was thinking of this one.

8:55 AM  
Blogger nige said...

Thanks, Louise.

That's an excellent U-tube video that Kea links to, by the way.

You are brilliant at delivering information clearly and concisely. It would be great if you could get a role as a science presenter on TV.

10:14 PM  

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