Professor Johnson’s insistence on calculations to back up ideas

I was particularly interested in Professor Clifford Johnson’s new post at Asymptotia, ‘On Good Ideas’:

‘What makes a field of physical science like physics work is computations – all of that business with calculations (including checking that your computations conventions are internally consistent) is vital to the field.

‘Frankly, “Good Ideas” are a dime a dozen. Anyone in my field ought to be able to think of at least six of them before breakfast. What makes a good idea go from a good idea to an idea that actually is useful and relevant is those several hours of muddling away with computations and calculations, testing out the idea and seeing how it fits into the scheme of things, and how it fits into the larger tapestry which is all the calculations that have ever been done in physics for generations. You can’t just make up stuff out of whole cloth, you see. Sitting around dreaming or talking is important to do too, but it is all utterly worthless (as science) without calculation. This is vital to what makes what I do science, at the end of the day. Finally, if I were working on an aspect of the subject that was directly related to a physical phenomenon “out there” in the world (this project is not so directly related, as far as I know, it is more about what’s going on “under the hood” of string theory), then the value of the good idea and the computation is also tested by comparison to a well-designed experiment, which has its own sequence of stages of ideas and computations (and worrying about conventions) to go through to bring it to fruition.’

I like this very much. Partly because it encapsulates my understanding of how physics works, but also because it explains a great deal about why string theory has been studied so intensely.

It’s of course a fact that string theory is full of calculations which is why it’s been allowed in physics departments. That’s actually sometimes a problem, because string theory at present requires so many calculations (due to the fact that it has a landscape of 10^500 or so different metastable vacua, each due to a separate set of stabilized moduli of shapes and sizes of the compactified 6 dimensions assumed to exist in invisibly small Calabi-Yau manifold) that it’s too difficult to evaluate it to make falsifiable predictions at present, even when the anthropic principle is used to try to pick out a vacuum that resembles the observed Standard Model of particle physics.

Ideally (for ready acceptance of the new idea) the new calculations should contain previous calculations as either a subset or as an asymptotic approximation for a particular limiting case. E.g., you might want a gravitational gauge theory with a spin-2 propagator so that it is consistent with calculations that quantum gravity should be mediated by spin-2 gravitons to achieve attraction. There’s a nice calculation proving this in Zee’s book. But when you examine his proof closely, he just considers two masses exchanging gravitons with one another, which ignores two important aspects of reality:

1. there are more than two masses in the universe which are exchanging gravitons and in fact the majority of the mass is in the surrounding universe; and

2. when you want a law for the physics of how gravitons are imparting force, you find that only receding masses forcefully exchange gravitons with you, not nearby masses. Take Hubble’s recession law which is empirical: v = HR. Differentiate: a = d(HR)/dt = (H*dR/dt)+(R*dH/dt) = Hv = HHR. This predicts the Perlmutter’s observed acceleration of the universe. It also gives receding matter outward force by Newton’s second law, and gives a law for gravitons: Newton’s third law gives an equal inward-directed force, which by elimination of the possibilities known in the Standard Model and quantum gravity, must be mediated by gravitons. Nearby masses which aren’t receding have outward acceleration of zero and so produce zero inward graviton force towards you for their graviton-interaction cross-sectional area. This produces an asymmetry, so you get pushed towards non-receding masses while being pushed away from highly redshifted masses. You can then do calculations to predict the strength of gravitation.

This mechanism proves that you don’t need a spin-2 propagator to be the gravitons; instead you can have a very simple spin-1 graviton to do the job of both ‘dark energy’ (the outward acceleration of the universe) and gravitational ‘attraction’!

Fig. 3

This is the key diagram working out, without a fancy path integral formulation, the net sum of spin-1 graviton contributions: the ‘shield’ area is the cross-section for spin-1 graviton back-scatter from a fundamental particle such as an electron (or rather the effective cross-sectional area for graviton interactions, because the electron’s mass or gravitational charge according to the Standard Model comes from a Higgs-type bosonic quantum field surrounding the core of the electron; the Higgs field interacts with both the electron core and with gravitons, so it acts as a man-in-the-middle and mediates gravitational force from gravitons to the electron).  For evidence that this effective cross-section for gauge boson back scatter is (exchange of gauge bosons between gravitational charges such as masses) is the event horizon cross-sectional area of a black hole with the mass of the electron or other fundamental particle being accelerated by gravity, see this post and its links; for evidence that the black hole event horizon cross-sectional area is also that for electromagnetic interactions see the calculations summarised in this post. (There is other evidence as well published in other posts. I’ll try to organize everything better when time permits.)

At low energies, i.e., for propagation long distances in the vacuum, gravitons are exchanged between masses in a simple way, travelling directly without interferences caused complex loop phenomena which become important at high energy and small distance scales. For this reason we can use geometry to sum all the possible histories, just as Feynman did in his book QED: we simply don’t need to use calculus for the path integral for quantum gravitation at low energy, because we represent the physics of the exchange radiation by a simple geometric mechanism like adding up Feynman’s arrows to work out the summation of individual gauge boson interactions. The path integral is essential where you get loop phenomena described by successive terms in the perturbative expansion to a path integral, these terms being represented by Feynman diagrams containing looped (pair production type) interaction histories.

1. Outward force of receding matter (recession velocity v = HR where H is Hubble constant and R is apparent distance) is

F = ma

= m.dv/dt

= m.d(HR)/dt

= m[H.dR/dt + R.dH/dt]

= m[Hv + 0]

= mH(HR)

= mRH2.

This is on the order of F = 7 * 1043 Newtons, but there is a correction to be applied for the apparent increase in density as we look back to earlier times (great distances in spacetime), and for relativistic mass increase of receding matter.  But for simplicity, to see how the maths works, ignore the correction:

F = ma = [(4/3)πR3r].[dv/dt] = [(4/3)πR3r].[H2R] = R4rH2/3. 

2. Inward force (which must be carried by gravitons or the spacetime fabric, according to the possibilities from what is available in the empirically defensible Standard Model and quantum gravity frameworks), is equal to the outward force (action and reaction are equal and opposite – a simple empirical law usually called Newton’s third law).  However, there is a redshift of gravitons approaching us from relativistically receding, extremely redshifted masses, which reduces the effective graviton energy when received.  (This redshift effect offsets the infinity-approaching outward force effects of relativistic mass increase and the increasing density of the earlier universe at ever greater distances.)

3. Gravity force,


(total inward-directed graviton force, F = ma = m.dv/dt = mRH2).(fraction of total force which is uncancelled, due to the asymmetry in inward graviton force which imposed by the lack of graviton force from black hole event horizon cross-sectional area π(2GM/c2)2 for the non-receding nearby mass labelled ‘shield’),

= (total inward-directed graviton force).(fraction of total inward force which is uncancelled to to the asymmetry imposed by the shield, e.g. the greyed cone area)

= (total inward-directed graviton force).(area of end of cone, as labelled x)/(total spherical surface area out to radius of R = ct where t is age of universe, t = 1/H instead of the old Friedmann-Robertson-Walker prediction for a critical density universe with zero cosmological constant of t = (2/3)/H, since there is no observable long-range gravitational deceleration on expansion rates, e.g., at long ranges there is no curvature of spacetime because the acceleration of the universe offsets gravitation)

= (total inward-directed graviton force).(area of end of cone, as labelled x)/(4πR2)

= ((ma)*π(2GM/c2)2).(x)/(4πR2)

=  ((ma)*π(2GM/c2)2).((shield area).(R/r )2)/(4πR2)

=  ((ma)*π(2GM/c2)2).(π(2GM/c2)2.(R/r )2)/(4πR2)

= (4πR4rH2/3).(π(2GM/c2)2R2/r2)/(4πR2)

= (4/3)πR4rH2G2M2/(c4r2)

We can simplify this using the Hubble law because at great distances/early times (where the density of the universe is highest) it is a good approximation to put HR = c, which gives R/c = 1/H, so:

F(gravity) = (4/3)πrG2M2/(H2r2)

Notice the inverse square law, 1/r 2. There are several consequences from this beyond the obvious ability to uniquely make theoretically justifiable quantitative calculations of the strength of gravity when compared to Newton’s semi-empirical law of gravity (which was deduced from Kepler’s laws of planetary motion and Galileo’s law of terrestial gravitational acceleration), e.g. the force of gravity for quantum phenomena between fundamental particles is proportional not to M1M2 but instead to M2suggesting quantization of masses as to be compared to a similar result in QED where the electromagnetic inverse square force is proportional to the the square of the unit electric charge, not to the product of two different charges (i.e., the quantization of fundamental charges).

It’s tempting for people to dismiss new calculations without checking them, just because they are inconsistent with previous calculations such as those allegedly proving the need for spin-2 gravitons (maybe combined with the belief that “if the new idea is right, somebody else would have done it before”; which is of course a brilliant way to stop all new developments in all areas by everybody …).

However, I’m getting way off the topic. Which was that calculations are vital in physics, because they are something that can be checked for consistency with nature.  In string theory, so far there is no experimental possible, so all of the checks done are really concerned with internal consistency, and consistency with speculations of one kind or another.  String theorist Professor Michio Kaku summarises the spiritual enthusiasm and hopeful religious basis for the string theory belief system as follows in an interview with the ‘Spirituality’ section of The Times of India, 16 July 2008, quoted in a comment by someone on the Not Even Wrong weblog (notice that Michio honestly mentions ‘… when we get to know … string theory…’, which is an admission that it’s not known because of the landscape problem of 10^500 alternative versions with different quantitative predictions; at present it’s not a scientific theory but rather 10^500):

‘… String theory can be applied to the domain where relativity fails, such as the centre of a black hole, or the instant of the Big Bang. … The melodies on these strings can explain chemistry. The universe is a symphony of strings. The “mind of God” that Einstein wrote about can be explained as cosmic music resonating through hyperspace. … String theory predicts that the next set of vibrations of the string should be invisible, which can naturally explain dark matter. … when we get to know the “DNA” of the universe, i.e. string theory, then new physical applications will be discovered. Physics will follow biology, moving from the age of discovery to the age of mastery.’

As with the 200+ mechanical aether theories of force fields existing the 19th century (this statistic comes from Eddington’s 1920 book Space Time and Gravitation), string theory at best is just a model for unobservables. Worse, it comes in 10^500 quantitatively different versions, worse than the 200 or so aethers of the 19th century. The problems with theorising about the physics at the instant of the big bang and the physics in the middle of a black hole is that you can’t actually test it. Similar problems exist when explaining dark matter because your theory contains invisible particles whose masses you can’t predict beyond saying they’re beyond existing observations (religions similarly have normally invisible angels and devils, so you could equally use religions to ‘explain dark matter’; it’s not a quantitative prediction in string theory so it’s not really a scientific explanation, just a belief system). Unification at the Planck scale and spin-2 gravitons are both speculative errors.

Once you remove all these the errors from string theory, you are left with something that is no more impressive than aether: it claims to be a model of reality and explain everything, but you don’t get any real use from it for predicting experimental results because there are so many versions it’s just too vague to be a science.It doesn’t connect well with anything in the real world at all. The idea that at least it tells us what particle cores are physically (vibrating loops of extradimensional ‘string’) doesn’t really strike me as being science. People decide which version of aether to use by artistic criteria like beauty or fitting the theory to observations and arguing that if the aether was different from this or that version we wouldn’t exist to observe it’s consequences (the anthropic selection principle), instead of using factual scientific criteria: there are no factual successes of aether to evaluate. So it falls into the category of a speculative belief system, not a piece of science.

By Mach’s principle of economy, speculative belief systems are best left out of science until they can be turned into observables, useful predictions, or something that is checkable. Science is not divine revelation about the structure of matter and the universe, instead it’s about experiments and related fact-based theorizing which predicts things that can be checked.

3 thoughts on “Professor Johnson’s insistence on calculations to back up ideas

  1. Very interesting. I discovered the graviton particle. Like myself, you enjoy the use of Pi.
    I couldn’t find a solid explanation for Pi, so I worked on it for 27 years. What I found is circles don’t exist. Using Tomahawk Cruise Missile grinding equipment I made the most perfect round object ever created by man. But upon very close examination, I found that it was made of atoms & the spaces between the atoms were straight lines. What I created was a polygon. They are all polygons. Circles don’t exist. Pi describes a polygon. Each digit is a new number of sides.

    1. Very interesting, Al, but those “straight lines” between the atoms were created only as the shortest distances between two points. They could just as easily been arcs with a degree measurement variant upon the number of atoms composing the edge of a circle. In conclusion, neither circles nor polygons exist but in the minds of man. And neither do gravitons. Yet.

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