Time past T in Hubble's law v = HR = H(cT) is related to time t since the big bang by t + T = 1/H. => v= HcT = Hc[(1/H)-t] = c - (Hct) => a = dv/dt = d[c-(Hct)]/dt = -Hc, the outward acceleration. Force, F = ma. Newton's 3rd law gives a reaction force, inward directed gravitons. Since non-receding nearby masses don't cause this reaction force, they shield graviton exchange with more distant masses in that direction; an asymmetry which produces gravity.
Why didn't Einstein really write that, getting outward force and then inward force, and using the latter to calculate the strength of gravity? Perhaps he had a bad couple of weeks when his cosmological-constant drive static universe model fell apart in 1929.
posted by nige @ 1:53 PM
9 comments
Mathematical symbols in this blog: your computer’s browser needs access to standard character symbol sets to display Greek symbols for mathematical physics. If you don’t have the symbol character sets installed, the density symbol "r" (Rho) will appear as "r" and the "p" (Pi) symbol will as "p", causing confusion with the use of "r" for radius and "p" for momentum in formulae. This problem exists with Mozilla Firefox 3, but not with Microsoft Explorer which displays Greek symbols.
‘Dr Edward Teller remarked recently that the origin of the earth was somewhat like the explosion of the atomic bomb...’ – Dr Harold C. Urey, The Planets: Their Origin and Development, Yale University Press, New Haven, 1952, p. ix.
‘But compared with a supernova a hydrogen bomb is the merest trifle. For a supernova is equal in violence to about a million million million million hydrogen bombs all going off at the same time.’ – Sir Fred Hoyle (1915-2001), The Nature of the Universe, Pelican Books, London, 1963, p. 75.
‘In fact, physicists find plenty of interesting and novel physics in the environment of a nuclear explosion. Some of the physical phenomena are valuable objects of research, and promise to provide further understanding of nature.’ – Dr Harold L. Brode, The RAND Corporation, ‘Review of Nuclear Weapons Effects,’ Annual Review of Nuclear Science, Volume 18, 1968, pp. 153-202.
‘It seems that similarities do exist between the processes of formation of single particles from nuclear explosions and formation of the solar system from the debris of a [7*1026 megatons of TNT equivalent, type Ia] supernova explosion. We may be able to learn much more about the origin of the earth, by further investigating the process of radioactive fallout from the nuclear weapons tests.’ – Dr P. K. Kuroda, University of Arkansas, ‘Radioactive Fallout in Astronomical Settings: Plutonium-244 in the Early Environment of the Solar System,’ Radionuclides in the Environment (Dr E. C. Freiling, Symposium Chairman), Advances in Chemistry Series No. 93, American Chemical Society, Washington, D.C., 1970, pp. 83-96.
How would a 1055 megaton hydrogen bomb explosion differ from the big bang? Ignorant answers biased in favour of curved spacetime (ignoring quantum gravity!) abound, such as claims that explosions can’t take place in ‘outer space’ (disagreeing with the facts from nuclear space bursts by Russia and America in 1962, not to mention natural supernova explosions in space!) and that explosions produce sound waves in air by definition! There are indeed major differences in the nuclear reactions between the big bang and a nuclear bomb. But it is helpful to notice the solid physical fact that implosion systems suggest the mechanism of gravitation: in implosion, TNT is well-known to produce an inward force on a bomb core, but Newton's 3rd law says there is an equal and opposite reaction force outward. In fact, you can’t have a radially outward force without an inward reaction force! It’s the rocket principle. The rocket accelerates (with force F = ma) forward by virtue of the recoil from accelerating the exhaust gas (with force F = -ma) in the opposite direction! Nothing massive accelerates without an equal and opposite reaction force. Applying this fact to the cosmological acceleration of matter in the universe which was predicted accurately in 1996 and later observationally discovered in 1999 (by Perlmutter, et al.), we find an outward force F = ma and inward reaction force by the 3rd law. The inward force allows quantitative predictions, and is mediated by gravitons, predicting gravitation in a checkable way (unlike string theory, which is just a landscape of 10500 different perturbative theories and so can’t make any falsifiable predictions about gravity). So it seems as if nuclear explosions do indeed provide helpful analogies to natural features of the world, and the mainstream lambda-CDM model of cosmology - with its force-fitted unobserved ad hoc speculative ‘dark energy’ - ignores and sweeps under the rug major quantum gravity effects which increase the physical understanding of particle physics, particularly force unification and the relation of gravitation to the existing electroweak [SU(2) x U(1)] section of the Standard Model of fundamental forces.
A type Ia supernova explosion, always yielding 7*1026 megatons of TNT equivalent, results from the critical mass effect of the collapse of a white dwarf as soon as its mass exceeds 1.4 solar masses due to matter falling in from a companion star. The degenerate electron gas in the white dwarf is then no longer able to support the pressure from the weight of gas, which collapses, releasing enough energy as heat and pressure to cause the fusion of carbon and oxygen into heavy elements, creating massive amounts of radioactive nickel-56. Type IA supernovae occur roughly once every 400 years in the Milky Way galaxy. When the solar system formed 4,540 million years ago, a supernova occurred 100 light years away from the solar system, and the heavy radioactive debris expanded at 1,000 miles/second. On 4 July 1054, Chinese astronomers observed in the sky (without optical instruments) the bright supernova in the constellation Taurus which today is still visible as the Crab Nebula through telescopes. The Crab Nebula debris has a diameter now of 7 light years and is still expanding at 800 miles/second. The supernova shock wave triggers star formation; bright stars are observed in the Orion Halo, the 300 light year diameter remains of a supernova. Essentially all of the heavy elements including iron, silicon and calcium in the Earth are products from a supernova explosion.
Currently designing secure active server page (ASP) front ends for client SQL databases. In 1982 I began programming in basic, and at college learned Fortran while a physics undergraduate a decade later. Afterwards, I switched from mainstream physics and mathematical education to part-time programming student, while working in a series of jobs including four years in credit control. www.quantumfieldtheory.org http://glasstone.blogspot.co.uk/2015/07/capabilities-of-nuclear-weapons.html/ http://www.math.columbia.edu/~woit/wordpress/?p=273#comment-5322. http://www.math.columbia.edu/~woit/wordpress/?p=353&cpage=1#comment-8728. http://www.math.columbia.edu/~woit/wordpress/?p=215#comment-4082.
9 Comments:
http://christinedantas.blogspot.com/2006/03/dark-energy-mystery-of-millennium.html
Anonymous said...
LeSage's gravity idea of 1748, put into the big bang context, solves this. Treat the big bang as a real explosion, and general relativity (gravitation and the contraction) is a physical result of the dynamics of the spacetime fabric.
In the Oct 96 issue of Electronics World, this model predicted there would be no gravitational retardation of the motion of distant supernovae.
It was confirmed by Perlmutter's results in 1998. Nature, CQG, PRL, etc., wouldn't publish the prediction before or the confirmation after. They won't review it, just claiming all alternatives to ST are crackpot.
Recently, Edwin Budding, a Research Fellow of the Carter National Observatory in New Zealand, and currently at Canakkale Onsekin Mart University in Turkey, sent me his paper on inertia and gravitational mechanism. It is 16 pages in length and the basic physical ideas for gravity and inertia are somewhat similar to http://feynman137.tripod.com/, although the mathematical treatment is interestingly different.
Nobody can post this to arXiv because their official policy for endorsers forbids new ideas:
'We don’t expect you to read the paper in detail, or verify that the work is correct, but you should check that the paper is appropriate for the subject area. You should not endorse the author … if the work is entirely disconnected with current [string theory] work in the area.’ - http://arxiv.org/help/endorsement
3/07/2006 10:59:59 AM
Anonymous said...
Dark energy, by the way, is the false epicycle you must put into the normal application of general relativity to cosmology.
The usual application of GR to cosmology implicitly assumes no mechanism for gravity is associated with the big bang.
Hence the usual GR application allows the most distant matter to be slowed down by gravitation.
You then have to add dark energy to make this fit Perlmutter's observations of supernovae redshift.
If you instead treat the big bang as a simple explosion, you get GR out of it in such a form that there is no predicted slowing down due to gravity on very distant matter. Hence, you have no need to "fix the error" using dark energy (which is adding an epicycle to a false theory to make it work).
Nigel said...
Dear Christine,
The material in a "fireball" from a detonation in a vacuum does obey the Hubble law, the velocity increasing steadily toward the speed of light.
We already know from the +/- 3 mK cosine variation in the 2.7 K microwave background that there is a motion of the galaxy at 400 km/s toward andromeda. This is probably largely due to the gravity of andromeda, but it does indicate a kind of absolute motion.
Taking the 400 km/s as an order-of-magnitude figure of the motion of matter in the milky way in the 1.5 x 10^10 yr since the big bang, that indicates we've moved 0.1% of the radius of the universe since the big bang.
Hence, we are near enough in the middle. You've know the regular "expanding cake" model with everything receding from everything else, but the problem is that nobody has ever looked at the universe from different places, so they really don't know, they're just speculating.
Spacetime is still created in the instant of a real explosion, so you can treat the big bang as a real explosion of 10^55 megatons. It predicts gravity within 2%
Thanks
Nigel
http://christinedantas.blogspot.com/2006/03/dark-energy-mystery-of-millennium.html
Nigel said...
Dear Christine,
I have done a course in classical cosmology, and the book you link to looks the sort of thing I know. But I'll obtain it. Briefly...
General relativity can be obtained from quantum field theory in such a way that the dark energy vanishes, and the correct density of the universe is proved to be exactly 0.5e^3 ~ 10 times lower than the standard critical density.
The Earth is contracted by 1.5 mm due to the contraction term in general relativity, which is given mathematically in the usual treatment by energy conservation of the gravitation field. But you can physically calculate the general relativity contraction from the FitzGerald contraction of length by the factor (1 – v2/c2)1/2 = [1 – 2GM/(xc2)]1/2. I obtain this starting with the Newtonian approximate empirical formula, which gives the square of escape velocity as v2 = 2GM/x, and the logical fact that the energy of mass in a gravitational field at radius x from the centre of mass is equivalent to the energy of an object falling there from an infinite distance, which by symmetry is equal to the energy of a mass travelling with escape velocity v. By Einstein’s principle of equivalence between inertial and gravitational mass, this gravitational acceleration field produces an identical effect to ordinary motion. Therefore, we can place the square of escape velocity (v2 = 2GM/x) into the Fitzgerald-Lorentz contraction (1 – v2/c2)1/2 which gives the gravitational contraction [1 – 2GM/(xc2)]1/2 ~ 1 – GM/(xc2) using the first two terms in the binomial expansion.
This is a physical mechanism for the essential innovation of general relativity, the contraction term in the Einstein-Hilbert field equation. Because the contraction due to motion is physically due to head-on pressure (like wind pressure on your windscreen at high speeds) from the spacetime fabric, it occurs only in the direction of motion, say the x direction, leaving the size of the mass in directions x and z unaffected.
For gravity, the mechanism of spacetime fabric pressure causes contraction in the radial directions, outward from the centre of mass. This means the amount of contraction is as Feynman calculated about (1/3)GM/c2 = 1.5 mm for the Earth.
If you look at Feynman's account of this, which is one of the most physically real, he gets his equation confused in words: Professor Feynman makes a confused mess of it in his relevant volume of Lectures, c42 p6, where he gives his equation 42.3 correctly for excess radius being equal to predicted radius minus measured radius, but then on the same page in the text says ‘… actual radius exceeded the predicted radius …’ Talking about ‘curvature’ when dealing with radii is not helpful and probably caused the confusion.
Lorentz-FitzGerald empirical theory can be summarised as "physical contraction due to ether pressure + Michelson Morley result => variable speed of light depending on motion".
Special relativity is : "Michelson Morley result => invariant speed of light. Invariant speed of light + laws of nature independent of inertial motion => contraction".
So special relativity is ad hoc and is completely incompatible with FitzGerald's prior analysis. Since experimental data only verifies the resulting equations, Ockham's razor tells us to accept FitzGerald's simple analysis of the facts, and to neglect the speculation of special relativity. Furthermore, even Einstein agrees with this:
‘The special theory of relativity … does not extend to non-uniform motion … The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion. Along this road we arrive at an extension of the postulate of relativity… The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, that is, are co-variant with respect to any substitutions whatever (generally co-variant). …’ – Albert Einstein, ‘The Foundation of the General Theory of Relativity’, Annalen der Physik, v49, 1916.
The dynamics of the QFT mechanism do predict general relativity and gravity constant G within 2%. If there is an error, it seems to be in the mainstream model.
Best wishes,
Nigel
3/08/2006 11:34:49 AM
http://christinedantas.blogspot.com/2006/03/dark-energy-mystery-of-millennium.html
Nigel said...
Dear Christine:
General relativity, based on general covariance, is the fact. I don't want an alternative to the field equation, just a way to get it from QFT facts which sorts out the observational facts from astronomy.
Einstein said:
‘The special theory of relativity … does not extend to non-uniform motion … The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion. Along this road we arrive at an extension of the postulate of relativity… The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, that is, are co-variant with respect to any substitutions whatever (generally co-variant). …’ – Albert Einstein, ‘The Foundation of the General Theory of Relativity’, Annalen der Physik, v49, 1916.
Thank you,
Nigel
3/09/2006 06:11:55 AM
http://christinedantas.blogspot.com/2006/03/announcement-to-contributors.html
Anonymous said...
Dear Christine,
I respect your guidelines.
Presumably you are well aware of this from the lectures and the discussion of them you give.
You need to clarify "relativity" when you say that the correct unified theory must be identical to the existing form of special/general relativity.
For one thing, general relativity can be obtained in more than one way (of course the basic field equation was obtained by different routes by both Einstein and Hilbert), and a better understanding of how general relativity should be obtained theoretically using quantum field theory will probably result from quantum gravity.
Lee Smolin has lectured on how to go from a spin foam vacuum representation of path integrals in quantum field theory, to obtain the field equation of general relativity, without a metric.
This problem, to unify the quantum field theory with general relativity, is quantum gravity.
It is only likely to be interesting if it results in some prediction. To do so it may well alter the form of existing quantum field theory or of general relativity slightly.
What is important is that the right approach is consistent not with previous versions of theories, but is instead consistent with nature.
The debate in physics over modifications to the cosmological constant and other generally controversial aspects of "relativity" may be settled by the correct proof of the field equation from some kind of work along the lines Smolin suggests.
I do hope you will not call any correct derivation of the field equation of general relativity an "alternative" to be dismissed.
General relativity can be viewed in several ways, and what matters ideally is how much each predicts and whether it is based on empirical facts or speculations (fitting cosmological constant to observations, for instance).
If you read John Baez's crackpot list, it would dismiss string theory for being based on abject speculation, and for not making any useful or unique definite predictions.
Baez does not, however, automatically dismiss all new ideas. Because cosmology is based on the existing form of general relativity, if you say that existing general relativity is perfect and beyond improvement, then you are assuming that the unification of gravity and the standard model can only be achieved by some change in quantum field theory to accommodate existing general relativity.
There is no evidence that this is the case.
Best wishes
3/09/2006 06:44:51 AM
http://christinedantas.blogspot.com/2006/03/announcement-to-contributors.html
Anonymous said...
Dear Christine,
Thank you very much for this clarification:
"What I really do not like to be discussing here is things like "Einstein was wrong", etc. Special and General relativity are substantial and robust theories in their domain of validity."
The way to do this would be to keep all discussion constructive, and to emphasise that general relativity is more complete than special relativity. The special theory is a simplification of the more complex facts, and only gives the right answers for cases of uniform motion. (General relativity is not merely special relativity plus gravity, which string theorists falsely claim.)
Best wishes
3/09/2006 09:12:23 AM
EINSTEIN'S PRINCIPLE OF VARIABILITY OF THE SPEED OF LIGHT
Einstein's 1911 equation c'=c(1+V/c^2), where c' is the speed of light as measured by an observer, c=300000km/s is the initial speed of light relative to the light source and V is the gravitational potential relative to the point where light is emitted, proves the validity of the following principle:
Since the probability that V=0 is virtually zero, light NEVER travels in space with speed c=300000km/s; its speed is either higher or lower than that value (V>0 or V<0).
Pentcho Valev
pvalev@yahoo.com
EDUCATION IN EINSTEIN'S WORLD
http://www.sussex.ac.uk/Units/publications/sabroad2007/courses/Physics%20and%20astronomy/12930
Courses at Sussex
Physics and astronomy
Relativity
Level 1
6 credits in summer
Teaching method: Lecture, Workshop
Assessment modes: Unseen Examination, Coursework
Topics include: historical perspective. Inertial frames and transformations. Newton’s laws in inertial frames. MICHELSON-MORLEY EXPERIMENT - OBSERVED CONSTANCY OF SPEED OF LIGHT. Einstein’s assumptions. Lorentz-Einstein transformations; Minkowski diagrams; Lorentz contraction; time dilation. Transformation of velocities - stellar aberration. Variation of mass, mass-energy equivalence. Lorentz transformations for momentum and energy.
http://www.hawking.org.uk/lectures/dice.html
Stephen Hawking: "But a famous experiment, carried out by two Americans, Michelson and Morley in 1887, showed that light always travelled at a speed of one hundred and eighty six thousand miles a second, no matter where it came from."
Elsewhere Einstein's educators teach:
http://en.wikipedia.org/wiki/Speed_of_light :
"It should be noted that the Michelson-Morley experiment said little about the speed of light relative to the light’s source and observer’s velocity, as both the source and observer were travelling at the same velocity together in space. Indeed, if light is understood to be due to quantum photon “bullets”, then the Michelson-Morley result is exactly as expected."
Amazingly, this type of education has proved extremely efficient - no relativist would see anything disturbing when comparing the three teachings.
Pentcho Valev
pvalev@yahoo.com
Hi Pentcho Valev,
I don't quite see the point you are making, but your earlier comment quoting Einstein's 1911 analysis of light is definitely suspect. Firstly, Einstein's claim is that the frequency of light varies (Doppler shift). Since there is no mechanism in relativity for anything (it's purely a combination of semi-empirical "principles" with rigorous mathematical reasoning), there isn't really much physics in it, so there is little that can go wrong. Secondly, Einstein's 1911 result is superseded by his 1915 field equation (see my latest post) which introduces various modifications for light. For example, the deflection of light by gravity in Einsteins's 1915 correct analysis is twice that of his 1911 Newtonian theory, and the 1915 paper is correct theoretically and experimentally in this regard.
No space in the universe is 100% vacuum, hence no light in the universe goes strictly at c.
In addition, if the contraction of matter in the direction of motion is the full explanation for the Michelson-Morley experiment showing no interference fringes, then the velocity of light may vary with the motion of the receiver.
This is because the contraction was invented by FitzGerald (1889) and Lorentz (1893) to save absolute motion. So the Michelson-Morley result can be taken two ways:
(1) No absolute motion (explanation by relativity)
(2) Absolute motion, but this absolute motion wasn't in evidence because the Michelson-Morley instrument always contracted in the direction of motion just enough (by the ratio of (1-v^2/c^2)^1/2) that the light beam travelling along the path of motion has a shorter distance to go (unlike the light going perpendicular to the direction of motion), and this offset the predicted interference fringes, giving the null result. This is the FitzGerald-Lorentz interpretation, which is foolishly dismissed by people who claim that the length of the arms should make a difference (this doesn't because the instrument is just measuring interference fringes and hence relative velocities, not measuring velocities; in any case, the arms of the M-M instrument were never the same anyway because the instrument was massive and wasn't - and could not have been - built to the tolerance of having each perpendicular arm exactly the same length to within a fraction of the wavelength of light, and temperature gradients in the lab would make relatively massive differences in arm lengths due to contraction and expansion effects anyway).
‘According to the general theory of relativity space without ether is unthinkable.’ – Albert Einstein, Sidelights on Relativity, Dover, New York, 1952, p23.
‘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), Space Time and Gravitation: An Outline of the General Relativity Theory, Cambridge University Press, Cambridge, 1921, pp. 20, 152.
What has not been tested is the effect of the motion of the emitter of light on the speed of light. The Michelson-Morley experiment merely tests the effect of moving the receiver.
See http://en.wikipedia.org/wiki/Talk:Herbert_Dingle#Disgraceful_error_on_article_page for more about my views and http://mrigmaiden.blogspot.com/2006/09/update-to-riofrio-equations-post.html for an idea to experimentally check the speed of the extremely redshifted cosmic background radiation
Thanks,
Nigel
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