Dr Cormac O’Raifeartaigh has kindly illustrated in detail the kind of confusion that exists in the mainstream over the Hubble recession law, velocity v = HR where H is Hubble’s constant and R is radial distance. (For evidence that this is a real expansion and not ‘tired light’ redshift, see Ned Wright’s article ‘Errors in Tired Light Cosmology’).
In the older mainstream model of cosmology, i.e. the Friedmann-Leimatre-Robertson-Walker metric of general relativity, the effective radius or scale factor of the universe increases as t2/3 where the 2/3 power is due to gravitation slowing down the expansion rate of the universe. However, this prediction was discredited after 1998 when it was observationally discovered, by Perlmutter et al., that supernovae at half the age of the universe (7,000 million light years) were not slowing down as predicted by the Friedmann-Leimatre-Robertson-Walker metric. In order to deal with this discovery, a small lambda (cosmological constant or universal repulsion between masses powered by ‘dark energy’), of sufficient value to negate the previously-predicted long range cosmological slowing down effect of gravity, was introduced. This was a very much smaller cosmological constant than Einstein’s in 1917 when he was attempting to keep the universe static, and in agreement with all of the observations at that time. Rather than cancelling out the expansion of the universe as Einstein had tried to do in 1917 with his massive cosmological constant, the new small cosmological constant introduced after 1998 merely cancelled out the gravitational deceleration of the universe predicted for large distances. This made it replicate (as a purely ad hoc fit, since there was no theoretical prediction of the value of lambda from the mainstream theory) observed expansion rates, the observed scale factor being directly proportional to time t since the big bang. Since the horizon radius of the universe is ct, it is identical to the scale factor in this case. Things are very simple:
The Hubble expansion empirical law is
v = HR
On the right hand side, H = 1/t where t is the age of the (non-decelerating) universe, and R = cT where T is the time past corresponding to observed distance R (light takes time to travel distance R, so you are seeing events there as they occurred at that time in the past). Hence:
v = HR = [1/t][cT ] = cT/t.
Now, since Hubble discovered that v/R = H = constant in spacetime (i.e., looking to increasing distances, you find that v is directly proportional to R), it follows that since H = 1/t, both H and t are constants in spacetime! This fixed value of t proves that t in this equation is the time after the big bang in the frame of reference of the observer taking the picture of the sky, and not the time after the big bang for the different individual stars being observed in the sky. Hence, the variables in the equation v = cT/t are v and T, not t.
Hence we differentiate with respect to time T, giving:
acceleration a = dv/dT = d(cT/t)/dT = c/t = Hc = 6×10-10 ms-2.
This was the prediction of the acceleration of the universe which I made in 1996. You can rewrite T in terms of time since big bang if you want, and then have that as the variable. However, the predicted numerical value is the same, apart from a minus sign (because time past increases while time after the big bang decreases when looking to larger distances: see Fig. 1 below).
Fig. 1: Proof that the 6×10-10 ms-2 cosmological acceleration of the universe is implicitly present in the normal v = HR Hubble expansion law, using ‘time since big bang’ (instead of ‘time past’ which was used in the blog post text for simplicity; the only difference in the result being a minus sign as explained earlier).
Copy of a comment to: http://dorigo.wordpress.com/2008/08/09/problems-with-authority
‘I have no problems with authority. Meaning that I do not feel an inferiority complex, or a defensive instinct, when I deal with people who have titles or power which can affect their interaction with me. I however have to acknowledge that it is a very common problem for many people, even intelligent, instructed, realized individuals.’ – Tommaso Dorigo
‘Problems come with this definite consensus in a number of ways, for instance when [it]:
‘1) seems to leak out and apply to decisions out of its initial scope.
‘2) becomes fixed, neglecting new knowledge
‘3) is altered via opinion instead of knowledge.’ – Alejandro Rivero, comment #4
‘Problems arise when authority is misused.’ – Tony Smith, comment #10
I like the following quotation about authority from Feynman:
‘It does not make any difference how beautiful your guess is. It does not make any difference how smart you are, who made the guess, or what his name is – if it disagrees with experiment it is wrong.’ – Feynman, http://www.vigyanprasar.gov.in/scientists/RichardPFeynman/RichardPFeynman.htm
In politics and in the media, beauty, intelligence, star-quality, and fame are more important than facts. String theory is currently being hyped by authority criteria (beautiful, intelligent, star-quality and famous). Here’s a personal example of how authority deals with unwanted facts:
Sent: 02/01/03 17:47
Subject: Your_manuscript LZ8276 Cook …
Physical Review Letters does not, in general, publish papers on alternatives to currently accepted theories. Yours sincerely, Stanley G. Brown, Editor, Physical Review Letters
It’s a falsehood that there is a ‘currently accepted theory’ predicting gravity, because although Edward Witten claimed ‘String theory has the remarkable property of predicting gravity’ (April 1996 issue of Physics Today), this claim was repudiated by Roger Penrose on page 896 of his book The Road to Reality: ‘in addition to the dimensionality issue, the string theory approach is (so far, in almost all respects) restricted to being merely a perturbation theory’. String theory does not predict anything falsifiable about gravity. So this is a good example of how authority is abused.
When I challenged it, editor Stanley just got his associate editor to email me a message ignoring my point completely, claiming falsely that I was complaining, and stating that he supported the editor’s decision (I was asking for the mainstream theory prediction that my theory is allegedly merely an alternative to). At IoP’s Classical and Quantum Gravity, the editor tried to be more reasonable but sent my paper for ‘peer-review’ by a string theorist (not a ‘peer’!), who came back saying that the paper should not be published since it was not based on string theory.
There is no inferiority complex required in order to have a problem with authority. All you have to do to be falsely attacked by an authority, is to challenge that authority using empirical facts which the authority can’t find a rational basis to reject. If you look at the example of the USSR, e.g. Trotsky’s The Revolution Betrayed (Trotsky was of course famously murdered with an ice-axe in Mexico on Stalin’s orders), you see the problem is not with the dissenter, but with the authority which can’t find a rational way to respond. Doubtless Stalin thought he was doing what was best…
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‘Here at Padua is the principal professor of philosophy whom I have repeatedly and urgently requested to look at the moon and planets through my glass which he pertinaciously refuses to do.’
– Letter from Galileo to Kepler, 1610.
‘In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use.’
– Galileo Galilei, 1632.
‘There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors.’
– J. Robert Oppenheimer, quoted in Life, October 10, 1949.
But Oppenheimer was a terrible censor! See Freeman Dyson’s video account of Oppenheimer’s horrendous attacks on Feynman’s path integral work on QED in 1948:
http://video.google.co.uk/videoplay?docid=-77014189453344068&q=Freeman+Dyson+Feynman
“… the first seminar was a complete disaster because I tried to talk about what Feynman had been doing, and Oppenheimer interrupted every sentence and told me how it ought to have been said, and how if I understood the thing right it wouldn’t have sounded like that. … we couldn’t tell him to shut up. So in fact, there was very little communication at all. … I always felt Oppenheimer was a bigoted old fool. … Hans Bethe somehow heard about this and he talked with Oppenheimer on the telephone, I think. …
“I think that he had telephoned Oppy and said ‘You really ought to listen to Dyson, you know, he has something to say and you should listen’. And so then Bethe himself came down to the next seminar which I was giving and Oppenheimer continued to interrupt but Bethe then came to my help and, actually, he was able to tell Oppenheimer to shut up, I mean, which only he could do. …
“So the third seminar he started to listen and then, I actually gave five altogether, and so the fourth and fifth were fine, and by that time he really got interested. He began to understand that there was something worth listening to. And then, at some point – I don’t remember exactly at which point – he put a little note in my mail box saying, ‘nolo contendere’.”
Tony Smith points out at http://www.math.columbia.edu/~woit/wordpress/?p=189#comment-3222 that Oppenheimer was later a dictatorial tyrant to David Bohm:
“Einstein was … interested in having Bohm work as his assistant at the Institute for Advanced Study … Oppenheimer, however, overruled Einstein on the grounds that Bohm’s appointment would embarrass him [Oppenheimer] as director of the institute. … Max Dresden … read Bohm’s papers. He had assumed that there was an error in its arguments, but errors proved difficult to detect. … Dresden visited Oppenheimer … Oppenheimer replied … “We consider it juvenile deviationism …” … no one had actually read the paper … “We don’t waste our time.” … Oppenheimer proposed that Dresden present Bohm’s work in a seminar to the Princeton Institute, which Dresden did. … Reactions … were based less on scientific grounds than on accusations that Bohm was a fellow traveler, a Trotskyite, and a traitor. … the overall reaction was that the scientific community should “pay no attention to Bohm’s work.” … Oppenheimer went so far as to suggest that “if we cannot disprove Bohm, then we must agree to ignore him.” …”. (Bohm biography Infinite Potential, by F. David Peat (Addison-Wesley 1997), pages 101, 104, and 133.)
Tony Smith at the page http://www.tony5m17h.net/goodnewsbadnews.html#badnews additionally quotes Feynman on the problem of the false ‘authority’ of ‘critics’ who dismissed (for bogus reasons) his path integral formulation of QED. These authority figures were not just Oppenheimer, but included other expert physicists such as Teller, Dirac and Bohr at the 1948 Pocono conference:
“… take the exclusion principle … it turns out that you don’t have to pay much attention to that in the intermediate states in the perturbation theory. I had discovered from empirical rules that if you don’t pay attention to it, you get the right answers anyway …. Teller said: “… It is fundamentally wrong that you don’t have to take the exclusion principle into account.” …
“… Dirac asked “Is it unitary?” … Dirac had proved … that in quantum mechanics, since you progress only forward in time, you have to have a unitary operator. But there is no unitary way of dealing with a single electron. Dirac could not think of going forwards and backwards … in time …
” … Bohr … said: “… one could not talk about the trajectory of an electron in the atom, because it was something not observable.” … Bohr thought that I didn’t know the uncertainty principle …
“… it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further.
“I gave up, I simply gave up …”.
– The Beat of a Different Drum: The Life and Science of Richard Feynman, by Jagdish Mehra (Oxford 1994) (pp. 245-248).
It was just as well that after Feynman had given up, Dyson and Bethe managed to convince Oppenheimer to take it seriously. I think this kind of story about authority problems in physics should be widely known. There is too much hero worship of mortal famous authority figures whose judgement is worth damn all assessing new work.
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For more on string theorists using irrational arguments to attack scientific critics of string, see: https://nige.wordpress.com/string-theorist-urs-schrieber-attacks-critics-of-pseudo-physics/
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Copy of a comment to Backreaction blog:
http://backreaction.blogspot.com/2008/08/equivalence-principle.html
Cecil,
The equivalence principle amounts to treating inertial mass and gravitational mass as exactly the same thing in general relativity. So all accelerations are curvatures due to the gravitational field, i.e. curved spacetime.
It’s difficult to find a good mathematical treatment from a physical perspective, and when you do find the mathematical and physical facts, they aren’t always satisfying. Here are some useful online links for the technical details:
Riemann tensor for curvature (acceleration)
Stress-energy tensor (source of gravitation
This page is good for explaining exactly why Einstein’s law differs from Newton’s: e.g., when Einstein wrote Newton’s law in terms of spacetime curvature, he had to add a term containing the trace of the Ricci tensor to satisfy conservation of mass-energy. The effective divergence of the stress-energy tensor must be zero (i.e. the vector sum of gravitational field lines from any mass/energy must be zero). Since it isn’t zero, an extra term had to be included in the field equation to make sure that there is zero curvature wherever the divergence of the stress-energy tensor is not zero. This term is the reason why Einstein’s field equation predicts twice the deflection of starlight by gravity that you get predicted by Newtonian gravity.
Physically, if a non-relativistic particle or bullet passes by the sun, half of the acquired gravitational potential energy from the approach is used for speeding up the bullet, and half is used for changing the direction (deflecting) the bullet. For a photon moving at c, none of the energy gained from approaching the sun can be used to speed up the photon, so twice as much deflection occurs than would occur for a non-relativistic bullet (100% instead of 50% of the acquired gravitational potential energy gets used to change the direction of the photon).
This is the kind of physics that general relativity delivers: it’s a kind of accountancy. Feynman gives a nice explanation of curvature in general relativity in his lectures, pointing out that the Earth’s gravitational field makes the Earth’s radius contract by 1.5 millimetres or MG/(3c2).
It’s pretty interesting that you can get this contraction from the Lorentz transformation (1 – V2/c2)1/2 factor for lengths of moving bodies.
Clearly, in quantum gravity you have exchanges of gravitons between masses. Therefore a moving body will experience front-side graviton interactions which may cause the contraction (possibly like the net air pressure on the nose of a moving aircraft, or the water pressure on the front of a moving ship).
If so, whatever graviton effect causes the contraction of length of moving bodies, will also cause the radial contraction of static masses.
Because of the equivalence principle between inertial and gravitational masses, there should be an equivalence between the contraction you get when moving at relativistic velocity and that you get in a strong gravitational field. One way to relate these is by the fall of a small particle from a long distance in a gravitational field. The velocity gained when a small particle is dropped from an immense distance and falls to the earth’s surface (ignoring air drag) is be equal to the escape velocity from the earth’s surface. The relativistic contraction of that small particle due to freefall from a very large distance should be identical to the amount of contraction of static mass you get due to gravity at the earth’s surface, if inertial and gravitational mass effects are indistinguishable.
If you put the escape velocity law (V2 = 2GM/r) into the Lorentz contraction, and then expand the result by the binomial expansion, as a first approximation this predicts that gravity contracts length by the amount GM/c2. However in the case of a moving body only one dimension gets contracted (that in the direction of motion), whereas three dimensions are contracted by gravity effects on static masses, so the average contraction amount per dimension will be one-third of GM/c2, which gives the result Feynman gives from general relativity in his lecture on curvature in ‘Lectures on Physics’.
So it’s easy to understand the physics behind the mathematical laws in general relativity. All contractions in relativity are real effects from graviton exchanges occuring between masses.
Curvature is not real at the fundamental (quantum field) level because quantum particles (gravitons) will accelerate masses in a large number of small steps from individual discrete interactions, not as a continuous smooth spacetime curvature. For large masses and large distances, the graviton interactions produce effects that average out to look like a smooth curvature. The argument for 4-dimensional spacetime in general relativity is, as Feynman pointed out, based on the fact that in a gravitational field the radial field lines are contracted (e.g. the earth’s radius is contracted by 1.5 mm), but the transverse lines (like the earth’s circumference) aren’t contracted. So this contraction of radius but not circumference would produce an increase in Pi if Euclidean 3-dimensional space were true. Having 4-dimensional spacetime is justified because it means that you can keep Pi fixed and account for the distortion by having an effective extra dimension appear! One thing I don’t like about general relativity is that the source for the gravitational field (the stress-energy tensor) is a continuously variable differential equation system, and we know that mass comes in discrete particles. So all the solutions of general relativity which have ever been done are fiddles, using smoothed distributions of mass-energy. There is no way to get general relativity to work by having discrete particles produce the field: it only works for statistically averaged smooth distributions of matter and energy. You have to assume that the source of a gravitational field is a perfect fluid with no particulate qualities, so it varies smoothly and works with the differential equations being used.
So despite the fact that general relativity has made many accurate predictions, its mathematical framework is that of classical physics (differential equations for fields), instead of being inherently compatible with quantum fields. It’s certainly accurate as an approximation where large numbers of gravitons are involved, but even Einstein himself had very serious reservations on whether continuous field structures were right:
‘I consider it quite possible that physics cannot be based on the [smooth geometric] field principle, i.e., on continuous structures. In that case, nothing remains of my entire castle in the air …’
– Albert Einstein in a letter to friend Michel Besso, 1954.
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For more on fact-based falsifiable work which isn’t an ‘alternative’ to speculative, non-falsifiable, non-fact based string theory see: https://nige.wordpress.com/2008/01/30/book/
I notice that Lubos Motl has, in a comment at the Not Even Wrong blog, attacked string theorist Urs Schreiber’s standing in the theoretical physics community:
Motl’s attack is completely opinionated drivel: “… people who don’t really mean anything in physics, such as Urs Schreiber, A.J., or someone like that, can be ambiguous …”
I think this sort of comment is typical of the behind-the-scenes sneering officialdom of physics. I’m glad to have escaped mainstream physics academia, a vile mixture of political thuggery and religious orthodoxy, where dictatorial censorship rather than reason presents the barrier to genuine new (i.e. initially unorthodox) ideas (holding them up on non-scientific grounds that sound scientific or authoritive to most people).
http://en.wikipedia.org/wiki/Ad_hominem :
‘An ad hominem argument, also known as argumentum ad hominem (Latin: “argument to the man”, “argument against the man”) consists of replying to an argument or factual claim by attacking or appealing to a characteristic or belief of the person making the argument or claim, rather than by addressing the substance of the argument or producing evidence against the claim. The process of proving or disproving the claim is thereby subverted, and the argumentum ad hominem works to change the subject.
‘It is most commonly used to refer specifically to the ad hominem as abusive, sexist, racist, or argumentum ad personam, which consists of criticizing or attacking the person who proposed the argument (personal attack) in an attempt to discredit the argument. It is also used when an opponent is unable to find fault with an argument, yet for various reasons, the opponent disagrees with it.’
For more about Urs Schreiber’s recent string theory comments at Not Even Wrong which Motl apparently objected to, see my post: https://nige.wordpress.com/string-theorist-urs-schrieber-attacks-critics-of-pseudo-physics/
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More light is thrown on Oppenheimer’s dictatorial mannerism as a typical in-a-bluster busybody mainstream physicist, in the autobiography of neutron bomb inventor and Manhattan Project veteran Samuel T. Cohen, F*** You, Mr President! Confessions of the Father of the Neutron Bomb, 3rd ed., Athenalab, 2006, page 24:
‘Oppenheimer’s personality … could be intolerant and downright sadistic … he showed up at a seminar to hear Dick Erlich, a very bright young physicist with a terrible stuttering problem, which got even worse when he became nervous. Poor Dick, who was having a hard enough time at the blackboard explaining his equations, went into a state of panic when Oppenheimer walked in unexpectedly. His stuttering became pathetic, but with one exception everyone loyally stayed on trying to decipher what he was trying to say. This exception was Oppenheimer, who sat there for a few minutes, then got up and said to Dick: “You know, we’re all cleared to know what you’re doing, so why don’t you tell us.” With that he left, leaving Dick absolutely devastated and unable to continue. Also devastated were the rest of us who worshipped Oppenheimer, for very good reasons, and couldn’t believe he could act so cruelly.’
Quantum field theory 
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