Intelligence, creativity and passion/motivation are obviously important. But selectivity is crucial. No matter what you do, science, art, journalism, or something else, if you are not able to recognize and discard your bad ideas then you’re not getting anywhere.

Because even among the most talented people bad ideas are the norm and good ones the exception, being creative but not selective is the same thing as not being creative at all.

Best,

-cvj

“… but I do know the basics of general relativity and its solutions from a course on cosmology and also I’ve studied quite a bit more about it independently…” - NIGEL COOK.

See also feynman:

‘Science alone of all the subjects contains within itself the lesson of the danger of belief in the infallibility of the greatest teachers in the preceding generation … Learn from science that you must doubt the experts. As a matter of fact, I can also define science another way: Science is the belief in the ignorance of experts.’

- R. P. Feynman, The Pleasure of Finding Things Out, 1999, p186-7.

http://feynman137.tripod.com/#h

‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’

- R. P. Feynman, Character of Physical Law, November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.

I have learned it! Liar

No I know tensor analysis (a little rusty as I did it a decade ago and have been shut out of academia) - my point to anon and also to Jacques is that the physics of the contraction which is introduced by general relativity needs to be more widely understood.

“Just because someone cleverer than me can use tensors analysis to do the above, doesn’t itself discredit intuitive physics.”

No I didn’t say that, so you need to go to school and learn to read things or properly quote. Read what I wrote, and learn, please. And grow up a lot.

nc did not actually say he was unfamiliar with GR. You should read what people say more carefully.

Rather than saying: “Just because someone cleverer than me can use tensors analysis to do the above, doesn’t itself discredit intuitive physics.” , why don’t you follow the advice of Baez above and try to learn it. People who can do the tensor analysis of GR can do so because they decided to put in the time and effort to learn it (and the prerequisites). And they decided to learn it because (probably) they felt that they wanted to work with it, something that you probably like as well.

GR has a landscape of solutions for cosmology, all of which assume that the basic form of the Einstein-Hilbert field equation is correct for any quantum gravity that might emerge as the final theory of quantum gravity.

In particular, any exchange of Yang-Mills gauge bosons to produce a Feynman type coupling for quantum gravity interactions suffers from the problem that recession of all masses from one another will produce a long-range weakening of gravity (caused by redshift of gauge bosons).

So if you’re a physicist, what you want is correct physics. The vital thing about GR is not the maths so much as the physical contraction predicted for energy conservation. Drop a test object above a mass and it gains kinetic energy (accelerates). How is the mass supplying that gravitational potential energy? If you move the mass very fast, does the field surrounding the mass move with it? Clearly it suffers contraction effects.

In his essay on general relativity in the book ‘It Must Be Beautiful’, Penrose writes: ‘… when there is matter present in the vicinity of the deviating geodesics, the volume reduction is proportional to the total mass that is surrounded by the geodesics. This volume reduction is an average of the geodesic deviation in all directions … Thus, we need an appropriate entity that measures such curvature averages. Indeed, there is such an entity, referred to as the Ricci tensor …’

Feynman explained that the contraction around a static mass M is simply a reduction in radius by (1/3)MG/c^2 or 1.5 mm for the Earth. You don’t need the tensor machinery of GR to get such simple results. You can do it just using the equivalence principle of GR plus some physical insight:

The velocity needed to escape from the gravitational field of a mass M (ignoring atmospheric drag), beginning at distance x from the centre of mass M, by Newton’s law will be v = (2GM/x)^{1/2}, so v^2 = 2GM/x. The situation is symmetrical; ignoring atmospheric drag, the speed that a ball falls back and hits you is equal to the speed with which you threw it upwards (the conservation of energy). Therefore, 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, giving g = (1 – v^2/c^2)1/2 = [1 – 2GM/(xc^2)]^{1/2}.

However, there is an important difference between this gravitational transformation and the usual Fitzgerald-Lorentz transformation, since length is only contracted in one dimension with velocity, whereas length is contracted equally in 3 dimensions (in other words, radially outward in 3 dimensions, not sideways between radial lines!), with spherically symmetric gravity. Using the binomial expansion to the first two terms of each:

Fitzgerald-Lorentz contraction effect: g = x/x_0 = t/t_0 = m_0/m = (1 – v^2/c^2)1/2 = 1 – ½v^2/c^2 + …

Gravitational contraction effect: g = x/x_0 = t/t_0 = m_0/m = [1 – 2GM/(xc^2)]^{1/2} = 1 – GM/(xc^2) + …,

where for spherical symmetry ( x = y = z = r), we have the contraction spread over three perpendicular dimensions not just one as is the case for the FitzGerald-Lorentz contraction: x/x_0 + y/y_0 + z/z_0 = 3r/r_0. Hence the radial contraction of space around a mass is r/r_0 = 1 – GM/(xc^2) = 1 – GM/[(3rc^2]

Therefore, clocks slow down not only when moving at high velocity, but also in gravitational fields, and distance contracts in all directions toward the centre of a static mass. The variation in mass with location within a gravitational field shown in the equation above is due to variations in gravitational potential energy. The contraction of space is by (1/3)GM/c^2.

There is more than one way to do most things in physics. Just because someone cleverer than me can use tensors analysis to do the above, doesn’t itself discredit intuitive physics. GR is not a religion unless you make it one by insisting on a particular approach. The stuff above is not “pre-GR” because Newton didn’t do it. It’s still GR alright. You can have different roads to the same thing even in GR. Baez and Bunn have a derivation of Newton’s law from GR which doesn’t use tensor analysis: see http://math.ucr.edu/home/baez/einstein/node6a.html

He gave T_{ab} the units of density without any c^2 or c^4 terms.

No, he didn’t. In his 1915 paper, Einstein describes the components of the stress energy tensor as pressures and energy density, which are the same dimensionally. (Correction: he used this language explicitly in a later 1918 paper applying the equations which I happen to have lying around; I don’t have Einstein’s 1915 “Field equation” paper handy right now.) With that choice of units, the prefactor is G/c^4. This can be hard to find in many textbooks since they typically choose units with G = c = 1; it’s quite easy to convert. Wald gives a table of conversion factors in Appendix F.

At any rate, this is all tangential. The key thing is that the stress energy tensor is not simply matter density, though it can reduce to that for particularly simple mass energy distributions (and for a particular observer! — for all other observers, T_{ab} will be more complicated). It represents a flux of 4-momentum; indeed, this is how one formulates local energy/momentum conservation. This understanding of the meaning of the stress-energy tensor leads directly to the correct relationship between T_{ab} and the Einstein tensor. The constant of proportionality must then be a constant in order for the Bianchi identity to be equivalent to local conservation of the source.

stevem’s discussion above about the Lagrangian formulation is particularly cogent. In order for the Lagrangian density associated with spacetime to agree dimensionally with the Lagrangian’s for matter and fields, you need factors such as he describes. For GR, this precludes any variation of c. You can include additional fields which allow c to vary, but when you do so, it isn’t GR anymore. That’s not necessarily a bad thing. But you have to understand what that theory is. It strikes those of us who are criticising you that you have not understood this point; hence the frustration.

HI anon! What is “Wrong. Simply wrong, and every other equation on the first page comes from someone named Albert Einstein, who had not read any books about Relativity. He gave T_{ab} the units of density without any c^2 or c^4 terms.” When a discussion is this much fun, how can it be pointless?

I do appreciate your “intelligent, creative and passionate remarks”and realise that you mean the best. I have taken your advice to heart and am working on something else that will be equally controversial. That has brought me to the top of an active volcano.

You are welcome to check this week’s posts, for I do appreciate your comments. I have been to Hollywood parties, and science is ultimately more satisfying. One of these days I must post some photos for Clifford.

-cvj

I can then visualize you holding a drink and a cocktail snack standing all alone in the crowded room

“I work in the higher operad approach to Quantum Gravity, and GR is just something simple that will be recovered via a categorifed twistor correspondence from the correct Machian gravity in terms of, say, Motivic Cohomology. Have you come across Category Theory by any chance?”

The very next Hollywood party I’m at, that is the very first line I am going to use when one of the beautiful people ask me what I do. I am going to memorize it now!

-cvj

Thank you for your comment. Actually, I’m not trying to apply General Relativity. I work in the higher operad approach to Quantum Gravity, and GR is just something simple that will be recovered via a categorifed twistor correspondence from the correct Machian gravity in terms of, say, Motivic Cohomology. Have you come across Category Theory by any chance?

If you don’t understand what basic concepts in general relativity mean and yet are trying to apply general relativity, then reading a textbook or two might in fact constitute a useful first step.

Wrong. Simply wrong. The meaning of T^{ab} is the flux of the density of 4-momentum component p^a in the x^b direction as measured by the observer who foliates spacetime using the x^b coordinates. Hence, for example, T^{00} (or T^{44} if you prefer) is the flux of energy in the timelike direction — ie, energy density as measured by that observer.

Thanks for your clear answer, though. You’ve made it clear you’re not willing to listen, which makes it clear that this discussion is pointless.

You really could use some basic, basic, basic general relativity study. The point being discussed here can found in any basic GR textbook; I personally like Schutz for this really elementary stuff, but they’re all good. If you don’t accept this, I have no doubt that the rest of your theory follows — after all, if you start with 1 + 1 = 3, you can prove just about any wrong mathematical idea.

I hope this doesn’t come off as too harsh; if anything, you are seeing frustration being expressed. It’s sad seeing someone who is clearly intelligent, creative, and passionate about science wasting their talents in such a misdirected way.

“Normalising to the Friedmann equations requires a factor 8 /pi G, without any c^2 or c^4″
The field equations of gravity must be dimensionally correct before whatever else you want to try, So Anon and Stevem’s questions have not been answered by this.

“S = \int ((k R + L_m) d^{4}x)”
This too is dimensionally incorrect if k does not include factors of c^4. L_m has dimensions of energy density, therefore so must kR, and [R] =L^{-2}, so [k] =[c^4]/[G].

“Theory fits BBN data, is locally Lorentz-invariant, explains the 4.507034% proportion of baryonic matter, CMB uniformity, lack of large-scale fluctuations, and supernova redshifts.”

Again if you mean your ‘theory’ this is untrue. For, even forgetting names that you want to give to different variables, the solution you come up with is r=constant* t^{2/3}. Now, as has been pointed out to you before, this is a well known solution to the Friedmann equation (often called the matter-dominated spatially flat/Einstein de-Sitter Universe). However, this solution is *inconsistent* with the data for late times.Let me add that r=const*t^{2/3} does not imply that the speed of light is changing, because the parameter that you call c(t) is NOT the speed of light, and you have not given us any reason why it should be so. (In fact the above discussion with Anon and Stevem suggests that you have implicitly set the real speed of light c=1)