### Thoughts

Mahndisa's Thoughts are most valuable. Over the weekend she posed some very thoughtful questions. I hope to answer them adequately. Mahndisa, you are welcome to ask more. Hopefully this can answer Q9's question too.

1) When you speak of 2 objects separated by a distance in spacetime, from what frame are you taking the measurements; the observer frame, the frame of the moving object, or what?

Separation ds between two objects is an invariant as in Special Relativity, regardless of where it is measured from.

2) Are the objects moving with respect to one another as the most general case of your equations?

That separation ds is also invariant if they are moving with respect to one another.

3) Are calculations in the non inertial reference frames a feature of your theory, or are you performing calculations in the weak gravity limit only?

Someone should have asked this of Albert, because Special Relativity makes no allowance for gravity. SR can be modified to account for gravity, which will lead to a c change.

4) When you invoke a changing c, how is the expression modified in non inertial frames?

Change in c results directly from a non inertial frame with gravity included.

5) What is the mechanism for the change in c?

This results from unifying the local conditions of Special Relativity (which do not account for gravity) with the large-scale Universe of General Relativity. In SR, the interval ds is given by:

6) Are you assuming that the large scale structure of the Universe is Euclidean, given the expression R = ct?

No, it only appears Euclidean on the local scale. In the large scale it is spherical of radius R = ct.

7) Given this information, how have you applied the Minkowski metric to your derivations of distance and your distinctions between timelike, lightlike and spacelike separations?

As should be seen above, this curved metric with changing c reduces to the Minkowski metric. The math links SR and GR.

8) I also thought that you assumed a spherically symnetric spacetime in your model.

Correct. R = ct applies to the distance from the Big Bang singularity. On the local scale, distances can be considered as little r = ct. On the large scale, those distances are geodesics. For instance, the distance light has travelled since the Big Bang is (3/2)ct.

9) Do you think that your equations are scale invariant?

Not quite, because all this predicts that the Universe has a limited size. For example, the power spectrum of the CMB is not scale invariant, something the WMAP team blithely ignores.

10) Are your equations diffeomorphism invariant?

Yes, they are the same under all coordinate systems. This math should show that they are also Lorentz invariant.

I wish to expand upon question 5, to answer both Mahndisa and Quasar. As Einstein figured out in 1917, mass of the Universe will cause light to follow circular paths, like satellite orbits. Every photon that we see today appears to have the same velocity, because they are orbiting at the same Space/Time distance from the Big Bang origin. When the Universe expands, that distance increases. Like a satellite shifting to a higher orbit, velocity goes down.

Gebar, you are right about the equations of the Lorentz transformation. They are the equations of a sphere!

## 23 Comments:

"R = ct applies to the distance from the Big Bang singularity. On the local scale, distances can be considered as little r = ct. On the large scale, those distances are geodesics. For instance, the distance light has travelled since the Big Bang is (3/2)ct. ... As Einstein figured out in 1917, mass of the Universe will cause light to follow circular paths, like satellite orbits. Every photon that we see today appears to have the same velocity, because they are orbiting at the same Space/Time distance from the Big Bang origin." - Louise

Hi Louise,

This section is a very nice summary of the standard explanation of general relativity.

Just some comments of mine on curvature and the correct number of dimensions.

You're assuming implicitly that a final quantum field theory will conform to general relativity's description of curvature. I think general relativity is too vague on curvature. The curvature of a geodesic, say the path of a photon in a grvitational field, is well defined in general relativity. But if you consider effects along the field vector, you just get contraction of the distance. Therefore, curvature talk is obfuscating as the cause of a force field.

I think the best way to describe a problem here is to look at the gravitational contraction of mass. General relativity says that the Earth's radius is shrunk owning to the gravitational field energy conservation effect by the amount MG/(3c^2) = 1.5 mm.

Feynman points this out in his Lectures. This shows the warping effect more clearly than the picture of a light ray merely being deflected by gravity (which also occurs to a rocket or even a bullet in a gravitational field, and so is quite compatible with Newtonian gravity, although the deflection of light in Newtonian gravity is only half that in GR because light can't get speeded up in the latter case, so the entire gravitational potential energy gained by a photon approaching a mass is used for deflection or velocity change, instead of half of it being used for speed changes as occurs at low velocities compared to c).

The problem with imagining the 1.5 mm radial contraction of earth as an ideal fluid pressure effect by the spacetime fabric of GR is that there is no corresponding transverse contraction (of circumference).

Hence, from this result, Feynman argues that in 3-d the value of Pi effectively changes since the radius of the Earth shrinks but not its circumference.

The only way to preserve Pi is to add extra dimension so that the contraction effect becomes due to the presence of an extra dimension, just like drawing a circle on a non-flat surface.

However, physically the contraction results from the atoms inside the earth being bought closer to one another radially. The effect on circumference is is not clearly defined because there is just no physical contraction or force created transversely.

Physically, it isn't even made clear whether the contraction term is applicable to spacetime itself in a void or just to atom composed matter.

It is pretty obvious that spacetime is not going to contract if there is no force to cause that. Contractions only occur where matter is present with a forcefield between the particles of matter that causes the contraction.

Spacetime can't contract orthagonally to the field vector and that would be undefined anyway (how far sideways would spacetime be contracted - would it be contracted for billions of light years ?). It is physically absurd to assume that contraction is any more than an effect caused in accelerated matter or matter in a gravitational field. The spacetime dimensions of the universe go on expanding.

So general relativity is a mathematical approximation to a quantum field theory. What is usually omitted is that GR doesn't physically define what can be contracted (matter, spaces between masses) and what can't be contracted (spacetime generally), plus the fact that the added "timelike" dimension in the metric has opposite sign to the others (which you disguise by using the complex conjugate, i).

Why have one extra dimension for spacetime? There are three expanding dimensions around us which indicate absolute time from the big bang, so three extra dimensions makes more sense; one expanding spacetime dimension for each of the contractable matter-measuring spatial dimensions.

In particular, 6-dimensional spacetime predicts electrodynamics and gravity correctly, indicating that the cosmlogical constant is zero, see http://cdsweb.cern.ch/search.py?recid=688763&ln=en

I don't think general relativity is wrong, but it makes wild approximations due to its oversimplicity. A quantum field theory for gravity will need to address the physics concerning the actual exchange of gauge bosons between gravitational charges (masses). This seems to be what Lee Smolin sets out to do in loop quantum gravity, although he may be steering in too abstract seas instead of keeping the approach tied completely to empirical factors.

I'm trying to understand the physical dynamics in string, and there really are none. It is all so completely abstract, speculative and vague it looks like religion from the engineering perspective:

When you look at string theory, the static string is 1 dimensional, but moving it gives you a time dimension so you get two dimensions. You then have to add an extra 8 or 24 dimensions to account for supersymmetric (1:1 boson:fermion supersymmetry) or bosonic symmetry respectively, because the different standard model forces are assumed to come from symmetry breaking in an original extradimensional hyperspace, and the Ramanujan function satisfying conformal symmetry has 24 modes (ie vibration states) when applied to a bosonic string or 8 modes when generalized for fermionic strings.

To make this 2 + 8 = 10 or 2 + 24 = 26 dimensional ad hoc model of particle physics in the standard model consistent with general relativity which is 3+1 = 4 dimensional, they then have to say that in 10 dimensions 6 are curled up into the 6-dimensional Calabi-Yau manifold which results in 10^500 solutions of the ground state of the universe for quantum field theory (the landscape of stringy solutions).

The 11 dimensional supersymmetry is related to 10 dimensional supersymmetric string by M-theory since it is the classical string limit (11 dimensional supergravity was discovered in the 80s and then forgotten by the mainstream until M-theory in 1995). The 10+1 = 11 dimensions for gravity appears to be similar to the 4+1 = 5 dimensional Kaluza-Klein theory from 1927 which claimed to unify gravity and electromagnetism by adding an extra dimension which was rolled up too small to be observed (add an extra dimension to GR to create 5 dimensions, and the metric can be interpreted as containing a description of the photon given by Maxwell's equations).

What really annoys me about string theory is that despite the fact that ad hoc extra dimensions are fiddled in value just to make the model account for particle physics and gravity, these fiddles are then called 'predictions'.

So you have a fiddled theory with loads of speculative assumptions just to make it consistent with existing physics, and then the assumptions are called predictions.

For example, Kaku claims that string theory predicts gravity and the standard model. This is a fraud because the number of dimensions in the string theories have been selected to make it work with gravity and the standard model.

If you win a lottery by deliberately selecting the winning ticket in advance, you are just a cheat. String theory is just a cheat.

The string theorists are prejudiced that the universe is explained b extra dimensions. They aren't genuinely searching for reality, they are just trying to force an extra dimensional 'explanation' on physics, which fails to explain anything useful or checkable concerning anything that is real.

How long will string theory last? It is being supported by brainless hype and propaganda, mainly from Motl's desk at Harvard (although he has many quiet stringy supporters).

Until it is widely perceived as a complete failure, people won't be motivated too much to work on alternatives.

Kind regards,

Nigel

Fermat's principle of optics, in its historical form states:

The actual path between two points taken by a beam of light is the one which is traversed in the least time.

Louise said: "Every photon that we see today appears to have the same velocity, because they are orbiting at the same Space/Time distance from the Big Bang origin. When the Universe expands, that distance increases. Like a satellite shifting to a higher orbit, velocity goes down.Louise, there is light photons and radiation being emitted today NOW in Space Time, as well as that which we observe reaching us from some distant past.

I can see you are trying to create a mathematical equation to show the speed of light is slowing, but I still see no physical evidence to support it.

Louise said: "As Einstein figured out in 1917, mass of the Universe will cause light to follow circular paths, like satellite orbits. Every photon that we see today appears to have the same velocity, because they are orbiting at the same Space/Time distance from the Big Bang origin. When the Universe expands, that distance increases. Like a satellite shifting to a higher orbit, velocity goes down."Louise, in this scenario it would not the speed of light changing, but the distance it has to travel. The greater distance making it appear to be travelling slower, because it takes longer to reach the 'observer'

Hi Louise,

I just saw your post, thanks for the link.

Isn't it beautiful how everything ties together? Many things in physics are based on the Minkowski space, and a lot of difficulties arise from the fact that this space is flat and static. And yet it turns out that the Minkowski space, although it seems flat, is in fact a projection of the underlying reality of the curved expanding universe. And it only seems static because it shows all time moments simultaneously. If you take the succession of time moments you derive again the curved expanding universe. All this is perfectly clear through simple high-school algebra.

Just an additional note. I have not updated my site for quite some time now, because I am in the process of a major overhaul as mentioned in my last blog post. I will be setting up a community site with forums, blogs, and most importantly, a Wiki in which the development of the theory will be taking place. Everybody is welcome to contribute (with attribution), and especially you will be considered an honored guest, as you have come up with another very important piece of this puzzle. Let's see what an «open participation model» can do in physics theory development.

Nice to hear from you all. I think there is hope, for more and more people realise that silly strings are not even wrong. It is a sign of desperation that people attack theories that actually make testable predictions, completely ignore all the supporting evidence, or make sexist comments.

This is an exciting time because we will see alternative theories come to the fore.

09 26 06

Hello Louise:

I am not sure I get your explanations and am a a bit concerned about linear, Newtonian euqations being used in this way. On the one hand I thought you said you were unifying GR and SR, yet I see no factor of gamma for time dilation if we are in SR and no factor for time gravity dilation if we are in GR. Also when you use terms like R=ct reference frames DO matter. From which frame are you taking these measurements? If I am not in the proper frame with the proper time, I will suffer a length contraction. Since we cannot travel at light speed but oft make measurements of things going at light speed our reference frame biases our measurements to an extent and we should specify from which frame we are taking measurements.

Regarding ds being an invariant. No ds^2 is the invariant. And I do not understand how you are getting R=ct from the Minkowski metric. Since you said that r=ct is local but that R=ct applies for all of the universe I am also confused. There seems to be no difference between r and R and also you have not sufficiently explained why one can use R=ct on a large scale.

Regarding questions of scale invariance, let me clear up a bit. What I was asking was not whether the universe was bounded, but whether or not your equations work on any scale, whether Plank or on the order of 1AU. My concern was that your equation works for small scales but not for the large scale structure of the universe because Minkowski space is

locallyEuclidean.You mention the CMB anisotropy. This anisotropy very well means that we are not describing the large scale of the universe with Euclidean geometry though. In fact, the CMB and WMAP data has given rise to many different theories on the large scale structure of the universe, whether it is simply connected or multiply connected, whether it has spherical cross sections or a horn shape with finite volume and infinite area (Gabriels horn). So your invocation of the CMB further obscures any new theoretical additions you may have, as GR was developed before the anisotropy was discovered. In what way have you modified your equations to take this into account?

Regarding questions about weak field limits, since you said that you are unifying GR and SR, I expect to see some talk of the underlying geometry such as curves or something in a large scale description of the universe. if we are in curved space, again we need geodesics to specify shortest distances between points.

Regarding Nigel's comments about absolute time, I don't get that Nige. I mean time is affected by the topology of the spactime in a GR framework so I didn't know terms like absolute time make any sense. Sure using time as a complex parameter may seem strange and somewhat ad hoc, but this formalism has some accuracy to a certain limit;) I am not sure if that is the end all be all metric, However, I am quite certain that time gets affected by field deformations etc. This doesn't seem to be taken into account here.

Regarding the R=ct equation, depending upon whether or not our universe has mass, the expression for T would similarly have to be modified because T would suffer from deformations due to gravity. Also length contraction is a feature of SR and all ojects would suffer that the closer to c they move. Maybe you can clear all of these questions up by giving an example of what happens when a stream of neutrinos hits the Earth's atmosphere. From SR there are known calculations taking into account the reference frame of the neutrinos v. the reference frame of the lab. If you can replicate that data with your theory, then I might see it.

What I am not getting is how your theory is anything new and what it predicts. I still don't get how c is changing in your framework. You have mentioned that a scenario with G changing makes no sense, yet your equations dimensionally yield that possibility because by rearranging GM=tc^3, we get that G=tc^3/M if t is varying, then necessarily G needs to be varying too. We cannot set a constant equal to a variable. Perhaps you can explore this further?

Yes Q9 said that the distances are greater and that c isn't changing. I think he was right, but if you can demonstrate a field theoretic or topological approach to disprove this assertion, that would be nice. Regarding the article you cited about constants changing, I know this has been an intense area of debate for quite some time. But I thought that the underlying thought was that scale factor constants such as c and h are free to be varied because they are defined really as scaling factors, whereas things like the fine structure constant will never change because they cannot be defined in terms of other quantities. This thought might be good for your theory, however you have to demonstrate the mechanism for the c change a bit more in depth.

Regarding string theory, I wonder why you say it is not even wrong? Although I like LQG, Lee Smolin has made a very strong effort to unify both approaches and I see nothing wrong with a notion that lqg can quantize strings. The issue is whether or not the quantization yields something that makes sense;)

At this time, I see a few inconsistencies and am not certain if you have a theory here. It seems like you have used quite a bit of classical GR mixed with a flavor of SR but some crucial details have been missing. I thank you for your time in answering my questions, however.

Louise

I might be able to

sneaka paper onto the arxiv for you. Last time I tried this I got into trouble, but we could give it a go! Email me at UC.Kea, great idea! Your work and posts are fascinating too.

Mahndisa, I will try to answer your 11 paragraphs as time provides.

With a nod to Nigel, it may be possible to have a changing G, especially near the Big Bang. A future post may talk about interesting varying-G theories.

The time dilation factor gamma is derivable from local conditions of SR. I refer to Gebar for very interesting derivations.

R = ct should apply to distance between the Big Bang and any reference frame. R = ct is not derived from the Minkowski metric because it is something new.

When a satellite shifts into a higher circular orbit, does its velocity change?

Note that a theory makes falsifiable predictions, which is more than "not even wrong."

I hope that you ask such challenging questions of your SFSU professors too.

Sigh. I nominated Louise for a Nobel Prize on Woit's new thread on that topic, but of course it got deleted!

Hi Mahndisa,

I'm not disputing that local time is slowed down by gravity and by motion.

However, I think you can always tell the absolute time (approximately at least) by the recession of the stars. Measure the Hubble constant H, and since the universe isn't decelerating, the age of the universe is t = 1/H.

By measuring time from the big bang, you have absolute time. You can easily work out the corrections for gravitation and motion. It is easy to work out gravitational field strength because it causes accelerations which are measurable. Your absolute motion is given by the anisotropy in the cosmic background radiation due to your motion. See

Muller, R. A., "The cosmic background radiation and the new aether drift", Scientific American, vol. 238, May 1978, p. 64-74:

"U-2 observations have revealed anisotropy in the 3 K blackbody radiation which bathes the universe. The radiation is a few millidegrees hotter in the direction of Leo, and cooler in the direction of Aquarius. The spread around the mean describes a cosine curve. Such observations have far reaching implications for both the history of the early universe and in predictions of its future development. Based on the measurements of anisotropy, the entire Milky Way is calculated to move through the intergalactic medium at approximately 600 kms."

- http://adsabs.harvard.edu/abs/1978SciAm.238...64M

Hence time dilation is just the amount of local slowing down of time as measured by the motion of the measuring instrument (the caesium atoms in an atomic clock, a quartz crystal, or even a pendulum). Because length is contracted due to motion, if the velocity of light appears unchanged then time must be dilated similarly. This is because c is distance per unit time, so a contraction in distance must be accompanied by a similar contraction (dilation) in time or the value of c will change.

I think you are right that the topology of spacetime varies time across the universe.

After all, if the Milky Way has an absolute motion of 600 km/s according to the CBR, that is a small value compared to c, so time dilation is small. Presumably galaxies at immense distances have higher speeds.

The current picture of cosmology is an infinitely big currant bun, expanding in an infinitely big oven with no edges so that each currant moves away from the others with no common centre or "middle".

However, the universe is something like 15,000,000,000 years old and that although the 600 km/s motion of the Milky Way is mainly due to attraction toward Andromeda which is a bigger galaxy, we can still estimate that 600 km/s is an order-of-magnitude estimate of our velocity since the big bang.

In that case we are at a distance of about s = vt = 600,000t m/s = 0.002R where R = ct = radius of universe. Hence we are at 0.2% of the radius of the universe, or very near the "middle". The problem is that the steady state (infinite, expanding) cosmology model was only finally discredited in favour of the BB by the discovery of the CBR in 1965, and so people still today tend to hold on to the steady-state vestage that states it is nonsensical to talk about the "middle" of a big bang fireball! In fact, it is perfectly sensible to do so until someone actually goes to a distant galaxy and disproves it, which nobody has. There is plenty of orthodoxy masquerading as fact in cosmology, not just in string theory!

Best wishes,

nige

Dear Louise,

I hope the following considerations will be useful in your investigations.

1) For the kind of universe models you seem to be interested in (spatially homogeneous, isotropic universes), you should use the Friedmann-Lemaitre-Robertson-Walker spacetime metric.

2) In any case, if you are assuming a (spatially) spherically symmetric distribution of matter, then you should move to a spherical coordinate system first of all. The coordinates that I assume here on are the time, radial (more on it below), theta and phi coordinates, in order to make my considerations as clear as possible.

3) You seem to be using Newton's Second Theorem in a misguided way in your cosmological context. The theorem reads: "The gravitational force on a body that lies outside a closed spherical shell of matter is the same as it would be if all the shell's matter were concentrated into a point at this center". Of course you can say that you can calculate the classical gravitational potential at any point "inside" your universe model by adding (linearly) the contribution of the potentials of a series of spherical matter shells, under the assumption that you are working on the limits of low speeds and weak gravitational field of GR; it is well known the overall applicability of Newtonian dynamics in cosmology. However, you push this concept of applicability to the limits of identity and insert it on the metric in what seems to be a misguided way. Also, one thing is the motion of the cosmic fluid, another, is the kinematics of light signals, which inevitably involve non-Euclidean geometry. That is, if you want to test your theory against Type Ia supernovae, for instance, or other measurements involving redshifts and luminosities, you should use full GR, not Newtonian mechanics. In any case, you seem to mix concepts throughout your derivation.

4) Be careful in your definition of r. What is exactly r? And R? Notice the following. Assume first you have *no* central mass M. You have a series of concentric reference spheres of area 4 pi r^2, made of rigid rods all over (including coordinates theta and phi) and with synchronized clocks all over the intersection of the rods. Then you can say that r is the distance from a given point to the center of the spheres. That is, dr measures the (proper) distance between two points along a radial line. But when you put a central mass, THE ORIGIN CANNOT BE USED AS A POINT OF REFERENCE! Two effects occur when you place the central mass: the space becames curved, so that the spheres are no longer at proper distances from the center point, and clocks on each sphere are no longer synchronized. If you are careful on this, you will see that it is still possible to use these coordinates to measure distances in space and the passage of time near the massive sphere alowing for such effects in an appropriate manner. You will then get the Schwarzschild metric. This has nothing to do with what you need in your cosmological model, even considering the exterior solution of the Schwarzschild metric (the flat spacetime limit), because then you would have to be "outside" the universe to make the appropriate use of it in such case, which does not make sense at all.

5) You wrote "R = ct applies to the distance from the Big Bang singularity". It makes no sense. First, such "sigularity" is everywhere now, it is not at a point in the universe today. Even if this made sense, it would mean that R is the coordinate from the most distant object that one observer "placed at the Big Bang singularity" would see at a given time in his coordinate frame. Even then, you would have to INTEGRATE over the time coordinate. Make sure you know what a particle (object) and event horizons are.

Etc, etc... There are much more I could write about, but I'm really tired now, and just focused in the elementary issues, and I am not willing to go further on this. Hope others will continue the discussion.

Louise, I hope you think over these objections and look for further orientation. I suggest you read:

- Flat and curved space-times (Ellis & Williams)

- Principles of Cosmology and Gravitation (Berry)

I'll stop now.

Best wishes,

Christine

Christine

You forgot about quantum physics.

Not at all. There is no

hbarin Louise's derivation, as far as I could see. So where is quantum physics?Best wishes,

Christine

10 02 06

Louise:

I am sure you are busy, but am curious as to your response to Christine's concerns, as well as mine. I feel as though your idea of some constants changing in time is a creative idea. However you have not substantiated a claim to any such mechanism for a changing

cat all. You have also not adequately explained why you haven't gone to curvilinear coordinates in your expressions.Given the lack of

10 02 06

explanations I have seen, my only observation is that I don't think you have a bonified theory.

. However, I believe you need to severely modify your approach.I wish to support you and any other women in physics and mathematicsThis is something that all great minds go through at some point. Linus Pauling was right about lots of things and wrong about others. I pray that you do come up with a comprehensive theory but honestly know that G=tc^3 is not right. I say this with the best intentions, given my knowledge of physics and mathematics. But I always wish you well.

Just commenting about the relation R = ct, physically light emitted shortly after the time of the sungularity, ~15,000 million years ago, could be used to define what R = ct refers to. It is the distance of the source of the light (or microwaves in the case of the redshifted 3000 K blackbody IR which is now the CBR).

The CBR radiation was emitted 300,000 years after BB because that was when hydrogen de-ionised and the universe became transparent.

To me the question is how fast the CBR radiation is coming towards us at. If the conventional picture of it as transverse radiation is correct, then it goes at c = 300,000 km/s.

However, nobody has actually measured the speed of the CBR towards us. Besides, what is the transverse oscillation? Faraday in his 1846 paper "Thoughts on Ray Vibrations" had light waves represented by lines of electric and magnetic field oscillating each other by electric and magnetic inductions. However, Maxwell, in making a proper mathematical model, had to have charge oscillating in the light wave, and so he invented an aetherial displacement current, and predicted that the speed of light is absolute. Maxwell died shortly before the Michelson-Morley experiment disproved his prediction of the aether's effect.

Personally, I don't see how any aetherial charge can oscillate transversely in a light wave, because the vacuum's QFT Dirac sea only becomes polarizable at fields above the IR cutoff, about 10^18 volts/metre (allowing a real "displacement current" while polarization occurs around charges created by pair production).

This is way too high to allow Maxwellian "displacement current" radio waves, where typically the electric field strengths only are 0.1-10 volts/metre or so. Therefore, I don't believe there is any physical Maxwellian aetherial charge transverse oscillation in a light wave. So Maxwell's model is very flawed.

Louise's ideas on slowing down of light would only make sense to me if there was a physical mechanism. The only mechanism I can see that might be physical is if redshift is associated with slowing down.

In a longitudinal wave like a sound wave, redshifts (lowered pitch of sound) are caused by the source moving away from you (like a train's whistle) don't slow the wave speed. The sound comes at the same speed, but the wave fronts are more greatly spaced out. The actual frequency shift occurs at the moment the sound emerges from the train's whistle and enters the surrounding still air.

This model is wrong for light. First, sound is a longitudinal wave, not a transverse wave like light. Second, sound has an absolute speed, while light doesn't (any change in light speed due to absolute motion of both source and receiver can't be measured, because any measuring instrument contracts in the direction of its motion, and clocks slow).

So it is possible that light behaves in a totally different way to longitudinal sound waves. Instead of not being slowed down by the motion of the emitter, perhaps light is redshifted because the speed of the radiation is absolute relative to the motion of the emitter? In this case, the speed of the CBR towards us would be c x (300,000 years)/(15,000,000,000 years) = 0.00002c = 6 km/second.

I recall someone at one time tried to publish a refutation of the relativistic redshift equation and was rejected for heresy. These are extremely "crackpot"-looking ideas so if you don't check them carefully, you end up ignoring them completely. However, CBR microwave radiation is slowed down to 6 km/s, then it is originating from a distance of only 0.00002ct = 300,000 light years away.

Similarly, the normal distance-redshift relationship for galaxies at intermediate distances would be seriously altered.

I agree with the GM = tc^3 equation because physically it can be represented by from E = mc^2 = GM/x where x = ct = distance of mass of universe M from test mass m.

However, don't think the solutions

R = (GMt^2)^(1/3) (Equation 1)

and

c = (GM/t)^(1/3) (Equation 2)

are automatically physical solutions in consequence. First, the physical basis of gravitation means - to my way of thinking - that there needs to be a dimensionless constant like e^3 ~ 20 added in to the basic equation and its solutions to allow for the dynamics of quantum gravitation. Also:

Equation 1 is - despite Christine's comment - a little bit like the classical Friedmann solution to GR where R increases in proportion to t^(2/3) for a critical density cosmology (ignoring CC).

I don't buy the idea of the radius varying as t^(2/3). The only reason for this in GR is that at critical density, gravitation is constantly decelerating the expansion of the universe.

This is nonsense because gravitons would be redshifted in an expanding universe when being exchanged over vast, expanding distances, and this would reduce the strength of the quantum gravity coupling constant. (This redshift of gravitons is only significant over vast, cosmic scale distances, not short ones, where recession speeds are trivial.)

Because of the redshift of exchange radiation for gravity, gravity effects are wiped out entirely at the greatest distances! Hence, there is no gravitational retardation on the cosmic scale evolution of the universe. This, expansion should be like R is directly proportional to t, not R is proportional to t^(2/3).

However, neglecting this major quantum gravity effect, and the e^3 factor, the solution looks fine.

The second solution,

c = (GM/t)^(1/3),

depends directly on the first solution by the relationship t = R/c.

Since I think the first result should be modified for quantum gravity effects to something like R = ct, the second solution should be modified to c = R/t, which is a constant.

Nevertheless, the speed of light coming from great distances may be slowed down in proportion to the amount of redshift. Orthodoxy may dismiss the idea, but that doesn't mean much really until somebody measures the speed of substantially redshifted transverse radiation.

All the Michelson-Morley data show is that you can't measure absolute variations in the speed of light because the instrument gets contracted which exactly cancels out the expected effects of absolute motion so you get a null result every time.

But if you could measure the speed of the grossly redshifted CBR, you would find it to be either 300,000 km/s (orthodox prediction) or 6 km/s (redshift linked to velocity for transverse radiation with no mediating aether). I think this would be easily detectable in space by a suitable instrument.

Thoughtful posts all. Why don't people ask questions like this of inflation and DE. What is the mechanism behind them? How do you prove it? Are they theories at all or just inferrences? Mahndisa, I hope you question your SFSU professors this way.

Today I will answer some of Christine's questions.

1) As Nigel said, this is the expansion rate of classical Friedmann expansion when k = 0.

2) We choose a reference frame where spatial coordinates phi, rho and theta go to zero. You have not mentioned a 4th dimension at all.

3) Newton's Second Theorem works in 2, 3 or 4 dimensions. Pushing the limits is how you break the barrier.

4) No, the volume of a 3-sphere is 2 \pi^2 R^3. The GR metric can be solved for the Schwarzhild metric, though I have not room for that. Since light signals from every other point in the sphere take a finite time to reach us, we are indeed "outside" the sphere.

5) No centre in Space, but a centre in Time. We are connected to the BB by a light signal of length R = ct.

6) That comes from considering hc constant and varying h, an exciting possibility that I am working on now.

In closing, young people should not be stuck to old ways of thinking. Take heart all, we win when others run out of arguments and flee from the room. We will never convince everyone, but it is pleasing to tire them out.

P.S. I heard from Michael Turner last week and varying constants is at the top of his list of things to be investigated.

1) No, I see no scale factor R(t) in your equations, except of course if you are assuming R(t) = 1 (constant, no expansion). You seem to be saying that your metric is the FLRW with k=0, but this doesn't seem so because of the absence of R(t) in your metric. The curvature has a one-to-one correspondence with the density parameter (in a Lambda=0 model). And that's it.

2) Yes, I have mentioned all 4 dimensions. But what you are saying makes no sense to me because your choice of coordinates seem to behave badly at x1=x2=x3=0. What is r? To what does it tend to when these coordinates tend to 0?

3) Then state that you are generalizing this theorem to the weak field limit of GR (present the proof) and be consistent throughout (see next point).

4) No, I'm talking about the area of concentric 2-spheres in order to define rigid rods (spatial grid) with synchronized clocks in their intersections. And I again ask you: what is r and R? It seems that you are referring to spatial quantities (radius) in R^3, not in R^4, when, for instance, you write "this spherical Space". But then you say you have a 3-sphere. The FLRW metric is a consequence of the symmetry of 3D position space, expressed in 4D language.

5) Even if what you are saying makes sense, then still the right way of doing things is:

dr = - (c/R(t)) dt

r = comoving distance coordinate

R(t) = scale factor

6) What is the physical motivation for this?

Overall, I should make Mahndisa's words my own. But I should also add something that may not please you, but I must do it because I do care about you and your progress, given the way you close your last reply: be careful on Baez's crackpot index, specially this one:

"40 points for claiming that when your theory is finally appreciated, present-day science will be seen for the sham it truly is. (30 more points for fantasizing about show trials in which scientists who mocked your theories will be forced to recant.)"

And yes, I am tired, but not stuck with anything for sure.

Best wishes and good luck.

Christine

Christine's 55 cm of questions have been reduced to 35 cm, so I hope that we are making progress. Thanks to all for the most intelligent comments on blogger.

1) As stated, R(t) = (GM)^{1/3} t^{2/3}. That is Einstein-de Sitter expansion rate for k = 0.

2) See on second slide that I use x1=x2=x3=0. r is Einstein's distance to a centre of mass, which here is the BB.

3) I have also stated a weak field case of M = 0. Then it reduces to ds^2 = -(dx1)^2 -(dx2)^2 -(dx3)^2 + (dx4)^2, the SR metric.

4) Once again R = ct, here substituted for distance r to centre of mass.

5) I think you are referring to a dimensionless scale factor R(t) which is normalised to unity because c is the variable. We have dr = cdt, r = \int{c(t)dt} = (3/2)ct. Fascinating, the distance light has travelled since the BB is (3/2)R(t). Simple, is it not?

6) Because multiple measurements indicate that hc is constant and c is changing.

Kea has shown herself unafraid to post on other blogs even if she risks getting deleted. Kea, Gebar and Nigel are the top of the curve.

Hi Louise,

I want to say a bit about Christine's point concerning the Baez index: "40 points for claiming that when your theory is finally appreciated, present-day science will be seen for the sham it truly is. (30 more points for fantasizing about show trials in which scientists who mocked your theories will be forced to recant.)"

Here are four examples of this:

(1) Professor Herbert Dingle of Imperial College, London University. He was anti-special relativity. He wrote "Relativity for All" in 1922 and was chosen by the BBC to give the Eulogy when Einstein died in the 1950s. However, he had frosty relations with Einstein. About 1948, Dingle wrote a paper for a commemorative book on relativity, and Einstein publically ridiculed Dingle's paper. In the 1970s, Dingle tried to ridicule Einstein's reputation by attacking special relativity. He was suppressed for this.

(2) Professor Eric Laithwaite, also of Imperial College, London University. He was a secret heretic but kept quiet sensibly until the Royal Institution asked him to present the 1974 Christmas lectures, which were broadcast on BBC television. He then claimed to disprove Newton's laws of motion, Ohm's law, and all kinds of stuff, and asked "What's wrong with the scientific world?" It was too late to stop the lectures going out (they were transmitted live on TV), but the Royal Inquisition (whoops, I mean Royal Institution!) did ban the publication of the script as heresy. Laithwaite then quoted Professor Freeman Dyson's 1958 Scientific American article: ‘Most of the crackpot papers that are submitted to the Physical Review are rejected, not because it is impossible to understand them, but because it is possible. Those that are impossible to understand are usually published.’

(3) Theo Theocharis graduated in physics from Imperial College of London University. As you can guess from what I've said about Professors Dingle and Laithwaite of the same establishment, Theocharis was infected with dissent. He stayed on to do a PhD but it was too heretical to be awarded. Then he started writing attacks on the scientific orthodoxy in Britain, getting a paper on this into a peer-reviewed journal: ‘Where Science Has Gone Wrong’, Nature, v329, p595, 1987.

That led to a row, not acclaim for Theocharis:

‘Teachers of history, philosophy, and sociology of science ... are up in arms over an attack by two Imperial College physicists ... who charge that the plight of ... science stems from wrong-headed theories of knowledge. ... Scholars who hold that facts are theory-laden, and that experiments do not give a clear fix on reality, are denounced. … Staff on Nature, which published a cut-down version of the paper after the authors’ lengthy attempts to find an outlet for their views, say they cannot recall such a response from readers. ‘It really touched a nerve,’ said one. There was unhappiness that Nature lent its reputation to the piece.’ – Jon Thurney, Times Higher Education Supplement, 8 Jan 88, p2.

(4) Dr Arnold C. Lynch was at Cambridge in the 1930s where he met the aged J.J. Thomson who told him about his original experiments which discovered the electron. Lynch took a PhD in physics. During WWII, he designed vital parts of the Colossus vacuum tube computer which cracked the Nazi "Fish" code, which was harder than the "Enigma" code.

In 1997, Dr Lynch was asked by the IEE to give the centenary lecture on about the discovery of the electron (which occurred in 1897), because he was the only person remaining who had heard about it from J.J. Thomson.

However, he was then suppressed when he got involved with Catt and myself. He offered to use his enormous prestige to help get a paper published exposing the Catt anomaly. He ran into arguments and only managed to present the paper to a minor group on the History of Electrical Engineering where it was published in HEE/26, 1998, "A difficulty in electromagnetic theory." The IEE responded by not publishing an obituary when he died.

The mainstream never recants, and it is not possible to swim against it as the current is too strong. It is a big problem. However, I think that by working further on the theory, it will make the heresy problems smaller.

Best wishes,

nigel

I think you are referring to a dimensionless scale factor R(t) which is normalised to unity because c is the variable. We have dr = cdt, r = \int{c(t)dt} = (3/2)ct. Fascinating, the distance light has travelled since the BB is (3/2)R(t). Simple, is it not?Please elucidate how you reach that result (r=(3/2)ct). Is R(t)=1? Or is it R(t) = (GM)^{1/3} t^{2/3}? You seem to assume the former in the dr expression. Then your calculations (if correct) imply r = (3/2) * R(t) = (3/2) * 1 = constant.

I do not consider your other responses satisfactory. Specially number 2, it is quite worrisome in an obvious sense (at least to me).

Louise, my approach to science is that I can always be wrong, I'm always open to that possibility. I try to be very very careful, and attempt to accept the criticisms to the extent they are reasonable, coherent, and constructive. I hope my observations are useful to you.

I think you have a good opportunity to improve your scientific writtings and review your basic assumptions.

I'm not willing to go on into this. I hope others will help you clarify your reasonings.

Best wishes,

Christine

HI Christine:

dr = c(t)dt

r = \int c(t)dt

r= \int (GM)^{1/3} t^{-1/3} dt

Integrated from t=t_0 to t=0

r = (3/2)(GM)^{1/3} t_0^{2/3}

GM = tc^3, so (GM)^{1/3} = t_0^{1/3} c_0

r = (3/2)c_0 t_0

Where t_0 is present time, c_0 is present value of c.

For christine and mahndisa. who are also mothers: Do I ask repeated questions about your babies, and then conclude that you have no babies?

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