Redshift and scalefactor

[john hunter]

Is there any way to distinguish these two cosmological models, by experiment?


i) a universe where the scale factor of the universe depends on 1+z, and Hubble constant is H,

and ii) a universe where the scale factor depends on sqrt(1+z), and the Hubble constant is 2H ??

John Hunter.

[antoniseb]

Do you think that the SN type 1a data doesn't distinguish these two models?

[Nereid]

What do you mean by 'scale factor'?

Depending on what this is, there could be a very large number of different ways!

For example, if this scale factor has to do with gravity, but not the weak, strong, or electromagnetic forces, then you'd see stuff that is different from what we see in our earthly labs (decay times for radioactive nuclides, perhaps, or differences in spectra - wavelength ratios, transition intensities, widths, Zeeman effect, Stark effect, ...).

A good test might be the constancy of fine structure constant, alpha.

[Ken G]

The scale factor is 1/(1+z), that's what it is. Take any H you like.

[Nereid]

The scale factor is 1/(1+z), that's what it is. Take any H you like."Scale factor" as in the distance between any pair of comoving objects (http://www.astro.ucla.edu/~wright/cosmo_02.htm) (etc).

However, somehow (possibly incorrectly) I got the impression the OP has some other definition.

[Ken G]

Well, given the bizarre question, I agree we have no idea what the OP means!

[john hunter]

Dear Nereid, Ken and Antoniseb,

'Scale factor' did mean the distance between two comoving objects.

However, Ken, there is an assumption in your answer that might not be right. The alternative suggested in the OP is that the scale factor is proportional to 1/(sqrt(1+z)) , instead of 1/(1+z).

What experimental evidence could distinguish these two models? The SN1a data, might be a way, but given the strange results using the 1/(1+z) model, this can hardly count as support for that model.

All the best,

John Hunter.

[Ken G]

However, Ken, there is an assumption in your answer that might not be right. The alternative suggested in the OP is that the scale factor is proportional to 1/(sqrt(1+z)) , instead of 1/(1+z).

The only assumption is that the wavelength of light follows the scale factor, so 1/(1+z) is the exact same thing as the scale factor. This is not an assumption either, as it comes from general relativity, which is a darn good theory.

[john hunter]

Dear Ken,

You are right that General Relativity is a 'darn good theory', but its not perfect. It predicts singularities, and an accelerating universe, which isn't explained yet. Also dark matter which hasn't been found.

So the question is valid. How could we distinguish experimentally between the two alternatives mentioned earlier?

John Hunter.

P.S. Our interpretation of the redshift-scalefactor relation might need reconsidering, even if General Relativity is about right, (in other respects).

[john hunter]

Dear antoniseb,

Could you give more details please. How could the supernova data could distinguish between the two models?

John Hunter.

[Ken G]

How could we distinguish experimentally between the two alternatives mentioned earlier?

The scale factor is impossible to determine independently from some theory of how things move, and how light is bent. As all we have to go on is the light, we have to understand the geometry of its propagation and how fast it moves. Am I to imagine that you will allow that light always moves at c, but that it doesn't redshift with the scale factor? On what basis would I make that assumption, anyway? You see, observations only have meaning in the context of some kind of physical theory explaining how they came to be that way. Then other observations test the consistency of the theory. That is how science works. If we relax general relativity, you must specify what other rules you are going to keep, or the very meaning of scale factor is lost (for example, "distance" itself relies on general relativity when it is extended over nonlocal scales. The only nonunique way to measure distance is locally, and that's no good for cosmology.) In short, the very concept of "scale factor" is part of general relativity, because it is definable within that theory. To use it with some other theory, you must specify the theory, or it is not at all clear that the concept is meaningful.

P.S. Our interpretation of the redshift-scalefactor relation might need reconsidering, even if General Relativity is about right, (in other respects). Everything we know or think might need reconsidering, this is also a given in the scientific process. Without giving any specific examples of what you mean, you are not saying anything here.

[john hunter]

Dear Ken,

Here are more details, and a correction of a mistake on the OP.

R = scale factor, H=Hubble constant, t= time of journey of photon.

i) standard theory with R=exp(Ht)

Rdot/R=H
1+z=exp(Ht)


ii) alternative theory R=exp(0.5Ht) from www.gravity.uk.com/redshift_of_light.html

Rdot/R = 0.5H
1+z=exp(2*0.5Ht), so 1+z=exp(Ht)

In the second model the scale factor is sqrt(1+z)
So can we distinguish between these two models experimentally?

General Relativity is assumed correct, but it is the interpretation that is different in the second model. The change of scale factor leads to a change of every length, and every physical constant containing length dimensions. This is why Plancks constant changes in this model, www.gravity.uk.com/cosmological_model.html .

John Hunter.

[Ken G]

i) standard theory with R=exp(Ht)

Note this is only a theory of inflation, not the Big Bang, but it does appear that the acceleration of the expansion will indeed take on this form many billions of years from now. As you are talking about the past expansion, this expression is quite irrelevant. Nevertheless, I think I will be able to answer your question.


ii) alternative theory R=exp(0.5Ht)
That's not the alternate theory part, that's the same theory with a different H. The alternate theory is the completely unsubstantiated idea that you should arbitrarily insert a "2" in:
1+z=exp(2*0.5Ht)
Had there been any physical justification for that 2, then yes, the 1+z would evolve with time in the same way as the inflating solution you wrote above. As I have no idea where that 2 comes from and am highly skeptical it comes from anything meaningful or even mathematically correct, I cannot investigate the even smaller possibility that it will also be there if a real Big Bang model solution had been used instead of an inflating one.

The change of scale factor leads to a change of every length, and every physical constant containing length dimensions. This is why Plancks constant changes in this model.
The Big Bang model is built on three pillars: the CMB, the H/He ratio, and the Hubble expansion. It is also consistent with the theory of relativity. Your description of this ATM model sounds like it cherry-picks the Hubble expansion part, and loses the other two pillars and also is not consistent with relativity. Exactly why should this be given any further thought, other than as a kind of academic exercise in the ATM forum? It shouldn't, and that is the answer to your question about "can we distinguish between thee two models experimentally". I am assuming that you have no particular stake in this model, you are just curious about its ramifications. If you want to debate the model, you'll have to take it to ATM.

[john hunter]

Dear Ken,

You wrote "I have no idea where that 2 comes from"

The reason is in www.gravity.uk.com/redshift_of_light.html - as mentioned previously.

Also the other two pillars of the Big Bang are included in this theory, as there is a Bang due to a reduction of G that occurs at the moment of the Bang.

John Hunter.

[Ken G]

The reason is in www.gravity.uk.com/redshift_of_light.html - as mentioned previously.

All right, I checked the website, though it would have been easier if you had just simply stated "I am rescaling length with age (exponentially, for some mysterious reason), and leaving time alone". What you have not done is show that a single observation is consistent with this idea, or that it leads to any self-consistent physics as the universe ages. Take it to ATM, the folks there will have a ball with it.


Also the other two pillars of the Big Bang are included in this theory, as there is a Bang due to a reduction of G that occurs at the moment of the Bang.
Nice claims, color me highly skeptical. Back them up-- but on ATM threads, please. (I'm not a mod, but this is obviously an appropriate topic only for ATM, until you can support your claims to the point that the theory actually works at all, and which point you should be publishing somewhere other than here or an a website.) As I understand your question here, you are suggesting that if the scale factor evolved like a distance, while energies (connected with wavelengths) evolved like a distance squared, then we could not tell the difference. This is wrong, in your system, the proportionality between frequency and wavelength is time variable, and so is physics, and so are the process we would observe. But that's wrong, we see the same physics. Take it to ATM.

[john hunter]

Dear Ken,

The rescaling would not lead to any noticeable effects in my opinion, the diagram in www.gravity.uk.com/cosmological_model.html shows this (re: the frequency/wavelength idea, the speed of light rescales too, (and all lengths, so the changing speed of light is not measureable))

The topic has been discussed in ATM, and they have not 'had a ball', in fact there has been no evidence against a rescaling, nor against the conjecture that G reduces for dense matter. They have asked for more evidence in support of the ideas - hence the question here.

There are definite advantages of the proposals
i) solution of flatness problem, giving omega matter = 1/3
ii) avoidance of singularities in GR
iii) a deceleration parameter of -1
iv) an explanation of the distribution of dark matter in galaxies.
v) form of the large scale structure (spherical voids, due to the reduction of G)

Thanks for having a go, I'll take your answer to be that you know of no way to distinguish between the two models.

John Hunter.

[Nereid]

Moved from the Q&A to the ATM section.

[Thanatos]

Nice try John Hunter, you offer convenient answsers that duck all the hard questions. I see hoof prints.

[john hunter]

Nice try John Hunter, you offer convenient answsers that duck all the hard questions. I see hoof prints.

Dear Thanatos,

What questions have you got in mind. I'll try to answer them.

John Hunter.

[grav]

So what is this, now? Is it because the expansion of the universe has been found to accelerate that the formula for redshift is now believed to be e-Ht and not the direct redshift to distance relationship, 1-Ht, anymore? Or has it always been this way, and I just didn't know about it? I don't know if anybody realizes this (or maybe I am not looking at something the right way), but this is the formula for tired light. That is, anything that causes light to lose energy as it travels through space, which is what this particular formula calls for, is a tired light mechanism, which is why the initial cause for redshift was changed from the "stretching" of light with the universe as it travels through space to more of a Doppler shift effect produced by the velocities of the galaxies themselves. It matters not whether it is an interstellar medium or the "fabric" of space-time itself that causes it. In this case, they are one and the same. This is its formula (except for a value of two thrown in with the exponent). I may be going out on a limb somewhat with all of this, but as far as I know, it would basically mean that space is flat, static, and infinite, there are no singularities, and the Big Bang never happened.

[Nereid]

Dear Ken,

The rescaling would not lead to any noticeable effects in my opinion, the diagram in www.gravity.uk.com/cosmological_model.html shows this (re: the frequency/wavelength idea, the speed of light rescales too, (and all lengths, so the changing speed of light is not measureable))

The topic has been discussed in ATM, and they have not 'had a ball', in fact there has been no evidence against a rescaling, nor against the conjecture that G reduces for dense matter. They have asked for more evidence in support of the ideas - hence the question here.

There are definite advantages of the proposals
i) solution of flatness problem, giving omega matter = 1/3
ii) avoidance of singularities in GR
iii) a deceleration parameter of -1
iv) an explanation of the distribution of dark matter in galaxies.
v) form of the large scale structure (spherical voids, due to the reduction of G)

Thanks for having a go, I'll take your answer to be that you know of no way to distinguish between the two models.

John Hunter.(my bold)

I don't recall that we covered these - would you please give us a link to the relevant ATM thread/posts?

[john hunter]

Dear Nereid,

The distribution of dark matter in galaxies is discussed in www.gravity.uk.com/galactic_rotation_curves.html

John Hunter.

[Nereid]

Dear Nereid,

The distribution of dark matter in galaxies is discussed in www.gravity.uk.com/galactic_rotation_curves.html

John Hunter.Thanks; I will ask questions about your ATM idea, per the material on that webpage, later.

What about "v) form of the large scale structure (spherical voids, due to the reduction of G)"?

[john hunter]

Dear grav,

..but as far as I know, it would basically mean that space is flat, static, and infinite, there are no singularities, and the Big Bang never happened.

There would be no singularities in the 'rescaling' model, but it dosn't necessarily mean that the Big Bang never happened. The model predicts a reduction of G for collapsed matter (where GR would predict a singularity), so according to this model the Big Bang was due to a reduction of G at such a collapse.

The universe would appear static (in scale size), but there can still be motion of matter, and even a changing density of matter for large regions.

John Hunter.

[john hunter]

Dear Nereid,

The there are no calculations for the large scale structure question, but the appearance of large spherical voids in the large scale structure may well be capable of explanation by a 'reducing G' model.

Regions of collapsing matter would re-explode instead of forming black holes, giving such a structure. link is www.gravity.uk.com/large_scale_structure.html

There is an article in physics review letters about gamma ray bursts being 4 times more common in the directions of galaxies, as apposed to other directions. So (as speculation), maybe gamma ray bursts are caused by brief explosions at the centres of galaxies, when the mass/radius ratio reaches c^2/G and G momentarily reduces. The radius of the central core would increase at the moment of the burst, and G increases back to its normal value.

John Hunter.

[Nereid]

Dear Nereid,

The distribution of dark matter in galaxies is discussed in www.gravity.uk.com/galactic_rotation_curves.html

John Hunter.Let's see if I understand this John Hunter idea correctly ...

All (large, massive) spiral galaxies will have flat rotation curves (beyond some particular distance) - right?

Does this same John Hunter idea apply to (large, massive) elliptical galaxies too?

Ditto, for satellite galaxies?

Ditto, for galaxy clusters?

If the John Hunter idea does not apply to them, what makes these systems different from (large, massive) spirals?

[john hunter]

Dear Nereid,

It could be that for flat spirals, there is an easier route matter to be ejected from the centre i.e. perpendicular to the spiral, in jets.

So, (as speculation) the dark matter is created, in bursts, by high energy particles, perhaps positrons and electrons, ejected from the centre of flat galaxies and dispersing, some combining to give off gamma rays.

If undisturbed the dispersion might reflect the ammended gravitation theory as in www.gravity.uk.com/galactic_rotation_curves.html

For ellipticals, not being flat, there is no easy route for matter to escape the galaxy, and it is reabsorbed in the galaxy.

John Hunter.

[Nereid]

Dear Nereid,

It could be that for flat spirals, there is an easier route matter to be ejected from the centre i.e. perpendicular to the spiral, in jets.

So, (as speculation) the dark matter is created, in bursts, by high energy particles, perhaps positrons and electrons, ejected from the centre of flat galaxies and dispersing, some combining to give off gamma rays.

If undisturbed the dispersion might reflect the ammended gravitation theory as in www.gravity.uk.com/galactic_rotation_curves.html

For ellipticals, not being flat, there is no easy route for matter to escape the galaxy, and it is reabsorbed in the galaxy.

John Hunter.Let's make sure that we're on the same page to begin with, shall we?

I'd like to propose that we do this by agreeing on some key concepts, in your idea, and highlight any aspect which may differ from how such concepts - apparently the same - may differ from what you'd find in a standard physics text; OK?

G:
1) is this the constant of proportionality, in the Newtonian F = G m1 m2/r2?
2) if so, can it reliably be determined, by Cavendish-style experiments (http://en.wikipedia.org/wiki/Torsion_bar_experiment) (in principle)?
3) for the 'm', can we use standard tables of the atomic mass of isotopes, together with a count of the number of atoms in the bodies in the Cavendish-style experiments, to independently determine the m1 and m2? (in principle)
4) how would we measure 'r'?

Galaxies: there are many environments within a galaxy where we could measure 'G'. Which of the following are 'legitimate', in terms of the scope of the John Hunter 'reducing G' idea:
6) on the surface of Earth-like planets (in sol-like solar systems)?
7) close to the surface of non-degenerate stars?
8) near the centre of globular clusters?
9) in the plane of a large, massive spiral galaxy, many dozens of kly from the nucleus (and at least several ly from the nearest star)?
10) in the halo of a massive galaxy (spiral or elliptical), many dozens of kly from the nucleus?

[john hunter]

G:
1) is this the constant of proportionality, in the Newtonian F = G m1 m2/r2?
2) if so, can it reliably be determined, by Cavendish-style experiments (http://en.wikipedia.org/wiki/Torsion_bar_experiment) (in principle)?
3) for the 'm', can we use standard tables of the atomic mass of isotopes, together with a count of the number of atoms in the bodies in the Cavendish-style experiments, to independently determine the m1 and m2? (in principle)
4) how would we measure 'r'?

Galaxies: there are many environments within a galaxy where we could measure 'G'. Which of the following are 'legitimate', in terms of the scope of the John Hunter 'reducing G' idea:
6) on the surface of Earth-like planets (in sol-like solar systems)?
7) close to the surface of non-degenerate stars?
8) near the centre of globular clusters?
9) in the plane of a large, massive spiral galaxy, many dozens of kly from the nucleus (and at least several ly from the nearest star)?
10) in the halo of a massive galaxy (spiral or elliptical), many dozens of kly from the nucleus?

Dear Nereid,

About G:
1) and 2) Yes, G is the constant of proportionality, and it could be determined (in principle) by measuring the force between two (small) masses, in a Cavendish type experiment, in any environment.

3) yes, but all energies inside the body would be included too, due, to E=mc^2
4) the r, as measured by the person doing the experiment, could be found by an accurate ruler (in principle)

Galaxies:

G would be measured in each environment, by an observer in that environment to be G(effective) = c^2/[(c^2/G) + (m/r)]
for 6) surface of earth: m = mass of earth, r = radius of earth
for 8) centre of globular cluster :m = mass of globular cluster, r = radius of globular cluster

The only difference between 6) and 8) is a small numerical factor e.g. 2/5 before the m/r term, depending on whether the experiment is done on the surface, or centre of the nearby body.
This comes from the original conjecture which gives G(effective) = c^2/(sum of all (m/r))
The sum is for all other masses in the universe. In the above equation the c^2/G represents the sum of all m/r for the rest of the universe, (excluding the nearby body).

John Hunter

[Nereid]

Dear Nereid,

About G:
1) and 2) Yes, G is the constant of proportionality, and it could be determined (in principle) by measuring the force between two (small) masses, in a Cavendish type experiment, in any environment.

3) yes, but all energies inside the body would be included too, due, to E=mc^2
4) the r, as measured by the person doing the experiment, could be found by an accurate ruler (in principle)

Galaxies:

G would be measured in each environment, by an observer in that environment to be G(effective) = c^2/[(c^2/G) + (m/r)]
for 6) surface of earth: m = mass of earth, r = radius of earth
for 8) centre of globular cluster :m = mass of globular cluster, r = radius of globular cluster

The only difference between 6) and 8) is a small numerical factor e.g. 2/5 before the m/r term, depending on whether the experiment is done on the surface, or centre of the nearby body.
This comes from the original conjecture which gives G(effective) = c^2/(sum of all (m/r))
The sum is for all other masses in the universe. In the above equation the c^2/G represents the sum of all m/r for the rest of the universe, (excluding the nearby body).

John HunterThanks for the clarifications.

One minor question: in 4), is the ruler local?

One not so minor question: in 6), are all bodies other than the planet on which you're doing the test to be ignored? The Sun, the Moon (if there is one), Jupiter, the local open cluster (if there is one), the distant binary star (if there is one), the local arm of the galaxy, the galaxy, the cluster, ... none of these contribute to the observed G (other than as "the sum of all m/r for the rest of the universe")?

[john hunter]

Dear Nereid,

About 4), the ruler is local, - so that the distance between the masses in the Cavendish type experiment can be measured locally by the person doing the experiment.

For 6)
The c^2/G represents the 'rest of the universe', which is taken to be the part which is at a fixed distance from the experiment.
It is changes in G which are the thing of interest. If the radius of a galactic nuclei were to change, the m/r term shows that a Cavendish experiment, done near the surface of the nuclei, would show a changed value of G.

The contributions from the 'rest of the universe' to c^2/G increase with distance from the experiment. For a universe at constant density, shells of thickness dr at a distance r from the experiment have mass depending on 4*pi*r^2, but the P.E is proportional to 1/r, so the contribution is proportional to r.
So actually contributions from a distant binary, would not be significant for the 'earth G' , but the distance of of the experiment from the centre of the earth might be, e.g. a different value would be obtained by doing the experiment on a mountain, as opposed to down a deep mine shaft.

Unfortunately, since G is rather poorly known (compared to other physical constants), this couldn't be used as a test of the proposal.

If contributions of more than one body are thought to be important, the formula
G(effective) = c^2/[c^2/G + m(1)/r(1) + m(2)/r(2) + .....] could be used.

All the best,

John Hunter.

[Nereid]

Dear Nereid,

About 4), the ruler is local, - so that the distance between the masses in the Cavendish type experiment can be measured locally by the person doing the experiment.

For 6)
The c^2/G represents the 'rest of the universe', which is taken to be the part which is at a fixed distance from the experiment.
It is changes in G which are the thing of interest. If the radius of a galactic nuclei were to change, the m/r term shows that a Cavendish experiment, done near the surface of the nuclei, would show a changed value of G.

The contributions from the 'rest of the universe' to c^2/G increase with distance from the experiment. For a universe at constant density, shells of thickness dr at a distance r from the experiment have mass depending on 4*pi*r^2, but the P.E is proportional to 1/r, so the contribution is proportional to r.
So actually contributions from a distant binary, would not be significant for the 'earth G' , but the distance of of the experiment from the centre of the earth might be, e.g. a different value would be obtained by doing the experiment on a mountain, as opposed to down a deep mine shaft.

Unfortunately, since G is rather poorly known (compared to other physical constants), this couldn't be used as a test of the proposal.

If contributions of more than one body are thought to be important, the formula
G(effective) = c^2/[c^2/G + m(1)/r(1) + m(2)/r(2) + .....] could be used.

All the best,

John Hunter.Could you do a simple calculation for me please?

What would the value of G be, at a distance of, say, 1,000 km above the Earth's surface, expressed as a % (+ or -) of the value at the Earth's surface? I'm guessing that since 1,000 km is tiny wrt the distance to the Moon, and even tinier wrt the distance to the Sun, only the Earth's mass (which is the same, ignoring the mass of the atmosphere) and the Earth's radius need be included in the calculation.

[john hunter]

Dear Nereid,

On the earth's surface it is
G(effective)= G (1-(G/c^2)*(m/r)) from the formula mentioned previously (Binomial approximation)

Dividing by the same, but with r replaced by r+10^6, gives a difference from 1 of (Gm/c^2)*(1/(r+10^6)-1/r), which is approx. Gm*10^6/(c^2*r^2)
m = 6*10^24Kg. G = 6.67*10^-11, r = 6.37*10^6m c^2 approx 10^17

so the answer is approx. 4*10^20/4*10^30 approx 10^-10 or
+0.00000001 percent higher above the earth, compared to value on surface.

Since G is only known to 3 or 4 significant figures, this couldn't be used as a test of the theory.


A better test is to try and detect a change in G , 6 months apart, on the earth, as the earth/sun distance changes.
Then use Lunar Laser Ranging to try to measure the change in orbit of the moon, due to the change in the earth, and moon, G.

The predicted change in earth-moon distance is about 6cm , which has been measured, although there is a different interpretation by the McDonald observatory as to the cause, they believe it is a General Relativistic effect, due to time dilation.

All the best,

John Hunter.

[Nereid]

Dear Nereid,

On the earth's surface it is
G(effective)= G (1-(G/c^2)*(m/r)) from the formula mentioned previously (Binomial approximation)

Dividing by the same, but with r replaced by r+10^6, gives a difference from 1 of (Gm/c^2)*(1/(r+10^6)-1/r), which is approx. Gm*10^6/(c^2*r^2)
m = 6*10^24Kg. G = 6.67*10^-11, r = 6.37*10^6m c^2 approx 10^17

so the answer is approx. 4*10^20/4*10^30 approx 10^-10 or
+0.00000001 percent higher above the earth, compared to value on surface.

Since G is only known to 3 or 4 significant figures, this couldn't be used as a test of the theory.


A better test is to try and detect a change in G , 6 months apart, on the earth, as the earth/sun distance changes.
Then use Lunar Laser Ranging to try to measure the change in orbit of the moon, due to the change in the earth, and moon, G.

The predicted change in earth-moon distance is about 6cm , which has been measured, although there is a different interpretation by the McDonald observatory as to the cause, they believe it is a General Relativistic effect, due to time dilation.

All the best,

John Hunter.Some quick OOM calculations suggest the 'john hunter effect' (JHE) would be approximately:

* ~1 ppm, in the cores of main sequence (MS) stars

* ~0.1 to 1 part per thousand, in/near white dwarf stars

* ~1% to 20% in/near neutron stars.

All these would have, I suspect, observable consequence:

* at least some of the rates at which the various nuclear reactions that power MS stars are very sensitive to 'environmental parameters', such as the temperature, pressure, ... and G. I expect that making the modifications to standard codes, to allow for a variable G, would produce differences in MS stars that would be observable (cf the standard, constant G, models).

* similar dependence on 'environmental parameters', both nuclear reaction rates (-> novae and Type 1a supernovae differences) and things like surface gravity (line broadening, for example) and temperature (observable as cooling rates, in ensembles of WD stars perhaps).

* likely the most clearly observable would be in the orbits of binary neutron stars, esp the double pulsar. There is now a great deal of high quality data on these, from decades-long radio observations; given the size of the JHE in these systems, I would think any variable G signal, of the size predicted by the JHE, would stick out like a very sore thumb.

So, how well does the predicted JHE fare, when tested using binary pulsar data?

[john hunter]

Dear Nereid,

Some quick OOM calculations suggest the 'john hunter effect' (JHE) would be approximately:

* ~1% to 20% in/near neutron stars.

So, how well does the predicted JHE fare, when tested using binary pulsar data?

The percentages you mentioned are presumably for a change in G, near a neutron star, these have to be distinguished from a different mass. That is, the product GM might be easily measurable to this accuracy, but G itself and the change of G with distance to the partner, might only just be measurable from binary pulsar data (even without the following).

It turns out that the decrease in G, is balanced by an increase in mass for two stars moving towards each other, to illustrate this lets imagine a mass m, falling towards the sun mass m(s). First it's at radius r(1), then a closer distance r(2).

From conservation of energy 0.5mv(1)^2 - Gm*m(s)/r(1) = 0.5mv(2)^2 - Gm*m(s)/r(2)

giving 0.5v(2)^2 = 0.5v(1)^2 - Gm(s)/r(1) + Gm(s)/r(2) ....................equation (*)
---------------------------------------

At r(1) : G(1) = G(1 - G/c^2*m(s)/(r(1)) : and m(1) = m(1 + 0.5v(1)^2/c^2) from reducing G, and relativistic mass increase respectively,using binomial expansions.

so at r(1) the product G(1)m(1) = G(1 - G/c^2*m(s)/(r(1)) *m(1 + 0.5v(1)^2/c^2)
which gives
G(1)m(1) = Gm(1 + 0.5v(1)^2/c^2 - G/c^2*m(s)/r(1)) .....equation (1)
--------------------------------------

and at r(2) the product G(2)m(2) = G(1 - G/c^2*m(s)/(r(2)) *m(1 + 0.5v(2)^2/c^2)
which gives
G(2)m(2) = Gm(1 + 0.5v(2)^2/c^2 - G/c^2*m(s)/r(2)) .....equation (2)
-----------------------------------------------------------------------------------------------

so from equation (*), substituting for 0.5v(2)^2 into equation(2) and expanding gives,

G(2)m(2) = Gm(1 + 0.5v(1)^2/c^2 - G/c^2*m(s)/r(1) + G/c^2*m(s)/r(2) - G/c^2*m(s)/r(2))
which gives
G(2)m(2) = Gm(1 + 0.5v(1)^2/c^2 - G/c^2*m(s)/r(1))..... equation (3)
---------------------------------------

Because equation (1) is the same as equation (3) i.e. G(1)m(1) = G(2)m(2) then the curvature of space time created by the mass dosn't change as it approaches the other mass (as viewed from a distant observer).

However this dosn't mean the effect is just an illusion , because if a lot of masses were to fall together and then combine to form a star, then after combination, there would not be the mass increase from relativity (apart from a residual temperature), but the reducing G effect would remain, and be higher if r was small.

For this reason (speculation), there is something wrong with the relativistivic gravitational mass equation rho + p/c^2, the reducing G effect might cancel the p/c^2 term.

This would allow stationary compact objects such as AGNs to experience a net reduction of G and re-explode or emit jets.

John Hunter.

[Nereid]

Dear Nereid,Some quick OOM calculations suggest the 'john hunter effect' (JHE) would be approximately:

* ~1% to 20% in/near neutron stars.

So, how well does the predicted JHE fare, when tested using binary pulsar data?The percentages you mentioned are presumably for a change in G, near a neutron star, these have to be distinguished from a different mass. That is, the product GM might be easily measurable to this accuracy, but G itself and the change of G with distance to the partner, might only just be measurable from binary pulsar data (even without the following).All it is is exactly what we discussed earlier; if a Cavendish-type experiment were conducted 'near' a neutron star, it would measure a G that differs from what we measure, here on Earth, by ~1% to 20%. There is no "product GM" involved; earlier you agreed that "M" could be determined, unambiguously, by 'counting atoms'. Have you changed your mind?It turns out that the decrease in G, is balanced by an increase in mass for two stars moving towards each other, to illustrate this lets imagine a mass m, falling towards the sun mass m(s). First it's at radius r(1), then a closer distance r(2).

From conservation of energy 0.5mv(1)^2 - Gm*m(s)/r(1) = 0.5mv(2)^2 - Gm*m(s)/r(2)

giving 0.5v(2)^2 = 0.5v(1)^2 - Gm(s)/r(1) + Gm(s)/r(2) ....................equation (*)
---------------------------------------

At r(1) : G(1) = G(1 - G/c^2*m(s)/(r(1)) : and m(1) = m(1 + 0.5v(1)^2/c^2) from reducing G, and relativistic mass increase respectively,using binomial expansions.

so at r(1) the product G(1)m(1) = G(1 - G/c^2*m(s)/(r(1)) *m(1 + 0.5v(1)^2/c^2)
which gives
G(1)m(1) = Gm(1 + 0.5v(1)^2/c^2 - G/c^2*m(s)/r(1)) .....equation (1)
--------------------------------------

and at r(2) the product G(2)m(2) = G(1 - G/c^2*m(s)/(r(2)) *m(1 + 0.5v(2)^2/c^2)
which gives
G(2)m(2) = Gm(1 + 0.5v(2)^2/c^2 - G/c^2*m(s)/r(2)) .....equation (2)
-----------------------------------------------------------------------------------------------

so from equation (*), substituting for 0.5v(2)^2 into equation(2) and expanding gives,

G(2)m(2) = Gm(1 + 0.5v(1)^2/c^2 - G/c^2*m(s)/r(1) + G/c^2*m(s)/r(2) - G/c^2*m(s)/r(2))
which gives
G(2)m(2) = Gm(1 + 0.5v(1)^2/c^2 - G/c^2*m(s)/r(1))..... equation (3)
---------------------------------------

Because equation (1) is the same as equation (3) i.e. G(1)m(1) = G(2)m(2) then the curvature of space time created by the mass dosn't change as it approaches the other mass (as viewed from a distant observer).This is all very nice, but it seems (to me) to contradict what you said earlier, about how G varied.

Specifically, you seem (now) to be introducing a (special?) relativistic factor where earlier you had not.

So, could you please state, unambiguously, just what this 'john hunter effect' really is?However this dosn't mean the effect is just an illusion , because if a lot of masses were to fall together and then combine to form a star, then after combination, there would not be the mass increase from relativity (apart from a residual temperature), but the reducing G effect would remain, and be higher if r was small.At first read, this is gooble-de-gook; if you've got an alternative theory of gravity, then you need to state, unambiguously, how it operates in strong fields such as those experienced in binary pulsars.

Specifically, you need to be crystal clear just how different the 'classical GR' effects, which have now been observed to merely several hundred ppm, would be, under the 'john hunter effect'. Do I need to make this even more clear? OK, how well, does this 'john hunter effect' (JHE) match the observed advance(s) of the perhelion (perihelia), the orbital decay(s), the .... ?For this reason (speculation), there is something wrong with the relativistivic gravitational mass equation rho + p/c^2, the reducing G effect might cancel the p/c^2 term.

This would allow stationary compact objects such as AGNs to experience a net reduction of G and re-explode or emit jets.

John Hunter.Indeed, it might.

However, as you accurately note, it is (at the moment) speculation.

How about you show that, under the JHE, that there is at least as good a match with the large amount of data on binary pulsars as with GR (and please, no hand-waving)?

[john hunter]

Dear Nereid,

Let's start from first principles.
The theory is from the rescaling principle, which led to the following conjecture, from conservation of energy.

** Conjecture: The total potential energy due to each mass is equal to its rest-energy. G varies to keep this true. **

Let's also stick to stationary masses for now.
from the conjecture, for a small mass m

mc^2=GMm/R......G(effective) = Rc^2/M.... This represents a very natural solution of the flatness problem.

M = mass of universe, R = radius (c/H) c=speed of light , H= Hubbles constant. Small numerical constants omitted for simplicity.
-------------------------

For a large mass m, of radius r

mc^2 = GMm/R + Gm^2/r

so for a large mass, the self gravitational P.E is not negligible and..

G(effective) = c^2/(c^2/G + m/r)

This formula show a reduction of G for masses whose m/r ratio approaches c^2/G.
If you want to use John Hunter Effect (JHE), then this is it.
------------------------------------------------------------------------------------------------------------

General Relativity is accepted as the true theory of gravitation, with the only change that the gravitational mass of an object (amount of curvature of space time due to the mass) should incorporate a G which is specific to each mass, according to the formula above.

There has been strenous efforts for over 10 years now, to confirm or deny this effect.
the most promising are:
i) LLR
ii) Binary Pulsar orbits.

Personally I would like to have this effect confirmed or denied for sure, so I can stop wasting time on it.

Unfortunately i) LLR gives data in accord with the conjecture, but the same data can be explained by a time dilation effect of General Relativity - so maybe the conjecture is a different way of interpreting GR.
ii) There is no difference between GR and the conjecture as the increasing mass, of the pulsars, balances the reduction of G, as illustrated a couple of posts ago.

The situation where the conjecture differs from GR, is for a single stationary mass where m/r approaches c^2/G, such as an AGN. The predicted reduction of G may account for jets.

One ray of hope is LISA. Due to the amazing sensitivity of LISA, it may be able to detect a change in the sun's G, due to solar oscillations causing the m/r ratio, of the sun changing.

If you want a testable prediction from the conjecture there are two
i) LISA : arm lengths may change by micrometers.
ii) omega(matter) = 1/3 , measured so far by WMAP to be approx 0.3

John Hunter.

[Nereid]

I'm still confused ... are you claiming that the JHE is exactly the same as GR, except for a G which has an environment dependence (it's value depends on the distribution of mass 'nearby')?

That the advance of the perihelion of a 'test mass', in orbit around a big mass (Sun, neutron star, sol-mass BH, SMBH, ...) is exactly the same (to an external observer)?

That the loss of energy, due to gravitational radiation, in a binary (NS-NS, BH-NS, WD-NS, ...) is just the same?

That an 'inspiral event' will be the same (whether we see it as a short GRB, or a unique signature in a LIGO-type GW detector)?

That the details of the core collapse of a massive star (leading to a Type II SN) will be exactly the same (to an external observer) - GW, formation of an NS or BH, ...?

That gravitational lensing (shear, deflection, whatever) will be the same?

More fundamentally, don't you have some issues with any definition of "total potential energy"?

[john hunter]

Dear Nereid,

I'm still confused ... are you claiming that the JHE is exactly the same as GR, except for a G which has an environment dependence (it's value depends on the distribution of mass 'nearby')?

That the details of the core collapse of a massive star (leading to a Type II SN) will be exactly the same (to an external observer) - GW, formation of an NS or BH, ...?

More fundamentally, don't you have some issues with any definition of "total potential energy"?

The JHE is exactly the same as for GR, however the G for every mass has an environment dependence. The deviations from GR only occur when the environment is such, that the sum of m/r of all nearby masses exceeds c^2/G

So the effects you mentioned in the last post will be the same as for GR, apart from the one quoted - i.e. core collapse, where a black hole would not form.

For the last point quoted, the definition of total potential energy due to the mass m is the sum of Gmm(i)/r(i), where the sum is over all masses m(i), in the universe, up to the Hubble radius. r(i) is the distance from m to m(i).

John Hunter.

[Nereid]

Dear Nereid,



The JHE is exactly the same as for GR, however the G for every mass has an environment dependence. The deviations from GR only occur when the environment is such, that the sum of m/r of all nearby masses exceeds c^2/G

So the effects you mentioned in the last post will be the same as for GR, apart from the one quoted - i.e. core collapse, where a black hole would not form.

For the last point quoted, the definition of total potential energy due to the mass m is the sum of Gmm(i)/r(i), where the sum is over all masses m(i), in the universe, up to the Hubble radius. r(i) is the distance from m to m(i).

John Hunter.Well, that is somewhat clearer .... except that:

a) "potential energy", in GR, is not the same as the way you've defined it*

b) "r(i)" would seem to be frame-dependent (you measure 2m with your ruler; I measure the same "r(i)", but find it is not 2m)

c) you may be defining "m" differently too.

To what extent have you started with GR, and worked through your idea, making sure everything stays consistent?

*in fact, in the john hunter version of GR, how is this defined?

[john hunter]

Dear Nereid,



a) "potential energy", in GR, is not the same as the way you've defined it*

b) "r(i)" would seem to be frame-dependent (you measure 2m with your ruler; I measure the same "r(i)", but find it is not 2m)

c) you may be defining "m" differently too.

To what extent have you started with GR, and worked through your idea, making sure everything stays consistent?

*in fact, in the john hunter version of GR, how is this defined?

a) Potential energy is defined in the Newtonian way.
b) The distances are those measured by an observer stationary relative to the mass whose G is to be determined.

The conjecture does not claim to be a fully fledged new theory of gravity, rather a useful starting point for theorists.

It has the advantages of giving possible explanations for:
i) the 'flatness problem', why omega(matter) = 1/3. www.rescalingsymmetry.com
ii) the spherical void large scale structure
iii) the flat shape of galactic rotation curves
iv) the apparantly accelerating universe

whereas Big Bang (without the conjecture) cannot explain these things.

John Hunter

[Nereid]

Dear Nereid,a) "potential energy", in GR, is not the same as the way you've defined it*

b) "r(i)" would seem to be frame-dependent (you measure 2m with your ruler; I measure the same "r(i)", but find it is not 2m)

c) you may be defining "m" differently too.

To what extent have you started with GR, and worked through your idea, making sure everything stays consistent?

*in fact, in the john hunter version of GR, how is this defined?a) Potential energy is defined in the Newtonian way.
b) The distances are those measured by an observer stationary relative to the mass whose G is to be determined.

The conjecture does not claim to be a fully fledged new theory of gravity, rather a useful starting point for theorists.

It has the advantages of giving possible explanations for:
i) the 'flatness problem', why omega(matter) = 1/3. www.rescalingsymmetry.com
ii) the spherical void large scale structure
iii) the flat shape of galactic rotation curves
iv) the apparantly accelerating universe

whereas Big Bang (without the conjecture) cannot explain these things.

John HunterOK, so here's an obvious question: if 1) "[t]he JHE is exactly the same as for GR" and 2) "[p]otential energy is defined in the Newtonian way", what leads you to conclude that you have discovered anything more profound than (a possible already well-known) inconsistency between 'Newtonian gravity' and GR?

Or perhaps 'inconsistency' is too strong a word; 'difference' may be better?

I think it would make more sense to iron out these sorts of things, before tackling the application of GR to the universe (cosmology); after all, 'potential energy' is essentially a useless concept, when GR is applied to the universe.

Or, if you feel otherwise, perhaps you could define 'potential energy', in GR, in a consistent way, where GR is applied to the universe as a whole?

[john hunter]

Dear Nereid,

Your suggestion is reasonable, but I'll need some time to work on things now.

All the best,

John Hunter.

[john hunter]

Dear Nereid,

Thanks, I've had some time to work on things, and the results were presented a few days ago in the new thread (because of the delay) - "supernova - evidence for rescaling". If you refer to the OP of this thread, the new thread seems to follow on from there.

All the best,

John Hunter.