Refractive Field Theory of Gravity

[utesfan100]

Do you think the space is not continuous as in GR but discrete as in GR ?
What kind of a structure is the space then ?
The observation of the Gamma Ray Bursts suggest there isn't a structure of the space. How can you find the refractive index if the space is empty and homogeneous ?
http://www.centauri-dreams.org/?p=18718

This thread is focusing on the continuous limit of my theory. As such, this space is continuous in space-time.

This space is not curved, but the time dilation/index of refraction can be determined by observing the difference in clock rates at different gravitational potentials. It is also not empty, as it contains the CMBR and the gravitational field.

As for speculation on how I think space will be modeled in the final form of this theory, eventually I hope to map pseudospace-time to the Hurwitz integers (on the Plank scale), paired with a space-pseudotime phase space over the algebra of the split-octonions. I have not yet figured out how to make this scale shrink. This is because I also expect the redshift to eventually be explained as an increase in the fine structure constant with the Hubble expansion. This paragraph is speculation, in response to a direct question, and not part of the theory being defended here.

Edit: The linked article suggests that the final lattice must be much smaller than I suggested above.

[utesfan100]

I wish to expand on what I meant in post 90 by expanding the conversation. I have a sketch of how the full theory impacts cosmology.

The first impact is that mass/energy is being generated (with an equal and opposite field), so the temperature/density values will be less than standard models for a given radius. To match the predictive value of the current theories (relative to neucleosynthesis) it is said that only the photon to baryon ratio must remain the same. I'll take these ratios as an empirical fact.

With a smaller density and temperatures, however, it would seem that these reactions would be slower, and thus the expansion slower than standard models. Specifically, I anticipate a pure DeSitter space.

Originally, I anticipated that the fine structure constant started at 1, and shrinking at a rate equal to the Hubble constant since the origin of the universe, a single Plank radius blackhole. This would have given an age of the universe of 4.9 Hubble times, or 68 Billion years.

Unfortunately this requires a change in the fine structure constant six orders of magnitude larger than observations allow.

http://tf.nist.gov/general/pdf/2280.pdf

[grav]

This is also the value of the precession for GR.The singular surface a gravitationally collapsed object is expected to be 1/4 the size of an event horizon from GR.

From the OP. GR predicts for precession, doesn't it? If your r_g is 4 times smaller than r_s, then shouldn't

[utesfan100]

Gr predicts for precession, doesn't it? If your r_g is 4 times smaller than r_s, then shouldn't

The precession of Mercury is given in terms of GM_0/c^2, which is similar to my r_g=GE(∞)/c^4. Your formula for GR has twice too much precession.

http://farside.ph.utexas.edu/teachin...n/node116.html

The difference between my theory and GR is not at the Newtonian/PPN limit, where both have the same r_g, but at the singularity. GR predicts the horizon to occur at twice this value. I predict a singularity at half this value.

[grav]

The precession of Mercury is given in terms of GM_0/c^2, which is similar to my r_g=GE(∞)/c^4. Your formula for GR has twice too much precession.

Oh right, I forget r_s = 2 GM/c^2, so yours should only be twice as great.

The difference between my theory and GR is not at the Newtonian/PPN limit, where both have the same r_g, but at the singularity. GR predicts the horizon to occur at twice this value. I predict a singularity at half this value.

But r_g = GM/2c^2 is the singularity according to your theory, 1/4 r_s, right?

[utesfan100]

But r_g = GM/2c^2 is the singularity according to your theory, 1/4 r_s, right?

No. I define r_g to be GE(∞)/c^4, so I don't have to worry about that annoying factor of 2, and then find the singularity is at r_g/2.

r_g/2 is 1/4 r_s.

[grav]

No. I define r_g to be GE(∞)/c^4, so I don't have to worry about that annoying factor of 2, and then find the singularity is at r_g/2.

r_g/2 is 1/4 r_s.

Right, okay. What is E(∞) for the sun? How do you find it?

[utesfan100]

Right, okay. What is E(∞) for the sun? How do you find it?

Using classical mechanics we have measured M(∞)_sun=1.98892 × 10 E30 kg, and c=299 792 458 m/s.

Thus E(∞) = M(∞)c^2 = 1.78755 × E47 J.

The differences between this value and the value my theory predicts at r accounts for the parameter beta in the PPN formalism. Thus, rather than introduce length contraction, I increase the gravitational energy of the source.

[grav]

Using classical mechanics we have measured M(∞)_sun=1.98892 × 10 E30 kg, and c=299 792 458 m/s.

Thus E(∞) = M(∞)c^2 = 1.78755 × E47 J.

But your theory predicts that we would measure different acceleration at different r from the square inverse law, so different M using classical mechanics at different r, depending upon the energies of both gravitating bodies in the field, each of which vary with r, right?

Going by what you have here, E(∞) = M(∞) c^2, where M(∞) is the measured value for the sun, so M(∞) = M_sun, what we measure to first order anyway. Substituting that into your equation for precession, then, we have

6 pi r_g / p = 6 pi (G E(∞) / c^4) / p = 6 pi (G M_sun / c^2) / p,

whereas GR gives 6 pi r_s / p = 6 pi (2 G M_sun / c^2) / p. Your value still seems to be half as great as what it should be.

[utesfan100]

whereas GR gives 6 pi r_s / p = 6 pi (2 G M_sun / c^2) / p. Your value still seems to be half as great as what it should be.

According to the link I provided in post 124, I think you forgot to apply the Sz operator, which I usually don't pay attention to, and don't want to go into the details at this time.

[grav]

According to the link I provided in post 124, I think you forgot to apply the Sz operator, which I usually don't pay attention to, and don't want to go into the details at this time.

Oops, oh yeah. That Sz operator gets me every time lol. I'll get some rest and start again tomorrow.

[czeslaw]

The refractive index is caused by a space which has to have a properties which allows to interact with a photons in a defined way. How is created such a medium for photons ?

[utesfan100]

The refractive index is caused by a space which has to have a properties which allows to interact with a photons in a defined way. How is created such a medium for photons ?

The issue you raise applies to the model in the article you posted. This is not an accurate picture of the refractive field theory.

In my theory the refractive index is not caused by space. Space is Minkowskian, flat. Unlike GR, in the standard interpretation or the version in the article you posted, there is no spatial curvature.

The PPN effects of curvature are produced by a gravitational field with a well defined energy density. This requires us to include the weight of the gravitational field.

It is this actual gravitational field that is the medium that has an index of refraction.

[czeslaw]

The PPN effects of curvature are produced by a gravitational field with a well defined energy density. This requires us to include the weight of the gravitational field.

It is this actual gravitational field that is the medium that has an index of refraction.

Here I agree. (Some people say the gravitational field = space-time). Lets write about the gravitational field only. It is very simple idea how to explain the Dark Matter problem if the gravitational field is something.
My particular question is: how the gravitational field is created then around a massive particle ? What is Vacuum ?

[utesfan100]

Here I agree. (Some people say the gravitational field = space-time). Lets write about the gravitational field only. It is very simple idea how to explain the Dark Matter problem if the gravitational field is something.

The gravitational field does a better job explaining dark energy, as it has a negative energy density. When positive mass formed from the vacuum, an equal and opposite Dark Energy would be required in the gaps of the Large Scale structure of the universe.

My particular question is: how the gravitational field is created then around a massive particle?

After the initial separation into massive regions and dark energy regions, massive regions should collapse further, generating a negative energy gravitational field and gaining internal energy.

This separation of positive and negative energy is irreversible.

What is Vacuum ?

My theory has no vacuum. It has a Minkowskian space-time that has an independent axiomatic existence to define space and time. This flat space is filled with CMBR radiation and gravitational fields everywhere.

[utesfan100]

Substituting that into your equation for precession, then, we have

6 pi r_g / p = 6 pi (G E(∞) / c^4) / p = 6 pi (G M_sun / c^2) / p

Ok. For the Sun, and the values listed in post #128, and G = 2/3 E-10, give r_g = 1471 m.
For Mercury p=5.55 E10 (a(1-e^2)).
δ = 6 pi r_g / p = 5 E-7
Now we multiply by θ/T; θ=1 rad=2.1 E5 arcseconds and T = 0.0024 centuries; to get:
δ = 43.7 arcsec/century

A more accurate treatment would give the well known 42.98 value.

[grav]

Okay, I went a different route. I made a gravity simulation program a while back that is sensitive enough to measure precession, so I put your value of E(r) in for the sun. Basically this just amounted to substituting M_sun with M(r) = M_sun / [1 - G M_sun / (2 c^2 r)] according to your equation for E(r) = E(∞) / [1 - G E(∞) / (2 c^4 r)], where E(∞) = M(∞) c^2 and M(∞) is the measured value M_sun, and r is the instantaneous distance between their centers. It gives about 1 / 12 the precession for Mercury, giving 42.96 arcseconds per century if I instead use M(r) = M(∞) / [1 - 6 G M(∞) / (c^2 r)]. What do I need to do to get the rest of the precession?

[utesfan100]

I suppose I would need to see the program to answer these questions. I presented my Lagrangian and the solutions based on them. This gives the values in my previous post.

Okay, I went a different route. I made a gravity simulation program a while back that is sensitive enough to measure precession, so I put your value of E(r) in for the sun. Basically this just amounted to substituting M_sun with M(r) = M_sun / [1 - G M_sun / (2 c^2 r)] according to your equation for E(r) = E(∞) / [1 - G E(∞) / (2 c^4 r)], where E(∞) = M(∞) c^2 and M(∞) is the measured value M_sun, and r is the instantaneous distance between their centers. It gives about 1 / 12 the precession for Mercury, giving 42.96 arcseconds per century if I instead use M(r) = M(∞) / [1 - 6 G M(∞) / (c^2 r)]. What do I need to do to get the rest of the precession?

I am not sure where this comes from. The source I have gives a value for GR of:
M(r) = M(∞) / [1 - 3 L^2 / (c^2 r^2)]
Where L is the orbital angular momentum, with L^2 roughly GM(∞)p, where p is the semilatus rectum. (The first order corrective terms for L are not needed here, as this is already a first order correction). This includes the time dilation effects.

http://farside.ph.utexas.edu/teachin...n/node116.html

It looks like you are modeling a Newtonian f this is supposed to be modeling the force, you need to include the increase in energy of Mercury with r. e(r)=e(∞) / [1 - G E(∞) / (2 c^4 r)]^2, so the force is proportional to [1 - G E(∞) / (2 c^4 r)]^-3.

Now, G E(∞)=L^2 c^2/r, and a derivation similar to that in the link below so this really should be M(r)=M(∞) / [1 - L^2 / (2 c^2 r^2)]^3

This should get you half the value.

An equal portion should come from properly including a time dilation of [1 - G E(∞) / (2 c^4 r)]^-2.

[czeslaw]

The gravitational field does a better job explaining dark energy, as it has a negative energy density. When positive mass formed from the vacuum, an equal and opposite Dark Energy would be required in the gaps of the Large Scale structure of the universe.

After the initial separation into massive regions and dark energy regions, massive regions should collapse further, generating a negative energy gravitational field and gaining internal energy.

This separation of positive and negative energy is irreversible.

My theory has no vacuum. It has a Minkowskian space-time that has an independent axiomatic existence to define space and time. This flat space is filled with CMBR radiation and gravitational fields everywhere.

In general I agree. But how massive region knows that it has to collapse ? How is the information transfered by the gravitational field ? What is the structure of the gravitational field that it allows to transform the information about the mass of the body ?

[utesfan100]

In general I agree. But how massive region knows that it has to collapse ?

This will happen when there is no force to counter the inward gravitational pressure around a positive mass.

How is the information transferred by the gravitational field ? What is the structure of the gravitational field that it allows to transform the information about the mass of the body ?

This thread focuses on the continuous limit of this theory. In the continuous limit, the field has an energy and momentum. Like the classical electromagnetic field, it is its own structure.

To bring the quantum aspects of the theory into this discussion, how I think it really addresses these questions, would introduce more topics than I can manage to defend in one 30 day thread. So I saved that aspect of the theory for next month

[czeslaw]

This will happen when there is no force to counter the inward gravitational pressure around a positive mass.

This thread focuses on the continuous limit of this theory. In the continuous limit, the field has an energy and momentum. Like the classical electromagnetic field, it is its own structure.

To bring the quantum aspects of the theory into this discussion, how I think it really addresses these questions, would introduce more topics than I can manage to defend in one 30 day thread. So I saved that aspect of the theory for next month

OK. The gravitational field may have a refractive index if it is the same as vacuum with its energy. The energy has its relativistic mass and has to have its relative "weight". We observe it as Dark Matter effect around a galaxy. But it is true if gravitational field =Vacuum with its energy only. Do you see another possibility ?

[utesfan100]

OK. The gravitational field may have a refractive index if it is the same as vacuum with its energy. The energy has its relativistic mass and has to have its relative "weight". We observe it as Dark Matter effect around a galaxy. But it is true if gravitational field =Vacuum with its energy only. Do you see another possibility ?

I see the vacuum as the background Lorentzian space. It is not a dynamic object, only a coordinate chart. The field is a distribution of energy within this chart. This weight alters the inverse square law, and contributes half of the precession of Mercury, as I am discussing with grav.

It has a negative energy density, so it provides a repulsion, thus it does not explain the extra attraction attributed to dark matter. It is a far better candidate for Dark Energy, which I model as a by product of the initial formation of gravitationally interacting units, equal and opposite to the matter generated.

[czeslaw]

The energy is negative if you compare it with a higher level of the energy. The precession of the Mercury is caused by a larger weight = Mass of the Mercury + Relativistic Mass of the gravitational field between the Sun and Mercury. Here the energy of the gravitational field is positive, I think. The weight of the gravitational field accelerates the precession:
http://en.wikipedia.org/wiki/Two-bod...ral_relativity

[icarus2]

It has a negative energy density, so it provides a repulsion, thus it does not explain the extra attraction attributed to dark matter. It is a far better candidate for Dark Energy, which I model as a by product of the initial formation of gravitationally interacting units, equal and opposite to the matter generated.

Hello! In my opinion,

Centripetal force effect in the galaxy from dark matter(negative mass) halo out of the galaxy

Computer simulation :
http://www.youtube.com/watch?v=ylEi2gpnD08

If the negative energy(mass) is disposed at the outline, the test mass vibrates, and a kind of restoring force (This corresponds to the centripetal force when considering rotation of the galaxy) exists.

This suggests that the halo, dark matter (negative mass(energy)) of the external Galaxy could get additional effects of centripetal force to the inner Galaxy.

More information.
http://www.bautforum.com/showthread....27#post1765927

[utesfan100]

Hello! In my opinion,

Centripetal force effect in the galaxy from dark matter(negative mass) halo out of the galaxy

Computer simulation :
http://www.youtube.com/watch?v=ylEi2gpnD08

If the negative energy(mass) is disposed at the outline, the test mass vibrates, and a kind of restoring force (This corresponds to the centripetal force when considering rotation of the galaxy) exists.

This suggests that the halo, dark matter (negative mass(energy)) of the external Galaxy could get additional effects of centripetal force to the inner Galaxy.

More information.
http://www.bautforum.com/showthread....27#post1765927

While such a halo may exist as a residue of the process that generates dark energy, in the present theory the negative energy density is attributed to the gravitational field, and should be strongest at the heart of the galaxies, not the extremities.

[icarus2]

While such a halo may exist as a residue of the process that generates dark energy, in the present theory the negative energy density is attributed to the gravitational field, and should be strongest at the heart of the galaxies, not the extremities.

Oh, I'm sorry! I misinterpret it.

[utesfan100]

The energy is negative if you compare it with a higher level of the energy. The precession of the Mercury is caused by a larger weight = Mass of the Mercury + Relativistic Mass of the gravitational field between the Sun and Mercury. Here the energy of the gravitational field is positive, I think. The weight of the gravitational field accelerates the precession:
http://en.wikipedia.org/wiki/Two-bod...ral_relativity

Gravitational energy is related to mass by E=mc^2. Negative energy means that the acceleration/velocity is opposed to the force/momentum being carried. It is not a relation to some potential. I provide an outline for the derivation of the energy density in post #84.

In my theory, Mercury's gravitational mass changes, since its's velocity changes its energy, and the Sun has an increase in observed mass at some finite radius, due to the removal of the negative weight of the field outside that radius. This change in the inverse square law alone provides half the precession of Mercury due to the classical theorem of revolving orbits.

[czeslaw]

The deflection of light by the Sun due to Newton gravity is also half the deflection due to Einstein GR.
I agree with an idea of the refractive index of the gravitational field but only if it has a vacuum energy with its relativistic mass.

[utesfan100]

I agree as follows:

The deflection of light by the Sun due to Newton gravity is also half the deflection due to Einstein GR.
I agree with an idea of the refractive index of the gravitational field but only if it has a vacuumnegative energy with its density, resulting in a relativistic mass density.

A vacuum has no energy, and contains no field.

[grav]

I suppose I would need to see the program to answer these questions. I presented my Lagrangian and the solutions based on them. This gives the values in my previous post.

I am not sure where this comes from. The source I have gives a value for GR of:
M(r) = M(∞) / [1 - 3 L^2 / (c^2 r^2)]
Where L is the orbital angular momentum, with L^2 roughly GM(∞)p, where p is the semilatus rectum. (The first order corrective terms for L are not needed here, as this is already a first order correction). This includes the time dilation effects.

http://farside.ph.utexas.edu/teachin...n/node116.html

It looks like you are modeling a Newtonian f this is supposed to be modeling the force, you need to include the increase in energy of Mercury with r. e(r)=e(∞) / [1 - G E(∞) / (2 c^4 r)]^2, so the force is proportional to [1 - G E(∞) / (2 c^4 r)]^-3.

Now, G E(∞)=L^2 c^2/r, and a derivation similar to that in the link below so this really should be M(r)=M(∞) / [1 - L^2 / (2 c^2 r^2)]^3

This should get you half the value.

In terms of the instantaneous orbital speed v, a = a_classical / (1 - 3 v^2 / c^2) gives the precession as well as does a = a_classical / (1 - 6 G M / (r c^2)]. I know it seems that for a nearly circular orbit we should have v = sqrt(G M / r), but v and r are the instantaneous values in each of these cases which are constantly changing during the orbit, not the mean radius and speed, so they do not relate directly as they would for the mean speed and radius of a circular orbit. For instance, using the mean speed and/or radius rather than the instantaneous values gives no precession, but just a constant larger value for a, only acting as if the mass of the body is slightly greater, but the gravity would act classically otherwise.

If you are considering the angular momentum with L^2, which should use some form of the instantaneous v, then yes, 1 / [1 - L^2 / (2 c^2 r^2)]^3 would give half the precession. But if instead you are using 1 / [1 - G E(∞) / (2 c^4 r)]^3 in terms of the instantaneous distance between the centers of the bodies during orbit, then you only get 1/4 of the precession. The equations you gave for E(r) and e(r) were both in terms of the instantaneous position r in the field, not the instantaneous speed. Using that gives only 1/4 the precession. But also, since the force between the bodies is F = G E(r) e(r) / r^2, wouldn't e(r) divide out when determining the acceleration of the object in the first body's field, leaving just a = G E(r) / r^2? If not, why not and what is the acceleration for each of the two bodies in terms of E(r) and e(r)?

An equal portion should come from properly including a time dilation of [1 - G E(∞) / (2 c^4 r)]^-2.

Okay, that would be the gravitational time dilation I presume and provide 1/6 of the precession. How does gravitational time dilation make the acceleration of gravity stronger on an object? What about the kinetic time dilation due to the motion of the object? Shouldn't that be figured in also?