Mordred

That is an example for water which does show how refractive index does change for different wavelengths. Particularly with a material depending upon the materials properties. It is a good example of the dispersion effect So I will grant +1 for that graph and your effort in taking the effort based on our feedback. Now in gravitational lensing or gravitational redshift we do not have the frequency dependency. If I look with a spectrograph at a gravitational lens I do not see or measure a different ratio of change with a frequency dependancy

Good point particularly when it comes to GW waves. +1

As well as providing the same degree of accuracy and flexibility. The Einstein field equations can literally be used for any field theory. Which makes it incredibly useful as you can describe how all fields evolve with the energy momentum relations. At least until quantization becomes important.

Wrong the index of refraction depends upon the wavelength of light. You should really try learning a topic before making wrongful statements. Here is a brief article covering Snells law and dispersion https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.cis.rit.edu/class/simg232/lab2-dispersion.pdf&ved=2ahUKEwiKgobX7r7pAhVIj54KHTzECuAQFjAAegQIAxAB&usg=AOvVaw2BN4rxnCdl4Wu8zkJTi4sJ As previously stated any attempt to employ refractive index to spacetime will fail. Let's try the following thought experiment. The LIGO detector uses lasers in its 4 km arms. The location is fixed yet they calibrate the detector by placing a test weight near each detector. So the only thing that changes is the amount of mass near the detector. Yet the laser paths will experience a time delay. The elevation does not change nor does the local fields except for the addition of mass nearby. It is the mass term that causes the above delay the spacetime path becomes curved. Secondly a rocket ship travelling at near c will also experience time dilation So how does your model account for two rocket ships travelling at different speeds in space away from any gravitational bodies By the Principle of equivalence inertial mass and gravitational mass are indistinguishable from one another. [math] m_i =m_g [/math] nothing I have seen in your model accounts for this. I won't even get into your explanation of electron and photon behavior. You don't even require an EM field to have spacetime curvature or time dilation. All matter and force fields contribute to the mass term. Including mass less particles such as the Higgs boson. There is two main types of mass in GR. Invariant mass or rest mass and variant mass (relativistic or inertial mass}. Your theory doesn't have a chance of succeeding. For several of the reasons myself and others have mentioned.

Why would I ask to keep the frequency of light cobstant ? How would you get gamma rays, microwaves, x rays UV rays or even a color spectrum? I am asking you to learn how dispersion is frequency dependent. Then you would recognize a gravitational lens nor spacetime involves refraction. You have an emitter frequency (or more exact a range of frequencies from a distant star. ) Gravitational redshift affects that wide range of frequencies equally. Where a refractive index would not. Due to dispersion.

And yet I have zero problem understanding time dilation. The problem is explaining it to laymen. (Though it took understanding mean lifetimes and it's connection to the Langrangian) Refactive index is the wrong approach. Try gravitational redshift under refractive index.

Maybe you should look more closely at what causes a refractive index. Ie permittivity of a material for starters then step into how dispersions occur.

A refractive index requires scatterrings. Those scatterrings and the degree of change in angles will involve the wavelength. If I look at an Einstein Ring I will get distrortions that do not depend on wavelength. I have been involved in doing those tests studying the CMB as my speciality is early universe dynamics. In order to get a telescope even the Hubble telescope on must often use a gravitational lens to extend the distance to get deep field imaging. A simple analogy for time dilation would be signal propogation delay. Take a digital signal in electronics you can delay that signal through electrical cross talk. Now extend that analogy to the 18 coupling constants of the standard model of particle physics.

No I am a Professional Cosmologist with degrees in particle physics. I can prove any refractive index treatment of spacetime wrong. I can do the same with any treatment of spacetime as a medium wrong. Lol all I have to do is point out previous research papers. I have even been hired to research refractive indexes by a survey camera manufacturer. That grant paid my income for a year. I have also done spectronomy research on a couple of gravity wells.

No forget refractive index. The correct application is Principle of least action via the Langrangian. Which is completely different from refractive index. How can you have a refractive index when the mean average number density of particles amounts to 5 protons per cubic metre in interstellar space ?

What curves is the principle of least action which relates the potential of the field to the kinetic energy of the particle. If you really want to understand curvature then you need to study the Principle of least action with the geodesic equations. (Do not mistake a field as a medium) a field is an abstract descriptive of values or mathematical objects under a geometry descriptive.) Of course it does. Spacetime has no refractive index... Particles behave in accordance to how they couple with a field or other fields. The couplings is what lead to the mass terms. Mass is resistance to inertia change.

No light doesn't require a medium to travel. This is where it differs from sound waves. It was this very thought that led to Eather theories. The Michelson and Morley experiment is one of the numerous tests that proved the medium view incorrect.

Spacetime isn't a medium. Any treatment of spacetime as a medium will be easily proven inaccurate to observational evidence. As to the first part. The geodesic equations do not involve electrons. A good example is light curves in the FLRW metric. (Universe geometry) however after the CMB there are no free electrons and this no Compton scatterring. How one describes mass must also work in cosmology applications as well as near massive bodies. GR and the FLRW are fully compatible theories that do not depend on any medium or specific particle composition.

Correct and never examined the effect of frequency in accordance to Snell's law. Let alone the one way two effects of a medium on light as per the M and M experiments. (Lol a little side note I had the opportunity to prove a peer reviewed article wrong on applying Snell's law to describe gravitational lensing to a PH.D in astrophysics. He pulled his article off Arxiv)

Spacetime curvature does not involve any refractive index. The mass term cannot be described under refractive index. Or radiation pressure (pressure has directional components).

The statement of the photon gravitating to a higher refractive index in the above will not work for gravitational lensing. Different frequencies of light respond differently in a medium. (Prism being one example) A Gravitational lens doesn't have the same effect. Ie a spectrograph looking at a gravitational lens will not see the same prismatic effect. Spacetime curvature doesn't depend on frequency. (If you try to treat spacetime as a medium you will invariably get the wrong answers) I could easily falsify any medium association.

No I am describing a rank two tensor under GR ( though just the starting steps to understand a rank two tensor). I hadn't gotten into components of a vector. (A special rank two tensor would be the Dyad.. The reason you need a rank two tensor describe gravity is that you a gradient to describe gravity.

Well that would certainly involve a lot of antisymmetry relations. Acceleration caused a rotation due to rapidity. Torsion would give antisymmetry to the metric tensor. Ie to describe torsion using the metric tensor you would have to specify a direction of rotation. What you actually need is a covector vector and a vector. The covariant vector is the column vectors while the vector is the row vectors. Using the two vectors above will preserve invatiance under coordinate transformations. Gravity itself is a form of flux of the energy momentum stress tensor. With the Minkowskii tensor you have already made a coordinate choice (cartesian) so you can use the inner product of two vectors. Which will return a scalar value [math]\mu\cdot\nu=s[/math] the Minkowskii tensor is orthogonal all orthogonal groups are symmetric and commute. [math]\mu\cdot\nu=\nu\cdot\mu[/math] However this would not be invariant under coordinate transformation so the column vector would use a covector.

Somehow I don't want to know. 😖

Every physics theory has competitive theories this is true of inflation. The CMB itself is supportive evidence through big bang nucleosynthesis of the BB. One of the difficult things to explain is how the supercooling due to rapid expansion and reheating due to the inflation slow roll leads to the metalicity values measured at z=1090. When you get right down to it the percentages match those predicted by inflation and quite frankly limit the range of viable inflation models. So it really doesn't matter what one believes. The only thing that matters is what observational evidence tells us. If you want a listing of viable inflation models that match observational evidence (though the last update was 2013.) See here https://arxiv.org/abs/1303.3787 The opening section explains the criteria. Personally I'm a fan of a single scalar field with a low kinetic term Higgs inflation. However my opinion doesn't mean it's factual. Lol at least that one is still viable according to Planck datasets.

It describes the probability wavefunctions. An oscillator isn't restricted to object motion but can also be used to describe any repeating varying value. A sinusoidal waveform in electronics is a good example.

With the uncertainty principle one cannot accurately measure the position and momentum of a particle at the same time. Measuring one observable P or Q will interfere with the other. Also the more accurately you measure one the less accurate you can determine the other. Both observable's will have a probability amplitude.

I like your reference four paper, there is several Langrangians in that paper I will latex later on to have a handy copy of them. I also like what you did with the overbrace and underbrace. I don't see any problems thus far

Looks good thus far the reference 7 page 11 equation 47 has the covariant derivative of the graviton propogator, as your employing the same tensors you should be be good.

See here for further detail you will also find the one loop vacuum polarization propogator handy https://arxiv.org/abs/1504.00894 Lol this article does mention the k term