Mordred

Well physics does apply the mathemical definition. However as gauge groups tensors etc became more common. The need for higher dimensions such as M theory etc caused the commonly understood definition to be refined to include degrees of freedom. Kaluzu Klien 5d is another example. Anyways your theory specifies 4d Spatial dimensions which in itself I have no issue with. An example of this could be the addition of the circle group U(1) under gauge group theory. Which describes a topological space embedded on 3d space. The mathematics in your model is sorely lacking in needed details. You need to start with mathematically defining your two layers. Then describe the connection between the two layers mathematically. Images are insufficient. You should be able to mathematically describe your theory completely without the use of a single image. Also I will not open your xlsx document you linked. Please convert to off. This is incorrect. If you look at expansion itself you will find it is homogeneous and isotopic. (No preferred direction and location) A blast wave has a point of origin and a preferred direction. Observational evidence does not support this. If you take the galaxies as reference points expansion causes separation of those galaxies without any change in the angles between multiple galaxies. You cannot get this from a blast wave that is inhomogeneous and anisotropic. I would honestly suggest you study the FLRW metric of the LCDM model. If you did you would realise that cosmology applies the thermodynamic laws and the subsequent fluid equations. Ie via the ideal gas laws of a adiabatic and isentropic expansion.

Please don't make the mistake of thinking science stopped at Einstein with regards to relativity. I lost count how often I hear quotes from Einstein, Lorenz, Minkowskii etc. They become largely irrelevant with current research. We have extreme precision tests that GR is highly accurate. Even going so far as to measure time dilation at a distance of a single meter. Your paper needs far far more work if it ever has a chance of overturning relativity. ( not that I can see anything in it that has a remote chance as written thus far)

Use the mathematical definition. You will find you will need this to understand higher dimensions such as those in configuration and parameter space. The key is the effective degrees of freedom or parameters. Obviously every professional physicist disagrees with your objection as time is a mainstream accepted dimension under relativity. This is because time can be graphed on a spacetime graph. One can treat any graph under a configuration or parameter space. Not all spaces are topological spaces. Though under GR8 you have coordinate time. As well as proper time. This is because every coordinate in a field has its own potential. In a simplification each coordinate can have its own rate of time that depends upon the potential of its locality.

Not quite. You need to study the Principle of equivalence in regards to the time dilation of moving bodies. The shorthand for the principle is inertial mass is equivalent to gravitational mass. [math] m_i=m_g[/math] Relativistic moving bodies gain inertial mass (used to be called relativistic mass) however the current accepted term is the variant mass. The rest mass is now described as in invariant mass. (Mass all observers can agree on). The variant mass obviously depends on the observer. If you have any form of mass including gravitational mass then you will always have time dilation. However miniscule. To give you a clear example time dilation has been measured at a single meter difference in elevation. https://www.nist.gov/news-events/news/2010/09/nist-clock-experiment-demonstrates-your-head-older-your-feet For rotating bodies you need to study the Sagnac effect. https://en.m.wikipedia.org/wiki/Sagnac_effect Coincidently this is another test against the eather theories. PS glad to see your using the term fields as well as starting to look more into current studies of relativity. +1. This is an open source textbook on SR that the author wrote to cover many of the misconceptions common to science forums. The author is a PH.D who specializes in SR and GR. I have had numerous conversations with him over the last decade or so. http://www.lightandmatter.com/sr/

Correct now gravity is described under the Stress energy momentum tensor. This under GR is the portion that in essence curves the metric. So here is a simplified sample showing the Dust solution. Dust is matter only equation of state p=0. Dust solution no force acting upon particle. (No acceleration) [latex] T^{\mu\nu}=\rho_0\mu^\mu\nu^\mu[/latex] [latex]T^{\mu\nu}x=\rho_0(x)\mu^\mu(x)\mu^\nu(x)[/latex] Rho is proper matter density Four velocity [latex]\mu^\mu=\frac{1}{c}\frac{dx^\mu}{d\tau}[/latex] Leads to [latex]ds^2=-c^2d\tau^2=-c^2dt^2+dx^2+dy^2+dz^2=-c^2dt^2(1-\frac{v^2}{c^2})^\frac{1}{2}=\frac{1}{\gamma}[/latex] [latex]T^{00}=\rho_0(\frac{dt}{d\tau})^2=\gamma^2\rho_0=\rho[/latex] [latex]\rho[/latex] is mass density in moving frame. [latex]T^{0i}=\rho_0\mu^o\mu^i=\rho^o\frac{1}{c^2}\frac{dx^o}{d\tau}\frac{dx^2}{d\tau}=\gamma^2\rho_0\frac{\nu^i}{c}=\rho\frac{\nu^i}{c}[/latex] [latex]\nu^i=\frac{dx^i}{dt}[/latex] [latex]T^{ik}=\rho_0\frac{1}{c^2}\frac{dx^i}{d\tau}\frac{dx^k}{d\tau}=\gamma^2\rho\frac{\nu^i\nu^k}{c^2}=\rho\frac{\nu^i\nu^k}{c^2}[/latex] Thus [latex]T^{\mu\nu}=\begin{pmatrix}1 & \frac{\nu_x}{c}&\frac{\nu_y}{c} &\frac{\nu_z}{c} \\\frac{\nu_x}{c}& \frac{\nu_x^2}{c} & \frac{\nu_x\nu_y}{c^2}& \frac{\nu_x\nu_z}{c^2}\\ \frac{\nu_y}{c}& \frac{\nu_y\nu_z}{c^2} & \frac{\nu_y^2}{c^2}& \frac{\nu_y\nu_z}{c^2}\\ \frac{\nu_z}{c} &\frac{\nu_z\nu_x}{c^2}&\frac{\nu_z\nu_y}{c^2}&\frac{\nu_z}{c^2}\end{pmatrix}[/latex]

Here is a thought experiment. Let's start with an expression. "Matter tells spacetime how to curve, spacetime tells matter how to move" So let's look closer at the first part. First remove all matter (the full standard model of particles). End result curvature equals zero zip Nada. Now when you add other fields such as the Higgs field, weak field EM field, Strong field. Now you can get curvature bit only if the distribution of those fields is Non uniform. (Anistropic) I mentioned the path of least action previously in this thread. It is this principle that determines the path taken The descriptive spacetime is curved is actually a sloppy descriptive. What really is curved isn't the volume. What curves is the Geodesic paths for massless particles this is the null geodesic. The fields of the standard model and how they interact or couple to the particle in motion is what determines the amount of curvature of the geodesic path. Space is just volume. Spacetime is a metric that describes space with time as a dimension under a geometry basis. However spacetime without particles is simply a volume.

Energy doesn't exist on its own. It simply the ability to perform work. Space devoid of all particles is simply a volume. Light can transverse that volume without the need of a medium or eather. Space or spacetime isn't a medium to have permeability. It isn't some mysterious fabric which you often hear described in pop media or poorly written literature. It is far more than semantics with regards to the actual physics and the relevant applicable formulas. A term that no physicist would argue is to use the term field. This is a mathematical descriptive that entails any set of values or mathematical objects such as vectors, tensors, spinors etc under a coordinate treatment. In essence a field is an abstract mathematical object.

I suggest you look at velocity dispersion in astrophysical measurements. Quite frankly dispersion occurs in galaxy clusters etc. If you have a medium light no longer propogates at c.

The correct definition for a dimension is an independent mathematical variable or object. The X,y ,z coordinates are three spatial dimensions while time becomes the fourth dimension. All four variables can change value without affecting the other. Though relativity gives time dimensionality of length by using the interval ct.

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.

Cool paper but off topic to this thread.

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.

Bingo

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.

A good tool is calculus of variations to understanding the Langrangian.

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.

The Langrangian in QM and QFT or even GR applies the same principle. A good example is in GR if you take a curve you can find infinitisimal portions of that curve that is approximately flat.