Mordred

No it also applies to every other field strong, weak, Higgs, gravitational etc.

As to instantaneous action at a distance it's well established the speed of information limit (c) always applies.

Not sure how you define instantaneous as rates of change in the EM field have been measured to extremely small units of measure. Also not sure on what your referring to on strong disagreement with relativity with regards to heat. However you may may not experimental evidence however there may be possible research and experiments already done you can draw upon via arxiv. It's common practice to draw upon other lines of research and experiments done by others as supportive evidence provided those lines of research are applicable.

Christoffels for the FLRW metric in spherical coordinates. \[ds^2=-c(dt^2)+\frac{a(t)}{1-kr^2}dr^2+a^2(t)r^2 d\theta^2+a^2(t)r^2sin^2d\phi\] \[g_{\mu\nu}=\begin{pmatrix}-1&0&0&0\\0&\frac{a^2}{1-kr^2}&0&0\\0&0&a^2 r^2&0\\0&0&0&a^2r^2sin^2\theta \end{pmatrix}\] \[\Gamma^0_{\mu\nu}=\begin{pmatrix}0&0&0&0\\0&\frac{a}{1-(kr^2)}&0&0\\0&0&a^2r^2&0\\0&0&0&a^2r^2sin^2\theta \end{pmatrix}\] \[\Gamma^1_{\mu\nu}=\begin{pmatrix}0&\frac{\dot{a}}{ca}&0&0\\\frac{\dot{a}}{ca}&\frac{a\dot{a}}{c(1-kr^2)}&0&0\\0&0&\frac{1}{c}a\dot{a}r^2&0\\0&0&0&\frac{1}{c}a\dot{a}sin^2\theta \end{pmatrix}\] \[\Gamma^2_{\mu\nu}=\begin{pmatrix}0&0&\frac{\dot{a}}{ca}&0\\0&0&\frac{1}{r}&0\\\frac{\dot{a}}{ca}&\frac{1}{r}&0&0\\0&0&0&-sin\theta cos\theta \end{pmatrix}\] \[\Gamma^3_{\mu\nu}=\begin{pmatrix}0&0&0&\frac{\dot{a}}{ca}\\0&0&0&\frac{1}{r}\\0&0&0&cot\theta\\\frac{\dot{a}}{c}&\frac{1}{r}&cot\theta&0\end{pmatrix}\] \(\dot{a}\) is the velocity of the scale factor if you see two dots its acceleration in time derivatives. K=curvature term Newton limit geodesic \[\frac{d^r}{dt^2}=-c^2\Gamma^1_{00}\] Christoffel Newton limit \[\Gamma^1_{00}=\frac{GM}{c^2r^2}\] Covariant derivative of a vector \(A^\lambda\) \[\nabla_\mu A^\lambda=\partial_\mu A^\lambda+\Gamma_{\mu\nu}^\lambda A^\nu\]

If you understood how robust and accurate models are developed, then you would give thanks to anyone that attempts to debunk your theory under development. That's precisely how one develops a good strong working theory. A good physicist tries to debunk his own theories as well. For any evidence counter to his theory or mathematics etc. That same theorist would seek ways to explain or improve his theory to cover a given experiment that ran counter to it previously. I come up with theories all the time. I typically debunk my own and spend far more effort to debunk it than build it more often than not.

Agreed, on that I tend to think more on global distributions lol which makes sense as that's my field as a cosmologist lol so oft forget to recall some of the metrics of localized spacetimes when replying to threads

Here's the thing how the FLRW determines it's curvature terms differs from GR. It still uses GR and is fully compatible with GR however it's curvature is based on the critical density formula. It looks specifically at pressure and energy density relations. The Schwartzchild solution is static to depend on radius only. IN THE critical density formula it a matter solution to determine when the universe will expand or collapse. It is the actual density compared to that matter only solution for a value that determines if the universe is flat actual density perfectly matches the critical density. But pressure really means the energy density term coupled with the equation of state. The biggest difference is whether the universe is curved or not has nothing to do with localized spacetime that lends itself to gravity effects. It's mass and energy distribution is always uniform. That's a huge difference from spacetimes described around massive bodies. With what described above no you haven't as stated the two will always different from one another in mass terms. The weak equivalence principal though it applies isn't particularly involved the mass that would lend itself to gravity is uniformly distributed. So under Newtons Shell theorem gravity is zero in a uniform mass/energy distribution. That is certainly not a Minkowsii treatment. The curvature term of the Global metric also doesn't have the same time dilation effects that the Minkowsii metric does on a global scale. It's mass distribution being uniform (that includes observational evidence too huge to list them all). Doesn't affect time not like a blackhole does. That's a localized anistrophy which has a tidal force (gravity). Best to think gravity as the result of the stress energy tensor for gravity effects rather than it's curvature. The FLRW metric using whe Newton limit the only entry is the T^(00) entry. The mass/energy is uniform so only that entry really applies Try that under Minkowsii and be able to produce curvature to get gravity. All observational evidence supports the uniform mass distribution.

That I agree with, neither can the Minkowsii either...

By claiming to explicitly producing either the FLRW metric and the Minkowsii metric. Both of which are homogeneous and isotropic. The term explosion in vector algebra in and of itself is not homogeneous and isotropic. So how do you possibly combine the two to reproduce a homogeneous and isotropic field ? The only way to do so is to factor out the influences that causes the divergences . In essence eliminate the vector field to restore the original metric. Take an example if you perform any math operation on a matrix or tensor you produce a new tensor or matrix.. THE Minkowsii metric is a tensor so performing any math operation on it produces a new tensor.

Your claim of the Schwartzchild metric for example of homogeneous and isotropic is incorrect. Spherical coordinates are only locally homogenous and isotropic. That's part of the issue. Spherically symmetry is not the same thing as homogeneous and isotropic That's without having a constant vector. Now in your mathematics post your constant velocity vector without anything else from an explosion. Then apply your vector dot products. Let's use an example of parallel transport under the weak equivalence principle. Doesn't matter if the bodies are freefalling towards the CoM or away from the center of mass the two objects will approach one another as they near the center of mass. They will move apart as the radius from CoM increases. Now no forces are involved well the pseudo tidal force is aka gravity in the first case. The moving away portion is simply for symmetry . So ask yourself this as imploding is symmetric with explosion under change in sign. Why wouldn't the Schwartzchild metric be usable for an exploding universe from some central point ? Now does any of this describe the orthonormality of the Minkoskii metric. NO IT DOES NOT. Can we perform transformations to restore orthonormality ? Yes we can the process is the same for renormalization in any gauge theory including the renormalized Hamilton. One of the most useful visuals to understand vector field divergence is to take a slow moving propeller in water. If the spinors remain the same radius from 0,0 that field is not divergent. If they move away or approach it is divergent or convergent. Now in the Minkowskii metric when you perform a transformation to restore the metric that means the metric altered (time dilation/,length contraction). However the Spherical coordinates is not the Minkowskii metric to begin with its coordinate basis is not orthonormal. However any theory must not depend on coordinate choice. If any quantity depends on coordinate choice then you have an artifact of the metric. The event horizon is one example. The Minkowsii metric has numerous limitations in this regard . Those limitations directly apply to why the Schwartzchild metric is used in even the weak field Newton limit for spacetimes such as those produced by planets and stars. Had you syated you could use the Schwartzcild metric to describe an exploding universe I wouldn't have an issue with that by itself. I simply would tell you that wouldn't be our universe due to the mass distribution not supporting an explosion nor would the temperature history however mathematically dealing just with the metric I wouldn't have an issue. At least until you start getting into the Christoffels etc (the christoffels are different from the FLRW Christoffels as well as for the Minkowskii and Schwartzchild. As the Rheimann curvature tensors is one method of calculating Christoffels (its actually easier using Integrals via the Langrangian). That should make it obvious that there are rather important distinctions between these spacetimes. (A large part of those distinctions is how pressure and energy density is handled)

Thanks for the link I had lost track of that site.

Is not V denoting a vector yes or no. Did you even look at the vector field mathematics I posted for you. How do you treat a vector of first order in 3d space. I already provided that detail. Let me ask you another question does a homogeneous and isotropic field have divergence ? Tell me something why is the Schwartzchild metric NOT considered as a Minkowsii metric ? Answer that one as the Schwartzchild metric does have a preferred location and a direction. It has a center of mass with constant velocities it's certainly not homogeneous and isotropic by definition verbally or under math. It is only locally homogenous and isotropic not the global metric. Aka curviliear coordinates

Sigh you don't have a homogeneous and isotropic explosion. Please define homogeneous and isotropic as your definition isn't one used in physics apparently Yeesh let's do basic vector addition. You have an observer moving with the constant vector monitoring some other observer or event and you try and claim that the second observer will get the same gamma factor when his movement is parallel to the constant vector as am observer moving in a perpendicular vector. Tell me have never looked at transverse doppler shifts ?

In those regards I even suggested a test methodology previously. One that mathematics could be applied towards.

If V is a vector how do you square root a vector ? You can square root the scalar quantity but not the direction. \[(v_x, v_y, v_z, \tau) = \dfrac{c\ \tau}{\sqrt{c^2 - v_x^2 - v_y^2 - v_z^2}}\]

Mass and energy are not equivalent. If they were equivalent m=E. Not \(E^2=(pc)^2+(m_o c^2)^2\).

You claimed a mystery involving inertia frames. There is no mystery involved the only mystery is to those that have never studied kinematics.

Well your getting closer I will give you credit for that. Your missing some key details assuming \(V_[n)\) are vector spaces. (Hint if that's the case it's a matrix). I don't know if you misses the details here. I assume your working on how to get a set of constant vectors as per the vector algebra example in that quote. Key note incorporate your constant vectors into the permutation tensor ([h_{\mu\nu}\) for the non vanishing terms due to the vectors. Good example to look at is look at the examples under gravity waves. However if the vector involves any terms directly relating to energy and momentum you also need the stress energy momentum tensor.

There is no mystery inertial frames were used as early as the 16th century under Galilean relativity. An inertial frame is simply put an observer at constant velocity. A non inertial frame is an accelerating observer. Might I recommend before making declarations with regards to physics you might consider a little research.

point taken in so far as the Schwartzchild is a static spherically symmetric mass solution lol setting static in terms of the stress tenser though may be a bit too high level for the discussion. As static also requires the metric to not depend on time and its pressure and energy/density terms must also only depend on radius using curvilinear coordinates

\[R^{\mu'}_{\phantom{\mu'}\nu'\alpha'\beta'}=\dfrac{\partial x^{\mu'}}{\partial x^\mu}\dfrac{\partial x^\nu}{\partial x^{\nu'}}\dfrac{\partial x^\alpha}{\partial x^{\alpha'}}\dfrac{\partial x^\beta}{\partial x^{\beta'}}R^\mu_{\phantom{\mu}\nu\alpha\beta}\]

Lol everyone always seems to have the wrong idea of what Einstein was seeking or physicist seek in a theory of everything. The only reason we haven't got a theory of everything at this moment of research is simply renormalizing gravity above one loop integrals for divergences. The main reason we haven't got that is we have no effective cutoff for the maximum mass density to put it simply. We can already renormalize every other fields including the EM field so I don't see how anything you have stated helps in that as we already have a solid understanding of the EM field for the TOE. Same goes for the strong and weak force. Part of the problem is unless you read textbooks or good physics articles most people don't even know what the term "normalize" means let alone renormalize. Yet we see posters all the time trying to present some TOE. Granted you stated yours won't get a TOE but rather help however everything I read in this thread deals primarily with your brain conjecture and how it relates to EM based observations. So I don't see how it helps when physicists already have the EM field covered in that regard

The research done by Sir Roger Penrose applies physics and formulas in his research papers. That's a big difference from what you have presented.

As to the first do you consider a variable which is a number set of possible answers deterministic. Depending on the answer is any formula that uses a variable deterministic. The probability functions of QM uses variables just as does relativity. Subatomic particles once observed are determined for the predicted properties we look for. Pretty much every particle in physics was mathematically predicted with predicted properties that once observed matches the predictions. Just an FYI on the last part

We use the best tool for each application mostly the one that best simplifies a problem. However we can still use any of the above methods