Mordred

There is so many mistakes in everything you have posted that everything you have in this thread is literally useless. Obviously your not heeding anyone's advise so have fun with that. I prefer dealing with those that wish to learn so I'm out. Good luck

When you try to describe physics in a non mainstream manner that is the equivalent of reinventing physics. In the last example above gravity waves do not behave in the manner you described and neither does its related mathematics You tried redescribing time with your math and ended up with incorrect equations that don't match observational evidence. Relativity is one of the most rigorously tested theories in physics with precision in all its predictions. Instead of trying to develop your own mathematics and conjecture. You would be far better off learning the mainstream physics and formulas instead of trying to invent your own. GR is such a successful theory that it predicted the possibility of gravity waves Long before ever measuring one. The mathematics was so convincing that governments invested millions of dollars on huge gravity wave detectors (LIGO) with only the possibility of detection. They also knew it was limited in the gravity wave frequencies but it's polarity isn't dipolar as the EM field but quardupolar. That required a different design of detector. The L shape of LIGO. Once again predicted by its mathematics. We have measured time dilation countless times far to many to name all the tests and every time the mathematics of SR/GR give the correct answers to match what is observed. So I seriously ask you with all GR's incredible successes. Why wouldn't someone take the time to understand it and its mathematics to understand why it's so incredibly accurate instead of trying to come up with their ideas. An expression you may be familiar with " If it isn't broke, don't fix it". Another expression that applies. " You can't fix something if you don't understand how it was built." For example think about the fundamental purpose of gravity theories. It is to explain why objects move in spacetime the way they do. That is one the primary reasons velocity is used in its equations. It is also why using the Interval for time is convenient as we can now apply vectors in the same manner as the motion of particles. Every formula in physics always derives from other well established formulas. They form the basis of their mathematical proofs. In GR all the main formulas has Newtons laws of inertia as part of their mathematical proof. Including \(E^2=(pc^2)+(m_o c^2)^2\). This is why it's so incredibly successful. It derived from known physics primarily kinematics. So instead of trying fix something that works incredibly well. Your time would be far better spent learning how and why it's so successful. As a side note in order to ever get a paper peer reviewed approved. You would need to prove you understand and can use those mainstream formulas that apply to any new theory. So if you ever want a good working theory you will need a good working knowledge of the mainstream physics. Its not guess work or sudden Eureka moments its painstaking work starting with known formulas. Let's take another GR equation proper time \[\Delta \tau =\int \sqrt{1- \frac{1}{c^2} \left ( \left (\frac{dx}{dt}\right)^2+ \left(\frac{dy}{dt}\right)^2+ \left (\frac{dz}{dt}\right)^2\right )}dt\] one wouldn't think Newtons laws of inertia is involved in the above unless one studies the kinematics of the four momentum, four velocity. Every equation applies other known equations.....

No matter how hard I try nothing you've shown makes sense. I can't find anything that even correlates to physics in this last post.

Big mistake however is assuming tine dilation is only electromagnetic. It affects every interaction of every force and every particle to particle interaction not just EM. That isn't nearly the only mistakes but to point everyone out will take far too long.

Yup agreed let's reinvent physics

Only had 30 percent eclipse at my neck of the woods but still looked cool. Least we had clear skies for once.

That alone tells me what your doing is incorrect. Let me guess you never factored in length contraction ? The Lorentz transforms include both so if v=c d=0. Hence it's not a valid frame of reference. It is also the primary reason massless particles follow null geodesics. The "null" indicates this relation.

The reason why I asked you to look over the Lorentz equations again is that is precisely what used the "Interval" \[t=(ct)\] it is usually just shortened to t. With that you already tallied the distance.... Multiple lasers at different angles and observer points is already done in GR. The Interval is already included. Nothing in your experi.ent adds anything new that hasn't already been done on an experimental basis. You simply have to properly understand it. Believe me it's far more easier to use velocity particularly once you start using instantaneous velocity for acceleration. Of course you can also do so using rapidity under the Lorentz boosts but most ppl don't know how to use tensors for that. There are very good reasons velocity is used. For example using velocity then \(\gamma\) is simply a constant of proportionality. Of course the other details is that you also have length contraction as well as time dilation both occur at the same time

It's still an experimental setup designed not to show any time dilation one that has unnecessary steps. Simply take a transmitter or reciever and move it further away from the sender/reciever at near c. You require relative velocity on the distance rate of change between sender and reciever. Quite frankly the scenario I just described is a common example in textbooks. You won't get time dilation unless either the transmitter or reciever has a relativistic velocity. You seem to be implying you get time dilation in a static setup. (Which is likely not your intention ) but the transformation formulas between Galilean relativity and Lorentz are near identical with the exception of the Gamma factor. Study the Lorentz transformations here and then revisit your setup. https://en.m.wikipedia.org/wiki/Lorentz_transformation Start with the simple setup before you get into angle changes and an event following a circle (acceleration) which leads to Lorentz boosts (rapidity)

Just a side note if you have a metric with off diagonal terms such as the Kerr metric one can perform a blockwise inversion. Strictly an FYI for others as I'm sure KJW already knows this detail just in case anyone thinks only orthogonal tensors can be metric tensors that isn't always the case.

Your not going to find time dilation using your setup your using a setup that can be described under Galilean relativity as well as the Lorentz transforms. It was once thought Galilean relativity was usable for all speeds up to c. So the mathematics works on paper. However actual measurements showed the error not thought experiments. It is when you actually perform the tests that you realize that there is an error in the Galilean relativity calculations. Also you need to recognize both the above are under constant velocity. Any change in direction results in acceleration just as a change in velocity. So additional transformations are involved . However from what I read so far I suggest you study Galilean relativity as well as apply vector algebra before tackling the Lorentz transforms. You will learn the only difference between the two is the Gamma correction for length contraction in the direction of motion typically assigned x axis and the interval for time.

You are aware that the E and M fields are mediated by a gauge photon correct ? That article includes the Maxwell equations and is in normalized units. If c is finite and constant as the EM field mediator this also means the E and M field has the same speed limit. No massless particle including any field gauge boson exceeds c. Every field propagate at maximum c.

Not too familiar with the Kasner metric I will have to look into that one. Lol it will give me something new to study do thanks for that. Though I have run into a few papers on it. Hadn't put a lot of time studying it

https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://arxiv.org/pdf/1705.04397&ved=2ahUKEwiIodbJsq-FAxUYBDQIHSx2AJoQFnoECB0QAQ&usg=AOvVaw054EguS3mqzq8k-KfOkm8o https://www.forbes.com/sites/startswithabang/2019/05/25/ask-ethan-what-is-the-fine-structure-constant-and-why-does-it-matter/ https://arxiv.org/abs/gr-qc/0008009 Last link helps better understand how the fine structure constant relates to c. There is also numerous articles on precision tests for Lorentz invariance the speed limit is also tested through the Lorentz invariance tests as the two are linked. Modern tests have gotten us to incredible accuracy. If you think about how particle accelerators work were constantly testing GR.

No it isn't a consequence of relativity. Relativity simply recognizes the limit. It is simply a fundamental constant of nature much like the fine structure constant. In point of detail even the claasical formula for the fine structure constant which was established long before relativity was developed showed the speed limit. A great deal many professional physicists have tried disproving relativity. So far they usually end up proving the sheer accuracy of relativity. It's literally one of the most rigorously tested theories we have.

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)