Mordred

That's why mathematics using known physics would be required. There is no viable option that avoids that requirement.

Unfortunately none of the above makes sense concerning the atom which as mentioned QM describes completely different. The atom of any element can readily be examined using spectography for orbitals. A method of doing so has been around since 1913 using Moseley law even under the Bohr model (naturally Mosely Law required numerous corrections to the point of impractical) by later spectography researches. However the above wouldn't even match that body of evidence.

Funny I'm quite familiar with the mathematics of LQC. It doesn't make any of the claims you do. Perhaps at some point (required by Speculation forum guidelines) applying the necessary rigor and show mathematically how LQC makes the claims you have made here.

Simply through the increase in surface area. Much like refrigeration by taking air from a small tube to a larger chamber the mean density/kinetic energy decreases resulting in cooling. Here is a basic table covering linear expansion cooling coefficients for different materials. https://courses.lumenlearning.com/suny-physics/chapter/13-2-thermal-expansion-of-solids-and-liquids/#:~:text=The dependence of thermal expansion,which varies slightly with temperature. If you think about it heat sinks are simply increasing surface area. Now with the above your better equipped to consider glaze vs no glaze ( ceramic is rather pitted greater surface area) as opposed to smooth. Though you would also need the conductivity of ceramic as opposed to glaze as well

Not sure on those ones but my 1920's textbook mentions using a small ceramic bowl in a larger ceramic bowl filled with water in the larger one. The cooling results from the expansion from the smaller bowl to the larger bowl. What effect the glaze itself would have on evaporation I wouldn't know but the example I provided didn't require glazing except for water proofing.

That being stated entanglement and Hawking radiation isn't a problem. There are already research papers on that. However DM and DE with regards to the above will be highly problematic as in the DM case it's needed to for early BH formation. In the case of DE the distribution is far too uniform by indirect observational evidence. Hawking radiation would have also the wrong equation of state (radiation) as opposed to DM (matter) and DE (scalar field uncharged)

Simply telling us anything isn't sufficient. You need far greater rigor than that

Bounce Cosmology are models where our universe originated from a previous collapsed universe. Other universe origin models are universe from nothing and cyclic (which is very similar to bounce). Didn't see this question earlier. If you ever want to seriously build a model you really are going about it the wrong way. It's never guesswork and there isn't any method that avoids the mathematics.

agreed the tricky part here is coming up with a physics way to describe the boundary conditions of a finite space. Mathematically this is done through the use of constraints. For a simple example the constraints on the Observable universe event horizon is determined by causality to the observer. Finite groups are also constrained in one fashion or another including renormalization as well as Feymann integrals example one loop integrals. I suppose an accurate description could be that the volume of space is determined by the boundary conditions with the applicable constraints of the theory for finite space as opposed to infinite unbounded space. A good example of this is Stokes theorem directional/vectorial surface element as applied to hypersurfaces under GR

I do recall that statement but cannot recall who said it. I was studying something else when I came across an intriguing definition of spacetime. "Spacetime is a manifold \(\mathcal{M}\) on which there is a Lorentz metric \(g_{\mu\nu}\) the curvature of \(g_{\mu\nu}\) is related by the matter distribution in spacetime by the Einstein Equation \[G_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G_N}{c^4}T_{\mu\nu}\] https://amslaurea.unibo.it/18755/1/Raychaudhuri.pdf The above statement clearly defines how GR treats spacetime I actually like that definition far far better than the one I provided in the OP.

Interesting thought, I should add not all spaces are physical spaces in physics such as momentum, phase, lattice, etc space. Numerous mathematical spaces to show relations are more often than not confused with physical spaces. good question one might state the quantum fields exists in regions where there is no particle such as the electron but then you get into the question are fields fundamental. From a mathematical angle fields are simply a geometric treatment and are not descriptions of fundamental reality but a means of describing nature without defining nature. Its one of the reasons I always feel that the best way to treat space is simply the volume aka the arena. Particularly since particles such as the electron has no internal structure but are on close examination best described as a field excitation. I suppose one could argue that space is filled with field interactions involving field coupling constants in essence the potential energy terms. However the danger of that is that neither mass nor energy exist on its own but are simply properties. I seem to recall a very old paper that argued all of nature can be described in terms of source and sink. Somehow seems appropriate. Seriously doubt I can find that paper now I read it roughly 30 years ago.

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 \(A^\lambda\) \[\nabla_\mu A^\lambda=\partial_\mu A^\lambda+\Gamma_{\mu\nu}^\lambda A^\nu\] Using above to break down Local maximally Symmetric subspace (local Euclid) from reference https://www.sissa.it/app/phdsection/OnlineResources/104/Adv.GR-Lect.Notes.pdf Killing equation \[\nabla_\mu x_\mu=\nabla_nu x_\mu=0\] where x is the killing vector and defines an isometry \[\mathbb{M}=\mathcal{R}\times\sum^3\] due to symmetries and Corpernicus Principle we can reduce to 2 dimensions for curvature terms Possible curvatures flat, spherical, hyperbolic \[ds^2=-dt^2+R(t)d\sigma^2\] \(d\sigma^2\) =space independent scale factor (a) \[d\sigma^2=\gamma_{ij}dx^idx^j\] \[d\sigma^2=\frac{d\bar{r}^2}{1-k\bar{r}}^2+\bar{r}^2\Omega^2\] Using Raychaudhuri equations reference below setting shear and twist to zero and Raychaudhuri expansion is \[V=\frac{4}{3}\pi R^3\] \[R=R(t)=a(t)R_0\] \[\theta=\lim\limits_{\delta V\rightarrow 0}\frac{1}{V}\frac{\delta V}{\delta\tau}=\frac{1}{\frac{4}{3}\pi 3 R^3}\frac{4}{3}\pi 3 R^2\dot{R}=3\frac{\dot{a}}{a}=3H\] Raychaudhuri for expansion becomes \[\dot{\theta}=-\frac{\theta^2}{3}-R_{\mu\nu}u_\mu u^\nu\] where \(u^\mu\) is purely time-like \[3\dot{H}=-3 H^2-R_{00}\Longrightarrow 3\frac{\ddot{a}}{a}=R_{00}\] \[R_{00}=8\pi G_N(T_{00}-\frac{1}{2}T g_{00})\] with relations in article below (missing in above reference) and employing last equation becomes \[\frac{\ddot{a}}{a}=-\frac{4\pi G_N}{3}(\rho+3p)\] https://amslaurea.unibo.it/18755/1/Raychaudhuri.pdf \[G_{\alpha\beta}=\frac{8\pi G}{c^4}T_{\alpha\beta}\] \[ds^2=g_{\alpha}{\beta}dx^\alpha dx^\beta\] \[g_{\alpha\beta}=\begin{pmatrix}1&0&0&0\\0&-\frac{a^2}{1-kr^2}&0&0\\0&0&-a^2r^2&0\\0&0&0&a^2r^2\sin^2\theta\end{pmatrix}\] with stress tensor components \[T_{00}=\rho c^2,,,T_{11}=\frac{Pa^2}{1-kr^2}\] Einstein tensor components \[G_{00}=3(a)^{-2}(\dot{a}^2+kc^2)\] \[G_{11}=-c^{-2}(a \ddot{a}+\dot{a}^2+k)(1-kr^2)-1\] with time evolution of scale factor \[\frac{a}{a}^2+\frac{kc^2}{a^2}=\frac{8\pi G}{3}G\rho\] \[2\frac{\ddot{a}}{a}+\frac{\dot{a}}{a}^2+\frac{kc^2}{a^2}=\frac{8\pi}{3}P\]

precisely

No in order to get decent answers to start with you have to ask the right questions. If the user relies too heavily on an AI to do their thinking for them. The user never learns and can never ask the the right questions to advance the users understanding. I come to forums to help teach physics to people not an AI. If I wanted to argue with the AI I would download it myself and argue with it directly

So that circuit diagram is not accurate to your setup ? Why don't we start with an accurate circuit diagram with component values where applicable

Yes hence why I have no interest arguing with an AI

This came up in one of the earlier pages. You hear a lot of current YouTube videos stating fields are fundamental. Yet at the same time under QFT fields are simply a geometric distribution of values. Some quantities being physical (measurable) in this case and strictly mathematical. The problem with occupancy with fields is under QFT is the probability density functions. Using Higgs as an example with the above the field encompasses all spacetime however at each location there is a probability of occupancy of a Higgs boson. However the Higgs boson is extremely short lived. Also to get a Higgs boson that probability also requires sufficient energy that in essence requires another particle interaction. In essence the Higgs field is not a sea of Higgs particles flying around to get a Higgs boson requires another particle interaction to mediate. This is the problem with all gauge boson fields (specifically gauge boson fields) force fields for short) While the field may be described as existing everywhere the occupancy will be in a state of constant shifting occupancy where every location has a probability of having a particle. So the best we can state is everywhere there is in spacetime a field however that also does not mean that all of spacetime is filled due to fields In essence space still serves as the arena the volume , whose occupancy is determined by the field probability density functions. This is true for all particle fields under QFT. Including matter fields Now there's a mouthful lol. To borrow a line from the Sean Carroll video in one of our pinned threads. "To get a Higgs boson one must poke the field "

@studiot +1 nice demonstration video I also noticed the equation 10 (b) of the Elihu Thomson ring was highly applicable to the circuit shown

Let's start with time. Time is a property of a system, state etc. It never exists on its own. Secondly the Interval (ct) is what gives time dimensionality of length not time by itself. Can there be multiverses and time prior to our universe absolutely (bounce cosmology or cyclic universe cosmology). However your approach is far too hand wavy there is plenty of mathematical examples with regards to multiverses.

For the record Fourier analysis is used for the entire model of particles it isn't restricted to MRI. It's essential in QFT

Seems both @Studiot and I agree on this. I will leave this in Studiot's court as engineering is far more his specialty.

forgot to add you will also want to be familiar with Stokes theorem for the curl of a vector with regards to curved spacetimes

As Studiot mentioned there is no need to consider magnetic field lines in the above except as it applies to the transformer primary and secondary windings. Its really basic induction if you supply the motor details, transformer winding ratio between primary and secondary windings and capacitance value it should be trivial to run calculations on this circuit. The capacitor is providing the phase shift via capacitance reactance. I would be curious to see the 3 phasor diagram this circuit produces It would not surprise me to find your introducing phase imbalances that will eventually ruin your motor windings. A quick way to confirm that is to take voltage readings between (T1 T2).( T1 to T3), (T2,T3) they should all have identical voltage if not then your damaging you motor. (PS its also likely your back-feeding harmonics back into the power grid) which your electric supply company may take issue with) edit forgot to add Induction can also cause capacitance reactance. For example an inductor is impossible to burn into an IC chip but one can replace an inductor with a capacitor which is easily burned into an IC.

As @studiot mentioned were dealing with foliations with the line element its not as straightforward as one might think looking at the equations You have to look at what geodesic congruences are being applied. This typically requires using covariant derivatives provided in the article below for PG coordinates \[ds^2=dT^2-(dr^2+\sqrt{\frac{2M}{r}}dT^2-r^d\Omega^2\] the Euclidean space is the surface of constant T. One of the better articles covering this detail and showing the light-cone shift is here https://www.sissa.it/app/phdsection/OnlineResources/104/Adv.GR-Lect.Notes.pdf The above is the reason I was seeking decent coverage of geodesic congruence however there is far too many prerequisite steps such as Leibniz product rule. Knowing one forms and 2 forms etc if you aren't familiar with their usage and reasons for usage under GR. As they are needed in this case In curved spacetime the only way to remain Lorentz invariance is to use a minimum of a vector and a convector. If you never worked with convectors then that is a preliminary step you will need. For example with the above the Kroneckeer delta affine connections using Leibniz gives the maximally symmetric spacetime (Minkowskii, De-Sitter/anti Desitter) spacetime region. (local) the global metric above the affine connections follow the Levi-Civita affine connections. This is used in regards to aspects such as the killing vectors with regards to the Ricci scale term the maximally symmetric spacetimes the Ricci scalar is constant. That is some of the preliminary details with regards to geodesics and also a huge part of understanding the Christoffel term of the geodesic equation for null geodesis. You already mentioned your not too familiar with GR how much calculus have you taken ? The latter parts can be found in Calculus textbooks they tend to have the best coverage of the Kronecker delta and Levi-Civita. The lesson you need to learn is as follows the acceleration of the object is determined entirely by the connection coefficients of the geometry and has nothing to do with the properties of the object

@externo I would like you to consider the following with regards to the raindrops or Lemaitre frames. Take any number of raindrops. Each raindrop has its own geodesic. now examine the deviations between each geodesic. In the freefall state the equations of motion are the first order velocity terms (free fall). The geodesic deviations due to the curvature terms (easiest example to understand towards a common center of mass in the Newtonian limit) is the tidal force what we see as the second order acceleration term. Both links I posted earlier (the two lecture notes) include the relevant mathematics. This is what you will need to understand geodesic congruence in The PG coordinates. You will also need to look into the maximally symmetric spacetimes (local) vs global and how to transform one to the other. All those details in those lecture notes.