Mordred

Lets do a simple example (though unless you understand QM won't really be simple) Unitary space \[\langle u,v\rangle=\mathbb{C}^n\] you have the inner products of a complex unitary space (Hilbert space). In terms of the Schrodinger equation the continous evolution must take the form \[\rho\rightarrow U\rho U^\dagger\] where U is the unitary operator. the Hamilton governing this is \[H=\sum^d_{j=1}\lambda_j|j\rangle\langle j|\] which gives unitary form \[U=\sum^d_{j=1}e^{\lambda_j t}|j\rangle\langle j|\] in other words one requires a bit of preliminary mathematics and QM to understand the above. Example the d above the sum is not dimension it is an integer defined by a renormalization scheme. Seeing that above the sum automatically tells me its a normalized state

Key word Unitary operator. For example how is an operator defined under QM ? What makes that operator Unitary? 2 key operators in QM position and momentum. These however are not the Unitary operators Doesn't describe the Unitary operator itself given as \[U^\ast U=1\] The Unitary operator must preserve the inner product of the Hilbert space. Keep in mind I'm trying to avoid terminology such as bounded, isomorphism , adjoint etc. An easy example is the rotation matrices these are Unitary operators. A unitary operator can change to orientation, coordinates or state itself but cannot change the magnitude (norm of the state). Every Unitary operator is normal. Categories of Unitary operators being Unitary space, Unitary transformation, or Unitary matrix. A Unitary space is a complex vector field with a distinguished positive definate Hermitean form A Unitiary transform is a surjective transform between two Unitary spaces U,V. A Unitary matrix is a complex valued matrix whose inverse is equal to its conjugate transpose. See why I stated very rough and gritty in the above ?

Unitary is equivalent to normalized in essence. So take a unit vector that unit vector is normalized to value 1. So for example \(c=\hbar=K=1\) Now as you cannot have a negative probability by multiplying the square of the probability amplitude you get a positive value. The conserved portion requires a closed group or system where you have no forces involved for conservation of momentum example being the Schrodinger equation you normalize the group and that group is finite. Example 1 loop integral is a closed group. That's a rough and gritty explanation the details get more intense.

New paper regarding Hubble contention https://arxiv.org/abs/2408.06153 Edit forgot to add a few years back local cluster measurements by HOLICOW were not matching up to CMB measurements. The bulk of the research as to cause from what I've been able to gather have been in regards to local group calibrations similar to the above paper.

It's one of the possibilities though one that I find rather tricky particularly when you further consider a few details. Those details include the need for DM for early universe large scale structure formation. Gravitational lensing effects not fully accountable by nearby baryonic matter. Another detail is often missed is that when one goes to measure galaxy rotation curves it's necessary to use mass to luminosity relations. The Mass to luminosity relations show that only 10 to 20 percent the total luminosity can be accounted by baryonic matter content. Even though DM doesn't interact with the EM field it does affect gravity. It is this effect that further shows up in the mass luminosity relations. Part of my courses was using spectography to examine M31 and other local galaxies and examine the mass-luminosity to rotation curves. This is one detail Zwicky noted when he first examined rotation curves and pushed the examinations beyond mathematical error. One you rarely ever see discussed is the integrated early and late time Sache Wolfe effects due to overdensity and underdensity regions (this effect also includes localized expansion rates ). Other possibilities not mentioned yet being Machos and axioms. Though those possibilities I don't follow but they are still current approaches.

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As far as opinions on DM I've always leaned toward sterile neutrinos even though I have examined treatments using Majaronna mass coupling RH neutrinos and 3 species I still haven't seen how to account for the total mass. The research is still ongoing in that regard.

Interesting product and yes a pocket size Geiger counter would be useful for a large number of industries provided they have accuracy. Thanks for pointing +1

Bye hopefully when you come back your attitude is improved.

For someone who claims to be correct you certainly missses applying Newtons three laws of inertia. Which is the reason Swansont gave you the correct reply. Think about your scenario and apply all three laws.

Been examining a newer way of looking at Feymann integrals that greatly helps simplify some of the mathematics. The method employs the charge conjugation relations to simplify allowable interactions on Feymann integrals. https://arxiv.org/pdf/hep-ph/9601359 Figured this would get a bit of interest for discussion.

I will have to read that book sometime could be enertaining

It's done in the FLRW metric for any time period prior to the dark ages prior to recombination and the detection availability is the CMB (indirect signature detection). However that requires math using known physics.

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 \[\frac{a}{a}^2+\frac{kc^2}{a^2}=\frac{8\pi G}{3}G\rho\] \[2\frac{\ddot{a}}{a}+\frac{\dot{a}}{a}^2+\frac{kc^2}{a^2}=\frac{8\pi}{3}P\]