Mordred

As mentioned by Swansont further detail is needed. However first off I recommend you forget any imagery of particles as little bullets as your descriptive seems to apply. You are correct in so far as certain particles do interact more readily with other particles however your solution makes little to no sense. mass is resistance to inertia change or acceleration it results in a particles via the particles ability to couple with its respective fields. This includes the Higgs field. To examine how mass arises as a result of the Higgs field you can apply the Weinberg angles of the CKMS matrix using the particles cross section.

apply Newtons shell theorem a uniform mass distribution wouldn't have gravity as you wouldn't have any net force at any arbitrary coordinate treated as center of mass. Gravity itself requires non uniformity of mass distribution

Not precisely Newton physics also includes the Newton Shell theorem. In that shell theorem a uniform mass distribution would have no gravity. However if you have an anisotropic distribution such as the the Earth where gravity is weak we don't have significant time dilation effects. so the Newton method for everyday measurements are still accurate. It is only when you get extremely fine tuned in your examination that the time dilation becomes measurable. so there is curvature aka gravity but the curvature isn't significant and we can still get good approximation under Euclidean flat geometry. Ok lets take two falling objects you can do this with a pen and paper easily enough Draw a circle. the Center of the circle is your center of mass. Choose two angles from that center of mass say 15 degrees and 345 degrees. Let those represent the two infalling particles toward the CoM. You assign a variable to represent the separation distance between the two infalling particles at a given radius. The common symbol used is \[\xi\] the value will decrease as the particles approach the CoM. this is termed tidal force due to the geometry (curved spacetime though under Euclidean approximation ) this is often described as gravity as the tidal force due to curved spacetime

Under GR through the Principle of General Covariance it would be represented under the Newton approximation solutions of the Einstein field equations. The simplest transform is the Minkowskii metric, Euclidean space or flat space. This is denoted by [latex]\eta[[/latex] [latex]\mathbb{R}^4 [/latex] with Coordinates (t,x,y,z) or alternatively (ct,x,y,z) flat space is done in Cartesian coordinates. In this metric space time is defined as [latex] ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/latex] [latex]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex] the metric above works well to describe The Newton limit provided provided you don't have significant relativity effects due to either inertia or extreme mass. Though these equations do describe the essentials of SR, they still readily apply for situations not involving gamma of the Lorentz transforms.

My interest in Cosmology started back in the late 70's. However in the early 80's when Alllen Guth's first published his false vacuum inflation model accelerated that interest even further. That interest has been a primary focus of my studies ever since. Back then inflation often involved quantum tunnelling from a false vacuum state to a true vacuum state. These models typically had the energy density graph transitions as in a similar fashion to https://www.wolframalpha.com/input?i2d=true&i=plot+Power[x%2C2] thoough they would often include a higher potential of the same curve to represent the stable region of the higher potential false vacuum state. Those graphs then were employed to define quantum tunneling from the two potential VeV's through the separation potential barrier between their corresponding stable regions. Modern models however use the Mexican hat potential as per the inflaton and the Higgs field. Their effective equations of state are close matches. Today there is strong supportive evidence that Higgs inflation is highly viable. However the inflaton is also equally viable. The latter includes chaotic eternal inflation leading to pocket multiverses defined by separate expansion regions with the causal connection of the same inflation mechanism that rapidly expanded our universe in early times. I had also had to ask myself the question. Is there a connection between inflation and the cosmological constant ? " given the behavior of inflation I found that this is highly likely. I will support this with the relevant equations however it will take time to place them into the thread. ( I will be saving often during edits)So starting from our hot dense state at 10^{-43} seconds. (prior to this leads to infinite blueshift as well as other infinity problems. ( The Big Bang mathematical singularity conditions) so first we need our metric LCDM FLRW Metric equations \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] \[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\] setting \[T^{\mu\nu}_\nu=0\] gives the energy stress mometum tensor as \[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\] \[T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0\] which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0. the related GR solution the the above will be the Newton approximation. \[G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\] Thermodynamics Tds=DU+pDV Adiabatic and isentropic fluid (closed system) equation of state \[w=\frac{\rho}{p}\sim p=\omega\rho\] \[\frac{d}{d}(\rho a^3)=-p\frac{d}{dt}(a^3)=-3H\omega(\rho a^3)\] as radiation equation of state is \[p_R=\rho_R/3\equiv \omega=1/3 \] radiation density in thermal equilibrium is therefore \[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3 \] \[S=\frac{2\pi^2}{45}g_{*s}(at)^3=constant\] temperature scales inversely to the scale factor giving \[T=T_O(1+z)\] with the density evolution of radiation, matter and Lambda given as a function of z \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] the above typically has the equation of states cosmology given by https://en.wikipedia.org/wiki/Equation_of_state_(cosmology) where the scalar field is the given equation of state for the cosmological constant. \[w=\frac{\frac{1}{2}V\dot{\varphi^2}-V(\varphi)}{\frac{1}{2}V\dot{\varphi^2}+V(\varphi)}\] Higgs Inflation Single scalar field Modelling. \[S=\int d^4x\sqrt{-g}\mathcal{L}(\Phi^i\nabla_\mu \Phi^i)\] g is determinant Einstein Hilbert action in the absence of matter. \[S_H=\frac{M_{pl}^2}{2}\int d^4 x\sqrt{-g\mathbb{R}}\] set spin zero inflaton as \[\varphi\] minimally coupled Langrangian as per General Covariance in canonical form. (kinetic term) \[\mathcal{L_\varphi}=-\frac{1}{2}g^{\mu\nu}\nabla_\mu \varphi \nabla_\nu \varphi-V(\varphi)\] where \[V(\varphi)\] is the potential term integrate the two actions of the previous two equations for minimal scalar field gravitational couplings \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] variations yield the Euler_Langrene \[\frac{\partial \mathcal{L}}{\partial \Phi^i}-\nabla_\mu(\frac{\partial \mathcal{L}}{\partial[\nabla_\mu \Phi^i]})=0\] using Euclidean commoving metric \[ds^2-dt^2+a^2(t)(dx^2+dy^2=dz^2)\] this becomes \[\ddot{\varphi}+3\dot{\varphi}+V_\varphi=0\] \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] and \[G_{\mu\nu}-\frac{1}{M_{pl}}T_{\mu\nu}\] with flat commoving geometry of a perfect fluid gives the energy momentum for inflation as \[T^\mu_\nu=g^{\mu\lambda}\varphi_\lambda \varphi_\nu -\delta^\mu_\nu \frac{1}{2}g^{\rho \sigma} \varphi_\rho \varphi_\sigma V(\varphi)]\] \[\rho=T^0_0=\frac{1}{2}\dot{\varphi}^2+V\] \[p=T^i_i (diag)=\frac{1}{2}\dot{\varphi}^2-V\] \[w=\frac{p}{\rho}\] \[w=\frac{1-2 V/\dot{\varphi^2}}{1+2V/\dot{\varphi^2}}\] ***method by Fernando A. Bracho Blok Thesis paper.*** https://helda.helsinki.fi/bitstream/handle/10138/322422/Brachoblok_fernando_thesis_2020.pdf?sequence=2&isAllowed=y Now any scalar field state dominated by the potential energy density will have negative pressure. a negative pressure to energy density ratio of w=-1 will describe a state that does not vary over time. However this also involves the critical density. \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] the initial conditions will have a different critical density value at the false vacuum state prior to inflation. A critically dense universe is a k=0 flat universe. However it derivatives employ a pressure less w=0 equation of state to derive the critical density value. This corresponds to the equation of state for matter. in essence the universe is thermodynamically evolving from a hot dense state of a negative vacuum with opposing force relations given by replacement \[\rho_{(V\varphi)}\] to \[V(\phi) \[DU=\rho_{V(\phi)}DV\] work is defined as \[dW=\rho_{V(\phi)}dV\] \[p_{V(\phi)}=-\rho_{V(\phi)}\] the slower the roll from false vacuum potential to VeV today allows for greater number of e-folds. The greater the e-fold ratio the higher the number of pocket universes that can result in locally anisotropic regions during inflation. Examinations under the eternal chaotic inflationary theory can lead up to an infinite amount of bubble or pocket universes. This arises with the result of a locally different rate in inflation to the global rate. Once inflation slow rolls the VeV reduces on a gradual but not necessarily smooth rate, smaller metastable states arise due to thermal dropout of particle species as well as base elements such as hydrogen and lithium. The expansion and Cosmological redshift following the thermodynamic laws also contribute to the evolution to the scale factor. I will add further detail later on (long work day)

Higgs Inflation Single scalar field Modelling. \[S=\int d^4x\sqrt{-g}\mathcal{L}(\Phi^i\nabla_\mu \Phi^i)\] g is determinant Einstein Hilbert action in the absence of matter. \[S_H=\frac{M_{pl}^2}{2}\int d^4 x\sqrt{-g\mathbb{R}}\] set spin zero inflaton as \[\varphi\] minimally coupled Langrangian as per General Covariance in canonical form. (kinetic term) \[\mathcal{L_\varphi}=-\frac{1}{2}g^{\mu\nu}\nabla_\mu \varphi \nabla_\nu \varphi-V(\varphi)\] where \[V(\varphi)\] is the potential term integrate the two actions of the previous two equations for minimal scalar field gravitational couplings \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] variations yield the Euler_Langrene \[\frac{\partial \mathcal{L}}{\partial \Phi^i}-\nabla_\mu(\frac{\partial \mathcal{L}}{\partial[\nabla_\mu \Phi^i]})=0\] using Euclidean commoving metric \[ds^2-dt^2+a^2(t)(dx^2+dy^2=dz^2)\] this becomes \[\ddot{\varphi}+3\dot{\varphi}+V_\varphi=0\] \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] and \[G_{\mu\nu}-\frac{1}{M_{pl}}T_{\mu\nu}\] with flat commoving geometry of a perfect fluid gives the energy momentum for inflation as \[T^\mu_\nu=g^{\mu\lambda}\varphi_\lambda \varphi_\nu -\delta^\mu_\nu \frac{1}{2}g^{\rho \sigma} \varphi_\rho \varphi_\sigma V(\varphi)]\] \[\rho=T^0_0=\frac{1}{2}\dot{\varphi}^2+V\] \[p=T^i_i (diag)=\frac{1}{2}\dot{\varphi}^2-V\] \[w=\frac{p}{\rho}\] \[w=\frac{1-2 V/\dot{\varphi^2}}{1+2V/\dot{\varphi^2}}\] ***method by Fernando A. Bracho Blok Thesis paper.*** https://helda.helsinki.fi/bitstream/handle/10138/322422/Brachoblok_fernando_thesis_2020.pdf?sequence=2&isAllowed=y now to examine it to other Higgs single scalar field field methodologies. in particular https://arxiv.org/abs/1402.3738 equation 16 of the above article matches 2.38 and 2.39 of the Brachoblok paper with two different methodologies. (cool need to further study both methods) \[\rho=T^0_0=\frac{1}{2}\dot{\varphi}^2+V\] \[p=T^i_i (diag)=\frac{1}{2}\dot{\varphi}^2-V\] https://arxiv.org/abs/1303.3787 (for this I will need to research Jordon frame) in particular page 23 (single scalar Higgs) goals check list. (single scalar field (Higgs prior to electroweak symmetry breakings. For symmetry break (Higgs and Yukawa couplings of the CkMS unity triangle.). Follow through with each particle species including generations via Higgs). (details and preliminary work aforementioned). Hydrogen, lithium and deuterium dropout. (Saha equations) for particle species Maxwell Boltzmann, Bose-Einstein and Fermi Dirac. statistics). Apply Principle of General Covariance throughout.

To add to Phi for All's excellent reply time is simply ratevof change. It is given dimensionality equivalence to length via the interval defined as (ct). Spacetime is simply the geometry where particles reside. Space being simply the volume.

Lol currently I'm at minus 42 Celsius. Gotta love Canada

Interesting article, even if it allows for compensating for the Non Kepler curve in galaxy rotation it doesn't address other indicators of DM such as early large scale structure formation or gravitational lenses without the presence of baryonic matter. Think I may have forgotten a rule on the inverse of a tensor. In so far as the signature doesn't match up from II.1. Likely just me forgetting the inverse tensor rules will have to look into that.

There is an instantaneous acceleration treatment by applying the four acceleration equations. A specific equation that describes this is \[\alpha=\gamma^3 a\frac{1}{(1-u^2/c^2}\frac{du}{dT}\] where \[\alpha\] is the proper acceleration for objects with mass The large T is specifying coordinate time to be more obvious. u here is the instantaneous velocity. you can further simply that equation by applying motion on the Minkoskii hyperbolic curve the above equation leads to which simplifies to \[g^4/c^2\] \[x'^2-ct^2=x^2\]. the equation above works for both forms of acceleration via change in velocity or direction. This equation has been used in Born rigidity examination as well. An interesting consequence of relativity is the observer effects. Place an observer at a static location your classic rest frame. The train has length so he's going to observe different parts of the train at different angles. Even if we only consider the observer along the x axis on top of the train he will observe a different length front to rear. The approximate point of simultaneity of signals received from the front and rear would be the center of the train. The only way to preserve that simultaneity from any two equidistance points either in the x+ or x- direction the length contraction must occur in a symmetric fashion from that observer point of view. In a linear acceleration case that isn't too hard if you allow some mechanism that the entirety of the bus gains speed. however once the train starts to turn your going to lose simultaneity from that same location. At least I don't know of any solution where you won't. treating simultaneity in terms of signals received by an Observer

Yes in the sense you can have virtual strings which would be similar to the propogator action in QFT. Here is a reference if your still interested. https://arxiv.org/abs/math/0310218

+1 on that reply. To add to it though we can account for the redshifts though the procedure is somewhat complex as it involves additional data and surveys. In truth the redshift formulas commonly shown are the rudimentary forms. They can get rather complex depending on the circumstances. We also don't depend on strictly redshift the cosmic distance ladder has different methods to cross check distance measures such as intergalactic parralax

For those that want to better understand expansion and redshift including the three types of redshift. Doppler Gravitational redshift Cosmological redshift Read this article I wrote years ago http://cosmology101.wikidot.com/redshift-and-expansion

Well first off atoms didn't exist yet they come later. The particles of the SM were in a state called thermal equilibrium. I'm essence they are so energetic and short lived that individual particles cannot be distinguished from one another (similar to a Bose Einstein condensate state). You can't think of mass being some weight or matter object mass is resistance to inertia change. It is a property objects, states, fields have not a thing unto itself

As mentioned the BB model starts at a hot dense state from 10^{-43) forward. It does not describe what caused the BB itself. Infinitesimal crop into the mathematics before the time above. The FLRW metric is valid for the entire expansion history. The FLRW metric is well supported by the observational evidence. Starting from a BH isn't part of the model thar is simply one of the many alternative models to describe how it started.

lol that's the one accidently replied in the other thread. The T=1490 with T=4000 is 50% decoupling. Hence the recombination Epoch where the mean free path of photons becomes near infinite is set at the T=3000 K Z-1100. age 366,000 T=6000 can be representative of the early stages of decoupling at Z=2189 giving age at 112,000 years calculation based on 2018 dataset

That's the one, I have a luminosity distance to z relation I wanted to verify however may also look at determining age of stars.

Interesting in the following article it describes the reaction rate of Hydrogen as it drops out of thermal equilibrium. Using the temperature to redshift relation T=T0(1+z) or alternateIy the inverse of the scale factor a. I calculated the temperature of 4000 kelvin to z= 1492. The article evidently rounded this to z=5000, this corresponds to universe age 218,000 years old for the universe. The table also shows the reaction rate for higher and lower temperature values. https://iopscience.iop.org/article/10.3847/1538-4357/ab2d2f/pdf. This additionally tested the mathematics I was examining using a method by Juan Garcıa-Bellido. Details are in the following thread. For the Nucleosynthesis calculation to get an accurate method to correlate redshift to temperature relations so as I examine when different particle species drop out of thermal equilibrium I can calculate the age of the universe, volume, and subsequently the number density of each particle species. You often see in literature the value of 3000 kelvin given. Results are in the above article, using the method of said article. This corresponds to Z=1100 roughly 350,000 Years age for the Observable universe. The conjecture I am going to examine next is that at Higher temperature in the chart of said article the photon interactions with hydrogen atoms will cause higher scatterings of the atoms. Hence the 3000 Kelvin value is the more stable decoupling temperature but does not represent the beginning stages of hydrogen decoupling. this may also help explain some of the earlier universe star formations. Though certainly not solve the entirety of issue of early star formation in terms of how rapidly they formed in the early universe. I will also likely examine the methodology of equation 25 of the above article and compare it to the classical Bose_Einstein, Fermi-Dirac statistics method mainly to get a feel for the deviations that may occur between the two methods. Thoughts ? pS @Sensei I seem to recall a few years back you had an examination regarding star formation. If you still have that work handy and if you feel it would relate to this I wouldn't mind looking over it again.

No the big rip requires the negative kinetic energy term to occur. However current evidence support that the big rip as being unlikely to occur as the cosmological constant shows strong supportive evidence of being constant. Provided it remains constant the heat death scenario is more likely

well piece of advise study the basic definitions and related formulas for mass, energy, and work then apply those to the EM equations that are posted in this thread. in order to properly learn physics you will want to start at the beginning and not jump somewhere in the middle. You will just confuse yourself. Also make sure your familiar with the linear and angular momentum equations those will be involved in every level of physics.

FLRW Metric equations \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] \[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\] setting \[T^{\mu\nu}_\nu=0\] gives the energy stress mometum tensor as \[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\] \[T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0\] which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0. the related GR solution the the above will be the Newton approximation. \[G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\] Thermodynamics Tds=DU+pDV Adiabatic and isentropic fluid (closed system) equation of state \[w=\frac{\rho}{p}\sim p=\omega\rho\] \[\frac{d}{d}(\rho a^3)=-p\frac{d}{dt}(a^3)=-3H\omega(\rho a^3)\] as radiation equation of state is \[p_R=\rho_R/3\equiv \omega=1/3 \] radiation density in thermal equilibrium is therefore \[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3 \] \[S=\frac{2\pi^2}{45}g_{*s}(at)^3=constant\] temperature scales inversely to the scale factor giving \[T=T_O(1+z)\] with the density evolution of radiation, matter and Lambda given as a function of z \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\]

To add to Lorentz Jr answer you might want to study Newtons laws of momentum https://en.wikipedia.org/wiki/Newton's_laws_of_motion there is a section there specifically on electromagnetism while your at it memorize the following statement "Mass is the resistance to inertia change" then look and see how that applies to the Laws above the reason I suggest the above is that you seem to lack in basic physics and the above applies to every physics theory. So its highly important to understand the above. for example your title Could mass be grounded by Mass makes zero sense if you apply the definition given By substitution it would read as Could resistance to inertia change be grounded by resistance to inertia change ? the answer is obviously no once to use the definition of mass, the others are doing an excellent job helping you on the EM field so I wont interfere with their progress .

support document list https://physics.nist.gov/cuu/Constants/codata.pdf Fundamental constants 2018 https://physics.nist.gov/cuu/pdf/wall_2018.pdf Cosmic inventory (2004) https://arxiv.org/abs/astro-ph/0406095 2018 Planck datasets https://www.aanda.org/articles/aa/full_html/2020/09/aa33910-18/aa33910-18.html Planck cosmological parameters 2018 https://www.aanda.org/articles/aa/pdf/2020/09/aa33910-18.pdf Equilibrium temperature of Hydrogen https://iopscience.iop.org/article/10.3847/1538-4357/ab2d2f/pdf

You would likely Sir Roger Penrose "100 roads to Reality of interest. Just an FYI so we don't derail this thread. The term you posted is commonly applied in QFT wavefunctions just an FYI

The description I typically use for fields is a collection of values under geometric treatment but yours is excellent