Mordred

I don't care what the title is. If your claiming you formula does this or that it requires the terms that relate to those claims.. Claiming redshift with no time component to describe frequencies is simply wrong old math or new math. Describing past and future gravity terms without anything relating to a force term is just as wrong. Claiming details concerning different observers without a coordinate system is another example. So far your equation only shows volume changes you need additional mathematics to do anything beyond that. This is the equation you posted does it describe anything at all beyond change in area ? The time component used in that equation would be observer dependent it's not proper time. proper time using a coordinate system is this for Euclidean geometry (flat spacetime) \[\Delta\tau=\sqrt{\Delta t^2-\frac{\Delta x^2}{c^2}-\frac{\Delta y^2}{c^2}-\frac{\Delta z^2}{c^2}}\] that's one of its simplest forms. The equation I posted only shows how to convert from coordinate time to proper time for 4d Spacetime using Cartesian coordinates it does nothing else... to have it do anything beyond that requires additional mathematics its as simple as that

You still require some term for rate of change as well as some terms regarding force for gravity etc. If your equation is now different than what you have posted so far you should include it. Though as I have already mentioned a uniform mass distribution has zero gravity as per Newtons Shell theorem. Even how we measure energy also depends on observer just as how one measures redshift depends on the observer. For that matter how measures volume can sometimes depend on observer a good example being the event horizon of a BH. Different observers will measure the event horizon at different volumes and radius. SR also teaches us that distance can also be observer dependent hence the length contraction of SR. I'm sure as an engineer your familiar with signal propagation caused by an EM field. Time dilation can readily relate to this as the coupling constants of the SM produces the mass term. Mass being resistance to inertia change. Just as I'm positive that you understand redshift involves frequencies which requires a rate aka time component.

We look into the past the further away we look. That's well established it's also why our equations use proper time and proper distance in its equations. The mathematics you've shown so far do not have any time dependency. You haven't got anything equating to a rate of change. Not from the equations you have so far posted and as how one measures time is relative to the observer you will need a GR treatment.

You have to understand that Hawking radiation is a thermodynamic process it's radiation equates to photons as the mediator for the EM spectrum which is used also for blackbody temperature. All equations involving blackbody temperature uses the photon as the mediator for its radiation terms. The other detail to recognize is that any object of any mass can be a blackhole if it's mass is contained in less than Schwarzschild radius. The Smaller the volume of the EH means the rate of Hawking radiation produced increases as the EH shrinks due to mass loss. The smaller the EH the greater the Hawking radiation. The singularity or as close to singularity as possible ie near infinite density would still have sufficient gravity as well as other related forces to maintain an EH even if that EH is smaller than a soccer ball etc.

At that range you wouldn't really need much deflection something as miniscule as a 1 degree defection would likely be sufficient if even that. Likely some form of craft that has sufficient mass to gravitationally causes a change in angle by using its thrusters to simply stay near the asteroid . One could also feasibly save fuel using solar sails to get there. At the mass of the asteroid tethering wouldn't be practical. Though the outgassing method is also viable. Those are the two methods I see as most viable out of the ones I'm aware of.

What you described above really doesn't make much sense sorry to say. Particularly in how your describing causality in regards to past and future events in regards to gravity. For starters there is no antigravity. Also if you have a uniform mass distribution according to Newtons Shell theorem.

Just to add to the good answers already posted. One hurdle to overcome is thinking of atoms in accordance to the Bohr model. Which modern physics knows to be incorrect. Instead the atom has a probability cloud with different configurations. All described via the Schrodinger equation. https://www.khanacademy.org/science/physics/quantum-physics/quantum-numbers-and-orbitals/a/the-quantum-mechanical-model-of-the-atom This article from Khan University has a decent coverage.

Theoretically viable it would depend on distance, asteroid size and composition.

Prior to the Higgs field dropping out of thermal equilibrium the universe would certainly have rapid expansion. Simply put all particles are in thermal equilibrium and massless. So their kinetic energy term for momentum certainly overpowered the potential energy terms from any fields present. Once the Higgs field drops out of thermal equilibrium and particles gain mass this definitely helps slow down the expansion. The slow roll stages of inflation corresponds to this. However not all particles drop out equilibrium at the same time even though the Higgs field has. They drop out a different times this can also be seen by the different particle generations of the SM model. For that matter even the Higgs field had stages of how it drops out of equilibrium. Every type of particle that drops out of equilibrium affects the expansion rate. So no Higgs was certainly not the last field to drop out of equilibrium. Any particle type can be treated as a separate field in a multiparticle state.

Simply put the way it's done in current modelling is multi body as per a field treatment. One main disadvantage you are having is not knowing just how flexible, interconnected between models physics really is today. For example using a very high particle count there have been some incredible simulations simply to test our theories and applying the formulas of mainstream physics. One of my favorite involved several supercomputers nearly a year if I recall but it is incredible in its detail. It tested not only large scale structure formation, it also tested metalicity,(Big Bang nucleosynthesis). Galaxy formation, etc. It's really worth watching and then realizing that it's applying the mainstream mathematics. This is an example of just how capable the way main stream physics does things mathematics truly is. One further detail there is no restrictions on what mathematical method one uses. You can integrals, derivatives whatever you choose. Physics will use any mathematical method provided it accurately describes the system or state. It prioritizes symmetry relations for invariance to all observers, independence of coordinate choice etc for very good reasons. A good way to learn these is gauge group theory. Just to give you some idea of just how detailed our models are mathematically. Truth of the matter is. If you can mathematically and accurately describe a given system or state etc. The method used isn't incorrect. It becomes a valid method. It may simply not be the most flexible method or may be too restrictive to what it can accurately describe.

Well the universe is expanding its why the equations I provided show the expansion with the energy density and pressure relations. The basic relation however being Hubbles law. The greater the distance the greater the recessive velocity. Key note this isn't a kinetic based velocity but rather an observer based velocity that depends on separation distance. \[v_r=H_O d\]

Your right I didn't bother responding to your logic. As I stated I lost interest. Particularly when you have statements such as information travelling faster than c that you cannot back up with any real physics or mathematics. This includes your holonomic toroid allowing a faster than c wave. This runs counter to well known and understood physics. So any logic based on this is meaningless if you cannot show how that's even possible under mathematics using known physics. Another example is some mysterious toroid travelling at c. It must be something massless to do that. However you can't describe it beyond your verbal claims. I also have no interest in downloading a paper from an outside source when the rules requires that material to presented here.. Who knows you might catch my interest once you start applying some real physics or mathematics. Rather than nothing more substantial than your logic

Sorry to break to you the math is always relevant on physics. You will never convince any professional physicist without that math. As it's your model and conjecture I certainly will not do the work for you. In essence all we have is your claim. With nothing more substantial than a claim. Quite frankly I have already provided clues on what would be needed to prove a hidden variable with regards to the math. The geometry itself is extremely easy. Quite frankly there simply isn't anything of substance beyond your claims. So I have no further interest GL.

The first two paragraphs are accurate enough. It's more accurately described by As a result of expansion particle fields including the Higgs field drop out of thermal equilibrium in accordance to thermodynamic ideal gas laws involving tempersture/ density/ pressure and volume relations. Once the Higgs field drops out of equilibrium particles acquire mass leading to electroweak symmetry breaking. All particles and particle fields has a temperature contribution As for any personal proposals this isn't the section for that. If you choose to pursue personal ideas and a personal hypothesis our rules require that gets done in our Speculation forum. We may not currently know the cause of the cosmological constant. It may be quantum fluctuations due to the Heisenburg Uncertainty principle of the quantum harmonic oscillator which all fields are effected by. Or it may be the Higgs field. There is plenty of research papers suggesting either possibility however nothing is conclusive enough to make any determination between those two possibilities

I beg to differ on this score the FLRW metric is a GR solution and in GR time has dimensionality of length via the Interval (ct). It is that relation that includes length contraction and time dilation. Whether or not its required depends on the spacetime geometry. The simple reason you only really need the spatial component is that observational evidence shows a flat spacetime geometry. That's not some arbitrary choice of the metric. That the findings of all observational evidence. We have very useful methods for seeking spacetime curvature terms at our disposal. One example is distortions curvature causes light paths to bend this leads to distortions. Those distortions are constantly looked for. They can also be useful such as boosting viewing distance by gravitational lensing. That's just one method of detecting spacetime curvature there are others. The point being the metric does factor in the time component simply by being a GR solution. It's simply not needed due to all observational evidence. As far as observer effects, we do indeed need to take those into consideration. The dipole anistrophy due to Earths motion through spacetime in relation to the object we are observing must be factored in. A clear example was the findings of the first Planck dataset that had a dipole anistrophy in its first dataset. That dataset didn't have the correct calibration. That led to all kinds of pop media and scrambling. The next dataset had eliminated that dipole as we then had a better understanding of Earths momentum. As well as other localized effects. There isn't any arbitrary choice made the FLRW metric is quite capable of dealing with curvature. It's simply not needed beyond the weak field limit. You really only need the Minkowsii metric for the weak field limit. In a flat curvature parallel beams will remain parallel. If you have positive curvature those beams will converge. They will diverge for negative curvature. The converging or diverging is detectable and quite apparent in spectography in particular....which makes hydrogen a particularly useful test for distortions in its spectrographic readings. In particular the 21 cm line. That is what spacetime geometry ddescribes. All major findings show miniscule at best curvature best fit of a global geometry is flat. So the FLRW metric follows GR in the appropriate manner described by GR for a flat geometry

https://en.wikipedia.org/wiki/Floquet_theory for A(x) aka Floquet coordinates https://personal.math.ubc.ca/~ward/teaching/m605/every2_floquet1.pdf https://www.cfm.brown.edu/people/dobrush/am34/Mathematica/ch2/floquet.html

Accelerator physics Frenet-Serret Frame/coordinates Hamilton form reference reference 1) https://arxiv.org/pdf/1502.03238 reference 2) Particle accelerator Physics by Helmut Weidemann third edition particle trajectory r(z)=ro(z)+δr(z) define 3 vectors as ux(z) unit vector ⊥ to trajectory uz(Z)=dro(z)dz unit vector || to beam trajectory uy(z)=uz(z)+ux(z) "to form an orthogonal coordinate system moving along the trajectory with a reference particle at r0(z) . In beam dynamics we identify the plane defined by vectorsux and uz(z ) as the horizontal plane and the plane orthogonal to it as the vertical plane, parallel to uy . Change in vectors are determined by curvatures " dUz(z)d(z)=kxUz(z) dUy(z)dz=kyUz(z) k_x and k_y are the curvatures in the horizontal and vertical plane. gives particle trajectory as \[r(x,y,z)=r_o(z)+x(z)U_x(z)+y(z)U_y(z)\] "where\( r_0(z)\) is the location of the coordinate system’s origin (reference particle) and (x,y) are the deviations of a particular particle from \(r0(z)\). The derivative with respect to z is then \[\frac{d}{dz}r(x,y,z)=\frac{dr_o}{dz}+xz\frac{dU_x(z)}{dz}+\frac{dU_y(z)}{dz}+\acute{x}(z)U_x(z)+\acute{y}(z)U_y(z)\] \[dr=U_xdx+U_ydy+U_zhdz\] \[h=1+k_{0x}x+k_{0y}y\] curvilinear coordinate beam dynamic Langrangian \[\mathcal{L}=-mc^2\sqrt{1-\frac{1}{c^2}(\dot{x}^2+\dot{y}^2+h^2\dot{z}^2)}+e(\dot{x}A_x+\dot{y}A_y+h\dot{z}A_z)=-e\phi\] reference 2) 1.8O and 1.81 see floquet coordinates below

Night

Lets put it this way. The SM model including QFT has been so successful that just like the Higgs boson. It was able to predict long before detection over 90 % of the standard model of particles. There is still open questions so it's not complete. However it is simply the best fit for predictability and observational evidence. The VeV is part of that for the Higgs. If it weren't for the VeV range prior to Higgs detection. CERN wouldn't have known what range to look for to calibrate it's detectors.

Yes I do work with these on a professional level. Its also one of my primary focusses in regards to my primary expertise in Cosmology. Feel free to ask any questions and I will be glad to help you on it. Most articles including dissertations on Higgs will likely have those equations. Its certainly covered under papers regarding CKMS mass mixing. So resources are readily available to learn how to eventually understand the above. A big step is knowing vector and spinor relations under math. LIttle hint every SM model for every particle interaction (Feymann path integral) applies the Principle of least action via the Langrangian. Which forms also applies to the Hamilton

This is where we have to be careful. You may recall that the VeV is a probability function correct? That probability function will have a probability current. The term "expectation" value denotes this. So it has a weighted average that is described by the 246 VeV value. The other important detail is the Higgs field isn't just one field it is an SU(2) doublet. \[\phi=\begin{pmatrix}\phi^+\\\phi^0\end{pmatrix}\] however these are complex fields \[\phi^+=\frac{1}{2}(\phi_1+i\phi_2)\] \[\phi^0=\frac{1}{2}(\phi_3+\phi_4\] now these two statements describe rotations ( matrix, tensor operations) simply put. Yes those two equations do form a matrix but we can ignore that for now. now fermions have a few properties the Higgs mediates with each has a mass contribution the Higgs relation to charge Q, weak isospin eigenvalue \(T_3\), and hypercharge Y is related for the Higgs by \[Q=(T_3+\frac{Y}{2})\phi_0=0\] only the \(\phi_0\) current that gets a VEV...a probability current giving the weighted average likelyhood the last equation directly relates to the W, Z and photons gaining mass or not. Unfortunately this is where I'm going to have to turn it up a notch or a dozen notches quarks and lepton fields are organized in left-handed doublets and right-handed singlets: Matter is left handed, antimatter is right handed the covariant derivative is given as \[D^\mu=\partial_\mu+igW_\mu\frac{\tau}{2}-\frac{i\acute{g}}{2}B_\mu\] \[\begin{pmatrix}V_\ell\\\ell\end{pmatrix}_L,\ell_R,\begin{pmatrix}u\\d\end{pmatrix}_,u_R,d_R\] The mass eugenstates given by the Weinberg angles are \[W\pm_\mu=\sqrt{\frac{1}{2}}(W^1_\mu\mp i W_\mu^2)\] with the photon and Z boson given as \[A_\mu=B\mu cos\theta_W+W^3_\mu sin\theta_W\] \[Z_\mu=B\mu sin\theta_W+W^3_\mu cos\theta_W\] the mass mixings are given by the CKM matrix below \[\begin{pmatrix}\acute{d}\\\acute{s}\\\acute{b}\end{pmatrix}\begin{pmatrix}V_{ud}&V_{us}&V_{ub}\\V_{cd}&V_{cs}&V_{cb}\\V_{td}&V_{ts}&V_{tb}\end{pmatrix}\begin{pmatrix}d\\s\\b\end{pmatrix}\] mass euqenstates given by \(A_\mu\) an \(Z_\mu\) \[W^3_\mu=Z_\mu cos\theta_W+A_\mu sin\theta_W\] \[B_\mu= Z_\mu sin\theta_W+A_\mu cos\theta_W\] \[Z_\mu=W^3_\mu cos\theta_W+B_\mu sin\theta_W\] \[A_\mu=-W^3_\mu\sin\theta_W+B_\mu cos\theta_W\] this is how the mass terms are generated using eh CKMS mass mixing matrix above. Unfortunately this is a stage where I had to resort to under the math to be accurate enough on how the mass terms apply for W,Z, and why photons do not acquire mass. However this table may help visualize what is going on \[{\small\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline Field & \ell_L& \ell_R &v_L&U_L&d_L&U_R &D_R&\phi^+&\phi^0\\\hline T_3&- \frac{1}{2}&0&\frac{1}{2}&\frac{1}{2}&-\frac{1}{2}&0&0&\frac{1}{2}&-\frac{1}{2} \\\hline Y&-\frac{1}{2}&-1&-\frac{1}{2}&\frac{1}{6}&\frac{1}{6}& \frac{2}{3}&-\frac{1}{3}&\frac{1}{2}&\frac{1}{2}\\\hline Q&-1&-1&0&\frac{2}{3}&-\frac{1}{3}&\frac{2}{3}&-\frac{1}{3}&1&0\\\hline\end{array}}\] in the above table you also have Yukawa couplings as well for example for a quark \[\mathcal{L}=q_d\overline{Q}_L\phi d_R+g_\mu \overline{Q}_L\phi_c U_R +h.c\] h.c. is the hermitean conjugate in QM don't worry about the last equation its just to show that the mass terms isn't strictly due to Higgs. Yukawa couplings also contributes and it uses the same table as above. Also I did not show the right handed singlets in the above. for antineutrinos they have different mixing angles as singlets and will involve Majarona what I have shown may likely make your head explode as is lol. oh forgot to add prior to symmetry breaking the SM model uses the Goldstone bosons

well your on the right path see section 4 https://cds.cern.ch/record/348154/files/9803257.pdf "(4) In the unitary gauge, the isodoublet is replaced by the physical Higgs eld ! [0; (v+H)=p 2], which describes the uctuation of the I3 = 1=2 component of the isodoublet eld about the ground-state value v=p 2. The scale v of the electroweak symmetry breaking is xed by the W mass, which in turn can be reexpressed by the Fermi coupling, v = 1=qp 2GF 246 GeV. The quartic coupling and the Yukawa couplings gf can be reexpressed in terms of the physical Higgs mass MH and the fermion mass" it doesn't copy over well from the document please note this is a pre Higgs discovery paper published prior to confirming the Higgs mass so some of the numbers will be off. but it explains the VeV and how its set.

nice I wish there was a way to show the propagators better in latex. As there is two symbols for propagators in the Feymann rules. Wavy line being one the other dotted line (ghost propagators) the problem isn't the horizontal but the diagonals for triple and quartic interactions. lecture_16.pdf (usp.br) second link has the ghost propagators https://arxiv.org/pdf/1209.6213

Are you familiar with spontaneous symmetry breaking and the Mexican hat potential of the Higgs field ? Yes the VeV can be described as a fundamental property of the Higgs field in so far as it sets the scale where spontaneous symmetry breaking occurs to give the particles it interacts with their mass terms. At a certain temperature is when the spontaneous symmetry breaking occurs ( the precise value depends on the model ) however wiki gives the value 159.5 GeV which I for one do not trust. ( the paper wiki used didnt include the U(1) gauge. The value I have commonly seen is roughly 10^15 GeV which make more sense. Regardless of the temperature value the VeV describes the temperature where spontaneous symmetry breaking (electroweak symmetry breaking) occurs. At a higher temperature all particles are massless. At that temperature spontaneous symmetry breaking occurs and particles acquire mass. Here is a link to spontaneous symmetry breaking and it shows the Mexican hat potential https://en.m.wikipedia.org/wiki/Spontaneous_symmetry_breaking https://en.wikipedia.org/wiki/Electroweak_interaction the second link describes the VeV "above the unification energy, on the order of 246 GeV,[a] they would merge into a single force. Thus, if the temperature is high enough – approximately 1015 K – then the electromagnetic force and weak force merge into a combined electroweak force. During the quark epoch (shortly after the Big Bang), the electroweak force split into the electromagnetic and weak force. " this link has the correct value. I didn't bother including the link with the incorrect value.

Blackholes could exist at the time of the CMB but the blackbody temperature Migl mentioned would still be far lower than the blackbody temperature at that same time period. So they would be growing and not dying. We really do not know what occurs beyond the Event horizon so any statement made would be nothing more than guess work There has been some research papers suggesting this as one possibility. They have even developed tests for this possibility. One of those tests directly relates to the article you posted concerning GW wave data.