Mordred

Yeah but when you factor in the speed of information exchange c (this includes baryonic matter as well as DM) and the scale of the universe it gets rather complicated. The equations I mentioned is below https://en.m.wikipedia.org/wiki/Press–Schechter_formalism For galaxy rotation curves the methodology including DM is the NFW profile.. https://en.m.wikipedia.org/wiki/Navarro–Frenk–White_profile Essentially this profile is a power law in point of detail one can derive a log function for the above profile that shows that by enveloping a galaxy with DM so the mass is uniformly distributed with mass greater than the mass of the galaxy itself you get the observed galaxy rotation curves. Without this distribution and no DM the mass terms of strictly baryonic matter would give what's called a Kepler decline. As to the first set of equations they ger applied primarily in predictions involving early universe large structure formation due to DM halos in the early universe. Which is another factor in cosmology where DM is needful.

The truth is in order to understand the E field and B field as it pertains to the phase windings of a motor. Maxwell equations are essential. This includes any current calculation pertaining to motors such as that used in your OP. However Maxwell equations include several other key relations. Gauss law \[\nabla \cdot E\] the dot refer to the inner product between two vectors. However E is the E is a vector field. First diagram supplied by Joigus. Has a point of origin and diverges as an outgoing vector field. https://en.wikipedia.org/wiki/Gauss's_law Amperes law \[\nabla \times B\] Here the × refers to the second graph supplied by Joigus above. This the curl, a curl is a complex vector function called a spinor. Now this field is not divergent details under Lorentz force law next link. It also states that there is no magnetic charge. Link below includes both Amperes law and Lorentz force law https://web.mit.edu/sahughes/www/8.022/lec10.pdf Lorentz force law this one applies all the above. I will use the SI unit format from the above link F=qv⃗ ×B⃗ this law directly pertains to the directional components and the force vectors of the E field. Maxwell equations also include the Biot-Savart law Specific to the magnetic flux density however thats often overlooked https://en.wikipedia.org/wiki/Biot–Savart_law Another key law being Faradays law https://en.wikipedia.org/wiki/Faraday's_law_of_induction In essence Maxwell equations provides us a means to account for all the above. see 13.3.1 https://www.scienceforums.net/topic/134409-electromagnetic-field-lines/ Those will provide the essential equations pertaining to motors however each type of motor due to its design may require different relations using the above example 3 phase motor windings with alternating current, number of poles etc.

Piece of advise it would be impossible to stitch together some model for DM without having a sufficient mainstream understanding in the related mainstream physics theories and models. For example how does one determine the measurable effects via indirect evidence unless one knows how calculate galaxy rotation curves or what influence DM would have on expansion. If you cannot perform those calculations then you have zero ability to test any theory with regards to DM. There is also mainstream formulas that describe and define the most likely distributions of DM in terms of their early universe large scale structure formation contributions. (Trust me it's not an easy formula to use). The formula will return a Gaussian distribution (it's also one I've never mentioned before on this forum)

The detail to understand is that magnetic field ie the B field does not perform work it is the E field that does the work.

A good solid reference with regards to EM field lines including the relevant Maxwell equations can be found with introductory to electrodynamics by Griffith. The first 6 chapters if I recall should have all the relevant equation you will likely need. If you like after work as I have time I can post the relevant equations and relations between E and B fields.

As I stated any errors in those statements do not particularly matter as those relations are not part of the calculations involved for the acceleration equation used by the FLRW metric itself Those are nothing more than heuristic reminders as an assist they have zero importance to the FLRW metric beyond a brief description of what an adiabatic and isentropic system entails. Those posts your referring to was also several years ago. The only relevant mistake was trying to find some heuristic way to get the thermodynamic relations involved through to you in the first place instead of using related Euler langrangian equations which actually determine the energy/density to pressure relations. Quite frankly your making me regret trying to use a heuristic explanation to get you to understand it at that time Truthfully I would thoroughly enjoy watching Carrock struggle for several hours on a single post full of equations in latex. Some of my larger posts full of equations can take me up to 8 hours to get through. It's extremely easy to miss typos under those circumstances. It has nothing to do with struggling with the math for all my edits. It's literally fixing latex errors and saving often so I don't lose those latex expressions already done.

Correct not once have you ever math yourself glad we agree on that. You have never done in any of your claims of me applying pseudoscience. Nor have you ever supplied any reference showing an error in my thinking. Here is a little detail those statistical mechanics terms are simply reminder relations of what gets involved when one describes an adiabatic and isentropic system they aren't even used by the FLRW metric itself. The equations of state relations are what gets used. Those statistical mechanical terms are simply heuristic reminders. They aren't essential to the FLRW metric the equations of state are.

The conventionalistics you mentioned are stating differently than your assertions. So at this point you need to provide the mathematical detail showing otherwise. As Markus has already requested. You already concluded that simultaneaty is lost in accordance to the conventional methodologies. It's up to you to show why that shouldn't be the case mathematically at this point.

So do I the problem with Harking radiation is that he never did specify which particle/antiparticle pair is used. There is a reference I believe already posted in this thread though will have to double check that after work mentioning that detail. That same paper examines different gauge bosons in regards to Hawking radiation and the ramifications of each using the ( cpt) symmetry relations. The reason photons are typically used is it is the mediator for blackbody temperatures.

I didn't speed read the article that article describes how particle physics in mainstream physics describes an anti particle. The thing is not once have you ever posted anything mathematicsvof your own to ever show I have been incorrect on something in every single claim of my being incorrect in any post where you and I have a conflict in understanding. I have done in nearly every instance. You have not. Nor have you ever bothered posting any reference showing where I am in error beyond blind assertions that I am. You wanted a reference you got one. In regards to thermodynamics you already know from the link you already provided yourself that the FLRW metric models expansion as an adiabatic and isentropic expansion. That is the basis behind the equations of state the FLRW metric uses for the acceleration equation. Your last post has always been your typical tactic. Ignore Any reference given. That last reference is a CERN lecture note. Your refusal to accept my answers even when references have been provided in those past conversations does not mean I am talking pseudoscience. That is a false accusation. To put it bluntly not once have you ever provided any mathematics or reference paper showing any claim of me being incorrect. (Not once) That is precisely why I don't waste my time defending myself vs your accusations. You never do the same steps you require from me ie supplying references as one example. As far as those equations I provided in regards to thermodynamics the textbook those equations came was from my notes from when I was studying Andrew Liddles textbook. Years back I might add . That was back when I was trying to find more classical treatments for the benefit of the average poster on this forum.

A reference frame does not require a convention of simultaneaty. Simultaneaty is typically lost in curved spacetime as mentioned several times by Markus. The infalling clock falls along a specific curved spacetime path in PG coordinates. That is provided by the PG line element.

Nice post couldn't agree more +1 haven't read that one I may pick it up One detail to add though in PG coordinates we are using a new time coordinate defined by tr=t+a(r) related metrics here https://en.wikipedia.org/wiki/Gullstrand–Painlevé_coordinates Edit the equation Markus posted still applies. Even under that new time coordinate definition.

Lets get a couple of details out in the open. I'd like to quote a certain section of the link I lasted posted. to quote. In conclusion, we started with a negative energy solution of the Dirac equation and we end up with a solution which has positive energy and reversed 3-momentum. Indeed, if we reverse the momentum 4-vector this is identical with one of the positive energy solutions of Lecture 6. Hence, by reversing the momentum 4-vector of the negative energy solutions we obtain solutions which describe antiparticles with positive energy (physical particles). Another observation is that we started with a negative energy particle solution, which moves backward in time, since p 0 = E < 0 , and we found that this is equivalent to an antiparticle solution which has positive energy and moves forward in time because p 0 = ∣E∣ > 0 . In other words, negative energy particle solutions going backwards in time describe antiparticle solutions which have positive energy and move forward in time. Now think in terms of those particle antiparticles with regards to Hawking radiation. key note the statement " The physical antiparticle is a positive energy solution" you can certainly model as a negative solution but the physical antiparticle will always have positive energy. Hence you need to understand the charge conjugation terms and how that term includes the particle momentum and helicity terms. In QFT for Lorentz invariance the Klein Gordon is used as opposed the Schrodinger. Unfortunately that is the method I most commonly use for anything relating to particle physics. So that is the method I typically use when answering questions relating to anything involving particles. This includes Hawking radiation. As noted the antiparticle has positive energy. Even though literature often refer to the negative energy solutions. Hawking radiation articles also don't typically cover the charge conjugation aspects that identify and define the particle/ antiparticle. In higher grade articles such as arxiv articles your already already to expected to know this detail.

For aid to the OP cosmic time which is the standard for the FLRW metric used to describe our universe is of the form. \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] An important relation is the critical density relation \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] the equations that detail the FLRW metric acceleration equation are below. \[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\] now in the first equation the proper time is the \(-c^2dt^2 \] term above. However in order to understand how that time component is used by the FLRW metric one has to also understand which class of observers are involved and how the cosmic clock is connected to the Hubble flow (commoving time). As opposed to how SR or GR handles it. GR in this metric the time dependence is directly tied to the scale factor a(t). This wiki link actually has a half decent coverage of the time component of the FLRW metric. https://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric

Thank you for providing a solid workable reference +1. That article (well the actual dissertation paper corresponding to that article) is used as a baseline test for the cosmological calculator in my signature. (Just an FYI) on that part. There is a couple of important lines here that directly relates to how the time components of the FLRW metric is applied and some considerations with regards to blindly treating the recession velocity under strictly SR transformations. That is denoted in the the opening statement of the article. We can see beyond the Hubble sphere and a strictly SR transformation will give infinite redshift at the Hubble horizon. The Z value provided being z=1.46 roughly (depends on the cosmological parameter dataset used). The article also mentions that standard candles can be used to rule out SR interpretations of redshift. section 4 mentioned on page 6. section 4 being where the details relating to cosmological redshift under GR becomes essential as opposed to SR the article goes on that the equations in 7,8,9 do not accurately describe expansion due to the treatments applied with recession velocity top of page 15. section 4.3 now changes the scenario in how expansion is treated by the following statement. "In this article we have taken proper distance to be the fundamental radial distance measure. Proper distance is the spatial geodesic measured along a hypersurface of constant cosmic time" So time is now treated differently via the proper time defined by that last statement as supported by statement "Time can be treated differently eg correctly calculate recession velocities from observed redshifts . However to do this we would have to sacrifice homogeneity of the universe and the synchronous Proper time of commoving object". lets stop there for the time being ( no pun intended to see how far the OP understands the article and what I just described) Particularly since a huge set of common misunderstandings of how time is treated by the FLRW metric exists most common trying to apply SR directly to recession velocity

while your at it I hope you look up charge conjugation of the photon being -1. With regards to particle/anti particles including neutral particles such as the photon. Here is a reference paper on charge conjugation as it applies to particles and antiparticles. https://alpha.physics.uoi.gr/foudas_public/APP-UoI-2011/Lecture10-Charge-Conjugation.pdf see page 14 for the negative energy solution top of page. That is the QFT treatment applying the creation and annihilation operators in regards to all particle/antiparticle pairs. This article also directly describes the Helicity terms in regards to all particle/antiparticle pairs. Good luck understanding the equation on page 14 without understanding QFT under those groups The group relations outside this article are the U(1) SU(2) groups you need as you will need both the Dirac matrices and the Gamma matrices. Those equations are previously posted including the covariant derivative for each group.

energy density is always positive for every particle in the standard model left hand particles are doublets under weak isospin the singlets are the antiparticles. Left handed helicity is the normal particle. Right handed helicity is the antiparticle. That is in textbooks. Tell me something if the photon wasn't its own anti particle then where does the issue with baryogenesis and leptogenesis in Cosmology come into play ? You would already would have a matter positive universe simply by having photons. So obviously even though the photon is charge neutral it still has charge conjugation. those negative energy states are negative FREQUENCY modes described with helicity. Now lets apply some every day classical physics. What happens when a Negative frequency encounters a positive frequency ? You only need to look at the elastic and inelastic scattering equations to answer that question.

yeah they are typos not pseudoscience. Carrock have you ever bothered to look into charge conjugation with regards to photon/antiphoton yet and look at how Helicity is involved between standard model particles vs their antiparticle ? Can you identify which is the doublet and which is the singlet ? If you have then under QFT the sum of amplitudes given by their cross sections is what determines what occurs in Feymann path integrals. That equation you posted above is literally the photon/antiphoton integrals used in Feymann diagrams. That's the barrage of math I used to provide the needed formulas the key equation though falls back to \[Q+I^3+\frac{\gamma}{2}\] however you have to understand at least U(1) symmetry group mathematics ideally SU(2) as well. Which is what a large bulk of those equations I posted earlier this thread directly apply to

I'm getting tired of accusations from posters that never show any mathematical argument to support their claims. I think I am well within my right that if someone claims I am wrong they are expected to prove just that beyond bland statements. For example those equations you posted Carrock are contained in textbooks on Cosmology with regards to the thermodynamics. Accusing me of pseudoscience when I am describing textbook equations and relations doesn't work in your favor For one thing I have never seen this article before I don't use screen shot reference papers from some lecture for something inclusive in standard textbooks. The reason those equations look familiar is precisely for the detail they are in standard textbooks.

Due to the Cosmological principle and the homogeneous and isotropic expansion no point of reference has any preference for showing expansion. It might be easier to understand expansion as a decreasing energy/density. This should lead you to the FLRW metric acceleration equations and the relevant equations of state for radiation, matter and Lambda. The rate of volume change are determined by that equation. In essence the FLRW metric treats the universe as a perfect fluid with adiabatic and isentropic expansion. Should also indicate another piece of evidence of expansion (density changes and CMB blackbody temperature changes.)

Can you show that using the FLRW metric and not relying on a YouTube video. The proper time statement is inclusive in the FLRW line element but one has to recognize that we have different time treatments involved (proper time) commoving time, conformal time and look back time. The common treatment being commoving time to a commoving observer.

A forum label certainly doesn't alter anything career wise nor does it affect any of my physics credentials. Nor will it prevent me from continuing to answer any threads that involve GR/SR. Quite frankly I have never seen Md65336 ever answer any questions involving relativity beyond Minkowskii. For example there hasn't been any effort on his part to help in the PG thread. He questioned my post yet when shown the perturbation tensor being applied doesn't even acknowledge it. As a point of example anyone that knows how the EFE works knows that you have the metric tensor and the perturbation tensor which acts upon the metric tensor. So should have recognized the statement that md65336 posted in this thread as having validity by recognizing how \[h_{\mu\nu}\] Gets applied it's one of the more commonly used tensors in GR treatments and is also used in renormalization procedures. Nor has any error in any mathematics I have ever posted has been shown erroneous by md65336. So the issue is largely how something is verbally described and not how the mathematics itself directly applies.

Whatever you wish to believe quite frankly I've never seen you look at relativity beyond Minkoskii. As such I certainly don't find your opinion of my understanding of relativity as an expert opinion from yourself. As I mentioned I have no interest in defending myself because you don't agree with my understanding of relativity. Have a good nightl

You know so something I'm not going to bother Believe what you like take the Resident expert label for all that it matters of the record one can have expertise in a particular field of physics without being an expert in another.. I' not about to sit here and defend my position over the course of my membership on this forum to you because you disagree with how I understand relativity as opposed to how you understand it. Quite frankly I posted you dozens of references over the course of our discussions in my defense and you typically ignored them. In particular with our discussions on rapidity... In case you haven't figured it out I don't cone to forums to defend my expertise I come to forums to help others. I don't particularly care if you consider me an expert or not.

now were bringing up a different thread ? on a different discussion ? what is your reply to mathematics I just posted ? please link the threads in question I sincerely hope at some point in time you will defend your accusations with some relevant mathematical arguments