Mordred

Wrong our universe does in fact have a slight curvature term. It only approximated as flat. However that curvature term specifies a relation called the critical density formula. Which isn't quite the same as a GR curvature term. All in the papers being discussed. Expansion and contraction does in fact alter the null geodesic paths of massless particles such as photons. Gr curvature typically involve a center of mass hence it only assists the FLRW metric ( the FLRW metric is a specific class of solution that applies GR ) however the k curvature term itself for the FLRW metric directly involves the critical density relationship. If the actual density precisely matches the critical density term then and only then is our universe critically flat.

That's your hangup then as you refuse to understand why the authors state what they do. The key difference between SR and GR. Is that SR does not account for the spacetime curvature terms. Where as GR is specifically dealing with the spacetime curvature terms. The FLRW metric is a very specific coordinate system. That coordinate system is not accounted for strictly by the equations you posted. By ignoring the rest of the paper your understanding and conclusion is in error.

Here is the complete dissertation paper https://people.smp.uq.edu.au/TamaraDavis/papers/thesis_complete.pdf No you must understand the entirety of a paper before judging it in error.

There is no errors in the Lineweaver and Davies article. If their was it would have been pointed out when the dissertation paper was examined in order for the authors to recieve their Ph.D. It also one reference often mentioned as a reliable reference. You must understand how GR and SR applies in a commoving volume with curvature terms and not just focus on the SR equations and assume thats sufficient. Secondly mainstream physics section require answers that are mainstream concordance answers. It is not the place to post personal theories we have a separate forum for that. Focusing on just the equations you copy pasted is literally ignoring the rest of the article

All I'm interested is something with actual physics practicality.

\[ ct,x,y,z\] Done there is your 4 spatial components using interval for time. Is there some way you can think of to make that statement more intuitive ? Normalize the units \[c=\hbar=g=k=1\] and the majority of your equations are far easier to work with.

Your really are not grasping the time component. It is not a spatial dimension. We use an interval to measure the rate of signals between observer and emitter via (ct) which gives dimensionality equivalence to length but time itself has no spatial dimension. So modelling time using a tesseract or any other 3d object with an secondary object that can shift is not the same thing as time. Yes you can use 4 dimensions to describe the tesseract but it's simply 2 3d objects with a degree of movement of the secondary object that is independent of the main 3d object. That has nothing to do with time which is a property describing rate of change.

Considering there isn't a single equation used. How is there any usefulness to begin with its simply hand waving conjecture. Even correlation functions that do not involve any cause and effect would be something you should look into. Least then you can compare statistical studies. You might consider looking into some of the works with regards to the mind by Sir Roger Penrose least he is applying actual physics.

You never have a magnetic field without an E field for starters. Secondly amperes law shows that electric current generates the B field. Work requires force. Force is a vector if you apply the right hand rule to Lorentz force you find the direction of the force terms which is not on the curl of the B field. Cross posted with Swansont.

No problem whichever explanation works best with you as we're both stating the same answer

That detail gets into expansion rates vs jeans instability. (Which includes the speed of information exchange (often described as accoudtic oscillations ) example BAO of the CMB. This of course also includes baryonic matter to generate localized anistropies lending itself to localized gravity terms hence the halo formations Essentially early universe expansion rates will generate anistropies in mass distribution because baryonic matter and DM are limited by c. While expansion rates due to inflation are not limited by c. This lends itself to halo formation as well as galaxy and LSS formation. The first equation above applies jeans instability and expansion rates. Should add this also directly applies the virialization mentioned above by @joigus

We both x posted There but our answer is the same lol

A good way to understand the difference is that DM doesn't interact with the EM field nor the strong force. So lets use a simplified analogy. Two DM particles approach one another. Without EM interactions or strong force interactions they will simply drift by each other. Whereas two baryonic particles will have a higher likelyhood ie form into atoms etc. It is the lack of strong force and EM interaction that keep DM from clumping though they can form halos due to gravity.

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.