Mordred

precisely

No in order to get decent answers to start with you have to ask the right questions. If the user relies too heavily on an AI to do their thinking for them. The user never learns and can never ask the the right questions to advance the users understanding. I come to forums to help teach physics to people not an AI. If I wanted to argue with the AI I would download it myself and argue with it directly

So that circuit diagram is not accurate to your setup ? Why don't we start with an accurate circuit diagram with component values where applicable

Yes hence why I have no interest arguing with an AI

This came up in one of the earlier pages. You hear a lot of current YouTube videos stating fields are fundamental. Yet at the same time under QFT fields are simply a geometric distribution of values. Some quantities being physical (measurable) in this case and strictly mathematical. The problem with occupancy with fields is under QFT is the probability density functions. Using Higgs as an example with the above the field encompasses all spacetime however at each location there is a probability of occupancy of a Higgs boson. However the Higgs boson is extremely short lived. Also to get a Higgs boson that probability also requires sufficient energy that in essence requires another particle interaction. In essence the Higgs field is not a sea of Higgs particles flying around to get a Higgs boson requires another particle interaction to mediate. This is the problem with all gauge boson fields (specifically gauge boson fields) force fields for short) While the field may be described as existing everywhere the occupancy will be in a state of constant shifting occupancy where every location has a probability of having a particle. So the best we can state is everywhere there is in spacetime a field however that also does not mean that all of spacetime is filled due to fields In essence space still serves as the arena the volume , whose occupancy is determined by the field probability density functions. This is true for all particle fields under QFT. Including matter fields Now there's a mouthful lol. To borrow a line from the Sean Carroll video in one of our pinned threads. "To get a Higgs boson one must poke the field "

@studiot +1 nice demonstration video I also noticed the equation 10 (b) of the Elihu Thomson ring was highly applicable to the circuit shown

Let's start with time. Time is a property of a system, state etc. It never exists on its own. Secondly the Interval (ct) is what gives time dimensionality of length not time by itself. Can there be multiverses and time prior to our universe absolutely (bounce cosmology or cyclic universe cosmology). However your approach is far too hand wavy there is plenty of mathematical examples with regards to multiverses.

For the record Fourier analysis is used for the entire model of particles it isn't restricted to MRI. It's essential in QFT

Seems both @Studiot and I agree on this. I will leave this in Studiot's court as engineering is far more his specialty.

forgot to add you will also want to be familiar with Stokes theorem for the curl of a vector with regards to curved spacetimes

As Studiot mentioned there is no need to consider magnetic field lines in the above except as it applies to the transformer primary and secondary windings. Its really basic induction if you supply the motor details, transformer winding ratio between primary and secondary windings and capacitance value it should be trivial to run calculations on this circuit. The capacitor is providing the phase shift via capacitance reactance. I would be curious to see the 3 phasor diagram this circuit produces It would not surprise me to find your introducing phase imbalances that will eventually ruin your motor windings. A quick way to confirm that is to take voltage readings between (T1 T2).( T1 to T3), (T2,T3) they should all have identical voltage if not then your damaging you motor. (PS its also likely your back-feeding harmonics back into the power grid) which your electric supply company may take issue with) edit forgot to add Induction can also cause capacitance reactance. For example an inductor is impossible to burn into an IC chip but one can replace an inductor with a capacitor which is easily burned into an IC.

As @studiot mentioned were dealing with foliations with the line element its not as straightforward as one might think looking at the equations You have to look at what geodesic congruences are being applied. This typically requires using covariant derivatives provided in the article below for PG coordinates \[ds^2=dT^2-(dr^2+\sqrt{\frac{2M}{r}}dT^2-r^d\Omega^2\] the Euclidean space is the surface of constant T. One of the better articles covering this detail and showing the light-cone shift is here https://www.sissa.it/app/phdsection/OnlineResources/104/Adv.GR-Lect.Notes.pdf The above is the reason I was seeking decent coverage of geodesic congruence however there is far too many prerequisite steps such as Leibniz product rule. Knowing one forms and 2 forms etc if you aren't familiar with their usage and reasons for usage under GR. As they are needed in this case In curved spacetime the only way to remain Lorentz invariance is to use a minimum of a vector and a convector. If you never worked with convectors then that is a preliminary step you will need. For example with the above the Kroneckeer delta affine connections using Leibniz gives the maximally symmetric spacetime (Minkowskii, De-Sitter/anti Desitter) spacetime region. (local) the global metric above the affine connections follow the Levi-Civita affine connections. This is used in regards to aspects such as the killing vectors with regards to the Ricci scale term the maximally symmetric spacetimes the Ricci scalar is constant. That is some of the preliminary details with regards to geodesics and also a huge part of understanding the Christoffel term of the geodesic equation for null geodesis. You already mentioned your not too familiar with GR how much calculus have you taken ? The latter parts can be found in Calculus textbooks they tend to have the best coverage of the Kronecker delta and Levi-Civita. The lesson you need to learn is as follows the acceleration of the object is determined entirely by the connection coefficients of the geometry and has nothing to do with the properties of the object

@externo I would like you to consider the following with regards to the raindrops or Lemaitre frames. Take any number of raindrops. Each raindrop has its own geodesic. now examine the deviations between each geodesic. In the freefall state the equations of motion are the first order velocity terms (free fall). The geodesic deviations due to the curvature terms (easiest example to understand towards a common center of mass in the Newtonian limit) is the tidal force what we see as the second order acceleration term. Both links I posted earlier (the two lecture notes) include the relevant mathematics. This is what you will need to understand geodesic congruence in The PG coordinates. You will also need to look into the maximally symmetric spacetimes (local) vs global and how to transform one to the other. All those details in those lecture notes.

@Markus Hanke I've been trying to find a decent method to explain geodesic congruence in regards to PG and Lemaitre frames without getting too technical. Have you perchance come across any decent treatments. Blau and Wald may be a bit too intense

Ok with PG coordinates there is some very different treatments from the Schwarzschild Metric the first is the use of the raindrops. Each raindrop has its own clock falling in from infinity. The other feature is that for the lifting operation (singularity treatment) the time coordinate is tied to the scale factor a in a similar fashion as a commoving observer for the FLRW metric (but don't confuse the two). The light-cones are also defined differently in This case the tilting has a different cause. That cause is due to the above two conditions which lead to a different light-cone definition. This is where a reference you have been using would be helpful If you don't have a reliable reference either Markus or myself can likely find one for you. However it may be best to use a reference that you find easier to understand and relate to. Recall earlier I linked the following https://en.m.wikipedia.org/wiki/Lemaître_coordinates this formula is not included in that link but arises from the raindrop coordinates using the Symmetries mentioned in the above link \[dT=\frac{\partial T}{\partial{t}}dt+\frac{\partial{T}}{\partial{r}}dr\] I'm going to drop this reference as it certainly will lead to unnecessary confusion particularly since you already stated afterward that you are not strong in GR mathematics. That and were not really concerned with Kruskal diagrams at this stage https://link.springer.com/article/10.1140/epjc/s10052-023-11370-9

Lol truthfully wasn't worried on that score to begin with not that it matters in the slightest. As far as multiverses go, each universe can indeed have its own mass/energy distribution leading to different expansion rates and critical densities. However our region of causality will be limited to our universe unless some collision occurs. There is a line of research that looked directly for signatures in the CMB and the axis of evil from the first Planck dataset was a contented possible signature at that time prior to realizing that the dipole anistrophy was due to unaccounted local effects from our peculiar motion. Calibi-Yau doesn't particularly deal with multiverse but you do see papers suggesting such much like you do in the many worlds interpretations of QM. In all honesty though I myself focus on this universe as multiverse theories are far too speculative Just a side note though our Observable universe is simply our region of shared causality. When runaway inflation in early inflationary theories was determined attempts were made to solve runaway inflation. One of those attempts being Chaotic eternal inflation which leads to bubble universes (different regions with different expansion rates ). Sometimes coined Hubble Bubble universes. One can however readily determine shared causality regions such as is done for our Observable universe (Cosmic event Horizon) It's been a long time since I saw the movie but there was a lot in that movie that wasn't very realistic when it came to that universe. If I recall even in space they had an atmosphere such an maas/energy density would have likely collapsed but hey it's Sci fi

Lol +1

Yes but look back on the T relations I provided back on page 1 the links to that site never seem to direct me to where it should be going and the site being in French makes figuring out why I'm getting redirected isn't helping. Been kind of busy atm hopefully this eve or this weekend I will have time to assist on the Time components specific to PG as it uses its own time for proper time T and replaces \(\tau\)

T being the PG time it might be best to agree on a specific article at this point as nomenclature between treatments can lead to confusion. We have to look directly at the covectors and vectors at this stage. Covectors are needed in curved spacetimes whereas in Euclidean space vectors are sufficient.

Now your getting it recall \[ x^\mu\] is the particle. X is always the coordinate axis for the particles momentum. In the Minkowskii case the changes to x is only the rescaling for length contraction. In curved spacetime however the x axis is changing orientation as it's the tangent vector on the hypershere. That should be a huge help to making the mathematics of GR easier to understand +1

Hiding behind authority meaning recognizing and using GR correctly. The problem here is you keep repeating claims that run counter to GR itself yet have made zero effort to show mathematically where GR is wrong using mathematics and not mere assertions. However as you stated your not proficient in the mathematics of GR so quite frankly stating others who are proficient in the mathematics is incorrect isn't a very useful tactic. A good example is stating the equation Markus posted was wrong when the truth is you didn't understand the equation. Mathematics aside do yourself a favor take a beach ball and place a ruler on the surface of a beach ball without deforming the ball The point of contact of the ruler to the ball surface is the only portion (localized region) where the Ricci curvature can be approximated as zero. That is only region where the Minkowskii metric will work. You cannot globally apply Minkowsii to a curved manifold. Precisely as Markus has been stating. PS the point of contact (tangent to the surface) is where the affine connections reside and you are using covectors /contravectors under GR. Now think of your ruler as the basis tangent vector for your lightcones give you a hint why the lightcones are changing angles ? Now move that tangent vector around the circumference of the ball ( that's what is being described by the Levi-Civita affine connection) as well the geodesic equation in curved spacetime. The kronecker delta only applies for the Euclidean portions (localized hyperslices ) with regards to Minkowsii (The RULER is the particles momentum) the surface of the ball is the Worldline.

Surveys is how you get a mean average response study on a populace of ppl. It's commonly done under phycologist studys

Surveys for starters Then where is the physics ? The entirety of physics requires at some point measurements and mathematical relations hence requiring units Here is the nitty gritty detail. Every physics field you mentioned above has momentum terms they can all be described for all its interactions via kinematics. Specifically under the Euler- Langrangian. How are planning to integrate emotion to kinematic action ?

Ok apparently a different approach is needed. @externo I would like you to consider the following we all agree that particles follow geodesics just as we all agree that the massive particles follow a different geodesic than a massless particle. So here is what you need to figure out What are the affine parameters of the null geodesic with regards to the Schwarzschild metric and PG coordinates and why are affine parameters needed in the massless particle case as they are not needed in the massive particle case. You can find the answers to the above in pretty much any GR textbook though I recommend Wald, Mathius Blau or Sean Carrol recall in the null geodesic case \[ds^2=0\] here is Sean Carrols lecture notes https://arxiv.org/abs/gr-qc/9712019# here is Mathius Blau's http://www.blau.itp.unibe.ch/newlecturesGR.pdf I would also highly suggest you look at the Levi-Civita affine connections and the Kronecker Delta with regards to Riemannian manifold with the above

Your welcome. If I may make an assumption your reason for asking is solar panel efficiency. So the article should prove useful in that regard.