Mordred

Well the ground is conductive but conductivity will vary location to location. An easy way to see this is lightning strikes. This is a good example of the EM field in our atmosphere interacting with the Earths surface. (The term grounding) in electrical circuits dissipates unwanted electrical charge via Earth surface the grounded conductor is bonded to.

We still don't know the fate of the universe. Collapse is one possibility however we could eventually get heat death instead due to expansion. Other scenarios is the big rip however that one isn't too likely. If the cosmological constant aka dark energy stays constant then we're likely heading to heat death. However if at some point the cosmological constant does reduce then a collapse can occur. I should note expansion isn't directly due to expansion per se but via the thermodynamic relations of the various particles residing in our universe. Photons and neutrinos as well as other relativistic particles (radiation) gas a different equation of state to matter. https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) How those relations in the link above evolve over time is given by [math]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/math] This equation is used to calculate the value of Hubbles parameter \[H_z\] at a given cosmological redshift compared to the value today \[H_0\]

That's the impression I have as well hence trying to keep my answers applicable to how it's taught in high school aka flow of charge.

Good coverage Studiot +1

I wouldn't say stubbornly we hope to find it but I don't believe we achieved the necessary energy levels yet. The reason isn't because we need the graviton to explain spacetime curvature aka gravity. The graviton if ever found would be a tremendous help to renormalize gravity.

Yeah I've read proposals on different parts of the rigid body requiring different accelerations at each part so I do understand where your coming from on that aspect. One of the distinctions between Newton rigid bodies and relativistic rigid bodies is literally in how one defines the criteria of a rigid body. The relativistic rigid body allows for length contraction, while the criteria for the Newtonian version must maintain its length. If I recall the articles I've come across though there is still causation issues in signals propagating greater than c in particular with acceleration/rapidity which relates to the hyperbolic rotation of the Minkowskii metric. The different accelerations will result in differing Hyperbolic rotations throughout the rigid body. If I recall but would have to double check the Born rigidity article under SR article I linked also refers to that. to be honest though as far as the OP is concerned I'm still trying to fathom what he means by neutral simultaneity. Might just be a translation error Would those involved in this discussion prefer I stick to SR treatment as opposed to GR treatment as things can get immensely complex under GR for rigid bodies ?

I have yet to see a treatment where Born rigidity holds true. Care to provide one ? Lol course we can also examine Ehrenfests treatment https://en.m.wikipedia.org/wiki/Ehrenfest_paradox Though that will be a bit off topic though still involving a rigid body. Edit if you have a good example of Born rigidity that doesn't violate spacetime causality feel free to post it.

Good night hopefully the discussion goes better another time Lol maybe in conformal time lmao Correction to above timelike isn't as I described. Null is light like timelike v<c

G GR does not use rest frames all reference frames are inertial . What is the definition of an inertial frame ? A frame under constant velocity. Equal free fall it is not the equivalent to a rest frame. Do you have a reading problem ? The above propertime that clock on the worldline AS PER the WIKI link........ shall I go and quote each instance I stated the clock along the worldline for you for proper time... What don't you understand about that ? Is it the term reference frame ? A reference frame is an inertial frame of reference I already have summarized it's not my fault you refuse to read or understand

I see so we have from the topic at hand to you arguing the definitions given by GR that were not set by me. Let's make this simple in GR there is no rest frame unlike SR. In GR all observers frames of reference is the coordinate time. This is because the coordinate time is not invariant.. it is coordinate dependent. The rate of time will vary at any given coordinate as well as the observer. Got that so far ? The only invariant reference frame is the clock that follows the null geodesic worldline it is path dependent. This means it will depend on that worldline between different geometries , flat curved, Schwartzhild metric, Kerr Metric etc. This is why it's the proper time it is the only Lorentz invariant frame of reference in different geometries between different observers If you still have questions on that free to ask. I don't know your math skills but here you go http://web.mit.edu/edbert/Alexandria/notes1.pdf Now why does the wiki link specify the timelike geodesic (null geodesic) ? Well for starters c is Lorentz invariant. All observers measuring the velocity of a photon will measure the same value. Does that help to make better sense of the clock following the null geodesic ?

Look I'm going to answer questions as I choose to answer them. At any point in time I can back up any statement I make with literature or the mathematics.. I supplied links explaining proper time and coordinate time if you choose not to read those links and attempt to understand what I'm referring to that's your choice. I have also supplied two articles that directly show the rigid rod analysis including taking the time to find a mathematically simplified version.

You are correct the electrons do move slow in an electric wire, hence it is the flow of charge that moves near c. https://www.physicsclassroom.com/class/circuits/Lesson-2/Electric-Current here. In the EM field the force carrier is photons. When photons i interacts with an electron, the energy of the photon can be transferred to an electron as potential energy. When the electron loses potential energy, the electron can account for the energy difference by emitting a photon. This is under QM treatment

Ok let us get back on track here no pun intended. I located an easier to understand SR treatment "Rigid body motion in special relativity" https://arxiv.org/pdf/1105.3899v3.pdf hope this helps the dscussion, the equations are readily applicable to the train

its more commonly used in electrical and electronic textbooks for one thing. Also if the poster is a student his physics class in Highschool will specify flow of charge and not flow of electrons which propogate through a medium at different rates

to add to this your better of following the flow of charge

trolling tactics you are aware I am a Resident Expert on this forum correct ? Any clock at a given reference frame is the coordinate time. Proper time is a clock that follows the Worldline given by the line element of the applicable geometry. usually denoted by the separation distance between two events. For Euclidean geometry ( I did provide links earlier to coordinate time and proper time ) \[ds^2=dx^2+dy^2+dz^2\] The worldline is the null geodesic path which is represented by the line element or if you prefer the affine connections given by the Christoffel connections. The line element is typically easier to understand though lol. Though the geodesic equation includes the Christoffel here is the Minkowskii line element \[ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\]

your welcome. the criteria to meet is given in the first equation that the distance does not change between any two particles. \[ V(r,t)=V_0(t)+\Omega(t)r\] is the solution to the first equation \[\Omega(t)\] being an antisymmetric tensor that's the criteria. the rest of the article deals with the examination Ok your not familiar with GR terminology fair enough https://en.wikipedia.org/wiki/Coordinate_time please note that the following from the article.

Correct it is precisely about the rigid rod have you looked at the link I posted or did you miss it?

Have you looked at the article I posted yet Lorentz ?

This is mainstream physics my earlier statements stress that under GR there is no rigid rods thus applies to the train no matter how its being examined

Sure I can go with that Here is the Born Rigidity examination https://fnegari.github.io/files/notes/009.pdf From this article it should be clear just how tricky any rigid rod examination can get

No we're still talking about the same topic a train are we to assume the train never turns ? not that it matters in the Lorentz gauge acceleration is a rotation called rapidity.

I still believe your missing the point. Even if every single coordinate was effectively it's own engine and you could contrive some means of synchronization. Once the train needs to turn you would end up with differing accelerations. So once again we're stuck with needing communication. The reason I asked how much GR you understood is that I wanted an idea of your math skills. Are you familiar with the four momentum in mathematical form ?

Nope just examining the situation under GR I do believe this is the relativity forum unless things have changed. I know you ate familiar enough with relativity to recognize the rigid rod conjectures in regards to relativity I was making Lorentz aware that proper time differs from coordinate time in regards to Each engine clock will be in coordinate time. Anyways it will be interesting when the train tries to turn.... so far the examination has been strictly linear.

Ah so now we're changing goalposts. I was showing the problems of Born rigidity. Either way there are no rigid objects under GR.