Mordred

Thread reported I'm tired of your attitude

No it can involve rapidity but is not the only methodology. I do recall that discussion lol I actually enjoyed that discussion.

Sigh (hopefully you don't get insulted again) lets show you how this works. start with the Lorentz transformation. \[\acute{t}=\gamma(\frac{vx}{c^2})\] \[\acute{x}=\gamma(x-vt)\] \[\acute{y}=y\] \[\acute{z}=z\] the two equations most relevant are the first two note the velocity term velocity is the vector rate of change in position and direction. As you doubt everything I state and argue everything I state here https://www.physicsclassroom.com/class/1DKin/Lesson-1/Speed-and-Velocity Oh my it specifies inertia frames https://en.wikipedia.org/wiki/Lorentz_transformation you can read it for yourself and don't take my word for it if you choose acceleration is handled via rapidity the equations are also in that link. https://en.wikipedia.org/wiki/Free_fall Newtons laws of inertia https://en.wikipedia.org/wiki/Newton's_laws_of_motion note that the freefall link specifies no force acting upon the body it is in freefall no net force however Newtons laws of inertia still apply. The body is in motion, one can arbitrarily choose any event as the rest frame under SR it could be the twin leaving the planet or the stay at home twin both twins are in inertial frames (not accelerating, constant velocity). the same applies to freefall Alice is the observer on Earth. Bob is the Observer in freefall. The choice of who is the rest frame is arbitrary with the above transformation. Hopefully in the freefall state your know \[m_g=m_i\] equivalence principle gravitational mass is equivalent to inertial mass. if not google Principle of equivalence. we wont get into tidal forces just yet but succinctly if you have two bodies in freefall the vector direction is towards the CoM. the tidal force between the two bodies is \[\frac{d^2x}{dt^2}-\frac{MG}{r^3}x\] now I suggest you study again the above further applies to the addition of velocities \[U=v+\acute{U}\] where v is the velocity between observers U and \[\acute{U}\] is the two observers.

I Strongly suggest you study the terminology you will find those statements are 100% accurate under both SR and GR. You do not need to take my word for it pick up ant SR or GR textbook Seriously you post something for everyone to read where does reading thoughts enter the picture ? This is a forum anyone can respond at any time whether you like it or not. That's is part of the rules on a public forum that you agreed to when you signed up.

If your addressing a specific individual you should state that but when you leave a question on a physics forum. Anyone can answer said question. That is precisely the purpose of this forum

You asked what real waves I directly answered this question and answered it correctly

I don't particularly see describing it as a non causal wave to be an issue here. As long as it's understood to represent individual components of the train separately powered via the engine. I've still been considering the hyperbolic Lorentz transforms in regards to the different acceleration rates.

Will you please stop trying to insult me. I personally couldn't care what your opinion of me is but this is starting to get old real fast. Stick to the forum topic...

Well sorry if you took that as an insult it's a simple statement of fact nothing more. There are after all other readers

If I choose to reply I will do so.

Good analysis +1 Unfortunately no real wave travels faster than c. I will have time to respond further later on RL

Dissipates into the ground and effectively neutralizes.

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