Mordred

Both velocity and accelerations are boosts in the the Lorentz transforms. Rapidity is just a particular type of boost. I know you and I had tried discussing this in the past. Later on when I'm not at work I will try to get you far better detail on the difference of a boost due to velocity as opposed to acceleration.

I doubt using a laser from Earth regardless of how powerful would be of much use. Ideally you would want to use the laser on a side perdendicular to its trajectory. If you fire from Earth you would thr asteroid head on and outgassing wouldn't be as useful.

It would really help if one understands a physics theory correctly before you try to interpret a theory. It's rather pointless otherwise. Anyone that understands relativity by knowing what the mathematics of the theory states. Simultaneaty is of little use in this case as it's coordinate dependent. This is due to time not being constant. For example an observer looks at his watch. However that's simply his coordinate time. The other observer does the same for coordinate time. Due to time dilation regardless of whether it's due to gravity or inertia his clock will appear to run normal. However once you compare clocks then the difference is noticed. The two clocks are no longer simultaneous welcome to relativity and it's time dilation

Wiki isn't written by a physicist. It has zero authority in the physics. Any discussion involving physics to have any use whatsoever must always include the math. It's rather useless to discuss interpretations of any physics theory without knowing what those mathematics actually describes.

You know it's funny to declare GR cannot solve the twin paradox when it's in nearly every textbook on GR. Acceleration is easily handled in both SR and GR. It's simply a type of boost called rapidity. You can alternately use instantaneous velocities. So really it's a poor defense for a theory Long shown inaccurate specifically the Lorentz ether theory. Particularly since it ties into Lorentz invariance which current tests is something of order of 1 part in 10^(18) for any deviation on the constancy of c. That is rather conclusive for any potential of any ether based theory being viable. Yes I've read lots of attempts to salvage LET over the years including professional written articles and examinations none of have ever born out though. I even have copies of those various models. Though it would take time to search for them.

That comment makes no sense but so far without seeing your math. Nothing you have stated makes much sense. The CMB is literally everywhere in our observable universe you can even hear it's static on older radios that don't filter it out. It may surprise you to know that expansion has little to do with gravity but rather it's due to thermodynamics via the equations of state for each particle species. https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) If you take a uniform mass distribution and apply Newtons Shell theorem gravity is zero.

Hence why I stopped adding to the mix. Once I saw you were progressing from their comments I didn't want to add any potential confusion. Threads can get too easily derailed.

No you get a daily allotment

I gave them the +1 each for you.

Depends on the asteroid composition. The usefulness of a laser is to generate outgassing. For example an icy asteroid if you shoot a laser at it would more readily generate water vapors which would then provide thrust.

The first relativity never used the ether for the observer nor the emitter. It used the ether to describe how photons travelled between the two prior to proving ether wrong through the Michelson and Morley experiments. Those experiments are far far more precise in modern tests. Either way if you look at SR the emitter isn't ether and the observer isn't ether. Nor did Galilean relativity which the Lorentz transforms is simply an extension of (the Gamma factor constant of proportionality)

Everything in this post tells me you never actually studied the mathematics yourself. Had you ever studied the mathematics You would know Neither theory uses Ether. Nor does it uses the ether for a observer or relative to. Your claims is not what either theory states. Each frame of reference is emitter /observer relative to each other not the Ether. So forget thinking Ether is involved in either theory. That is absolutely incorrect

As I mentioned you would need the math to show this. You keep mentioning your math so you should already have the math handy for us to examine. I can easily show you all the mathematics behind the FLRW metric but that wouldn't help determine why you have an issue with it. If it's an issue with not knowing how to latex the math in let me know and I can demonstrate how our format uses \[\frac{1}{2}\,] I placed a comma in the last part to prevent it from activating. Your description of using spheres for example tells me you should have a spherical coordinate system with some constant of proportionality for the scale factor however that's based on your description. I need your math for confirmation.

Monopoles is an interesting study for example it's potential would fall off at 1/r as opposed to 1/r^2 for dipolar, 1/r^3 for quadrupolar ie the combination of two dipolar fields. As opposed to quadrupolar in gravity waves. Boit-Savant law can be uses to solve for the above if I recall.

Absolutely both SR and GR are able to solve the twin paradox. The paradox wasn't due to any lack of ability of either SR or GR. They both have the same transformation rules. The paradox arose in SR simply because of the constant velocity treatment which was incorrect. Take the acceleration into account and both SR and GR will get the same answer. Fundamentally the only real difference between the two is GR is better suited for field treatments and handles curvature terms better. The other difference is that in GR there is no "at rest observer" . Both SR and GR use the same transformation rules. They both employ the Minkowskii metric though in GR the Minkowskii metric is used in the weak field approximation. \[G_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}\] Both are part of the SO(3.1) Poincare group. As they both use the same Lorentz transformation rules claiming one is incorrect while the other is correct is in error. Let's put it another way the solution to the twin paradox is identical in both SR and GR when correctly done

You might try including the math you speak of. First off you seem to have missed the detail that spacetime curvature vs flat directly describes the null geodesics of massless particles such as photons through spacetime. Hence we can test the curvature term by looking for distortions in the CMB.

My favorite method requires early detection take your spacecraft and instead of trying to trap it in a net. Which as mentioned isn't practical. Simply maintain distance from the asteroid and let gravity do its thing. Use the spacecraft plus the gravitational interaction between the two divert the asteroid to a new vector path. The further away you can do this the less change in vector angle that would be required for a miss.

I would like to touch a bit on this using Maxwell equations but also Lorentz force law divergence and curl of the Electrostatic field Gauss Law \[\nabla \cdot=\frac{1}{\epsilon_0}\rho\] \[\nabla \times E=0\] magnetostatic Field Amperes law \[\nabla\cdot B=0\] \[\nabla \times B=\mu_0 J\] Lorenz force law with Maxwell for the presence of both the E and B field (Maxwell equations fundamentally is another way of stating Biot-Savart Law (with superposition) just a side note. \[F=Q(E+v\times B)\]. so the electric field diverges away from a positive charge, (Gauss law) the magnetic field curls around a current (Amperes law). Electric fields originate form a positive charge and terminate on a negative charge. Magnetic lines do not begin or end anywhere and form closed loops as they have zero divergence. (though divergence can be forced). There is no point source for B ( not unless they ever discover magnetic monopoles lol). Now something interesting to note the magnetic field specifies an electric current.( A permanent magnet induces an electric current). So with the 90 degree phase shift between E and B using the right hand rule for Lorentz force law. The following statement applies. The magnetic field does no work.... so take for example a magnetic crane the work isn't performed by the magnetic field but rather the electric field as well as the cranes mechanical energy. This is something that isn't well known among laypersons unless they studied introductory electrodynamics and the Maxwell equations. Hence why I decided to mention it here as its related. The above is better detailed in Griffiths "Introductory to Electrodynamics". I've found his simplified approach useful as a reference in many of his books.

No problem, it all depends on how detailed or how far you choose to pursue the concept. One thing to consider however is that in order to look at stress and stain aspects. You require the force/work terms as well. For example far too often I've seen perpetual energy articles discussing some popularized perpetual device use nothing more than first order equations. However when the same setup gets examined using second order relations by others that the energy loss is found exceed the output power. As Swansont mentioned in physics one cannot arbitrarily choose to ignore this interaction (in this case different forces) or that but should take everything in consideration. Stress tensors are particularly useful in that as all forces are applied with a means of keeping track via the tensors regardless of angles. Not saying perpetual energy is involved here however the above is also useful for efficiency calculations.

We cross posted see my last post

Look at your own image is not the rotor plate larger than the magnets and the placement off center ? Now am I correct those magnets will be shifting inward and outward ? So as it shifts outwards as opposed to inwards you will get variations

Really explain how it's going to be distributed uniformly across the plate if the surface area of the plate is greater than the magnet. Go ahead give it your best shot. I honestly don't know why you can't determine your PE relations in regards to applied force I shouldn't have to explain something already shown via Hookes law you won't need the spring constant per se but the elastic and gravitational potential energy is applicable. Every detail I have provided including the stress tensors are applicable. Regardless of your opinion. I take it you never lifted a sheet of plate steel using a magnet and seen the outer edges flex downward due to gravity ?

Ok so your lifting the plate in say the center so the only upward force is at the center but you have a downward force uniform throughout the plate. Obviously there will be differences of the sum of forces from the edges and the center. Potential energy is energy due to location so obviously there will be differences as there is differences in the sum of forces at different points on the plate. Put simply which leads to non uniform strain.

What I stated still applies if the sheet will move without deformation it's still detailed under the Cauchy stress tensor. As far as the RH rule apply it separately to the E field and B field. The results may surprise you. The B field is perpendicular to the E field.

Yes the RH rule is precisely what applies but so does the stress/ strain relations I mentioned. Hence referring you to continuum mechanics. Your sheet will not have uniform strain as it's mounted on one side so to get an accurate calculation will involve more than Hookes law.