Rockinghorse

There are not any kinds of infinities in the universe. Everything that is infinite by its nature is also infinitely improbable.

Saying that "the context of discussion was SR", is pretty much the same as saying that "Let's assume that the laws of physics do not apply in our thought experiment."

But in real physical world clocks can always be synchronized. This is hard for people to understand that in real world there is no such thing as twin paradox.

Thanks for your answer. I am starting to like the idea of electric turbo pump. It saves some fuel, so rocket engine thrust to weight ratio is not that important. E.g. silicon anodes gives very high energy densities, but the problem is swelling, so the cycle life of silicon batteries is low (<<200). But this should be enough on space propulsion purposes. There is also nanomaterials available that gives great energy densities, but they are not economic to mass produce, although they are certainly possible. I have also pondered myself an idea of hybrid Turbofan Jet Engine for the airplanes. Where the turbofan is powered using electric motor instead of gas turbine. This concept should make sense if the energy density of batteries gets slightly better in near future. There is additional benefit with less noise from the engine.

The principle of relativity (the Galilean relativity) requires euclidian spacetime. This is dead serious, because this is the most common misconception of theory of relativity. You can understand this if you think that time is physically real. The time dilatation of GPS satellite is real and it can be measured in real time in all frame of references without twin paradoxes. Of course if it is only looked Newtonian physics and the Einsteinian relativity is ignored, then of course it makes sense to talk on relative motion. But in the context of general relativity there is no such thing as relative motion.

This has nothing to do with idealized models. The point is that Twins can always communicate in real time and synchronize their clocks, so there is no such thing as relative motion, but time dilation is always physical phenomena and it can always be measured. This is extremely hard thing to understand, because laypersons typically do not understand special and general relativity and they fail to visualize when it is required to comprehend more than three dimensions.

Yes, but the point is that cosmological constant ≠ dark energy.

The context of special relativity is irrelevant, because it does not refer to the real physical world, but it is refering to purely non-existing imaginary world.

What if the expansion is caused by cosmological constant and not dark energy? Anyway there is absolutely no good guesses why the cosmos is expanding. According our best cosmological theory (i.e. general relativity) the expanding universe is impossibility, so I would say that it is fair to say that we are missing something relevant. EdEarl, if Harry Potter can do the rearrangement of magnetic dipoles atom by atom without braking any laws of quantum physics, then I accept it. If I recall correctly the minimum energy deeded to magnetize/demagnetize the 1 cm³ neodymium magnet is about 300 mJ. It is perhaps not too big energy bill for Harry Potter.

According to general relativity GPS satellite is not accelerating, but it is in uniform motion at curved space-time. The broken symmetry in twin paradox is important, because it implies the physical reality of time dilatation. This is especially important question when we start pondering the nature of simultaneity in non-local quantum systems. It turns out that if symmetry is anyway broken, there is no need to object non-local nature of quantum systems. E.g. Lee Smolin has therefore concluded that hidden variables are plausible, because the symmetry of special relativity is by definition broken. I personally do not believe hidden variables, but I do believe in non-local quantum systems and simultaneity due to broken symmetry of relativity.

This applies only when the curvature of space-time is Euclidian. In real universe however there is no flat geometry anywhere in the universe, therefore this symmetry is always broken. And twins can always synchronize their clocks in real time and they can observe whose clock is slowing down due to uniform motion. More clear example is that GPS satellite can always synchronize its atom clock with Big Ben and therefore we can say that the clock of GPS satellite is slowing in real time. GPS satellite is in uniform motion, but it travels in curved space-time.

Actually, universe as a whole is the ultimate perpetual motion machine as it popped out from nothingness. I think that if we could switch permanent magnets on/off at will, it would be possible to create perpetual motion machine. But I am not sure how much there is wasted energy on switching magnetic field on/off, so it might negate the efforts and no net energy is generated. Permanent magnets are however interesting, because only the arrangement of magnetic dipoles determines the magnetic force. This idea is hard for classical physics to handle philosophically. Also spiral galaxies could be considered as perpetual motion machines, as they generate complexity and ordered shapes using only the force of gravitation. It is irrelevant whether or not you can exploit it. Only the philosophical principles of science matters in real life!

It is not very vise to use lithium-iron-phosphate batteries as they have poor energy density. E.g. NCA chemistry has double the energy density of lithium polymer (about 800 kJ/kg) and still very high power density and long cycle life. It is also possible to ask from manufacturers a prototype batteries that have much higher energy densities, 1.4 MJ / kg or even more. In space it is not needed long cycle life, therefore ultra high energy/power density batteries are viable. It is not necessary to go to the asteroid belt to mine asteroids, but there are millions and millions near earth objects with Δv few hundred m/s from high lunar orbit. C-type near Earth asteroids may have very high concentration of volatiles (e.g. water (22 %), methane and nitrogen). About one third of the total mass could be volatiles. The reusable Merlin 1D rocket engine has about 5 MW turbo pump. But also the thrust to weight ratio is very high. About 150:1. Therefore, are you sure that electric turbo pump could boost this ratio even further?