Halc

There's always an object stationary in almost any arbitrary frame choice, even if it's just a muon or neutrino somewhere. Observer, no, but observers in relativity don't actually observe anything except instruments, which can be done by anybody regardless of motion. For instance, a fast approaching clock is observed to run fast despite actually running slow in the observer's frame. His role is to run the the computations and provide a name for the frame, neither task requiring any actual observation. As for my assertion that say length contraction is not a physical effect, there are examples that can demonstrate it so. Rotation is absolute so via rotation, coordinate effects have physical consequences. A spinning ring will fit through an identical (*) ring not spinning. That's real contraction and not just coordinate like the barn pole thing is. Another example is a circular train track packed with cars. As they pick up speed, more cars will fit in the same track who's circumference is unchanged, despite the fact that relative to any one train car, the track just below it is shorter and one would think that relative to the cars, fewer would fit in the same contracted circle. Not so. * Unless really thin (2D), a spinning 3D object cannot be identical to a non-spinning one.

But the perspective of Earth was not mentioned. Just "co-ordinate mass of the Falcon 2 is approaching infinte at 99.99%c", which is true of me now relative to some frame. No fancy ship needed. But sure, if that speed is relative to some other object, then relative to the ship, it is the moving object (Earth??) that gains coordinate mass. Gian also implies that acceleration and/or energy is required for something to have a large coordinate speed. This isn't true at all since several examples have been given of Earth moving at nearly c. It's a coordinate effect. Nothing is physically different in such a frame.

Pretty much that answer, yes, except I don't remember Earth being involved in the question. I had just chosen a frame where the ship (and Earth too) were moving at .9999c But yes, in the frame where the Falcon is at rest, its coordinate mass and mass are identical, by definition.

Tidal disruption (the breakup of moons that fall below the Roche limit) is essentially Newtonian physics and has been fairly well understood since the 19th century. It has little if anything to do with gravitational waves and more with physical stress on orbiting objects. Earth for instance puts out a total energy of about 200 watts in the form of gravitational waves. It has plenty of tidal gradient to say destroy the moon if it ever gets close enough (it will be destroyed before this happens), but that 200 watts will not register on any detector we make. Yes, an orbiting GW detector will presumably be more sensitive than LIGO, but would lack the redundancy of the multiple GW detectors on Earth unless they orbit several of them. Not sure how much redundancy is needed in space where trucks driving nearby are not going to trigger false positives.

OK, it does seem to be a measurement topic, and not one of expressability or predictability Measurement of planets is hard due to the long delay between where it is and where you see it. The OP didn't seem to reference prediction Your OP seemed to have little to do with entropy. Your card shuffle example was one of a chaotic function, but the deck seems no more entropic before or after the shuffle, as opposed to if you play 52 pickup. This seem to have nothing to do with relativity theory. Choice of coordinate system was necessary even in Newton's physics. The sun's frame is an accelerating one, more complicated. I chose an inertial frame, but I didn't compute many numbers in it. Just >180 and 'faces the other way'. This is true, and you need two of them, not just one. Given distant stars not in the system, we have that reference. The OP said to ignore the gravitational influence of the rest of the galaxy, but that doesn't mean we don't have external references. Without it, picking a stable reference is possible (since rotation is absolute), but not as easy. But I chose the CoM as the reference. That's not an absolute reference, sure, but the relationships between the planets can be derived from each planet's coordinate relative to that CoM. Measuring it all is another problem since there's nowhere to be that sees where everything is at a given time since the distances are so large.

Well, you posted this in relativity, so it needs to be stated that you seem to be referencing states at times relative to some inertial frame, say the frame of the center of mass of the collection of objects, which is stable in isolation. The question seems to be how to express the states 1,2,3 Sure, in state 2 the Earth object has rotated just over 180 degrees and is facing the other way. It has also moved around the solar system just like all the other objects. I referenced the solar system center of mass, so given that reference, each of the objects has a position relative to that at each of the times 1,2,3. It's a stable point of reference, so nobody is worrying about saying where Earth is relative to Jupiter since both have moved. Measuring it is another thing, but measuring doesn't seem to be your question.

This two-year old topic started with the below comment. I've not read almost any of it, but I see a lot of word salad that seems unrelated to this original question. 1) No rigid object can instantly change its velocity without breaking, per Bell's spaceship scenario. You can accelerate it over time (finite proper acceleration), and how much time that takes depends on what clock is used to do it. There are limits. I worked out the minimum time it takes to move a 100 LY rigid train a distance of one light day, being stopped at beginning and end of trip. It takes almost 2 months and cannot be done faster without violating rigidity. It cannot be done at all without applying force to all parts of the object instead of say pulling it with an engine up front. Now regarding this latest post, forgive me if I am unaware of any context that might help make sense of any of it. How can a velocity be treated as a distance? This seems meaningless. How does a simultaneity or a nonsimultaneity have a size? Two events not simultaneous in some frame would have a time difference in time, but that difference would be a time, not a speed. You are seemingly comparing a time to a speed, which is total nonsense. How is any of the posts (in any of 2024) relevant to the topic? Is this just one of those blogs left open to keep the forum from filling up with dozens of crazy topics from one user?

No, not at all. As swansont points out, the term is used to refer to mass issues involving frames of reference. Mass of any kind is a resistance to acceleration. Coordinate mass is simply a coordinate dependent mass that you've been speaking of: Say your proper (physical) mass is 80 kg and so is your coordinate mass relative to the frame of your shoe. Relative to the frame of some muon, your mass is still 80 kg but your coordinate mass (some sites call it relativistic mass) would be say 500 kg. Notice that all we did was an abstract change of reference frames (coordinate systems) and there was no requirement for energy or acceleration. Mass is physical and frame independent: it is 80 kg in any frame. But coordinate mass is a frame dependent abstraction, ranging from 80 on up to any arbitrary value depending on the coordinate system chosen. Notice also that no mention of location was made in any of that.

Time lords live in a universe with significantly different laws of physics. Same for Star Wars/Trek. The problem is that there are two kinds of mass: proper mass (frame invariant) and coordinate mass (frame dependent). Use of the term 'mass' was sort of ambiguous until around 1950 when the term was formally assigned to mean proper mass. But using it to mean coordinate mass (as Einstein did) persists in pop sources to this day, and chatbots will likely still use it since those pop sources are the larger percentage of its training data. The article is nice, but makes a lot of errors, some of which are just in clarity, but some actually wrong. The wonderland example for instance treats a bicycle as a brick instead of a system with moving parts. The cycle wheels contract if they rotate, so the spokes would become slack and the bicycle would fail (collapse) if a plodding walking pace was approached. The article treats speed as absolute, which violates special relativity. You're moving at 0.99c right now relative to some muon. No fancy acceleration or Time Lord engine required. Do you mass more because of that? No. Hence their choice of what 'mass' means. It starts with: "nothing can move faster than [the speed of] light", which should read that it's only true relative to an inertial frame. For instance, if I shine a light to a reflector on Mars and measure the round trip, it will go faster than c. Not much, but it will, and it is due to spacetime not being flat between here and there, so inertial frames are not applicable. Reading more, I see SR, 1905 "begins with the astonishing experimental fact that c never changes". This is wrong. It is a premise, not a fact, and to date it has never been experimentally verified. It says that an object's mass increases with speed, but that's a coordinate effect, not a physical one, so only the coordinate mass thus increases, and they don't correctly say that. It later says 'ship time is flowing at less than 7/8 the normal rate' which is confusing. Ship time is at 100% per the first postulate of SR. The wording makes it sound like time dilation is a physical effect instead of a coordinate one. Again, does your clock run slow because it is moving at .99c relative to some muon? No, it doesn't. Discussion of a more general version of E=mc2 is given by other posters. The bottom left of the 2nd page says something crazy about a journey to 283 light years away taking just over a year from Earth's point of view. That's totally wrong. It might take that much proper time on the ship, but that's not an Earth observer.

The Lorentz factor is almost exactly 7. Some call the 1.4 million kg the relativistic mass but technically the mass of the ship is the frame invariant proper mass of 200,000 kg. That's just a terminology thing. The ship relativistic momentum goes up to γvm, so you can compute its kinetic energy by multiplying that by v. Also note that once you've given your ship a specific mass, one has to wonder how it accelerates without losing any of it, which is why most hypothetical scenarios avoid any mention of masses since it introduces so many problems that are not illustrative of the point of the exercise. Not sure how your fusion engine produces thrust. Most fusion reactors only produce heat, and maybe electricity from that, neither of which immediately translates to thrust. So anyway, unless you are firing this object out of an insanely long rail gun, any calculation of energy usage needs to factor in where the energy is produced and where it is going, and what is left at each point. Don't know what that phrase means. You talk about energy, but then follow it up with a specification of power (so many joules per sec). If the ship is accelerating at 1g, then it's power consumption is presumably proportional to its current mass, so integration is needed. One also has to factor in energy imparted to the reaction mass, and all that scaled by some kind of efficiency rating. The most efficient engine might be something like an ion drive, but those don't put out enough force for 1g of acceleration. 200 tons is seemingly not enough to provide life support for Joanne for all those years, let alone any left over for trivialities like propulsion. Perhaps it is really good at recycling.

Acceleration in physics is a vector change in velocity over time (and is not a scalar increase in speed, the dictionary definition). That change can only be in one direction, so if you're using lateral jets and still are maintaining 1G of proper acceleration then you're just finding an inefficient way of accelerating at some angle. Anyway, if you're getting up to .99c in the solar system frame, your circle at 1G would be at minimum far larger in diameter than the distance to AC, and you'd be using your main engines pointed sideways to maintain the turn radius, with no increase in speed. This would take at least 7 years to get up to this speed linearly and far more if you maintained a circle centered on something like Earth. It would take decades to do one 'orbit', one lap of this huge circle. Once you 'cruise' and go straight, you'd be heading away from your destination since at no point in that circle are you heading toward it. Fastest way to get there at fixed acceleration is straight out and back, but getting up to a speed higher than your ability to stop in time is just wasted effort. It would take at least 3g to get up to .99c and still stop 4 light years away

You can't orbit anything much faster than its escape velocity at 1G, so no, dropping to the sun requires one to lose energy rather than gain it, which is what you want to get to AC. OK, technically a ship always loses energy as its fuel drains, but I'm talking about the mechanical energy (potential and kinetic) of the payload. So orbit of anything is likely just a waste of time since one cannot exceed some low speed while going in circles, at least not if acceleration is confined to 1G. Suppose the sun could be condensed into a neutron star or black hole. Presuming Joanne doesn't mind a little (a lot) of tidal stress, one could orbit such a thing at super high speed near c but it would take a lot of time to drop into this orbit. And then it gains you nothing getting to AC since all that kinetic energy must be wasted over a long time just to get back to where Earth is orbiting, all the energy being expended not accelerating to AC, but rather just climbing back out of that gravitational well you were in. When back at Earth, no net speed remains. The trip is no shorter.

6 years 1 way Earth time, 3.58 years on the ship. The figures reflect more the actual distance and not just 4 light years exactly. If it was 4 light years exactly, it would be 3.46 years on the ship.

I won't accept such cookies normally, but I pasted the link in an incognito window and it let me in without challenge. It seems to be a Newtonian calculator and yields 1.18c if I put in 10k hours at 1G Really, there are very good calculators for relativistic space travel. One of the best: https://gregsspacecalculations.blogspot.com/p/blog-page.html That one presumes fixed proper acceleration, not coordinate acceleration like a Newtonian calculator would use.

That's coordinate acceleration, and 1G of that for almost a year would kill poor Joanne, and it could not continue at all for a full year. I do realize the OP did not specify explicitly, but 'comfortable' was used, so my figure is based on a comfortable 1G proper acceleration, and that takes almost 2.7 years (ship time) to get to that speed and around 6.8 years Earth time. Fixed proper acceleration can in principle be kept up indefinitely. Oh, and your link is behind a paywall, or at least a subscribe wall. I could not view it.