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The description in the article is oversimplified. Relativistic dynamics is different from Newtonian dynamics in a lot of ways. Force isn't parallel to accelera
by knzhou 7y ago
The description in the article is oversimplified.
Relativistic dynamics is different from Newtonian dynamics in a lot of ways. Force isn't parallel to acceleration anymore. Acceleration gets harder the faster an object moves. You can mimic some of these changes by just pretending that you still have Newtonian dynamics but the mass can change with velocity, but we don't use this language in physics because it's misleading -- there are many effects this idea can't capture. (For example, the fact that force is not parallel to acceleration.) It is a very fragile analogy that causes a lot of conceptual mistakes.
It's easy to prove that Newtonian mechanics conserves momentum. It's also easy to prove that relativistic mechanics conserves momentum. A weird hybrid of Newtonian mechanics plus a magically changing "relativistic mass" does not conserve momentum, but nobody has ever thought this was a correct description of nature. It's the result of taking a helpful simplifying analogy too far. Any reactionless drive formulated using this Frankenstein theory doesn't work.
If you just bounce an object back and forth, in either Newtonian mechanics or relativistic mechanics, you won't get anywhere. If you change the rest mass of the object to be different going right than left, you will go somewhere, but it will cost momentum to do this, as explained in gus_massa's comments. So we haven't gotten thrust for free.
- ben_w 7y ago> For example, the fact that force is not parallel to acceleration. This is the first I’ve heard of this and I would like to learn more, partly because of my own harebrained not-quite-reactionless engine idea that I know can’t possibly work really, but I can’t see why yet. Where should I look?
- diffeomorphism 7y agohttps://en.wikipedia.org/wiki/Relativistic_mechanics#Force https://en.wikipedia.org/wiki/Relativistic_mechanics#Force This includes the relativistic version of Newton's second law, which shows that F is generally not parallel to a.
- cygx 7y agoBut note that the 4-force is parallel to the 4-acceleration. However, its spatial component only agrees with classical acceleration in the comoving frame. In general, there's an additional contribution that's however smaller by a factor of (v/c)^2.
- knzhou 7y agoConceptually it's because it gets much harder to speed something up, but not that much harder to change the direction of its velocity. So for a force with both radial (along velocity) and tangential (perpendicular to velocity) components, the acceleration points more tangentially than the force does. A really excellent, conceptually clear exposition of relativity is given in chapters 11 and 12 of Morin's Mechanics. The modified version of F=ma is covered in section 12.5.
- crdrost 7y agoI would also say that I have been at least somewhat successful in teaching people about relativity by ttuncating the Lorentz transform to first order in β, as you can prove that you get the full results back from this as the matrix limit N lim [1 -φ/Ν]^ N→∞ [-φ/Ν 1] ... basically the physical content of Galileo’s transform is that as you accelerate forwards things start moving backwards. The physical content of Lorentz’s transform adds just one thing to first order: that as you are accelerating, clocks ahead of you appear to tick faster, and clocks behind you slower, proportional to their distance in the direction you are accelerating. That key basic insight is not just the resolution to the twin paradox but the basis for event horizons near black holes and such. (There is a surface at coordinate -c²/a where time stands still.)
- z3t4 7y agoSo it should not be possible to ride a swing?
- knzhou 7y agoIn a swing, the back-and-forth linear momentum comes from the tension in the wires, while the energy comes from your legs. No conservation laws are broken.
- labawi 7y agoIt is not possible to ride an unanchored (and non-couterbalanced) swing in a vacuum.
- steve_taylor 7y agoWhat special properties does an atmosphere confer to a swing?
- gpderetta 7y agoMaybe they meant in 0g?
- dean177 7y agoYou need “downwards” acceleration for a swing. The vacuum bit isn’t important, it’s the gravity. They probably meant 0g rather than vacuum.
- SSLy 7y agonone, but centers of gravity do
- labawi 7y agoIt slows you down :) The vacuum part was an emphasis on requiring a counterpart to change momentum. In an atmosphere you could flap your wings, or use electric fans, and argue what it means to ride a swing, but it would be besides the point, as in an atmosphere there is no need for propellant-less engines from the article.
- elcomet 7y agoHow could NASA allow research on such a topic if it is obvious for physicists that this is impossible ?
- sgift 7y agoEven things we think we know very well may be wrong, so having a certain budget for "fringe" subjects which may yield unexpected results is not a bad idea. At the same time it's probably a good idea to assume everything they report is a measurement/test setup error until further proof.
- _0ffh 7y agoYup. As it is said "If a physicist says it's possible, then it's possible. If a physicist says it's impossible, then it's undecided."
- lonelappde 7y agoThe actual saying is that everything that an elderly distinguishes scientist has an opinion about is probably possible. It's a complicated way if saying almost everything is possible so don't believe old dogs who have given up on optimism. https://www.brainyquote.com/quotes/arthur_c_clarke_100793 https://www.brainyquote.com/quotes/arthur_c_clarke_100793
- antonvs 7y agoEverything in their field, that is. Since some elderly scientists have come up with some pretty nonsensical ideas about things outside their field.
- IanCal 7y agoI don't think they have in this case. > Burns has worked on his design in private, without any sponsorship from NASA
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- phayes 7y ago"Oversimplified" is one way of putting it. I'd prefer to call it "simply incorrect". The manner in which the ring's rest mass is increased [decreased] is ignored[1]. If you don't ignore it, and apply conservation of (relativistic) angular momentum to the box-ring system, you'll see there's no reason to expect a net thrust at all. [1] https://iopscience.iop.org/article/10.1088/1742-6596/1141/1/012131/pdf https://iopscience.iop.org/article/10.1088/1742-6596/1141/1/...