So space itself is compressed into a 0 sized point to stop things from moving at C (from the perspective of the photon). But that isn't allowed because that stuff has mass. From the photons frame of reference, everything else is moving at C. The entire rest of the universe has mass. (Simplified) The entire affair is necessary because only things not having mass can move at C (and in turn, must move a C, a massless particle like a photon must always move at C). From ours it's moving at the speed of light for a long time.īecause these are different frames of reference, it's not as easy to compare speeds experienced in one to the other, especially if one is moving at C relative to the other. From the photon's perspective, it's speed is not infinite, it's not moving at all, it's created and annihilated at the same point in space and time. From the perspective of the outside observer, the photon is not traveling 0 distance, it's moving at the speed of light to a far away destination. In turn that means travelling to some point in the universe, from the perspective of that photon, is instant. It also doesn't mean the speed of light is infinite, rather, from the perspective of the photon, ignoring the time part, the universe is exactly 0 in size. Time passes infinitely slow to the point that the time passed becomes zero. When you travel at C, then this effect becomes infinite. This process is exponential, so if you double the speed you travel at (as a number relative to four) the effect on your time and distance covered will quadruple. If you move in a train, the time you spend inside the train moving and the distance you cover from your perspective will differ from the time that is shown on the clock at the station as well as the distance between the stations. I guess one thing would be to accept that distance and experienced time aren't objective. It's a bit of a hard subject to digest, I admit that. Maxwell realized that light is just vibrations in the electromagnetic field, and he died in 1879, yet we still start by writing down Maxwell's equations when learning how light operates under the laws of quantum electrodynamics. I'm discussing the implications of chaotic dynamics for quantum systems, and scientists generally do not live to see the implication of all their ideas. > I also see Lyapunov died in 1918, while the uncertainty principle was introduced in 1927. I think I'm going to have to pull rank on you and just say you're wrong on this one :) There's a whole field of quantum chaos that explores the relationship between these things in depth.
> "Irreducible quantum uncertainty" is something else that has nothing to do with Lyapunov time. All I'm saying is that the meteor's path, on long enough timescales, is random in the same sense as radioactive decay.) (You can make a philosophical move where you say the wavefunction is deterministic even if the results of our measurements are indeterministic, and the wavefunction is the "real" thing, but that's orthogonal to the point I'm making. But the world isn't classical, it's quantum, and quantum systems are fundamentally indeterministic. > My understanding is that chaotic systems are still deterministic,Ĭlassical chaotic systems are indeed deterministic in principle, and only effectively unpredictable due to finite measurement precision. That’s why I doubt it has any practical impact. If so, radio-active decay that emits a particle that escapes from an orbit around the meteor (relatively easy, given the lack of atmosphere and low mass of the meteor) has a (minute) random effect on the velocity vector of the remaining larger part.īecause individual decay events are uncorrelated, adding up all the effects of radio-active decay over time will make the already extremely tiny effect a lot smaller (by the square root of the number of decays, if I’m not mistaken, but there may the timing of decays gives earlier decays a larger effect on the eventual course, so it may be slightly less dramatic). Our current understanding of radioactive decay is that it is 100% random, and that the law of conservation of momentum also holds at quantum scale. I am sure it has zero impact in practice, but theoretically, there’s a random component that isn’t part of the initial conditions. ”the state at some later time is just very sensitive to the initial conditions”
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