= 27d567bc2d48d9f40e9ccc20ea370b15)
SilasBarta comments on Open Thread: April 2010 - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (524)
Question about Mach's principle and relativity, and some scattered food for thought.
Under Mach and relativity, it is only relative motion, including acceleration, that matters. Using any frame of reference, you predict the same results. GR also says that acceleration is indistinguishable from being in a gravitational field.
However, accelerations have one observable impact: they break things. So let's say I entered the gravitational field of a REALLY high-g planet. That can induce a force on me that breaks my bones. Yet I can define myself as being at rest and say that the planet is moving towards me. But my bones will still break. Why does a planet coming toward me cause my bones to break, even before I touch it, and there exists a frame in which I'm not undergoing acceleration?
I have an idea of how to answer this (something like, "actually, if I define myself as the origin, the entire universe is accelerating towards me, which causes some kind of gravitational waves which predict the same thing as me undergoing high g's"). But I bring it up because I'm trying to come up with a research program that expresses all the laws of physics in terms of information theory (kinda like the "it from bit" business you hear about, except with actual implications).
Relative energy levels have an informational interpretation: higher energy states are less likely, so less likely states convey more information. So structrual breakage can be explained in terms of the system attempting to store more information than it is capable of. Buckling (elastic instability), in turn, can be explained as when information is favored (via low energy levels) to be stored in a different degree of freedom than that in which the load is applied on.
Gravitational potential energy and kinetic energy from velocity also have an informational interpretation. So: how does this all come together to explain structural breakage under acceleration, in information-theoretic terms?
No. Moving non-rigidly breaks things. Differences in acceleration on different parts of things break things.
The classic pithy summary of this is "falling is harmless, it's the sudden stop at the end that kills you."
You know, really, neither falling nor suddenly stopping is harmful. The thing that kills you is that half of you suddenly stops and the other half of you gradually stops.
Well put. And the way I can fit this into an information-theoretic formalism is that one part of the body has high kinetic energy relative to the other, which requires more information to store.
Yes, but the sudden stop is itself a (backwards) acceleration, which should be reproducible merely from a gravitational field.
(Anecdote: when I first got into aircraft interior monument analysis, I noticed that the crash conditions it's required to withstand include a forward acceleration of 9g, corresponding to a head-on crash. I naively asked, "wait, in a crash, isn't the aircraft accelerating backwards (aft)?" They explained that the criteria is written in the frame of reference of the objects on the aircraft, which are indeed accelerating forward relative to the aircraft.)
The sudden stop is a differential backwards acceleration. The front of the object gets hits and starts accelerating backwards while the back is not,
If you could stop something by applying a uniform 10000g to all parts of the object, it would survive none the worse for wear. If you can't, and only apply it to part, the object gets smushed or ripped apart.
Actually, from a frame of reference located somewhere on the breaking thing, wouldn't it be the differences in relative positions (not accelerations) of its parts that causes the break? After all, breakage occurs when (there exists a condition equivalently expressible as that in which) too much elastic energy is stored in the structure, and elastic energy is a function of its deformation -- change in relative positions of its parts.
Yes, change in relative positions causes the break. But differences in velocities caused the change in relative positions. And differences in acceleration caused the differences in velocities.
Normally, you can approximate that a planet's gravitational field is constant with the region containing a person, so it will cause a uniform acceleration, that will change the person's velocity uniformly, which will not cause any relative change in position.
However, the strength of the gravitational field really varies inversely with the square of the distance to the center of the planet, so if the person's head is further from the the planet than their feet, their feet will be accelerated more than their head. This is known as gravitational shear. For small objects in weak fields, this effect is small enough not to be noticed.
Okay, thanks, that makes sense. So being in free fall in a gravitational field isn't really comparable to crashing into something, because the difference in acceleration across my body in free fall is very small (though I suppose could be high for a small, ultra-dense planet).
So, in free fall, the (slight) weaking gravitational field as you get farther from the planet should put your body in (minor) tension, since, if you stand as normal, your feet accelerate faster, pulling your head along. If you put the frame of reference at your feet, how would you account for your head appearing to move away from you, since the planet is pulling it in the direction of your feet?
Spaghettification.
Your feet are in an accelerating reference frame, being pulled towards the planet faster than your head. One way to look at it is that the acceleration of your feet cancels out a gravitational field stronger than that experienced by your head.
But I've ruled that explanation out from this perspective. My feet are defined to be at rest, and everything else is moving relative to them. Relativity says I can do that.
Relavtivity says that there are no observable consequences from imposing a uniform gravitational field on the entire universe. So, imagine that we turn on a uniform gravitational field that exactly cancels the gravitational field of the planet at your feet. Then you can use an inertial (non accelerating) frame centered at your feet. The planet, due to the uniform field, accelerates towards you. Your head experiences the gravitational pull of the planet, plus the uniform field. At the location of your head the uniform field is slightly stronger than is needed to cancel the planet's gravity, so your head feels a slight pull in the opposite direction, away from your feet.
An important principle here is that you have to apply the same transformation that lets you say your feet are at rest to the rest of the universe.
In a gravitational field steep enough to have nonnegligible tides (that is the phenomenon you were referring to, right?), there is no reference frame in which all parts of you remain at rest without tearing you apart. You can define some point in your head to be at rest, but then your feet are accelerating; and vice versa.