posted
Let's start with Einstein's relativity. Part of it says that there is no absolute frame of reference -- all frames of reference are equally valid. You cannot hold still, you can just be motionless with respect to something else.
Now let's take a rotating space station/ship. The occupants feel the effects of a pseudo gravity due to the centrifugal/centripdal effect of the rotation.
But why? If all frames of reference are valid, then you cannot say whether the space ship is rotating or the universe is spinning around the stationary ship. And yet this force is felt. It is real.
Why? What am I missing?
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posted
It doesn't say that all frames of reference are equally valid -- it says that all non-accelerating frames of reference are equally valid (actually, equally arbitrary might be a better phrase). A rotating frame of reference is an accelerating frame of reference.
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posted
Hmm.. Maybe you are right. Does anybody have a better explanation? I'm not saying you are wrong, but I'm hoping for an answer that *makes sense* to me.
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posted
This is actually a very deep question, because in general relativity there is a difference between solutions in which an object is rotating and those in which the universe is rotating around the object. So rotational motion is not purely relative, even in the most fundamental theory of relativity.
This is part of what leads me to believe in the reality of spacetime in GR. If you believe that spacetime exists, and consists at least partly of the set of inertial trajectories, then you have an explanation for why objects deviating from those trajectories (by accelerating) feel inertial forces.
There are other difficulties involved here, though. For one we don't really have a consistent definition of what it means for an object to be rotating in GR. David Malament of UC Irvine has a famous theorem along these lines that he proved a few years ago.
posted
I guess I was hung up on the idea that a rotating body is accelerating. As an engineer, I am used to thinking of rotation as having accelration some of the time, but other times just thinking of it as rotational velocity. Is it *really* accelerating? I'm used to thinking that it is not.
Destineer's more elaborate answer was enough to pacify me. Thanks for all of your answers.
I'm releived that my response to the answer was "Really? I didn't know that about GR" instead of "Duh! I cannot believe that I am so stupid that I never thought of that before."
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posted
Yes, I realize that is true. It's just that in engineering, about half the time we treat rotation as velocity in a circular axis. Of course it's not, because an axis by definition cannot be circular. But that analogy works well for solving many different engineering problems. That's the power (and problem) with analogies. They sure are helpful, but the more helpful they are the more likely they are to be taken too far.
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quote:A rotating frame of reference is an accelerating frame of reference.
Mr. Porteiro Head kind of addressed my concern here. Is this statement really true? If there's a constant velocity rotation, how is that an accelerating frame of reference? Because the vector is constantly changing?
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posted
Yes. Constant velocity means constant speed in constant direction. Velocity is a vector. In order to make something travel on a curved trajectory, there has to be a force continually applied. In the case of a solid body, the force is the tensile strength of the object itself. Think about it. If you throw a spinning snowball, and the snow is too dry to stick together, what happens? (Southerner that I am, I tried this in Michigan once, never having encountered dry snow before. You can imagine the results. <laughs> I covered my own self with snow and didn't get any on the person at whom I aimed.)
So, if you are in a spinning space station, for instance, the girders and strength members of the station are holding it together. If you were on the edge and let go, you would go flying off, continuing your straight line trajectory. That means that when you are standing up inside, you feel the force applied on your feet by the station as though it were gravity.
In fact, relativity states that there is no difference between (straight line) acceleration and gravity. In essence, the surface of the earth is accelerating you away from the earth's center, where the curvature of local spacetime is saying your straight line least resistance trajectory should take you.
posted
Gravity can be thought of in different equivalent ways. One is as I said above, acceleration away from the "path of least resistance" in curved spacetime.
That's just another way of saying, though, that masses attract each other.
Richard Feynman put it very well, I think. He was explaining to his students how in medieval times people believed that the planets went around the sun because of angels flying along behind them pushing with their wings. Now we have a different theory, he said. Now the angels push INWARD. (He was pointing out that calling it gravity, and understanding HOW it works, is not really any more explanation of WHY it works than we had with the angels theory. )
posted
I think Feynman was one of the most brilliant and insightful physicists we've ever had. I loved his book "The Character of Physical Law". In there he talks about how the physics we know, the deepest understanding humans currently have of how the universe works on a material level, isn't explanatory in a mechanical sense at all.
He gives an example of a mechanistic type explanation of gravity. Say there was some unknown stuff pouring in from every direction, and say it impinges on masses and exerts a force on them. If that were true then the stuff coming from the direction of the sun, for example, would be partially blocked by the sun, looking from the earth's viewpoint. That would mean a little less force coming from the sun's direction, which would mean the earth would tend to fall toward the sun, and look like it was being attracted to the sun. That would be an example of mechanical "nuts and bolts" type theory of gravity. The trouble is, it doesn't work. There are all sorts of observations that contradict that view of things.
Saying GmM/R^2 is just a description of what happens. It's just an equation that says masses attract, and explains exactly how much they attract, without showing why.
But it turns out that our most successful (in terms of predicting what is going to happen, and correctly matching experiments) theories are all like that. They are equations. The universe seems to be made of math, as its fundamental stuff. Matter is just knots in the fields, as we now know, and fields are just numbers in space. I find that highly interesting.
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posted
I remember reading a book by Scott Adams (creator of Dilbert, but I can't remember the title of the book) where he talks about different ways of looking at things. He proposed a different explaination for gravity. He knows that the explaination breaks down when you examine it closely enough, but it was just an example of how you can look at something differently that everyone takes for granted. He proposed that gravity was caused by all matter doubling its size at a constant rate. I thought it was a fascinating idea, certainly one I never would have thought up. Anyone read that book and remember the title?
By the way, thanks for the responses on this physics question. It has been bothering me for a long time too. Porter and I asked several very knowledgable people who could not give us an answer. I knew the answer had to be simple, and apparently, it was. I knew that rotating objects were thought of as having acceleration, I learned that back in high school physics. But I never made the connection between that and how it would effect a frame of reference. I am satisfied now.
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posted
I was unaware that general relativity only works with a non-rotating frame of reference. But then, even if I had known that, my preconceptions taught to me by years of university education probably would have kept me from seeing the simple truty.
Thanks so much for the answer. Posts: 16551 | Registered: Feb 2003
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quote:I was unaware that general relativity only works with a non-rotating frame of reference.
GR does work with rotating frames. The theory governs all frames. But it does predict that there are no inertial trajectories which correspond to rotating bodies, so rotating objects will feel forces due to their deviation from inertial paths.
quote:Saying GmM/R^2 is just a description of what happens. It's just an equation that says masses attract, and explains exactly how much they attract, without showing why.
I agree that's true for Newtonian gravity, but I would count GR as a nuts-and-bolts theory, more so than the example of the force-exerting stuff. Gravitational "forces" in GR are carried by the medium of spacetime. Objects alter its structure, and the structure in turn affects the motion of objects. I'd call it the most mechanistic and physically explanatory theory ever put into wide use.
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posted
Okay, now I'm thinking of a carnival ride called the "round up" where you stand inside a huge but shallow cylinder. It spins and the whole cylinder can be raised (or in some instances the floor dropped)but the people stay stuck to the sides.
But if someone was not in contact with the sides, they wouldn't be affected. How does a rotating space station produce the effect of gravity on bodies not in contact with it? Since we have to break contact in order to walk or run.
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posted
I used to wonder about this too. Keep in mind that the people inside the cylinder are spinning. If the cylinder were to disappear they would all fly off into space. So the cylinder floor's rotation is not causing the effective gravity -- it's caused by the rotational motion of the people. It's just that the cylinder floor stops them from completing their natural free-fall motion of flying away from the center of the cylinder, and so they feel attracted to it.
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posted
OK, Here is a physics question that has been bothering be for months. According to Feynman's Lectures on Physics, the principle of conservation of momentum proceeds from the assumption that the laws of physics are independent of position. It is, however, possible to transform a particle with mass into a photon and then back into a particle with mass. Such processes have been observed and the resulting particle does not have the same velocity vector as the original particle. Momentum is not concerved in this process. Does this necessarily imply that the assumption that the laws of physics are independent of position is invalid?
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posted
Yes, the people up against the wall feel a normal force from the wall that roughly mimics the normal force felt from the ground.
If someone were to depart from the wall they would not move directly back towards the wall, they would stay moving in a linear velocity that was mostly (plus the vector they added by departing from the wall) perpendicular to the axis of the rotating cylinder. However, there would be a bit of cylinder there to stop them . Not only that, but because the cylinder is rotating, for short distances from the wall the bit of cylinder run into would be the same bit of cylinder departed from (approximately), because over short distances the arc of a circle (in this case the distance rotated, at a speed (not velocity) identical to the speed of the person perpendicular to the axis) is roughly identical to a straight line at the same speed.
Thus by increasing the size of the rotating ring, the more approximate to gravity it appears, as the less far (as compared to the radius) a human can jump away from the wall.
Of course, there are still plenty of things that give it away in even not particularly sensitive experiments, but for most everyday considerations a large rotating ring would "feel" quite like the ground.
And to address an earlier point already answered in a slightly different, GR definitely does deal with rotation, it just doesn't say that rotating frames of reference are equally arbitrary.
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posted
Rabbit -- I don't have a complete answer, but it may be tackled by the fact that a photon does have mass, just not rest mass.
Also, while newtonian momentum may not be preserved, relativistic momentum may be (which highly approximates newtonian in slow speed cases).
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posted
Destineer -- there is no natural free fall motion of flying away from the center, at least not in the usual sense away is meant.
The natural motion of someone departing from the normal force bounding them on a cylinder is sideways (that is, perpendicular to the radius where they departed the normal force). This just happens to bring them back into contact with the cylinder approximately where they were earlier, because the cylinder has rotated back under them (as I go into more detail about above).
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quote:but it may be tackled by the fact that a photon does have mass, just not rest mass.
I've thought about this but it doesn't work. It might work for the particle-->photon half but it you look at all three steps, particle-->photon-->particle, it doesn't matter whether the photon has mass or not, momentum should be concerved throughout the process so the resultant particle should have the same momentum as the original particle but it does not.
I'm not sure if this is part of the conflict between quantum physics and relativistic physics which still hasn't been resolved or if there is some simple resolution that I am missing.
[ March 08, 2004, 01:50 PM: Message edited by: The Rabbit ]
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posted
Is it a pure conversion? That is, no extraneous particles at any stages (like, say, a virtual photon cloud that is made real?
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posted
Fugu -- Right-o about the tangent motion, I was thinking lazily.
In answer to Rabbit's question, photons do carry momentum. This is sometimes called radiation pressure. In relativity the relationship between mass, energy and momentum is mass^2 = energy^2 - momentum^2. So a zero-mass particle can carry both energy and momentum if their squares cancel.
Edit to say that "mass" in the above equation refers to rest mass.
posted
Rabbit, I asked my dad about your question. (Any errors here are due to my lack of comprehension. )
quote: According to Feynman's Lectures on Physics, the principle of conservation of momentum proceeds from the assumption that the laws of physics are independent of position. It is, however, possible to transform a particle with mass into a photon and then back into a particle with mass. Such processes have been observed and the resulting particle does not have the same velocity vector as the original particle. Momentum is not concerved in this process.
If I understood him correctly, it's like this: Feynman's pictures (which are models of complex equations) do show such transitions. However, they have never been actually seen. Feynman can do this, apparently, because the model was for such brief times that Heisenberg's uncertainty applies -- but it's just a model, not an actual phenomenon.
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posted
I can't verify this, but maybe someone can. According to a Stephen Baxter novel I read recently, it can be proven that a circular matter flow around a stationary object would produce exactly the same apparent (centrifugal) force as the object rotating. Baxter usually knows his science, but obviously I can't trust him not to occasionally make up ideas that don't exist yet. Anybody know?
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Mass flow around a circular object exists when the (I'm assuming "viscous") forces in the flow pattern are strong enough to overcome the separation forces trying to prevent that mass flow from conforming around that object.
Place a stick in a fast-flowing stream. Some of the water will wrap around the stick, and continue downstream from the trailing edge of the stick. The only reason it wraps around is that the viscous forces in the stream (I'm thinking water here--a real stream!) keep the flow attached to the stick at lower velocities. At higher velocities--away from the stick, the water flows fairly straight (Newton's first law). The force making the water wrap around the stick is balanced by the centripetal force on the water as it wraps around. If the flow rate is to slow, the flow stagnates. If the rate is too fast, it separates from the stick (does not wrap around).
So, the answer is, "Yes," assuming similar rates of rotation.
posted
Back to Rabbit's question -- oh, you're talking about for short times . For short periods of time, pretty much anything can happen. The "bigger" (usually more massive) a happening is, the less time its allowed to happen in.
The Uncertainty Principle allows the violation of pretty much any rule in the book, provided that violation is limited in proportion to its grossness.
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