md65536

Wrong thread.

Yes, where r is the radius (or side length, etc) of the mass. With astronomical sizes of nebulae, the mass would be astronomically larger (note the 3 dimensions of emphasis!). Note that this use of r is different from the previous use, where it was used to denote distance from us. However, the ratio of radiusnebula/distancenebula was chosen to be the same as radiusmoon/distancemoon. -- So in this case I guess it's proportional to r³ whether r is radius or distance. Even though the mass of the mythical moon-density nebula is cubically proportional to r, its gravitational pull is only linearly proportional to r, as described earlier. It would still be astronomically greater though, because the radius of the nebula is astronomically many times the moon's.

I agree. The idea of a nebulae-sized moon-like mass is pretty absurd in reality. I'm sure that it would have many (billions of?) times the mass of the entire universe. Even the sun is a lot less dense than the moon. I was thinking of calculating it for comparison, but I feel too lazy to.

Actually, it can. The result is a model with well-tested correspondence with observed reality. Ugh, yawn. I guess the supply of troll food ran out in the other thread. Plenty of fresh blood here! Start suckin!

Blurgh, sorry, thought everyone's forgotten the thread. It seems that at least it had slipped from my head. Who am I then? Certainly you don't know me. Find out and what I mean I'll no longer be. I am a word, and I have more than one stem, It takes some license to remove one of them, but if I've become stronger (look at me, see that I am) put back the stem and I'm where I began. In what sense correspondence? Its mention was terse. It's of terminal sounds of words or of lines of verse. As riddles go, this one's about fun as cancer You might roll your eyes when you find out the answer.

What about causality? Does it work in reverse identically to forward? What about non-determinism? Certainly the past is determined; does that mean the future must be? Or is the future undetermined and so is the past (if we reverse time we get a different past)? Are you speaking from opinion/belief, or from the standpoint of accepted science? What about entropy? It has a meaningful arrow.

Still out of my league but for fun: Yes. By the very nature of a "decimal expansion"... just map the n'th decimal place to the n'th natural number, and you have a 1-1 mapping between the number of digits and the natural numbers. If you have an infinite number of digits on both sides of the decimal (not sure if that makes sense) then alternate between them when counting. The even naturals will map to the digits on one side of the decimal, and the odds will map to digits on the other side.

I'm out of my league, but I think there are further problems. See http://en.wikipedia.org/wiki/Aleph_number The cardinality of the set of symbols representing digits in your proposed irrational number would be countably infinite and so would be aleph-naught. The cardinality of the reals is 2^aleph-naught, and the set is uncountable. It sounds like the "continuum hypothesis" implies that this really is a valid form of "infinity plus one". I suspect that the ability to construct a set is similar to the ability to count it, so you could construct a set of symbols representing the digits of an irrational number -- or at least you could construct every given symbol in that set, which I guess isn't the same as constructing the complete set. Either way you couldn't do the same for the set of reals. I would say that setting C to infinity and then manipulating it arithmetically and expecting relations to hold (like 2^C > C) is an error. Anyway, your statements above might still be logically true in that "If we can do something impossible, then we can do something else impossible."

You mean like "infinity plus one"? Yes, I misread what you wrote. I think the mistake is in treating infinity as a normal number. But the number you're imagining would be a real number. It just wouldn't require "more than infinity" symbols to describe it.

Is that, "there would have had been", or perhaps "there would soon be"? I suppose you mean relative to the number or quality of future "cooler" gizmos that we should still expect. It will just have to be someone else who makes them a reality. I suppose if there's something we can learn from Jobs, it's that... If you think that something is possible, don't rest until someone else makes it a reality. That's not meant as an insult; Jobs was a leader more than an engineer, and if we all did only what we're capable of doing ourselves, then we'd probably mostly give up soon after dreaming up an idea. If more of us work with persistence to make imagined possibilities real, we should have some pretty cool gizmos in the next 20 years.

The cardinality of the reals is infinite. You're right in that infinity is not in the reals. Intuitively thinking of this number (infinity) as a real number is the error.

http://en.wikipedia.org/wiki/Present Related is the notion of an instant: http://en.wikipedia..../Cauchy_surface Another quote from above: http://en.wikipedia....s_.22present.22 Personally, I disagree with Einstein's quote there. If every event can be ordered in a sequence, with all causative events placed "before" and all effected events placed "after" (and any non-causally related event placed arbitrarily maybe), then the past and future relative to an event can be consistently defined (with many possible consistent choices for those arbitrarily placed events). Then the present can be defined relative to any event. The act of observing or experiencing a moment of time can be called an event (or a set of events); the present would be a set of events simultaneous to that. -- In agreement with Einstein this set is not distinct, and the separation between past and future can be made arbitrarily... However, the only real significance of past and future involve causally related sequences of events, and causally related sequences of events have a distinct ordering. If the present can be defined relative to any event (as in, any event happens in that event's present), then the present is different for everyone and for every observation. Philosophically I would say that the present for a given person is the set of events simultaneous to the perception of being in or at any particular moment. Edit: But I wouldn't try to define a true present in terms of human perception, because the brain probably mixes a lot of recent "past" into its perception of the present, and probably deals with events out-of-order by different parts of the brain, in order to function. Our perception of the present is probably quite fuzzy and technically inconsistent.

Thanks for the support but unfortunately I have to disagree. The case is never really closed. We can often "rest our case" based on existing evidence and have a generally accepted theory, but it will always be open to considering new evidence. owl is not by the way providing any evidence, because the reality he describes ("the Earth is round according to all observations humans have ever made of it") is consistent with relativity. Relativity predicts that all our past observations would have been the way they were (it wouldn't be accepted if it didn't actually correspond with reality, as owl seems to believe). Not all of the claims you made are certain by any stretch. If I've made or tried to make anyone believe that "things are a certain way and that's the exclusive truth" then I haven't won; I've lost, and I'm a loser.

The rest frame of one bucket or of the other or the average of the two are all valid, as are an infinite other possible frames of references. The buckets can "push off each other" like two dancers, and thus can have proper acceleration. One bucket will always be able to "tell" that it is spinning relative to the other bucket AND vice versa. If you start two identical buckets at rest with no proper acceleration, and then use one to push off the other symmetrically, the "equal and opposite" forces will ensure that they each experience equal and opposite proper acceleration. If you use something else in the universe to "push off of", then they will always have a momentum I think, relative to that other mass (even if the momentum is eventually "absorbed" by the rest of the universe). In such cases you could have one bucket feeling "at rest" while the other feels like it is spinning, or both feeling like they're spinning in the same direction at different rates, or spinning in opposite directions at different or equal rates. I'm not sure I know what I'm talking about!, but for now it feels like it makes sense. I no longer think there is anything in relativity that would deny correspondence with classical physics. If one bucket is at rest with the rest of the universe, and the universe is "spinning in the opposite direction", then the bucket is also similarly spinning. It would not experience frame dragging relative to the rest of the universe; it would not have proper acceleration; it should remain at rest relative to the universe (ignoring negligible frame-dragging of the other bucket). Another question: If the universe only consisted of two buckets with a relative spin to them, would frame-dragging cause their spins to slow over time until they are relatively at rest? And same with the linear case; would frame-dragging mean that any pair of masses with relative velocity will tend towards being at relative rest? I can't think of how to set up such a thought experiment so that the gravitational influence of the masses on each other doesn't overwhelm the effect of frame-dragging. Edit: Okay I thought of a way. 1. A bucket spinning inside another bucket... or a spinning mass inside a spherical shell (with a net gravitational attraction of 0) should come to rest relative to the shell. 2. Two masses orbiting each other with such eccentric orbits that they're practically oscillating linearly, but not so much that they collide, should constantly have the size of the orbits reduced and eventually collide. Or maybe the orbits would just become more and more circular.

Excellent. I think we can all leave it at that. There are plenty enough arguments for your version of realism and plenty enough challenges to it throughout this thread. Sorry but we are clearly not done yet until you cite evidence for length contraction. And 'it looks good on paper' (the "model") is not experimental evidence. Oh my. I dare say you may have gone and trolled yourself there!

The only way that I could make sense of this thread is to understand that what any observer feels is the same independent of frame of reference. "Feeling" acceleration means measuring it, and my (mis)understanding of acceleration was that the acceleration that is measured is acceleration. Google schooled me (schoogled?): http://en.wikipedia....er_acceleration "In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. This contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers." If you rotate a bucket, the rest of the universe feels negligible acceleration from it. If you consider a frame where it is the rest of the universe rotating, the universe still feels negligible acceleration and the bucket (though at rest) is affected by proper acceleration. No matter how it is done, if you accelerate the entire universe in a way that is physically equivalent to rotating just a bucket, then the universe is only undergoing coordinate acceleration. Since the two frames are equivalent, in neither will anyone experience any measurable difference to be able to distinguish the frames. When we say "we're rotating the bucket in the universe" vs "we're rotating the universe around the bucket", we can't say that we're doing only one but not the other. It is not just that the "physical forces are equivalent", but rather that both scenarios are actually occurring. Whatever can be said to be happening in any valid frame, is happening. So I think you and IM Egdall are right, it's just taking me awhile to get it. This all must mean that coordinate acceleration alone has no effect on the physical universe. I think it means that all proper acceleration must be relative to some other mass, which still makes for some confusing thought experiments. But I think they all eventually end up with a conclusion of "Of course it must be so!" For example, even in a universe that contains only the bucket of water, if you want to "set the bucket spinning" in some way that maximizes its proper acceleration, you still need something to make it spin. If some force pushes it, you need something to push against. Say for example that the bucket has water jets and it can use some of its contents to set it spinning. It shoots water out into the otherwise empty universe. Here, it should still be able to experience some form of proper acceleration because it is accelerating relative to the water it sent out. I'm not sure, but my guess is that the proper acceleration the bucket experiences relative to this expelled water is significant enough that a classical treatment of this mostly empty universe would correspond to a relativistic treatment -- it wouldn't matter if there was a massive universe at some great distance all around it or not. Edit: That is... it wouldn't matter if there was a universe originally at rest around it. If the bucket is spinning relative to the universe around it, it must have at some point in the past accelerated relative to the universe's mass... or something like that...

Yeah, I agree. I've been mixing up inertial motion and acceleration. I think you're saying that if you accelerated all the mass in the universe around a bucket, it would be equivalent to accelerating just the bucket into a spin. I'm saying that if you were to try to do that, frame dragging would make it so that you're not actually accelerating anything anymore, except the bucket. Whether you try to spin the bucket, or the universe, it is the bucket that will accelerate. In either case, the bucket is not an inertial frame. This implies that you cannot accelerate (uniformly?) the entire universe. If you could somehow try, then frame-dragging would undo your work and the universe would remain an inertial frame. Rotating an empty frame of reference and rotating some mass (like a bucket) are not equivalent. However, rotating an empty frame of reference, and rotating all the mass in the universe, are equivalent. Also, choosing a frame of reference where a mass is moving relative to you is equivalent to choosing a frame of reference where it's at rest relative to you, but they're not identical, due to length contraction and time dilation. Yes, there is no absolute space in relativity, but if you choose a different frame of reference you change distances and times. I don't think it's possible to choose a valid frame where normal matter is moving faster than c relative to space in the frame.

Not sure if I count as a soul but I'll say it. I think that reality as we observe or measure it is completely dependent on how it is observed, and that what exists independently of measurement is not anything like what we describe as reality. Note that this doesn't exactly fall into owl's dichotomy as subjective idealism. But I think he's sold his version of Realism so poorly (trying to associate it with "reality" when really he's describing things that are inconsistent with reality other than the reality he has set in his mind... I think it's more of an Absolutism that requires no correspondence with reality at all), that I'm willing to distance myself from "realism". My opinion is speculative and can be safely ignored in this thread. However I think it's worth posting it, because a scientist should never be so absolutely certain of anything that she takes it for granted and stops accepting the evidence, in favor of beliefs. What we "know" is not the final word; the best we can hope for is that our theories accurately describe the reality we know, and that the predictions of future theories will pass smoothly into our current theories (a correspondence principle).

The goal in doing this would I suppose be better control and measurement of the distance to reduce any errors. The distance would be 1/733 of that for OPERA. If the same c+v speed of neutrinos was detected, they would no longer arrive 60ns earlier, but 1/733 that... less than 0.1ns expected discrepancy. This is less than the error in the timing systems; the error would completely dominate the measurements. If anything you'd want the difference in timing between these neutrinos and c to be as significant or large as possible, which means as large a distance as possible. Also it's not very practical: neutrino detectors are huge underground things (http://scienceblogs....o_fun_facts.php has pictures of Gran Sasso and Super Kamiokande-III). ALSO if you're suggesting that they use two detectors (one to mark the start and one to mark the end), that is not so. The way neutrinos are detected is through interaction with normal matter, in the form of a collision that destroys the neutrino (its energy converted). Neutrinos are mostly (nearly all) not detected at all, but when they are detected it is only at the end of their journey. BUT, yes, repeating the experiment using different locations is a good idea and should happen (I think someone mentioned such plans, earlier in this thread), especially if OPERA's results remain unexplained. Edit: I suppose if you did the experiment with as short a travel time as possible, that might tell you some useful things about the system besides travel time of neutrinos. For example if they found a similar 60ns difference in timing in a 1km distance, it would suggest that it's not due to the travel time (and speed) of the neutrinos. I guess, such an experiment would be useful then, only if it gave extremely unexpected results. The expected result is that error would dominate the measurements.

What's important is that the stars are not moving through space, but rather that space itself is moving (rotating around you), and there's no speed limit on that. That's the real reason that SR's rules are not violated. The energy required to rotate all of space (corresponding to rotating a frame of reference with no mass at rest in it) would necessarily be zero. That's fine, because you don't actually have to move anything through space to do this, and that's where energy expenditure happens. But here's where I'm getting confused: My limited understanding of space/spacetime is that its properties are defined by mass. My limited understanding of frame-dragging is something like... when you move mass through spacetime, spacetime gets dragged along with the mass (but since spacetime is defined both by the moving mass and other mass that it's moving relative to, the mass both pulls space along with it AND moves through the space (leaving it behind)... depending on how much mass is moving). So according to the basic ideas of this thread: If you were to say accelerate a certain amount of mass in the +x direction by a certain amount, it would require some amount of energy. If you increased the amount of mass you were applying this acceleration to, it would require more energy. However, due to frame dragging, any accelerated mass would pull on other mass, making it slightly easier for a second unit of mass to be accelerated than the first. The total energy required relative to the amount of mass accelerated would look maybe like one half-cycle of a sine wave, increasing slower and slower until it leveled out... at "half the mass of the universe (assuming the half that gets accelerated and the half that doesn't are symmetrically distributed)". The most energy you would expend would be in taking half the universe and moving it relative to the other half (you could tweak it higher by optimizing the choice of mass, but if you've already chosen a symmetric half, you shouldn't be able to use more energy in accelerating it, just by choosing additional mass to accelerate). At the halfway point, the inertial effect of all the "rest" mass equals the frame-dragging effect of all the accelerated mass. After that point, the frame-dragging effect outweighs inertia and it actually becomes easier to accelerate more mass. Or perhaps what I'm trying to say is that by accelerating that much mass, you're moving spacetime along with the mass more than you're leaving spacetime behind... ??? sorry for my confused words. The more that spacetime moves with your mass, the less you're having to move the mass through spacetime. Beyond the half-way point, your "rest frame" is no longer the best rest frame... the frame of the accelerated mass is a better rest frame, and it's equivalent to having all of the remaining mass that you haven't touched accelerate in the opposite direction. If you keep adding mass, eventually you've accelerated all the mass in the universe, and dragged all of spacetime effortlessly along with it, and have used 0 energy, and it's equivalent to accelerating an imaginary massless frame of reference in the opposite direction. If what I wrote makes sense and is true or at least "kinda true" then I think I understand now. So the point would be that rotating a bucket through space is not technically equivalent to moving the rest of the universe through space around the bucket, BUT because moving that much of the universe would bring space along with it, either way the only thing that is moving through space is the bucket.

Okay wait... you're saying that a rotating frame of reference (say where a bucket is at rest and the universe is spinning around it) is equally valid as a frame of reference where only the bucket is spinning? If I go outside and twist my head around, and consider my head's frame of reference, then the sun is moving around me at many times the speed of light. How can that be valid? (Though its distance to me doesn't change. Is it only the rate of change of distance between something moving and something at rest that cannot exceed c? In polar coordinates with my head at the origin, the sun's movement when I twist my head seems minor.)

I'm not going to get this for some time. I can imagine some thought experiments but can't yet make sense of them. Why do you say that? Perhaps this is not true. Edit: Okay I just realized that this question was already asked verbatim and answered. http://en.wikipedia....ravitomagnetism says "The main consequence of the gravitomagnetic force, or acceleration, is that a free-falling object near a massive rotating object will itself rotate." Clearly this requires a rotating mass. I think that the Pfister and Braun results suggest is that the same effects happen with a nearby mass, and don't require an entire universe filled with mass to produce the effect??? There's a "strenuous" objection at the bottom of the entry that I'd like to check out but I guess I'll have to wait while Sub-Etha is down. On a bit of a tangent, http://en.wikipedia..../Frame-dragging mentions "static mass increase". It implies that yes, if you remove mass from the universe, other masses will decrease (may be negligible except for nearby masses). I'm not sure what the effect of removing nearly all of the mass in the universe would be. If the effect is big, then... Given that "we live in an accelerating Universe, one in which the objects which are not gravitationally bound to us right now (i.e., not in the local group) will eventually speed away from us and accelerate out of the Universe we can observe" (http://scienceblogs....f_the_unive.php), as mass disappears from our observable universe, the mass that remains in the observable universe will also decrease. If it's significant enough (eg. enough to completely change how a bucket of water behaves), it could be that gravitationally bound objects could cease to be gravitationally bound. However, given the Pfister and Braun reference, large nearby masses should completely overwhelm the effects of the rest of the universe, so we shouldn't float away from planets or have planets break free from suns or anything, I guess. ? Now I'm feelin too dum for this thread.

The reference you give doesn't seem reputable. I can't think of any way to disprove what you're saying, and the more I think about it, the more it seems reasonable. The equivalence principle in GR implies that if you were in an enclosed space, you wouldn't be able to detect any distinguishing difference between say a rocket accelerating through space, vs. a box sitting stationary in a gravitational field of the right characteristics. You're saying that you would also not be able to distinguish between having the box shook, vs. having everything else in the universe except the box shook. But since acceleration is equivalent to being in a gravitational field, then if accelerating the box is equivalent to accelerating the rest of the universe, then being stationary in a gravitational field is equivalent to accelerating the entire universe. So frame dragging is equivalent to gravity. I could buy that... I can imagine gravity as a sort of "standing wave" of dragged (or simply curved) space that provides a constant dragging-like effect. I think this is similar to what your link talks about. Is this speculative, or is it accepted science? Another way to look at this though is to consider the case where the different parts of the bucket are not part of the same frame, but are instead moving independently in different directions. Then if you have the material of the bucket keep the bucket together (through tension, which acts as a force that would be proportional to the inertia of the moving parts of the bucket that must be overcome), you have the force of tension accelerating the different parts also in different directions, and the end result is that the parts of the bucket remain essentially fixed relative to each other. In this case you're claiming that the inertia of different parts of the bucket aimed in different directions, is equivalent to the frame-dragging force of a rotating universe pulling on different parts of the bucket in different directions. Again I can't prove you wrong and it sounds reasonable. But I'm not yet convinced and I think that the rotating frames you're describing better corresponds to multiple frames that are being accelerated in different directions. It could also be "both", if there is also an equivalence principle that says that any (or some specifically configured) sets of different frames are equivalent to some single frames. Addendum: After posting that I got to thinking about how you could distinguish between a rotating system that is made up of multiple frames, vs a single rotating frame of reference. http://en.wikipedia.org/wiki/Inertial_frame_of_reference may have an answer: "The presence of fictitious forces indicates the physical laws are not the simplest laws available". The quote applies to distinguishing inertial frames from non-inertial... so I don't know if it fully answers the question for this thread. But I think that in the case of spinning the whole universe and the bucket vs spinning only the observer's frame of reference, the former is not an inertial frame of reference but the latter is. If you are in a frame where "the physical laws are not the simplest laws available", then a physical law that has a generally covariant formulation would not be the simplest formulation of that law in another frame in which simpler laws are available. However!, since frame-dragging forces would also be fictitious forces (http://en.wikipedia.org/wiki/Gravitomagnetism), they could still be equivalent to inertial fictitious forces. In conclusion I may not have any clue about what I'm talking about here.

I'm confused. Reason 1: Suppose you're rotating a tremendous amount of mass around the bucket, which causes gravitational forces that have the exact same effect as the classical pseudo-forces present when rotating just the bucket. Now suppose that you remove some of this tremendous mass (half, or nearly all, or whatever). The gravitational force effect should decrease. With a negligible enough mass rotating around the bucket, the force on the bucket will be negligible. Then, if the forces involved in rotating the bucket are equal to forces when rotating the universe around the bucket, then it must be the case that rotating a bucket of water in a mostly empty universe will not cause the water's surface to curve. -- This is an intriguing idea, because it means that the mass of the water in the bucket depends on the amount of mass in the universe. But I've never heard of that before. It would imply that the gravitational pull on the mass in the bucket by all the rest of the mass in the universe is what gives the water its inertia. Reason 2: Suppose you're rotating a tremendous amount of mass around the bucket, which causes gravitational forces that have the exact same effect as the classical pseudo-forces present when rotating just the bucket. Now suppose that you also rotate the bucket to match the rotation of the tremendous mass. What happens in this coordinate system should be the same as in another coordinate system, such as a frame that is also rotating with the universe and bucket. In the latter frame, nothing is rotating, and so there should be no curvature of the water's surface. This means that in the former frame (in which everything is rotating) there should be no surface curvature. Does this mean that the fictitious forces evident when rotating a bucket cancel out the forces that would be caused by rotating the universe around the bucket?

I don't really know about any of this but I still have doubts and questions: I don't think GR says that any reference frame will do (according to http://en.wikipedia....eral_covariance, general covariance applies to "arbitrary differentiable coordinate transformations", while GR involves "local Lorentz covariance (which applies to all frames)". The link to Lorentz covariance says "In standard physics, Lorentz symmetry is 'the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space'. Lorentz covariance is a related concept, covariance being a measure of how much two variables change together." So about the bold parts: The second implies what I thought, that the equivalence principle in GR doesn't apply directly to the fictitious forces in rotating systems???? Yet, the first bold part seems to imply that the "frame" of a rotating bucket would count. The quotes at the bottom of http://en.wikipedia....reference_frame seem to help: Treat the fictitious forces like real forces, and pretend you are in an inertial frame. — Louis N. Hand, Janet D. Finch Analytical Mechanics, p. 267 This equation has exactly the form of Newton's second law, except that in addition to F, the sum of all forces identified in the inertial frame, there is an extra term on the right...This means we can continue to use Newton's second law in the noninertial frame provided we agree that in the noninertial frame we must add an extra force-like term, often called the inertial force. — John R. Taylor: Classical Mechanics; p. 328 What this means to me is that rotating a bucket vs. rotating the universe around a bucket are not equivalent, because there is nothing (to my knowledge) that would make the fictitious forces equal. The suggestion that a massive vs. massless universe would produce different fictitious forces (due to frame dragging I guess) makes me more confident that there is nothing that would ensure that the fictitious forces are always equal. The only way I can see the fictitious forces equaling each other (when spinning a bucket vs. spinning the universe around the bucket, where the universe has an arbitrary mass) is if the mass of the bucket is dependent on the mass of the rest of the universe... which could be the case but again I know of nothing that suggests it is so.