# md65536

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## Posts posted by md65536

### Cardinality of Real Numbers Paradox?

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.

### The present time

http://en.wikipedia.org/wiki/Present

The present (or now) is the time that is associated with the events perceived directly and in the first time, not as a recollection (perceived more than once) or a speculation (predicted, hypothesis, uncertain). It is a period of time between the past and the future, and can vary in meaning from being an instant to a day or longer. In radiocarbon dating, the "present" is defined as AD 1950.

It is sometimes represented as a hyperplane in space-time, typically called "now", although modern physics demonstrates that such a hyperplane can not be defined uniquely for observers in relative motion. The present may also be viewed as a duration (see specious present).

Related is the notion of an instant: http://en.wikipedia..../Cauchy_surface

Another quote from above: http://en.wikipedia....s_.22present.22

Special Relativity's "present"

It follows from Albert Einstein's Special Theory of Relativity that there is no such thing as absolute simultaneity. When care is taken to operationalise "the present", it follows that the events that can be labeled as "simultaneous" with a given event, can not be in direct cause-effect relationship. Such collections of events are perceived differently by different observers. Instead, when focusing on "now" as the events perceived directly, not as a recollection or a speculation, for a given observer "now" takes the form of the observer's past light cone. The light cone of a given event is objectively defined as the collection of events in causal relationship to that event, but each event has a different associated light cone. One has to conclude that in relativistic models of physics there is no place for "the present" as an absolute element of reality. Einstein phrased this as: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion".

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.

### Frame of Reference as Subject in Subjective Idealism

Case closed.

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 scientist has a lot of experience with ignorance and doubt and uncertainty, and this experience is of very great importance, I think. When a scientist doesn't know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty damn sure of what the result is going to be, he is still in some doubt. We have found it of paramount importance that in order to progress, we must recognize our ignorance and leave room for doubt. Scientific knowledge is a body of statements of varying degrees of certainty — some most unsure, some nearly sure, but none absolutely certain. Now, we scientists are used to this, and we take it for granted that it is perfectly consistent to be unsure, that it is possible to live and not know. But I don't know whether everyone realizes this is true. Our freedom to doubt was born out of a struggle against authority in the early days of science. It was a very deep and strong struggle: permit us to question — to doubt — to not be sure. I think that it is important that we do not forget this struggle and thus perhaps lose what we have gained.

-- Richard Feynman

### The Whole Universe - Frame Dragging

And if you have two buckets spinning in opposite directions is the universe spinning the other way to boths buckets at the same time

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.

or two buckets spinning in the same direction at different rates. What about if only one bucket is spinning (and the universe is therefore spinning in the opposite direction) would this not cause the other bucket to spin.

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.

### Frame of Reference as Subject in Subjective Idealism

I will let my case against length contraction rest with this post.

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.

Ps: I said:

I will let my case against length contraction rest with this post.

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 Whole Universe - Frame Dragging

In a coordinate system where the background mass accelerates (the rocket is at rest) the force that the people on the rocket feel is gravitational. The accelerating background mass creates a uniform gravitational field throughout the universe pointing in the rocket's aft direction. So, the rocket is fixed in this coordinate system... 'held' in place. Everything else in the universe is falling, and accelerating as it falls toward the rear direction of the rocket. The background stars don't feel as if they are accelerating because they are falling weightless in a uniform gravitational field. The rocket feels as if it is accelerating because even though it is at rest in this frame, it is at rest in a gravitational field... like a person standing on a planet's surface.

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.

"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...

### The Whole Universe - Frame Dragging

boy, this is getting tough to sort out. I think rotating the bucket is technicallly equivalent to rotating the rest of the universe. This is Einstein's Principle of General Covariance -- there is no "preferred" frame of reference. Any reference frame is as valid as any other one. So the bucket spins in the universe frame, and the universe spins in the bucket frame. And both ways of looking at it produce identical physical results.

I also think your talk of moving through space for the bucket but not moving through space for the universe is not quite right. There is no absolute space in relativity -- so space doesn't move along with the universe. Both the bucket and universe are moving though space and through time or spacetime.

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.

### Frame of Reference as Subject in Subjective Idealism

Not a soul here has indicated that they thought there was not a real universe that would continue to exist even if we were not here to see it.

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).

### Faster than lightspeed achieved?

Theoretically the two points detection results are the same. But the two point detecting methods are different . How about making a new start detection point far from the CERN about 1km away?

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.

### The Whole Universe - Frame Dragging

And yes, when you spin around, from your point-of-view, stars that are far enough away are moving faster than the speed of light. But you can not use this effect to send a signal faster than the speed of light -- so relativity rules are not violated.

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.

### The Whole Universe - Frame Dragging

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.)

### The Whole Universe - Frame Dragging

I'm not going to get this for some time. I can imagine some thought experiments but can't yet make sense of them.

If there were no other mass/energy in the universe, per GR the water would still become concave.

Why do you say that? Perhaps this is not true.

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???

h2g2 not reputable!?!?

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 Whole Universe - Frame Dragging

Good arguments. Let me try to answer them:

As to reason 1 -- I think you are rediscovering the equivalence of gravity and inertia. See link: http://philsci-archi...1287/1/A1085285

As to reason 2 -- I believe if the bucket rotates to match the rotation of the universe, then there is no relative rotation between the two. This is equivalent to a reference frame where the bucket and universe are at rest. I think you have to consider only relative rotation. There is no absolute rotation in Einstein's construct.

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?

Einstein says there is no absolute space. The bucket itself is a legitimate reference frame, per the Principle of General Covariance. But in this frame, the bucket is at rest. So what makes the water go concave" From this point-of-view, the rest of the universe is rotating in the opposite direction. And through frame-dragging, this causes the water to go concave!

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.

### The Whole Universe - Frame Dragging

The thing that makes the fictitious forces equal is the mass itself. In the frame where the bucket is at rest there is a tremendous amount of mass rotating around the bucket. In GR, if you move mass you get a gravitational force analogous to the way moving a charge classically gives you an electromagnetic force. So, rotating a lot of mass around something should create a gravitational field that seems to have the exact same effect as the classical pseudo-forces.

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?

### The Whole Universe - Frame Dragging

The idea of this thought-experiment is to show one effect of Einstein's Principle of General Covariance. Per general relativity, any reference frame will do. Newton says the only legitimate reference frame is absolute space itself. The bucket is spinning with respect to absolute space.

Einstein says there is no absolute space. The bucket itself is a legitimate reference frame, per the Principle of General Covariance. But in this frame, the bucket is at rest. So what makes the water go concave" From this point-of-view, the rest of the universe is rotating in the opposite direction. And through frame-dragging, this causes the water to go concave!

I learned this from Brian Greene's The Fabric of the Cosmos, beginning of Chapter 14. He also gives references in the endnotes: D. Brill and J. Cohen, Phys. Rev. vol 143, no. 4, 1011 (1966) and H. Pfister and K. Braun, Class. Quantum Grav. 2, 909 (1985).

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.

### The Whole Universe - Frame Dragging

General relativity says: the rotation of the rest of the universe causes the water to become concave in case 2. This is due to frame dragging.

This doesn't sound right to me. Do you have a reference?

The water becoming concave was explainable before GR and certainly doesn't need frame dragging (a very small effect that requires sensitive instruments to detect) to explain it.

Perhaps with the right conditions, having the universe spin around a bucket of water would produce an effect (due to frame dragging) similar to spinning the bucket (either coincidentally or by choosing an appropriate bucket size or spin rate or whatever... I don't really know enough to say), but that doesn't mean that the 2 effects are equivalent.

### Area of a blob

Newton devised some way to measure the area of a blob by using some infinite triangle theorem, but I have no idea what the theorem is right now.

Either this is meant to be only moderately informative, or your name is curiously ironic.

It sounds kind of like integral calculus to me.

### Frame of Reference as Subject in Subjective Idealism

Alpha Centauri and earth are no different from the ships in Owl's latest jousting thought experiment. If they are approaching one another with any speed then the speed of light relative to one needs to be the same as the speed of light relative to the other... and they both need to be c to be consistent with Owl's worldview. He obviously can't make that work.

Unless the sun, Earth, and Alpha Centauri are all part of the same preferred frame of reference and don't behave like the "moving flashlight source".

Perhaps Realism asserts that the Earth and the sun are fixed in space and do not move relative to each other.

### Frame of Reference as Subject in Subjective Idealism

So you're saying that the person holding the flashlight will measure the velocity of the light beam as 1/2 c relative to him? That's what this seems to imply.

I think he's saying that the person holding the flashlight will measure the velocity of light to be c, using the Earth's frame of reference. As far as I can remember, owl has never admitted acceptance of "there are no preferred frame of reference".

But what I wonder is, what if the person holding the flashlight is on the Earth, which is orbiting the sun, pointing the flashlight in the direction they're orbiting? Then are they "catching up to the light beam" as owl suggests, and thus measure a speed of light less than c? Or does the Earth not "catch up to light" the way that the flashlight holder in your example does? Is the earth really a preferred frame of reference, the only place where you can truly say "This place is at rest, as far as measurements of the speed of light are concerned. Everything else in the universe truly does move around the Earth."?

### Frame of Reference as Subject in Subjective Idealism

That's how I explained it, yes. From an observer's point of you, the light source is moving at half the speed of light, so it "chases" the projected light beam. In one second, the light moves half a light-second away from the flashlight, since the flashlight is chasing it.

Now, what does the light source observe? From the light source's perspective, it's not moving -- if you measure your velocity relative to yourself, you get 0. After one second, how far away is the light?

That's an interesting question and I'm wondering where you're going with it. I don't think it should be ignored and brushed under the rug along with everything else in this thread.

From the observer's perspective, the light should move one light-second in one second, and the source flashlight moves half a light-second in one second, so the light is half a light-second away from the flashlight, after one second.

From the flashlight's frame of reference, the light should move one light-second in one second (as with any observer since the speed of light is c in every frame of reference), and the flashlight is not moving relative to the observer, so the light is one light-second away from the flashlight after one second.

Does anyone disagree?

### Sorry, the Hilbert hotel is full.

You can accomodate one at a time:

Yes. That's the answer I was looking for.

The key to accommodating guests is the assumption that the new guests will be specifically small enough to fit in the rooms (which approach a volume of 0 ie. infinitesimal as the room number, or number of guests, approaches infinity). The original bad algorithm of trying to put each new guest in room 1 means that incoming smaller guests are put in a large room with a lot of wasted space, and the larger guests that we try to move can't fit into the smaller higher-room-number rooms.

If we allow the new incoming guests to be similarly compressed as the "original" guests, such that they can be compressed to fit into room 2n, where n is the room they're first put into, then it should also be possible to accommodate an infinite number of infinitely large groups (that is: large in terms of count, not volume), and after each check-in have all of the rooms occupied and spatially full.

I think...

### Faster than lightspeed achieved?

I think few are assuming anything.

True... and assuming that "it couldn't possibly be blah" is a good way to miss something.

It makes me think of the analogy of "picking the low-hanging fruit first" and looking at what's easiest, first.

Suggestions like "maybe they forgot that the Earth is round" would be fruit that's hanging so low that it's on the ground and 2 weeks rotten. If it was something like that I'd be embarrassed for them.

Extending this analogy, you have this tree with low-hanging fruit which is problems like GPS precision and altitude that we should expect the scientists to have thought of and fully analyzed.

Then at the top of the tree is a glowing angel ornament that is "relativity has been toppled!!!". Near the bottom of the tree is other measurement problems, up higher may be obscure problems, maybe higher is exotic but known effects, maybe never before seen with neutrinos. I dunno... whatever! But there's a whole middle section of this tree where there is new and earth-shaking (to varying degrees) science, which doesn't invalidate relativity. The only news and blogs etc I've seen seems to ignore this whole middle of the tree.

(A Christmas tree shape, probably with a very very wide bottom, may be a good analogy for the probability of where the explanation "fruit" will be found?)

### Frame of Reference as Subject in Subjective Idealism

However, it does bring up an interesting "notion" I have been entertaining. We (us humans) are really in no better or worse position than any other entity in the universe to experience the universe. There are some direct analogies between what we are and do, and what a "non thinking" entity is and does.

This is why when we speak of an "observer" we don't speak of a human, but instead of an abstract prototypical observer. It doesn't need to be a physical thing or "alive" or a human with all the connotations and assumptions that come along with that. All the assumptions should be defined, and so minimized.

It is argued mathematically that somewhere in space and time there is a duplicate TAR. I totally disagree. It is not possible. Cause if he where to point at me, and I were to point at him we would be pointing in opposite directions in space and time, making us each unique at least in the direction we would have to point. Nevermind the fact that I would be pointing from the Milky Way and he would be pointing AT the Milky Way.

Apologies for this off-topic reply, but... in most models if it's mathematically possible that another exact TAR exists it's statistically certain that an infinite duplicate TARs exist. So your duplicate TAR could be pointing in the same direction, toward the next one in line (and another would be pointing at you). But then there would be an infinite number of TARs that are pointing in different directions, or are picking their noses instead, etc. I don't think these models are correct, either.

Anyway this "notion" leads me in the direction of considering what "arrives" here now is of great importance, greater importance than what we imagine will arrive here later. We are

YES. I'm not going to try to talk about "updates to simultaneity" but this intuition of yours is true and a very important part of it. I imagine Einstein having similar insights and being guided by them while figuring it all out for the first time.

(This can also be seen as an insight into how reality, and what is observed, are very closely connected.)

### Faster than lightspeed achieved?

I think the important thing to realize is that no individual neutrinos were measured to be traveling at v > c.

It is only the statistical distribution of observations that best matches a calculated speed of slightly more than c.

Starts With A Bang describes this better than I can and explains some possible problems with misinterpreting such data:

http://scienceblogs.com/startswithabang/2011/09/are_we_fooling_ourselves_with.php

I think that assuming there's a measurement error is a tunnel-vision approach to this that misses other possibilities.

An important question to ask is: Is it possible to detect a change in the neutrino source faster than if that information is transmitted at c?

I think the answer based on the existing measurements is "no". You can't determine the statistical distribution until you have enough samples, by which time you've lost any advantage over c.

If this is the case, then relativity is still safe. There are other examples in quantum mechanics where you can "look back" at past information and see a pattern that suggests superluminal information, but that information is only retrospective. These other examples don't invalidate relativity, and neither would this experiment.

It would certainly suggest something new though.

I believe that if there is some "wave pattern" that is carried at superluminal speeds, then it is not received via the same neutrinos that were transmitted, but by ones that were transmitted slightly earlier. If so, then repeating the experiment with individual neutrinos would result in no observations of anything with v > c.

### Frame of Reference as Subject in Subjective Idealism

Relativity assumes a halfgod like now that extends even 100,000 million lightyears from here and beyond. It takes the eyes of a zillion observers scattered all amongst everywhere and gives them all the ability to report what they observe back to us, instantly, using halfgod radio, that operates instantaneously, with no consideration that any speed limit such as C exists. But ALL these observers are stationary in respect to us, they have no velocity toward us, away from us, or tangent to us. They are all in our frame of reference. Events anywhere in the universe will happen in a particular order at particular distances from each other. All the reports will agree on this order and the distances involved. And always the speed of light is the measured, and found to be 300,000,000 meters per second.

Schrödinger's hat and Iggy are probably each more knowledgeable than I, and it sounds like you've figured out some important aspects of relativity...

but I don't think this analogy is a good one, for developing a solid understanding of relativity. There are complications that can make it invalid -- namely "updates to simultaneity", which happen if you change inertial frames, say by accelerating. An update to simultaneity relative to something should happen I think any time that you change length contraction to that something. Since simultaneity is relative, it can be changed, and that can sometimes imply weird things... which I won't get into except to say that the "instantaneously communicated" observations of your zillion eyes can change; these instantly communicated observations are not always valid.

There's a reason that SR implies that no information can travel faster than c. If you do thought experiments using your analogy, or anything that involves information transmitted faster than c, you'll be able to derive contradictions and paradoxes.

If you modified your analogy to say that only the instantaneously made observations that eventually reach us (at a speed of c) are valid observations, then I think it'd be okay. If that ruins your analogy so that it no longer makes intuitive sense, then the analogy (at least your above paragraph of it) might not be that useful.

An intuitive understanding of SR will coincide with an intuitive understanding that c is a universal speed limit for all information.

But don't worry! There are always "further complications" no matter how well you understand relativity, and that shouldn't detract from the aspects that you do understand!

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