md65536

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. See http://en.wikipedia.org/wiki/Fictitious_force 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.

Either this is meant to be only moderately informative, or your name is curiously ironic. It sounds kind of like integral calculus to me.

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.

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."?

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?

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

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?)

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. 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. 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.)

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.

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!

Naw. Maybe time for a clue: The meaning of the words danger and stronger, as well as the answer, don't matter. The specific meaning of the words 'stem' and 'correspond' are important.

http://www.youtube.com/watch?v=3a2HqtH4aiE There's a clock on the bottom right of the video, but I'm not sure exactly what it means. I don't think this is true, because space would appear to warp severely... so I think that the distance to the center of the black hole would change as you fell in??? Some thoughts: According to the traveler, time (in local space) will tick at a normal rate. However, with severe enough gravity (or is it gravitational gradient?), "local space" will become smaller and smaller, so that at some point your ship is not entirely in local "flat" space. Eventually your body won't be in local space, meaning that different parts of you will be experiencing time at different rates relative to other parts of you. You'd probably be dead anyway from tidal forces (http://en.wikipedia.org/wiki/Spaghettification). But if you imagine it as a point observer, time would pass at a normal rate. I don't think anyone knows what would happen inside a black hole especially regarding a theoretical singularity (like whether it can become "infinitely many kilometers deep" when approaching it or whatever) so I think any answer would be speculative.

This certainly adds some complicated details and proves to me yet again that my understanding of relativity is inadequate. I'm not sure now what of my previous posts can be salvaged. Note that this can only be true when the instantaneous position of the gravitational mass (sun) is known from the delayed light. Otherwise it is a violation of causality. This is just another way of saying: In light of these details, I'd like to change my answer: - Ignore anything I've said. - Assume no acceleration (at least until the thought experiment makes complete sense with constant velocity) - Consider the frame of reference where the 2 objects are relatively at rest, which will be the simplest perspective. - All other frames of reference will observe something that is consistent with that. Clearly, in the rest frame the only gravitational attraction of the objects would be directly towards each other.

I really don't think it'll be something "easy and obvious". This is a "large group" of physicists working for a few years on this. They're not idiots. They didn't spend an hour thinking about it only to say "Well I'm stumped. Maybe the internet will know!" That does not rule out something simple and obvious. Science isn't about a fixed set of knowledge; everything that is scientifically obvious today was missed consistently up to some point in history. In some science blogs about the story, I'm seeing a kind of hostility toward the scientists, such as here: http://motls.blogspot.com/2011/09/italian-out-of-tune-superluminal.html Some people appear to feel that relativity is such a crucial part of their understanding that a challenge of it feels like a personal attack (as I tend to feel about causality), and that any challenging evidence must necessarily be wrong and thus the experimenters must have made a mistake and thus they are incompetent retards. This is a typical view of science these days, due to politics or lack of understanding or whatever it is... there's this general idea that scientists don't know what they're doing, or that someone "off the street" -- whose knowledge of the experiment or the science behind it might consist of "I read about it in a news story and then looked it up in wikipedia" -- is just as knowledgeable about the science as the experimenters, and likely to think of something "obvious" that the experimenters missed. It could be. No one person will think of everything. The entire "large group" of scientists could all have overlooked something. It's likely a systematic error; it could be a simple one. I'm not going to assume it though. I think they know what they're doing.

There's some interesting info on the story here: http://scienceblogs.com/startswithabang/2011/09/this_extraordinary_claim_requi.php

I searched for those values to ascertain their meaning and I came across another user on various forums who has the exact same IQ scores. This other user has been banned from scienceforums.COM, sciencechatforum.com aka philosophychatforum.com, and possibly the Genius Forums and myspace. I found this post from a staff member of one of the sites especially interesting: This other user seems to roam from site to site over the years, pissing off a lot of people trying to "enlighten" them with the same crap over and over, wasting a lot of people's time getting into similar closed-minded arguments. He, too, is also a psychotherapist, but only with "a private practice by word of mouth with no advertising and no listing", so I assume no license or doctoral training. My point is that high IQ is not credentials.

The abstract says, "The measurement is based on high-statistics data taken by OPERA in the years 2009, 2010 and 2011." My guess is that they didn't measure any individual neutrinos traveling at v > c, but can infer that they did from a distribution of a large number of neutrino measurements. Unless it turns out to be measurement error, I speculate that this is some kind of "entanglement" effect between the neutrinos. If so, this would NOT violate SR, for the same reasons that the results of Delayed choice quantum eraser experiments do not violate SR. In the quantum eraser experiment, results collected after a large number of photon events show an interference pattern, which indicates information having traveled faster than light. However, the information is only available in the form of the interference pattern, which cannot be determined by any single photon event. The information is only extractable after the fact. There is no useful information that can possibly be transmitted faster than light. Causality is not violated. SR survives. I'm willing to bet that similar results will be found (because "measurement errors" is boring and I'm an optimist! )... - The explanation will be "quantum weirdness". - It'll be proven that there is no way to use it to send information faster than light and thus causality remains intact. - News stories will explain it like "The scientists say that this is allowed in relativity and Einstein's theory remains on solid ground... for now."

You took some intuitive assumptions based on observations, and you logically deduced some conclusions that were not intuitive. Yes, it felt like you were arguing that this doesn't make immediate intuitive sense... but -- refreshingly for this thread -- you didn't actually say "Therefore it must not be true." This is probably the reason for the double-takes. Einstein and many others probably went through the same thing, accidentally deducing something puzzling, and then figuring it out instead of denying it. To figure out the puzzle often requires trusting the logical deductions, over preconceived intuitive ideas or beliefs. If the solution to every puzzle was intuitive and something you already knew, you wouldn't learn anything new from it.

I'm going to take a stab at this to see how well I get this. I would not consider this post as an answer until it is approved or corrected by someone who knows! The expansion is equivalent to the larger spacetime intervals between pairs of objects on a Cauchy surface, relative to the spacetime intervals of the same objects on past Cauchy surfaces. If you imagine a plane in space-time that is the set of all points where t=0, for all clocks that have been synchronized to some arbitrary single clock that has arbitrarily been set to 0 (sorry if I'm unnecessarily obfuscating this!), then you'll be imagining one possible Cauchy surface. Now if you sweep this plane forward through time*, you'll be sweeping it through the fixed spacetime manifold. The spacetime intervals between expanding regions will be larger on subsequent future Cauchy surfaces that you sweep through. * My guess is that there are many ways to do this, and some ways but not all will result in new Cauchy surfaces.

Iggy, I think you were fully awake when you wrote the previous "That's not right." tar, the second paragraph that you wrote is... fine... but the first paragraph is more confusing than good. Whether a statement like "a meter is not always a meter" is right or wrong depends on how you interpret it, and whether the two "meters" refer to separate things. Wrong: A meter is by definition a meter. Right: One's measure of a meter's distance is not always the same as another's measure of the space. I don't think I can explain what I mean in a helpful way without explaining relativity and I don't think I'd be any good at that. I think that understanding relativity first, and then understanding the meaning of length contraction, is better than trying to grasp relativity by first figuring out the meaning of length contraction. But this is all "learn SR... trust us it makes sense in the end... mostly" which can only be experienced for yourself. Philosophically, I think that what this all says is this: If you think about how you know and understand the concept of distance, what is it ultimately based on? Is it the length of a stick or the diameter of the Earth? If so then is it because there are a certain number of molecules lined up side-by-side in those lengths, and each molecule has a certain size and spacing? How do you intuitively know that what you consider the definition of a meter will not vary? I would argue that our intuitive understanding of distance comes from the speed of light. Since anything we've ever observed or measured in history was done with an invariant speed of light, we intuitively have a very consistent perception of distance. The caveat is that distance must adhere to the rules of light, rather than the number of molecules in a stick etc. Edit: Okay so I can't read. tar actually your first paragraph is a good example of how treating distance and time inconsistently leads to contradictions, which leads to the correct conclusion in the second paragraph.

I think I understand now. Just as the 3d shape of a pancake doesn't change depending on its 2d representation (which can change as you turn it), the 4d shape of the Earth doesn't change when its 3d shape is affected by length contraction. I didn't realize that's what you were saying throughout the thread. owl, I dare say you've won this discussion, using a technique that I've found very useful over the last few years called "proof by redefinition". I still think that there are some contradictions and inconsistencies to work out, but basically I accept that your own definition of realism and your own definition of distance deny the reality (as you define it) of your definition of relativity.

Thanks for the link. I'll have to read more of it. The two velocities would be P's change in O's measurement of distance divided by O's delta time, and P's change in P's measurement of distance divided by P's delta time. I guess that's the same as "velocity measured in O's frame" and "velocity measured in P's frame". I guess that any observer would agree on what P measures... and trying to express this from O's perspective is an unnecessary complication? Good point. It's not quite a velocity at all. If it has no name I'll just refer to its description; it represents the change in rest distance per unit of relativistic time. But this isn't a robust definition so I'll have to be careful!

Suppose we're considering the velocity of a point P relative to an observer O. P's velocity can be expressed as a change in the distance to P as measured by O, divided by the change in time as measured by O. It can also be expressed as a change in the distance measured by P, divided by the change in time of P. These two velocities are the same value; the speed that O measures P approaching is the same speed that P measures O approaching. If we're talking about everything from O's perspective, do these 2 velocities have different names? That is "change in locally defined distance over local time" vs "change in remotely defined distance over remotely defined time"? There is also the idea of dividing O's distance by the change in P's clock. Does this value have a name? It usually comes up when one mixes frames, or tries to calculate P's velocity in terms of rest distance instead of relativistic distance. "rest velocity" comes to mind but that term is obviously nonsensical. Does this "invalid velocity" value have a practical application other than in mistakes? I'd like to refer to it as a useful value. Thanks.

Thanks, this helps. Is it fair to say that causality is simple in SR (any two causally related events are within each other's light cone (one's future and the other's past cone unless the events share a point in spacetime)), but that it's not always that simple with GR?

My feeble understanding of inflation is that just because 2 regions are causally disconnected now doesn't mean they always were. As with Guth's pre-inflation period that you mention, if regions are close enough together for enough time, they can share information, and still then be separated by inflation faster than c and become causally disconnected. So I guess that without Guth's inflation, this would not happen. Even if these regions were once a fraction of a meter away from each other in the first conceivable moments after the big bang, inflation separated them early enough and fast enough that light didn't have enough time to cross even those small distances. This would allow those 2 disconnected regions to "never" (in all well-defined time) have been causally connected with a common causal parent event, and yet still have a common cause in the BB singularity. Yes, but I would say that the tip of my nose and the tip of my right index finger at a single moment one second after noon are within the light cone of my belly button at noon. Am I not using the terms correctly? I guess what you're saying is that 2 objects might be separated by a time-like interval at one pair of times, and be separated by a space-like interval at another. It doesn't require inflation or even for the objects to move. My fingertip yesterday and my nose today are connected by a time-like interval, but my fingertip now and nose now are connected by a space-like interval. All these events have fixed coordinates on the spacetime manifold. I was in error in trying to reason about spacetime intervals as somethings that move or evolve in space or time.