md65536

Well no one seems to want to answer but I'm interested in whether my reasoning is right, so...

No, the equations are based on mathematical and logical consequences of observations of the speed of light. Physicists determine the equations based on what is observed, not the other way around. Nothing will ever appear to be moving at greater than c, relative to any observer. If you can imagine objects moving relative to you at near c, then you'll also have to imagine length contraction and time dilation. If you do this (guided by the equations to figure out precisely what will happen), you'll see that time will dilate and space will contract and make it impossible for anything to actually move or appear to move faster than c relative to you. If you follow derivations of the Lorentz transformations you'll probably come to understand why--or at least that--this must be so.

Out of curiosity, is it possible to define some type of abstract curved space where two things can separate faster than 2c? It would require that while each thing travels away from you at < c, the distance between the 2 increases at a greater rate than the sum of the change in distance relative to you. If possible, would it require that the 2 things are not traveling on the same geodesic which intersects you? Or would it simply require inhomogeneous spacetime curvature? OR is it true that the distance between any 2 points A and C is <= the distance from A to B + distance from B to C, for all possible points B? Is this true for any metric space? Or for any conceivable spacetime curvature? Probably "separation velocity" but after a quick glance at the website I didn't see anything specific. I think you may be giving a specific example of a situation that is handled by more general SR math that can be used to figure out that example as well as many more examples. To see what I mean, try flipping the problem over, and instead of imagining an inertial observer in between 2 relatively separating objects, imagine it instead from the perspective of one of the separating objects. For example, if one object C is moving away from another A at 0.9 c, and then you imagine a third object B in the middle that's moving away at half the speed -- from A's perspective nothing is moving relative to anything else at > c -- and then calculate the velocities relative to the middle object B you should find that A and C are each moving away from each other with a separation velocity greater than c...

I don't think we're talking about the same thing here. Coordinate time and proper time of events are the same thing in SR only according to clocks that are at the same location of the events (or relatively at rest and synchronized to the observer's clocks) [second paragraph of http://en.wikipedia....Coordinate_time]. When we speak of time dilation, we're speaking of one clock ticking at a different rate relative to another clock. http://en.wikipedia..../Lorentz_factor The former refers to coordinate time (is this incorrect?), the latter to proper time. If I'm using the term coordinate time incorrectly, then what term should be used instead to describe the time according to a remote moving clock that ticks slower relative to "wristwatch time"? Edit: I think I see my mistake...s... - Coordinate time and proper time don't inherently refer to different clocks. In SR, the coordinate time and proper time of a given clock and observer are the same. - Each clock will have its own proper time. - The time of a remote moving clock is just the "time of that clock according to the observer"... it doesn't have a special name.

Isn't the proper time of one observer a coordinate time of another observer? I don't understand how curved spacetime prohibits correspondence to a real clock. Any observations of a distant clock (or signals from one) would arrive via a geodesic, which would define a distance to the clock, and thus a specific time delay of the observation, regardless of curvature. So it seems that the observer could calculate the time registered by the real clock -- and wouldn't this correspond to the coordinate time? EXCEPT... the time delay would be measured in proper time. With SR you could just divide by gamma to find the delay in terms of coordinate time? Is there no similar thing in GR?

The observer on Earth would use my clock (which travels to Mars) to measure coordinate time, correct? If they use their own clock, is that wristwatch time? It couldn't count as proper time. Or would it be coordinate time also? I was calling this "local time" but that seems a misleading phrase for measuring the time of remote events (using a local wristwatch). We could say that to an Earthbound observer, the time between my leaving and the observation on Earth of my arrival on Mars, can be measured in proper time.

Is proper time equivalent to "local time in the frame of reference of an observer, for events that happen at the location of the observer"? And local time (is there a better term?) is a bit more general, because it can also be used to describe the timing of remote events? And is coordinate time then basically time according to any clock that is remote from the observer? Is it correct to use these phrases when speaking of relativistic scenarios? Eg. a traveling observer's ideal clock measures proper time and always ticks at a constant rate. For other observers the same clock measures coordinate time, which ticks at a variable rate in general. Are there other related or better terms for describing time according to various observers and clocks?

True, I was sloppy with semantics. To be precise I should have said that logical validity doesn't imply logical soundness. If correct evidence contradicts a logically valid argument, the premises are incorrect. The logic is still valid but it's useless. The examples in this thread suggest building logical arguments out of flimsy premises, as if the logic will solidify them. (Or more likely, the examples in this thread are also confusing 'logical' with 'intuitive'.) It is not just "formal verbal logic" or "common logic" that is important to science, but logical soundness, as you've pointed out. I don't know of any examples in science of where logical soundness is shunned, so I must disagree with the OP.

Can you explain which meaning of 'absolute' you're using, and if that doesn't make it obvious, describe how SoL is not absolute? We don't have to suppose it, but we did. It's not about what we want to believe but what the evidence suggests. So far the evidence doesn't contradict it; it is within the range of what is possible. It's still an open question so of course the evidence isn't conclusive, however the evidence does rule out some other possible early universe scenarios that many people might find much more logical (young earth hypothesis, for an extreme example). If the evidence contradicts the logical, the logical is incorrect.

If it doubled for 12*3600 seconds there would be 2^43200 algae, which is quite a bit more than the number of atoms in the universe. I'd say that though the lake was full at 12pm, it was probably also full a lot earlier than that. I'd say it was half full within the first minute (~10^18 "alge").

Step 1. Kidnap every person the victim knows, keep them in the well in my basement, and torture them daily. Uh... I don't think your rules are very well specified, because I think this plan fits but that it isn't quite what you were looking for. I think my plan would do that.

Just to be on the safe side, make it a 30 ft. pole.

I recently saw an astronomy picture that had the moon in it and a nebula which looked as big as the moon. I can't remember where I saw it... does anyone know if there are nebulas that actually look as big as the moon from Earth? And how far away would such a nebula be? Here's my puzzle: Suppose you had a nebula that looks as big as the moon. Suppose that this imaginary nebula happens to be as dense as the moon. Which would have a stronger gravitational pull on us? You can assume the nebula is spherical and whatever distance away you want. Say, 100 light years.

At most 49 / 99 are troublemakers.

Go through both doors in superposition. Collapse the wavefunction of whichever reality is nicer.

I think Feynman makes a good argument here: This is from the first of a series of lectures that can be found here: http://www.vega.org.uk/video/subseries/8 If you take his quote out of context you might twist it to support your case. But what he's saying is that the math isn't sacrosanct. It is just a set of techniques used to arrive at the "final count of beans" of a theory without counting every bean individually. It's not the math that's important but the predictions made by that math, and they're accepted when they best predict the outcome of whatever they model. The story of the Mayans that he uses is that they were interested in predicting when Venus would show up in the morning vs. the evening, and they figured this out by observing it and counting days, and creating the math for that. This allows them to make accurate predictions. From this, they (we assume) had no idea why Venus followed those predictions, and as Feynman points out, trying to figure it out based only on the observations (the counts of days) is not likely to get you anywhere. The explanation "it's because Venus and the Earth each orbit the sun with different periods" is nice to know and it's certainly important to us, but it gets you nowhere towards predicting when Venus will show up in the morning or the evening, without complicated math involved (more complicated than the Mayan method). So beyond what Feynman says, my point is also: - A new theory doesn't replace an old one just based on explanations, but based on new observations, and on predicting/modeling new phenomena or the same phenomena more accurately. - New theories do not replace math with logic, but with different math (typically the math doesn't get simpler, I should think). I do agree that in the future, the explanations for why the math works will become simpler and more satisfying in many cases. As Feynman says several times in that lecture, nobody knows why it works. But that is not how it is judged. Feynman also points out that it's incredibly successful at predicting a large range of phenomena with high precision, and that is why the math is so valued.

If the math doesn't change, the predictions don't change, and the theory doesn't change. Different explanations for the same predictions are different interpretations of the same theory. I agree, these ideas lead to new or modified interpretations of the existing theory. It happens all the time and it will keep happening, and progress will be made. If one interpretation (ie. explanation) shows itself to be logically "right" vs another interpretation, it will probably only do so by improving or expanding the theory (and its math), or by suggesting a new way to test the different interpretations. Otherwise, even if an explanation is "completely logical", yet it makes the exact same predictions as another explanation, mathematically, with no test, then there is no way to show that the other explanation is wrong.

"Never been detected" is not the same as "not detectable". If something is theoretically undetectable (and not just that detection is currently unfeasible), then it can never be detected according to that theory. If it is ever to be detected, the theory must be modified or replaced. It doesn't matter who you are (Shroedinger, Einstein etc); if an idea is based on belief and not theory and observation, then including that idea in a model is an interpretation of the theory. Particles traversing distance may be a simpler to conceive interpretation than leaping. However, "simpler" is not just about what seems to make the most sense without having additional questions to ponder. Its about specifying the model as efficiently as possible to minimize the number of additional assumptions that aren't a consequence of the observable evidence. So, the idea of particles leaping may be abhorrent, but if all that it means is that the particle is in one location at one time and in another location at another time and you don't specify or care about what goes on between those 2 spacetime coordinates, then it is simpler. I'm not sure what QM predicts is undetectable or unobservable, but I know that it does predict that some things are. For example the uncertainty principle says that some measurements are physically impossible to make, even with any yet-to-be-imagined measuring technology. To be able to measure things that the uncertainty principle says are unmeasurable, you wouldn't need just better instruments, you would need a new theory. I'm not sure what the various theories say about the detectability of particle traversal vs. leaping.

Well yes, a finite speed of light makes it easy to consider events being seen at different times from different locations. But consider this: If the current moment is a universal present, then it seems safe to assume that any previous moment could also be considered a universal past moment. Then if you consider a past momentary event, that event would have to have occurred in a universal moment. Some other event at a different time would have to have occurred in another universal moment. Since these moments are universal, they would have to occur in the same order according to anyone (otherwise, when the first event occurred according to one person in a universal present, it had already happened according to another person, in which case it was a past moment, not the present). Therefore, presentism and this line of reasoning implies that lack of simultaneity (not just the appearance of it) is impossible. Yet SR implies lack of simultaneity. Is there any flaw in my reasoning? It might be possible to argue that once the "present" passes, it loses its universality, and that past moments are not universal, making it possible to change the order of past events. However I don't know if this argument could be tenable. Lack of simultaneity is a reality; the simplest form of presentism must not be.

If there is no possible detectable difference between particles "leaping" from one place to another, vs. traversing the distance in a classical sense, then either case would be equally valid in a model of reality. Unless some test can show that one or the other is invalid, there is nothing to say that one is right and the other is wrong. If there's no difference, the two should be interchangeable. But, I think it would be pointless to say that something exists in a location if there is no way to detect that it was ever there, so if there is no evidence that particles traverse distances, then leaping those distances would be a simpler explanation (ie. a model would have the particle existing in one detectable place, and then in another detectable place, and not specify any other locations for which there is no evidence of the particle existing). I think it's important to consider that any "leaping" would have to obey the law of causality. If information is transfered over a distance (the leap), then it must do so at a speed <= c (but probably =c). So if energy disappears from one location and appears in a distant location, it would also need to appear at a later time than it disappeared.

How do you reconcile this presentism with lack of simultaneity? No matter how you explain it, you will be able to find examples where events--non-causally related ones--are seen and determined to occur in different orders for different people. Do you have an explanation for that that is compatible with presentism? I have my own interpretations of SR that I thought were compatible with presentism. I tried to make it work but I just can't provide an explanation of how different events could occur in different orders, and yet have a single "present" that is shared by the different observers. The only way I've been able to make it work is to "flatten" time at all locations to a single instant (meanwhile treating the universe as a point singularity). This treats "duration" as completely subjective or perceptual. If you remove duration to make presentism work, then time becomes nothing but causal relationships with no concept of anything "taking time". But this removes so much from the concept of time, that the meaning of present is completely changed, if not lost entirely. Are you willing to consider such bizarre ideas, or does your version of presentism work with evidence from "plain everyday experiences", while denying things like lack of simultaneity? If the latter, then I'm not interested.

I dunno but if no one else has an answer I'll stab at it... Yes? There are multiple mathematical models because there are multiple possible "shapes" of gravitational fields. The typical example of an accelerating rocket is not exactly equivalent to typical gravitational fields, ie. those around spherical bodies. I believe the rocket would be exactly equivalent to a homogeneous gravitational field maybe? An observer in a rocket sitting on a (tiny) planet's surface might be able to detect subtle differences in the direction of gravitational force at different locations within the rocket, or the gravitational gradient between the top and bottom of the rocket. I suppose the equivalence principle works exactly for different types of acceleration and corresponding gravitational fields. Gravity on Earth would be equivalent to some imaginable rocket whose parts are not all accelerating exactly the same.

I believe that anything can be considered to be moving at c. It is more of a standard speed than a maximum speed. c is essentially a constant linking distance and time. I'm pretty sure this view requires some misinterpretations of accepted science! Hopefully someone can correct me. The details are: - All energy, unobstructed, travels at c. - Energy and mass are equivalent. One might consider mass to be "made of" energy, however I remember reading comments that suggest this is misleading? - Therefore all particles or energy that can be considered to be moving < c according to some frame of reference (including their rest frame), must oscillate or change directions. If the energy moved in a single direction, it would move at c. - If energy is moving at c, but oscillates or changes direction, then after a time t its total displacement will be less than the total distance traveled by the energy. So if you consider a moving particle, the energy that makes up that particle is moving at c, but the particle itself can move at speeds < c. As an analogy, if a sailing ship moves from point A to B in a time of t, its (average) velocity is ||B-A||/t, but if it is tacking in the wind its speed through the water can be much greater. So, if you are considering a mass moving in a straight line, its velocity is its displacement over a given time, while the speed of its constituent energy is the total distance that energy oscillates over the same time (which will always be c). With this view, the maximum speed occurs when displacement and distance are the same, ie. movement in a straight line. In which case, light etc. travels at c in a vacuum because it travels in a strictly straight line in a vacuum.

Yes, I think that the link provided gives an answer to the question. In the "Analysis" section, they set up a good simplification (treating Frank and Bert in our examples as point masses). The applicable bit is: "This implies that xA(t) − xB(t) = a0 − b0, which is a constant, independent of time. In other words, the distance L remains the same. This argument applies to all types of synchronous motion." They go on to show that "when switching the description to the comoving frame, the distance between the spaceships appears to increase by the relativistic factor [gamma]. Consequently, the string is stretched." In other words: If the front and back of the ship can be accelerated using synchronous motion, then yes, the length of the ship will remain the same, and will appear to remain the same for observers which see the front and back synchronized. It should be easy to show the following: Iff all points on the ship can be accelerated using synchronous motion, observers which see it synchronized would see no length-contraction deformations of the ship. Otherwise, sections in between the synchronized points would stretch in accordance with the wikipedia article.

I'm replying to a post in another thread that I think this thread is based on? My reply seems more applicable here. I couldn't find any actual links that you're referring to. Can you repost the links, or a link to the post containing the links? Links to specific papers and even references to sections within them would be appreciated... no one wants to wade through the ISASS site trying to find writings that back up your views. Is the author you're referring to Dennis Dieks? Have you read any of Hans Reichenbach's work? I myself haven't, but I see references to him in stuff that makes sense to me. I don't get Dieks, personally. For example, in the first section of http://www.phys.uu.nl/~wwwgrnsl/dieks/becoming.pdf, he references Reichenbach and an idea (Conventionalism) that makes sense, but then concludes from it an idea that I can't make sense of (a "global shifting Now"). Conventionalism (http://en.wikipedia.org/wiki/Philosophy_of_time#Conventionalism) seems like a useful idea for your "ontology of time", because it seems to provide a means to sidestep GR, perhaps treating it as an arbitrary interpretation of time that is agreed on by convention. However, defining an authoritative distance (a fixed diameter of the Earth, etc) seems to be aiming in the exact opposite direction (Asbolutism or something).