md65536

A light cone is a 3d surface with a 4d interior. A simple intersection of an observer's (past) light cone and a (past) hyperplane "moment" is a sphere (2d surface), corresponding to all the events simultaneous with that "moment" that the observer now sees. I think it's intuitive enough. In flat space, everything from a moment 1 year ago that I can see right now happened along a sphere around me, events that are a distance of 1 lightyear away. The union of all possible spherical "observable moments" makes a light cone surface, which from an observer's perspective in a single moment appears exactly as what I see: a volume of space where different distances correspond to different times in the past. And a hyperplane "now" corresponds to what I can't see: A volume of space all at the same time, according to my frame of reference. The light is measured discretely, not continuously... each photon is independent and not connected with the others. The source is moving, and each photon will travel on its own path. So there's no single physical "stream" along which all of the photons travel. The paths are geodesics, so basically "straight lines through curved space". I would say yes to both (a) and (b), depending on who observes the line. I think that to the receiver of the photons, the lines are straight.

Big-O proofs are proofs. Doing a proof doesn't always give you an answer you're looking for, so often some other method would be used to arrive at a guess, and the proof would be used to show the guess is correct. Isn't it the same with maths proofs? Big-O provides an upper limit, so anything in O(x^2) should also be in O(x^3), right? So you don't need to know what to look for to arrive at a correct proof. But proving something is in O(x^2) is more useful than proving it's in O(x^3).

Why would one call "the present", events that "belong to one's past"? I don't. You're talking about one's "past light cone", which is of course considered to be one's relative past. Yes, it's what one experiences in a given moment. There's no confusion of the two, given a finite speed of light. A distant event observed in the present is a past event. A distant present event can't yet be experienced. To confuse things though, if we speak about events without specifying a reference frame, then two events that are outside each other's light cones (both past and future cones), are separated by a space-like interval, in which case "Generally, the events are considered not to occur in each other's future or past." [http://en.wikipedia....e-like_interval]. Observation events or experiential events imply an observer which implies their reference frame. --- Back to the original question... I think it might be best understood with mathematical concepts? All of the following is based on wikipedia entries... it is only my understanding of it, which is lacking!, but it's not hard to look up the entries. Perhaps someone can tell me if the following makes any sense! A "moment" --- as in a set of simultaneous events --- is frame-dependent, so let's consider a given observer's frame, with the observer as an object. The observer has a world line which represents all of the observer's locations through spacetime, in order. It is like a sequence of all its possible "now"s. At any point (event) on that world line, a moment "now" including that point can be represented by a Cauchy surface... that is tangential to the world line? Now is, when: At the proper time of the event, and where: anywhere on the surface. Note: "when" is according to a specific clock, and I'm using the observer's clock, but it could be expressed instead using any clock whose world line intersects the Cauchy surface, with "when" being the time on that clock at the point of intersection...blegh! It all depends on choice of frames and clocks, and it doesn't matter which is used as long as it is specified. The set of all Cauchy surfaces tangential to the observer's world line essentially "slices up" 4-d spacetime into a set of moments, each considered to be a "now" that is simultaneous with an event on the observer's world line, where it intersects the surface. (Does that make the set of surfaces a foliation of spacetime? Or is it not a foliation due to relative simultaneity, which can result in multiple such Cauchy surfaces intersecting the same distant event? ie. the surfaces are not generally parallel?) At each moment on the world line there is also a light cone. Inside the past light cone is all past events that can influence "now" (ie. events that can be known about, now), and inside the future light cone is all events that can be influenced by "now". At http://en.wikipedia....wiki/Light_cone, the image illustrates the distinction between the "present surface" and "presently visible past lightcone". I think this might be less confusing to note that we're talking about unpredictable events here. We can discuss predictions of events, based on information we've received up until now, but we can't discuss any new information from an event until we observe it. I don't think there's any physical difference between predicting past, present, or future events outside your light cone.

I don't know any of the equations. Hopefully someone more knowledgeable can weigh in. The equations for "what's happening, hidden by light's transmission delay" are different from those for what we see. For example in SR the Lorentz transformations model what's happening at a remote location, while relativistic Doppler equations model what we see. They're not the same equation but they're mutually consistent. Physical predictions can be made for both what we'll see tomorrow, based on what we've seen so far, or for what is happening billions of light years away, based on information we received that is considered to be billions of years old. I think both of your statements are sort-of true, for the hypothetical galaxy that "currently" is exceeding a recession velocity of c. There is an event horizon separating us from it. We are currently receiving photons from a past state, from which we can estimate its current --- but never to be visible --- state. When I first posted in this thread I hadn't considered apparent time-dilation effects which allow the remaining light from an object crossing an event horizon to be delayed for the rest of eternity. I think that Krauss understands this a bit better than I do, and didn't make that mistake. Yes, there should always be an opportunity to receive additional photons from an object in its past state before it crossed an event horizon. But I don't think that matters. Why? Because even if say a few hundred billion years in the future some technology is invented to be able to distinguish these very sparse, low-energy photons from noise, and from that deduce the existence of a galaxy that emitted it, then just wait a few trillion more years, when the photons will be rarer and their energy will be even lower. Eventually Krauss will be right (unless accepted cosmology is fundamentally incorrect). For that galaxy to be detectable at an arbitrarily distant future, its light will have to be detectable at arbitrarily low energy. That's inconceivable, practically, but I think there must also be some reason that it's theoretically impossible.

Yes, c must be taken into account... none of this would be the same without it. There would probably be no concept of "objects are unobservable beyond an event horizon" without a speed limit. No law is broken, unless you're speaking of some "godlike perspective", but I never do (unless speculating), and I don't even know what it is (is it a perspective that can take on an arbitrary simultaneity, or is it a universal simultaneity??? If the latter, I don't think it has any connection to physical reality that would help in understanding GR and inflation). Due to relativity of simultaneity, if you consider a "moment" across a distance, you are implying a specific frame of reference, because the events of that moment won't in general be simultaneous in other frames of reference. I don't think that "now" always means the same thing in cosmology (it may be observations made "now", or it may be a prediction based on such observations, depending). The value of physics lies in its predictive power. Scientists have evidence of stuff going all the way back to just after the big bang, and they can extrapolate. Theories are evaluated based on their accuracy and precision, and we end up with degrees of confidence in various predictions. I don't think Krauss or anyone else is more confident in the ideas discussed in this thread, than say that the laws of gravity won't change in the foreseeable future. And even though the laws of gravity have extremely reliable predictive power, it's not completely certain that they'll never change. I don't see Krauss or any physicist speaking of absolute certainty in anything (I'm sure some do, but I'd call that a belief), and I wouldn't call it a pretense to make physical predictions based on GR and inflation, or the laws of gravity for that matter.

No, but not all particles can be observers, either. Photons for example have no frame of reference and do not observe anything.

I don't see that as a terrible problem. Why can't you imagine doing the same thing for photons? Or on the other hand, how to do imagine practically freezing say a lightyears-long line of ants? Either it's a problem of imagination, and "freezing" photons or ants mentally are both possible, or it's a problem of practicality, and neither are possible. Any analogy by definition will be dissimilar in some ways, so it can be picked apart by being too literal. Certainly it is possible to imagine a photon being transmitted at the same time as another one is received. Doppler effects (redshifting) complicate things, for example if the distant object is emitting a photon every second, we won't receive them at a rate of one per second. It's the same with the ants... they will also be Doppler shifted. I think it is consistent, because in both cases it's about accepting what the evidence tells you, and not accepting ideas for which there's no evidence. Ironically the argument is that in the very distant future there may eventually be no evidence of a universe, and anyone who believes in only what the evidence says, will be wrong. No, the photon isn't stretched. It's the same with other types of waves... if you change the wavelength of ocean waves by changing the water depth, it doesn't stretch the water molecules. If you have corks bobbing on the surface it doesn't change the distance between corks (only the distance between wave crests). A photon is a particle, not the entire wave. If both wave-like and particle-like properties could be completely expressed in the same thing (a photon) there would be no wave-particle duality of light. You can add a wave-like property to the ants... Suppose the rubber band is twisted so the ants spiral around as they walk. Sometimes they're on top of the band, and sometimes they're hanging upside down. If it's 400,000 LY between points where they're at the top of the rubber band, you wouldn't say that the ant was stretched to 400,000 LY. Or if the band is vibrating, or if the ant is breathing once per second or whatever... the wavelength is not the length of the ant.

I was hoping someone more knowledgeable would reply but instead you get this! I think the ant analogy is fine, and it can be tweaked to match the details of cosmological inflation. I don't see any details that are more confusing than useful. Wavelength is not the same as "length of a photon." A photon is a point particle (no width or radius). Anywhere a photon is measured, it is measured as a point. Any effect of a single photon on anything else is consistent with the photon behaving as a point particle (otherwise it would constitute a measurement of the photon as something other than a point particle). Regardless of wavelength, it will be measured at a point and a time that is consistent with c. I guess the "phase" of a photon might be anywhere along the wavelength... but a photon of light with a wavelength of 400,000 LYs arrives 1 second after traveling 1 LS, or 100 B years after travelling 100 B LYs. Krauss said he was talking about some distant-future civilization that is not connected with us. It's so far in the future that presumably our civilization and all of its knowledge would be destroyed. He's speaking of that hypothetical situation. Then, even if they become exceedingly advanced, they still would not be able to detect evidence of some of what we can see now. It's interesting to see how the expression of a belief turns into a barrier to understanding. Like, "That's what GR says, but I still believe there must be some way that it's wrong." There's less desire to understand things we don't believe in. Yes, our scientific understanding will change and there's a lot we don't know. It's not the case that we expect far-away objects to become unobservable because we can't imagine any way for them to be visible --- it's that to the best of our knowledge and a few assumptions we can prove that they will be invisible. If Krauss is wrong, it would take more than just incomplete knowledge on our part. It would require that what we know is fundamentally wrong.

I dunno if this would make a good science fair project but an idea I once had was to try to make a home-made "laser image projector" with a laser pointer and a tiny mirror somehow attached to two speaker cones or some equivalent. Each speaker would tilt the mirror on a different axis. Then convert the outline of some test images you want to draw, into waveforms, and play it through an amp to control the mirror. Lasers of course command a lot of interest from industry and government. All's you'd need is a tracking system, and a large spinning mirror and you could vaporize a human target from space.

I wouldn't say so. Yes, it's true that there's no absolute simultaneity of distant events, so different observers can disagree on exactly when an event occurs relative to themselves (ie. local events). However, events have proper times (the time of the event according to a clock at the event's location) which is invariant. An event's proper time is a true "when" at which the event happens. No observer will disagree. In other words the disagreement is between the event's local clock and the observer's local clock. It's impossible to make all clocks agree. --- Also note that the meaning of clock is representative of time itself... I think often people assume it refers to a particular device but it refers to all measurements of time, ie. to the behavior of time itself. Also, in terms of causality, an event truly occurs after any other events that can influence it, and before any events that it can influence. There is no room for disagreement there either. It is only remote, disconnected events (with a space-like interval) that have no true ordering.

It's not the simplest treatment. I think Feynman explains (in the Douglas Robb Memorial Lectures for example) that considering all possible interior paths of light passing through a lens is equivalent to considering only what happens at the surface points, which is a lot simpler. I'm not sure what I'm trying to say. I think it's that, if there are equivalent treatments (which always arrive at the same answer and have no differing measurable effects), then it doesn't make sense to say that one interpretation is right and the other is wrong. And I'm not sure about this, but I believe there is an interpretation that involves light traveling at c through a series of interactions within a medium, which provides the correct answer given a proper QED treatment. If so, then whether light "actually" travels at c through a medium, or is actually slowed, is only a matter of interpretation.

But wouldn't you have to treat this properly wrt. QED, and find that the probability of a photon emerging from a medium at a given location with a given direction, after a photon enters the medium at a given location/direction, is the sum of probabilities of all the possible paths such a photon could take through the medium? That is, every possible sequence of absorption and re-emission by electrons. Then, while you wouldn't speak of specific "photons" in the medium, you also wouldn't speak of specific "electrons" either, because light behaves as if it's doing the average of all specific possibilities. I think that it's fair to speak of the light traveling at a speed of c through the medium, but only in a "sum of probabilities" way. The observed behavior of light traveling at a speed < c is only the average, macroscopic description of what happens at a quantum level.

The ant doesn't get stuck locally. It appears stuck relative to its destination. It keeps moving along the (local) rubber band at the same rate, but the entire length of rubber band in front of it keeps expanding at the same rate that it is moving along it. Yes, the receding galaxy really does disappear in ITS moment that it exceeds a recessional speed of c. However, with the extreme apparent time dilation that comes with extreme red-shifting, that galactic moment will appear to pass very very slowly from Earth. Suppose that an object is about to reach a recession rate of c relative to Earth. (I'm not sure how it would know because, to it, Earth would also be redshifted to nothingness, but say it has calculated the exact moment.) Suppose this object wants to signal the Earth, and it sends a huge blast of say 2^1,000,000 photons in the final second before hitting c. Then after some many billions (or trillions or higher??? i dunno) of years, Earth receives the first of these photons, and say it detects them though they're terribly redshifted. Earth will receive the rest of the photons over the rest of time, at ever-decreasing rates. For the sake of argument, say that each year it receives half of the remaining photons. Well after a million years, it is receiving only one photon per year. Yes, it can theoretically still receive photons from the object (and know that it existed) essentially forever, but those photons are all from the object before it reached a recession rate of c. You may say that the rate of expansion of intervening space is "mild" when less than c, but if the space between the object and Earth is expanding at a rate of c, then the photon will always have a continuously expanding space left to go no matter how many light years it travels (according to an observer on Earth). Edit: I think I see a source of confusion... If we think of the object as moving through space at near c, and that an emitted photon has a fixed distance to travel to Earth, then certainly the photon will make it. However, it's not a fixed distance, because the space between it and Earth are expanding at a rate of near c. In fact I think it's best to consider Earth and the distant object not to be moving at all, only that the space between them is expanding at a great rate. This is like saying "Now that you understand special relativity, ignore it! because this is a very different complication than the rules of SR in flat space." The problems with detecting the object (as an image of it in a much much younger state), include: - It is red-shifted to nothingness. The photons carry very little energy, and I guess require a very big antenna. - The image is time-dilated to apparent stillness. Supposing that the rate of photon release from the object is constant, the rate you receive them is ever diminishing. It appears dimmer. - The object appears to be moving away at nearly c, and appears smaller and smaller ie. you receive an ever-decreasing fraction of its light. The object would become practically impossible to detect before it became theoretically impossible, but at some point the energy from it would be less than say random noise, or perhaps less than from vacuum energy or something?, in which case the object really would be theoretically impossible to detect.

Perhaps, but... it's not just the end of the rubber band that's accelerating away. It's the stretching across the entire rubber band that's accelerating. With the right conditions you should be able to have a situation where one ant never makes it, even though the ant immediately in front of it does, even if the ants are as crowded as possible. Suppose that every 1m of a rubber band stretches to 1.1m every 1 second, and that an ant will have traveled .1 m along that stretched rubber band after 1 second. If you start with a 1m band, after 1 second, the band is 1.1m but the the ant is still 1m away from its destination. After 2 seconds the band is 1.21m but the ant is still 1m away from its destination. Repeat forever... This apparently "stuck" ant happens in this case when the ant leaves the start of the rubber band at the moment that the start of the band is moving away from the destination at the same speed that the ant moves. The main thing is that I've defined the acceleration in terms of how fast a given length expands over time, and kept that as a fixed rate. So each "stretched" meter of rubber continues to stretch at the same rate, however there are ever more meters there that are stretching. In the case of photons you wouldn't consider one "stuck", perhaps rather you'd say that the distance the photon must travel is expanding at a rate that is as fast as the rate at which the photon can cover that distance. --- Edit: I thought about it some more and I think perhaps you're right. Yes, if you fill up the rubber band with an infinite amount of ants you should continually be able to have ants stepping off the far end. At the same time, as per the above, you can have an ant "stuck" at a fixed distance from the far end, and all the ants behind it getting farther from the destination end. A red shift would be accompanied by an apparent slowing of the observed object's clocks. If the object were infinitely bright and you received an infinite density of photons from it, then you'd see it red-shift to a frequency of 0 while its clock appears to slow to a halt. You'd still have trouble seeing a finitely bright object because the photons that approach 0Hz approach zero energy. So I guess it would fade to nothing over infinite time, however the image that you see of the object would approach its "last" visible state as it reaches its horizon. So it's true that you won't be able to see the object in any of its states that occur after it passes a recession speed of c, but it's also true that you should be able to see the object in a state before that, forever or until you are no longer able to detect the increasingly redder and lower energy light from it.

No, that's backwards. The correct deduction is: What is observable is in existence, therefore what is not in existence is not observable.

I think that anything that is observable is by definition part of our universe. So we should never be able to directly detect anything from "another" universe. To prove the existence of other universes you would have to indirectly infer their existence by showing that any case where they don't exist is impossible. You could also have an accepted theory that implies their existence, in which case they would be accepted as theoretically existing without proof. I guess like gravitons are considered now? An actual existing multiverse is an interpretation of some scientific theories. It is not a required consequence of any accepted theory... There are other ways to interpret accepted theories that don't require multiple universes. So there should be no way to prove the existence of multiple universes without proving that those accepted theories and/or their non-multiverse interpretations are inadequate.

No, I think that's a misunderstanding of this. I also don't understand but I'll try to reason through this; I might be wrong. Suppose a distant object is so far away and that all of the space between us and it is expanding, such that it is being separated from us faster than c. Then photons leaving that object now will never reach us, not after infinite time (assuming the expansion continues). There is nothing to see at any wavelength. But consider a closer object that is visible. The space between us and it is expanding, and because there is always more intervening space, which itself will also be expanding, so the object will appear to be accelerating away from us. Thus the apparent speed of an object will be proportional to its distance. It will appear red-shifted because it is moving away from us, and it will get redder and redder because it is accelerating. As it appears to approach a speed of c, its red-shifted light will approach a frequency of 0. Yes, any speed infinitesimally less than c will produce a frequency infinitesimally greater than 0 and is theoretically detectable. But once the separation speed reaches (and exceeds) c, there is no longer anything to detect, even theoretically. So visible objects that are receding at speeds less than c are expected to recede faster, and redder, until they disappear at a separation speed of c and a color with zero energy. Any objects that have reached that speed are theoretically undetectable. I guess the misconception might be that the frequency would approach 0 as the separation speed approaches infinity, but it hits 0 at c, while the separation speed keeps increasing beyond that.

Please note that instead of derailing the discussion or discouraging the asking of questions with semantic arguments, swansont has already answered the original question in post #3. Yes, that's the twin paradox (a common sense paradox but not a physical one). Usually you would start and end with the two clocks at rest and at the same location, to remove ambiguities in the possible measurements. Acceleration doesn't directly matter except that it affects velocity. It adds complication; the twin paradox with periods of constant acceleration is covered here: http://en.wikipedia....spacetime_paths --- I think that the link shows that the time difference depends on the spacetime path of each twin. The relative velocity of the twins is important but only to the extent that the elapsed travel times affects their spacetime paths. Likewise acceleration is important only to the extend that it affects their spacetime paths. That is, a near-c burst of speed for only a second (according to the "stay at home twin" at least) will not make the clocks off by more than a second. The "paradox" refers to the twins' clocks relative to each other. You can't have one object moving at constant speed relative to the other, while the other moves with great acceleration relative to the first. The twins' speeds relative to a third reference point doesn't factor in.

Probably the same as in our universe. There is no absolute motion; so with nothing to move relative to there would be no relative motion either. If it's a point particle perhaps you could consider the universe a singularity, with all measures of distance contracted to zero, so all motion occurs across 0 distance.

I agree. I'm impressed by the creativity of some of the explanations. I searched for "I think" to quickly find some of the theories. Poe's law certainly applies. It is interesting as both examples, and satire, of the unscientific reasoning people use to explain phenomena. I especially like the perhaps Lovecraft-like story about the cube found in the arctic.

That's what's so amazing about it! It read your mind, time-traveled over the part where you pick a card, and STILL got it right without you ever knowing what happened (or didn't)! Here's the start: http://sprott.physics.wisc.edu/pickover/esp.html The trick is in the Quantum Consistency value used. With the values it's reporting, it's no wonder weird stuff is happening. I suspect the server is located on some isolated island near a source of unique electromagnetic fluctuations.

I think this finally proves soundoflight's "holographic scenario"... http://www.sciencefo...post__p__593878

http://en.wikipedia.org/wiki/Compiler#History answers both questions. "Towards the end of the 1950s machine-independent programming languages were first proposed. Subsequently several experimental compilers were developed. The first compiler was written by Grace Hopper, in 1952, for the A-0 programming language. The FORTRAN team led by John Backus at IBM is generally credited as having introduced the first complete compiler in 1957. COBOL was an early language to be compiled on multiple architectures, in 1960." "Early compilers were written in assembly language. The first self-hosting compiler — capable of compiling its own source code in a high-level language — was created in 1962 for Lisp by Tim Hart and Mike Levin at MIT. Since the 1970s it has become common practice to implement a compiler in the language it compiles, although both Pascal and C have been popular choices for implementation language. Building a self-hosting compiler is a bootstrapping problem—the first such compiler for a language must be compiled either by hand or by a compiler written in a different language, or (as in Hart and Levin's Lisp compiler) compiled by running the compiler in an interpreter." Two things I can think of that would help in writing self-hosting compilers are: 1. A compiler needn't output a working executable. It might output say assembly code, or even c code. So the "first version of a self-hosting compiler" would not need to do all of the work involved in having a running compiler. I would assume compilers are built in steps, with a more-complex version of a compiler using a previous simpler version to compile itself. The earlier simpler versions would rely on other existing programs, or hand-compiled code, more than later versions would. 2. You do not need to use all of the complex features of a language in order to implement those features. For example, a c++ compiler can be implemented using only c code, which the resulting c++ compiler can still compile.

Why would a 2D being be unable to perceive depth? Even if they were only able to "see" lines, why can't they extrapolate a 2D shape from multiple viewpoints? I think you're making bad assumptions. Human eyes for the most part act as a 2D array of sensors. Our understanding of depth is "processed" out of that 2D data. We don't fully see a 3D image of an object nor do we need to to understand a 3D shape from images of its surface. Another way to think about your idea is this: Assume that humans are four-spatial-dimensional beings. Suppose you made a model of a human in three spatial dimensions. How would such a model be unable to perceive three spatial dimensions? What is lost in the model, eg. why is it unable to perceive depth where we normal 4D humans can? If there is something hidden that can't be explained using 3 dimensions, what is it? As far as I know, the understanding of human perception of three dimensions is fairly well understood using only 3 spatial dimensions.

Nah. Entanglement doesn't allow other laws to be broken and special relativity prohibits this. There is no accepted, testable theoretical prediction of FTL communications. All quantum mechanical experiments so far, even the weirdest, are consistent with the conclusion that no useful information travelled faster than light. There must be something flawed about using fractions or statistics to estimate something like this. It seems to me it is like asking "What fraction of species on Earth have developed use of a written language?" It's meaningless as a fraction because there's only one (assumed), but the fraction depends on how many other unknown species there are. Well, we're pretty sure we're the only such species on Earth, but if we were to assume we weren't then how could you possibly come up with a reasonable estimate for that fraction? It's meant to be a measure of the subset of species with intelligence, but its value ends up being a measure of that set's complement. If the true value of that fraction is 1 in ten million, or if it is 1 in a hundred million, how many species who have developed written language does either value represent?, and how does either value relate to the probability of a chance encounter with such a species? I think the problem is that we think like "There must be others like X", where X is something that we only know about because we're like X. We realize it's a bad assumption to think that we're somehow the only "special" thing in the universe, but that doesn't mean that it can't be common for things to be unique in the universe. Current human-known communications methods might be somewhat unique. Our concept of intelligence might be unique to Earth. True, evolution seems like a universal principle, but what we consider to be "intelligence", and our idea that it is universally advantageous, might be only an assumption based on it being the only thing we know. There may be other forms of "highly evolved advancement" that are not like what we know as intelligence, that we can't even fathom and may be unable to recognize, because it's not what we know. Humans wondering about what form of languages (systems of symbols) an alien life might use might be like ants wondering if there exist any creatures that use really advanced pheromones. Related: http://xkcd.com/638/