Schrödinger's hat

Almost, except it was sort of the other way around. Given that the object described by the Schwarzschild geometry exists (this is not the thing that we normally look for when we look for black holes), what would we be seeing? I stumbled around the internet and found an answer to something similar to my question, sort of dual to it. Seems it was wiki diagrams to the rescue again. Still don't know where one would look for the outer event horizons, but the penrose diagram on the realistic collapsing star makes a lot of sense. If I'm reading this right, the white-hole-ish bit only exists in the limit of a path of events which is approaching the angle of a null line, and thus an angle of infinitely far in the past. It only reaches the angle of a null line when this path intersects the in-going event horizon. Trying to talk about it in terms of Schwarzschild coordinates says that point is 'where infinitely far in the past meets infinitely far in the future'. This further reinforces the idea that Schwarzschild coordinates are the wrong way to try and think about this, but unfortunately they're as far as my intuition will stretch at this point. Earlier on in the star's collapse (given that we're some observer in the top-leftish area), it was finitely far in the past, and the only stuff we see come out is the stuff that isn't following the path towards the eventual event horizon. This'd be all the supernova explody. If we find situations closer and closer to a Schwarszchild black hole (maybe a slowly accreting neutron star until it collapsed) I think we may actually wind up with the situation you described. The world lines of stuff that escaped during the accretion and collapse would be approximately the same as the white hole exit world lines, and then there'd be a black hole.

I think -- and I'm getting way out of my depth here, take this with a grain of salt -- that the gluons are the virtual particles that hold the protons and neutrons together. The only way the quarks can attract each other and stay in a proton is by exchanging gluons, much like virtual photons are exchanged to keep electrons in their orbitals. This seems more like a situation in which color conduction would be a thing. If the quarks are un-bound then they could carry color around much like a regular plasma can carry charge. I'm still not sure how you would go about inducing a color-current, as the range of the strong force would mean the thing you're exciting it with would have to be inside the QGP. Maybe you could excite it using the charge that the quarks also carry and an EM field? Maybe you could set up some situation in which the different color quarks have different potentials? Or use some kind of resonance/inertial effect if they have different masses...I don't know that color changes the mass. I'm not even sure the idea of these forces/charges being separate things makes sense at the energies required for QGP.

There's always the chance that there's one that never passed in front of another star while anyone was looking, and that it has nothing left to accrete (and thus emit x-rays). I can't seem to find any info after a brief search, but a very poorly informed guess would be that the chances that there's one closer than 10ly are extremely slim.

I made it up in trying to explain what I was talking about. Upon further reading, I think the correct term is just Schwarzschild geometry. This does not fit my understanding of what I have read, or is not quite the answer to the question I was trying to ask. Here's another Kruskal diagram from the wiki page in a hideous shade of yellow: I can see that region IV will clearly be at negative radius and so will one of the regions I or II, but the area I was trying to ask about is not (as far as my understanding goes). Let's say we're in the universe represented by region I. The null line bordering region I and IV represents [math]t=-\infty[/math] for a Schwarzschild observer. If I were an observer in an area of region I where space is approximately flat (Ie. I can deal with things in my immedeate vicinity using first order terms, or possibly use Schwarzschild metric if needed, it doesn't really matter). Obviously this diagram does not represent my coordinate system. But I know where the area near the border between I and II would be, I can look around to see an accretion disc and some lensing and say 'that's the event horizon of a black hole', and point to it. I can also make some predictions about the coordinates of a probe I send towards it in my frame (at least until the probe gets very close to the event horizon, then I get bored of waiting for new measurements/my Schwarzschild coordinates start playing up). In short I can put some bounds in the region containing those events in my coordinates, even in in a naive model where I assume space to be roughly flat. What about the region between I and IV (a bit on the I side of the border so I can use my nice, comfy Schwarzschild coordinates)? If I am to believe my interpretation of the other diagram it is at the same r coordinate as the black hole, but at a time in the distant past, but I cannot reconcile that with my intuition. My question is how do I go about looking for evidence of the event horizon of the white hole in this model? I apologise. The axes for this diagram are the Kruskal coordinate (timelike) V or [math]u^1[/math] on the new diagram and (spacelike) U or [math]u^0[/math]. The blue lines are alledgedly constant r.

Look up the Tolman–Oppenheimer–Volkoff limit. I'm pretty sure the Schwarzschild radius is always inside a neutron star unless it is too big to be supported by degeneracy pressure.

So you're angular sizes are not part of reality? According to my model, the angular size of the moon from London exists whether or not there is a person there to measure it. It's just that one of the parameters required to fully define an angular size is position. In the same way we have been trying to explain that (according to SR) one of the parameters required to define a distance is velocity. Proper distances are defined with the implicit statement 'the velocity of this thing is 0'. If you are trying to say that distance being in the same category as angular size means that we are somehow saying reality is subjective then we may finally have grounds on which to start an actual philosophical discussion. Let's just ignore the issue of rotation for a good long while, it makes things too complicated, and I do not understand all the consequences of using a rotating frame. At any rate anything we encounter/think of will not be spinning fast enough to matter. I continue to fail to understand the point you were trying to make and how it pertains to special relativity. We appear to be making progress on the other matter, so maybe we can come back to it in a few posts. I was discussing proper length. If someone were to make some measurements of the length of earth, then make the corrections to calculate the proper length, he would always get 12740km* no matter which frame he was in. *(rounded, diameter is twice radius, the 6370 figure was radius rounded to 3 non-zero digits because earth is very-slightly-oblate in all frames, and the uncertainty from this is in the 10s digit)

Where and when (in schwarzschild coordinates) is the white hole which appears in the eternal singularity model? Or if we want to avoid the mis-behavior of Schwarzschild coords, where and when is a region of comparatively low curvature outside of the white hole? Hmm, this is harder to word than I thought. I guess what I'm trying to ask is, were there to exist an eternal black hole like those dealt with in Schwarzschild geometry, where would I -- a roughly inertial observer in a very weak field -- look to try and find it? In watching this Kruskal diagram: It looks like it's at [math]t=-\infty[/math] and in the same place as the black hole. Or would it only be at [math]t=-\infty[/math] if I was an observer who came out of it?

Conservation laws usually come from some kind of symmetry. Can you put a rigid definition on what life is and suggest some symmetry that may be satisfied by conservation of life?

Yeah, I saw my mistake now. I thought some of those odd things also happened in Kruskal coordinates (forgetting that was exactly why they were derived), and then spent a little while mis-understanding the wiki page on them before understanding what abj said. Thanks

This is close to what I'm trying to say, although the conclusion is different. I'll use angular size as an analogue again. The angular size of the moon is part of reality. It's not subjective, if you go out and measure it I can predict before hand what value you will get, but do do this I need some information: Your location (and your velocity if we're taking into account aberration and/or relativity, but ignore that for now). If I input your location relative to the moon into the laws of classical optics I will get the angular size you measure. (to within accuracy of tools that are likely to have. If you have a really precise apparatus I'd need to include factors like velocity, temperature and pressure of the air, altitude and so on). In SR distances fall into the same category. From where I'm sitting, with measurements I could make of some objects. No matter your FOR, I can predict any distances that you measure relating to those objects with one piece of information: Your velocity (either relative to the objects, or relative to me -- from one I can work out the other). There is a concept known as proper distance which is invariant. Ie. Earth's proper radius if you assume it's not spinning (or is spinning so slowly that it doesn't matter -- which is true) and ignore GR is: 6370 km (this may work for or there may be a similar property which works for spinning objects, but I do not know. Rotating things require maths more similar to that used in GR than SR). I can predict this from any frame of reference if I take measurements of the times and places of events that happen on Earth in my frame. But not all objects or arrangements of objects have a proper distance. To illustrate let's imagine we have some objects carefully arranged (I'm imagining performing spaceships in the relativistic equivalent of an air-show just for kicks) so that they came from lots of different directions at velocities close to c and were all in a straight line for a moment. This line they make for that moment is a real object, if they had robust enough hands they could reach out and high-five each other so that they were all connected for a nanosecond. But which velocity do we use to measure this? The line isn't moving in any particular direction. There are plenty of other situations, what is the area of a triangle made up of three objects with different velocities?

Although these are entertaining, perhaps you could restrict them to a single thread (or use this site's (or another's) blog feature?), maybe give each post a sub-heading. This will both make it easier for anyone who wants to read them, and avoid cluttering up the forum for those who want to avoid them.

Hahah, I probably have almost the same answer for you as Phi did, but I'll expand on it a little more. I'd place it in the same category as homeopathy. It's definitely not science, it's also not neurology as the shape of the head does not reflect the structure of the brain to a significant enough degree to determine personality traits and similar. I suppose you could squeeze it into the heading of natural philosophy if you made your definition wide enough, but most people I know have a separate category for these things which they call psuedoscience. I don't really have a word for the subset of psuedoscience that I put homeopathy in, but I can describe the similarities: Something that was fashionable and considered right by reasonably mainstream groups at some point, but is based on a mechanism that does not match anything known to modern science. For phrenology this mechanism is that the structure of the brain is reflected in the shape of the outside of the head. Barring outliers this is not usually true. They propose to make testable predictions based on observable phenomena, but the predictions or parameters of the observations are often vague enough that it is impossible to design a good experiment. As a result they share a lack of any evidence produced under the modern scientific method supporting them.

Wait, silly me. I was looking at the animation on the wiki page of lines at constant r and thinking that the ones on the light cones looked like they represented something indeterminately smeared around the entire event horizon -- without actually realising that was the concept which that part of the diagram was trying to get across (ie. not realizing that a line of constant r at the event horizon is a line of constant r at the event horizon ). My confusion was furthered by looking at the closed form conversion from Schwarzchild to Kruskal, the badly defined bit there comes from the Schwarschild coordinates.

Wait, I thought they were also ill defined at the event horizon. Or is it enough that the limit exists from one side for each function? If that's the case wouldn't it make events on the event horizon degenerate? Can they be distinguished in other coordinate systems?

We were trying to talk about things moving faster than c. As there's no situation which could result in moving faster than c (barring some strange stuff in certain varieties of string theory that I have absolutely no comprehension of other than it is the reason people prefer different varieties of string theory to these ones) we had to make up a step and then try and see what happens. The step I made up was as close as I could think of to the suggestion you made (suddenly jumping to faster than c from a speed the same amount lower). I then followed the same logic that leads to other results in SR (such as the derivation of length contraction) and came up with the conclusion that things moving faster than c would be all stretched (but in a very weird way) and other kinds of strange stuff. Bear in mind this is purely speculation. It is restricted and informed by what I know of SR, but does not represent anything I (or anyone I know of) believe to be related to actual physical events. This part is the science, and it is observed.

I didn't mean anything to do with which frame we'd want to do our experiment in. I meant, Which frame are our measurements (such as measurements of the laws of physics) correct in. You said that light can't be pushed along by a moving object, so say I have a million objects in random places moving at a million random velocities in a million random directions. Say I set up a million experimental apparatus which consist of two sets of two sensors, a light, and a clock. On each object, each pair of sensors picks a random object, lines up with it, and will record (on each sensor) the time it sees the light on that object turn on. So I will wind up with a distance and a time for each pair of sensors. We divide each distance by the corresponding time. Which object or objects get(s) the right value for the speed of light? Here we go. This is why I didn't want to do this. Define "how far it is" from one point to another. You've already used 'distance' so you can't say that. And saying 'the thing measured by meter sticks' is out too because you told me that's tautilogical. Hint: If you feel like saying something along the lines of 'how many meters/other units of distance it is' just skip it and define a meter. You appear to be following roughly the same train of logic I was intending to lead you on with Capn, but I'll respond anyway. So if we take here and now as a frame in which the laws of physics are correct (and the speed of light is a law of physics) then from my point of view, wherever I am, and however I'm moving, a beam of light aimed towards/away from me will get 3*10^8 metres closer/further to/from me every second, in addition to this the measurements I take are just as valid/correct as those from any other here and now. I might be able to find out that isotropy/everything else I can see is moving at some rate in my frame (to pick a value at random they might be moving at 0.1c +/- 500km/s), but I am still stationary. If this is wrong, then there is a preferred frame in which measurements are right (in which case we go back to my question, of which one is it?) In which case in your buoy experiment either taking measurements from the FOR of the lamp is just as valid as measurements from the frame of the buoys, or: One of the assumptions (postulate of relativity or constant c) is wrong. In terms of the defining distance thing, that was mostly aimed at Owl, but you can play along at home if you like. The rules are basically: 1) Write down 'Distance is __________' then, 2) if ________ is just a synonym for the concept of distance, write down '__________ is _________' 3) If you're not sick of it yet go to step 1, else go to step 4 4) Point to a ruler and say 'this is a foot/metre/30 centimetres/yard etc' -- ie. distance is the thing we measure with metre sticks. You can do the same with time, too. You keep saying things like this which reinforces my belief that you don't quite understand the postulate of relativity. This is basically the thinking physicists had in the late 19th/early 20th century, but the thought process that came from this goes something along the lines of: If I had a lot of mes moving at different velocities, only one of them would be right We can determine some quantity/law of physics before hand and all the mes can measure it Then we know which me is right So we know which way the ether is moving compared to us In spite of experiment that was done, and all the data that could be found, no experiment could be conceived of that would tell you how fast you were moving, unless you looked at something else and said 'I'm moving at ____ relative to that' Every theory that anyone could think of got crossed off of the list one by one until two remained: Relativity and, Lorentz Ether theory, possibly a bit misnamed, as what has come to be known as Lorentz Ether theory isn't exactly what Lorentz proposed. It posits that moving objects actually do morph and slow down, but they do it in such a way that it is completely undetectable and that there is no way you can know which object is slow/squished and which one is stationary. It also posits a completely undetectable Ether which defines a completely undetectable rest frame. Of these two, special relativity is the least hairy. It is also compatable with general relativity, which explains gravity -- I do not know whether anyone has put the time/effort in to make a variant of Ether theory which explains gravity. I imagine it would be hugely convoluted and even more difficult than GR. Also I'm not sure if the principles quantum physics would make any sense in Ether theory.

I guess one could go directly to superconductivity without having an analogue of conductivity. If you were to get the whole thing (whatever type of thing we're talking about) in a single quantum state, then pushing another charge carrier into it would increase the potential of the one (which would be indistinguishable) on the other end. The problem is in trying to conceive what kind of system we're even talking about. I admit I'm almost completely lost when it comes to QCD, but as far as I knew gluons could only act over tiny distances, and non-white collections of quarks aren't stable.

Hahah, so have I somewhat -- as of the last post. Which is why I suggested moving to speculations earlier.

Huh? Negative interval squared (imaginary interval) just means more (real) distance than (real) time. At no point did I suggest distance squared would be negative. Putting an imaginary number in x, y, or z is has no meaning that I can think of without further context. If we try and use the length contraction and time dilation equations we will get imaginaries, but if we were to take each point on the object's world line (assuming you came up with some consistent way to do our magical v<c --> v>c transform in a consistent way over the whole thing) and apply further lorentz transforms it would work fine. I think this is the same sort of thing as having to be careful and manually input signs/add 2*n*pi when dealing with functions such as asin or picking the right sign of your square roots.

Okay, was really trying not to go here, but what the hell do you mean? Define duration. Define distance. No circular logic or tautologies. Very close. According to SR, distance is not an invariant. It's not a frame independant qauntity, exactly the same category as angular size, or height. Angular size is still objective. If I tell you to measure the angular size of the moon from New York on the 10th of December 2011 you will get an answer that anyone with skills in geometry can predict by taking their own measurements from another time or place. Height also requires a frame before it is meaningful, I think this old joke illustrates the point best: An engineer, a mathematician, and a physicist were standing around the university flagpole when an English professor wandered by. "What are you doing?" he asked. "We need to know the height of the flagpole," said one, "and we're discussing the formulas we might use to calculate it." "Watch!" said the English professor. He pulled the pole from its fitting, laid it on the grass, borrowed a tape measure and said, "Exactly 24 feet." Then he replaced the pole and walked away. "English professor!" sneer the mathematician, "We ask him for the height, and he gives us the length." I could not make any sense of your thought experiment nor think of any sensible reply. Possibly due to you operating on some definition of distance unknown to me.

There are a few details, but you got the gist of what I was trying to say. For one, this kind of transformation is not in the Lorentz group. There's no boost which makes you move faster than light. It'd have to be some other kind of thing. I guess in this makes it not really in the realm of SR. My logic was as follows: 1) Have something moving less than c 2) Something mysterious happens st. v>c. You could, say, change from a dX/dtau with a positive magnitude squared* to one with equal negative magnitude squared and with the same direction in its spatial components. 3) What would SR say about the situation afterwards. Yeah, that's pretty much what I was trying to say. Or it at least works out for a little while. If you thought about it for too long either your head or the universe (in your model which includes tachyons) would probably explode. It'd do all sorts of weird things, like if you were to watch it, you'd only see it after it'd passed you. Then you'd see it in two places (if you could see it...don't know how it would interact with light), moving away from you in opposite directions. I don't even know how to think about objects that aren't point-like in this context. Depending on how close 1/v was to 0, they'd do some sort of weird length-dilation until they took up the entire universe (in that direction) for a few moments -- as measured by your currrent frame. What you'd see would be more like the previous paragraph. Trying to think about other things, such as how doppler shifted would it be -- ie. what would you actually see rather than where would you see it? I'm not sure if SR has anything meaningful to say. @moderators: could we move this thread to speculations? Although it's fun to talk about this model of FTL, I don't think it has a place in the physics forum. *is magnitude squared the right word? I shall specifiy with maths just in case: This thing: [math]\frac{dX}{d\tau}^T \left[\begin{matrix}ct&0&0&0 \\ 0&-1&0&0 \\ 0&0&-1&0 \\ 0&0&0&-1 \end{matrix}\right]\frac{dX}{d\tau}[/math] Edit: Fixed typo and changed the sign of my metric to be consistent with text.

I don't think any one product does all of what Alpha does, especially if you're talking about its integrated access to large amounts of data. There are a number of different computer algebra systems that have similar mathematical abilities to Alpha, but I do not know how many (if any) have its natural language input capabilities. I had typed up a nice long reply discussing these, but lost it due to a browser mishap. Instead here's a list: http://en.wikipedia....algebra_systems Edit: read through the list a bit as I hadn't heard of many of them. From that list alone it's hard to tell what might be useful. Maxima is usually what I use when I want something free/not Alpha. Sage is probably one of the most powerful, as it integrates many of the other systems under a common interface.

I think you both have a point there. The less well you know a topic, the harder it is to explain to someone else. This relation is, of course, not one-to-one. There are many other factors. Every now and again we get a Feynman who can explain complicated things in simple terms, but this is rare, and there are limits on how much a concept can be simplified and retain meaning. On top of this, explanation (both in general and in the specific) is a technology that improves with time. In the 19th century electromagnetism was considered a very hard subject. This mystified me until I got hold of an EM textbook from 1908 (I do not know when the first edition was published). The author either had little knowledge of, or had to assume that the reader would have no knowledge of, linear algebra and vector calculus (let alone tensors). All of the equations were in component form and it was extremely hard to follow compared to modern books.

...I don't even... Uhmm, some kind of freaky exotic matter where some quarks are free to travel and carry color? I have absolutely no idea how one would interact with this.

Oh yeah: Here's a list of MIT's EE and Comp-Sci courses with further links to (most of) their course material. http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/ You'll probably find the maths a bit daunting at some stage, so browse ocw further for maths courses (not always the most accessable) or try khan academy http://www.khanacademy.org/