Schrödinger's hat

One thing that really helped me realise this is looking at a Rindler chart, or other charts/coordinate systems built around objects (in flat space) undergoing hyperbolic motion. My understanding of GR is still rather lax so I don't know how long the analogy lasts, but looking at the universe using a Rindler chart is a lot like trying to use Schwarzschild coordinates near a black hole. You have this big scary event horizon beside you, nothing ever crosses it, and light beams or other geodesics will always curve towards it. Even though you're accelerating hard you don't get any further away from it, and if your friend Bob turns his engine off he'll fall towards the event horizon, slowly red-shift away and never be heard from again. If you change to a more suitable set of coordinates (such as Minkowski) you'll see that it was all in your head and it's actually safe to turn your engines off (except you may never be able to contact your friend Steve, who wouldn't listen to you and kept his engines on). The event horizon around a black hole is a bit more objective, but if you change to some other coordinates such as Kruskal you see similar effects.

I don't quite understand what you're trying to say here. One thing that might help is distinguishing carefully between 'things' which are a series of events (the lines on that x/t diagram) and exist over time and events, which exist at a specific time. Another distinction is between: The white/red/blue stuff that appears when you turn apparent positions on. This represents what someone at the cross would see -- and events that ocurred in the past and, The stuff represented by green lines/dots, this is only visible to our godlike being and represents what is happening in the now of the cross. Also regarding stuff above the line. If we introduce concepts such as free will or (the traditional view of) non-determinism then things above the line certainly are distinct in their reality from things below the line (or at least things above the past-cone are distinct from those below it), but special relativity does not contain this distinction on its own. Not only this, the bit below the white line or in the cone is different for each observer. The usual way this is taught is to discuss this simplified map, and only later add these other features. Filling in detail, but being careful not to involve any contradictions. Unless I state otherwise, or perhaps such a time comes that we are all on the same page with regards to SR, you can usually¹ assume I am talking about the map. Physicists in my experience very rarely discuss the territory because anything our tiny little minds can have the slightest inkling of is almost definitely completely wrong. The territory is more the domain of philosophy and ontology. This is where we should discuss what is not on the map, but any discussion must be consistent with the map where it says anything². So you can't say something like 'only the bits below (or perhaps on) the white line exist'. Because different frames of reference have a different white lines, and without some reason to single out one frame of reference as special (a preferred frame -- note again that this isn't the preferred frame for some experiment, but for all observations and experiments everywhere) such a statement makes little sense. ¹When I say things like 'the universe is four-dimensional' this is a bit ambiguous. I very definitely mean that our measurements (in flat space) will be consistent with hyperbolic 4D geometry in the strictest mathematical sense -- barring any interpretation of what that might mean ontologically. I also might mean that my philosophy considers time to be the same entity as space (but I don't know what type of thing that is) and that the cup beside past-me full of hot coffee 5 minutes ago has the same ontological status as the cup beside me now, half-full of cold coffee. You are most welcome to dispute the latter if you have an internally consistent replacement (or even if you don't, I suppose), but the former would require you to have some experiment overturning relativity. ²This is not quite true, there is another map you can use, but it's somewhat hirsute and needs a jolly good shave.

Basically, we look at what's happenening now, build some rules based on that, then extrapolate them while making as few extra assumptions as possible. We see some quantities (mass charge parity etc) and see that they are conserved (well we're starting to see that some of them aren't conserved in very extreme circumstances, but that's a whole different story). So in any case where a lack of one of these quantities turns into some of it, we assume its opposite also appeared (so the total stays the same). This is a gross simplification of something I already don't have a complete grasp of, so don't try and take too much from my words, but this outlines the general process.

Can't see anything wrong with your logic. And that matches quite closely to the tuning of a real piccolo (roughly 525-550Hz depending on whether it's C or D flat). Well step 1 would be to find the wavelength that corresponds to this new frequency. There will be more than one full wave in the flute. It will (barring complicated effects we're ignoring), at least, have a pressure node at the open hole closest to the mouth-piece. So we expect it to be a lot shorter. [math]v=f\lambda \rightarrow 340ms^{-1}=4000s^{-1}\lambda[/math] Then the distance between two nodes/antinodes would be half of that.

The portia genus of spider display a lot of behavior that seems more intelligent than their tiny brain would indicate. http://en.wikipedia.org/wiki/Portia_%28spider%29

Tar, I think you might still be getting hung up on the idea that light delay is linked to the definition of now. The non-simultaneity does not come from signal delay, it comes from the assumption that there is a speed (whatever entity travels at that speed) that does not change when measured in different frames. I am trying to get to this derivation in my present discussion with Owl. The equations that are derived only have the t coordinate changing between different frames for events that are far away, but this is not linked to light delay. As an analogy, imagine a table or flat plane. This defines a set of positions at a constant z (or up) coordinate. Merely moving along the table will not change your z coordinate, or your perception of the z coordinate of other points, but if you tilt the table, then different points in space will be different coordinates. As you see, if you tilt to your right, things to your right will become higher (or later for the Lorentz transform) than they were before, depending on how far away they are. This is almost exactly how the lorentz transform works, but the geometry is a little bit different (you wind up with a minus sign in some places). It might help to play with this for a little bit. Select the demo Han and Greedo to get one with some stuff at different positions. Don't unpause it, press t to display some time information then scroll down to the x vs t diagram. The horizontal white line in the middle represents what is happening 'now' in the frame that matches the stationary cross. No matter where you are along this line you still see the same now. Unless you also accelerate. To fall back to my table analogy you could move along the table as much as you liked, nothing would change height, but if you rotated the table about your new position things (far away from your new position) would change height. Play with accelerating left and right (a and d, you still don't need to un-pause it). You'll see things that are a long way in time, but not in space wind up far away in space as well (because you are now moving away from them). In much the same way things that are far away in space (but at the same time) become far away in time. The light delayed signal would be what is crossing the boundary between the red and blue regions. You can press c (or click on the display apparent position button) to turn on the light delayed view. This represents what you could see if you were at the cross. You'll see a white/red/blue (depending on doppler shift) wire-frame objects in the top view, and some same-colored dots appear on the past light cone (bottom red-blue intersection). One thing to note is that (while it is still paused) no matter what frame you change/accelerate to you are still seeing the same set of events. The tau value displayed is what a clock on each of the objects would be displaying. If you un-pause it so -- say -- tau: 0s intersects with your light cone. Then re-pause it, you'll see that those events stay on your light cone. This is another way of saying 'you are seeing that event now' -- note that this definitely does not mean that this event happened now. Those would be the events that cross the horizontal white line and match the green wire-frame. How long ago and how far away you see these depends on your position and matches what you seemed to be describing. Note that this is definitely not what we mean by now in relativity. Also if you look at the light white lines that represent photons, they will never change angle (so they always go across the same amount for the same amount they go up, or have constant velocity). And this angle always matches your light cone.

I suppose there might be some similarities, conductive fluid vs plasma, but generally plasmas do a lot of weird stuff that you don't tend to see elsewhere, so I would hesitate before assuming they're going to be too much alike.

Well it becomes part of the black hole. Every time light hits something it gets absorbed and turned into other forms. It just carries spin and some energy-momentum. These things are conserved but the light itself is not. Examples of this are the sunlight hitting your arm, it gets wam (absorbs the energy) and if you had very very sensitive instruments you'd feel it pushing ever so slightly. If it was circularly polarized light (all with the same spin) you'd also feel it twisting even more subtly.

Well this works with (classical) acceleration for pairs of objects too, on one condition. The centre of mass is the centre of force. If you have two equal massed opposite charges 'orbiting' each other you'll find that the magnetic and electric fields work out just right so that you can use the coulomb guage, ignore the magnetic force, and still get the right result.

Well we do distinguish between timelike things (which can carry causality, although forward and backward causality are not really distinct) and spacelike things (which don't involve causal links). I don't think the concept of 'now' is really present as a first class entity in SR. As I said, we have to look to other scientific theories (thermodynamics, quantum etc) to gain insight here. Relativity, much like classical mechanics has nothing to say on the matter. Once you bring entropy into the picture there's a good reason why the me from yesterday doesn't remember today, but it still doesn't really answer why I perceive being this me rather than yesterday's me. This issue is still well within the realm of philosophy, and somewhat tangled with the problem of measurement. One thing that may be a good starting point is to imagine some kind of 3d steady-state computer that can only carry information east. If you were to construct an AI on such a computer, then wander east for a while until you reach a point where it has learned a bit about itself. At that position you can set up some input so as to ask it a question about what 'moment' (amount of east-ness) it perceives itself to be at. It won't remember anything further east so it will form answers based on that position and things further west. This is somewhat of a distinct concept, so perhaps a new thread might be appropriate if you want to discuss this further.

No. Which is not to say that it's nonsense, just that there is insufficient context to glean any information from it.

I apologise, I was a bit frustrated, my comment was out of line. Glad that you refused to rise to it. You're conflating a couple of different ideas again. There are more than two concepts that apply here. No known preferred reference frame (experiments done to determine the laws of physics on a moving space-ship are just as valid as, or at least indistinguishable from those on earth) Presentism (ie. the universe is 3d and defined only in the now) Speed of light that will be measured as unchanging between different reference frames (ie. it's a law of physics). Realism These four concepts are incompatable. You are assuming the second, and projecting that assumption onto us. This leads you to conclude that we are not realists, or are being logically inconsistent. With the laser jousters thought experiment, and Capn's earlier attempts we were hoping to show you some of the logical consequences of takin Philosophy, or rather philosophy that pertains to reality, must be compatable with physics. Capn and I have been trying to guide you towards a logical conclusion that follows from the assumption that the speed of light is measured as the same by all experimenters (moving or non-moving). This conclusion is incompatable with (my understanding of) the assumptions you have stated. The reason I was trying to take the discussion away from length contraction is that it is a logical consequence of non-simultaneity. If you do not accept relativity's version of simultaneity then any discussion over length contraction is completely moot. Again, the thought experiments were intended to show you how it is derived, and provide an opportunity for you to query the assumptions on which it's based. None of that addressed the speed of light in different frames of reference. All I can gather from that is 'here is a description of some things happening'. The cases where the logic behind SR (agreement between observations in different frames of reference) were not included. Also I would not (yet) consider the title of physicist as entirely appropriate in all contexts, as I have not finished my degree. I tried to respond to that. See the diagram in #399. It is intended to represent this scenario. In case it's still a bit unclear, read it by imagining a thin horizontal slice, each slice represents a different moment in time, as if someone was observing the rockets (and knew exactly where they were at each moment in time -- by maths or magic or whatever.) and just recording the positions of things at each moment of time. The blue dots will be our jousters, the red is where the front of the beams of lights are. Is this clear? Does it match what you were trying to explain? This is the philosophy of presentism. In relativity 'now' is simply a name for a set of events. Much like 'yesterday', and similar in many respects to 'left' (note that spatial position has nothing to do with it). At any rate. Ignore this issue, and everything else I've said for the moment and focus on the jousters scenario. I just want to examine the logical consequences of this thought experiment. I am not assuming anything about length contraction or simultaneity, just trying to describe the situation you outlined.

Anyone who would be able to do anything useful with that information will know to look on arxiv, or ask someone who would know where to look for the article.

To be fair, one would either have to be incredibly intelligent or incredibly, belligerently stupid to keep this many physicists/physics students/etc responding for this long when it clearly hasn't achieved anything so far.

There's this on arxiv http://arxiv.org/abs/1109.4897 I don't expect they published anything, as the vibe I've gotten from the news stories is "we've made a mistake, help us find it".

@toastywombel Tachyon is just a name for something travelling faster than light. So these (if it's not a mistake) would be netrinos that are also tachyons, or objects identical to neutrinos other than that they are tachyons. Hmm, good point. The only thing I can think of is that it would mean the object would have a different time-like dimension, but then again that's a bit like saying, "At least 90% of tautologies are tautilogical."

While we don't really have a good model for time travel, and as such paradoxes abound freely, I've been trying to chase a thought about entropy and time travel for a while. I vaguely recall discussing this, but I cannot seem to find any reference to it in my past posts, so it may not have been here. If we could send information back in time (and act on it in a paradox free manner), would this violate the laws of thermodynamics somehow?

Is there actually anything in relativity that says no tachyons? I mean you cannot cross the speed of light, and it would probably break a lot of other physics, not to mention causality. But I've never seen anything within relativity, other than common sense (and to be honest, when has that been useful in physics recently?) that says things can't follow space-like geodesics.

I'm....uh...confused. This doesn't appear to be a response to what I think I posted. I was querying the implication that someone working at a particle accelerator would ever have a reason to run a non-relativistic simulation (and thus wondering about the circumstances around such an event). I was definitely not questioning the suitability of a relativistic model in this situation.

Do you mean something like this? The x axis is distance approximately in Au, the y axis is time in minutes. Red lines are the lights, blue are our jousters. Similar, but without conflating measurement of objects and measurement of distances. Contracted length reflects an accurate measurement of distances, which are only an accurate representation of objects to the same degree angular size is. If one were to put a metre stick beside that object as it moved past it would be that length. One would be able to fit it in a box of that size if closing and opening the lid were very carefully timed, but it is certainly not measuring the same entity that would be measured with a meter stick in the frame at rest with the object. Just as if one were to take a photo it would subtend a certian angular size. The photo represents an accurate measure of the angular size of that object, but this is not a frame or position invariant quantity. Also taking photos from different angles produces a 2d representation of a different part of the 3d object. We also have to be careful what we mean by object here. I am talking of the four dimensional entity, because the length contracted version does not represent the same set of events (the back is older than the front in a frame where it's moving) I can find an object's proper length by taking the length I measure in my frame, making some assumptions about it being non-accelerating/rotating, and doing some calculations based on its velocity in my frame. This is the quantity/entity that would be measured in a frame moving with the object. To go back to my angle analogy, I could find the height of the Statue of Liberty if I had a record of its angular height (or the height on a photograph of known angle/size) and the distance from which the measurement was taken.

Yes, this is why we select a FOR, and do calculations/experiments and such in it. It's also a metaphysical/philosophical question which is somewhat outside the realm of SR. Why time appears to go one way rather than another, whether or not things are deterministic (in SR, just like Newtonian mechanics, there is no concept of choice or non-determinism. This is a limitation of the theory rather than something it asserts), issues like free will etc. are all open philosophical questions which should be informed and guided by thermodynamics and quantum physics, not just SR in isolation. As to this "me" business, I look at it this way. If there was a deterministic machine operating by a set of highly complicated rules in order to mimic me, but it didn't perceive this 'here and now'ness (or have any perception about reality), noone would notice. It would act exactly the same and be perceived exactly the same by everyone else's me. If it can trick the whole rest of the world, why couldn't it trick this entity I think of as me -- whatever that is? It was this lovely little piece of cognitive dissonance which lead to my sig. I see no objective evidence that free will is not just an illusion, but it makes me happier to have it. So I'll choose to pretend it exists. Sure, you do everything in a FOR based on your here and now. I'll do everything in mine, but I won't pretend mine is any more or less significant than yours. When we talk about a preferred frame, we mean one that is special, and should be singled out no matter who, where,or when you are. We've never been able to detect one of these, so Occam's razor says we should prefer a theory which doesn't have one over a compatable theory which does. (Assuming for a moment we accept all this special relativistic nonsense) The reason we need to consider the four dimensional picture, rather than just our own now goes something along these lines: Let's say we have a universe with you, me, and Jim. We're all a long way off, having a chat over intergalactic radio, but we're immortal so the time lag isn't much of a worry. We're also both moving at different speeds relative to Jim. I do my calculations, and work out that in my frame, the Jim that is synchronous with me is (to pick a random number) 21,080 years old. But when you do your calculations you get 18,900. If we try and consider an ephemiral, transient Jim we have to consider that he's both 21,080 and 19,800 years old. For a 3D, transient Jim this is paradoxical. But eternal four-dimensional-worm Jim has a part of him that is every age, so this is okay. If we had a preferred frame we could say we're all 3d, existing only in the now (in that frame), and the laws of physics are just conspiring to make us think some times that are not now, are actually now. This is -- in essence -- the Lorentz Ether theory that I've been mentioning. However, if you go down that road you find an endless series of little holes that need patching so that the conspiracy can trick you in every experiment we've done. Most scientists find that unpalatable, so instead of the myriad little theories, concepts and patches to keep this un-measurable preferred reference frame, they use the 4D model. Aside: A good reason to think that our experiences will be 3 dimensional in appearance in this 4D world is that all of the interactions between different world lines are along our light cone (slight misnomer really, as this is the four dimensional equvalent of a cone). Also remember that everything we perceive (sans gravity) is mediated by photons. Even when you grab something, it's still the electromagnetic force. Other aside: A mental image which might help with a conception of interactions which doesn't include a notion of evolution is this: Imagine a series of strings, pulled taught. Like a very coarse net. Normally if we were to pull it tight, all of the cells/sections of the net would be squares, but if we were to tie a piece of thing string from one part of the net to another, the two bits of the net will be interacting with each other, even if the net is static.

I don't quite understand the question. Photons in a gravitational field will follow paths that we classically think of as curved if that's what you are asking.

Well, we cheat slightly in that we just calculated the velocities off of the energies/potentials used. But there are clocks accurate enough to measure velocities this high if you had a circular accelerator. Just count the EM pulses as your Ion's go by, multiply by the distance around your accelerator (I don't know to what accuracy this is known, probably not 12 sig figs so by this measurement technique you'd probably have 0.999999c+/-0.000001c) and divide by the time. Yes, no matter how much kinetic energy we put in to the electrons (even thousands or millions of times as much) we'll only asymtotically approach c. For the LHC accelerating protons, there is around 3700 times as much energy-momentum (the generalisation of mass) in the proton as it would have at rest. Do you have a link to the specific page? I don't doubt what you're saying, but I'm curious as to what they were talking about.

Oops, had a bit of a brain failure there. Apologies. Ignore this: And this one: (the magnitude is c as DrRocket said. I had my factor of gamma wrong, the magnitude of [math]\frac{dX}{dt}[/math] is [math]\frac{c}{\gamma}[/math]). That said, I think my comment about the concept of velocity not fitting exactly still stands. Mathematically it is the logical extension of the concept, and fits exactly, but when most people think about things from a three dimensional perspective, velocity usually implies evolution -- ie. a three dimensional object moving to a different location. Thinking about things in these terms can lead to confusion when dealing with objects as world-lines.