Schrödinger's hat

Just to clarify, DrRocket is using [math]\frac{dX}{dt}[/math] (where X is the four-position). I have seen both referred to as four-velocity, but I believe this is the more common. Edit: Wrong, see DrRocket's comment and my response The other thing that's useful with [math]\frac{dX}{dt}[/math] is it's defined for light (where [math]\frac{dX}{d\tau}[/math] is not), but my personal preference is for [math]\frac{dX}{d\tau}[/math]. It seems neater not to have factors of gamma floating about, and you don't have to re-normalize after Lorentz transforms. I also like [math]P=m\frac{dX}{d\tau}[/math] rather than [math]P=m\gamma\frac{dX}{dt}[/math]. The disadvantage is the magnitude is [math]\gamma c[/math] I find it also helps with my intuitive picture of Minkowski space. I think of [math]\tau[/math] as the parameter which takes an object through spacetime along its worldline. [math]\frac{dX}{d\tau}[/math] can then be thought of as analogous to a velocity* through spacetime according to this parameter. *in this interpretation, velocity isn't a perfectly accurate concept because spacetime does not evolve, nor do the worldlines of objects in it.

I apologise, this was just so unexpected that I was not sure I had read your post correctly. According to your model, would the clocks in the Sol system tick faster or slower when measured from a lab orbiting Barnard's star (which is moving at about 140km/s relative to Sol)? Would a clock orbiting Barnard's star tick faster or slower when measured from Earth? Edit: Changed observed to measured for clarity. Note that measured means the measurement you get after taking into account the effects of the doppler effect and light delay.

I imagine the easiest way would be to use the bernoulli effect. Get an industrial fan of some kind and put a cowling around it. Then put whatever system you normally use to generate the foam in the air stream.

I don't pretend to understand current cosmology, but as I understand it, the proto-matter stuff, whatever you want to call it would still contribute to the stress energy tensor, and as such would produce gravity. It would do this in much the same way photons do. We talk about matter inducing gravity largely because that is the only thing with significant energy-momentum (and the other components of stress-energy). If you had enough light, or anything else with energy it would have the same effect.

And the (4d) earth as modelled by relativity doesn't change shape with the variable "width" as seen from different frames of reference. I have mentioned on several occasions that the quantity proper length or proper distance (distance measured when at rest w/ respect to an object) exists in the literature. It is also invariant where it is defined. But this quantity is not sufficient to explain all phenomena. Two that come to mind are rapidly rotating objects, and systems of non co-moving objects. If you were to follow your jousting lasers experiment through to its conclusion you'd find that it implied a non-constant speed of light. I would cover this in a series of thought experiments, but I need a common base of assumptions to work from. Yet again, you present a false dichotomy. Noone here is advocating a three dimensional universe in which length contraction works. Noone here is advocating a universe with a universal well defined now in which length contraction works. Both the three dimensional universe and the well universal now are assumptions you have made. They are inconsistent with a constant speed of light. We have tried to explain over and over again that the following are inconsistent: Speed of light which appears constant in any non-accelerating frame Universal now No Ether theory* But the chain of reasoning is quite long and you have an uncanny ability to derail any train of logic heading in that direction. I'm willing to draw up some diagrams and try and explain why this is so, but I will not bother if it will just fall on deaf ears. But you just said moving clocks tick slower, Clocks moving relative to WHAT tick slower? Any explanation I give to any questions about length contraction is contingent on assumptions about the relativity of simultaneity. You are asking me to answer questions without accepting the premise on which I base the answers. Any response I give will be useless. In addition I very carefully worded my statement to avoid assuming that anything depended on frame of reference, this is intended to be my conclusion. Here are the assumptions with a bit more explanation, seeing as I failed to communicate my point. I mean that, no matter what experiment you perform, or what velocity your laboritory is moving at (relative to, for example: Earth), so long as you assume you are stationary any experiment you do to determine the speed of light will come up with the value 299 792 458 m/s. The second assumption was: I can weaken this further if you like to "The frame of reference we are using for our thought-experiments has an unknown velocity relative to some object (say, Earth)." if you like. Note carefully that I am assuming nothing about length contraction, time dilation, simultaneity, or which variables depend on frame of reference. *Ether theories are ones in which there is a universal 'still' frame and a speed of light which appears to be constant in all frames, but actually is not. They also share a result in that objects moving relative to this frame do physically contract, as opposed to relativity which posits that length contraction is a phenomenon caused by measuring things without taking the time coordinate into account. Other than the struggle of whether philosophy (or religion) can tell nature how it behaves. But surely there were philosophers around in the 1910s as well?

The events on earth that are viewed as synchronous in the moving frame are not the events that are viewed as synchronous on earth. If the events at different times did were not real outside of this present then we would not see earth at all in the moving frame. The reason the earth we measure becomes contracted is because we are not seeing the different parts of it at the same time any more, (if you wish to consider the positions of the events that the earthlings consider synchronous then you will have to consider different times). We are not saying that anything is subjective. Merely that one of the inputs required to define a distance is a frame of reference. Just like one of the inputs required to define an angular size is a position. What if I'm measuring something that involves two or three different objects with different velocities? Then any discussion over length contractions is completely irrelevant. Resolve the simultaneity issue first. No it does not. Are you saying moving clocks tick slower, or are you saying that they don't? How do we define not moving? A clock is just a physical process. If a clock (as in the abstraction of clock -- ie. any physical process) slows down, then all physical processes slow down. @Owl, capn's a bit busy to continue his train of reasoning and I'd like to continue before everyone forgets what he said. Are you willing to proceed with some more thought experiments on the following assumptions: 1) The speed of light appears to be constant when measured on the assumption that one's laboratory is stationary. No matter the velocity of the laboritory. 2) Either: There is no absolute rest frame or; There is no way to know (or physicists are as still not smart enough to know) whether or not we are in the stationary frame, or what speed we are moving.

I think you just perfectly summarized this whole thread. Hear hear. It's best to start by completely ignoring all the weird effects, and just focus on what a constant speed of light means. Yes, it's hard enough to wrap one's head around it when you trust those who are explaining it to you. I can't imagine the level of dissonance involved when one believes that all scientists are crazy kooks and/or conspiring to teach a warped version of reality. Addendum: At times I feel like I've travelled back a century. This debate seems more appropriate to the early 20th than 21st.

I'm not sure if this comes up often enough to have a succinct name. If I wanted to refer to it succinctly I'd just use the mathematical terminology: Things like [math] \frac{dx_P}{dt_P'}[/math] or [math]\frac{dx_P'}{dt_P}[/math] Define 'the primed frame is the frame in which O is at rest, the non-primed frame is the frame in which P is at rest' etc, then read Read "the change in the three-position of P in the non-primed frame with respect to the change in the time coordinate of P in the primed frame" etc. You could also use proper times: [math]\frac{dx_P}{d\tau_O}[/math] These are all clear, concise and unambiguous, but one would have to be careful about transforming these between frames. (proper times are often better in this regard, as [math]x_a(\tau_{b1}) + \frac{dx_a}{d\tau_b}\Delta \tau_b[/math] will alwaysrepresent a set event. Generally the easiest quantity to work with is a four vector. Ie. A four-displacement from an origin: [math]X_P[/math], with coordinates ct,x,y,z Then you can define four velocity as either [math]\frac{dX_P}{dt_P}[/math] This needs some care, because dt is frame dependant. So another definition of four-velocity is often used: [math]\frac{d X_P}{d\tau_P}[/math], which is the change in the four-displacement for each tick of a clock on P. You can transform this vector exactly as you do X, so it's easier to think about, too (no memorizing a separate velocity addition formula).

Yup! Spot on. You forgot to take into account that the only way for the metres and seconds to change size is by changing to a different frame of reference. Ie. by changing your velocity. If something has a certain velocity in your frame (for example a train moving at 90km/h) then when you change velocity it'll have a different velocity (in our example, you might get on the train, then it'd be moving at 0km/h). There are some invariant parameters though. If our object was travelling at some exact percentage of the speed of light between two planets, then no matter which frame you use: The clock on the object will show the same time when it is a set percentage of the way there, The clocks on the planets will show the same time when it arrives or leaves and a few other things, basically they will all agree on any events that happened. We observe these at the same time, so the observations are simultaneous. This does not mean that the events were simultaneous. As I said (tried to say?) earlier, you get time something happened in your frame only once you account for light delay. Also these events are exactly too close together in space and too far apart in time to happen at the same time in any frame, as one is in the light cone of the other. Nearly. The point is that simultaneity is relative. We can define an imaginary universal now seen from a godlike position, but this imaginary now changes with our reference frame.

Just as the pancake does not actually change its reality, neither does earth. Simply the three dimensional piece that we consider to be 'now'. All of our interactions are based on a 3d slice of the 4d object, so this is what we perceive at any given time. I don't see any problem with putting time on the same philosophical ground as space. It seems to be supported by Occam's razor. Replacing two concepts (time and space) with one (albeit a less intuitive one). At any rate, all there are, are events. Our perceptions of reality are three dimensional, so three dimensional slices of events are what are the most sensible. It's also three dimensional slices of events (our light cone) that we effect, and that effect us. It's natural to think of the stuff in between as three dimensional. SR (specifically Minkowski geometry) says it's actually a very thin four dimensional wedge.

There is nothing about image travel time in the bulk of the responses here. The one time I did mention it, I was responding to tar pointing out that sometimes the word simultaneous is used in different contexts to mean different things. The meaning of simultaneous I have been using is that events occur at the same time coordinate as the one right here and now in my frame. You are correct in your conclusion that this denies presintism's concept of now and simultaneous, as this type of now depends on my frame of reference (your now, and my now may not be the same). Well now there are three. Ignore the first one. Noone was talking about images until tar brought it up. The third concept of simultaneous which you can't seem to distinguish from light delay is usually explained thusly: Imagine you were to move some clocks out in all directions -- infinitely slowly so time dilation wouldn't effect them (if it were a real effect). Events are simultaneous in the frame those close are stationary in, if the clocks each event is nearest have the same reading on them. In a universe without a constant speed (one where galilean transforms work) all of the clocks from all of the different frames will agree as to what is simultaneous. If you accept a constant speed of light, things are different. As Capn has been trying to explain, and I shall endeavour not to derail that conversation. The 3d slice we view of these 4d objects depends on the frame of reference chosen. Distance is not one of these intrinsic properties, just as the pancake changes from a circle to a line, the 4d things change from spheres to oblate sphereoids (if you slice them along a line of constant t). You are assuming presintism again. This is incompatable with a constant speed of light. The experimental evidence points to one of the following: 1) The speed of light is constant in all reference frames, or 2) The laws of physics conspire in a highly convoluted, specific, and arbitrary way to make it seem like they do. Unless you want to deny experiment, these are your only two options. The first denies presentism, leaving you with 2), which leads to Lorentz Ether theory. Everyone I know who has studied the matter goes with 1). Well I have no idea what you mean by space other than amount of distance, or what you mean by duration other than a period of time. This definition appears indistinguishable (other than being more vague) from my version with 'the thing we measure with meter sticks' and 'the thing we measure with clocks'. At any rate, the point I was trying to make is there is no definition (I know of) that isn't circular to some/all readers. Well you believe two contradictory things then. (the speed of light is constant, and presentism) Ignore signal delay. We're not talking about signal delay (other than my response to tar, conceding that some people include signal delay, and that 'simultaneous' in the context of relativity ignores signal delay)

*peers* I don't quite comprehend. Wouldn't any model that you're using in a particle accelerator be Lorentz invariant at the very very least?

Have you got references for any of this? Thorium reactors needing plutonium is news to me. I had read in places that there was concern over the amount of neutrons produced as it pertains to breeding enough fuel for the next part of the cycle, but I was under the impression it was not a theoretical limit.

What baric was saying was that most of the numbers you have used are arbitrary values which were picked because they were a roughly convenient size for the humans who invented them. There's nothing fundamental about dividing the circle into 360 units, or twelve hours in a day, or the length of a second compared to the length of a metre Mashing these numbers together isn't going to be meaningful. At least any more meaningful than measuring the width and and weight of your refrigerator in furlongs and stone, and using those numbers as a source of universal insight.

The LHC is the state of the art and it accelerates proton beams to 3.5 TeV, or about 0.9999c, or gamma of approximately 3700 if I did the conversions right. They're going to turn it up to full power eventually (7TeV for proton beams), so double the energy for a speed of roughly 0.99994c. In terms of physical property changes you'll probably have to be more specific. Are you asking about relativistic effects from being in a different frame (eg. the time of a moving object moves slower in our frame)? Or something else? Particle accelerators are designed to produce unusual physics when the beams collide rather than when they are moving.

We only call two supernovae simultaneous in the strict sense (as it is used in discussing, say, relativity) if: After we subtract out the light delay, they still happened at the same time. So if we saw two supernovae in different directions in a single event (e.g. a single super-wide-angle camera took a single photo with both supernovae happening in it) we would only measure them as having happened simultaneously if they were equally far away.. Due to aberration effects the distance the light you view appeared to come from, changes between different frames. This will match up with the different distances and times Yes, this is pretty much spot on. This is what SR (and science in general) attempts to be. A few other things to say about this. One of the aspects of this model is it does not elevate one now above any other. The concept of simultaneous is just a convenient label we can put on a certain set of events to make it easy to reason about them. They are no more or less real than those at any other time. There are four categories of events which do have physical meaning (for a given observer) The past: Things that can effect me. No matter what frame I'm in, these events are always at a negative t coordinate (if I call here and now t=0). This event: Right here, right now The future: Things that I can effect. No matter what frame I'm in, these events are always at a positive t coordinate. Other: These are events that I can neither effect, nor be effected by. They are too far away fro a signal to reach. At small distances this category is indistinguishable from events at t=0, because light travels so fast. This is why the concept of the present makes so much sense to our minds.

I think I get it now. It represents the point any irrotational geodesics started. So anything that isn't accelerating in its own frame (and only travels radially) looks like it came from there. Also would it be fair to say that: Kruskal coordinates are to Schwarzschild as Minkowski are to Rindler?

Also many of the concepts you use in group theory (thinking about things in terms of applying an operation on a thing and getting a different thing, and examining the rules of those operations) are useful for solving problems efficiently. There's the entire field of linear programming where you are restricted to a (non turing-complete) set of operations. Algorithms that are writtens as a series of these operations can be condensed into a single matrix and as a result are obscenely fast at solving problems to which they are applicable. Without some grounding in the study of algebras (note: This kind of algebra, not the elementary algebra you'll know from algebra class) the restrictions in place on such programming will not make sense. On top of this, understanding things like invariants of the code, or whether the vector space of the data you're working on is closed under some operation can be essential for proving that your code does what you think it does, or even just chasing down some bugs in less formal settings.

As I said, I'm WAAAAY out of my depth here, I could entirely be talking out of my posterior. The only thing I can think of is somehow having another property (regular charge, spin, mass etc) which varies in some way which is systematically linked to the color of the particles. I am given to understand that quarks/gluons have spin. Maybe there'd be something systematic about the way the colors of the quarks in some protons/neutrons are arranged. If one were to align them all in a magnetic field before making our super-dense matter, could a further EM field then have some effect? The one other thing is if there's something that goes whacky with the symmetries at very high energy levels, and you get some coupling to other types of field. How you'd have anything resembling what we think of as a machine or a device operating at such energies I have no idea. At this stage I think I might just give up and wait until I've learned some QCD before attempting to think about this again :/ Have fun!

I can imagine this perfectly well. The earth, sun, moon etc as they exist over time are all four dimensional objects that exist and have intrinsic properties, no matter which frame they are viewed from. Taking a few slight liberties with the definition of the word cylinder (Minkowski geometry is not like euclidean and what things are like depends on your choice of embedding), you can imagine something like earth as being a bit like a cylinder. Each point on earth represents a straight line through space-time, much like the lines in Capn's diagrams. Together the world-lines of any two-dimensional slice of earth would be a cylinder. If you take the world-lines of the entire earth you get the four-dimensional equivalent of a cylinder (a sphere in three directions, extruded along a fourth). Depending on which velocity or angle you look at this object from, you will see something a bit different. Our interactions and minds deal in three dimensional slices so at any given time It is by taking the results of this four dimensional model (one of which is length contraction), without taking the model itself that one reaches a contradiction. The entire study of relativity, especially General Relativity, is based on describing objects and geometries in a way that does not depend on any frame of reference or coordinate system. It is perfectly possible to use the mathematics and results of relativity without putting time in the same ontological category as space, but then you will have to do one of two things: 1) Create a hugely convoluted model based on an indetectable rest frame (ie. Lorentz Ether). In these models moving things actually do morph and change shape, rather than it being a relic of looking at them from a strange angle. 2) Deny realism As I said, earth almost exactly like the pancake Accelerating is almost exactly like turning it on edge. Your argument appears to be: There is a universal and well defined now. (assume presentism) Assume Realism Therefore relativity is wrong What you seem to be interpreting our argument as: There is a universal and well defined now (noone who accepts relativity believes this) Assume relativity Therefore there is no realism While ours is: Assume realism Assume 100 years of experiments showing constancy of the speed of light and disproving every elegant Ether model are correct Therefore Relativity is correct and presentism is not. Presentism, realism, constant speed of light, no preferred(unversal still) frame pick three. (we picked the latter three). Any more are logically incompatable. Also you still haven't given me a definition of distance or time that are any better than the ones I had, I'm most interested to hear one that's not tautological. When the word simultaneous is used it means: According the the observer of frame that is currently being considered, these events occur at the same time coordinate. Think of it as the same sort of thing as 'directly in front of' If I say one cup of coffee is directly in front of another on the table, I mean that according to some reference, they'd be at the same y coordinate. So unless they are also 'here', you can't see stuff that is 'now' until a while later. Now will also be a different set of events from different frames. Often cosmologists use 'just happened' or 'now' in place of 'long enough ago for a signal to reach us now' (eg. the supernova just reached maximum intensity), just to confuse the issue, but it's usually clear from the context. Sometimes For predictable objects they often observe past events and then extrapolate to now as well. Not quite sure how to answer this, to me they're both just as real, along with the Alpha Centauri existing at any other time in the past or future. To go any further than this I'd have to start discussing Bell's theorem, and the problem of measurement. This requires a decent understanding of quantum physics, and I'm not sure I have learnt enough yet to have a fully coherent philosophy on the matter, let alone communicate that to others.

Agreed, ydoaPs, also mathematics is a subset of philosophy. It should also be taught in schools to some degree. Critical thinking is one of the most important and undertaught skills a person could have. Also, hopefully the general populace will stop rehashing 3000 year old ideas and thinking they're coming up with something new, and actually think of something useful more often. There's plenty of useful philosophy, and even if we think we know what philosophy is worthwhile (I certainly think I do, and a lot of what I've read doesn't fall into that category) we should err a long way on the side of having people think about presently useless things. Never know what gem we'll need in another 2000 years. It is hard to distinguish between useless/nonsense ideas and those that are ahead of their time. Unfortunately the former are far more common. Random bugbear/thought. Natural Philosophy should be revived as a term for things like science which aren't quite. I'd put most variants of string theory in here, they are philosophy that pertains to reality, but until the kinks are ironed out enough that we can make definite predictions -- and we advance our technology to perform the experiments I find it hard to classify them as science.

Well, one other point that I forgot to mention is anything we build will be too late to help. There are problems that we need to be most of the way to a solution before any fusion reactor could be ready. Even if we had some sort of breakthrough that made it far more viable.

Well let's say you have constant force on an object accelerating from rest. f=ma, so ma is constant. [math] E=\int f dx=\int m\frac{d^2x}{dt^2}dx [/math] But dx = \frac{dx}{dt}dt So [math] E = \int m\frac{dv}{dt}v dt [/math] Which by chain rule is: [math] E = \int mv dv = \frac{1}{2}mv^2 + C[/math] You can also come to the same conclusion starting with gravitational potential energy (mgh) and using the algebraic kinematics equations (v^2-u^2=2*g*h) So starting at u=0 mv^2=2mgh=2E ->E=1/2mv^2

Hmm, I may be a bit cynical, but I mostly have negative thoughts. First of all, unless something happens to capitalism, we'll probably just increase production and wind up paying just as much (only using more energy to produce more stuff). Or even worse, just increase our population. It might turn out good for the people who currently have energy as the limit on their food/water etc, but in terms of stopping people from harming the environment, I'm not so sure. (They might just start mining instead of cutting down the trees for wood, to get more rare minerals). Here is a good explanation of why we can't have unlimited exponential growth, it doesn't matter what technology we get, we're still going to have to deal with the problems in the way society is structured if we want to get some kind of utopia. Second downer: Our fusion generators aren't very good. As far as I know only the tokamaks are anywhere near commercially viable, and they are limited to comparatively low energy reactions (..I think it's D H?) which have neutrons as a byproduct. This results in fairly large quantities of low grade radioactive waste as all the shielding needs to be dealt with. They're also big, complex and expensive. There's some potential with Thorium fission breeder-reactors. These are supposed to be simple, comparatively cheap, safe and produce roughly the same amount of waste as the fusion reactors (but some of it is higher grade). I'm not sure why there isn't more enthusiasm for this technology, I think there may be worries due to the technology being untested and concerns over proliferation. Solar is looking better and better, there's really no shortage of sunlight, and we're closer to having solar panels that about the same price as normal roofing materials than we are to having good fusion reactors. The down side here is it only gives you power for part of the day. This would be fantastic if we could re-structure the social aspects of manufacturing and energy use, but people want their 9-5 work days, and their shift working factories and air conditioning that works whenever they want it.

Maybe you could make it clearer by adding some return-journey light lines to your diagram, point out when/where the me sees them and when/where a (or two) observer(s) on the tracks do(es)?