Schrödinger's hat

Umm does not compute. At the risk of repeating what lemur said in case I don't get it. Information about future events could reach past events. That is effects could precede causes. I just realised this would do strange things to the laws of thermodynamics and OWWW MY BRAIN!

Nearly there. Without point of reference we'd call the bit we remembered (when we were younger and the universe was more ordered) the past, and the other one the future. If everything was in the state it's in right now, then we'd call the end where things looked all scrunched up the beginning. So in short, if we reversed time, NOTHING would happen. If we flipped it right now, we wouldn't notice as long as it was flipped back eventually (well it might come out differently, assuming quantum things are truly random), but even if we didn't we wouldn't notice as noticing is contingent on time.

On the other extreme. I find wasps are satisfyingly non-resistant to fire. A quick burst from an aerosol can with a lighter under it usually won't even mark paint, but any wasps present will lose their wings at the very least. This is a good backup if you go to spray them with insecticide, and they start stinging. Disclaimer: Don't set fire to your house. If you don't get how and when dust can turn into a fireball, or when to pay attention to how much surface area something has, fire is not the tool to use.

Uuhm, look closer. Note how the x,ct and x',ct' don't make 90 degrees? Everything here is drawn in a frame such that the yellow lines are the speed of light, and Alice and Bob are travelling at equal velocities in opposite directions. This brings me to something I've been musing over for a while. I sort of re-invented Minkowski diagrams without knowing they existed a while back, but adding a few features and musing for a while lead me to some geometric techniques whereby some reasonably advanced SR student problems (Anything involving instant acceleration, and all of the 'paradoxes' that undergrads are given to muse over) can be solved without any calculators or algebra. This lead to an idea for an ebook or set of notes for learning SR without an algebra requirement. Does anyone think this is a good idea? Edit: Plain forgot to answer michel before I went off on my tangent. You could alter the diagram so that the lines represented lightspeed signals, I suppose, but that would distract from the issue at hand and bring up all those issues about signal propagation delay and such. I think it is simplest to just have a line drawn parallel to the x axis in each frame, this is a line of events saying "The times is ___" in the given frame. It could be made clearer that this is what these are, by extending the line, removing the arrow head and putting crosses where it intersects with each world line. Looking into the way the wiki page is structured, they first take the geometry as a postulate, and hold off on talking about the constancy of lightspeed (these conditions are equivalent) until later. This is not a good pedagogical method for SR in my opinion, but then this is not the role of an encyclopaedia. It could possibly be structured in a way that was better for teaching without compromising its role as a reference, but going through a derivation SR for every tool or representation introduces a lot of redundancy.

Good observation. You're right about the interval between all those events being spacelike. This doesn't really change the point of the diagram though. Both observers could carefully record everything they did, then observe what they saw of the other some time later. They could then determine that, according to their reference frame (what is real for them) is that the other clock is running slower. There would be lots of factors to take into account before they could reach this conclusion from their measurements. One thing that trips people up is: if you are moving away from one another, then everything red shifts due to doppler effect. As the light you see redshifts, so too do the events it records. Say the clock was a beeping radio. The beeping you receive would be even slower than the rate at which the radio beeps in your reference frame, because each beep would have to travel further. It's important to note that this is not the time dilation, it's simple, non-relativistic doppler shift, and could be reproduced by an audible signal of an object moving near the speed of sound. If they turned around, the beeps would speed up. Once you correct for this and look at all the measurements you made, you still find the beeps are slower. Both parties will see that the other has the slow clock. This is time dilation. It's not important that they agree on the times and positions at which things happen, as they are not in the same frame.

Hi all, I'm about to start learning general rel. I learn best when I have someone to bounce ideas off of, or help explain things to. Someone who is struggling would be great as I find that gives me a lot more motivation to get ahead of the material (although if you're already in a class it may take me a month or so to catch up). Is anyone else currently learning, about to learn, or interested in learning GR? I don't mind helping someone catch up a little bit if they lack some of the pre-req knowledge that I have. Reviewing some topics would help me too.Although, I don't think I'd have enough time to help if you aren't fairly comfortable with vector calculus, special rel and linear algebra. I'm kind of shaky when it comes to differential geometry etc. and missing a largish chunk of knowledge when it comes to analysis, so will be going through them first/during. Anyone at a roughly similar knowledge level and game to learn with me?

Nonsense! What better way to get encouragement to go find the equipment? Just don't make presumptions about what the answers should be and you'll do fine.

For AC this sounds right. I can also see it working quite well on auto-electronics, as there is generally a fairly large fluctuation there, but for DC, if the current is steady, there is no travelling wave. It could work on magnetic and electric fields, or there could be more thermal fluctuation on a DC load than I thought. In reply to the OP the best analogy I have encountered for DC electricity is water. Think of a water tower with a long hose. Almost as soon as you turn on the tap (after a speed of sound-in water delay), the water level falls. But it can take a long time for a pebble, or bit of muddy water to reach the end. One way to show the distinction may be to get a hose, fill it with water so it turns on or off as soon as you turn the tap. Then unplug it from the tap (hold both ends roughly level so you don't spill too much) and add a few drops of dye. You can then turn the tap on and off, starting and stopping the water flow, but you have to wait some time before the water changes colour. The wave, or the energy or motion of the particles travels quicker than the water. Another thing to explore is that the wave always takes the same amount of time (there will be small variations due to effects of elasticity of the hose, and this will be quite small unless you have a very very long hose), but the flow depends on pressure, (how open the tap is, or the height of the reservoir) Other things you can explore: Gravitational potential is analogous to electrical potential. If you do not use a hose, and let water fall (a hose can store energy in elastic potential) then the amount of work you can do is proportional to how far the water falls, it can spin things, or push someone over. You have to bear in mind that water can also store energy in its velocity. Depending on your budget you can explore analogies to other elements too. A T-junction in a hose with a balloon on it acts much like a grounded capacitor. you can put a tap on one end, a nozzle or constriction on the other end and show how the capacitor (balloon) stores charge (water) and energy (pressure/elastic potential). As I stated, energy can be stored in velocity. This is somewhat analogous to an inductor, more accurate would be a turbine with a flywheel (it will resist flow until velocity is gained, and resist reduction of flow until it slows down) Constrictions are analogous to resistors. Make sure you make it clear that water isn't exactly the same as electricity. For one electrons don't run out the end if you leave the plug on because they do not have enough energy to leave the metal. (some analogy could be drawn with surface tension, i guess) Also magnetic fields are an important aspect of electronics which is completely absent. Hope this helps. I guess I forgot the physics. Although others appeared to answer this adequately. To simplify slightly, the same thing keeping the electrons moving is keeping the water moving. As one electron is moved, the field around it exerts a force on the next electron, this one then accelerates until the field from the one after balances it out. Eventually (after a few milli or micro seconds) they are all moving and slightly closer together (well the ones before a resistance are closer than those after, but this is not necessary for the basic theory). If there is a switch, you can imagine the electrons are bunched up (at a higher voltage) ready to push on other electrons they encounter when the switch is closed. The same thing happens in the water. The electrons on one molecule get pushed close to those on another, etc etc. If we have a tap, the water is at a higher pressure (bunched up) so it comes out immediately. The main difference is that it's not just pressure (How much the water is pushed together) that stores/transmits the energy in the water, but velocity, height (gravitational potential) and so on.

One thing I have seen done which may help is welding a drive-shaft and second wheel to the rear sprocket, turning it into a trike. Big, low pressure tires help too (they can be un-suitable for motorcross as they corner abysmally). Something else that is useful in getting torque out of low-torque engine, is a robust clutch, (centrifugal clutches are often seen on farm bikes) or automatic transmission. All in all, there is probably a fairly good reason why tractors don't look much like motorbikes, it might be a fun project, but I do not think it will be cheaper than acquiring a tractor unless you are a fairly adept mechanic or engineer who does not factor their labour into the costs.

Inverse is the often used term. 7 and -7 are additive inverses. They add to give the identity 0. A slightly different version of your waves: A sine wave and one 180 degrees out are also additive inverses. They add to give the identity in their space (a 0 function) 5 and 0.2 are multiplicative inverses. I guess you could use the same word for a particle/antiparticle pair. I haven't seen it done very often. The particles are time-reversed counterparts (or compliments). So are a the rising and falling wave.

Well there could be other factors for its efficiency. Is it spinning at full speed when you do the weight experiment.The blades could be optimised to turn at a certain speed relative to wind speed. (There are many complex aerodynamical things that I would have to do a lot of reading to understand involved in a well designed wind turbine. As a simplified and slightly wrong explanation, you can think of the blades as wings, and spinning too slow as being a bit like a stall so they don't produce optimal lift.) I don't quite follow this. If it is charging a 12 volt battery then it is outputting over 12 volts, even a flat car battery is usually over 10V (under that and they tend not to work anymore). The current that most generators can output at given rpm is limited (think of it as internal resistance) and so the power you can draw from them will be maximised at a certain load resistance.

One sorely underestimated way of encouraging kids is letting them see you using it. Go build something that requires you to use Pythagoras. Play card games that involve maths. Start easy, blackjack, variants of memory where instead of making pairs you make a sum. As they get a little bit older try playing Mao (I'm not sure how well this would work with children as creating rules can be a bit subtle, maybe if they worked in teams with an adult). Use mathematical language in the house where you can. Use words from set theory or statistics when explaining things (this will also aid communication between adults, as nerdy as it is ). In response to talk of making a game of things, and of being too condescending. If you are genuinely interested in something and think it's neat then it shouldn't come off as condescending. Give them puzzles such as monty hall (playing cards with candy as a prize works great) or i have two coins, one of which is heads..... Don't explain the maths straight away, let them figure out the right strategy on their own, then explain the general concept, or refer to the previous puzzle.. Hell, design a boat. Rather than looking up some plans do a bit of reading, calculate some moments, tensions, strength of mast, for yourself. Kids naturally want to do whatever the adults are doing, even if they don't understand it initially. If you use a white board to do your calculations in front of them, they'll want to join in. Let them play just drawing random squiggles for a while, then maybe let them help with the arithmetic.

Biology isn't my strong point and I don't know all your jargon, so I'm going to have to make some assumptions. If any of these are wrong, then my explanation is probably wrong. 1) You've done some kind of test based on diffusion, treating/separating the DNA for some proteins and allowing them to diffuse through some paper/similar. The DNA for each protein stayed intact (but separate from other genes) by some process which is arcane to me. 2) You have data sheets for these MW marker genes (ie. they're known molecules). 3) Everything diffused in the same way for the same amount of time, molecule size. Very crudely the distance something will diffuse comes out as an exponential based on time multiplied by a coefficient including size which, most proteins being made out of the same stuff, will corellate to mass. So thickness of your splodge will be related to mass by an exponential [math]W\propto e^m\times \text{Other stuff}[/math] [math]\text{or }\\log(W)+C=m[/math] Where m is mass, w is the width of the splodge and C is an arbitrary constant. So you want to take the log of the band sizes and plot against mass of your known proteins the paper will take the log for you, so just fit them on a scale of 0 to 10 ie. 100=10, 4=0.4 Then you can draw a line and use it to estimate the mass of the unknown. This is a graphical method for linearizing your data and doing a linear regression (As DeltaScience was talking about). So it should achieve roughly the same result. However you will not have repeatable error bars etc. doing it graphically. I could be entirely wrong on one of my assumptions, but given that you were provided with log paper mass will probably go on one axis and size on the other. If the dots are not forming a straight line at all then I probably have it the wrong way around.

Why did I not assume this forum would accept TeX. Thanks for the revelation, no more ascii for meeee.

Well the easiest way to convert torque to energy is integrating over angle. As it's (close to) constant torque, just multiply torque by angular velocity to get power. Make sure you remember to use consistent units. F=force at point of contact 1.16N r=radius of point 0.21m w=angular velocity angular velocity is given in rpm 200revs/minute=200*revs/min*(2*pi rad/(1 rev))*(1min/(60sec))=3.33*2pi rad/sec T=torque r*F=0.24Nm P=T*w = approx 5W Assuming all your numbers are correct and I haven't had a brainfart. Remember this would be at the shaft, your generator and transmission losses would have to come out of that. Also you could just use the energy you are putting into the weight you are lifting. Gravitational potential is mgh, so assuming you pick a weight that is the heaviest weight which will not slow your turbine, time it then power is mhg/t

Well, yes, until your capacitor got charged, then the voltage would become prohibitive or your dielectric would break down. AC would not work as you would constantly reverse your changes.

Because that's how we define mathematics. Any formal explicitly defined statements or inferences made using rules are mathematics.

I think mathematics is more than this. I think mathematics is the name that we give to all systems of rules and interactions of patterns. Whether we invent, or reverse engineer, a system of rules it is still mathematics, and if we find the rules by which something behaves we will put that with all of the other mathematics. Even if those rules were not bound by classical logic. So I think instead of mathematics being useful for describing nature, things useful for describing nature are mathematics. Were nature to follow any sort of rule, if we were to find it we would call it mathematics. As to it being an incomplete representation of the universe. We find an x that has the same properties as the object in question for the scope of our interest, but x is not the object. I have some incomplete thought linking back to representations but I'm not quite sure where I'm going here. Coming back to the topic The final question is, why rules at all? Well that's a little harder. Maybe the anthropic principle? Without rules there could be no reasoning beings. This seems a little weak and I think there is more here. Hummmm

Try the chat room (be a little patient, nothing more frustrating then coming back after 15 mins, starting to answer a question then seeing the person leave). Failing that there are some quick questions threads around.

As md said. It's defined. It is more sensible to ask why things happen at the rate they do given how big they are, (which I cannot answer). Maybe if things were bigger, we'd just consider that small and be in the same position. What I find more puzzling are the fundamental constants such as the Fine structure constant. These don't have units and so cannot be defined, but they also have very specific numerical values as far as any testable theory goes. As to why there is a limit, it's a bit like asking why do things fall. We know fairly precisely how they fall, and what is correlated to falling, but why? Physics isn't up to that yet. Even when it is, we will merely be putting two previously separate whys into the same why. The only semblance of an answer would still be well within the realm of philosophy.

Well there are some scifi drives that would do better than that. To find the absolute best case scenario lets assume we have infinite access to technology, but have to stay within the laws of physics where we know we would violate them. The most efficient drive possible (I have no idea how one would make it or attach it to a ship) with known physics is a small black hole. This is placed at the focal point of a parabolic reflector and fed matter. The hawking radiation is mostly low enough frequency that it can be reflected and you get between 50 and 100% efficiency. You can cheat again, by putting your fuel on a platform, and aiming the 'thrust' (light beam) at your ship's solar sail. That way red shift is not as much of an issue. Then your equation would be between: gMv=pmc where g is gamma and p is the efficiency, m is mass of fuel, M is payload, v is change in velocity and c is speed of light. and gMv=2pmc The 2 coming from the reflection of the solar sail. I cannot be bothered doing the integral right now, so lets just assume your ship absorbs all the light rather than reflecting it. gMv=pmc Or as a percentage of c 1/sqrt(1+(1/p*M/m)^2)=v Putting in, say, a 1,000,000 tonnes of fuel, with 1 tonne payload we get: 0.999999999998 Or gamma=500,000 So Stopping, or turning around would be out of the question, as the rocketeers (or rocketeer with such a small craft) would only be able to accelerate away from earth (or up to a 90 degree angle very slowly if they had a reflective sail). If they somehow managed to stop they would find only one second had elapsed on their ship for ever 5.8 days back on earth. Double your mass in fuel would get you to roughly half the speed of light. Of course, as soon as you start making any reasonable assumptions for the type of things we could engineer, things get a lot worse (See Janus' comment). This is just the upper bound for what might be possible.

Also, when you are walking, the contact friction with the ground points towards the direction of travel (which is rather counter-intuitive). As you push your foot back, the reaction (friction) propels you forward. Losses are mostly from other sources, the energy lost in converting from chemical to work. You put a little bit of energy into lifting yourself up each step, this is mostly lost as your tendons do not absorb very much. The kinetic energy of your foot is also lost as you put it down. Your muscles, impact with the ground, and some friction (this time pointing backwards) absorb that energy. Another inefficiency of human motion is our muscles do not work like, for example, an electric motor. To resist or slow a motion we have to put more energy in (rather than storing some of it) so we get a net loss both ways. As Mr Skeptic said, walking in the snow is more difficult because you spend energy compressing it, or you can think of this as the energy required to lift yourself back up to a comfortable height after sinking a little bit each step. You also walk less efficiently, your legs will not be in their optimal configuration, so less energy will be stored in tendons and muscles will not be working at optimum efficiency. You may also have to hold yourself in a position where muscles are taking your weight. This takes energy too. All in all, it's an extremely complex calculation. It could potentially be modelled in full, but usually the best way for a problem such as this is to study it empirically. You simply take measurements of someone's energy use (measured by heart rate, or CO2 exhaled or similar) in different situations and make some graphs.

Ooooh! I know! An array of really really big mirrors. Put them 100 lightyears away, and fire giant lasers at them so they play videos describing important knowledge (like how to read) in a loop. On a more serious note, the main problem lies in making your medium of storage not worth looting/burning etc. If stones are quarried people will build something out of them. In that case it seems metal is right out, it'll always be useful. Paper isn't durable enough, and can be burned. Glass...hmmm Glass is non-reactive, worthless if you crush/rearrange it, and not shiny enough that people will smash it for jewellery. The only problem I foresee is people polishing the writing off of it to use it as windows. Perhaps the information could be impregnated deeper than the surface? (Ie. 2 layers with the inner edge etched, then welded, I'm sure a process exists which would maintain the information.) A second option would be a series of tunnels with information carved into the walls. It could be placed somewhere that would not be likely to become strategic in military conflict, away from valuable resources. With the right placement, it could be both not worth attacking, and difficult for attackers to take. Modelled after the possibly apocryphal monasteries in Asia/Tibet. Taking that idea about jewellery, and my previous thought about coins leads to a thought. Synthetic gemstones with holograms imprinted would be a possible storage medium. People would covet them, but be unlikely to do anything destructive. This would increase the likelihood that their locations are known and that they are intact when someone learns their true nature. In terms of learning how to read, I suppose this could be part of the larger scale base information.

Well requiring there to be no reactants kinda puts a damper on any form of chemical reaction. Also studying physics I tend to look at every problem as needing some sort of electromagnetic field or quantum transition. When all you have is a particle accelerator everything starts to look like it needs something smashed into it at 0.9999c

Well something that would be a bit more plausible (and has bonus ick factor to boot) is a genetically modified parasite. There are numerous examples of everything from single celled creatures, to fungi, to invertebrates inducing their hosts to perform unusual actions (look up liver flukes for a good place to start, they're not the most interesting but it is the only name I recall off hand). The nervous systems controlled are usually very simple, but we can take liberties in a scifi. The most complex behaviours I can think of are spiders spinning a specialised web for the parasite after it hatches, and caterpillars guarding the parasite after it leaves the host, while it pupates. If one had the precise control over a genome required to get specific responses out of a human brain, then I do not see getting the parasite to develop an antenna being a problem. In terms of what such a parasite could achieve I suppose it would depend on how advanced the civilisation is. Things that I see as being possible with technology not exceeding today's by very far would be: Giving the host an overpowering urge to move (go forward/left etc); Turning them violent; Making them much more likely to trust whoever they were talking to; Altering emotions in general, but not very precisely (ie. causing them to hate someone by altering emotions whenever they are present); Training/programming behaviour or altering beliefs (ie. altering neurotransmitters to produce a Pavlovian response, or putting them in a receptive frame of mind} Causing specific hallucinations, visual hallucinations would not be easy to interpret without training (or further knowledge). Slightly more advanced but still plausible some time later this century: Direct control of body (probably quite clumsy); Determining in a general sense what they are thinking about; Altering thoughts and emotions on a finer scale, such as making them hungry when the topic of thought is cars (both of these would probably require extensive (years of?) observation, data, and fine tuning by an operator); I do not see reading or setting a specific thought as being anywhere near the same scale of technology (ie. kill john smith using the rifle hidden in the basement on december 14th). If the technology in the setting is advanced enough to have had strong AI for a few decades (post singularity type setting) then I suppose any type of control is possible. Nanobots would probably be about as likely as a biological agent (although whether there would be a distinction is unclear). One thought that comes to mind is Toxoplasmosis. It is a parasite that breeds in the gut of cats. Infected mice will be less fearful of cats, and ignore cat urine to a large extent. There has been some research indicating that humans infected with it will be more prone to take risks. Incubation time or remote activation could be induced in a number of ways. Air or water borne drugs seem to be the simplest.