Schrödinger's hat

Skeptic, it's not a missing 10^20 bits, it's a missing 10^20 times as much. If you extend the definition of write beyond what I had, photons would work reasonably well, but you'd have to have a high enough frequency so they didn't overlap (or be very very patient with your transmitter) Xitten, again, it depends on what you mean by write. There are probably more than a googolplex ways of rearranging even small systems if you use every single degree of freedom, but I interpreted using such a system as much the same as writing 10^10^100. I interpreted write as getting a thing we call a 1, and a thing we call a 0, then laying them out side by side. My idea of laying them out was predicated on them not flying of at the speed of light, but I suppose if you didn't mind that then photons are just dandy for the task, and radio-wave frequencies would probably give you the extra numbers you need with the mass available. Then it's just a matter of bandwidth, and how patient you are. I guess there would be entropy constraints too (you're getting a high entropy system -- the universe -- and putting it into a very low entropy state). My thought exercise was largely intended to portray the difficulty of writing such a thing, not theoretical impossibility.

I'm grasping at a way of explaining spin to myself, but I don't know the maths well enough to confirm or form this idea properly. I'll try to formulate a couple of questions that may help, maybe someone can answer. How does spin transform under Lorentz boost? I've seen it written as a vector or one form, but this is confusing to me, is there also a way to formulate it as a 2-form? Either way, how does it tranform? A lot of things that can be written as a vector in 3d are bivectors in 4d, so this set me thinking. Does a relativistic angular momentum 2-form of a spin-free object have magnitude? ie is its scalar product with itself 0?

My problem with rest mass for composite systems is where do you stop? You're going to have energy bound up in bonds of various kinds as well as thermal, pressure etc. You'd need to go to all the effort of figuring out how much that is (yes, I know it's usually <<1%, but it's the principle that irritates me) rather than weighing it. Most of the time, for a composite system we don't really have rest mass and energy. Instead we have some of the energy, and some more of the energy. To me this means that neither has any right to conceptual primacy. On the other hand, calling both of them mass is annoying to the highest degree as well. Maybe we need a new word for total energy when you put it in a box, and stop the box? Rest mass is often used for this, but then when you open the box and only photons fly out you suddenly have to rename it. </bugbear since 1st year when we were asked a question about mass after being told about relativistic mass, but before anyone had mentioned rest mass>

Most changes in an electric or magnetic field will cause an em wave which carries energy away. All changes will propagate at C, regardless of whether they cause a ripple which moves away from the object, carrying energy with it. If you have a charged particle moving at constant speed, or constant acceleration (or a magnet -- not 100% sure about accelerating magnets, can't see any logical reason why not. Moving ones are def. the same), it won't create a travelling wave, but if it changes acceleration, it will. These waves are more easily produced than gravity waves, and much easier to detect.

Your sentiment reflects what I understand to be that of the main thrust of quantum gravity and string theory research. It all gets very abstract before we even make it as far as the standard model/symmetry, we can build comforting stories and ontologies for everything up to QFT and GR (in fact, the story is a lot easier to understand than the theory), but eventually our analogies get stretched too fair. I feel the reason for this is twofold: We are starting to get to concepts that are very alien to our every day experience, and the language we use will be quite alien and seem very abstract as a result. These are the newest theories for the world, so we haven't had time to think of good stories (as relativity was a good story for the Lorentz transforms and the strangeness of Maxwell's equations) yet. Or find good ways of explaining the stories (most undergraduates today can understand the rockets-tied-by-string scenario, whereas it allegedly confounded a room full of researchers when first presented).

Well it's posted in psychology, so my guess is elaborate social experiment.

Well, there are some interactions between photons, they're very uncommon though. I'm not sure what level of explanation you're after, one thing that may help is the maxwell equation is linear (the equation for two photons is the same as the equation for 1 photon multiplied by 2 on both sides). Another way to put it is, particles with integer spin don't interact very often, this is related to the Pauli exclusion principle. This is the reason for the above point, but it gets more into the reasons behind the equations being the way they are. I'm not really very comfortable with this level of QM yet, so I'll leave it here. Maybe someone more familiar with the subject can help, if you're still having trouble.

Yes, even laser tweezers will tend to vaporise anything macroscopic before they push it around much, as you increase the momentum you're trying to impart, you vastly increase the amount of energy the object is increasing, and cube-squared will mean that energy dissipation will become an issue before very long. The maths these things are based on also tend to assume non-magnetic materials, there's also the difficulty of making exact -- or close to exact -- solutions for something as large and inhomogeneous as the moon so you know what type of beam geometry to use. This paper suggests that we can barely pull something of a specific size, with specific, homogeneous materials, as long as it doesn't absorb too much light (quite transparent), not a large hunk of rock. While I wouldn't rule it out, it's certainly out of the range of our current science, let alone our current engineering.

(the yes was a link if you didn't notice, but I suppose I was a bit curt) Well I guess it depends a bit on what you mean by speed of transition. Also it's not the frequency of the photon, but the range of frequencies, or the linewidth. If you have something like this: The position depends on the frequency, but some of the lines are fuzzier than others. It's a bit hard to distinguish from bloom in a photo, but if you get the chance to look through a good spectrometer it's easier to see. There's something called the time-energy uncertainty principle. [math] \Delta E\Delta t /geq \frac{\hbar}{2} [/math] (or sometimes h, depending on how many dimension you have) It follows naturally from the momentum-position uncertainty principle the second you think about relativity, but I think you can also derive it from non-relativistic models fairly easily, and I think it comes up if you apply some thermodynamics to the Schroedinger equation as well. Now I come to what do we mean by uncertainty in time? This was the source of a lot of argument, and you should read the wiki page for more info. Eventually the conclusion was reached that it is the uncertainty in the time the transition will happen, or how long the excited state lasts before decaying. This is what I took you to mean when you said it was the speed of the transition, but reading again, it may not have been (I'm not sure speed of transition is quite the right thing to ask of a quantum interaction, I certainly can't think of any way to gradually apply an operator).

I'm not talking about the history/real places upon which the myth is based.

Reading Genesis, the garden of Eden doesn't seem like a very nice place to me. Never changing, no challenges, nothing new or stimulating, not allowed to question anything or try anything, never dying. What use is free will if you can't exercise it? Does anyone really think living like that would be pleasant or have any meaning? This seems worse than the descriptions of hell I've seen. Discuss.

My thoughts were much along the same lines as those of Edtharan. Worshipping such a creature would be hell for me. Another point is that pain only bothers me because it is indicative of physical trauma or malfunction. It can be distracting and prevent thought if powerful enough, but who is to say I would not become accustomed to it and learn to function after a time? Or even that pain would have any relevance to a soul? I think that hell would be the least punishing of the two options, I would choose free will over whatever pleasures were offered for this reason alone. I think I would also choose it for the moral reasons alone, but it is hard to separate.

I, and a few other left handers I know have little difficulty writing mirrored with the left hand. For a while I found it both quicker and neater than writing forwards.

Umm, not really. Unless you mean using some kind of compression technique, then it'd be no different to writing 10^10^100Well, let's generalise the idea of 'write' to mean arranging some things which we will take as representations of 0s and 1s. Additionally, I shall take the mass of the observable universe as the largest semi-reasonable constraint on our ink-supply (more universe may become visible later, and expansion will put a lot of stuff out of our reach forever etc, but this the only reasonably upper bound I can think of) There's about 10^50 kg of mass we can observe (give or take a few orders of magnitude from error and whether or not you include dark energy/dark matter). There definitely won't be enough atoms to write it, photons will get away all the time, so I wouldn't really regard that as writing. So lets say we can convert the whole universe into positrons and electrons (I'm ignoring parity, colour and all sorts of other conserved quantities, but these would only put tighter constraints on it) mass of 10^-30 each This gives us 10^80 0s to work with. Still only about a billion trillionth of what we need to write down a googolplex. This is only approximate, and maybe you can eek out a few more orders of magnitude, but with any sensible definition of the term 'write in long form' the answer is no.

Lemur, your analogy works fairly well, up to a certain level, but thinking of heat as molecular motion is a concept that breaks down after a while. As do all analogies. You start to have to consider the change in the values of energy levels, versus the change in distribution of particles with respect to these energy levels. If you want to understand further you're going to have to study statistical mechanics and/or quantum physics for a while. Someone who has studied longer than I may be able to explain/translate these concepts better than I can, but there is always going to be a limit to what you can understand by going about it in this way.

Well, by time slowing down, we mean, 1 second in the car is a number of seconds outside. So it actually feels like you're going even faster (from your point of view you're going less far, everything in the direction you travel is shorter so it takes less time). If you travel at 0.866 times the speed of light, for 0.866 light years, people on earth will see it taking a year. For you it was only half as far, so it took you half a year. It's quite counter-intuitive to begin with. The problem is that not everyone's clock is measuring the same thing. If you think of someone with two rulers at right angles, they're measuring height and length, but then if you turn them height and length change. Time and distance work the same way. If you're moving compared to earth then your clock is measuring a little bit of what someone on earth would consider distance, your ruler measures a bit of time. To you, their clock would measure some distance, and their ruler would measure some time. You only agree if you combine the times and distances you measure together to get something called the interval between two events (a bit like how someone with the two rulers could measure the distance between two objects, then they'd stop disagreeing and arguing about how one event was above the other in one frame, and beside the other in the other frame, they'd both agree that they were one metre apart). With regards to earth, we don't feel it move because we're moving with it. It's making really huge circles, and takes a while to do it, so the Coriolis effect won't make you feel dizzy or like you're spinning. You can 'feel' the spin indirectly by doing an experiment, a really big, symmetric pool of water will spin if you let the plug out -- a lot of the twist of the vortices we see in baths etc is due to hydrodynamics and chaos (sometimes it'll even go the wrong way). The acceleration also alters how much force things exert on the ground. Local 'gravity' (this includes centrifugal acceleration) varies from the equator to the poles. None of this has very much to do with relativity. Time in orbit around the sun, and on Earth's surface does travel a little differently, but at these speeds it's only a minute amount. I read a neat result somewhere saying the General Relativistic corrections and the special relativistic corrections on earth's surface almost completely cancelled out, but I can't remember the source.

Of course philosophers are useless! I said philosophy, not philosophers. I agree that the science and maths should lead the way, but sometimes we should sit and ponder afterwards. Make up stories to help teach it to others and make it more understandable. There's something both comforting and helpful to the intuition about having ontological objects to work with. Be they little ball-like particles, wiggling electrons, or universe-permeating fields. Maybe even break down some concepts, find a little crack that we can wedge open with more maths and experiment. I guess that in many ways, this is indistinguishable from doing more physics. It's certainly not the thing that philosophers do (for the most part). I used the word because I wanted to distinguish between These two things: Breaking down or creating new assumptions and predicates. Along with finding new representations, stories and ontologies for theories which do not add any predictive power, merely make them easier to use. I call this philosophy for want of a better word. The kind of philosophy done by someone who is very familiar with physics. and Finding new mathematical objects, making new assumptions, combining predicates and assumptions, making predictions and doing experiments. I call this science. I'm not quite sure where to put the making new assumptions part, it fits in both to a degree, although better in the latter. Perhaps this is why we shouldn't draw these sharp distinctions and accept that there is a continuum.

Poor coldize, noone wants to answer you because it's ages since we've done any discrete and remembering how to do it takes effort. Perhaps you can appease our laziness a bit and use the left square bracket math right square bracket tag to rewrite your working with the forum's LaTeX embedding (there's a tutorial around somewhere too, use the search function)? On that note, sleepy time. May be able to summon the effort when I get up. (Alright, I gave in and played with it for a tiny while) Simplest (not shortest) way I can think of it is to just show directly that if a is not congruent to 2 mod 5 then a^2 is not congruent to 4 mod 5 There are only four cases to go through and you're done. (either that or you've disproven it) too brain-fried to go for anything shorter atm Edit: There's a trivial counter-example. try some single digit integers.

Nope, if you build a machine that does a quantum experiment and reacts based on the answers by throwing a ball at your head, classical mechanics will not help you /facetious

You're only constraining it's horizontal position, and thus unconstraining it's horizontal momentum. 3 degrees of freedom, x, y, z are independant. That includes the uncertainty principle as it applies individually to each (and to time, just the same) EM theory is almost identical to quantum theory for this situation (Spin-1 wave equation is just maxwell's equation with a mass term). Quantum versions of measurement, and interaction terms are left out in this regard, but the classical EM wave equations describe this effect perfectly adequately. Look up Fourier transforms and how they relate to EM. As to why the Fourier transform rocks up to the party whenever you try and do anything, this is a mystery. I didn't send invitations to e, pi, or i either, but they're off in the back room doing something unwholesome.

Most complex systems are chaotic to some degree. If you redistributed the center of mass (or even made motions that moved a large cluster of stars), then it was ejected during one interaction it could later nudge a galaxy into a slightly different course, and so on. But remember, we have to think of the scale of these things, individual stars to a galaxies are like raindrops falling on a mountain range, so many and so tiny that you'd have to wait a very very long time for any fluctuations to add up. And hope that the alterations you made were not too far into the stable solutions and negative feedback loops. Also, it would depend on how early you made the changes. If galaxies were still forming you'd be able to alter a lot. Now, not as easily

I'm not really sure what you're getting at. If you want me to respond you'll have to elaborate/clarify a bit.

Agreed, DrRocket. I'd also assumed this thread was in philosophy without looking. Could it be moved? I think this is more of a philosophical question than physical. I don't think philosophy is worthless regarding these questions, sometimes it provides useful insights. It's a good idea to stop the science every now and again, look at the fundamentals and see if you can make progress in this regard. In the same way, philosophising for too long is useful without spending a while on the science.

Yes, scientists usually use a pragmatic definition for these things. When someone asks 'what is ____' about something we can't conceptually break down any further, we point to one. You're either getting into the realm of symmetry/standard model where things get real strange and the 'shut up and calculate' mindset is common (I think following that road won't give you the type of answer you're looking for, either), or into the realm of philosophy. There's a topic on this already, join in http://www.scienceforums.net/topic/55326-what-do-we-men-by-space/page__p__593259__fromsearch__1#entry593259

Yes As this looks a bit like a homework question, I'll let you do a bit of reading and come back when you have trouble.