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so a photon goes at the speed of light, but does anything that goes at the speed of light have to be a photon? could you have some other object which has the property it goes at/faster than light, has no mass but isn't the usual EM field oscillations that make up light?

by asking the question 'what is space' you're really asking 'is there some classical object for which space is analogous to' and so you will never find a satisfactory answer, because an object lies within a space, but it cannot be a space itself, there's a fundamental distinction. you cannot say a tennis ball is like space in any way, same as you can't a cloud, a tank of water, a gas molecule, a quark, a galaxy, etc... you cannot make a satisfactory definition of space in terms of every day physical interactions existing inside space, because there you're defining something happening inside the space and not the space itself. the best you could try and do is to say that a space is a collection of points related mathematically by some function expressing (and also representing) the distance between any 2 points as a real, positive number (this number, although would be describing the distance, would only make conceptual sense to a being trapped within laws of physics where the word 'distance' means something conceptual to them, we are such beings). here a point could be defined as a mathematical entity who's numerical value is determined by the distance function in terms of the distance to other points. there is no absolute point from which you can call an origin.

wow, if hes found some way around the problem i'd be glad to hear it o.o but yeah i don't expect it to enable like.. malleable consciousness any time soon. though wouldn't it be cool if we could make our brains superpowerful and things

so in that sense, there isn't just one 'algebra' there are like.. algebras, each with different properties, and a commutative one is a particular algebra? @nicolas i guess I should, from what I've heard he's attacking the problem of consciousness from a physical point of view, and i have some doubts this would ever work, since i don't see how matter could become conscious through physical processes

sorry that i don't have the time to explain why but, i believe you're a little crazy and you aren't willing to try to see it

i can't help but be somewhat biased when i watch these rap battles, i always automatically say that the person who did the most for science wins, and although i think bill nye and neil degrasse tyson have done a great deal of inspiring and work in their fields i doubt any human can claim to have done as much for science as newton (perhaps some of the other greats, like einstein, feynmann, etc), so im just like 'newton every time maaaan'

@nicolas consciousness i think will always be the hardest mystery to solve, i'm not convinced it can be solved but .. well maybe somebody will find a way eventually @ajb im a first year student in a theorist's degree, the most maths i've learned so far is calculus 3, a little set theory/group theory, some complex numbers, so anything in diff-geo, manifolds, functional analysis all seems pretty far off to me. i mean whats a commutative algebra anyway? also topology looks really hard.. are all these subjects the kind of thing where it seems hard at first and then once you've got the hang of it you can do them in your sleep? (they certainly look way harder than anything i've learned in calculus) @zvb aren't you basically just saying that its logical to assume a theory of quantum gravity, or something more fundamental, exists? (one set of laws that apply at all distance scales)

@swans aha fair enough, I thought this seems too obvious to not already be thought of and being worked on @ajb thanks for the link but I took one look at it and realised this is way beyond me at the moment hehe. looks like some knowledge of topology is needed, or perhaps one of these weirder areas of geometry. I'm still someway through getting the hang of set theory and basic group theory so thats a long way off. @nicolas I .. half agree .. but I doubt that applies on all scales. what about if you compared the 'fuzziness' in a solar system with the 'fuzziness' in a galaxy? You could say the galaxy is much more complex and disordered than a solar system with just a star and a few planets, so in this case, in some sense, the 'fuzziness' has increased with zooming out. but i see what you're getting at xD As for whether the key lies between GR and QM, I think its enjoyable to consider what happens between these two boundaries. imagine what weird physics could explain such a contemplated mystery o.o I mean what if it is something like string theory that, say hypothetically, cannot be experimentally tested by any being in our situation? I guess then it'd forever remain an idea and never be that useful .. would be something of a shame, imo, if the answer to such a mystery doesn't open new roads into engineering or practical areas of science. I like when something seemingly useless allows you to build something really new/futuristic/useful.

ahh its gotta be newton imo

This is just a vague speculation but .. well I wanted to see if a similar idea has already been thought of and tested and failed by professional physicists. With unifying quantum mechanics and relativity, I've heard the problem comes from trying to combine a smooth spacetime 'sheet' with a fuzzy, uncertain quantum mechanical mess. What if general relativity is only an approximation to actual spacetime, and the fundamental description of spacetime is quantum mechanical. So what I'm saying is that... could spacetime really be fuzzy and uncertain like QM says, but just appear smooth on large distance scales? (enough so that the calculations would work fine unless you go to like a singularity)

sorry for not replying sooner, I'm still thinking about what you guys have said (will make a better reply soon)

What I'm asking isn't the cosmological question of what is expanding space, its asking how a 3D space can, itself, expand. trust me i've heard the usually cosmological stuff about the energy densities and the friedmann equation and things before, i'm just struggling conceptually to understand what it really means for space to expand. I understand how an object with volume can expand so that it occupies a larger volume of space, but how can space expand so that it occupies a larger volume of space? I don't' see how the idea makes any sense. @strange, if what i mentioned there is true, then isn't just our coordinate system that's expanding and not space itself? I mean say from hubble's law the expansion of the universe can be deduced, but can't the idea of galaxies moving away from each other in a non-expanding space also be deduced?

I've looked in a lot of places for a clearer explanation of the expansion of space but either I get psuedoscience or the typical balloon analogy, so i'm hoping somebody here is more used to this concept. I'm stuck with how space can expand. Like say I have a 3 dimensional space and attach a coordinate system to it, sure I can make the coordinate system larger or smaller, but how does that mean the space itself is smaller or larger? In my cosmology class we've done the scale factor and co-moving distance thing, where r(t)=a(t)x, where a is the scale factor and d is the co-moving distance, and this just flummoxes me, conceptually, completely. I'd be very happy if somebody could clarify this mess of ideas in my head.

I've never experienced myself but i assume it's one of these placebo like things, where people think something weird and wonderful happens if they sit in a certain position, with their fingers making like a circle shape, and try to meditate. tbh it's probably just them relaxing and feeling peaceful, therefore getting this idea that something spiritual is going on. but for all i know they could be in some other state of mind i've yet to comprehend. i don't feel any need to comprehend it if it exists anyway.

sorry if this sounds offensive but the first few paragraphs simply do not make sense at all (at least to me) as for the spiral idea, sure the spiral can cover all the area in a circle but then the length along the spiral tends towards infinity (you're coiling it around more and more times to make it cover more and more area, so it gets longer and longer)

what about if division is really a bunch of separate operators that give the same result when used on real or complex numbers in general, apart from 0. what i mean by that is like... one way of looking at division is the idea with the cake where you try to distribute pieces of a cake between people and situations like that. there the idea of dividing 1 cake into 0 parts is undefined. but suppose there's some other way of looking at division which isn't really division at all, like the limit of 1/x as x goes to 0 from either the positive or the negative direction. what if doing this is like doing a different type of division, which instead of just two numbers, would have arguments of two numbers and a sign (the direction which you approach 0 from). the answer to this type of division would be infinity or -infinity depending on the direction you approach 0 from. because if this was another division it'd look like the normal division when you use it on a non-divide-by-zero situation. like if you did the limit of 1/x as x goes to 2, you'd get 1/2, which is the same as the answer you'd get using cake type of division. this type of division would also work for 0/0, 0^0, 1/infinity. i think it'd be good if that was a new operator just because then it sorta solves the mystery of 1/0=? --> 1=0 * ?, because that's a problem with the cake approach but you wouldn't be able to just multiply by by the x in the limit approach: ?=lim[x->0] 1/x ---///---> ? * x=lim[x->0] 1 so like if that's true and there are 2 division operators, what if there are more? or would this new type of division just be a generalization of the cake approach :S

thanks, hehe i'll try now to see if i can get any kind of coherent answer (will edit this post if i find anything cool) edit: btw i think that since quantum mechanics is an empirical thing, involving it in mathematics would mean that you get like a mathematical structure that only makes sense 'in' our universe but.. well if it exists might as well try finding it xD

if you count mathematical results as knowledge, then i think you can have an infinite amount of knowledge, because maths is pretty much endless as you can just think of another question to solve without limit.

this is gunna sound ridiculous but just for crazed speculation's sake, what if you divided the cake into arbitrarily small pieces such that they were subject to the laws of quantum mechanics, and if not observed directly, the pieces would be described by a wavefunction and so would have no distinct position, as the wavefunctions would all superpose on one another. could that be considered dividing something into 0 parts? xD (im not serious here hehe, im not even convinced that would be the right QM-ical description, but idk maybe if that's right then you could form like a particular branch of maths which deals with what'd happen if that was a valid way to divide something by 0 o.o)

thanks for the textbookslinks, someday i should sit down and get a good list going of all the things to buy in the coming years. (am still in first year of my degree, stuff is still kinda foggy atm xD). and yeah so far i've found formal education to be a lot more productive than all these other types of education on the internet and things. some of them are quite useful i think, like khanacademy, but they seem to be a little rare. on the other hand there's a lotta people who seem like wannabe physicists on the internet, this place luckily seems to have plenty of pro's, if you will.

these people scare me because they reinforce this most likely false idea in my head that i can sense when somebody's a crackpot (without being 100% sure) and i did with him and now i see he is one (thanks to you guys) so .. bleh.. sigh lol such a shame whenever i start trusting youtube i remember that there is this vast reservoir of misinformation and foolishness hiding everywhere...

well yeah i guess .. i just don't like the feeling of being misled by frauds (hard to tell if they are or aren't, especially since im not an expert in cmb stuff (at least not yet))

I found a video of one of the newer criticisms of the BICEP2 project and they sounded quite.. radical: https://www.youtube.com/watch?v=hC_KkLvG22A#t=855 the guy says that both gravitational waves and the CMB simply do not exist... im guessing a quack but im not sure :S

I'd say anything that has some astrophysics in it will be helpful, tv documentaries, textbooks, lectures, internet and perhaps other students in your classes. we're lucky to be in a time where knowledge is nicely available to most people, as opposed to the dark ages where books were probably the only proper resource. awesome that there exist lots of youngsters who are interested

sorry i cannot come close to answering your question, can i ask you how many years it took to get to the level where any of that makes sense? :S