5 ms·
Things I know are true, but I don't really believe
- deleted 18y ago[deleted]
- michael_dorfman 18y agoI was skeptical clicking on the link, but it actually lived up to the title.
- 3pt14159 18y agoI was about to write the same thing
- Herring 18y agoIt should probably have been "Stuff i've been told is true but I don't entirely understand"
- ivankirigin 18y agoMost physics professors I've spoken to don't actually understand things like quantum entanglement. They just say "the math works. that is all." There is no intuitive understanding of a subject like that because neither 100K years of evolution of our brain now decades of real world experience expose us to it.
- Herring 18y agoSeemed more than just lacking intuitive explanations. In entanglement for example, the answer is because it can't transfer information & you learn that just fine in any intro to quantum class.
- timcederman 18y agoThank you. This is also the reason why faster than light 'travel' can occur, if it doesn't transmit information. Entanglement is slightly mysterious though as what is the physical mechanism behind it?
- yummyfajitas 18y agoThe physical mechanism is that quantum mechanics governs a probability distribution (the "wave" in "wave-particle duality") on configuration space, not "physical" space. Imagine you have two particles in 1 space dimension. The first particle has a position x (1 real number), the second particle has a position y (1 real number). "Physical space" would be the set of real numbers (R^1), while configuration space is the set of pairs of real numbers (x,y) (this set is R^2). The first number in the pair represents the position of particle 1, the second the position of particle 2. An entangled state is simply a probability distribution on R^2 which is not a product state (i.e. P(x,y) != P_1(x) P_2(y)). This means that knowledge of the position of particle 1 gives you (possibly incomplete) information about the position of particle 2. One example of this is "probability 1/2 that x=0, y=0, 1/2 that x=1, y=1". The minute you know x, you know y. That's what entanglement is. What makes it weird is the idea that "knowing x" (measuring it) changes things. An explanation of this is trickier. Still understandable in principle (not just 'follow the math'), but too long for this post.
- ericb 18y ago>> too long for this post. How about another post, then? :-)
- deleted 18y ago[deleted]
- DaniFong 18y agoIt's not exactly covered convincingly though. The reason it supposedly can't transfer information is because you'd have to measure it, and we assume that measurement strictly follows Born's rules, which is a whole other can of worms. Sometimes people talk about density matrices instead, but we only use those since they are consistent with Born's rules. Additionally, many physicists point out that what you seem to be doing when you perform a measurement is entangling the system with the many bazillion degrees of freedom in the measurement apparatus and the world at large. We don't know, exactly, where the separation between a 'measurement-like' physical process occurs, or even if there really is one. There isn't even a standard measure of entanglement for three or more particles. It's a pretty big mystery, still.
- Herring 18y agoer, ok then i'll rephrase - "we're mostly sure it can't transfer.." or "we've never been able to get it to" I doubt the writer meant it the same way you do. He was talking about the known things that hes not wrapped his mind around. In this case, explaining why the theories don't necessarily conflict should do.
- DaniFong 18y agoA few of the professors I've spoken to aren't even sure the math works.
- jmtame 18y agoError: unavailable?
- ivankirigin 18y agojust spotty
- pchristensen 18y agohttp://abstrusegoose.com/64 http://abstrusegoose.com/64
- noonespecial 18y agoYeah, I don't believe they give those people honey roasted peanuts while they ride in those metal tubes either.
- tdavis 18y agoDon't believe it. They're usually pretzels now. Too many people allergic to peanuts.
- tptacek 18y agoXKCD used to be this engaging, before it devolved into in-jokes and IRC memes.
- hugh 18y agoA late entry: the Banach-Tarski theorem: http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
- nickb 18y agoAhhh... you just caused a major flashback in my memory. I remember reading about Banach-Tarski paradox about 7 years ago or so and it gave me so many headaches. I think I read the paper explaining it trice and it still made no sense to me and on my second reading I was convinced there was an error in an equation somewhere.. I asked a math prof who's a brilliant theoretician and he explained it to me and it still made little sense. Then I read von Neumann's explanation and it finally started making some sense. The key to understanding it is, like with many other concepts, to ignore your intuition and trust the math behind it.
- andreyf 18y agoFor me, the key to understanding was to realize that reality is only a figment of your imagination ;) On a more serious note, it was understanding the Axiom of Choice, or that our "intuitive" notions of reality aren't really consistent with themselves: http://en.wikipedia.org/wiki/Nonmeasurable_set http://en.wikipedia.org/wiki/Nonmeasurable_set
- DaniFong 18y agoI personally thought that the Banach-Tarski theorem was a mess, and these non-measurable sets had to go. So I started studying nonstandard-analysis: analysis with infinities and infinitesimals as genuine, arithmetically viable, quantities. Imagine my distress: the same problem occurs, Banach-Tarski still holds, unless you go into the rather more weird, Smooth Infinitesimal Analysis or Synthetic Differential Geometry; basically, treating geometry as made up of little discrete infinitesimally small points.
- yummyfajitas 18y agoI'd say trust your intuition more than the math, but I'm more physicist than mathematician. To prove Banach-Tarski, you need to assume Zermelo-Frankel set theory (just ordinary set theory) plus the uncountable axiom of choice. In my view, this means the uncountable axiom of choice is false. This actually breaks far less than you would expect. For most practical purposes, you only need the countable axiom of choice, which is the intuitively reasonable version. The main thing the loss of the uncountable version breaks is the Hahn-Banach theorem on spaces of dimension higher than countable infinity. This in turn breaks quantum field theory on free space (not in a box), but that's broken anyway.
- tocomment 18y agoWhat's the well ordered one about?
- newt0311 18y agoA well ordering is just some way of ordering a set made formal. Basically, if you have a set, you can find a relation such that any subset will have a least element. I should also point out that the example given of a set that is not well-ordered is wrong. The proof was found to be erroneous.
- andreyf 18y agoA better example is the well-ordering of the reals. From wikipedia: From the [axioms of math] one can show that there is a well-order of the reals; it is also possible to show that [those axioms] alone are not sufficient to prove the existence of a definable (by a formula) well-order of the reals. http://en.wikipedia.org/wiki/Well-order http://en.wikipedia.org/wiki/Well-order So you can prove that set of real numbers can be well-ordered, but you can also prove that an order cannot be defined. Kind of how God exists, but cannot be perceived or comprehended ;) (or maybe not)
- apmee 18y agoThe Nonexistence one is what often gets me. If and when I ever give it more than a passing moment's thought, I have to take care lest it put me into an unsettling trance-like state of bewildered and bemused incomprehension and planar disorientation. Saves money on jazzy cigarettes let me tells you.
- paulgb 18y agoI can relate to that. I used to feel a bit of a high when I was a young kid just trying to contemplate what would exist if nothing existed. Not nothing as in no matter, but no dimensions or time either. Thinking about that still puts my mind into a weird state.
- apmee 18y agoSome people, including (I suspect) most theists, seem terrified by this, whereas I find it exhilarating and immensely humbling. Funnily enough, it was actually while I was sat in church with my family when I was younger (I've since lapsed profoundly and comprehensively, of course) that my mind first began to wander to and wrestle with such concepts.
- jodrellblank 18y agoThe scale one gets me whenever think of it. Reading Clarke and imagining being in a spaceship in orbit around Jupiter and seeing it dominate the exterior view. Trying to imagine a ball of fire as big as the Sun. Seeing the solar giants in images like these: http://www.rense.com/general72/size.htm http://www.rense.com/general72/size.htm or videos like this: http://sciencehack.com/videos/view/_WEL117xXpw http://sciencehack.com/videos/view/_WEL117xXpw Antares is huge, lol. Well, not lol, more ... scared. Hubble Deep Field. It's awesome in the literal sense of awesome.
- hsmyers 18y agoElves, definitely elves.
- marketer 18y agoWeird.. I submitted this link a day ago (with the same url) and the dupe detection wasn't hit. http://news.ycombinator.com/item?id=351975 http://news.ycombinator.com/item?id=351975
- bsaunder 18y agoCellular Automata ( http://en.wikipedia.org/wiki/Cellular_automata http://en.wikipedia.org/wiki/Cellular_automata ) Particularly rules 110 and 30