For those not familiar with RobotRollCall (the author of the linked comment) check out his profile and other answers. He is one of the best contributors to AskScience and can explain almost any theoretical physics topic in understandable terms. People joke that he is actually Neil deGrasse Tyson and that he should really get this own column / talk show.
Meta-comment: I often see the above pattern on HN. Someone writes a very informative comment with a minor inaccuracy. Someone replies to it only to correct that inaccuracy. The reply then gets way more upvotes than the original comment.
I don't particularly care about "karma", so what bothers me is not that the original commenter didn't get enough points, but rather what people in the community think it's important in a conversation.
I think the point that it was a she and not he is particularly important. I also think the point that the original commenter missed this point is particularly important. Knowing the HN community, that is the reason why the comment got voted up.
It shouldn't be relevant but given the state of female involvement in many traditionally male fields it is always important to highlight women making a contribution. The idea is it will both change perceptions without and within the field and attract more women.
What it really highlights is how English desperately lacks a gender independent way of saying he/she. I can't tell if you are a guy or girl based on your name, I bet most people don't know if the K in my name is Kevin, Kyle, Kris (guy or girl!), Kathy, Katrina etc. (for the record, it's Kevin). But most people when talking about me will just assume I'm a guy and use he.
I'm not offended by people incorrectly using gender pronouns, it is just really awkward to write something without knowing the gender of the person you are talking about.
No, we have two. A kludge: "he/she" (which I personally despise and refuse to use), and something which people have used for a long time, but educational-America refuses to accept: "they".
>The singular "they" is widely used and accepted in Britain, Australia, and North America in conversation and, often, in at least informal writing as well. It is important to note that this is not recognized by the SATs and other standardized tests.
It's also less efficient for anyone who's listening to you. Gender-specific pronouns help ensure you're talking about the same person. Personally though, I find myself saying "that's what they said" (or similar, in a non-joke-related context) pretty often. Usually past-tense, for some reason. * shrug * to each their own.
I do boggle that "they" isn't technically acceptable for cases where gender isn't known, though. "He/she" seems like insanity, both in writing and in speaking, when "they" sits there waiting to be used. It's extremely rare that context isn't sufficient to determine if it's plural or not. Heck, Japanese essentially does without plurals entirely, and that's a functioning language.
It may not be important by itself, but it is important to be right. Her nationality may also not be relevant but if someone writes that she is Chinese and she is actually Russian (example), it is important that it gets corrected.
Fortunately this is not a common scenario, because the nature of the English language doesn't make it easy to inadvertently imply that someone is Chinese, Russian, or indeed any nationality at all.
(I am aware that singular 'they' is grammatical. Doesn't stop it from sounding really awkward when the referent is a specific individual.)
Or, maybe just maybe, the community is signalling that it appreciates members making the effort to correct errors. For the life of me, I can't think why you would have a problem with that.
Often it isn't even that. It is just that someone has made a generalization, and there is an obvious exception that everyone knows about and normal people would just take as given, and then someone writes a one line 'toss off' reply, and rakes in the free karma. This is the utmost BS.
Giving someone that puts thought, time and effort into a response a tiny bit of karma - and then having the 'correction' which involves neither time, nor effort, nor thought 10x the amount of karma indicates a couple of things:
(1) Hacker News will rapidly descend into one line reply chaos where it is nigh impossible to have an interesting discussion
(2) Hacker news does not value time effort and thought
(3) Hacker news greatly rewards the absence of time, effort and thought
How can any of those be good? (#2) is the antithesis of reasoned debate, (#3) is actively rewarding anti-intellectualism. (#1) indicates that HN is either just a poorly implemented version of Slashdot (which would be sad) or it is going to descend into diggery (which is horrifying).
Put some thought into it and you might see why we have a problem with that.
I regret that my comment came off as being snippy -- indeed I was in a hurry to get to my sleep and chose not to remark on additional things.
> [...] and then someone writes a one line 'toss off' reply, and rakes in the free karma. This is the utmost BS.
I should hope that the HN community doesn't impulsively ascribe so much value and pride into winning some system of karmic points. I don't. I think it's a non-issue. And because of the HN interface being so sleek and minimal, we can at least afford to have a few one-liners here and there without wasting a significant amount of screen space.
Lastly, I would like to point out that my comment at least was not a derisive or snide one but one of an observation/correction which I thought was worth the trouble pointing out.
But, again, I do regret not supplementing my comment with more substance.
Since it was my meta-comment that spawned this sub-thread, I'd like to clarify that I don't think your comment was derisive or snide or bad. My point was that the original comment was more informative than your reply, and at that point your reply was more upvoted than the original comment.
Whilst your three points would indeed be bad, they really don't seem to be born out by reality - this is not what we see happening on HN. Slashdot style one-liners are not common, and generally speaking fare poorly in the karma stakes.
You also seem to be labouring under the misconception that the quality of a reply is proportional to its length. However, a short, pithy remark that cuts to the heart of an issue is far more valuable than a long-winded argument that makes the same point.
There's no reverse sexism at play here, just good old fashioned regular sexism, where a commenter assumed that the author of something insightful was a man.
This attitude (and your response to it) goes a long way to explaining why computerland is such a sausage party.
> If you were reading a relationship advice column, you'd assume it was written by a woman. That's not sexism.
Um... in what way is it not a sexist assumption?
> I really wish this ridiculous and unhelpful "There's no women in tech because of evil men" meme would die.
Evil? No. Sexist: a thousand times yes. The culture of technology, and especially startups, is quite frankly vile in this regard.
Is it the sole cause of "no women in tech"? Almost certainly not -- but I find the rampant sexism plenty objectionable in its own right, regardless of (speculated) effects on diversity.
> Um... in what way is it not a sexist assumption?
Because it's statistics. 99%+ of relationship advice columns are by females.
Is it sexist to give women lower rates for car insurance? Is it sexist to give men different rates for life insurance? I would say absolutely not. Women are safer in cars, and men die younger. Those are facts. (FWIW The interfering EU are due to vote on 'sexism' within insurance shortly)
It doesn't matter whether something is 51-49% or 90-10%. There is no excuse for allowing 'statistical' assumptions to translate into a burden or punishment upon the minority.
(If a culture or community does allow this to happen, then any slight tendencies will be artificially magnified and reinforced into an unnaturally lopsided distribution.)
Side notes: I put 'statistical' in scare quotes above, as it's all to easy to pull self-justifying statistics out of your ass, as you did.
> There's no reverse sexism at play here, just good old
> fashioned regular sexism, where a commenter assumed that
> the author of something insightful was a man.
No sexism there. Given the number of men in science vs. that of women it is pretty safe bet probability-wise.
> This attitude (and your response to it) goes a long way
> to explaining why computerland is such a sausage party.
It explains absolutely nothing. Girls not going to some field because of the attitude of people they don't know because they are not in the field yet?
And "sausage party" deserves a flag, imho.
[1] It was noted by many, while discussing demographics of Wikipedia, that women are less willing than men to contribute to the intellectual commons, particularly on sites which are not walled gardens. If this fact generalizes, we would expect women Physics PhD's to be underrepresented among people writing about physics.
There's a degree of sexism built into the English language, you can try to change it by creating a gender neutral grammatical personified ("it" usually doesn't work), but unless it's more useful than alternatives, I doubt it'll gain traction. Nouns are almost always assumed to be masculine if assigned gender and it's very easy to slip into saying "he" by default when describing anything you're not certain of. Anonymous internet aliases fall under that "default male" noun rule IMO. In the absence of knowledge, it's equally invalid to assume the author was female.
Automatically attributing all the high quality posts to men is enormously much worse.
And it will only perpetuate the problem or even make it worse, because it makes it harder for women to get the recognition they deserve.
You might say that the recognition they deserve is equal recognition. I would agree. IFF they were currently getting equal recognition, then everything you say about giving them extra recognition would be true. It would be condescending, belittling and sarcastic.
The problem is though that they don't get equal recognition. So until the day they do, you can put that "condescending, belittling and sarcastic" attitude right back where you found it.
If you're going into 'tech' to get recognition, you're probably going into it for the wrong reasons.
This debate reminds me of the failed 'Women only shortlists" debacle in the UK under the Labour government, where they put forward only Women candidates, in order to get more women MPs. Regardless of their merit to actually do the job.
From Wikipedia: In his essay "Homesteading the Noosphere", noted computer programmer Eric S. Raymond opined that open-source software developers have created "a 'gift culture' in which participants compete for prestige by giving time, energy, and creativity away". Members of the Linux community often speak of their community as a gift economy.
Hence in my opinion; recognition is the currency of hackers, and thus while it is the unfortunate case that in many areas women are under-recognised... it is particularly egregious when this happens in the technology arena.
I think another thing that plays into this is how the longer a comment is, the high the chance it will be disagreed with because there are more things to disagree with. The short and simple comment may 100% of the time be appreciated but the points inside a longer comment may mostly be 100% appreciated but a couple disliked. This leads to the larger comment getting less upvotes even though it contains much more agreeable points than the shorter comment.
Or, on the flip side, if a comment holistically seem strong, the weak points within (which, otherwise as isolates may have been viciously voted down) stand to get leverage by the strength of the comment's whole worth. And perhaps thereby granted earnest consideration and a chance to discussion (which arguably they may not have gotten a chance to otherwise as a one-liner).
Curiosity: the trend (in this case) has reversed itself with time. Quite possibly due to your reply, but that's impossible to tell from a single instance. How many maintain that reversed-upvoting trend after a full day or two?
As far as I could tell from that conversation, she is anonymous and wants to stay that way. So RRC could be somebody massively well-known in the science world using this as a non-tenure approved outlet, or is masquerading as knowledgeable but is a patent clerk with no scientific credibility.
I found that the author gave a great setup for an explanation, and then balked at giving the actual answer.
> For right now, if you just believe that four-velocities can never stretch or shrink because that's just the way it is
In other words, nothing can go faster than the speed of light because that's the way it is? The author needs to explain why the magnitude of this four-velocity vector is the speed of light! I was hooked after the first few paragraphs, but then felt like it dead-ended in a circular argument.
Someone else wrote my favorite answer: "Basically, the way to think of it is not that light is the fastest thing, but rather that there is a speed, c, which the geometry of space and time demands is the fastest possible speed.
One can also work out that anything without mass must travel at this fastest possible speed c. Light is one of those things, therefore light travels at c. It's only an accident of history that we call c "the speed of light": that's the context we discovered c's existence in.
As for why it's the speed it is, well, it's the speed in our universe. It's actually much more natural to say c=1 and all speeds are then unitless numbers between 0 and 1. From this point of view c is 300 Mm/s because of how we chose to define the meter and the second." http://www.reddit.com/r/askscience/comments/fjwkh/why_exactl...
via Wikipedia: The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
So I guess that means a meter is 30.66331898849836976219 cesium-133 transition periods.
A physicist can never certainly say that something doesn't happen.
We have models that describe the world very well, but those models are never the whole truth (and even it were, we couldn't be sure of it).
Special and General Relativity are experimentally very well tested, and these theories predict that a particle that has a speed < c can never acquire a speed > c. There are solutions for speeds larger than c, but those solutions are quite weird, and can't interact with "normal" particles.
But the mere scientific approach of observing facts, modeling and verifying means that one can never be sure that something can't be - only in the limits of the models can we be sure that a thing can't be.
The question why a certain velocity, c, cannot be exceeded, is what was actually asked (and answered very well). The question why it's that particular magnitude is a different question.
Yes, I haven't read the other comments but that is a terrible terrible explanation. OP had a genuine question about the nature of things and the person answered bringing up paper and arrows. This is the stuff that made Feynmann mad when they asked him about magnets.
The only reasonable answer to the original question is: we don't know. The whole schizofrenic theory of something that can be waves and particles doesn't make sense right now but that's the best we can come up with. Nothing can go faster than light because our equations tell us so but we don't know the mechanisms, exactly as we don't know what is creating gravity, for instance. Physics is full of deep mysteries still.
Yes, I haven't read the other comments but that is a terrible terrible explanation. OP had a genuine question about the nature of things and the person answered bringing up paper and arrows. This is the stuff that made Feynmann mad when they asked him about magnets.
Have you ever read the book QED? It's Feynman's best effort to explain Quantum Electrodynamics to a layman. In the book, he takes a genuine question about the nature of things (how does light work?) and answers it by "bringing up paper and arrows!" (I encourage you to read the book to see what I mean). Feynman disliked "explaining" nature with inaccurate and irresponsible metaphors. But arrows are the way it really is!
Yeah, I believe he proved a correspondence between the arrows and the Schroedinger equation (not in that book) at some point (and it's not hard to come up with a character of the proof). The grandparent is referring to something like this video, though, which you mentioned at the end: http://www.youtube.com/watch?v=wMFPe-DwULM
Bringing in arrows where they don't belong, or in the magnet case "rubber bands", is cheating the asker. I'm not familiar enough with GR to know if arrows are a useful representation like they are with complex amplitudes.
I haven't read that particular book. I pointed out Feynman's magnets because they were a bit of a recurring joke on reddit (I refuse to use the word meme) and found ironic redditors fell in the same trap.
It's often more helpful to explain why things work in terms of the physics we understand right now that not at all. Sure, it's dissatisfying to hear "the arrows can't stretch because that's the way it is", but it's a useful metaphor that can help explain time dilation and why we can't go faster than light. Physics answers often end up with "because that's the way it is", but that doesn't mean that the things you've learned up until then are useless.
The main takeaway for me is that of a deeper "that's the way it is":
* My understanding before: light has a constant speed and nothing can exceed that speed, but up until that limit everything can travel at a variety of speeds.
* My understanding after: everything travels through space-time at a constant speed. Light is "special" only in that it travels exclusively through space and not at all through time.
I'm not sure if that's entirely fair. She did shed light on the nature of the limit (the how): it's not a quantum speed limit, where suddenly more energy input to a body moving at c has no effect (as would probably be a classical interpretation), but rather that the very geometry of our universe constantly revises our notion of time as we move about space, such that the idea of a body moving "faster than c" is a violation of that geometry. I call that pretty insightful, for all that the idea of a universal speed limit could possibly imply.
The problem is that even answering that question just leads to another question. It ends up the way conversations go with inquisitive children - an endless stream of "why"s with no real end because we don't know everything. At some point you just have to reach a satisfactory answer and realize that the more you learn the more you come to understand how little you know.
The actual answer is just that the speed of light is the conversion factor between meters and seconds. You can measure time in meters and distance in seconds, and convert between them using C. Light goes at that speed because that makes the little packet of electromagnetic energy reinforce itself properly.
Nobody can explain why that is the case, as little as anyone can explain why the universe exists. It exists and has certain properties that define its existence. These are just irreducible facts of nature.
Not very long ago, people couldn't explain why things fell to the ground at 9.8m/s^2 instead of some other acceleration factor. The answer now seems straightforward to us. You can't tell the difference between an irreducible fact of nature and a reducible one until you've reduced it.
That they couldn't explain it did not mean they thought or claimed it was irreducible. The reason for claiming the exact numeric value of the speed of light is irreducible is not because we can't currently explain it: it is because it is part of the definition of the universe. The universe consists of space and time components and they are related by a ratio of c. Would the ratio have been 1, then nobody would have posed the question in the first place. You don't go around asking why pi has the value it has either. It may turn out it is possible to relate these values to other properties and values, but they can never be reduced to them. That would just be choosing a different basis for your description, while that basis is arbitrary.
I agree with your main point, I think, but c and pi are different. c has a unit and so can take any numerical value under a compensating choice of units.
Pi is unitless, however, and cannot be defined as any other value.
C and pi are similar also: c would be different, if the universe's geometry where scaled differently, even if meters and seconds were unchanged in transition to the alternate universe (assuming one can formalize what I am saying in a sensible way). Likewise, pi (circumference divided by diameter) would take a different value (or not even be a constant) in an alternate (non-Euclidean) geometry (assuming that a circle could still be defined there, which is more obviously possible than the c/spacetime hypothetical)
It's a shame that about 30% of the comments in this thread are about how the author of the Reddit comment is female. I have a feeling the discussion on Reddit actually trumps the discussion on HN for this one. What's worse is that you have to wade through this irrelevance to get to the "good" comments on here.
People keep asking this, and similar things like "if you were travelling in a vehicle at the speed of light and you turned on the headlights, what would happen?"
For me the easiest answer is to understand that from the point of view of the person travelling near the speed of light the beam of light moves away from them at the speed of light. So after ~1 second they are 300,000Km apart.
On the other hand, from the point of view of a 'stationary' observer, the light and the spaceship emitting it are moving at almost exactly the same speed. So after ~1 second they are maybe 1 meter apart.
How can this be? Our minds naturally want to reject this as nonsense. But the thing the gripping hand is holding that makes this true is that to the stationary observer and the person travelling near the speed of light time is moving at different rates.
The person who is moving ~1m slower than the speed of light is experiencing time enormously much slower than the person 'standing still'. The time difference is 300,000,000 times (sic).
Our brains reject this, because we think of time as an absolute rock solid constant, when in fact even with our primitive understanding and slow speeds we can demonstrate experimentally that time is in fact flexible, and it does slow down the faster you get.
Say you just flick the lights on and off quickly just to let one photon escape. Where will that photon be in reality in one second? 300kkm apart from the rocket? one meter apart?
The ill-formed part of your question is the "in one second" part. From the point of view of the observer on the spaceship, the photon will be ~300k km away after one second. From the point of view of an 'stationary' observer, the photon will be (one second * (c - spaceship_speed)) away from the spaceship.
How can this be? Answer, as the grandparent said: time is passing differently for the person on the spaceship than it is for the person outside. It is passing in such a way that, for each of them, the speed of light is exactly c.
The part that makes this so hard to grasp is that this question is ill-posed. The "in reality" part is nonsensical.
A primary insight to general relativity is that it makes no sense to define location (or motion) except relative to an observer. This means there's no "true" position or motion, simply an infinite set of equivalently meaningful but disagreeing ways to observe them.
(For interest's sake, acceleration is the lowest order local phenomenon. An object does not need an external observer to measure it's own acceleration due to the appearance of locally measurable "forces".)
So the answer is to excise "in reality" and then state that both answers are equally meaningful and correct.
You're over complicating things. Actually and this is the point it is not the 'in reality' part that is problematic, it is the 'in one second' part.
Your astronaut toggling the lights in their spaceship is experiencing time at a wildly different rate than the 'stationary' observer. We can't just say "well duh, just look at the watch or clock" because those are also slowed down by exactly the amount that the astronaut is slowed down.
I was just hoping to drive home the relativity of frames of reference using something more concrete than time dilation. It's less of a stretch to think of time having different values to different observers once you've already given up the idea of absolute position.
When I say 'in reality' I mean physically. Say the rocket earthbound and is 2x300kkm from the earth, the question again, will the photon collide with the earth or still be 300kkm from it?
The problem I have with light as a unit of reference is that 'perception' is not the same as 'reality' in the physical world.
Relativity demands and demonstrates that there is no such thing as "'reality' in the physical world". Events only occur and exist in the context of an observer.
From the perspective of an Earthbound observer, the photon emitted by the ship will travel from 600kkm away to 300kkm away in one second. (Actually the observer cannot see the photon until another second elapses and it collides with him on Earth.) This observer will see the ship and the photon moving almost together, the ship slower by whatever infinitesimal fraction of c.
From the perspective of a shipborne observer, the photon emitted by the ship will travel from 0 kkm (away from the ship) to 300kkm away also in one second. How do we reconcile this with the knowledge that the Earthborne observer sees the ship and the photon staying together? Length contracts in the direction of travel. So the shipborne observer's meters are very short. The small distance perceived by the Earthbound observer is perceived as a 300kkm distance by the shipborne observer. http://en.wikipedia.org/wiki/Length_contraction
In general, this is how you resolve paradoxes in relativity: work it out from the perspective of each observer and understand that there is no central objective reality. You will find that you made an assumption that does not hold true across both observers.
If you can wrap your mind around the Ladder Paradox, you're well on your way to understanding space-time transformations in relativity. The key to the ladder paradox is that there is no such thing as an objective standard of "simultaneous". Simultaneity is specific to each observer; two observers perceive the simultaneity of two events differently.
From the earth observer's point of view in one second the photon will have moved 300 megameters, and the spaceship with astronaut will be 1 meter behind it.
From the astronauts points of view only 1/300,000,000th of a second will have passed. They are going to smack into the planet and won't even know what hit them. The resulting explosion will make Tunguska look like amateur hour with a whoopee cushion.
As I read the Wikipedia article, the frame dragging effect is hypothesized and has not yet been observed, though experiments have been designed and some are in progress.
Here is what seems like a reasonable "explanation" to me -
--
We figured out a few things about electric and magnetic fields. In particular, a changing electric field creates a magnetic field and a changing magnetic field creates an electric field. So if you setup a changing electric field in a specific way, you can setup a cycle between the two field types. Now, these fields hold energy and by virtue of this cycle, become capable of carrying away this energy - what we call "light" - just as waves on water carry energy away from the starting point at a certain speed. The strange thing about E and B though is that this "speed" is a constant that is independent of the reference frame you choose to monitor it. In other words, this wave would move at the same speed relative to you no matter how you happened to be moving and you can therefore never "catch up" with it. Therefore no "thing" (matter) can move faster than light.
--
In physics, recursive "why"s always lead to "that's the way it is" tautologies. For instance, if atoms are mostly empty space, why don't we fall through the floor? Pauli figured out that no two fermions with same spin state can occupy the same space. Why can't fermions do that? They are spin-1/2 particles and their wave function amplitudes cancel out if you account for the fact that fundamental particles of the same type are indistinguishable. Why does the combined wave function cancel out? .. 'cos that's what seems to agree with experiment - i.e. because you don't see people falling through floors.
Progress seems to be about trying to extend this "explanation chain" by one step more. So string theory can step in and add "because vibrating strings, which is what we're made of, behave like this" .. and then it stops at some point again.
Two comments. First, as she alludes to in her edit, the "rotated arrow" picture that RobotRollCall uses here is subtly backward. It does suggest the right things and I used to think of it that way, but it eventually gets you in trouble. (In actuality, as you start to move through space, your motion through time speeds up... but this still leaves your arrow the same length because the geometry of space-time is hyperbolic: the Pythagorean theorem reads "x^2 - t^2 = c^2" instead of "x^2 + t^2 = c^2". This ends up avoiding LOTS of issues, some of which were stumbling blocks for people in the comments to her post. But it's certainly harder to visualize!)
Second, several people have complained that RRC avoided the underlying question by saying "the arrow is always the same length". I think they may not be giving that answer the credit it deserves. Her claim isn't that the speed of light is the longest possible arrow (which I agree wouldn't help at all), but rather that every object's arrow has exactly this same length. That shifts the speed of light from being an arbitrary constraint to being simply a label for this universal fact. The question "Why is every arrow the same length?" is still valid, but there's much less reason to worry about it: no known process can change that length, just as no known process can change the rest mass of an electron.
It doesn't stand on its own terribly well without some substantial discussion in class to back it up, but here's a handout that I've given to classes to try and discuss this stuff a little: http://othello.alma.edu/~jensens/teaching/classes/spacetime....
No answer can be given to this question, it is one of the axioms of relativity theory. The explanation is trying to explain the axiom in terms of the theory built on it.
The top answer on Reddit was not helpful to me, and seemed tautological even in the face of its length.
WHY can't the arrow stretch? That is the crucial question; that is the original question. The original question was not "is there/why is there a tradeoff between space and time." The question was "Why can't the arrow stretch, why can't we go faster than light allows?"
I found her lengthy explanation patronising and unhelpful.
"you change your direction of motion through spacetime, but not your speed of motion through spacetime."
This is article a long-winded way of restating the question, and leaves the reader thinking they know the answer when they simply have a different understanding of the same problem.
Yeah, but a misunderstanding that's somewhat closer to the truth than before. Unless you want to explain Minkowskian spacetime, hyperbolic rotation, and its connection to Maxwell's equations... I think that coupling "motion through time" and "motion through space" like she explains is a good step forward from "cosmic speed limit".
It's worth thinking a bit about what a satisfying answer might be like for you. Maybe there just isn't a way to understand or think about the question that's satisfying.
I would just explain that a photon has zero mass, but nonzero energy and momentum and finite velocity. Intuitively (meaning: in a Newtonian universe), one would think that a particle with zero mass would have to have infinite velocity to have nonzero energy and momentum, right? And yet, its velocity is finite. That demonstrates that the universe is not Newtonian. It also sets up an intuitive connection (which is what we're looking for here, right?) between the speed of light and one's intuitive sense of an infinite velocity.
Again, of course, this brings us to the question of why the universe is this way: why it is Einsteinian rather than Newtonian. But that question really belongs to the realm of metaphysics, not that of physics.
The universe is Einsteinian because otherwise e could not equal mc2.
And if that were the case then stars could not shine, and a TON of other things would not work. Atoms could not exist either.
The reason is that as you go faster you have more energy (obviously) and since you have more energy your mass increases. Since your mass increases you need even more energy to increase your speed (since now you weigh more).
Take that to the limit and you find that as you reach the speed of light your mass goes to infinity.
So it's necessary that it's impossible to exceed the speed of light - for example if you had two objects each traveling at 51% of the speed of light (relative to third placed in between them). Then relative to each other they are going faster than light - which means they have more than infinite energy.
Can't do that.
So relativity is necessary if you want mass to be interchangeable with energy.
So it's necessary that it's impossible to exceed the speed of light.
For example if you had two objects each traveling at 51% of the speed of light (relative to third placed in between them). You only gave them a certain amount of energy, but if speeds were additive and you compared them then it would appear that their comparative speed was greater than the speed of light!
And that would imply an infinite amount of energy, which would be a problem.
Even if they were each traveling at 49% of the speed of light, so there are no issues of infinity, it takes a lot less energy to accelerate two object to 49% of the speed of light than it does to accelerate one to 98% of the speed of light (because it's a lot heavier when it's going that fast, so it contains far more energy), so you would have issues with conservation of energy.
Because of all that, speeds are not additive, and they get adjusted in a way that keeps conservation of energy exactly correct.
Therefor relativity is necessary if you want mass to be interchangeable with energy.
I understand that you say that they're not additive, but I have a feeling you aren't really understanding what the actual math behind it is. Two objects traveling at 51% the speed of light relative to a third object placed between them (or anywhere else) would STILL travel at 81% the speed of light relative to each other.
Please take a look at a very simple relativity homework solution to see if you misunderstand the math or the concepts of relativity (that happens to be the top result for "two spaceships approach each-other" on google)http://www.phy.duke.edu/courses/143/homework/hmwk3_solutions... [It's problem #2]
I'm trying to show why relativity is necessary, I'm not trying to explain relativity.
I'm giving an alternate universe where relativity does not exist and showing why that universe could not work. And because it does not work, relativity is necessary.
Please go back to the original question I am answering: Someone wanted to know why the world is Einsteinian not Newtonian.
"Increasing mass" inevitably leads to so-called "perpendicular mass" which must change and "proper" mass which must not change for equations of motion to stay correct.
What helped me with a better understanding of time dilation is short paragraph from RobotRollCall:
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If you're moving through space, then you're not moving through time as fast as you would be if you were sitting still. Your clock will tick slower than the clock of a person who isn't moving.
Maybe it helped you, but it's utterly inaccurate and incorrect.
There is no such thing as "moving through space". There is only moving relative to another object. And BOTH of your clocks tick slower! Relative to each other.
"[...] it's utterly inaccurate and incorrect. There is no such thing as "moving through space"."
I think you're missing the point here. She's not trying to teach people the perfect semantics, she's trying to progressively teach them concepts that are tricky to understand and assimilate, step by step. And in a way they can relate to.
By the way, she addresses what you brought up in her first followup (with yet another compelling and easy to understand explanation).
This is not a matter of semantics, if you ever want to understand relativity the FIRST thing you need to do is get rid of the concept of absolute motion. As long as you think in those terms you will never be able to understand it.
And addressing something in a followup is no good - fix your initial post to be correct in the first place. Reddit allows you to edit your post.
If she had started by explaining relativity her post would have been twice the size and she would have lost half the audience. Doesn't it matter to you that people were actually interested in the topic and participative?
And why is a follow up no good? She didn't follow up to fix anything. She followed up to follow up. (And mentioned it by, yes, editing her article).
I went through your comments and you mentioned that "in a nutshell" the fact that there's no such thing as a full stop in space is why "this explanation is actually doing a disservice". But that's confusing to me because she clearly stated - relatively to motion - "Those things are true, but we're ignoring that kind of stuff right now."
Can you point out exactly where she crossed the line in your opinion?
The confusion being expressed among commenters here is what I'm basing my assertion off of. Simplification is fine, but I think in this case it pretty clearly set a lot of people down the wrong track.
The important part of relativity is that there is no absolute reference frame, all motion is relative, thus the name. The mathematics behind time dilation is an aspect of that. Teaching someone about time dilation without teaching about the fundamental nature of relativity is a disservice, in my opinion.
Well what if the coordinate system is in reference to one of the objects. That is what I had imagined in my head, I never supposed an absolute frame of reference. The faster the two objects accelerate from each other, the more the time vector (that she mentions in her explanation) rotates for both of them relative to each other so the slower the relative passage of time.
I'm pretty sure he explained that he was talking in terms of general relativity and his simplifying assumption of absolute directions and a stationary viewpoint. As far as I can tell, you haven't explained why that's wrong — merely asserted that there's another viewpoint that can describe the same thing.
This FIRST thing to remember is that you can only measure speed by comparing with something else. There is no such thing as the concept of "I am moving", but rather "relative to them I (or they, it's interchangeable) are/am moving".
Now when you compare speeds you can also compare clocks, and the same principle applies - you can only measure time by comparing to someone else.
Velocity is relative, but acceleration is not. The earth-dwellers and the astronaut will both agree that the astronaut accelerated and the Earth didn't.
Similarly, rotation rate isn't relative. Acceleration and rotation rate can both be measured against absolute states of no acceleration and no rotation (respectively). This is why our phones have accelerometers and gyroscopes which are entirely internal, but determining velocity, position, and direction require the external references provided by GPS and compass.
How can acceleration not be relative if velocity is? Isn't it just the derivative of velocity? How do you escape the relativeness? Or is that what all those theories of relativity are about?
It's possible to absolutely measure the change in a quantity without knowing the absolute value of the quantity itself. Think of a hole in the ground of unknown depth but known radius, filled with water. If the water level changes you can calculate the absolute change in water volume without knowing the total volume of water in the hole. Similarly, you can measure an absolute value for acceleration (change in velocity) even though an absolute value of velocity doesn't exist.
Therefore, you can measure acceleration with nothing but equipment (a simple spring-scale will suffice) in your car (reference frame), but you can only measure your speed relative to something outside of your car (traditionally, the road).
That might be a deeper question about the nature of the Universe.
Newton's first law (inertia): an object in motion tends to stay in motion. This gives rise to the idea of an "inertial reference frame" which is the idealized reference of a hypothetical object in motion. In simplistic terms, if you pretend that the Universe is merely Newtonian in nature and contains a preferred reference frame then you could imagine that an inertial reference frame can be described by a velocity vector (a speed and a direction). If an object has zero speed relative to the inertial reference frame that will tend to continue to be true so long as no forces intervene.
If you induce an acceleration on an object you will change it's velocity. In it's initial inertial reference frame it will appear to be accelerating. In any other inertial reference frame it will also appear to be accelerating.
There is no such thing as an accelerating inertial reference frame precisely because such a frame is not inertial, it would imply that forces are being applied to the objects involved. The laws of physics make sense if you apply them within any inertial reference frame, but they don't make sense in accelerating reference frames (mass, energy, and forces become inconsistent and confused).
I don't think acceleration is a torsor, quite, but if you understand a torsor, you understand how acceleration can be absolute even if velocity is not: http://math.ucr.edu/home/baez/torsors.html
In this example, the earth isn't in an accelerating reference frame, only the astronaut is. There isn't a "master reference frame", but that doesn't mean that acceleration is relative.
Despite the upvotes on reddit, this really is a topic that can only be done justice by good book or instructor. Any self-respecting library should have a copy of Relativity: The Special and General Theory by Einstein, it's written specifically for the layman. Come to think of it,... I should probably pick it up again myself.
Because unlike speed acceleration is not relative.
Acceleration can be measured without reference to anything else. If you are in a box and accelerating you can measure it - it feels exactly like gravity.
Awesome explanation. But what I've never understood is what the universe looks like to photons. What does it mean for a photon to travel between two points from the frame of reference of the photon?
Stephen Hawking predicted that things can travel faster than the speed of light through quantum uncertainty. This is how information can escape from a black hole.
Put simply it works like this: light travels at a constant speed, but due to quantum uncertainty nothing is in one exact place, it 'teleports' around an average point. Thus, if it 'teleports' in the direction that the light was travelling it has moved faster than the speed of light.
Another way to look at it that is arguably simpler (and with greater loss, of course): Imagine the XY plane with every point described by integers in both X and Y marked. That is, (0, 0), (1, 4), (-2, -5), etc. Connect each of them to their four neighbors with a line segment. Now suppose you are at (3, 4) and you want to move to (4, 5), and you may only use the lines given to you. You move to the right, you move up, you're there. And you can move the other way, too, all the line segments are bi-directional.
That works in space; that does not work in time. You can't stop moving or change direction in time. You can put X and Y on that grid and have something meaningful, but you can't say it's X and T; that would imply the ability to freely move back in time or forward at your discretion, which is not true.
A simplified explanation of space and time's actual shape is that when you are at (3, 4) and you are moving through time (in the first coordinate, let's say), you've got lines that lead to (4, 4.1) and (4, 3.9) and so on, but the lines only go to a certain angle, which for simplicity's sake I'll say is the obvious 45 degree angle, which means you've got lines that go to (4, 3) and (4, 5), but nothing else below 3 or above 5. You can only move along those lines, and as there is no line to (4, -2) from your start position, there is no way to get there. The bound of those lines is the speed of light. The pictures of the "light cone" you may have seen are in some sense not merely a helpful picture but actually a true picture of the universe.
You can not move faster than the speed of light because you can only move between connected points in the universe, and to move faster than the speed of light is to bypass that restriction. The universe is literally not shaped that way. The shape of the universe forbids faster-than-light. You don't have any choices other than those lines and none of the lines go faster than light.
This is a grotesque simplification, but I think the core point is accurate. Exceeding the speed of light is impossible for reasons above and beyond the mere "exceeding the speed of sound" or other things were. To travel faster than the speed of light requires changing the shape of the universe. (And to the extent that certain theories permit it under some circumstances, such as the Alcubierre drive theory[1], I suspect that we'd find that even if we could implement one of these things the universe would still find a way not covered in those theories to shut it down, cosmic-censorship-style[2], or like [3]. I would also note that all "practical" FTL drives proposed to date have inevitably required the existence of at least one impossibility, such as stable negative mass, and it means little to prove that if I have one impossibility like stable negative mass I can have another like FTL.)
Also, because this is a grotesque simplification, please note that picking apart holes in my picture is not even remotely the same as picking apart holes in the theory of relativity, let alone picking apart holes in the Universe. In particular don't get caught up with things that may appear to be going backward; that's an illusion of this attempt to embed an explanation into Euclidean space, not a real problem with the physics.
My gut feeling is that article is dragged :-) into somewhat irrelevant things like Poincare group et al.
Why maximum limit exist at all?
How Universe without this limit will look like?
How Universe with limit which is not equal to speed of light will look like?
Afaik the answer is that the limit is the limit, and the speed of light is unlimited - but there is a limit, so the speed of light is the same as the fastest speed possible. So the limit is not the light's speed, they just happen to be the same.
eh, it's more fun to imagine we will one day surpass the speed of light. It hasn't been disproved so conclusively that I know about said proof, so as of yet I can continue imagining the barrier will be broken.
I like the way the Asimov talks about hyperspace, a currently unknown dimension that allows for "jumping" through/over huge segments of space without technically traveling faster than light, completely circumventing the issue of faster than light travel and extreme time dilation.
If you were moving in a "completely horizontal" direction, wouldn't you not be moving through time at all, but only through space? That means you could move infinitely fast, not with a strict limit.
Yes, but that kind of motion (tachyonic) is unphysical. It violates causality: you can imagine that by "rotating" the "horizontal" motion very slightly "downwards", in a different reference frame it is backwards time travel.
The salient thing is that there are three disconnected classes of 4-vectors: timelike (massive particles), spacelike (tachyons), and lightlike (massless particles). Lorentz coordinate transforms can only take you between 4-vectors of a particular type: e.g. there's no inertial reference frame where timelike motion looks like tachyonic motion.
Compared to yourself you are always standing still, and your clock always ticks at what you think is a normal rate. Other things may be moving relative to you though and THEIR clock might be slow.
(Unless you accelerate, in which case things get more complicated.)
Following your argument to its logical conclusion, HN should stop linking to external sites because if people are in a site X mood, they will go to site X, for any value X.
For myself, I don't visit Reddit unless there's something interesting linked to from elsewhere, such as HN. Thus, I appreciate this being posted to HN.
> HN should stop linking to external sites because if people are in a site X mood, they will go to site X, for any value X
Your reasoning is flawed. The value of HN is its community and the discussions it's capable of spawninf. There are sites for discussing an ampler spectrum of subjects (like, for instance, the nature of the universe and laws of physics) and sites for discussing news that interest specifically to hackers (according to the definition implied in the "Hackers and Painters" book).
And that argument is exactly why the comment should be linked here. If the Reddit comment had been a blog post, everything would have been fine, right? I want to see the comment and get to stay here for the conversation.
I enjoyed reading the article, and I wouldn't have found it if it wasn't here on HN. If it shouldn't be here (according to the HN community) it wouldn't be sitting at the top of the news page.
I agree popular vote took it to the top of the first page, but it indicates a change in the composition of the community or a change of interests from startup-related technologies to more general discussion.
I'd think that this discussion is significantly more hacker-y than many of the others here. I mean, I can see your argument: HN is obviously becoming more and more mainstream, and hence, articles will tend more and more in that direction.
Oh, finally we got here cool discussion. Here is how I explain that one "could" travel faster then the speed of light! HOWEVER, and this is VERY IMPORTANT, this depends on your definition of the speed. So imagine following experiment:
There are two space ships which are built like these russian matroshkas. One smaller space ship is in the hangar of a bigger one. The bigger one starts from the earth and accelerates to the speed of light (or just until 0.999c). Now, the smaller ship starts and can again accelerate from the bigger ship point of view until 0.999c. So, if there is just a simple velocity measure instrument, which is measuring acceleration by F = m*a, and we know the relative space ship mass "m" as it was relative to the earth, then knowing how much force our engine produces we can compute the acceleration. And hence our velocity measurement device will add small "a" to the current velocity by every thrust of the engine.
So given that type of measurement, our smaller space ship can accelerate to the speed of 2c relative to the earth. HOWEVER, due to the relativistic effects the people living on the earth would never ever realize that this ship was moving with 2c, since they are measuring speed by looking how far the ship went in the certain amount of time. And due to the time dilation they will never realize that this ship was actually much farther away then it looks like.
So, regarding to this experiment, we can travel faster then the light. However, this is only due to the definition of the speed.
A counter argument would be that the mass "m" is also changing. However, one could argue that the mass is represented by the amount of particles per volume unit and hence remain constant if volume remain constant. Ok, another guy could argue again that the size of the volume shrinks, but I could then argue that if size of the volume shrinks, then the density of the particles per volume unit from the earth point of view would increase and could end up in a singularity or just black hole, so big bang ?:confused:
This kind of experiment fits well into my experience of the world, where I just cannot accept some of the constraints we get from the nature :) Yes, you cannot travel faster then the speed of light, BUT this is only because I stay at the earth and measure your speed by looking how fast you come back. But this pure guy who is traveling could measure the speed as I've proposed and would then realize that, in deed he was faster then the "earth's speed of light" :)
Unfortunately, you are trying to impose a traditional world, where speeds are additive, onto relativity. It just doesn't work that way. A light beam fired from Earth would overtake the smaller ship, so in Earth's frame it is going slower than the speed of light.
Yes, you are right, but you just didn't get the point what I was trying to say. In deed I was expected that I will be downvoted by this comment :)
I never claimed that speeds are additive. I've just claimed that it fully depends on what you define as a speed. If you define the speed the classical way (space unit per time), then due to the relativistic effects, it will never work out for you.
However, and this is the point, if you define the speed as just some counter running in front of you which add a value on every engine thrust, then it will work out for you that you are traveling faster, then the "earth's" speed of light!!!
Imagine just another experiment. You are waking up at a space ship and there is nothing around you where you can fix your view to see if you are moving or not. So, the speed-counter on this ship shows you 0.9c (here c is "earth's c"). No, you press the accelerate button and accelerates to additional 0.2c. There is nothing which would stop you accelerating, because in your frame you can assume that you are at rest! So, adding now the new velocity amount to your previous you get 1.1c, HOWEVER, this the "earth's c" ,so the speed of light as it is measured on the earth!!! In your frame, since you have no clue if you was moving or not, you should assume that you have now only 0.2c or just 0c, since you cannot measure the speed in the classical way anymore (there is no other point to fix on).
So, this is the way how to understand the relativistic effects. There is no "super-dooper" spaghetti-monster hand, which will for some reason stop you accelerating. No, this is just because everybody around you will never be able to measure your real speed, because they can only measure the speed relative to their frame.
The entire point of relativity is that there is no medium. There are plenty of particles that do not interact electromagnetically - the neutrino for example.
The speed of light has to do with the nature of reality, not the method of transportation.
You seem to want to talk about theoretical ideas that have no evidence.
You quite misunderstood that article, it's not the vacuum that produces the particles, it is the massive energy they are beaming that produces them.
The stuff in the wikipedia article is just ideas that may work mathematically but have little bearing on the real world. At least for now. Maybe someday we'll figure them out, but for now it's just ideas.
> You seem to want to talk about theoretical ideas that have no evidence.
:-/
We can test my ideas in your laboratory, of course.
> You quite misunderstood that article, it's not the vacuum that produces the particles, it is the massive energy they are beaming that produces them.
Do you really read article? Of course, energy is necessary, because two vacuum particles will cannot escape each other and will annihilate. But you cannot produce particle using just energy.
> The stuff in the wikipedia article is just ideas that may work mathematically but have little bearing on the real world. At least for now. Maybe someday we'll figure them out, but for now it's just ideas.
Some far galaxies are traveling from us much faster than speed of light because of space expanding. Thus theory of relativity will work correctly for distances less than 1B of light years, but it is not correct for larger distances. Are you agree?
Good explanation of space/time -- in short, you're always moving in space and time, and the more you move in space, the less you move in time. Vice-versa.
Brian Greene does a pretty good job of explaining all this in the Elegant Universe. If you're into this kind of thing, check it out.
You can only move relative to another object. You may even move fast relative to one object and slow relative to another, meaning your clock ticks at a different rate relative to each of those objects.
There is no absolute clock - you can only compare your clock with someone else's clock.
But the speed of light can only be measured relative to YOU. So what looks like 90% of the speed of light to you, can look like 10% of the speed of light to someone else.
Actually that's just flat-out wrong. Light has an absolute speed. It's the only absolute thing in the universe. It's not relative. And -- this comes directly from Brian Greene -- the speed of light always looks like the speed of light, no matter how fast you're travelling. The speed of light never looks like 10% of the speed of light. It's always the same -- a constant.
The speed of light is always 'the speed of light' regardless of your reference frame, however the speed of other objects is purely relative.
The 'what' in "So what looks like 90% of the speed of light to you, can look like 10% of the speed of light to someone else." is referring to something travelling slower than the speed of light. A train or bullet perhaps. In different reference frames it can be said that this train/bullet is travelling at different percentages of the speed of light.
That's why it gets weird.
EDIT: To illustrate this, lets say we're sitting on the earth watching an astronaut. Relative to our position, he is travelling at 1/2 the speed of light. Now, some joker decides to shine his laser pointer at the astronaut. From earth we see the laser beam^ blast past the astronaut at .5c (.5c + .5c = 1c, the speed the laser light is traveling).
NOW! from the astronauts perspective! Instead of seeing the laser pass him at .5c, he sees it pass him a nice proper 1c. weird, but it's how the universe works.
But the speed of light can only be measured relative to YOU
That's still wrong, though. The speed of light is an absolute; it's not My Speed + the Speed of Light.
The person I was who originally responded to me (ars) was trying to say that motion in space is impossible because it's always relative -- apparently even to the speed of light. That's not true; motion is relative to the speed of light, period. And what I had been trying to express (however badly) was that the faster you move relative to the speed of light, the slower you move in time.
I think ars was just in a nitpicky mood and was fixating on the particular wording I chose.
But it still makes you wonder how this idea should be understood: Does it mean it is actually impossible to travel faster than the speed of light, or just that you can, but bad things will happen (like coming back too late, or so big that no one will see you, etc)?
If you are within the event horizon of a black hole then you cannot escape.
Elsewise, from a greater distance you will be able (assuming you have the means) to escape the gravitational pull of the black hole as you would any other object of equivalent mass.
No analogy is perfect, in particular many analogies are trying to link our everyday experience with things that extend outside of it.
If we take this and your statement further, we could just declare that all analogies are doing a disservice, and all pop science writers should be flogged.
Afaik you can. Relative to an observer looking at a black hole, time is at a complete standstill on the surface of the black hole, thanks to the extremely strong gravity. This time stop is (again afaik) why black holes stop shrinking.
Photons and gluons are the only two particles that we know to be massless and therefore capable of moving at the speed c (some neutrinos might be massless, but we know at least 2 of them are not).
Since gluons are never observed as free particles and we're all familiar with photons, we call it the speed of light.
The motion I'm referring to is motion in the futureward direction.
May be you should consider the fact, that while you are not moving- let's assume that your are in space and way far from earth or any other thing-, your brain, heart and blood do. If they don't, you wouldn't exist. It's in my believe that we are living in a single dimension world, and it's not quite different than a dream; actually it's the same thing. Just think about it ;)
