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.
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...
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.
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.
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?
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.
What helped me with a better understanding of time dilation is short paragraph from RobotRollCall:
"""
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.
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.
[+] [-] chime|15 years ago|reply
[+] [-] jimmyjim|15 years ago|reply
[+] [-] tptacek|15 years ago|reply
http://www.reddit.com/r/askscience/comments/flzut/i_have_som...
More of her best-of comments would be most welcome. And, MORE THREADS LIKE THIS PLEASE.
[+] [-] wnoise|15 years ago|reply
[+] [-] cuchoperl|15 years ago|reply
[+] [-] jazzychad|15 years ago|reply
> 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.
[+] [-] kalvin|15 years ago|reply
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...
[+] [-] brazzy|15 years ago|reply
[+] [-] crocowhile|15 years ago|reply
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.
[+] [-] crux_|15 years ago|reply
* 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.
[+] [-] siglesias|15 years ago|reply
[+] [-] ryanelkins|15 years ago|reply
[+] [-] moultano|15 years ago|reply
[+] [-] Confusion|15 years ago|reply
[+] [-] coderdude|15 years ago|reply
[+] [-] Stormbringer|15 years ago|reply
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.
[+] [-] Kilimanjaro|15 years ago|reply
[+] [-] ck2|15 years ago|reply
http://en.wikipedia.org/wiki/Frame-dragging
It causes satellites around earth to move a few feet each year.
[+] [-] lurker19|15 years ago|reply
[+] [-] aufreak3|15 years ago|reply
-- 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.
[+] [-] Steuard|15 years ago|reply
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.
[+] [-] Steuard|15 years ago|reply
[+] [-] Jun8|15 years ago|reply
I found these answers to be more informative: http://physics.stackexchange.com/questions/2230/why-and-how-...
[+] [-] hammock|15 years ago|reply
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?"
[+] [-] thret|15 years ago|reply
"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.
[+] [-] tel|15 years ago|reply
[+] [-] akozak|15 years ago|reply
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.
[+] [-] ScottBurson|15 years ago|reply
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.
[+] [-] ars|15 years ago|reply
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.
[+] [-] rdtsc|15 years ago|reply
"""
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.
"""
[+] [-] ars|15 years ago|reply
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.
[+] [-] nazgulnarsil|15 years ago|reply
[+] [-] ars|15 years ago|reply
[+] [-] sambeau|15 years ago|reply
http://en.wikipedia.org/wiki/Hawking_radiation
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.
[+] [-] rbanffy|15 years ago|reply
Yes, but those fluctuations average out very quickly.
[+] [-] aerique|15 years ago|reply
[+] [-] jerf|15 years ago|reply
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.
[1]: http://en.wikipedia.org/wiki/Alcubierre_drive
[2]: http://en.wikipedia.org/wiki/Cosmic_censorship
[3]: http://books.google.com/books?id=_mo4AAAAIAAJ&pg=PA132&#... (reading pages 132 and 133)
[+] [-] boh|15 years ago|reply
"Scientists Make Radio Waves Travel Faster Than Light"
article:
http://www.universetoday.com/33752/device-makes-radio-waves-...
the paper it's based on:
http://arxiv.org/abs/physics/0405062
Anyone with a Physics background care to comment on the validity of this study?
[+] [-] statictype|15 years ago|reply
I really wish Instapaper worked with reddit comments. Lots of good reading there.
[+] [-] adobriyan|15 years ago|reply
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?
Antropic principle inevitably pops up.
[+] [-] ars|15 years ago|reply
In order for e=mc2 you are required to have relativity. And a world without that could not exist.
[+] [-] olalonde|15 years ago|reply
[+] [-] augustl|15 years ago|reply
[+] [-] ars|15 years ago|reply
If you are asking why the limit is this specific number then no one knows. But then again we don't know the reason for any of the constants.
[+] [-] retube|15 years ago|reply