I never really understood why the speed of light was the limit. If you double your speed, you just halve the time it takes you to get there. Now if you have reached the speed of light, doubling the speed will never make you go back in time, it will just halve the time it takes you yet again. So now one lightyear at the speed of light will take 6 months at twice the speed of light. The energy requirement for going faster than light is another matter.
Within your own frame of reference time slows down the faster you move. This is why from your own frame of reference light seems to always be moving at c no matter how close to c you get. Once you get to c time will be frozen. So if you travel for an entire year at c to you it will look like it was instantaneous, it wasn't, you could say you were "unconscious" the entire time. Somebody from a different frame of reference will notice you traveling at the speed of light and will notice that you are frozen in time.
Careful. Within your own frame of reference, time always progresses at a normal rate. When you are traveling near the speed of light, distances contract; at the speed of light, all distances in the direction of travel would be zero.
On the other hand, someone stationary watching you travel near the speed of light would say that your clock slows down more the faster you move, but lengths stay the same.
>>Careful. Within your own frame of reference, time always progresses at a normal rate.
You are correct. I don't think I said otherwise. I guess I should have been clearer, time slows down in the frame of reference traveling at c when looking at it from a different frame of reference. I'm sure we are saying the same thing.
>>at the speed of light, all distances in the direction of travel would be zero.
Yeah, but a person observing you in a different frame of reference won't see that. The fact that distances are zero is just another way of saying that time has slowed down in your frame of reference. Is just two faces of the same coin.
> The fact that distances are zero is just another way of saying that time has slowed down in your frame of reference. Is just two faces of the same coin.
Indeed. You can see this sort of effect in, say, the muon decay demo in my relativity simulator:
the speed of light, c, can be violated from your frame of reference, but the external observer doesn't see this - it's your perception of time that has slowed down.
you reach the speed of light (from the perspective of an external observer) when your local velocity is infinite (and then all travel becomes instantaneous).
I'm not sure what this means. c cannot be exceeded in any frame of reference. Your "local" velocity is always zero -- you always measure your own speed with respect to yourself to be zero.
From your perspective, reaching the speed of light causes all distances in the direction of travel to become zero. Your clock functions correctly and time travels at the ordinary pace. From a stationary observer's perspective, distances are the same but your clock has stopped.
But from my own frame of reference all I would see is people frozen in time traveling a the speed of light, not really instantaneous. So in essence, the laws of physics have a built in hibernation mode for anybody traveling at c </joke>.
If you were actually going the speed of light, light would still have to be able to go ~300kmh faster than you. To make this happen, time slows down for you.
That's what special relativity says - in any reference frame, light is always traveling v + c, where v is your velocity and c is the speed of light.
To make this happen, time itself slows down. But how would this actually work? Does this mean electrons would "orbit" within the electron cloud more slowly? (If not, then molecules larger than Z=137 may be possible.)
>>But how would this actually work? Does this mean electrons would "orbit" within the electron cloud more slowly?
Yes, all of the particles within that frame of reference slow down. Why? Who knows. Maybe space becomes more "viscous" which slows down all particles within it.
The "why" in the framework of special relativity would be "because the Lorentz transformations rotate points in four-dimensional spacetime."
If you imagine every event as having (x,y,z,t) coordinates in a particular reference frame, the Lorentz transformation is a 4x4 matrix which rotates events to show what would be observed in another reference frame. You trade spatial distance for temporal distance and vice versa.
This comes out of the structure of spacetime, rather than viscosity of some kind, which would be visible as a force.
Your answer does not explain why. It correctly predicts the universe but it is not a why. Why do all particles slow down as speed increases? I'm looking for a more fundamental answer here.
"Spacetime is a Minkowski space" is why. Remember that mysterious viscosity cannot explain particle slowdown, because the particles appear to be perfectly normal in a co-moving reference frame.
If you're looking for something more than a model that correctly predicts the universe, you're looking for something other than physics.
Edit: Let me see if I can make myself clear. We know that c is constant no matter how fast you are moving. If c is constant then it can be derived that time slows down and distances get compressed, etc. etc. etc. Einstein derived all of this by realizing that c is constant in all frames of reference. Now, if I ask "Why does time slow down?" and I get the answer "because c is constant" then we are just going in circles. It seems that that is what is happening here. Correct me if I'm wrong but are you not using a derivation of the fact that c is constant as an answer? I'm looking for a more fundamental reason as to why time slows down. Which is the same as asking why c is constant.
To felipemnoa (since there's no reply link under your latest post in my view)
All solid matter moves forward in time at the same speed, minus the speed in which it's moving in the other 3 dimensions. Light and other particles only move forwards in time.
*if you were actually going at the speed of light from a stationary observer, all travel becomes instantaneous from your reference frame.
the speed of light, c, can be violated from your frame of reference, but the external observer doesn't see this - it's your perception of time that has slowed down.
you reach the speed of light (from the perspective of an external observer) when your local velocity is infinite (and then all travel becomes instantaneous).
Also, when traveling at the speed of light the entire universe would appear to have collapsed down to a single point, because of length contraction. So really, the notion of movement or change completely breaks down when you are moving at the speed of light... except in your reference frame were everything is normal. Also, it would take an infinite amount of energy to accelerate something to the speed of light, so the speed of light is a limit that you can never actually reach (i.e. an asymptotic limit).
That's precisely why Einstein's theory of relativity was so groundbreaking. It stipulates that the speed of light must be the same relative to every frame.
Let's say you're moving nearly as fast as the speed of light. Are you flying side by side with light particles? No, because if they were, you would measure their speed as being close to zero relative to you. The theory says you will STILL measure the beams of light as flying away from you at the speed of light relative to you.
Imagine how the universe must conform to make that the case! The universe essentially makes your time tick slower in order for light to still travel that much faster relative to you.
This phenomenon has been confirmed (along with basically every other prediction that Einstein has made). There are some subatomic particles that we know has a half-life of X seconds. However, when they're traveling quickly, they actually end up living orders of magnitude longer because of time dilation.
In every day life, if you throw a ball at 70 mph on top of a car that's going 30 mph, the ball moves at 100 mph. You can't do the same math once you start reaching the speed of light.
More pedantically, the math you've been trained to do to find a velocity 's' as the sum of two velocities 'v' and 'u' in the same direction is s = v + u.
The real formula is s = (v+u)/(1+(vu/c^2)).
For small values of v and u, vu/c^2 is approximately 0, leaving you with the standard (Galilean) formula, but only as an approximation.
"Let's say you're moving nearly as fast as the speed of light. Are you flying side by side with light particles? No, because if they were, you would measure their speed as being close to zero relative to you. The theory says you will STILL measure the beams of light as flying away from you at the speed of light relative to you."
Something you said just clicked. I think I may now clearly "grok" relativity for the first time.
which calculates different distances given a vector field w/r to a Euclidian space.
It's not the same thing, but when thinking about what Mahalanobis distances measure, I used a helpful mental model of the measure forcing the vector field apart, enforcing a kind of constant distance between the vectors and then measuring that delta. It seems like a similar concept is at play here, only what we're measuring is different.
I'm aimlessly musing here, but I feel a kind of grokiness I haven't felt before after your post.
> Now if you have reached the speed of light, doubling the speed will never make you go back in time, it will just halve the time it takes you yet again.
It actually makes sense in that regard, because while accelerating, you will shrink along the acceleration vector.
Let's say you are 6 feet tall and fly Superman-style at 0.9c. You will then, from the outside, be 2.6 feet (or so). This means that if you from your timeframe accelerate by 1 km/s, to the outside you will accelerate by 0.4 km/s.
This acceleration in turn cause you to shrink even further, and as you approach the speed of light your external length will approach 0. So any further acceleration in your frame of reference, no matter how immense, would approach 0 from the outside.
You're implicitly assuming Newtonian mechanics and won't get anywhere until you stop. Here's an explanation of a simple thought-experiment based almost entirely on the assumption that the speed of light is constant that lets you easily derive time dilation: http://aeroja.blogspot.com/2011/01/moving-light-clock-ticks-...
Lorentz transformations, which are a consequence of the observation that the speed of light appears constant independent of the motion of the transmitter and the receiver. IIRC, the force required to double your speed goes up exponentially as your speed approaches the speed of light.
[Edit: "the force required to double your speed" is pretty damn meaningless. What I"m looking for is something like "your mass effectively increases exponentially as your speed..." Sorry.]
[Edit v2: How about this: "For a given force, your acceleration decreases as if your mass were increasing exponentially as your speed approaches the speed of light."]
Don't think about speed and such - there is a much easier way to understand relativity. From energy.
It should be obvious that if you travel fast you have energy. And the faster you go, the more energy, and the heavier you are the more energy.
Now comes the interesting part: That velocity energy you have increases your mass! As soon as you have this, some very interesting things happen.
As you get faster you get heavier, the heavier you are the more energy you need to go even faster. This positive feedback loop eventually results in you needing an infinite amount of energy to go any faster (since you are so heavy).
The point where you need infinite energy is at the speed of light.
Now comes the second interesting effect.
Suppose you accelerate to half the speed of light - you have a certain amount of energy - no problem.
Now someone else does that too - only in the opposite direction.
He too had no trouble accelerating, and needed only a finite amount of energy.
But what happens if the two of you are traveling toward each other? A problem - the total of your speed is greater than the speed of light! And even if it was slightly less, suddenly you got energy for free! (Because of the feedback loop going from 0 to 1/2 c takes MUCH MUCH less energy that from 1/2 c to 8/9 c. So where did that energy come from?)
That obviously is impossible - you can't get energy for free. Instead the very definition of speed is changed! You have no choice - you have to change it. The definition is changed in such a way that the energy remains constant. And if the definition of time and length has to change to make it work, so be it. Energy is more important.
Of course all this rests on a foundation: That the increase in speed results in an increase in mass. But this too is required. We already know that's it's possible to convert energy to mass. So we could use a trick - convert mass to energy, speed it up, then convert it back to mass and suddenly we have mass moving very fast without putting in energy. Nope, can't do that. What actually happens is that energy has mass too, and this doesn't work. (If energy didn't have mass you could do other tricks, like send the energy up to space, convert it back to mass and let it fall under gravity.)
Hopefully this should show you why relativity is required if you have conservation of energy.
Some of you guys seem to think that at the speed of light travel would be instantaneous, wouldn't light hitting your eye facing forwards be going at c*2 in relation to yourself, and light looking behind at you travel at 0 in relation to yourself.
Onlookers at your destination would not see you until you arrived but ones from your departure would see you leave and you would be invisible to another craft going at the same speed as you.
This only shows (it seems) that relativitic physics (meaning physics where some form of relativity holds, not necessarily einstenian special relativity) can be accomodated for the possibility of speeds faster than c, not that this possibility actually holds.
So the question still stands; only the argument that lightspeed is a limit because it is incompatible with relativistic physics should be abandoned (stated like this, it seems a fairly weak argument anyway).
If you can engineer transmission of information faster than the speed of light, you can violate causality. On a small scale, that means acausal computing in which results can be generated before inputs, thus allowing for infinite processing power per unit time. On the large scale, outright paradox in the form of event chains that prevent their origination. These outcomes would be problematic to account for in our understanding of physics, to say the least, and seem like a better argument than others for assuming that FTL and all things that would enable it (e.g. sufficient amounts of negative mass) cannot exist.
It remains an interesting challenge to prove that more rigorously, of course.
I'm so out of touch with physics these days that I'm probably not even arm-chairing it correctly. But I still like to ponder crazy stuff...
I'd put my money on a hypothesis that says causality is enforced whether we can perceive it or not. Say we had such a computer with FTL circuitry. You attempt to instruct the computer to halt the current program when an answer is received, thus preventing the inputs being supplied that would produce the given output. Our current time-based perception says "paradox" whereas this proposed hypothesis would say "the computer simply will not halt the program," not because it's designed with safeguards, but because the laws of physics maintain causality.
Except that the heliocentric model greatly simplified calculations. Take a look at Ptolemy's (and others) many epicycle model for something super complex and still not very accurate.
If the speed of light is not really a limit, then events will still have causes. It's just that the set of possible causes will be wider than your light cone.
It should be noted that this is a mathematical paper, and may have no basis in reality.
Just because you can calculate something, doesn't mean it actually exists. (Although the fact that it does sometimes exist is one of the true wonders of the world.)
This is also true of the Alcubierre drive that was in the news a little while ago: It's a mathematical solution, but my have no basis in reality.
46 comments
[ 3.2 ms ] story [ 107 ms ] threadOn the other hand, someone stationary watching you travel near the speed of light would say that your clock slows down more the faster you move, but lengths stay the same.
You are correct. I don't think I said otherwise. I guess I should have been clearer, time slows down in the frame of reference traveling at c when looking at it from a different frame of reference. I'm sure we are saying the same thing.
>>at the speed of light, all distances in the direction of travel would be zero.
Yeah, but a person observing you in a different frame of reference won't see that. The fact that distances are zero is just another way of saying that time has slowed down in your frame of reference. Is just two faces of the same coin.
Indeed. You can see this sort of effect in, say, the muon decay demo in my relativity simulator:
http://www.refsmmat.com/jsphys/relativity/relativity.html
The muon decay lifetime observations can be explained equally well in terms of time dilation or length contraction.
you reach the speed of light (from the perspective of an external observer) when your local velocity is infinite (and then all travel becomes instantaneous).
From your perspective, reaching the speed of light causes all distances in the direction of travel to become zero. Your clock functions correctly and time travels at the ordinary pace. From a stationary observer's perspective, distances are the same but your clock has stopped.
That's what special relativity says - in any reference frame, light is always traveling v + c, where v is your velocity and c is the speed of light.
To make this happen, time itself slows down. But how would this actually work? Does this mean electrons would "orbit" within the electron cloud more slowly? (If not, then molecules larger than Z=137 may be possible.)
Yes, all of the particles within that frame of reference slow down. Why? Who knows. Maybe space becomes more "viscous" which slows down all particles within it.
If you imagine every event as having (x,y,z,t) coordinates in a particular reference frame, the Lorentz transformation is a 4x4 matrix which rotates events to show what would be observed in another reference frame. You trade spatial distance for temporal distance and vice versa.
This comes out of the structure of spacetime, rather than viscosity of some kind, which would be visible as a force.
If you're looking for something more than a model that correctly predicts the universe, you're looking for something other than physics.
Edit: Let me see if I can make myself clear. We know that c is constant no matter how fast you are moving. If c is constant then it can be derived that time slows down and distances get compressed, etc. etc. etc. Einstein derived all of this by realizing that c is constant in all frames of reference. Now, if I ask "Why does time slow down?" and I get the answer "because c is constant" then we are just going in circles. It seems that that is what is happening here. Correct me if I'm wrong but are you not using a derivation of the fact that c is constant as an answer? I'm looking for a more fundamental reason as to why time slows down. Which is the same as asking why c is constant.
All solid matter moves forward in time at the same speed, minus the speed in which it's moving in the other 3 dimensions. Light and other particles only move forwards in time.
the speed of light, c, can be violated from your frame of reference, but the external observer doesn't see this - it's your perception of time that has slowed down.
you reach the speed of light (from the perspective of an external observer) when your local velocity is infinite (and then all travel becomes instantaneous).
Let's say you're moving nearly as fast as the speed of light. Are you flying side by side with light particles? No, because if they were, you would measure their speed as being close to zero relative to you. The theory says you will STILL measure the beams of light as flying away from you at the speed of light relative to you.
Imagine how the universe must conform to make that the case! The universe essentially makes your time tick slower in order for light to still travel that much faster relative to you.
This phenomenon has been confirmed (along with basically every other prediction that Einstein has made). There are some subatomic particles that we know has a half-life of X seconds. However, when they're traveling quickly, they actually end up living orders of magnitude longer because of time dilation.
In every day life, if you throw a ball at 70 mph on top of a car that's going 30 mph, the ball moves at 100 mph. You can't do the same math once you start reaching the speed of light.
The real formula is s = (v+u)/(1+(vu/c^2)).
For small values of v and u, vu/c^2 is approximately 0, leaving you with the standard (Galilean) formula, but only as an approximation.
See Wikipedia for a discussion and formulae for vector addition: http://en.wikipedia.org/wiki/Velocity-addition_formula
It's not really "the theory"; in this case, the actual experiment[1] predated the math.
[1] http://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experi...
Something you said just clicked. I think I may now clearly "grok" relativity for the first time.
It reminded me of the http://en.wikipedia.org/wiki/Mahalanobis_distance
which calculates different distances given a vector field w/r to a Euclidian space.
It's not the same thing, but when thinking about what Mahalanobis distances measure, I used a helpful mental model of the measure forcing the vector field apart, enforcing a kind of constant distance between the vectors and then measuring that delta. It seems like a similar concept is at play here, only what we're measuring is different.
I'm aimlessly musing here, but I feel a kind of grokiness I haven't felt before after your post.
It actually makes sense in that regard, because while accelerating, you will shrink along the acceleration vector.
Let's say you are 6 feet tall and fly Superman-style at 0.9c. You will then, from the outside, be 2.6 feet (or so). This means that if you from your timeframe accelerate by 1 km/s, to the outside you will accelerate by 0.4 km/s.
This acceleration in turn cause you to shrink even further, and as you approach the speed of light your external length will approach 0. So any further acceleration in your frame of reference, no matter how immense, would approach 0 from the outside.
[Edit: "the force required to double your speed" is pretty damn meaningless. What I"m looking for is something like "your mass effectively increases exponentially as your speed..." Sorry.]
[Edit v2: How about this: "For a given force, your acceleration decreases as if your mass were increasing exponentially as your speed approaches the speed of light."]
It should be obvious that if you travel fast you have energy. And the faster you go, the more energy, and the heavier you are the more energy.
Now comes the interesting part: That velocity energy you have increases your mass! As soon as you have this, some very interesting things happen.
As you get faster you get heavier, the heavier you are the more energy you need to go even faster. This positive feedback loop eventually results in you needing an infinite amount of energy to go any faster (since you are so heavy).
The point where you need infinite energy is at the speed of light.
Now comes the second interesting effect.
Suppose you accelerate to half the speed of light - you have a certain amount of energy - no problem.
Now someone else does that too - only in the opposite direction.
He too had no trouble accelerating, and needed only a finite amount of energy.
But what happens if the two of you are traveling toward each other? A problem - the total of your speed is greater than the speed of light! And even if it was slightly less, suddenly you got energy for free! (Because of the feedback loop going from 0 to 1/2 c takes MUCH MUCH less energy that from 1/2 c to 8/9 c. So where did that energy come from?)
That obviously is impossible - you can't get energy for free. Instead the very definition of speed is changed! You have no choice - you have to change it. The definition is changed in such a way that the energy remains constant. And if the definition of time and length has to change to make it work, so be it. Energy is more important.
Of course all this rests on a foundation: That the increase in speed results in an increase in mass. But this too is required. We already know that's it's possible to convert energy to mass. So we could use a trick - convert mass to energy, speed it up, then convert it back to mass and suddenly we have mass moving very fast without putting in energy. Nope, can't do that. What actually happens is that energy has mass too, and this doesn't work. (If energy didn't have mass you could do other tricks, like send the energy up to space, convert it back to mass and let it fall under gravity.)
Hopefully this should show you why relativity is required if you have conservation of energy.
Onlookers at your destination would not see you until you arrived but ones from your departure would see you leave and you would be invisible to another craft going at the same speed as you.
So the question still stands; only the argument that lightspeed is a limit because it is incompatible with relativistic physics should be abandoned (stated like this, it seems a fairly weak argument anyway).
It remains an interesting challenge to prove that more rigorously, of course.
I'd put my money on a hypothesis that says causality is enforced whether we can perceive it or not. Say we had such a computer with FTL circuitry. You attempt to instruct the computer to halt the current program when an answer is received, thus preventing the inputs being supplied that would produce the given output. Our current time-based perception says "paradox" whereas this proposed hypothesis would say "the computer simply will not halt the program," not because it's designed with safeguards, but because the laws of physics maintain causality.
Yup.
The same argument could have been waged against the heliocentric model. Occam's razor is not a natural law after all.
http://www.reddit.com/r/askscience/comments/fjwkh/why_exactl...
Essentially, it makes no sense because "faster than light" translates to "faster than as fast as you can possibly travel".
All you've done is explained a word by simply repeating it.
The reddit comment doesn't explain anything either - as the very first comment under it says.
If you want an actual accessible explanation see my comment: http://news.ycombinator.com/item?id=4637451
Just because you can calculate something, doesn't mean it actually exists. (Although the fact that it does sometimes exist is one of the true wonders of the world.)
This is also true of the Alcubierre drive that was in the news a little while ago: It's a mathematical solution, but my have no basis in reality.