I just realized we won't be able to go at the speed of light.

[bandit4910]

Well after reviewing some science I realized our spaceships won\'t be able to go at the speed of light. That is if Einsteins theories are correct. We have been able to send particles at ALMOST the speed of light. If we do actually go at the speed of light it could take maybe half a million years. Or we could find a way to make wormholes... But then again, we would need to find a way to make sure the wormhole leads where we want it to. Or we could find an unlimited power source.

[mincespy]

We can send particles at the speed of light already...

...If you count photons as particles.

[bandit4910]

We can send particles at the speed of light already...

...If you count photons as particles.

My bad we can send one type of particle at the speed of light...

[RedDwarfIV]

This is why we are building Dimension Shunters...

Oops. Said too much.

[Ascensiam]

*turns on lamp*

There, i just sent photons at the speed of light with human technology ???

[Charzy]

Well, if we can create a material with no weight...

[Ted]

We still need a theory of everything that encompasses sub-atomic/quantum mechanics and general relativity. Until then, many of the theories which we take to be true, could in fact be wrong.

Speed of Light travel could be possible, if not we could always use anti-matter engines, we can get quite the velocity from those.

[Lord Wasteland]

No you have to think about it another view. It can be considered FTL, but in fact waht about the principle of bending space? Wormholes bend space to touch two points, so if we were able to do that, essentially we could have FTL engines.

[socket7]

Well after reviewing some science I realized our spaceships won\'t be able to go at the speed of light. That is if Einsteins theories are correct. We have been able to send particles at ALMOST the speed of light. If we do actually go at the speed of light it could take maybe half a million years. Or we could find a way to make wormholes... But then again, we would need to find a way to make sure the wormhole leads where we want it to. Or we could find an unlimited power source.

Thankfully, All the models of physics are incomplete and don\'t mesh together correctly. Until we get a grand unified theory, FTL, warp drive, teleporters, and even a god or two could be hiding in the gaps of our knowledge.

Keep dreaming! And hope for some astounding new discovery that will enable us to go FTL.

[nibula]

warp engines?

[mincespy]

I thought muons went faster than light, or at least close to the speed of light.

[CaptainArbitrary]

There\'s a huge difference between 'close to the speed of light' and 'faster than the speed of light.' It\'s got to do with the geometry of spacetime and what the word 'speed' really, once you get right down to it, means in our universe.

When you\'re dealing with things that move slowly, it looks like relative speeds add like Euclidean vectors. In other words, here\'s you, and here\'s a thing moving away from you at one mile an hour, and here\'s a thing moving away from that in the same direction at two miles an hour. How fast is the second thing moving away from you? Well duh. You just add the vectors. Since they\'re in the same direction, the answer is one mile an hour plus two miles an hour, or three miles an hour. This is blindingly obvious even to the smallest child.

Trouble is, it\'s not right. It is, in fact, completely wrong.

Now, it\'s wrong in such a way that you can\'t spot the error on the scale of a few miles an hour. That\'s why it took us thousands of years to realize we\'d been adding velocities wrong this whole time. But once you start looking at things that move fast, you find that in fact velocity vectors don\'t add like Euclidean three-vectors at all. In fact, they add like hyperbolic angles.

I know that sounded like gibberish, so let me explain what it means. In essence, we have to replace the idea of Euclidean vector addition with the idea of rotation by a hyperbolic angle. Hyperbolic angles work just like circular angles —you know, 90° or whatever —only instead of going from zero to 360°, they go from minus infinity to plus infinity. You can go around a circle and come back to where you started, but you can\'t go around a hyperbola. Hyperbolas are, in a meaningful sense, 'inside-out' circles, so in a lot of ways they behave in opposite fashion to how circles behave. Hyperbolic angles going from minus infinity to plus infinity is one example of that.

When you describe relative motion —the motion between two things —in Euclidean geometry, velocities look like vectors. But like I said before, thinking about motion that way ends up giving you the wrong answers once you deal with things that move fast —like, yes, muons produced in cosmic-ray interactions in the upper atmosphere. So instead, you have to describe motion using hyperbolic geometry, and when you do that, velocities look like hyperbolic angles instead of Euclidean vectors.

So let\'s go back to the example from before: thing moving away from you at one mile an hour, other thing moving away from that thing at two miles an hour, how fast is thing 2 moving away from you? Like I said, if you write that out as a problem in Euclidean vector math, you get the wrong answer. It\'s very very close to the right answer, because three miles an hour is a small number, but it\'s still wrong. If you want the right answer, you have to convert 'one mile an hour' into a hyperbolic angle, and then convert 'two miles an hour' into a hyperbolic angle, and then add the angles, and then convert back to a velocity again to get a number you can intuitively understand.

That all sounds like mathematical nonsense and navel-gazing, I know. But here\'s why it\'s important: There\'s no fastest possible speed. Remember when I said that hyperbolic angles go from minus infinity to plus infinity? Since velocities are hyperbolic angles, mathematically speaking, and hyperbolic angles go all the way to infinity, for any given velocity —any given hyperbolic angle, in other words —you can always add a little more. There is no universal speed limit! This is an important insight!

Okay, but … speed of light. How do we reconcile the fact that there\'s no universal speed limit with the fact that the speed of light is the 'universal speed limit'? Like this: Remember I said before that after you do that math problem with the adding of the angles, you have to convert back to a velocity to get a number that makes sense to you. This is, in a sense, projecting hyperbolic geometry onto Euclidean geometry, in much the same way that you can project the surface of a sphere onto a plane to draw a map of the Earth. But remember how all flat maps of the Earth are distorted in one way or the other? Points which are actually close together look far apart on the map, because in projecting one geometric surface onto another you end up breaking isometry —which is just a fancy way of saying you distort the distances between points. Well, the same is true of projecting velocity space —which is hyperbolic —onto Euclidean space in order to convert angles into velocity vectors: You end up with a distortion.

That distortion is called relativity. It\'s the reason why accelerating an object that\'s nearly at rest relative to you creates a big change in that object\'s velocity, while accelerating an object that\'s going like stink relative to you by the same amount creates a small change in that object\'s velocity. The map is distorted. The map that relates actual changes in momentum and position over time to observed changes in momentum and position is distorted such that when things move slowly, the changes look big, but when things move fast, the changes look very small. It\'s actually the same change, just distorted by the projection of hyperbolic velocity space onto a universe that, to us, looks Euclidean.

Long story short, even though you can keep accelerating an object forever and ever —because the velocity angle goes all the way to infinity —the actual change in velocity a stationary observer sees as that object accelerates grows smaller and smaller the faster the object goes. What\'s the limit? The speed of light. If you accelerate an object forever, its observed speed, as seen by somebody at rest, will get closer and closer to, but will never exceed, the speed of light. If you look at the math, you find that the hyperbolic angle that corresponds to a velocity of the speed of light is actually infinite. Meaning you can get as close as you want to it —you can always go faster —but you can never actually reach it.

So on the one hand, you can say truthfully that there is no universal speed limit. You can, in principle if not in practice, accelerate an object forever, and it\'ll just keep going faster and faster and faster and faster. But on the other hand, you can also say truthfully that the speed of light is the universal speed limit, because no observer, no matter where he is or how he\'s moving, will ever observe anything accelerating to the speed of light. It\'s literally impossible, in exactly the same way and for exactly the same reason that it\'s impossible to count to infinity. You can keep counting forever —you can keep accelerating forever —but you can never reach infinity.

So the difference between a mile an hour slower than the speed of light and the speed of light itself might only seem like one mile an hour, but in fact it\'s a gulf that\'s literally infinitely wide. It only looks like one mile an hour because we\'re looking at a distorted map.

[Ted]

So the difference between a mile an hour slower than the speed of light and the speed of light itself might only seem like one mile an hour, but in fact it\'s a gulf that\'s literally infinitely wide. It only looks like one mile an hour because we\'re looking at a distorted map.

I suppose this is due to the sheer difference in the amount of energy it would take to increase it by one mile an hour from rest and one mile an hour to the speed of light?

Also, we would see things such as time dilation and space-time distortion start to occur which would technically affect our perception of \'velocity\'.

[CaptainArbitrary]

There is no difference in energy required. 'Relativistic mass' is a myth, a teaching tool that got out of hand and is now no longer in favor even in the classroom. Changing your velocity by one unit requires the same amount of energy regardless of how fast anybody else thinks you\'re going.

Time dilation (and length contraction; same thing) is a function of moving coordinate systems. You\'re in your coordinate system, and you refer to an interval of time as being one second. I\'m in my own coordinate system, moving differently from yours, so I can\'t just say that your 'one second' is the same as my 'one second.' I have to convert that interval from your coordinate system to my own. It turns out that this conversion is a hyperbolic rotation (there\'s hyperbolic geometry again), where the angle of rotation is equal to the hyperbolic arctangent of the velocity separating us normalized such that the speed of light is equal to one. When I apply that rotation to your vectors to get them into my coordinate system, I find that time components get stretched and space components get squeezed. That\'s all time dilation is; just a function of the conversion from one coordinate system to another.

It\'s really important, though, that we not ever be misled into thinking we\'re talking about 'perception.' There\'s nothing subjective about any of this. It\'s pure objective reality. The only thing that\'s subjective about it is the simple fact that we live our lives at a few hundred miles an hour, tops. That\'s why the fundamental truth about how motion works seems so weird to us. It\'s cause we literally can\'t see it in our everyday lives. We have to go looking for it to observe how the universe works.

[Endeavour]

CaptainArbitrary, that is the most impressive wall of text I have seen on these forums. And your explanation was great.

[LukeTim]

CaptainArbitrary, that is the most impressive wall of text I have seen on these forums. And your explanation was great.

Seconded. I thought I had a decent understanding of Relativity... now I understand that I didn\'t.

[vexx32]

I now see that even my Physics teacher is wrong on many points about relativity. To be fair, we do tend to simplify things as we don\'t often have the time to delve deep enough into the workings of everything whilst making sure everyone knows what\'s going on.

Still, I appreciate that wall of text, as it finally explains why the speed of light is in fact a limit... assuming that Relativity is true. Widely accepted and all, but that doesn\'t mean it\'s flawless or even right. If you knew nothing about how a lightbulb works, I\'m sure you could come up with a fair few explanations for it that make some sort of logical sense... but that doesn\'t mean you\'ll find the right answer. I\'m not getting into theoretical debates here, though.

Anyhoo, thanks 8)

[Endeavour]

So the reason we have relativity is because we see the universe as Euclidean, when its really not. And the projection from what it is to what we understand is the thing that gets distorted, not the universe itself?

[RedDwarfIV]

So, what, we need to build a drive that causes reality to become Euclidian?

[CaptainArbitrary]

So the reason we have relativity is because we see the universe as Euclidean, when its really not. And the projection from what it is to what we understand is the thing that gets distorted, not the universe itself?

Sort of. It all comes back to geometry. You know that we can describe space in terms of an orthonormal basis, right? X, Y, Z: three axes that are mutually perpendicular and isometric. Well, if you add time to that basis as a fourth axis, perpendicular to the other three (which takes some imagining, since in reality we can only visualize three mutually perpendicular axes, not four), you get Galilean relativity. That is, time becomes a coordinate just like the three coordinates of space, but it works just like the space coordinates do, and thus there is no relativity. It doesn\'t matter where you are or how you\'re moving, your coordinate system is the same as everybody else\'s in the universe.

Only that\'s wrong. It took a guy named Minkowski to figure out, based on the work of Einstein which was at the time still quite naive, that if you give spacetime a different type of geometry from the four-mutually-perpendicular-axes of four-space, instead of getting Galilean relativity (which is wrong, and contradicted by observations of the real world), you get Einsteinian relativity (which is right, and confirmed by observations of the real world).

I don\'t know how to explain in detail just how Minkowski\'s geometry is different from Euclid\'s without going into the deep topic of differential geometry, which is a fairly esoteric branch of math that most people never bother to learn about. It has to do with the signature of the metric, where the metric is a tensor that describes how coordinate systems transform. Suffice to say that if you use the Euclid tensor, you get Galilean relativity, and if you use the Minkowski tensor, you get the Einstein\'s theory of special relativity, which describes how coordinate systems transform between observers moving through space in the absence of either gravity or acceleration. (If you want to understand how gravity and acceleration work, you have to set the Minkowski tensor aside and look instead at the Einstein tensor, a much more complicated object that I won\'t even bother alluding to.)

What it really all boils down to is the fact that we can\'t see time. We can see space — we can draw lines on a piece of paper and go 'Oh, these are parallel,' and stuff like that. It was from such explorations of how space works that we got Euclid\'s geometry, and in particular his fifth postulate. Euclid\'s fifth postulate is the one that says, in essence, that two lines which are parallel in one place are parallel everywhere. But it turns out the fifth postulate is only true in the special case, a type of geometry which mathematicians call 'flat,' because you can illustrate how it works on a flat piece of paper. When we first started thinking about how time relates to space —Galileo, again —we all just assumed that the geometry in which space and time operate must necessarily be the geometry of Euclid: 'flat' geometry. Turns out this is wrong, which is where Minkowski came in, and so forth and so on.

If I can make an analogy which should not be taken very seriously just for purposes of illustration, you know how on a Mercator projection of the Earth the equator looks just fine but there\'s this awful distortion near the poles making Greenland look as big as Africa? It\'s that same basic kind of idea. If you try to represent curved geometry — the geometry of the surface of a sphere, like the Earth —in flat space —like on a piece of paper —you find that it just simply doesn\'t work. You end up with inconsistencies, like straight lines on the globe turning curved (lines of latitude) or parallel lines on the map intersecting (lines of longitude). That\'s not because we suck at drawing maps; it\'s because you can\'t draw a map of a globe. It\'s physically impossible, because the geometries just aren\'t compatible.

The relationship between space and time is kind of like that, roughly speaking. The part that makes it tricky is that we can\'t see time like we can see the globe. It\'s one thing to look at a map and then look at a globe and go 'Oh, the map is all wonky because it has to be.' If you could 'see time' (whatever that means), you would probably also be able to look at Galilean relativity and go 'Oh, the map is wonky because it has to be.' Instead, though, we have to observe time indirectly, by looking at things like how fast-moving subatomic particles age in different frames of reference, and suss out the geometry of time the hard way.

So, what, we need to build a drive that causes reality to become Euclidian?

Please don\'t take this the wrong way or anything, but that\'s exactly like saying you need a map that causes the Earth to become flat. It\'s just gibberish. The Earth isn\'t flat. Spacetime isn\'t Euclidean. These are facts, not things we can change. It\'s like saying you need to invent a space gizmo that makes two and three add up to eleven.

[Endeavour]

Thank you CaptainArbitrary. Everytime people tell or teach about relativity they say 'Now its too complex to actually go into, so I\'ll give the simple version'. And that leads to misunderstandings. About time someone told me what\'s what.

[RedDwarfIV]

In which case, I can mention that in my webcomic at some point.

Prof Teal - 'I thought about designing a drive that would make reality go Euclidian.'

MC Renaza - 'And then you realised it was a silly idea?'

Prof Teal - 'After I built it, yes.'

[cardgame]

There\'s a huge difference between 'close to the speed of light' and 'faster than the speed of light.' It\'s got to do with the geometry of spacetime and what the word 'speed' really, once you get right down to it, means in our universe.

When you\'re dealing with things that move slowly, it looks like relative speeds add like Euclidean vectors. In other words, here\'s you, and here\'s a thing moving away from you at one mile an hour, and here\'s a thing moving away from that in the same direction at two miles an hour. How fast is the second thing moving away from you? Well duh. You just add the vectors. Since they\'re in the same direction, the answer is one mile an hour plus two miles an hour, or three miles an hour. This is blindingly obvious even to the smallest child.

Trouble is, it\'s not right. It is, in fact, completely wrong.

I\'m listening.

Now, it\'s wrong in such a way that you can\'t spot the error on the scale of a few miles an hour. That\'s why it took us thousands of years to realize we\'d been adding velocities wrong this whole time. But once you start looking at things that move fast, you find that in fact velocity vectors don\'t add like Euclidean three-vectors at all. In fact, they add like hyperbolic angles.

Uhh... okay.

I know that sounded like gibberish, so let me explain what it means. In essence, we have to replace the idea of Euclidean vector addition with the idea of rotation by a hyperbolic angle. Hyperbolic angles work just like circular angles — you know, 90° or whatever — only instead of going from zero to 360°, they go from minus infinity to plus infinity. You can go around a circle and come back to where you started, but you can\'t go around a hyperbola. Hyperbolas are, in a meaningful sense, 'inside-out' circles, so in a lot of ways they behave in opposite fashion to how circles behave. Hyperbolic angles going from minus infinity to plus infinity is one example of that.

When you describe relative motion — the motion between two things — in Euclidean geometry, velocities look like vectors. But like I said before, thinking about motion that way ends up giving you the wrong answers once you deal with things that move fast — like, yes, muons produced in cosmic-ray interactions in the upper atmosphere. So instead, you have to describe motion using hyperbolic geometry, and when you do that, velocities look like hyperbolic angles instead of Euclidean vectors.

So let\'s go back to the example from before: thing moving away from you at one mile an hour, other thing moving away from that thing at two miles an hour, how fast is thing 2 moving away from you? Like I said, if you write that out as a problem in Euclidean vector math, you get the wrong answer. It\'s very very close to the right answer, because three miles an hour is a small number, but it\'s still wrong. If you want the right answer, you have to convert 'one mile an hour' into a hyperbolic angle, and then convert 'two miles an hour' into a hyperbolic angle, and then add the angles, and then convert back to a velocity again to get a number you can intuitively understand.

That all sounds like mathematical nonsense and navel-gazing, I know. But here\'s why it\'s important: There\'s no fastest possible speed. Remember when I said that hyperbolic angles go from minus infinity to plus infinity? Since velocities are hyperbolic angles, mathematically speaking, and hyperbolic angles go all the way to infinity, for any given velocity — any given hyperbolic angle, in other words — you can always add a little more. There is no universal speed limit! This is an important insight!

Okay, but … speed of light. How do we reconcile the fact that there\'s no universal speed limit with the fact that the speed of light is the 'universal speed limit'? Like this: Remember I said before that after you do that math problem with the adding of the angles, you have to convert back to a velocity to get a number that makes sense to you. This is, in a sense, projecting hyperbolic geometry onto Euclidean geometry, in much the same way that you can project the surface of a sphere onto a plane to draw a map of the Earth. But remember how all flat maps of the Earth are distorted in one way or the other? Points which are actually close together look far apart on the map, because in projecting one geometric surface onto another you end up breaking isometry — which is just a fancy way of saying you distort the distances between points. Well, the same is true of projecting velocity space — which is hyperbolic — onto Euclidean space in order to convert angles into velocity vectors: You end up with a distortion.

That distortion is called relativity. It\'s the reason why accelerating an object that\'s nearly at rest relative to you creates a big change in that object\'s velocity, while accelerating an object that\'s going like stink relative to you by the same amount creates a small change in that object\'s velocity. The map is distorted. The map that relates actual changes in momentum and position over time to observed changes in momentum and position is distorted such that when things move slowly, the changes look big, but when things move fast, the changes look very small. It\'s actually the same change, just distorted by the projection of hyperbolic velocity space onto a universe that, to us, looks Euclidean.

Long story short, even though you can keep accelerating an object forever and ever — because the velocity angle goes all the way to infinity — the actual change in velocity a stationary observer sees as that object accelerates grows smaller and smaller the faster the object goes. What\'s the limit? The speed of light. If you accelerate an object forever, its observed speed, as seen by somebody at rest, will get closer and closer to, but will never exceed, the speed of light. If you look at the math, you find that the hyperbolic angle that corresponds to a velocity of the speed of light is actually infinite. Meaning you can get as close as you want to it — you can always go faster — but you can never actually reach it.

So on the one hand, you can say truthfully that there is no universal speed limit. You can, in principle if not in practice, accelerate an object forever, and it\'ll just keep going faster and faster and faster and faster. But on the other hand, you can also say truthfully that the speed of light is the universal speed limit, because no observer, no matter where he is or how he\'s moving, will ever observe anything accelerating to the speed of light. It\'s literally impossible, in exactly the same way and for exactly the same reason that it\'s impossible to count to infinity. You can keep counting forever — you can keep accelerating forever — but you can never reach infinity.

So the difference between a mile an hour slower than the speed of light and the speed of light itself might only seem like one mile an hour, but in fact it\'s a gulf that\'s literally infinitely wide. It only looks like one mile an hour because we\'re looking at a distorted map.

[dt890]

nothing is absolute and if the speed of light is the maximum speed anything can travel then we never achieve the speed of light we can maybe do 99.99999% of the speed of light but we can never truly say we are are exactly traveling at 299 792 458 m/s

[sal_vager]

Has anyone in this thread touched on the problem of microscopic particles becoming a deadly hazard at near to light speed? Due to collisions?

I bring this up because I have recently read 'The songs of distant Earth' by Arthur C Clarke, and in this story, the spacecraft cannot exceed light speed, but instead can only get close to it, putting it at risk of destruction should it be impacted even by a piece of dust at such enormous speeds.

It gets around the space dust problem by carrying a shield of regular ice a few kilometres thick in front of it, water being a cheap and common material.

Thoughts?