## Faster than light

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Word
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### Faster than light

So, if you were standing in front of a brick wall and by whatever considerably impossible means, somebody a good distance in front of you were to throw a ball which traveled faster than light and impacted the wall behind you, what exactly would you witness? This is considering you were somehow capable of witnessing the ball actually moving toward you (say the speed of light had slowed considerably).

Most likely you'd first see the result of the impact, and then the ball flying through the air toward the wall, but then what? Would you watch it strike the wall twice or would it disappear prior to contact?

letterX
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### Re: Faster than light

Word wrote:Most likely you'd first see the result of the impact, and then the ball flying through the air toward the wall, but then what?

Why would you see that? If a plane is flying towards you, faster than the speed of sound, which do you hear first: the plane or the echo off the brick wall behind you?

Soralin
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### Re: Faster than light

Well if it was flying directly at you, you wouldn't notice anything, as a superluminal ball flies through your head.

If it were to pass slightly next to you, the first you would notice it would be at it's closest point to you. At which point, the light that it had emitted before it reached that point would catch up, and at the same time light from the back side of the ball as it went past you would be able to reach you. So basically, it would be like the ball appeared right next to you, and went flying off in two different directions. If it hit the wall, and bounced back at superluminal speeds, the same sort of thing would repeat. The first you would see of it would be when it was at it's closest approach to you, and it would appear to fly off in both directions, with both images of the ball disappearing when they hit the wall. These should both hit the wall at the same time I think, although the image from the one moving toward you will be traveling toward the wall faster than the one moving away from you, I think.

Yeah, thinking this out, the ball appears next to you, it splits, and one image moves quickly away from you in the direction that it came from, and the other moves more slowly in the direction that it's actually going, toward the wall. Then, if it rebounds and flies back, you see it appear next to you again, and see it split again, with one ball flying back toward the wall quickly, and hitting the wall at the same time that the previous slow image hits, at which point they both disappear (if it left a crater or something, this is when you'd see that happen as well), and the other as a slower image of the ball flying off in the direction it initially came from. If it doesn't rebound, you can just leave out that second ball appearance and split. At least I think that's how it should turn out.

Or, everything would be red-shifted and blue-shifted outside of the range of human vision. Or, you're dead from http://en.wikipedia.org/wiki/Cherenkov_radiation Or just the heat or concussive blast from the object, as it craters itself in the wall, or blasts through the air, or whatever medium it's traveling through..

Note, that doing this experiment is actually sort of possible, light travels slower through various materials than it does through vacuum. You just need your ball to be moving faster than the speed of light of the substance through which it's moving. For example, speed of light through water is only about 0.75c. Although actually trying to do so would likely end up rather destructive.

If you want to visualize it, you can draw it out with some graph paper, or think about it that way at least. Every unit of time, have the ball send out a pulse, as a circle, and then move x units, according to it's speed. And have each circle expand it's radius by 1 every unit of time as well. When an expanding circle reaches your eye, that's when you will see the ball, as being at the center of that circle. See for example:

mfb
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### Re: Faster than light

Two ideas how to realize this:

- send a bunch of high-energetic, charged particles through a big water tank, detect the photons from ionization (or something similar, but not cherenkov radiation) with a very high time-resolution (<1ns).
- find a way to have slow light in a full two-dimensional plane with less than ~10km/s. Shoot some dust particle along the edge of this plane (but outside and in a vacuum) with at least ~twice the speed of light in your medium, illuminate it with a laser tuned to the specific frequency where light is slow in this medium. While the phase velocity of the light is high (and therefore refraction does not produce strange effects), the slow group velocity allows you to do this experiment. Use high-speed cameras to observe it.

A wall with an impact might be possible in the second case, but don't expect the dust particle to bounce off. It will generate a very small explosion.

Sagekilla
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### Re: Faster than light

In your hypothetical universe where stuff can travel faster than light, you will actually see the object in two separate locations at the same time.

The basics you need:

Assume you are at the origin (0, 0).
The ball is traveling to the right with velocity v, starting at position (-L, -y)
The distance between you and the ball is given as: d(t) = sqrt(y^2 + (v t - L)^2)
The time it takes for the light to travel to you from the ball when it was at that position is tau(t) = d(t) / c

Solve tau(t) + dt = tau(t + dt) for dt. This is the time delay between when the ball first sends out photons and
when it sends out photons at a later time (t + dt) such that the photons from the ball at two times will reach
you at the same time.

If we substitute in tau, we get:
sqrt(y^2 + (v t - L)^2) + c dt = sqrt(y^2 + (v (t + dt) - L)^2)

Square both sides:
y^2 + (v t - L)^2 + c^2 dt^2 + 2 c dt sqrt(y^2 + (v t - L)^2) = y^2 + (v (t + dt) - L)^2

Expand and cancel:
c^2 dt^2 + 2 c dt sqrt(y^2 + (v t - L)^2) = v^2 dt^2 + 2 v^2 t dt - 2 L v dt

Rearrange in powers of dt:
dt^2 (c^2 - v^2) + dt (2 c sqrt(y^2 + (v t - L)^2) + 2 L v - 2 v^2 t) = 0

The only non-trivial root of this equation is given as:
dt = 2 (c sqrt(y^2 + (v t - L)^2) + L v - v^2 t) / (v^2 - c^2)

If you were to actually "see" this, the balls would appear in the following locations:

Red line points to the ball in the past, blue line points to the ball in the future.

The parameters are: L = 50 m, y = 10 m, c = 3E+8 m/s, v = 6E+8 m/s
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elasto
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### Re: Faster than light

It's not directly related to this thread, but the discussions put me in mind of a video I saw recently of a camera capturing at a trillion frames a second - fast enough to see the progression of light moving across and through objects and bouncing off walls etc.

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WarDaft
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### Re: Faster than light

That seems like an awful lot of work when you could just make a graphical simulation assuming a finite speed of light (people rarely bother considering that it actually takes time for light to cross a scene, because that time is smaller than anything else they are bothering to calculate by a factor of about a million.) Just set the speed of light to 0.3 mm/s, run a photon path tracing simulation at real time, and that's what you'd get.

Still really cool though, I would never have thought you could even pretend to actually record light pouring over an object.
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### Re: Faster than light

Argh. Get thee to the fictional science subforum.
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Soralin
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### Re: Faster than light

doogly wrote:Argh. Get thee to the fictional science subforum.

Things can move faster than the speed of light, they just can't move faster than the speed of light in a vacuum.

Technical Ben
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### Re: Faster than light

WarDaft wrote:That seems like an awful lot of work when you could just make a graphical simulation assuming a finite speed of light (people rarely bother considering that it actually takes time for light to cross a scene, because that time is smaller than anything else they are bothering to calculate by a factor of about a million.) Just set the speed of light to 0.3 mm/s, run a photon path tracing simulation at real time, and that's what you'd get.

Still really cool though, I would never have thought you could even pretend to actually record light pouring over an object.

It has many applications in scanning and scientific photography AFAIK. One example given in the video it testing for irregularities or defects in products and manufacturing. Let alone anyone who wants to test if simulations == real life results.

Oh, and in agreement with Soralin, things can also "appear" to move faster than the speed of light. See for example the movement of an extremely large shadow or a well timed Mexican wave (hint: those things do not move faster than the speed of light, but we can mistake them to be).

Oh, and as I'm totally confused with the 2d animated graph, does anyone have a 3d visual version? I'm imagining a FTL ship appearing out of nowhere, then a "copy" of it flying backwards away from me. If the ship is slowing down, this could get even more complicated with 3 ships visible right? (Future, "present" and past?)
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doogly
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### Re: Faster than light

You want to stop being in a vacuum? Well, alright. We can allow this, I suppose.
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Tupolev
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### Re: Faster than light

Technical Ben wrote:Oh, and in agreement with Soralin, things can also "appear" to move faster than the speed of light. See for example the movement of an extremely large shadow or a well timed Mexican wave (hint: those things do not move faster than the speed of light, but we can mistake them to be).

It's not a mistake at all. Those things can easily move far faster than c, and there's nothing contradictory about that. The key point to make is that the objects moving faster than c are not able to carry classical information faster than c.

This can be very easily visualized by imagining the example of aiming a laser pointer at a very distant wall. By rotating the laser quickly, you could move the dot much faster than light. However, a person standing at the wall could not simply attach a data packet to the dot and have the dot carry it FTL to another spot on the wall; in fact, if he wanted to use the dot to transmit information to another point on the wall, he could either:
1-Use a mirror to direct the laser beam itself (which propogates at c) to the other spot on the wall, or
2-Send a message with his own laser beam (which propogates at c) to the main laser operator, who could then rotate the main laser (the beam of which propogates at c) to the location of the message recipient.
Another important way to look at this is that moving the source laser doesn't instantaneously cause dot motion; it causes a wave to propoate along the laser beam which causes dot motion once the wave travels down the beam to the wall.

So yeah, we aren't wrong when we measure these things as moving faster than c. It's just that these things aren't carrying classical information about that fast. A shadow isn't some envelope that you can just stash a letter into.

Technical Ben
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### Re: Faster than light

I thought the point that shadows do not move means they cannot travel faster than light.
Nothing moved "faster than light". You just saw a disconnected series of events happen close together. For example the camera in the video linked above is not a camera working faster than light. It is 500 cameras (or whatever systems they used) working in unison. We could do the same with a Mexican wave. Just have the people timed in advance to lift their hands at intervals faster than the speed of light. Then the "wave" propagates faster than light. But you set it up ahead of time at lightspeed with a set of clocks and little notes say "we're gonna make the fastest Mexican wave in the world ever! You in?"

Or a simpler example, we could have asked the Luna crew to write their reply down in advance. Then to start reading it few seconds before we are due to start a conversation. Then it sounds like they are communicating FTL (no delay in communicating with the moon). But really, it was just a trick in out pre arranged timings.
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### Re: Faster than light

The shadow / laser pointer example allows us to continue this discussion solidly in the realm of non-fictional science: suppose you're standing near a wall, and someone far from you is shining a laser dot on the ground in front of you, and moves it toward the wall in such a way that the dot appears to move much faster than light for you. For the bouncing example, just suppose that the person with the pointer reverses its direction as soon as it looks like the pointer itself is directed toward the wall (which is before the dot will appear at the wall, if the pointer is sufficiently far away from it).
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curtis95112
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### Re: Faster than light

If we're talking about laser pointers, you'll just see the image move faster than light and backwards.
If we're talking about something really moving FTL, we'll see this:

(The colors show doppler shift, the translucent ball is the ball's actual position)
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### Re: Faster than light

curtis95112 wrote:If we're talking about laser pointers, you'll just see the image move faster than light and backwards.
Well yeah, but the question is what that looks like.
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WarDaft
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### Re: Faster than light

Well, you can't see the dot move away from you faster than the speed of light, but it could appear to move away arbitrarily close to the speed of light as swing speed of the reflection point reaches infinite (If the 'dot' hits every point on the wall at the same time, you will see a dot scoot away at the speed of light) and moving towards you... you will again see it move away arbitrarily close to the speed of light as the swing speed approaches infinite. Depending on how fast you swing it, you can actually show the person multiple dots shooting away from them at various intervals (that is, if you could actually see something that was moving away from you at close to light speeds)
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Soralin
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### Re: Faster than light

gmalivuk wrote:
curtis95112 wrote:If we're talking about laser pointers, you'll just see the image move faster than light and backwards.
Well yeah, but the question is what that looks like.

From what I can tell, that would look just like an FTL object would. The first you would see of it would be the light of the dot scattered at your feet. That would be the first to reach your eyes, over say, the light of the dot scattering 1ns ago, 1.5 light-ns away. And from there, you would see it head off in both directions, as the light from where it had been caught up to you, along with the light from further along it's course. Just like the image curtis has there.

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### Re: Faster than light

Soralin wrote:
gmalivuk wrote:
curtis95112 wrote:If we're talking about laser pointers, you'll just see the image move faster than light and backwards.
Well yeah, but the question is what that looks like.

From what I can tell, that would look just like an FTL object would.
Right, which is why I was confused that curtis95112 split them into separate cases. You'd get the same weird backward-seeming motion from the dot, but with no violation of relativity, as well as the splitting when it passed you and rejoining when the returning dot passes you on its way back from the wall.
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Technical Ben
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### Re: Faster than light

curtis95112 wrote:If we're talking about laser pointers, you'll just see the image move faster than light and backwards.
If we're talking about something really moving FTL, we'll see this:

(The colors show doppler shift, the translucent ball is the ball's actual position)

Thanks. I've filed that one for reference. Is that a tacyon in the image?
I was mainly confused about viewing, for example, a ship slowing down from FTL to just in front of the viewer. So would it be like the above image? You would see the ship appear as if from no where, then a copy/illusion of a second ship travelling back from it? Rather like the Star Trek warp effect but in reverse. Cool.
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curtis95112
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### Re: Faster than light

Oh yes, you guys are right. Both cases would look the same, except you don't get doppler shift with the laser pointer.

I confused the laser pointer case with the one where you do see apparent FTL motion. (For instance, you're in a large cylindrical room, and you spin the laser pointer fast enough)
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### Re: Faster than light

Technical Ben wrote:I was mainly confused about viewing, for example, a ship slowing down from FTL to just in front of the viewer. So would it be like the above image? You would see the ship appear as if from no where, then a copy/illusion of a second ship travelling back from it? Rather like the Star Trek warp effect but in reverse. Cool.

<trekkie>This is actually referred to in the lore as the "Picard maneuver"; he used it once against a Ferengi ship that lacked FTL sensors.</trekkie>
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