Faster than light?

[Just thinking]

Does observed and measured relativistic length contraction occur instantaneoulsy along the entire length or does the contraction propagate at the speed of light?

I ask in light of the following scenario. If one begins to travel at some everyday velocity towards some distant object (e.g.; the Andromeda Galaxy) the distance to that object will become less according to relativistic effects. This distance can be as great as several light hours, or days. Obviously, the everyday velocity does not move the observer that distance in the short time it takes him/her to achieve it. But the distant object is now that much closer ... is it not? In order for this to happen it seems to me that something physical had to travel faster than light as measured by some observer -- unless the contraction occurs at c along that path, but is that the case?

I would appreciate any thoughts on this.

 

[Dilb]

To measure the distance, the angle of photons in some arbitraty triangle are measured. The angle which a photon is travelling at changes when your speed changes (except when it comes straight towards/away from you). This occurs entirely over the acceleration.

The measured change is a result of photons already travelling towards you.

 

[Dilb]

If you mean that the object appears to have moved however much closer, moving closer faster than light, then the problem is that it's not moving. The geometry of space-time is changing, which means you can't meaningfully connect two points in two different reference frames and say something has travelled between them. The length contraction of the distance is entirely different from reducing the distance by moving closer to something.

 

[Just thinking]

The length contraction of the distance is entirely different from reducing the distance by moving closer to something.

Perhaps ... but how?

The distance to the object is now less, and traveling towards it at some measured velocity will resut in less travel time for the traveller than measured by someone watching him go there from an "at rest" position. For you (the traveller) the time takes less because it's a shorter distance -- for the one "at rest" it takes longer, but notes that you will be younger than he upon arrival, for your clock ran slower than his.

This allows one to travel to star systems thousands of light years away (given the technology to do it) within one's lifespan. The universe essentially shrinks.

 

[Schneibster]

Does observed and measured relativistic length contraction occur instantaneoulsy along the entire length or does the contraction propagate at the speed of light?

The contraction doesn't "propagate." It's not a change in the distance; it's a change in your perception of the distance. Think of it this way: as you accelerate relative to the Andromeda Galaxy, the Galaxy itself and all of the distance between you and it contracts, in your frame of reference, all at once, depending on how fast you're going at any given time during that acceleration. If you were to decelerate again, it would all expand again, in your frame of reference. Remember, the distance hasn't changed in the Andromeda Galaxy's frame of reference; your perception of it has changed in your frame of reference.

Remember, it's just as valid to say that the Andromeda Galaxy and all the distance between you and it is moving toward you and past you as to say that you are moving toward it.

I ask in light of the following scenario. If one begins to travel at some everyday velocity towards some distant object (e.g.; the Andromeda Galaxy) the distance to that object will become less according to relativistic effects.

Again, remember that there is no difference between this and if the Andromeda Galaxy and everything between you and it begins to move toward and past you, and it shrinks because it is moving relative to you.

This distance can be as great as several light hours, or days.

Errrmmm, the Andromeda Galaxy is 2.5 million light years away.

Obviously, the everyday velocity does not move the observer that distance in the short time it takes him/her to achieve it. But the distant object is now that much closer ... is it not?

No, you perceive it to be that much closer- as long as you keep that velocity. If you slow back down, it will expand again.

In order for this to happen it seems to me that something physical had to travel faster than light as measured by some observer -- unless the contraction occurs at c along that path, but is that the case?

I would appreciate any thoughts on this.

No. It ALL moved toward you TOGETHER, and so it all SHRANK TOGETHER. See?

 

[Just thinking]

The contraction doesn't "propagate." It's not a change in the distance; it's a change in your perception of the distance.

The distance to the Andromeda Galaxy is less for anything traveling in that direction. Yes, the galaxy and everything along that path between me and it (and beyond) have contracted.

... as you accelerate relative to the Andromeda Galaxy, the Galaxy itself and all of the distance between you and it contracts, in your frame of reference, all at once, depending on how fast you're going at any given time during that acceleration. If you were to decelerate again, it would all expand again, in your frame of reference. Remember, the distance hasn't changed in the Andromeda Galaxy's frame of reference; your perception of it has changed in your frame of reference.

I agree with all except of your use of the word "perception". The distance is less for me, the traveller. Isn't that how certain particles that enter the Earth's atmosphere at relativistic speeds survive radioactive decay even after making it to the surface? In other words, their halftimes are too short without relativistic effects. To us on the surface, their clocks slow down enough for the decay not to occur -- and to them, the Earth's atmosphere measures that much less, making it almost paper thin.

Errrmmm, the Andromeda Galaxy is 2.5 million light years away.

I meant that the length contraction at everyday velocities would reduce the distance by several light hours or days.

It ALL moved toward you TOGETHER, and so it all SHRANK TOGETHER. See?

I see that as making the distance less. And if the distance between me and something else is less now than it was at some earlier time, then I measure this object as now being closer.

 

[Dilb]

Perhaps ... but how?

A velocity is a change in position over a change in time, as measured in a reference frame. When your reference frame changes, your co-ordinates change, not reality. Your metres are not other frames metres, and your seconds are not other frames seconds. In space, the galaxy is exactly where it was before, but now you number that distance differently. It is a change in distance in your observations, not in reality. If we have 10 markers between earth and the galaxy, you still perceive 10 markers to the galaxy after the shift. Your co-ordinates, not the galaxy's position, changes.

If you try and do calculations involving two different coordinate systems, without transforming between them, you simply get the wrong results. The numbers don't mean anything to each other. Just like I can't add 4 feet to 2 metres and get 6 metres. 4+2=6, but the actual distance represented is inconsistant.

 

[Art Vandelay]

[Doc Brown]You're not thinking four dimensionally, Marty[/Doc Brown]
Remember, in spacetime, points are called "events", and they have four coordinates: x, y, z, and t. Note that events are eternal: some lie in the past, some lie in the future, but where they are in spacetime doesn't change. So points don't move; objects move.

Now, let's go through your scenario, this time thinking four dimensionally. Let's say that there are three spaceships, x, y, and z. x and y are at rest with respect to each other, and in that reference frame they're 100 lights years away. Now, keep in mind that as far spacetime is concerned, x and y are not points, they are lines. For each moment in time, there is a point associated with x, and another point associated with y. If you look over all time, this makes for an infinite number of points, forming a line. Now, let's say you travel in spaceship z. You start out next to spaceship x, at rest with respect to it. Then you accelerate to 3/5c, relative to x. Let's start labeling points. You leaving spaceship x is a specific event, so that's a point. Let's call that A. Now, I want to attach the label B to a specific event involving spaceship y, but to do that I need a specific time. So what if I take the same time as when you leave spaceship x? The problem is, how do we know what is "the same time"? Well, we can have a radio signal going from spaceship y to spaceship x which indicates the current year. We can look at what radio signal we get at event A, and add 10 to the year. That gives us event B. But why add 100? That is the distance between x and y, according to their reference frames. But once you're traveling at 3/5c, you'll have a new reference frame, and you'll measure the distance to be only 80 light years, so you'll only add only 80 years, and get a different event, event C. This is an important point: what is "the same time" depends on the reference frame.

Now, how far are these events from each other? Let's call the reference frame of x and y "the old reference frame" and the other one "the new reference frame". According to the old reference frame, A and B are at the same time, but 100 light years away apart. So they are separated by 0 of time and 100 of space. Now, what about A and C? They're separated by 20 of time and 100 of space.

What about the new reference frame? A and C are easy; they're separated by 0 of time and 80 of space. For A and B, we have to do a bit more work. Remember, the old reference frame will see the distance shortened by a factor of 4/5, and will see this as being 100 light years. So the original distance must be 125 light years. Why does the distance get larger? Remember, the two frames don't agree on what constitutes "rest" or "same time". While the old reference says that A and B are at the same time, and x and y aren't moving, the new reference frame says that B happens before A, and that during the interem, y moves at 3/5c. At A, the new reference frame says the distance is 80, and at B it says that it's 125. That's a difference of 45 light years, so the time difference is 75 years. So according to the new reference frame, the separation is 75 of time and 125 of distance.

Now, what you're doing is comparing A to B according to the old reference frame to A and C according to the new reference frame, which is a bit like comparing orange peels to apple cores. Let's pick one pair, say A and B. In the old reference frame, it's 0 time, 100 space. New reference frame, 75 time 125 space. The actual separation doesn't change (although the spatial separation actually increased). In relativity, the distance isn't determined by just the space separation or the time separation. It's determined by the square root of square of the former minus the square of the latter. For instance, sqrt(100^2-0)=100. And sqrt(125^2-75^2)=100. So even though it looks like the distance changed, it didn't really.

As an analogy, suppose that you're driving your car on a road that runs northwest, and you see that there's a nothbound highway 14 kilometers down the road. Then you turn your car onto a westbound road, and the highway is 10 kilometers down this road. Did the road actually move? No, of course not. You just changed how you're calculating the distance.

 

[Schneibster]

I agree with all except of your use of the word "perception". The distance is less for me, the traveller. Isn't that how certain particles that enter the Earth's atmosphere at relativistic speeds survive radioactive decay even after making it to the surface? In other words, their halftimes are too short without relativistic effects. To us on the surface, their clocks slow down enough for the decay not to occur -- and to them, the Earth's atmosphere measures that much less, making it almost paper thin.

But your frame of reference is not special. There is no special frame of reference. In your frame of reference, the direction toward the Andromeda Galaxy is moving toward you, and is foreshortened. To someone motionless with respect to your starting point, your time is dilated and you do not move faster than the speed of light; to you, the distance is foreshortened and you do not move faster than the speed of light. It's the same thing. You've traded motion in time for motion in space.

I meant that the length contraction at everyday velocities would reduce the distance by several light hours or days.

Actually, if you are moving at 99.9999...% of the speed of light, you might get there within your lifetime- but to an observer who stays home, you live in dilated time for a couple million years.

I see that as making the distance less. And if the distance between me and something else is less now than it was at some earlier time, then I measure this object as now being closer.

But you've traded time for space. Never forget that velocity in space is a rotation in spacetime.

 

[Just thinking]

... It is a change in distance in your observations, not in reality.

I'm having a bit of trouble with this thought ... here's why.

My observations regarding distances, velocity, etc. are (I believe) just as real to me (the one in "motion") as they are (were) to someone "at rest". (This "at rest" person could be someone who was standing next to me before I started "moving" towards Andromeda.) Relativity forces us to realize that there is no universal frame of reference with which to measure absolute distances -- there are no absolute distances. And your statement above seems to clearly imply that there are absolute distances. To me, the distance to Andromeda becomes less as I start moving towards it --- no? True, to the person "at rest" my time is dilated, but not to me. If I could move at 0.9999c, surviving the acceleration, of course, I should be able to get there within my lifetime (as measured by me). How is this possible? -- because the distance (as measured by me) is now much less. My time, clocks, still increase in measured time by me the same as when I was "at rest". To the one left behind, he sees me as being in a sort of suspended animation, my clocks essentially stopped -- slowed too much to measure. To him the distance to the galaxy is 2 million light years. To me it's 50 light years. I get there in 2 mllion years of his time, and only 50 of mine. The universe has contracted (to me) such that the distance to the Andromeda Galaxy is less.

Is anything I noted above incorrect?

 

[Just thinking]

...Now, what you're doing is comparing A to B according to the old reference frame to A and C according to the new reference frame, which is a bit like comparing orange peels to apple cores. Let's pick one pair, say A and B. In the old reference frame, it's 0 time, 100 space. New reference frame, 75 time 125 space. The actual separation doesn't change (although the spatial separation actually increased). In relativity, the distance isn't determined by just the space separation or the time separation. It's determined by the square root of square of the former minus the square of the latter. For instance, sqrt(100^2-0)=100. And sqrt(125^2-75^2)=100. So even though it looks like the distance changed, it didn't really.

I appreciate the lesson, and pretty much grasp where you're coming from, but perhaps I'm the one not making myself clear.

Let's make it simpler by looking at someone at rest (with respect to the Andromeda galaxy) who measures the distance to Andromeda to be 2 million light years. If this person suddely accelerated to some high fraction of c (say 99.999%) and then maintained that velocity in a linear inertial frame of reference (assuming he survived the acceleration), he would then upon measuring his distance to Andromeda come up with a different value. One much less than before -- let's make it 50 light years for convenience. Now, Dilb believes (as I understand him) that this change in distance is the effect of photons striking me sooner than they would have otherwise, making the effect of a change of distance only a perceived effect -- the actual distance is still 2 million light years. I don't buy that -- besides, that would make objects behind me stretch out, and that doesn't happen. I believe that the distance is now 50 light years (for me) and that I will arrive there in 50 of my years (as measured by me). Schneibster claims that the length contraction does not propagate, but happens all at once, which I go along with -- all objects along the line of my motion will contract; even those behind me. (Funny thing here, I can now have distant objects behind me become closer by means of length contraction even as I travel in a direction "away" from them.) Anyway, if all I've said in this paragraph is correct, then the Andromeda Galaxy (to me) gets closer by means of length contraction a whopping 1,999,950 light years in the mere time it took me to accelerate to 99.999% of c. Yes, as I apply the brakes, the unverse will stretch back out to how I measured it before my journey, but if I do this just as I'm about to come to Andromeda (and don't hit anything) it should leave me at the doorstep in only 50 years of my time. Hence, traveling 2 million light years in only 50 years time is like going faster than light. I know -- these are two different reference frames and should only be seen as moving within each one taken separately, but I think you might now get my drift -- no?

And yes, I understand that I've lost 2 million years (less 50) if I could somehow get back to Earth the instant I arrived at Andromeda.

 

[Dilb]

I'm having a bit of trouble with this thought ... here's why.

Is anything I noted above incorrect?

Yes. There is a sort of "absolute" length, the proper length. This is the length between two objects which are at rest.

For example, suppose earth and Andromeda are at rest with respect to each other. The proper length, as we will call it, is 25 ly (light years). I later realized this should be millions, but now I don't want to add in that clutter. Call it the space station Andromeda.

Ship A is moving at .9c as it passes earth, relative to earth.
Ship B is moving at .99c as it passes earth, relative to earth.

Ship B is moving at
[latex]$$ \frac{u_x-v}{1-u_xv/c^2} $$[/latex]

or 0.8257c.

Now Ship A sees the distance shortened by the gamma factor
[latex]$$ \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} $$[/latex]

or 2.294, giving an apparent length of 10.90ly to Andromeda.

Now since we're on ship A, let's see the length ship B sees. It's got a speed 0.8257c compared to us, for a gamma factor of 1.773. Our distance to Andromeda, by length contraction again, for ship B, would appear to be 6.149ly.

However, we've changed frames, which can introduce funny effects. Let's go back to the earth's frame, since we can be absolutely confident in the answer.
Ship B is at 0.99c, for a gamma factor of 7.089. The distance, by length contraction, is now 3.527ly. We have a problem.

What we've ignored is the fact that length contraction only works on the proper length of an object (or in this case, space between objects). The proper length is meaningful, and is the maximum length an object can be. Not all frames are equal for calculations involving time dilation and length contraction. What happened is we forgot that Andromeda is moving when we sit in ship A. We instead calculated the distance to ship A-A, a ship at Andromeda, which is moving .9c in the same direction as ship A. Note that although ship A sees ship A-A as being 10.90ly away from it, the earth-Andromeda system see them as being 4.725ly away (again using length contraction, which can be applied since ship A-A is in the same frame as ship A). The earth sees ship A-A as not being at Andromeda at the same time as ship A is next to earth, which is one of those funny simultaneous problems that make absolutely no sense.

The point of this is that you have to be very careful in defining exactly what you mean by everything, in SR. The easiest way to avoid problems like this is to only work in events (3 space dimensions plus time), and apply the Lorentz transformations. I know, I wrote an exam on it 2 weeks ago.

So to explain your error, you can't shift frames and assume things are the same. Going 50ly in ~50 years is perfectly valid, as is going 25 million ly in ~25 million years. They are equivalent, but not interchangeable (without applying Lorentz transformations).

Also, it is not that photons are striking you sooner. It's that by shifting your frame, the photons hit you at a different angle. The fact that they are already in transit is why you can "see" something change at apparently FTL (Why you don't have to wait 50 years for something to come off Andromeda so you can observe it). The effect on your observations happens entirely during the acceleration, nothing else in the universe changes.

When you think you seem to go FTL, everyone else (on earth) sees you go roughly c, and time dilate. Nothing goes faster than c in any frame, your perception of the time taken to cover the distance before you frame shifted is simply wrong. You correctly observe spending less time going a shorter distance. The earth says you took more time (and didn't feel it), you say you went a shorter distance. You're both correct, but only for earth-metres and earth-seconds, or ship-metres and ship-seconds. Your coordinates are different.

 

[Just thinking]

So to explain your error, you can't shift frames and assume things are the same. Going 50ly in ~50 years is perfectly valid, as is going 25 million ly in ~25 million years. They are equivalent, but not interchangeable (without applying Lorentz transformations).

I actually grasp all of the above, and have done those exact equations using the gamma factor (for time, length and mass changes).

But it is also possible to go 2 million light years in 50 years time (as measured by the one in motion). The 2 million light years is the "at rest" distance, which contracts to 50 ly's at speed.

Please re-read my most recent scenario posted just before your most recent one. And assume Andromeda and the person while "at rest" to be not moving with repsect to each other.

 

[Dilb]

I actually grasp all of the above, and have done those exact equations using the gamma factor (for time, length and mass changes).

But it is also possible to go 2 million light years in 50 years time (as measured by the one in motion). The 2 million light years is the "at rest" distance, which contracts to 50 ly's at speed.

Please re-read my most recent scenario posted just before your most recent one. And assume Andromeda and the person while "at rest" to be not moving with repsect to each other.

All right, then it's very simple. The clock is wrong. Despite taking 2 million years, it only records 50. Relativity makes the clock run slow. This does mean that you can go anywhere, yet only experience an arbitrarily small amount of time, but it is quite different from going FTL. It's no more going FTL than to take a broken clock and move it, recording the before and after times. It is a measurement error. The relativity one just happens to be inherent in the universe, as opposed to dead batteries.

 

[Just thinking]

All right, then it's very simple. The clock is wrong. Despite taking 2 million years, it only records 50. Relativity makes the clock run slow. This does mean that you can go anywhere, yet only experience an arbitrarily small amount of time, but it is quite different from going FTL. It's no more going FTL than to take a broken clock and move it, recording the before and after times. It is a measurement error. The relativity one just happens to be inherent in the universe, as opposed to dead batteries.

Yes, yes. As I said earlier ... "Hence, traveling 2 million light years in only 50 years time is like going faster than light. I know -- these are two different reference frames and should only be seen as moving within each one taken separately, but I think you might now get my drift -- no?"

 

[Dilb]

Yes, yes. As I said earlier ... "Hence, traveling 2 million light years in only 50 years time is like going faster than light. I know -- these are two different reference frames and should only be seen as moving within each one taken separately, but I think you might now get my drift -- no?"

It's really not though. It's like slowing down time. Faster than light would, at the core, mean outrunning a photon. That's not possible. Slowing down time is possible. Saying it's faster than light severely misses what really happens.

The change is entirely a change in your perceptions, your observations. It does not reflect a change in reality, it represents a different co-ordinate system. The point (x=3,y=4) can be written as (a=1, b=1), with a = x/3, b = y/4. The point does not move, our perception of it's location changes. I can say "the point moves from (3,4) to (1,1)", but it is not a change in the point. The thing I'm representing with these numbers is unchanged, despite the different numbers used. In both cases, the point is exactly the same distance from the origin, even though the origin stays at (0,0). The distance sqrt(2) in ab coordinates is exactly the same thing as the distance 5 in xy coordinates. The real idea is unchanged, which is entirely different from simply moving the point to (x=1,y=1).

The only odd thing in reletivity is that this is a change in our observations of the universe. Intuitively, we'd expect a second to be a second. As it turns out, a second is not always a second.

One other thing, if in your last scenario you somehow show up at earth the instant you reach Andromeda, you would see earth had only progressed half a day, though the earth would see it as being 2 million years later. You both see each other time-dilated, and you both are correct (you'd be slightly less correct, as to show up you'd have travelled faster than light). It's only when you frame-shift to go back that you lose time compared to earth.

Really, define events, and use the Lorentz transforms. Time dilation and length contraction do not work well when you want to shift frames or jump around the universe. To jump back to earth the instant you reach Andromeda (without changing frames, so it's definitely at (t=50 years) would actually require moving through time, according to the earth. It's quite easy to see if you draw up the Minkowski diagram.

If you change your frame, so no time changes during your instant teleportation to earth, then you have to change your "moving time" to "earth time", which means you shift your (t=50 years) to (t=2 million years).

 

[Just thinking]

It's really not though. It's like slowing down time. Faster than light would, at the core, mean outrunning a photon. That's not possible. Slowing down time is possible. Saying it's faster than light severely misses what really happens.

I understand you points, thank you ... I'm speaking of being able to travel to a distant object 2 million light years away (when measured at rest) within a mere human lifetime. In a conventional sense it would seem to require faster-than-light travel, but it doesn't due to relativistic effects, be they time dilation (as seen by the stationary observer left behind), or length contraction (as seen by the traveler).

 

[billydkid]

Not to derail or anything, but does anybody else remember seeing or reading about these guys who sent photons through a chunk of solid metal thereby transmitting information - I think it was a symphony - faster than the speed of light? I always understood that the idea of going faster than the speed of light was a fallacy in as much as what limits the speed of light is not a characteristic of light itself, but that it is inherent in the laws of physics that nothing can travel faster than the speed at which light travels - that light speed does not have to do with light per se, but rather that there is an upper limit at which anything can travel and that light merely bumps into that limit and to speak of going faster in meaningless. But I am not sure at all about this.

 

[Art Vandelay]

Not to derail or anything, but does anybody else remember seeing or reading about these guys who sent photons through a chunk of solid metal thereby transmitting information - I think it was a symphony - faster than the speed of light?

They didn't send information faster than the speed of light. They sent information slower than the speed of light, and in doing so they set up vibrations that can be modeled by waves that travel faster than the speed of light. As an analogy, suppose you walk along a line of swings, and as you pass each one, you push it, causing it to oscillate. If you plan it right, you can cause one to reach its highest point just before the next one, causing a wave that travels at any speed you want, including one greater than c. But if you want to change anything about that wave, that change will propogate slower than c.

Another way of looking at is that photons are interchangeable. Other than direction, frequency, and polarization, there's no way to tell one from another. So let's say you have 100 photons going from point A to point B in a stream, each one second apart. Moving all of the photons one light second would have the same physical effect as moving the one at point A to point B and keeping the rest still.

I always understood that the idea of going faster than the speed of light was a fallacy in as much as what limits the speed of light is not a characteristic of light itself, but that it is inherent in the laws of physics that nothing can travel faster than the speed at which light travels - that light speed does not have to do with light per se, but rather that there is an upper limit at which anything can travel and that light merely bumps into that limit and to speak of going faster in meaningless. But I am not sure at all about this.

Good point. It might shift the focus from light if it were more frequently referred to as "c" rather than "the speed of light", emphasizing that it's an abstract constrant rather than specifically a property of light.

 

[Just thinking]

As an analogy, suppose you walk along a line of swings, and as you pass each one, you push it, causing it to oscillate. If you plan it right, you can cause one to reach its highest point just before the next one, causing a wave that travels at any speed you want, including one greater than c. But if you want to change anything about that wave, that change will propogate slower than c.

This is not too unlike the idea of sweeping a light beam across the surface of some very distant object. The spot of light travels well in excess of c, but of course, no information is transmitted along that surface. (The moving spot is really a construct of the observer -- actually nothing is moving along the surface.)