Thread: It's a small world, after all.

I think the general consensus now is not that nothing can move faster than the speed of light, it's that information cannot travel faster than the speed of light.

In the example MK27 gave, the laser light moved across the moon faster than the speed of light, but no information could be transferred from one side of the moon to the other. In this case, the information was still just going from the earth to the moon, and that was still constrained by the speed of light. If you think of it as a question of, "how can I signal something at a different location faster than the speed of light", then it makes more sense as you realize none of the "faster than the speed of light" experiments can accomplish this.

Originally Posted by MK27

From the object's perspective, the Earth is moving. I suspect beyond that point, you could not make any further observations, so while the object relative to Earth might be moving faster than light, you would not see it. And the object, relative to itself, would still not be moving, but will no longer see Earth.

err... isn't that what I have been saying since the beginning?

Originally Posted by bithub

If you think of it as a question of, "how can I signal something at a different location faster than the speed of light", then it makes more sense as you realize none of the "faster than the speed of light" experiments can accomplish this.

Right, because any information the laser could confer is actually travelling at the speed of light, from Earth. You could not communicate from place to place on the moon that way.

Even if you used two lasers, one on earth, one on the moon, and worked out a system involving a football field sized set of semaphore receivers, it would still take the time it takes light to travel one way for changes to become apparent in the beam at the other end. However, once they begin, those changes (eg, the transmission of the message) would take place faster than the speed of light within the equipment, which could not actually be wired but would require a recursive set of semaphore laser-reciever assemblies on a smaller and smaller scale within itself*. Such a thing would be difficult to build and of dubious purpose.

Presumably NASA does not have the budget for this stuff, which is why they refuse to respond to my correspondence, so far.

@Mario F: alway tries to make everything seem like an argument, when I told him to start with I am simply explaining what he thinks - the AFF

*I guess that won't accomplish our goal tho, since a wire is a straight line.

Oh, missed that bit. My apologies.

See? there are some loopholes in the contract. According to this, for example, "If a laser is swept across a distant object, the spot of light can easily be made to move at a speed greater than c."* Which seems paradoxical -- making a light beam move faster than light, but of course, the light in the beam did not have to change speed.

That's misleading. Sweeping a laser across the entire *universe* in a one-second 360 degree spin would not amount to anything. It has nothing to do with the speed of light.

I suspect beyond that point, you could not make any further observations, so while the object relative to Earth might be moving faster than light, you would not see it. And the object, relative to itself, would still not be moving, but will no longer see Earth.

The object's speed relative to the earth would still never exceed the speed of light. For example, let's say that you accelerated to 99%C and cut off your engines. Assuming no other external forces, you would continue on at this clip indefinitely. From the point of view of your reference frame, though, you are stationary, and thus you conclude that if you were to repeat the process you would certainly reach 198%C. So you fire up the engines and try it once more, and indeed your onboard measurements confirm that you have reached 99%C relative to the previous "stationary" position. Just at that moment you pass a deep space satallite that is stationary to the earth and some known distance X from the planet that sends out flashes of light anytime an object passes by. Now if you are truly going 198% C, an observer on earth should measure the difference in time between your departure and receipt of the signal to be a value less than 2X, but in fact it is not! What has happened is that your space/time continuum has effectively "shrunk" and 99%C has a different meaning for two separate reference frames.

Mind you, from a "practical" standpoint you *are* travelling faster than light because you can effectively traverse much larger distances over a shorter period of time. In fact, provided you had enough fuel, you would essentially travel toward infinity, and ahead of you highly blue-shifted worlds could be seen going from creation to destruction in mere moments, while the ones behind you would appear extremely red-shifted and frozen in time. Were you to return to earth millions upon millions of years may have passed since your departure!

Originally Posted by Sebastiani

The object's speed relative to the earth would still never exceed the speed of light.

If you move away from the earth at .5*C and the earth moves away from you at .5*C then from the earth's perspective you move away at C

Originally Posted by ಠ_ಠ

If you move away from the earth at .5*C and the earth moves away from you at .5*C then from the earth's perspective you move away at C

Let's say that both were travelling in opposite directions at 99%C. You would still measure from either ship the speed of the other to be less than C. On the other hand, an observer standing at the "starting point" would measure the both of you, as a sum of velocities, to be going greater than C.

Originally Posted by ಠ_ಠ

If you move away from the earth at .5*C and the earth moves away from you at .5*C then from the earth's perspective you move away at C

That logic only works for objects traveling slow in relation to the speed of light (Newtonian physics from high school). You cannot just add velocities of moving objects in different reference frames. In this case, they would appear to be moving .8C away from each other. If you want to know why, read this.

Originally Posted by bithub

If you want to know why, read this.

crap, the equation's upper bound is the speed of light

edit:
Although I'm not sure that applies here, in 1 year the distance between you and the earth will be 1 light-year so if either one goes slightly faster then they shouldn't be able to see each other

Although I'm not sure that applies here, in 1 year the distance between you and the earth will be 1 light-year so if either one goes slightly faster then they shouldn't be able to see each other

The problem with that is it doesn't take time dilation into account. In other words, 1 year passes by differently depending on your reference frame. 1 year for someone watching the you and the earth move away from each other at 0.5C would only be .86 years for you.

Originally Posted by bithub

The problem with that is it doesn't take time dilation into account. In other words, 1 year passes by differently depending on your reference frame. 1 year for someone watching the you and the earth move away from each other at 0.5C would only be .86 years for you.

so 2 objects can't move away from each other fast enough to become invisible?

Originally Posted by Sebastiani

Let's say that both were travelling in opposite directions at 99%C. You would still measure from either ship the speed of the other to be less than C.

I believe part of the point about it being information transmission that cannot exceed C is that you could not take these measurements, except by inference. And, as you said, if you travelled from Earth to Alpha Centauri in less than 4 years, then the inference is that you did it faster than light. But since the speed of light on your ship would remain the same (light from behind, light from in front, light from any direction) relative to you, etc., there would be nothing real in your universe to indicate that, in fact, the combined relative velocity of you and some other object exceeds C.

I suppose such could already be the case; we already know of distant galaxies whose velocity, relative to us, is a noticeable portion of C. If it were in excess of C, we would not know about it at all.

Anyway, my point was just that there is not really a law that says one object cannot move away from another object in excessive of C. If two objects both going 0.75 C pass each other in opposite directions, their velocity relative to each other is 1.5C. Of course, there are laws that make this extremely unlikely.

The problem with that is it doesn't take time dilation into account. In other words, 1 year passes by differently depending on your reference frame. 1 year for someone watching the you and the earth move away from each other at 0.5C would only be .86 years for you.

So what would "your speed" be then? 0.5c, or (from your perspective looking at earth) 0.58c? Time concentration also occurs because of the presence of mass, eg, time is actually going faster in the sun* (and slower on a satellite), but it appears to be the same to us -- hmmm. IMO space and time are properties of matter and not independent realities in which some matter happens to exist. They are, in effect, "buffer zones" mediating state differences in matter.

According to Carl Sagan, the occupants of a ship crossing the Milky Way (100 000 light years) at light speed would only experience 56 years of time in the voyage (whereas the rest of the mass in the galaxy would experience 100000). Which raises some more interesting questions about relative velocity and how you'd "measure" it.

*I find stars very strange objects to contemplate.

I believe part of the point about it being information transmission that cannot exceed C is that you could not take these measurements, except by inference. And, as you said, if you travelled from Earth to Alpha Centauri in less than 4 years, then the inference is that you did it faster than light. But since the speed of light on your ship would remain the same (light from behind, light from in front, light from any direction) relative to you, etc., there would be nothing real in your universe to indicate that, in fact, the combined relative velocity of you and some other object exceeds C.

Sure you could measure it directly. Just send a light beam towards the other ship and measure how long it takes to make the round trip. You would find that the time it takes does not violate the speed of light. That is the measurable "fact", but the inference that you pointed out is another matter entirely.

Anyway, my point was just that there is not really a law that says one object cannot move away from another object in excessive of C. If two objects both going 0.75 C pass each other in opposite directions, their velocity relative to each other is 1.5C. Of course, there are laws that make this extremely unlikely.

Again, the law of relativity states just that. If there was no space/time dialation that would be true, but there is, so as measured from either ship C is never exceeded.

According to Carl Sagan, the occupants of a ship crossing the Milky Way (100 000 light years) at light speed would only experience 56 years of time in the voyage (whereas the rest of the mass in the galaxy would experience 100000). Which raises some more interesting questions about relative velocity and how you'd "measure" it.

I don't think there is a theoretical limit. Although you could never attain the speed of light, the closer you approach it the more that time dialates, so provided you had enough fuel, you could conceivable travel 50,000,000,000,000,000,000 years, or even much further, into the future. The only practical issue (besides keeping your tank full) is how long it would take to safely get up to that speed. You probably wouldn't want to subject yourself to an acceleration much stronger than gravity, so it would take a few years (say 10 - 15, I'm guessing) just to get close enough to C for an appreciable time dialation to kick in, and of course the same goes for decelleration.

Originally Posted by Sebastiani

Sure you could measure it directly. Just send a light beam towards the other ship and measure how long it takes to make the round trip.

It would not make the round trip, because the transmission of information cannot exceed the speed of light BUT the relative velocity of two objects CAN.

That is the measurable "fact", but the inference that you pointed out is another matter entirely. Again, the law of relativity states just that.

Not quite, qv:

Faster-than-light - Wikipedia, the free encyclopedia

Again, consider the time dilation factor and how you measure speed; for the ship travelling at near light velocity, time dilation is such that for the people on the ship, the ship is travelling thru the galaxy at much more than c.

This is partially a semantic obfuscation/complication that is acceptable (even in science) simply because 99.99999% of the known mass in the universe is not travelling anywhere close to the speed of light in relation to the rest of itself, so some small part of it doing that is extremely theoretical, altho apparently (very) small parts of it actually do, all the time, anyway. The actual value of "C" and the sum total of gravitationally engaged mass in the universe are considered related, methinks, and to the time compression caused by the relative proximity of matter.

But, logically speaking, you cannot discuss velocity as if it occurred against an absolute background -- on earth, velocity is velocity over ground, for example, in space it would be relative to some presumed "fixed points".

Also, I believe that some particles are considered to exceed C for durations but are not detectable or effectively "present" during that time (again qv the wikipedia article), and the phemomenon can be described in other terms to do with the energy level of the particle -- it becomes something else for us, not a ftl particle.