# Stars moving faster than the speed of light

1. Mar 17, 2013

### 42Physics

If two stars, each moving away from each other faster than the speed of light, how would the light behave? Let me add more detail, if you have two stars a light-year away from each other and "off" and then accelerated both of them in opposite directions traveling at say .60c and identically turned each one "on" how would the light behave? I mean, together, they're traveling past the speed of light, 1.20c to be exact, would the light of each one ever reach the other, and how would the light behave altogether? If anybody has a explanation I would greatly appreciate it.

2. Mar 17, 2013

### Legaldose

Light travels the same speed in all reference frames. Once the star is "turned on" the light from each star would still reach the other star.

3. Mar 17, 2013

### cwilkins

Intuitively you might assume that the light from each star shouldn't reach the other, but that isn't the case. Here's the problem with your reasoning: velocities don't add linearly. The formula you would use to find the observed velocity between the two stars is $v_{obs} = \frac{v_1 + v_2}{1+v_1 v_2/c^2}$. From that you find that the magnitude of observed velocity between the two stars is approximately 0.88 times the speed of light. This means that light can be transmitted and received between the two stars.

4. Mar 17, 2013

### Crazymechanic

Well in a local frame particles with rest mass can't travel faster than light and not even at the speed of light because that would require them to have infinite energy.Now obviously planets made out of such particle matter also can't travel faster than light or at the speed of c.So light would be faster in all these cases but in the case of universe it is different.The universe is separated by huge vast distances and planets and galaxies are actually receding faster because of the expansion of the universe.
And it is said that some galaxies far away are traveling away from us for example faster than the speed of light and after a while when the distance will become too great we won't be able to see their "light" or have any information about them only the one that they left behind when they were closer.

So if this is the case and you consider the point in our solar system our sun and the other one the sun or star in the galaxy that is traveling away I would say it is possible that light won't be able to reach the stars eventually after a certain amount of time.

As much as I understand I think that if the speed with which the galaxies are traveling apart would be constant light would eventually with time reach the other side but because this cosmological expansion is accelerating that is the main fact why the light after a certain period will not be able to reach the other side anymore.it has to do with the accelerated expansion.
Maybe not a perfect analogy but it's like two cowboys on two horses each running in opposite direction now they have a gun that shoots a bullet that travels at c (considering straight line in space with vacuum and no gravitational effects on light between those two objects) now these two horses are running faster and faster each second and even though one of the horse in his frame of reference isn't traveling at c but near it the other one also so together that is faster than c. Now when they were close the "light speed bullet" was capable of reaching the other horse but as the distance increased the bullets cannot reach the other side anymore as it is traveling away faster than light can cache it so the bullets now start to meet each other between the two horses and as further the horses go from each other the less that light bullet can catch the other one and at one point there is no more possibility for the light coming from one horse or galaxy to even catch the light coming from the other.

@42Physics see universal expansion light speed in google.It should show some scientific pages with good explanations.

Last edited: Mar 17, 2013
5. Mar 17, 2013

### Staff: Mentor

Nothing can travel faster than light, so your question doesn't make sense.

6. Mar 17, 2013

### hairygary

Regardless of the universal expansion I don't think an object with rest mass can "outrun" light. For instance we can detect light from galaxies moving away from us due to this universal expansion, its simply red-shifted (or whatever the proper term is). I don't know anything substantial about general relativity, so I can't explain exactly what would be happening during the acceleration, but one principle of general relativity is that acceleration and gravity are equivalent. They both curve spacetime, causing time and space to behave differently in the reference frame, so light in that reference frame will not behave classically, as in the example of the horse outrunning the bullet. The only objects I've heard of that actually seem to curve spacetime enough to influence light in such a drastic way are black holes. Also, if ever the acceleration stopped, according to special relativity light will travel at c relative to the observer, so it doesn't seem likely that during acceleration the light was left behind. Finally, no object can travel faster than light, so even with acceleration I don't see how light couldn't reach the object. As I said before though, I have very little knowledge of general relativity, so I may be wrong.

In regards to the original question, both stars would observe the light from the other star approaching them at c relative to them, regardless of their speed away from the light source and vice versa. Even a separate observer witnessing this exchange of light from a separate reference frame would see the light between both stars traveling at c relative to them, and space and time dilation would allow for all of these observations to be simultaneously correct in their reference frames despite seeming contradictory. These dilations lead to the velocity equation mentioned before. While classically the two stars are travelling apart at more than c, due to dilation of space and time it turns out they aren't.

Last edited: Mar 17, 2013
7. Mar 17, 2013

### 42Physics

Re: Question

Thank you so much, these explanations helped a lot, except PeterDonis , you didn't bother to read far enough in order to understand it.

8. Mar 17, 2013

### Crazymechanic

@PeterDonis Well nothing can travel faster than light in a straight line to the reference frame of light.Yes that's true but here we have a different situation were we have two massive objects traveling more than 0,5c away from each other in opposite directions now in each one of theirs reference frame they are not traveling faster than light but from a third reference frame which in our case would be an observer they are both traveling the opposite direction so if light from one would want to reach the other it would have to not only catch the other star but also get back where it was when it was emitted but because the objects from which it was emitted is itself traveling away from the other one it is trying to catch, now those distances double.

@hairygary pretty much the same i said to Peter that a massive object doesn't have to exceed the speed of light or even go at 0,999c to be to far away from us as an observer so that light couldn't catch us.Because if we would be perfectly stationary and the massive object "B" would be traveling with 0,90 c away from us then yes ofcourse we would still see the light from it , but we are in a position where the object "B" is traveling away from us at let's say 0,9c and we ourselves are also traveling at 0,9c only the opposite direction so the distance between us grows not with 0,9c but with 1,8c.(not taking into account the gravitational redshift caused by objects with mass in the way of the light traveling from one star to the observer)

The separate observer would ofcourse see the light from each of the oppositely accelerating objects as moving with c but the thing here is not about the redshift that we see from a distant star just because the light coming in a straight path to us experiences a planet or a object in that path and the objects gravity bends it around it slowing it down.
it's about the fact that if two bodies are very far away from each other and accelerating then their light sources can't reach the other side anymore after a certain speed of acceleration and distance traveled.

If the acceleration would stop then the light eventually would be able to catch the planets.The meaning here is in the fact of acceleration not the speed of light.Ok I'm gonna make one more analogy.
Two cars , two guns in the hands of two shooters , each one in his own car.The cars are parked back to back and stand.Let's assume vacuum for our purposes.Now the one car stands while the other accelerates.both guys fire their guns and eventually both bullets reach the other car.So far so good.Now both cars start to accelerate at the same rate of acceleration in the opposite directions now when they just started doing that in the first moments they were close to each other and the bullets still were able to reach the other car but as they get further apart each next bullet travels only at a fixed speed so now that bullet has to not only get back to the point from which it started but also catch the other car which is now the same distance away from the center as the one from which the bullet was fired.So that equals the distance x2 ad the car that is needs to reach is not standing but traveling with a speed that is near the speed of c so it has not only to get away from the car which is traveling at nearly c but also catch he other car which is traveling the same speed in opposite direction.But because the speed of the bullet is fixed (speed of light c) that means that as long as the two cars will be accelerating in opposite directions with speed near to c the light after a certain point of traveled distance between the objects will not be able to reach the other side anymore.It will be on a a constant journey after it's target but not able to catch it.Unless the target suddenly stops.
I hope I made myself clear. :)

@42Physics I hope this is the way you meant the OP question you wrote.I hope I atleast partly answered it.r atleast caught your thought.
P.S. the expansion and receding or large stars or objects in universe can happen at FTL because it's not the massive objects itself that is moving faster than light (which it couldn't ) but rather spacetime, the matrix of space itself expanding and hence separating those objects which it holds further away so the actual speed of the objects doesn't even need to be that big.It's like walking up an escalator you are moving quite slowly if at all but the space in which you are (the escalator) is moving quite fast.And if there is an opposite moving escalator in the other side of the shopping mall than from the point of reference to that escalator you are moving even faster away.And if somebody ripped the mall building in half and pulled each half away from the other one with each opposite escalators in each half then the total speed of receding would be even greater.The speeds add up in the global frame of reference each indivudal speed that is going in the same direction adds up and together with spacetime itself those planets can indeed travel away faster than light can reach each one of them from the other side.

Last edited: Mar 17, 2013
9. Mar 17, 2013

### Staff: Mentor

You're right, I didn't realize that you were making an incorrect assumption about how velocities add. cwilkins' post cleared that up. Sorry for the confusion.

However, I'm not sure whether you meant to ask only about flat spacetime, or whether you also meant to ask about scenarios where gravity plays a role, such as the expansion of the universe. I'll address that issue in a separate post.

10. Mar 17, 2013

### Staff: Mentor

The way you state this is somewhat misleading. First of all, there is no such thing as "the reference frame of light"; see the forum FAQ on this. I suspect what you mean is "in the reference frame of the light source", but I'm not sure.

Second, I'm not sure what you mean by "in a straight line". I suspect you mean "with zero acceleration", but your treatment of that doesn't seem right either; see further comments below.

Third, in curved spacetime there is no unique way to define the relative speed of spatially separated objects, so the statement "nothing can travel faster than light" won't work as it stands; there are interpretations according to which distant galaxies can be moving away from us "faster than light" due to the universe's expansion. Ned Wright's cosmology FAQ has a good discussion of this. The correct way to generalize the statement "nothing can travel faster than light" to curved spacetime is to say that "nothing can move outside the local light cones".

In flat spacetime (i.e., if the effects of gravity are negligible), which is what I think you intend here, this is not correct if the two objects are moving at constant velocity. (Acceleration does add a complication; see further comments below.) Velocities don't add in relativity the way they do in Newtonian mechanics. cwilkins gave the correct velocity addition formula, and that all by itself is enough to answer the OP's question. No matter how fast two objects are traveling in opposite directions, if they are both traveling at less than the speed of light (which they must be), then light emitted by either one will eventually catch up to the other.

The rate of change of this "distance between us" is irrelevant to whether light from one object can catch the other. The speed of light is independent of the speed of the source; so as soon as one object emits a light beam towards the other, that light beam is moving at c in our reference frame. Since the other object is moving at less than c in our reference frame, the light will eventually catch up to it if it is moving at a constant velocity. It doesn't matter that the object that emitted the light is moving in the opposite direction.

Now you're confusing me because you haven't mentioned acceleration or redshift at all up to now. What exactly is the scenario you are trying to describe? Are the two objects moving in opposite directions at a constant velocity of 0.9c (relative to "us")? Or are they accelerating? Also, is this scenario set in flat spacetime or in an expanding universe?

If either object is accelerating (meaning, firing a rocket to change its velocity relative to a given inertial frame), then there *will* be a region of spacetime that can't send light signals to that object. The boundary of this region of spacetime is called the Rindler horizon, and I recommend Greg Egan's discussion of it. Note that only one object has to accelerate for a Rindler horizon to appear; it isn't necessary that both objects accelerate (as you imply in your analogy with the cars and shooters).

But I'm not sure if that's actually what you mean by "acceleration"; you might mean the accelerating expansion of the universe, which is a different phenomenon. I can't tell for sure because your description isn't precise enough; but later on you do say this:

This is true, and *if* the expansion is accelerating (which in our universe, according to our best current knowledge, it is), it creates a "cosmological horizon", behind which objects are receding from us in such a way that we can't send light signals that will catch them. The Ned Wright cosmology FAQ that I linked to above explains this. Note that the expansion has to be accelerating for this to be true; it is *not* sufficient just for there to be galaxies that appear to be receding from us "faster than light".

11. Mar 17, 2013

### Crazymechanic

First of all excuse me if something from what I said was hard to understand or weird.
Now I was thinking that this should be clear that I was talking about the real scenario not some flat spacetime analogy.As the OP was asking a question about real life situations I was trying to answer with that in mind.So yes all I said was based on thinking that if the current model is actually true which I believe for some 90% it should then the space matrix itself is expanding and the galaxies riding on it do accelerate in opposite directions and can't be caught by light anymore.This is what I meant with the two cars and horses and escalators in previous posts.Ofcourse they are just analogies and not perfect but the picture I was trying to paint here I hope I did.

I know that light being the highest speed can't have a reference frame only lower speeds can compare themselves to something higher.
Also the straight line was thought just to agree to what you said and what is obviously right that there is nothing faster than light that travels from a stationary object "C" to a moving or stationary object "B" why i say this? because we were talking about galaxies receding away through the expansion of spacetime and also their own movement so in this scenario light is indeed not the fastest and that's why I made this remark about the flat spacetime straight line analogy.

12. Mar 17, 2013

### ghwellsjr

I'm not sure what you mean by this comment.

If you mean that we can specify any speed as a fraction of the speed of light, then, it is correct. That's what the term beta means.

However, if you mean that we specify a reference frame by comparing its speed to the speed of light as that would be impossible to do. Instead, we start by specifying a reference frame by comparing it to the motion of an object or observer and then we postulate that the speed of light is c in all directions in that reference frame. We can then transform to any other reference frame traveling at any speed less than c with respect to the first one.

13. Mar 17, 2013

### Staff: Mentor

This is true for galaxies sufficiently far apart in our current universe (according to our best current understanding), but as I noted before, that's not just because the universe is expanding; it's because the expansion is accelerating. In a universe which was expanding but in which the expansion was not accelerating (as was the case in our universe until a few billion years ago), there could be galaxies which would appear to be receding from each other "faster than light" but which could still exchange light signals with each other.

ghwellsjr already made good comments on what you say about reference frames and the speed of light.

14. Mar 17, 2013

### Crazymechanic

@ghwellsjr Yes that was what I meant that every speed slower than the one of light can be said in terms of how much slower it is to compared to light.
Just like there is a worlds tallest building at a given moment in time and all other lower building are usually compared in a chart with the tallest one as a reference so that we could actually grasp the height of it.And if you want to see how small you are you go and stand at the first level of that supertall building and someone makes a photo of you and the building both in one picture, so that picture now becomes the reference frame in which the building would be (light) and you would be anything that is slower than light.But because the building is the worlds highest that would make in the highest in every picture of people and buildings.Just as light is light in every frame of reference with the same speed.
I don't see any misunderstanding or contradiction here.

Last edited: Mar 17, 2013
15. Mar 17, 2013

### Staff: Mentor

But any speed slower than the speed of light is frame-dependent, so this comparison doesn't have any physical meaning. Two objects both moving slower than light have a well-defined relative velocity which isn't frame dependent; but the only comparison that's relevant with light is that light moves at c relative to *any* object moving slower than light.