Prosoothus
Registered Senior Member
Thed,
I posted this from my response to James R on another thread. The same applies here:
Tom
I posted this from my response to James R on another thread. The same applies here:
Tom
How accurate are atomic clocks??
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Prosoothus
Registered Senior Member
Merlijn,
The velocity of light is independent of any frame of reference.
Therefore, whether the observer is moving with the clock or whether the observer is stationary, the results are the same.
Tom
The velocity of light is independent of any frame of reference.
Therefore, whether the observer is moving with the clock or whether the observer is stationary, the results are the same.
Tom
Hi Tom,
"The velocity of light is independent of any frame of reference. Therefore, whether the observer is moving with the clock or whether the observer is stationary, the results are the same."
That is exactly what your intuition tells you, and it would seem that it has to be like that. Unfortunately, it isn't.
You have to very carefully dissect the problem and keep the observations of the two frames of reference seperate. On one hand you have the observer travelling with the clock, and on the other you have a stationary observer. It has been said before in this thread, but I'll repeat it once more:
The important point I think you are missing is that there is no right or wrong in this situation. Both observers are right when they say the time required is t or t' respectively ... even though t does not equal t'.
So to conclude: both observers measure different times. It is not because the speed of light varies, or because there is some magical fairy appearing that somehow changes the perception of one observer. From that simple experiment, one can comprehend that time measurement is relative to the observer.
The experiment with the atomic clocks confirms this discrepance of time measurement between two observers that move relative to eachother. An atomic clock is just a sophisticated way of performing the experiment with light bouncing up and downwards, but the conclusion is the same.
I'm sorry it doesn't fit into ones daily perception. I admit that it sounds incredible but this is how nature appears to work.
Bye!
Crisp
"The velocity of light is independent of any frame of reference. Therefore, whether the observer is moving with the clock or whether the observer is stationary, the results are the same."
That is exactly what your intuition tells you, and it would seem that it has to be like that. Unfortunately, it isn't.
You have to very carefully dissect the problem and keep the observations of the two frames of reference seperate. On one hand you have the observer travelling with the clock, and on the other you have a stationary observer. It has been said before in this thread, but I'll repeat it once more:
- The observer that moves with the clock has the most easily understandable observation. He sees light, emitted from a laser, flipping between two plates that are seperated by one meter. Hence the time required for the light to flip back and forth is, as you mentioned, t = 2/c seconds. This is exactly what that observer will say, and irregardless of his perception, that is also what is really happening.
- The outside observer seems a completely different scenario. Assume the apparatus travels in a horizontal direction while the light bounces upwards and downwards (vertical direction). For that observer, the light follows a curved path (triangular) and hence for him the time required for the light to pass that longer distance is a fraction more than 2/c. This is exactly what he sees, and because we assume that the speed of light is c, regardless of the motion of the source producing it, his measurement t' = t + Dt = 2/c + Dt, where Dt is the extra time required for the light. The faster the light apparatus is moving, the larger Dt will be.
The important point I think you are missing is that there is no right or wrong in this situation. Both observers are right when they say the time required is t or t' respectively ... even though t does not equal t'.
So to conclude: both observers measure different times. It is not because the speed of light varies, or because there is some magical fairy appearing that somehow changes the perception of one observer. From that simple experiment, one can comprehend that time measurement is relative to the observer.
The experiment with the atomic clocks confirms this discrepance of time measurement between two observers that move relative to eachother. An atomic clock is just a sophisticated way of performing the experiment with light bouncing up and downwards, but the conclusion is the same.
I'm sorry it doesn't fit into ones daily perception. I admit that it sounds incredible but this is how nature appears to work.
Bye!
Crisp
Prosoothus
Registered Senior Member
Crisp,
You are wrong. This is what would really be observed:
a) The observer that moves with the clock would see the laser light bouncing up and down between the two mirrors. As the observer and the clock move faster, the observer would notice that it takes longer and longer for the light to go between the two mirrors. The observer wouldn't understand because he/she does not see the horizontal motion of the light. The lights vertical motion would decrease in order for it's speed to remain constant as it's horizontal motion increased.
b) The outside observer would see the(almost) true path of the light(that it is moving horizontally and vertically) but he/she would also notice that it takes longer for the light to bounce of the mirrors. In other words, the time it would take for the light to bounce of the mirrors would be the same for the outside observer and the observer traveling with the clock. The only difference is is that the outside observer would know why the vertical speed of the light is decreasing as the clock travels faster, while the observer traveling with the clock would not.
Let me remind you, the speed of light is always constant regardless of the frame of reference. The direction of light is dependent on a frame of reference, but the speed of light is not.
If you were right, and the observer traveling with the clock did not see it slow down, that would mean that the light would be traveling faster than c, and as you know, that's not possible.
One last thing: Since the speed of light is constant regardless of any frame of reference, it means that the light travels in an absolute frame of reference. This would mean that the speed of light in a moving object could be used to determine the absolute motion of that object.
Tom
You are wrong. This is what would really be observed:
a) The observer that moves with the clock would see the laser light bouncing up and down between the two mirrors. As the observer and the clock move faster, the observer would notice that it takes longer and longer for the light to go between the two mirrors. The observer wouldn't understand because he/she does not see the horizontal motion of the light. The lights vertical motion would decrease in order for it's speed to remain constant as it's horizontal motion increased.
b) The outside observer would see the(almost) true path of the light(that it is moving horizontally and vertically) but he/she would also notice that it takes longer for the light to bounce of the mirrors. In other words, the time it would take for the light to bounce of the mirrors would be the same for the outside observer and the observer traveling with the clock. The only difference is is that the outside observer would know why the vertical speed of the light is decreasing as the clock travels faster, while the observer traveling with the clock would not.
Let me remind you, the speed of light is always constant regardless of the frame of reference. The direction of light is dependent on a frame of reference, but the speed of light is not.
If you were right, and the observer traveling with the clock did not see it slow down, that would mean that the light would be traveling faster than c, and as you know, that's not possible.
One last thing: Since the speed of light is constant regardless of any frame of reference, it means that the light travels in an absolute frame of reference. This would mean that the speed of light in a moving object could be used to determine the absolute motion of that object.
Tom
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Tom
You claimed a while ago that you wish to understand the truth. Yet every time some one tries to explain how modern physics describes things you 'correct' them, as if you and only you understand what is really going on.
Why is that?
Bit of a clue here. Velocity has direction, speed does not. The speed of light is invariant. The important word is invariant.
You claimed a while ago that you wish to understand the truth. Yet every time some one tries to explain how modern physics describes things you 'correct' them, as if you and only you understand what is really going on.
Why is that?
Bit of a clue here. Velocity has direction, speed does not. The speed of light is invariant. The important word is invariant.
Hi Tom,
"The observer wouldn't understand because he/she does not see the horizontal motion of the light. The lights vertical motion would decrease in order for it's speed to remain constant as it's horizontal motion increased. "
Why should this happen ? I think Thed pointed you in the good direction for the answer to this paradox.
Bye!
Crisp
"The observer wouldn't understand because he/she does not see the horizontal motion of the light. The lights vertical motion would decrease in order for it's speed to remain constant as it's horizontal motion increased. "
Why should this happen ? I think Thed pointed you in the good direction for the answer to this paradox.
Bye!
Crisp
Tom,
You're contradicting yourself. Compare your two statements:
<b>1</b>. "As the observer and the clock move faster, the observer would notice that it takes longer and longer for the light to go between the two mirrors."
and
<b>2</b>. "Let me remind you, the speed of light is always constant regardless of the frame of reference."
Now, I suppose you agree that for the observer moving with the clock, the distance between the mirrors doesn't change - right?
If that is the case then we can calculate the speed of light by taking the distance between the mirrors divided by the time it takes the light to bounce between them. The distance is constant, but your statement 1 says that the time increases with speed. Therefore the calculated speed of light decreases with increasing speed.
But then you make statement 2, which says the speed of light is independent of the frame of reference (i.e. the speed of the clock).
For consistency, you need to give up one of your two statements. Either you let the speed of light change, or you agree that the time taken to bounce between the two mirrors is constant for the moving observer.
Which is it to be?
You're contradicting yourself. Compare your two statements:
<b>1</b>. "As the observer and the clock move faster, the observer would notice that it takes longer and longer for the light to go between the two mirrors."
and
<b>2</b>. "Let me remind you, the speed of light is always constant regardless of the frame of reference."
Now, I suppose you agree that for the observer moving with the clock, the distance between the mirrors doesn't change - right?
If that is the case then we can calculate the speed of light by taking the distance between the mirrors divided by the time it takes the light to bounce between them. The distance is constant, but your statement 1 says that the time increases with speed. Therefore the calculated speed of light decreases with increasing speed.
But then you make statement 2, which says the speed of light is independent of the frame of reference (i.e. the speed of the clock).
For consistency, you need to give up one of your two statements. Either you let the speed of light change, or you agree that the time taken to bounce between the two mirrors is constant for the moving observer.
Which is it to be?
ImaHamster2
Registered Senior Member
Seems pertinent to the discussion.
“Ultra-precise clocks on the International Space Station and other space missions may determine whether Albert Einstein's Special Theory of Relativity is correct and could dramatically change our understanding of the universe.”
http://newsinfo.iu.edu/news/page/normal/406.html
“Ultra-precise clocks on the International Space Station and other space missions may determine whether Albert Einstein's Special Theory of Relativity is correct and could dramatically change our understanding of the universe.”
http://newsinfo.iu.edu/news/page/normal/406.html
Prosoothus
Registered Senior Member
James R, Thed, and Crisp
I don't know why I have to keep repeating myself.
The speed of light is always constant. As the clock travels faster, the light has to keep up with the horizontal motion of the clock. So the light must increase it's horizontal motion in order to keep up with the clock. If the light's horizontal motion increases, its vertical motion must decrease in order for the light's total speed to remain constant. The mirrors do not measure the total speed of the light, they only measure the vertical motion of the light.
To repeat myself again, the total speed of light does not change, but it's horizontal and vertical motion does.
Tom
I don't know why I have to keep repeating myself.
The speed of light is always constant. As the clock travels faster, the light has to keep up with the horizontal motion of the clock. So the light must increase it's horizontal motion in order to keep up with the clock. If the light's horizontal motion increases, its vertical motion must decrease in order for the light's total speed to remain constant. The mirrors do not measure the total speed of the light, they only measure the vertical motion of the light.
To repeat myself again, the total speed of light does not change, but it's horizontal and vertical motion does.
Tom
Yes, Tom. Your last post is perfectly correct. If you follow your argument through to its conclusion, you must therefore conclude that both space and time depend on the observer's frame of reference in order to keep the speed of light constant.
Congratulations. You're now a relativist.
Congratulations. You're now a relativist.
Prosoothus
Registered Senior Member
James R,
If I follow my argument to its conclusion, this is what I get:
1. The speed of light is always constant, therefore it travels in the absolute frame of reference.
2. The light clock appears to be indicating that time is slowing down as it travels faster, when in reality time remains constant.
3. The absolute velocity of any object can be determined using light, because the speed of light is always constant regardless of the frame of reference it is in.
James, it appears that I'm an anti-relativist.
Tom
If I follow my argument to its conclusion, this is what I get:
1. The speed of light is always constant, therefore it travels in the absolute frame of reference.
2. The light clock appears to be indicating that time is slowing down as it travels faster, when in reality time remains constant.
3. The absolute velocity of any object can be determined using light, because the speed of light is always constant regardless of the frame of reference it is in.
James, it appears that I'm an anti-relativist.
Tom
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Prosoothus
Registered Senior Member
ImaHamster2,
Thanks for the interesting link.
The only problem would be the actual construction of the clocks. The more complex the structure of the clocks, the more likely there will be a clash between the relativistic and the non-relativistic components of the clocks.
These clashes may lead to false readings.
Tom
Thanks for the interesting link.
The only problem would be the actual construction of the clocks. The more complex the structure of the clocks, the more likely there will be a clash between the relativistic and the non-relativistic components of the clocks.
These clashes may lead to false readings.
Tom
How can the constant speed of light be used to determine absolute velocity? No matter what velocity and direction you're moving, and no matter what velocity and direction the source of light it, you'll still measure it to be <i>c</i>. How do you determine absolute velocity if you measure the speed of light to be <i>c</i> no matter what? (This is assuming a non-accelerating frame of reference, of course.)
Tom,
<i>1. The speed of light is always constant, therefore it travels in the absolute frame of reference.</i>
Clearly you still do not understand the term "frame of reference", despite repeated, careful explanation. Nothing exists only in one frame of reference, because a frame of reference is only a point of view. Many observers can look at the same beam of light, or baseball or whatever from different viewpoints with different states of motion. It is meaningless to make statements like "light travels in an absolute frame of reference".
I suggest you review the earlier posts to this thread.
<i>2. The light clock appears to be indicating that time is slowing down as it travels faster, when in reality time remains constant.</i>
You have given no cogent argument to support that conclusion.
<i>3. The absolute velocity of any object can be determined using light, because the speed of light is always constant regardless of the frame of reference it is in.</i>
I have told you why this is mistaken already. Please review the thread.
<i>James, it appears that I'm an anti-relativist.</i>
Yes, but not a <b>reasoned</b> anti-relativist. What you have is a faith, not a rational position. I can't argue you out of that. Your faith is not based on anything rational, but only on a gut feeling driven by who-knows-what psychological motivation. Obviously, rational explanation is wasted on you.
<i>1. The speed of light is always constant, therefore it travels in the absolute frame of reference.</i>
Clearly you still do not understand the term "frame of reference", despite repeated, careful explanation. Nothing exists only in one frame of reference, because a frame of reference is only a point of view. Many observers can look at the same beam of light, or baseball or whatever from different viewpoints with different states of motion. It is meaningless to make statements like "light travels in an absolute frame of reference".
I suggest you review the earlier posts to this thread.
<i>2. The light clock appears to be indicating that time is slowing down as it travels faster, when in reality time remains constant.</i>
You have given no cogent argument to support that conclusion.
<i>3. The absolute velocity of any object can be determined using light, because the speed of light is always constant regardless of the frame of reference it is in.</i>
I have told you why this is mistaken already. Please review the thread.
<i>James, it appears that I'm an anti-relativist.</i>
Yes, but not a <b>reasoned</b> anti-relativist. What you have is a faith, not a rational position. I can't argue you out of that. Your faith is not based on anything rational, but only on a gut feeling driven by who-knows-what psychological motivation. Obviously, rational explanation is wasted on you.
Prosoothus
Registered Senior Member
SpyFox_the_KMeson,
I posted a link earlier on this thread to a device called a light clock. A light clock is just two parallel mirrors, one on top of each other, that has light reflecting between them. By counting how many times light bounces between these two mirrors per second, you can measure the absolute velocity of the clock.
In the case that the light clock is in absolute rest, the vertical velocity(up and down) of the light bouncing between the mirrors is equal to c.
But if the clock is in motion, the light's horizontal(forward) velocity has to increase in order for the light to keep up with the motion of the clock. Because of the increased horizontal motion of the light, the vertical motion of the light must decrease in order for the total velocity of the light to remain constant.
Because the mirrors of the light clock measure only the vertical motion of the clock, and because the lights vertical motion decreases the faster the clock travels as a result of the light's increased horizontal motion, the amount of time it takes for the light to bounce of the mirrors would increase the faster the clock is moving.
Therefore since the speed of light is alway constant regardless of the frame of reference it is in, the clock would be able to measure the absolute motion of any object.
Tom
I posted a link earlier on this thread to a device called a light clock. A light clock is just two parallel mirrors, one on top of each other, that has light reflecting between them. By counting how many times light bounces between these two mirrors per second, you can measure the absolute velocity of the clock.
In the case that the light clock is in absolute rest, the vertical velocity(up and down) of the light bouncing between the mirrors is equal to c.
But if the clock is in motion, the light's horizontal(forward) velocity has to increase in order for the light to keep up with the motion of the clock. Because of the increased horizontal motion of the light, the vertical motion of the light must decrease in order for the total velocity of the light to remain constant.
Because the mirrors of the light clock measure only the vertical motion of the clock, and because the lights vertical motion decreases the faster the clock travels as a result of the light's increased horizontal motion, the amount of time it takes for the light to bounce of the mirrors would increase the faster the clock is moving.
Therefore since the speed of light is alway constant regardless of the frame of reference it is in, the clock would be able to measure the absolute motion of any object.
Tom
Prosoothus
Registered Senior Member
James R,
If the speed of light is constant, in which frame of reference would the speed of light be c????
The answer is the absolute frame of reference.
The fact is that the speed of light proves that there is an absolute frame of reference. As I described earlier in this thread, a light clock can measure the absolute motion of any object.
What you can't face is the fact that light came along and crapped on Einsteins theory of relativity. I guess everything was going fine for Einsein until he found that the speed of light doesn't care what frame of reference it's in.
As I explained before, the light clock measures the vertical velocity of the light between it's mirrors, and NOT the total velocity of the light. If a stupid physicist would assume that the light clock measures the total velocity of the light, he/she would come to the conclusion that time slows down the faster the clock is traveling. This could be one of the many errors associated with atomic clocks.
Tom
If the speed of light is constant, in which frame of reference would the speed of light be c????
The answer is the absolute frame of reference.
The fact is that the speed of light proves that there is an absolute frame of reference. As I described earlier in this thread, a light clock can measure the absolute motion of any object.
What you can't face is the fact that light came along and crapped on Einsteins theory of relativity. I guess everything was going fine for Einsein until he found that the speed of light doesn't care what frame of reference it's in.
As I explained before, the light clock measures the vertical velocity of the light between it's mirrors, and NOT the total velocity of the light. If a stupid physicist would assume that the light clock measures the total velocity of the light, he/she would come to the conclusion that time slows down the faster the clock is traveling. This could be one of the many errors associated with atomic clocks.
Tom
Another attempt to clarify the situation...
Hi Tom,
"If the speed of light is constant, in which frame of reference would the speed of light be c???? The answer is the absolute frame of reference."
Wrong answer, the correct answer is: in ALL possible frames of reference. The direction the light is moving in is irrelevant, we're not talking about a vector component here, but the total size of the velocity vector.
"As I explained before, the light clock measures the vertical velocity of the light between it's mirrors, and NOT the total velocity of the light."
This is not correct. For the observer standing next to the clock, the light has no horizontal component. Since the speed of light is constant in every frame of reference, the speed would have a vertical component equal to c, which in this case happens to be the size of the velocity vector.
For an observer watching the lightclock passing by, the vertical component would indeed be different, and this is exactly the reason why that external observer would perceive the clock of the moving observer tick slower.
For you this seems to be a convincing argument for an absolute frame of reference. I don't have the slightest clue where that could possible ever fit in.
But there's even more. Assume we have two lightclocks that move relative to eachother. Each one will conclude that the other clock is ticking slower because the light will follow a triangular path from one clock's point of view. Both clocks are right: there is no experiment you can perform that shows that one clock should be preferred over the other, because they both undergo the same effects when moving relative to eachother. In fact, for ANY observer with a light clock this is true. This means that all frames of references are equal, or in other words: there is no prefered frame of reference.
Light cannot be used as a frame of reference: any frame of reference is bound to travel at a speed smaller than lightspeed, since in a frame of reference travelling at lightspeed, all laws of physics break down (all distances become zero, everything takes an infinite amount of time to happen - not quite an interesting frame of reference to observe reality in).
"What you can't face is the fact that light came along and crapped on Einsteins theory of relativity. I guess everything was going fine for Einsein until he found that the speed of light doesn't care what frame of reference it's in. "
Have you ever read any of the posts on frames of reference ? It was exactly Einstein who postulated that the speed of light was invariant for all frames of reference, and he started to work on his theory from there.
"If a stupid physicist would assume that the light clock measures the total velocity of the light, he/she would come to the conclusion that time slows down the faster the clock is traveling. This could be one of the many errors associated with atomic clocks. "
No, it is not the observer standing next to the lightclock that will see time slow down, but an external observer. For the observer standing next to the lightclock, nothing will change, regardless of the speed he is moving at (from the point of view from the external observer).
Bye!
Crisp
Hi Tom,
"If the speed of light is constant, in which frame of reference would the speed of light be c???? The answer is the absolute frame of reference."
Wrong answer, the correct answer is: in ALL possible frames of reference. The direction the light is moving in is irrelevant, we're not talking about a vector component here, but the total size of the velocity vector.
"As I explained before, the light clock measures the vertical velocity of the light between it's mirrors, and NOT the total velocity of the light."
This is not correct. For the observer standing next to the clock, the light has no horizontal component. Since the speed of light is constant in every frame of reference, the speed would have a vertical component equal to c, which in this case happens to be the size of the velocity vector.
For an observer watching the lightclock passing by, the vertical component would indeed be different, and this is exactly the reason why that external observer would perceive the clock of the moving observer tick slower.
For you this seems to be a convincing argument for an absolute frame of reference. I don't have the slightest clue where that could possible ever fit in.
But there's even more. Assume we have two lightclocks that move relative to eachother. Each one will conclude that the other clock is ticking slower because the light will follow a triangular path from one clock's point of view. Both clocks are right: there is no experiment you can perform that shows that one clock should be preferred over the other, because they both undergo the same effects when moving relative to eachother. In fact, for ANY observer with a light clock this is true. This means that all frames of references are equal, or in other words: there is no prefered frame of reference.
Light cannot be used as a frame of reference: any frame of reference is bound to travel at a speed smaller than lightspeed, since in a frame of reference travelling at lightspeed, all laws of physics break down (all distances become zero, everything takes an infinite amount of time to happen - not quite an interesting frame of reference to observe reality in).
"What you can't face is the fact that light came along and crapped on Einsteins theory of relativity. I guess everything was going fine for Einsein until he found that the speed of light doesn't care what frame of reference it's in. "
Have you ever read any of the posts on frames of reference ? It was exactly Einstein who postulated that the speed of light was invariant for all frames of reference, and he started to work on his theory from there.
"If a stupid physicist would assume that the light clock measures the total velocity of the light, he/she would come to the conclusion that time slows down the faster the clock is traveling. This could be one of the many errors associated with atomic clocks. "
No, it is not the observer standing next to the lightclock that will see time slow down, but an external observer. For the observer standing next to the lightclock, nothing will change, regardless of the speed he is moving at (from the point of view from the external observer).
Bye!
Crisp
Prosoothus
Registered Senior Member
Crisp,
You're not making sense.
If I'm in a frame of reference that is not moving, and I shine a beam of light, the light travels at the speed of c.
However, if I'm travelling at .99 c and I shine a beam of light forward, the light CANNOT be traveling at c in my frame of reference. If it were the total speed of the light would be .99c+c. This would mean that the light would be travelling faster than c in the stationary frame of reference.
Let me say again that speed of light is constant compared to an absolute frame of reference. If you are right, and the speed of light is constant in all frames of reference, then the speed of light would NOT be constant at all.
You can't say that the speed of light is constant and then say that it's relative to a frame of reference. The two statements contradict each other.
Tom
You're not making sense.
If I'm in a frame of reference that is not moving, and I shine a beam of light, the light travels at the speed of c.
However, if I'm travelling at .99 c and I shine a beam of light forward, the light CANNOT be traveling at c in my frame of reference. If it were the total speed of the light would be .99c+c. This would mean that the light would be travelling faster than c in the stationary frame of reference.
Let me say again that speed of light is constant compared to an absolute frame of reference. If you are right, and the speed of light is constant in all frames of reference, then the speed of light would NOT be constant at all.
You can't say that the speed of light is constant and then say that it's relative to a frame of reference. The two statements contradict each other.
Tom
Hi Tom,
Ok, it looks like we're getting to the fundamental difference here...
"However, if I'm travelling at .99 c and I shine a beam of light forward, the light CANNOT be traveling at c in my frame of reference. If it were the total speed of the light would be .99c+c. This would mean that the light would be travelling faster than c in the stationary frame of reference."
Wrong. If you travel at .99c and you shine a beam forward, it will move away from you at c. That is the beauty of the constancy of the speed of light, regardless of your own movement, the light travels at the same speed.
For an outside observer, the "total" speed of light would not be .99c+c. You are using the Galilean addition of velocities, which does not work for light, the proper velocity addition formula (which is based on the Lorentz transformations) takes the constancy of the speed of light into account. The resulting velocity for the outside observer would also be c.
Bye!
Crisp
Ok, it looks like we're getting to the fundamental difference here...
"However, if I'm travelling at .99 c and I shine a beam of light forward, the light CANNOT be traveling at c in my frame of reference. If it were the total speed of the light would be .99c+c. This would mean that the light would be travelling faster than c in the stationary frame of reference."
Wrong. If you travel at .99c and you shine a beam forward, it will move away from you at c. That is the beauty of the constancy of the speed of light, regardless of your own movement, the light travels at the same speed.
For an outside observer, the "total" speed of light would not be .99c+c. You are using the Galilean addition of velocities, which does not work for light, the proper velocity addition formula (which is based on the Lorentz transformations) takes the constancy of the speed of light into account. The resulting velocity for the outside observer would also be c.
Bye!
Crisp