# Thread: A relative speed of light problem?

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## A relative speed of light problem?

Isnt speed of light relative? For instance if im on a spaceship which is travelling at 50% the speed of light relative to a person standing on earth, and then on this spaceship someone points a beam of light in the direction the spacship is moving then isnt that beam of light now travelling at 1.5 times the speed of light?

Surely this could be tested on a slower spaceship because the experuiment would be to get the spaceship going as fast as possible then turn on a light beam, and measure the speed of it from inside the spaceship. If light has a universal maximum speed then the light in that spaceship would travel slower than normal light because we need to subtract the speed of the spaceship.

Also if light does have this max speed then it means the light somehow knows its being measured within a spaceship travelling at x speed.

Isnt that a bit spooky?

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Originally Posted by Jetlack
Isnt speed of light relative? For instance if im on a spaceship which is travelling at 50% the speed of light relative to a person standing on earth, and then on this spaceship someone points a beam of light in the direction the spacship is moving then isnt that beam of light now travelling at 1.5 times the speed of light?
You'd think so, wouldn't you?
Trouble is, experiments show that this doesn't happen. Whatever the state of motion of the transmitter and the observer, everyone always measures the speed of light to be the same.
In the case you describe, the observer on Earth would see the light moving at c, the constant speed of light, relative to the Earth, and the observer on the spaceship would see it moving at c relative to the spaceship. How do they get such different results? Each observes that the other is working with short rulers and slow clocks, so thinks the other hasn't done the experiment "properly". (This is the length contraction and time dilation effect Einstein described in the theory of special relativity in 1905.)

It's not so much that light "knows" what's going on, but that observers in relative motion can't agree on basic things like distance, time and simultaneity.

Grant Hutchison

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Good thinking, and you've hit on the central mystery of relativity. Einstein's insight was that the speed of light is constant for all observers, independent of the motion of the body emitting the light.

Lots of people concentrate on the first part (speed of light is constant), and leave it at that thinking it's just the same as a car travelling at a constant speed down a motorway (eg at "x" miles per hour). What you've spotted is that that's not the whole story.

Given that speed is a combination of distance (eg. miles) and time (eg. hours), then for a non-intuitive statement like "The speed of light is constant for all observers" means something non-intuitive must be going on with our concepts of distance and time - and that's what Relativity is all about.

It turns out that the greater the velocity between source and observer, then time will "lengthen" (ie. each will see a "clock" onboard the other's run slower), and distance will contract by the same ratio in just such a way that the constant speed-of-light will be maintained.

I know that's a mind-bending result, but I also know you'll have a lot of fun exploring it - Enjoy !

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Thanks for the answers - though i am still kind of confused.

So what about a spaceship travelling at 99% speed of light. An occupant then turns on a light beam in the direction the craft is moving. If light has a constant speed then that light would not actually show, or it would crawl forward at a pace which is the calculated differencne between 99% speed of light and the constant? Surely that is the only possible outcome if light really does have a max speed in our universe.

because if that light does behave and shines with light's normal charcteristics then to an earthboud observer - if he/she could see this light on the space shipp travelling 99% of c - would in fact be watching it travelling faster than its supposedly can travel?

Doesnt relativity contradict the notion of a universal constant?

5. Originally Posted by Jetlack
because if that light does behave and shines with light's normal charcteristics then to an earthboud observer - if he/she could see this light on the space shipp travelling 99% of c - would in fact be watching it travelling faster than its supposedly can travel?
Actually, the aspect of light depends on the motion of observers relative to the source. Refer to 'Doppler Effect'.

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Originally Posted by Jetlack
So what about a spaceship travelling at 99% speed of light. An occupant then turns on a light beam in the direction the craft is moving. If light has a constant speed then that light would not actually show, or it would crawl forward at a pace which is the calculated differencne between 99% speed of light and the constant?
Someone on Earth would see the light travelling at c, with the spacecraft behind it moving at 0.99c. So the relative velocity of light and spacecraft would be 1% c, as seen from Earth.
But the Earth observer would also see the spacecraft as being very short in the direction of travel, with all its clocks running slow. Any experiment done aboard the spacecraft would therefore use short measuring sticks and slow clocks, and the observers aboard the spacecraft would measure that 1% difference in velocity as being equal to c, according to "their" metres and "their" seconds.

Both observers measure the same velocity, but disagree about how the measurements are performed.

Grant Hutchison

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Originally Posted by grant hutchison
Someone on Earth would see the light travelling at c, with the spacecraft behind it moving at 0.99c. So the relative velocity of light and spacecraft would be 1% c, as seen from Earth.
But the Earth observer would also see the spacecraft as being very short in the direction of travel, with all its clocks running slow. Any experiment done aboard the spacecraft would therefore use short measuring sticks and slow clocks, and the observers aboard the spacecraft would measure that 1% difference in velocity as being equal to c, according to "their" metres and "their" seconds.

Both observers measure the same velocity, but disagree about how the measurements are performed.

Grant Hutchison
Okay i get it in that both observers would measure the same speed but only because the measuring scale or device was altered by the observers.

Doesnt this sound a lot like the same weirdness in quantum mechanics where an observer by observing actually forces an outcome. Its as if the speed of light is playing the same game. Or nature cheats in order to keep the speed of light constant?

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Originally Posted by Jetlack
Okay i get it in that both observers would measure the same speed but only because the measuring scale or device was altered by the observers.
Not really "altered by the observers".
It's just that if you and I are in relative motion, we can't agree about which events are simultaneous, and that leads on to our inability to agree about lengths and clock rates. Which leads on to the constancy of c, as measured by any observer.
At the root of all this is the idea that physics is always the same, no matter what your state of motion. If the apparent velocity of light in your lab (and your house!) was different in different directions, then all of electromagnetism would be affected. The Universe appears to be put together to prevent such irregularities, and that in turns leads to the predictions of Special Relativity.
Ken G is fond of saying that Special Relativity would prevail even if light didn't exist; from which I understand him to be saying that the uniform behaviour of physics is extremely fundamental.

Grant Hutchison

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## Depends on the Observer

Originally Posted by Jetlack
Or nature cheats in order to keep the speed of light constant?

With respect to the above quote, nature doesn't cheat, we do. For practical purposes, all of our activities take place at very small fractions of the speed of light. As a result, Newton's Laws work just fine for us (They are a special case of relativity, where velocities are very low.) So we don't have to take relativity into consideration in our day to day activities. One notable exception, and we don't see the calculations ourselves, is GPS positioning, which needs relativistic corrections to get that 3 foot accuracy.

10. Originally Posted by grant hutchison
Someone on Earth would see the light travelling at c, with the spacecraft behind it moving at 0.99c. So the relative velocity of light and spacecraft would be 1% c, as seen from Earth.
But the Earth observer would also see the spacecraft as being very short in the direction of travel, with all its clocks running slow. Any experiment done aboard the spacecraft would therefore use short measuring sticks and slow clocks, and the observers aboard the spacecraft would measure that 1% difference in velocity as being equal to c, according to "their" metres and "their" seconds.

Both observers measure the same velocity, but disagree about how the measurements are performed.

Grant Hutchison
That is probably the best explanation of this question I have seen. It makes perfect sense in layman’s terms.

However, it is still hard to imagine how you can be traveling at 99.9% of the speed of light and you can see a beam of light race past you, seemingly going 186,000mps faster than you are. Or seeing the light escaping from your headlights at 186,000mps faster than you are going.

11. Originally Posted by Arcane
That is probably the best explanation of this question I have seen. It makes perfect sense in layman’s terms.

However, it is still hard to imagine how you can be traveling at 99.9% of the speed of light and you can see a beam of light race past you, seemingly going 186,000mps faster than you are. Or seeing the light escaping from your headlights at 186,000mps faster than you are going.
This is where the time-dilation and length contraction comes in, as Grant indicated. Simply put, you experience time at its fastest and length along the axis of motion at its longest when you are at rest and at their slowest and shortest as you approach the speed of light. If were were able to reach the speed of light itself then theoretically time would stop for you and distances would become infinitely short. The amount by which you accelerate and your perception of time (your clock) and length are intrinsically linked in a way that means when you experience the maximum for one you experience the minimum for the other.

So you always measure the speed of light as being the same, whatever speed you have accelerated to.

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I have often thought of the following problem and I humbly ask for an explination:

An observer is waiting next to railroad tracks waiting for a collision to occur. There are two trains on the track (we'll call them train A and train B); both trains are an equal distance from the observer. Both trains are traveling toward each other. To the observer, it appears each train is traveling at .75c.

Please tell me what train A sees, what train B sees, and and the observer sees.

My intuition would tell me that the observer sees the distance between train A and train B disappearing at 1.5c. I know this can't happen. Will everyone observe the collision occurring at the same time? Will everyone experience the collision occurring at the same time (i.e. the observer will also experience the train reck because he's standing next to the tracks).

13. Originally Posted by Confunded
My intuition would tell me that the observer sees the distance between train A and train B disappearing at 1.5c. I know this can't happen.
Of course it can happen.

If you turn on a beam of light in one direction, and another in the opposite direction, the "ends" of the beams will separate at twice the speed of light.

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Originally Posted by Confunded
I have often thought of the following problem and I humbly ask for an explination:

An observer is waiting next to railroad tracks waiting for a collision to occur. There are two trains on the track (we'll call them train A and train B); both trains are an equal distance from the observer. Both trains are traveling toward each other. To the observer, it appears each train is traveling at .75c.

Please tell me what train A sees, what train B sees, and and the observer sees.

My intuition would tell me that the observer sees the distance between train A and train B disappearing at 1.5c. I know this can't happen. Will everyone observe the collision occurring at the same time? Will everyone experience the collision occurring at the same time (i.e. the observer will also experience the train reck because he's standing next to the tracks).
This question only raises more questions...

Who stands next to train tracks waiting for a collision to occur?
I mean I've heard of people waiting on trains, but not waiting on colliding ones

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From your vantage point near the track, each train will actually
appear to be rushing toward you even faster than .75 c, because
it takes less and less time for light from the trains to reach your
eyes as they get closer and closer to you. Because of that,
the clocks on the trains appear to you to be running faster than
they should. If it turns out that the trains are actually on parallel
tracks, and pass each other right in front of you without crashing,
you will see the the clocks slow way down as they move away
from you. The change in the clock rate matches the Doppler
shift of the light that you see. As the trains come toward you,
their colors are shifted slightly toward the blue, and as they move
away, the colors are shifted toward the red. As the trains go by,
you might notice that the wheels are just a bit out-of-round.
The wheels appear to be elliptical, because the trains look
squashed in the direction they are moving.

Observers on each train see the other train approaching at a
relative speed of something like .9 c. They each see light from
the other train as more strongly Doppler-shifted than you do,
and they each see the other's clocks ticking faster than you
see them ticking.

And yes, you see the trains approaching each other at more
than 1.5 c. But nobody sees anything moving faster than c.

See? Si!

-- Jeff, in Minneapolis

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Just an slight addition to Jeff Root,
"But nobody sees anything moving faster than c in their own frame of reference."

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Originally Posted by Freiddie
Just an slight addition to Jeff Root,
"But nobody sees anything moving faster than c in their own
frame of reference."
Nobody sees anything moing faster than c in anyone else's
frame of reference, either.

-- Jeff, in Minneapolis

18. Originally Posted by Jeff Root
Nobody sees anything moing faster than c in anyone else's
frame of reference, either.
The laws governing possession of reference frames are still being hammered out in the courts, and what it means to see someone else's reference frame is also ambiguous, but one could imagine a reference frame associated with train A and moving with train A. In that reference frame, you (outside the reference frame) would see train B moving at 1.5c. This is not much different than just imagining a coordinate system moving past us at 2c. In that reference frame, sedentary we are moving at twice the "speed of light".
Last edited by hhEb09'1; 2007-Dec-20 at 11:42 AM. Reason: Added quotation marks

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If I see the two trains moving toward each other at 1.5c, but each train sees the other train approaching at .9c then there seems to be a problem...

The observer will see the trains pass each other before the trains themselves think they've passed each other. In essence, the same objects will be in different places at the same time.

If I see the trains collide before the trains themselves collide...isn't that telling the future? In which case, the collision could be prevented...in which case I'm lost.

Thanks again.

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It's not a problem. The trains each see the track before them as shorter than you, as the observer, see it. So, the trains see their speeds relative to each other as less than 1.5 c, and in fact, still less than c, but with less distance to cover anyway.

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Originally Posted by Aristocrates
It's not a problem. The trains each see the track before them as shorter than you, as the observer, see it. So, the trains see their speeds relative to each other as less than 1.5 c, and in fact, still less than c, but with less distance to cover anyway.
I think I understand, please correct me if I'm wrong. The trains will still pass each other at the same instant for all observers (i.e. the event will not happen twice). The caveat is that each observer's clock may show a different time this single event occurred at. Yet, I still have another question.

If the person on the platform observed the trains heading toward each other at 1.5c, then isn't it possible to transmit information at faster than c? I.e. If the observer wanted to have a message passed from train a to train b, the message would be transmitted at 1.5c according to the observer? The people on the train wouldn't think they broke the speed of light, but the observer's message did.

22. To light itself, in the direction of travel, length contraction is infinite - I.E. to zero. However, this only means that from the reference frame of the light, it is everywhere along its path at once - to all other observers, it still takes time to travel and has a position.

23. Does it realy matter how it appears to outside observers?

That is of course if you could travel that speed, to you it would be instant, to everyone else it would be a long time, but to you it doesn't matter, you can be everywhere at once basicaly. Omnipresent and eternaly living, since time would stop. Very interesting.

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Originally Posted by Arcane
Does it realy matter how it appears to outside observers?

That is of course if you could travel that speed, to you it would be instant, to everyone else it would be a long time, but to you it doesn't matter, you can be everywhere at once basicaly. Omnipresent and eternaly living, since time would stop. Very interesting.
If information can travel faster than the speed of light to an observer; that implies I can send e-mail at faster than the speed of light, or my computer can make calculations faster than light, or I can communicate with astronauts faster than the speed of light. Of course, I can't do those things now, but these things can only be invented if they're possible. Is it possible?

It seems to be. This is very difficult for me to grasp. I would like to understand it though. Where can I read more? How did Einstein come up with something so counter-intuitive just by thinking about it?

25. He was a great mind

It was the facts. It was experimentally proven before that the speed of light is the same no matter in what direction the observer travels relatively to the light.
All the rest is a consequence of this. Of course it took a great mind to derive all that.

26. Originally Posted by Confunded
If information can travel faster than the speed of light to an observer; that implies I can send e-mail at faster than the speed of light, or my computer can make calculations faster than light, or I can communicate with astronauts faster than the speed of light. Of course, I can't do those things now, but these things can only be invented if they're possible. Is it possible?
To an outside observer light travels at the speed of light, not any faster, not any slower. I was speaking as if you were the light itself. If you were a beam of light you would be God-like. All seeing and eternaly living, at least to you, not to an outside observer.

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Originally Posted by Confunded
This is very difficult for me to grasp. I would like to understand it though. Where can I read more? How did Einstein come up with something so counter-intuitive just by thinking about it?
This article discusses how Einstein worked out special relativity. Without meaning to detract from his achievement, he certainly wasn't working from a blank slate.

The fact that there are so many counter-intuitive concepts in science is an indication that we should never rely on our intuition.

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Information can't travel faster than c.

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Originally Posted by Freiddie
Information can't travel faster than c.
I knew someone would say that.

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I thought the trains were racing toward each other at 1.5c according to my perspective? Is this the case or not?

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