Relativistic Riddle Racing Light.

[qwijibow 0]

Here's a riddle on relativity.hyperthetical situation.SpaceShip X can travel half the speed of light.LazerCannon Y can fire a Pulse of Light, which travels at the speed of light.There is going to be a race.The race track is 1 light year long (it will light one year to travel the distance) (the spaceship 2 years)The spaceship is given 1 year head start....so the spaceship, capable of half light speed, only has to race half a light year, the beam of light has to race one whole light year.There are 2 Observers in this race. A: the Driver of the space ship, and B the judge sat on the finish line.remember, the speed of light is relative to the observer.the observer on the finish line, sees the spaceship with half a yea head star, travel at half the speed of light, and the race is a draw... both spaceship AND laser beam finissh the race at th same time.to obserber on the space ship, traveling at half the speed of light, the laser beem is moving towards him at the speed of light... the laser beam overtakes at the 0.75 lightyear mark, and wind the race by 6 weeks (im estimating)Was it a draw ? or did the light win ?which observer is correct... they both are.this is what will happen according to the theory of relativity.This isnt too hard to accept... we already know electrons spin in all directions at the same time, and photons in dual slip experiments gotough 2 paths at the same time..BUT.... what if, there is a 4rd observer on the finish line, and the third observer bets hit by the laser beam to observer A, and permenantl blined.but to observer B, the light beam missed observer C by 6 weeks.then all 3 observers meet in the pub later....is obsever C Blind or not ????

[m3ch4 0]

Um....Not sure about the answer because I'm not sure about the question, could you possible be a bit more clear with the riddle? =Ssorry, thanks

[vizskywalker 0]

Okay, here's my answer. Observer C can see fine, but only out of his/her left eye. The other eye is blind. Observer A accepts this, but Observer B does not, and tests it the whole night. Around 2:00 a.m. Observer C gets fed up with Observer B and punches him in the mouth. This starts a bar brawl that results in total blindness through injuries of Observers A through C because of death, thus solving the issue. So I like pickles.~edit: I think I just figured it out seriously. Observer C is blind. Observer A saw the laser beam hit Observer C, and knows the reason. Observer B didn't see the laser hit Observer C and wil wonder why Observer C is blind.

Edited June 2, 2005 by vizskywalker (see edit history)

[mitchellmckain 0]

If you are trying to make a fool of me by predicting that I will be a bore and take your problem seriously as far as it can be, well you have my number.First of all any two people in the same place at the same time must see the same thing so if the judge sees the light arrive at the finish line at the same time as the pilot then so does the pilot. You have established that the judge sees the light start out when the pilot is already half way to the finish line. But although the rest of the race takes one year for the judge, it takes only .866 year for the pilot. The difficult part of the problem is what does the pilot see. Well the pilot does not see the light start out when he is halfway to the finish line but when he has gone a third of the remaining distance past that point. He sees the light leave .57735 light years behind him when he has about .288675 light years left to go. So the light takes only .57735 light years to reach him and it takes him .57735 light years to reach the finish line so that both reach the finish line at the same time.You may notice that when you add the .57735 light years to the .288675 light years you only get .866025 light years not a whole light year and this is why the whole trip takes him only 1.73205 years instead of 2 whole years.

[mitchellmckain 0]

Oh and of course if the laser beam hits the guy then it hits the guy to all observers the only thing that relativity affects is where and when the laser beam hits the guy. But in this case since he is at the finish line there are no disagreements at all. He must be hit by it when the races ends in a tie, if he is hit by it at all.

[szupie 0]

It was kinda hard to know what you were saying through all the typos... But I know what you're talking about. I've thought about a similar situation before, but still can't figure it out. I can think of 3 possible solutions to this:1. During this incident, 2 similar universes are created: one where Observer C is blind, one where he/she is not. (Actually, that wasn't really logical...) I don't remember if this is one of my own theories or one I've read about, but: there is a theory that at every instant, there are an infinite universes created, each is a different possibility of action (and even non-actions) of everything in the universe. As time goes on, these infinity universes multiply constantly, matching every possibility of everything.2. Because Observer B is moving at half of speed of light, time moves slower for him/her. The reason for Observer B to see the Laser move at speed of light is because time is moving faster outside of him even though he thinks it's normal speed. It's like playing a 2 year tape in 1 year's time to him. The tape would go fast, therefore the Laser seems relativly moving at speed of light. So, Observer B actually wouldn't see the Laser hit the Observer C, but still see the Laser move at speed of light. This might have sounded a little repetitive, but, hey, "repetition is the mother of learning"...But if anyone is still confused, I can explain this further...3. Eistein is wrong. The speed of light is not constant at every perspective. I mean, how did he prove that it is?Hmm, explaining my number 2 made me think clearer on the subject... Thanks, qwijibow!

[qwijibow 0]

It was kinda hard to know what you were saying through all the typos.

sorry about that, im getting used to a new keyboard, its much smaller than my last
Well...... so many different answers, and so many pickes fans.

i cant give a definate answer, because the theory of relativity is just a theory.
but the prefered answer is....

Observer C is fine. Because observer C is traveling at the same relativistic speed at observer B, and to observer B, the light missed be several weeks.

so one person got it right.... who was that ?

EDIT:
ohh, just in case you havn't been reading all my other posts in this forum, this is not my own riddle, it was posed by my phyiscs teacher some years ago in college.

[szupie 0]

Hmmm... Do you think my second theory is right? The one with the time slowing down? I thought about it all night, and the more I think about it, the more sense it made. But, I don't think that theory applies when light is moving in the opposite direction as you. Then, it would seem that it is traveling faster than lightspeed, relatively.

[mitchellmckain 0]

Well I am afraid that your physics teacher got it wrong because this following statement in the problem you gave is completely wrong.

to obserber on the space ship, traveling at half the speed of light, the laser beem is moving towards him at the speed of light... the laser beam overtakes at the 0.75 lightyear mark, and wind the race by 6 weeks (im estimating)

Here is how the calculation is done correctly using the lorentz transformations:x' = g (x - (v/c)t)
t' = g (t - (v/c)x)
where g is gamma and is equal to 1/sqrt(1-(v/c)^2)
c is the speed of light so v/c = .5 because the racer is at half the speed of light.
Now the lorenz transformations take the coordinates of an event for the "stationary" observer and give you the coordinates for that same event for the observer moving at velocity v.

So the first thing to do is calculate gamma: g = 1/sqrt(1-(.5)^2) = 1.1547
Next we set up a coordinate system for the judge for whom I made the midpoint of the journey x=0 and the time that the racer passes that midpoint t=0. This is a convenient choice because when we put these into the lorentz equations we get t'=0 and x'=0 for the racer right at the time and place when he passes the midpoint of his journey.

Since the judge sees the light leave at this same time his coordinates for that event is t=0 and x=-.5 light years. Now we put these into the lorentz equation.
x' = 1.1547 ( -.5 - (.5) 0) = -.57735 light years
t' = 1.1547 ( 0 - (.5) (-.5)) = .288675 years
This means that the racer sees the light leave the starting position .57735 light years behind him when he is already .288675 years past the midpoint of his journey.

When the racer arrives at the finish line the coordinates for the judge are clearly x=.5 light years and t=1 year. Putting these into the lorentz equations give
x' = 1.1547 ( .5 - (.5) 1) = 0
t' = 1.1547 ( 1 - (.5) .5) = .866025 years
This means that the event of the racers arrival is in the same place where he is at the time and it is .866025 years after he passed the midpoint of his journey.

If you subract the time at which he saw the light leave the starting position, you get .866025 - .288675 = .57735 years which is exacly the time it takes the light to get to him since the light was only .57735 years behind him (according to him) when the light started out.

I am surprised that your teacher would give this to your class without making sure it is right. It was probably not an active area of research for him as it is for me.

[mitchellmckain 0]

2. Because Observer B is moving at half of speed of light, time moves slower for him/her. The reason for Observer B to see the Laser move at speed of light is because time is moving faster outside of him even though he thinks it's normal speed. It's like playing a 2 year tape in 1 year's time to him. The tape would go fast, therefore the Laser seems relativly moving at speed of light. So, Observer B actually wouldn't see the Laser hit the Observer C, but still see the Laser move at speed of light. This might have sounded a little repetitive, but, hey, "repetition is the mother of learning"...But if anyone is still confused, I can explain this further...

You got the part about time correct, the real confusion is the incorrect statement in the problem. Yes the slower time is called time dilation and the formula (which is derived from the lorentz transformation equations) is
(t2' - t1') = (t2 - t1)/g
where g is gamma given in my previous post and notice it is a difference beteen two times or a time inerval on either side of the equation.
for half the speed of light gamma was 1.1547
which means that time is 1.1547 times slower for the racer. At least this is one way of explaining why the trip only took 1.73205 years for him instead of 2 years.

[qwijibow 0]

So now im confused...again, i cant remember the name of this experiment, but i will describe it.a long time ago, some physisist had an idea...we know, that if we put a sound pulse speaker in the center of 6 different microphones each one meter away from the sound source, and each microphone is positioned like the sides of a dice... above, below, left, right, front back arounf the speaker.by measureing the time delay between the pulse beeing given, and detected by each speaker, we can calculate the wind speed.. because sound travels at the speed of sound, relative to the medium it travels in... AIR.so this scientist assumed, that like sound, light traveled in a medium, they caklled this medium the ether.the earth is traveling how fast, around a sun traveling at anouther speed, in a galaxy traveling at what speed ? i dont know about now, but at the time, we didnt know how fast we were moving.the scienist set up the same experiment as sound, but with light, with a light aource and a detector, over a set distance, and times the speed in all directions.and the result was.....Light moved at exactly the same speed in all directions..which porvied one of 2 hypothesis...a: earth is the stationaly center of the universe (obviosly wrong)b: light does not travel relative to a universal 0 speed, but the speed of the observer.i can accept this...but here's what reeealy bakes my noodle....how many hundred thousand miles per hour do scientists think earch is traveling ??give that speed as a percentage of the speed of light.. we will call it speed E (for earth)it is relativisticly possable for me to travel the speed of light relative to earth.are we following so far ?so lets say i doo that, and i launch my space ship, from earth, traveling in th oposite direction to the current universal direction of earth.in other words, i an traveling at almost the speed of light, relative to earth, but slower than the universal relative speed of light...out of some coincidence, an alien, on anouther world which was traveling at the same speed as earth, but in the opposite direction. and he lauched in the same direction of travel to his home planet... he is traveling the speed of light faster than his relative zero, which itself was traveling at a speed.then we both meet in space... i am traveling at almost the speed of light, in the same direction.... only his relativistis zero was several hundred thousand miles per hour faster than me... and he overtakes me...again, this is almost believable..how how does the universe know where i was born.how does it remember what my relativistic zero is.and what if, one day i take a walk to the back of the space ship ?is my new relative zero the space ship im stood in...or is it still earch... is it possable for me to walk back to the front of the space ship, or would i be walking faster than light ????i dont understand relativity, because i cant grasp the explanation of the world relative... relative to what ??? relative to me, the observer ?no, becuase relative to ME, I am alwasy moving at my own relativistic zero. i can always go forward.WOULD i die at 99.99999% the speed of light because my heart couldnt make blood go fast enough to reach the front of my body ?would the ships computer fail to function because electrons from the back of the ship coultdnt move forwards ?

[mitchellmckain 0]

the scienist set up the same experiment as sound, but with light, with a light aource and a detector, over a set distance, and times the speed in all directions.and the result was.....
Light moved at exactly the same speed in all directions..

Yes this is the Michaelson Morely Experiment which directly led to the Theory of Relativity

how many hundred thousand miles per hour do scientists think earch is traveling ??give that speed as a percentage of the speed of light.. we will call it speed E (for earth)

The orbital velocity of the earth is 31 km/sec = 111,600 km/hr = .01% of the speed of light.

it is relativisticly possable for me to travel the speed of light relative to earth.  are we following so far ?

No it is not possible, you are not massless. But suppose you are a photon, then you have no choice but to travel at the speed of light. But if you are a photon you cannot talk about what you see for the simple fact that you would experience no time. For example, there could never be a massless particle which decays because decay takes time and a massless particle would never have time to decay.

so lets say i doo that, and i launch my space ship, from earth, traveling in th oposite direction to the current universal direction of earth.in other words, i an traveling at almost the speed of light, relative to earth, but slower than the universal relative speed of light...

If you are a photon you are traveling at the speed of light relative to everything. If you are a space ship with mass you are traveling at different speeds relative to different things but all of these speeds are less than the speed of light.

he is traveling the speed of light faster than his relative zero, which itself was traveling at a speed.

The speed of light is the only absolute speed and it does not add to any other velocity. By the way there is a velocity addition formula, here:v3 = (v1 + v2)/(1 + v1 v2 / c^2)
if one of the two velocities v1 or v2 is the speed of light then v3 is the speed of light: v3 = (c + v2)/(1 + v2/c) = c
and if both v1 and v2 are less than the speed of light then v3 is less than the speed of light.

then we both meet in space... i am traveling at almost the speed of light, in the same direction.... only his relativistis zero was several hundred thousand miles per hour faster than me... and he overtakes me...

If you are photons moving in the same direction then you never meet. If you are not photons then the alien could be traveling faster than you by any velocity less than the speed of light.

and what if, one day i take a walk to the back of the space ship ?is my new relative zero the space ship im stood in...
or is it still earch... is it possable for me to walk back to the front of the space ship, or would i be walking faster than light ????

See the velocity addition formula explaination above.

no, becuase relative to ME, I am alwasy moving at my own relativistic zero. i can always go forward.

Yes exactly. No matter how fast you are going it is the same as if you are not moving at all and you can always try speeding up towards the speed of light. But no matter how many times you do this it is still the same as if you are not moving. The only thing that changes is the how fast the place you left is moving away from you, which we call your relative speed to your starting place. And the speed relative to where you started is always less than the speed of light.

WOULD i die at 99.99999% the speed of light because my heart couldnt make blood go fast enough to reach the front of my body ? would the ships computer fail to function because electrons from the back of the ship coultdnt move forwards ?

No the sky would look really strange but otherwise you would not notice anything different. In fact, this is kind of the whole point of the theory of relativity, that no matter how fast you are moving the laws of physics are the same.

[qwijibow 0]

lol, none of what you said ade sence to me.if i was traveling in a space ship, 5 miles per hour slower than C...could i walk at 6mph relative to the ship. (amd therefore 1mph faster that c releative earth ?

[mitchellmckain 0]

lol, none of what you said ade sence to me.

Sorry I am trying. You cannot expect it to agree with common sense since common sense is based on everyday experience and nothing in everyday experience is like this.

if i was traveling in a space ship, 5 miles per hour slower than C...could i walk at 6mph relative to the ship. (amd therefore 1mph faster that c releative earth ?

No you would use the velocity addition formula. Let me change your question to make the caculation easier supposing your ship is traveling 99% of the speed of light relative to the earth and you are a really fast walker so you can walk toward the front of your ship at 2% of the speed of light.
then v1 = .99 c and v2 = .02 c then
v3 = (.99 c+.02 c)/(1+ (.99 c)(.02 c)/c^2) = 1.01 c / (1+.0198) = .9904 c
which means your velocity relative to the earth is 99.04% of the speed of light.

If this sounds really wierd, you are right. It distorts space and time all out of shape. For example, while you are walking if you compare the clocks at the front and the back of the ship they will show different times by a very small amount, but if you stop walking they show exactly the same time again. And I should say that this assumes you do not have to rely on light to read the clocks, but could somehow instantly know what time is on them without using light at all.

When you take into account that the light which you see by is limited to the speed of light you see a lot of other strange effects, besides those of relativity, called the abberation of light. This includes seeing things which are really behind you (though not directly behind you) as if they were in front of you.


Another example, going back to you and the alien. You could be traveling 99% of the speed of the light away from earth which means you see the earth going away from you at 99% of the speed of light. Now you see an alien pass you at 99% of the speed of light in the same direction, apparently traveling 99% of the speed of light faster than you. This means that the alien sees you moving first toward him and then away from him at a speed of 99% of the speed of light. But when the alien looks at the earth how fast does he see it going away from him? Using the velocity addition formula the anwer is 99.995% of the speed of light. You might say that from the alien's point of view (assuming he doesn't understand relativity too well) you are only moving at .995% (less than 1%) of the speed of light away from the earth.

[szupie 0]

No you would use the velocity addition formula.  Let me change your question to make the caculation easier supposing your ship is traveling 99% of the speed of light relative to the earth and you are a really fast walker so you can walk toward the front of your ship at 2% of the speed of light.

then v1 = .99 c and v2 = .02 c then

v3 = (.99 c+.02 c)/(1+ (.99 c)(.02 c)/c^2) = 1.01 c / (1+.0198) = .9904 c

which means your velocity relative to the earth is 99.04% of the speed of light.

<{POST_SNAPBACK}>

Hmm... That's really weird... I thought you'd just add the two speeds together to get the real velocity...

 

 

Another example, going back to you and the alien.  You could be traveling 99% of the speed of the light away from earth which means you see the earth going away from you at 99% of the speed of light.  Now you see an alien pass you at 99% of the speed of light in the same direction, apparently traveling 99% of the speed of light faster than you.  This means that the alien sees you moving first toward him and then away from him at a speed of 99% of the speed of light.  But when the alien looks at the earth how fast does he see it going away from him?  Using the velocity addition formula the anwer is 99.995% of the speed of light.  You might say that from the alien's point of view (assuming he doesn't understand relativity too well) you are only moving at .995% (less than 1%) of the speed of light away from the earth.

<{POST_SNAPBACK}>

That is really hard to believe that it's true, cause it doesn't seem to make sense... Isn't the alien traveling only a bit faster than us? If it is moving at 99%C, why would it think that we're moving at less than 1% of C? Or does this involve time and light distortion again?