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Author Topic: Relative Velocity Addition  (Read 6969 times)

Offline Jacob Mouritzen

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Relative Velocity Addition
« on: 08/12/2003 23:28:22 »
Im a 17 year old boy from Denmark. Science never really interested me, I'm more of a filosofer:) but I have a question.

If I am standing in a Train, traveling the speed of light (299,800 km/sec) and I run through it at the same time. Let's say with the speed of 10km/hour I would be travelling (299,800km/sec + 10km/hour)
What would happen then? Would I stand still to outside observers? would I travel back in time? or would I vanish? I know this is a weird and very theoretical question, but I would love to hear some suggestions! Thank you!

Jacob Mouritzen
« Last Edit: 03/05/2004 22:44:48 by tweener »


 

Offline qpan

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Re: Relative Velocity Addition
« Reply #1 on: 09/12/2003 01:28:26 »
Velocities cannot simply be added/subtracted to give resultant/relative velocities. It just so happens that at slow speeds, the variation of mass will be so negligable that you can just add them without causing very much error in calculation at all. At near light speeds, the variation of mass is very significant (which in turn greatly affects the k.e.)- to be perfectly honest, you will not be able to run at 10 km/h- your mass will approach infinity and quite simply you will not be able to accelerate to 10 km/h. That is, assuming somehow the train managed to accelerate to light speed anyway, which too, would be impossible.

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Offline Jacob Mouritzen

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Re: Relative Velocity Addition
« Reply #2 on: 09/12/2003 12:17:56 »
So in short, my mass would become so large that it would be impossible to move? And I guess this is because the faster you move the more you weight? Well thank you for your answer.

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Offline Quantumcat

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Re: Relative Velocity Addition
« Reply #3 on: 09/12/2003 15:05:44 »
I want to know why going fast adds on to your mass. I know why it warps time, but no one's explained to me the mass thing. Can someone?

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Offline chris

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Re: Relative Velocity Addition
« Reply #4 on: 09/12/2003 17:26:00 »
At a guess, E=mc^2 - so the more energy you have (through going faster) the more you must weigh since c remains constant.

Chris


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Offline qpan

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Re: Relative Velocity Addition
« Reply #5 on: 09/12/2003 18:15:47 »
The increase in (relativistic) mass can be explained by light speed constancy. The faster you travel, the more distance you actually need to cover to travel through the same amount of space-time. Therefore, to accelerate, you need to put in more energy than you initially did to obtain the same acceleration at slower speeds. Therefore, for f=ma to continue working at high speeds, the "m" needs to be increased. Mass can be viewed as resistance to change in momenutm, and as you can see, the resistance to change in momentum will be greater if you need to put in more force to accelerate it.
The particle, however, does not feel its mass increasing, thus why it is called relativistic mass.
(as the particle could say that it is the one at rest and the observers are travelling towards it at light speed).
If I rephrase your question slightly- if the train was travelling at 99.9% the speed of light (as because it has mass, it is not possible of it to travel at the speed of light) and you ran through it at 10km/h, the speed of you relative to the observers will becaome something like 99.9000000000000000000...etc..001% the speed of light (or something like that). This is due to the warping of space time (time would distort so that you would not break the light speed barrier- as to both you and the observers, the speed of light is constant).
I think i was wrong to say that you would not be able to run at 10km/h if you were travelling very fast. If you consider the train to be stationary and the observers to be travelling towards you at 99.9% the speed of light (as you are perfectly entitled to do due to relativity), then you could obsiously easily run at 10km/h, so this must still be true even thought the train is travelling at near light speed. However, your relative velocity to the observers would not change by 10km/h due to the distortion of space and time.

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Offline Jacob Mouritzen

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Re: Relative Velocity Addition
« Reply #6 on: 09/12/2003 23:04:57 »
Great, I think I'm getting the picture. But it doesn't make it any easier for me to understand because it's in English. But that's my problem :) I took this subject up for discussion with my science teacher today, and I completely shook him with my knowledge on this subject. Thank you guys, I think I just earned a higher grade :D



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Offline chris

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Re: Relative Velocity Addition
« Reply #7 on: 09/12/2003 23:52:22 »
Well done ! That's the idea - we all teach each other !

Chris

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Offline Dan B

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Re: Relative Velocity Addition
« Reply #8 on: 04/05/2004 00:56:33 »
Relativity sez that two objects cannot pass one another at greater than the speed of light...

Consider the velocity of an object at a redshift of 10 :D
 

Offline chris

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Re: Relative Velocity Addition
« Reply #9 on: 06/05/2004 03:55:35 »
Dan - can you elaborate ?

Chris

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Offline Dan B

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Re: Relative Velocity Addition
« Reply #10 on: 06/05/2004 05:16:25 »
I was tkaing the piss out of classical and relativistic definitions of redshift, which are both a bit crap....

The classical approx is z=v/c (i.e at z=10, the newest, furtherest claimed, cough cough, reshift) resessional v=10c!! In Special rel 1+z=sqrt((1+(v/c))/(1-(v/c))), which goes to v = 120c/122 - a bit better.

Anyway... its actual ressesional velocity depends on the cosmolgical model you use :D
 

Offline victor

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Re: Relative Velocity Addition
« Reply #11 on: 16/09/2004 19:54:21 »
quote:
Originally posted by qpan

The increase in (relativistic) mass can be explained by light speed constancy. The faster you travel, the more distance you actually need to cover to travel through the same amount of space-time. Therefore, to accelerate, you need to put in more energy than you initially did to obtain the same acceleration at slower speeds. Therefore, for f=ma to continue working at high speeds, the "m" needs to be increased. Mass can be viewed as resistance to change in momenutm, and as you can see, the resistance to change in momentum will be greater if you need to put in more force to accelerate it.
The particle, however, does not feel its mass increasing, thus why it is called relativistic mass.
(as the particle could say that it is the one at rest and the observers are travelling towards it at light speed).
If I rephrase your question slightly- if the train was travelling at 99.9% the speed of light (as because it has mass, it is not possible of it to travel at the speed of light) and you ran through it at 10km/h, the speed of you relative to the observers will becaome something like 99.9000000000000000000...etc..001% the speed of light (or something like that). This is due to the warping of space time (time would distort so that you would not break the light speed barrier- as to both you and the observers, the speed of light is constant).
I think i was wrong to say that you would not be able to run at 10km/h if you were travelling very fast. If you consider the train to be stationary and the observers to be travelling towards you at 99.9% the speed of light (as you are perfectly entitled to do due to relativity), then you could obsiously easily run at 10km/h, so this must still be true even thought the train is travelling at near light speed. However, your relative velocity to the observers would not change by 10km/h due to the distortion of space and time.

"I have great faith in fools; self-confidence my friends call it."
-Edgar Allan Poe
*************************************************************
""""""If the mass tends to become infinite as we approach the speed of light then light also should have infinite mass.my question is why doesnt light hurt us or why it has negligible mass or i mean no mass.why is it in quantas.can mass also be converted into quantas to travel at the speed of light?"""""""
******************************************************************



victor
 

Offline qpan

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Re: Relative Velocity Addition
« Reply #12 on: 17/09/2004 01:15:25 »
quote:
Originally posted by victor

quote:
Originally posted by qpan

The increase in (relativistic) mass can be explained by light speed constancy. The faster you travel, the more distance you actually need to cover to travel through the same amount of space-time. Therefore, to accelerate, you need to put in more energy than you initially did to obtain the same acceleration at slower speeds. Therefore, for f=ma to continue working at high speeds, the "m" needs to be increased. Mass can be viewed as resistance to change in momenutm, and as you can see, the resistance to change in momentum will be greater if you need to put in more force to accelerate it.
The particle, however, does not feel its mass increasing, thus why it is called relativistic mass.
(as the particle could say that it is the one at rest and the observers are travelling towards it at light speed).
If I rephrase your question slightly- if the train was travelling at 99.9% the speed of light (as because it has mass, it is not possible of it to travel at the speed of light) and you ran through it at 10km/h, the speed of you relative to the observers will becaome something like 99.9000000000000000000...etc..001% the speed of light (or something like that). This is due to the warping of space time (time would distort so that you would not break the light speed barrier- as to both you and the observers, the speed of light is constant).
I think i was wrong to say that you would not be able to run at 10km/h if you were travelling very fast. If you consider the train to be stationary and the observers to be travelling towards you at 99.9% the speed of light (as you are perfectly entitled to do due to relativity), then you could obsiously easily run at 10km/h, so this must still be true even thought the train is travelling at near light speed. However, your relative velocity to the observers would not change by 10km/h due to the distortion of space and time.

"I have great faith in fools; self-confidence my friends call it."
-Edgar Allan Poe
*************************************************************
""""""If the mass tends to become infinite as we approach the speed of light then light also should have infinite mass.my question is why doesnt light hurt us or why it has negligible mass or i mean no mass.why is it in quantas.can mass also be converted into quantas to travel at the speed of light?"""""""
******************************************************************



victor



Well, theoretically nothing with (invariant) mass can travel at the speed of light. Photons have no (invariant) mass but they do have momentum (which is why solar sails on spacecraft work). Invariant mass is independant of velocity whereas relativistic mass increases with velocity.

   invariant mass = mr = E/c^2
   relativistiv mass = m0 = sqrt(E^2/c^4 - p^2/c^2)

With regards to the increase in relativistic mass; the increase is in its relativistic mass rather than the invariant mass, so the rest mass of the object does not actually increase, which is why light (in small quantities) does not hurt when it hits us.

Not sure why photons have no mass, just the way they were designed!

"I have great faith in fools; self-confidence my friends call it."
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Offline gsmollin

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Re: Relative Velocity Addition
« Reply #13 on: 17/09/2004 04:25:37 »
The fundamental tenent of relativity is that the free-space magnitude of velocity of light is a constant, and is the maximum velocity that mass/energy may travel at. After that, neither space or velocity can be conserved, but are added together using the relativistic transformations originally developed by Lorentz, that work so that c+10km/hr cannot be added together.

Mass is also not conserved, but MOMENTUM (mv) IS CONSERVED. This is crucial. Since velocity is not conserved, but momentum is, then mass cannot be conserved. To observers moving at different relativistic velocities, a mass will change its value, so that the momentum of the mass is always mv. The velocities will add according to the Lorentz transformations, and so always add to less than c, but the momentum must be conserved, so the mass increases. This fact actually leads to the derivation of the mass transformation, with its famous result that the mass of an object traveling at c is infinite, and therefore no massive object can travel at c.
 

Offline victor

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Re: Relative Velocity Addition
« Reply #14 on: 19/09/2004 06:14:48 »

victor



Well, theoretically nothing with (invariant) mass can travel at the speed of light. Photons have no (invariant) mass but they do have momentum (which is why solar sails on spacecraft work). Invariant mass is independant of velocity whereas relativistic mass increases with velocity.

   invariant mass = mr = E/c^2
   relativistiv mass = m0 = sqrt(E^2/c^4 - p^2/c^2)

With regards to the increase in relativistic mass; the increase is in its relativistic mass rather than the invariant mass, so the rest mass of the object does not actually increase, which is why light (in small quantities) does not hurt when it hits us.

Not sure why photons have no mass, just the way they were designed!

"I have great faith in fools; self-confidence my friends call it."
-Edgar Allan Poe
[/quote]
*******************\\\\\\\*************
quote:

8) i think i got the idea(almost).But u have definetly encouraged me to do some research on this.I already got some books from the library to learn more about einstiens relativity.
INTRODUCTION TO SPECIAL RELATIVITY  By Robert Resnick
SPECIAL RELATIVITY By A.P.French
****HEY QPAN DO U HAVE ANY REFRENCES FOR ME WHICH U THINK WILL BE GREAT BOOKS TO READ.I MEAN DO U HAVE ANY FAVOURITES.*****

victor
 

Offline victor

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Re: Relative Velocity Addition
« Reply #15 on: 19/09/2004 06:22:14 »
quote:
Originally posted by gsmollin

The fundamental tenent of relativity is that the free-space magnitude of velocity of light is a constant, and is the maximum velocity that mass/energy may travel at. After that, neither space or velocity can be conserved, but are added together using the relativistic transformations originally developed by Lorentz, that work so that c+10km/hr cannot be added together.

Mass is also not conserved, but MOMENTUM (mv) IS CONSERVED. This is crucial. Since velocity is not conserved, but momentum is, then mass cannot be conserved. To observers moving at different relativistic velocities, a mass will change its value, so that the momentum of the mass is always mv. The velocities will add according to the Lorentz transformations, and so always add to less than c, but the momentum must be conserved, so the mass increases. This fact actually leads to the derivation of the mass transformation, with its famous result that the mass of an object traveling at c is infinite, and therefore no massive object can travel at c.


Quote
:)i think i got the idea(almost).But u have definetly encouraged me to do some research on this.I already got some books from the library to learn more about einstiens relativity.
******THANK U VERY MUCH FOR EXPLAINING ME THE IDEA******


victor
 

Offline qpan

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Re: Relative Velocity Addition
« Reply #16 on: 26/09/2004 22:13:47 »
Hi Victor - Brian Greene's The Elegant Universe and Jim Al-Khalili's Black Holes, Worm Holes and Time Machines are both extremely good books for explaining about relativity (along with a variety of other interesting topics). I'd definately recommend them as good reads - i read them a few years ago and found them very useful as a step by step introduction to relativity and quantum mechanics.

"I have great faith in fools; self-confidence my friends call it."
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Re: Relative Velocity Addition
« Reply #16 on: 26/09/2004 22:13:47 »

 

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