Relativity and c

[Weyoun]

Hi all

In preparation for my exam tomorrow, I started going over a year's collection of notes, and stubled across a problem with regard to relativity that I simply couldn't get my head around. I thought of this myself, so there could be some (probably gaping) holes in it. Anyway, what would happen if two spaceships travelled away from any given point at 0.9c each? would the ships still be able to see each other? I'd like any response to account for the 1.8c relative velocity between the two ships. This leads to another question, what are we measuring c relative to?

All replies much appreciated. Thanks

 

[daclayman]

on that spaceship comparo; No, the spaceships would not see each other. If light travels in waves (as sound does), these 2 ships collectively have exceeded the speed of light. I guess on the relative thingy (considering there is really nothing 'relative' to the speed of light), the prof wants you to compare c to proven stuff. I'm no theorist and have no edumucation in theory, but at least this thread gets a bump.

 

[Sohcan]

<< I'd like any response to account for the 1.8c relative velocity between the two ships >>



<< No, the spaceships would not see each other. If light travels in waves (as sound does), these 2 ships collectively have exceeded the speed of light >>

You guys are using Galilean Relativity, you need to use Special Relativity. Let's say the two spaceships are travelling in the z-direction (Vx and Vy = 0), with spaceship A's Vz = -.9c, and spaceship B's Vz = .9c. Transforming into a frame with Vz = -.9c (the frame of spaceship A), and using relativistic velocity transformation (Vz' = (Vz - Bc)/(1-B*Vz / c), where B = dimensionless velocity of transformation normalized to c), the velocity (Vz) of spaceship A = 0, and the velocity Vz of spaceship B = (.9c - (-.9c))/(1-.9c*(-.9)/c) = 1.8c / 1.81 = .9945c. Since the velocity of light in a vacuum is c in all frames of reference, the spaceships see each other (as is always the case in relativistic velocity transformation).

 

[flood]

Sohcan has it :-]

 

[Kuroyama]

 

[Weyoun]

Thanks for clearing that up sohcan

Thus far, we've only been taught the time dilation and length contraction transformations - damn this new year12 syllabus I was going through a paper last night, and found that 80% of questions pertained to contributions of past physicists and discussion of the impacts of generators on society.... Dammit, english and history teachers should be restricted to their own respective departments... Anyway, do you have a proof for that velocity transformation handy? I tend to remember something more effectively having derived it

Thanks once again

 

[Sohcan]

<< Anyway, do you have a proof for that velocity transformation handy? >>

Relativity notes (pages 15-18, though not a complete derivation). Typically you use the velocity four-vector notation, since the velocity transformation equations (especially in the x- and y-directions) are a bit cumbersome. But the formal four-vector approach to special relativity is probably beyond the scope of your class...it's something to which you are introduced in upper-level undergrad modern physics or relativistic electrodynamics.

 

[flood]

i got a derivation for you... but its not pretty

 

[flood]

here

looks a lot better than plaintext

 

[rgwalt]

<<

<< I'd like any response to account for the 1.8c relative velocity between the two ships >>



<< No, the spaceships would not see each other. If light travels in waves (as sound does), these 2 ships collectively have exceeded the speed of light >>

You guys are using Galilean Relativity, you need to use Special Relativity. Let's say the two spaceships are travelling in the z-direction (Vx and Vy = 0), with spaceship A's Vz = -.9c, and spaceship B's Vz = .9c. Transforming into a frame with Vz = -.9c (the frame of spaceship A), and using relativistic velocity transformation (Vz' = (Vz - Bc)/(1-B*Vz / c), where B = dimensionless velocity of transformation normalized to c), the velocity (Vz) of spaceship A = 0, and the velocity Vz of spaceship B = (.9c - (-.9c))/(1-.9c*(-.9)/c) = 1.8c / 1.81 = .9945c. Since the velocity of light in a vacuum is c in all frames of reference, the spaceships see each other (as is always the case in relativistic velocity transformation). >>



Owned.

Anyway, when I learned about special relativity, we did the derivation with a really cool geometric method. I could probably reproduce it on paper and scan it in if it would help.

Ryan

 

[Woodchuck2000]

Remind me to PM sohcan the next time I need help with my physics homework

Fairly on topic question:
Is this the only reason a body cannot exceed the speed of light: Mass increases exponentially with velocity.
As velocity -> c, mass -> infinity => force needed to continue accelerating body needs to hit infinity, and we can't get infinte force...

In fact, does that even follow as an argument?

 

[Fandu]

<< Remind me to PM sohcan the next time I need help with my physics homework

Fairly on topic question:
Is this the only reason a body cannot exceed the speed of light: Mass increases exponentially with velocity.
As velocity -> c, mass -> infinity => force needed to continue accelerating body needs to hit infinity, and we can't get infinte force...

In fact, does that even follow as an argument? >>




Mass does not increase with velocity.... Where did you get that from? In classical physics the kinetic energy increases exponentially with velovity, but mass is a fixed property. I'm through university quantum physics and relativity and I've never ran across any theory like that.

Special Relativity says that no matter how much kinetic energy we use to accelerate a particle, it will never exceed c in any refrence frame. We use the formula:

Ke = (mc^2 / (sqrt(1 - v^2/c^2) ) - mc^2

From which you can see that as the velocity approaches c, Ke approaches infinity....

limit of Ke as v-> c = oo

 

[flood]

<< limit of Ke as v-> c = oo >>


from one of my previous posts:


<<
Relativistic energy is defined as: (rest energy + kinetic energy)
E = m(c^2) + m(c^2)(gamma-1)
gamma = 1/sqrt(1-(v/c)^2)

so, the rest energy, we dont have to apply, just m(c^2)(gamma-1)
suppose you want to go .99c
then you have gamma = 1/sqrt(1-(.99)^2) = ~7
so youd have to put in 6 times the rest energy to get it to go .99c, which is a whole lot!
make it .999c and you have to put in 21 times the rest energy
make it .9999c and you have to put in 69 times the rest energy
make it .99999c and you have to put in 222 times the rest energy
make it .999999c and you have to put in 706 times the rest energy
make it .9999999c and you have to put in 2235 times the rest energy

And this is assuming 100% efficency and no friction!
This is why its only practical to make a single molecule travel at .99c or so, and those particle accelerators use a whole lot of power to do it.
>>



plot it on a graph, and you'll see that as v->c, you approach a vertical asymptote (KE)

 

[Sohcan]

<< Remind me to PM sohcan the next time I need help with my physics homework >>

Sure, but I charge by the hour.


<< Mass does not increase with velocity.... Where did you get that from? In classical physics the kinetic energy increases exponentially with velovity, but mass is a fixed property. I'm through university quantum physics and relativity and I've never ran across any theory like that. >>

That's "relativistic mass"...my quantum mechanics prof mentioned it once. Apparently it's an old interpretation of relativistic energy (E = (gamma)*mc^2); relativistic mass = (gamma) *m. It's a flawed conclusion, and no one uses it anymore.

 

[Fandu]

Flood: That's exactly what I said there......



<< That's "relativistic mass"...my quantum mechanics prof mentioned it once. Apparently it's an old interpretation of relativistic energy (E = (gamma)*mc^2); relativistic mass = (gamma) *m. It's a flawed conclusion, and no one uses it anymore. >>



That would explain why I've never seen it.

 

[flood]

<< Flood: That's exactly what I said there......
>>


I know
sometimes people better understand when they see the numbers rather than relations.