okay Veeky Forums, I have two spaceships that I launch from earth in opposite directions, both at 179875475 m / s (60% the speed of light)
Now, relative to one ship, the other one is travelling at 120% the speed of light. I broke the universal speed limit.
ebig
Okay say I have 300 million cars going 2miles per second.
the sum of them is 600,000,000 miles per second that's. I broke your universal mum.
Not in the frame of reference of a ship.
no you
Time fucks it all up. Hence Einstein.
No because time would change in order to keep their relative speed under the speed of light. Relative to earth they still travel at .6c but in relation to each other they move at a speed lower than c.
gama
in a more serious note, how is the proper time of each ship is measured respect to the other and earth? I guess this is just another instance of the twin paradox, but adding a third accelerating object makes it weirder to me
Use Einstein's updated speed laws with the Lorenz transformation
Bear with me I don't know LaTeX
V2 = (V + V1)/(1 + V1V/C^2)
Where V2 is the relative speed, V1 is the speed of the reference frame we're in, and V is the speed of what we're measuring from an inertial frame
We get V2 = (1.2c)/(1 + .36c^2/c^2))
Or V2 = (1.2c)/(1.36)
V2 roughly equals .88c
No
In your frame of reference the distance between them will grow faster then c so you're right.
...
you would have broken the universal speed limit, but you forgot that time slows down as you approach the speed of light.
>but adding a third accelerating object makes it weirder to me
It shouldn't, it's the same thing. The whole point is that everything has its own internal frame of reference where c=c.
[math] \displaystyle
v_2=\frac{v+v_1}{1+ \frac{v_1 \cdot v}{c^2}}
[/math]
No, thats just how relativity works. That's the same idea behind dark energy and the universe expanding at "above c"
What is "reference frame we're in"?
What is "inertial frame"? is it earth?
Say the left ship moves at 0.1c (compared to "inertial frame"?) and right ship at 0.2c (ditto?)
is this correct:
seen from left ship:
v = 0.2c
v_1 =0.1c
So you're saying if one car leaves your house going east at 60 mph and another car leaves your house going west at 60 mph, both cars are really going 120 mph?
Also, if you measure the speed of either spaceship, from any reference frame at all, you'll never measure it going over c.
Not him but relatively to each other yes that's why when your traveling really fast other cars look "slow"
is correct.
Einsteinian-velocities don't add the way Newtonian ones do. What _does_ add linearly is the "velocity potential".
Vp= inverse hyperbolic tangent of V.
0.693147 = inverse hyp tan (0.6)
Vp = 1.38629 = 0.693147 + 0.693147
V = 0.88235 = hyp tan (1.38629)
That's the same result you get from Hyperbolic functions pop us all through relativity because, basically, Einstein is describing a hyperbolic geometry.
The hyp tan method is more useful since it allows you to add more than two velocities at a time.
Consider: a photon rocket (exhaust velocity = 1) with a mass-ratio of 5 burns all its fuel. How fast is it traveling?
Newtonian: V = Ve x ln(R)
1.60943 = (1) x ln(5)
That would mean the rocket would be moving faster-than-light. But the value is only the velocity potential resulting for a huge number of small "kicks" as the fuel is expended, gram by gram.
The actual final velocity is hyp tan (1.60943 ) = 0.92307 c.
The hyperbolic tangent of any number, no matter how large, is always less than 1.
The distance between two objects can change at a rate that surpasses the speed of light but that's too abstract to really count.
lengths contract you fucking idiot
Gr8 b8 m8 I r8 8/8
Thank you :)
>Now, relative to one ship, the other one is travelling at 120% the speed of light.
no, relative to one ship the other one is traveling at 99.999% the speed of light, possibly even lower
that's why it's called the Theory of Relativity, because speed and mass and time are relative to the speed of light (which is really the speed of all fundamental forces)
>relative to one ship, the other one is travelling at 120% the speed of light
Uhm, no.
Reference frame we're in is the one you're measuring from, inertial frame is whatever speed a relatively inertial frame measures it as.
Because of the Lorentz transformation these discrepancies are eliminated
"Inertial frame" is any coordinate set not undergoing acceleration other than from gravitational force.
"Your" inertial frame is the one in which you are stationary in that coordinate system.
If you are freely-falling (no rockets burning) a light-year from the Sun, you are in an inertial frame.
Anybody else who is _also_ in an inertial frame will agree that you are in an IF -- though maybe a different one than theirs.
I kek'd
[math]c_{A:0°}[/math] [math]c_{B:180°}[/math]
in this example, you imply that A and B would only travel at c away from each other?
or that because A and B are traveling at c×2 relative to each other, A and B would not be able to see each other?
cause the latter is what attempts to explain the observable universal horizon.
get your shit straight.