- #1
ftr
- 624
- 47
v=? delta what/which X(distance) over delta what/which T(time)
http://en.wikipedia.org/wiki/Special_relativity
http://en.wikipedia.org/wiki/Special_relativity
DaleSpam said:The v is the speed of the origin of one frame in the coordinates of the other frame.
ftr said:I understand that part, but mathematically we can write v as differentials with appropriate symbols, what are they?
The position of the origin of one frame written in the coordinates of the other frame is ##x=v t##. So v is the standard ##v=dx/dt##.ftr said:I understand that part, but mathematically we can write v as differentials with appropriate symbols, what are they?
georgir said:I'm guessing OP is wondering for the cases with more than one space dimension...
DaleSpam said:The position of the origin of one frame written in the coordinates of the other frame is ##x=v t##. So v is the standard ##v=dx/dt##.
Nugatory said:In any frame, the velocity of any point is dx/dt, where x is the x coordinate of the point in that frame as a function of t and t is the time coordinate in that frame.
If I have two frames (primed and unprimed) and in the unprimed frame the origin of the primed frame is moving in the positive x direction with speed v, I'll write the coordinates of the origin of the primed frame as (x=vt, t=t) and dx/dt is v.
DaleSpam said:Why is there any recursion? The v for the forward transform is the same as -v for the backwards transform, as you showed. If the origin of the primed frame is moving at v in the unprimed frame then the origin of the unprimed frame is moving at -v in the primed frame. No recursion is needed.
Why would you do that?ftr said:I am substituting the ratio of delta x/delta t in equation 2 into v of equation 1
It is clear that you will see v again, and substituting for that you get v's again and so on.
ftr said:eq 1
\begin{align}
x' &= \gamma \ (x - v t) \\
\end{align}
\begin{array}{ll}ftr said:eq 2
\begin{array}{ll}
\Delta x = \gamma \ (\Delta x' + v \,\Delta t') \ , \\
& \Delta t = \gamma \ \left(\Delta t' + \dfrac{v \,\Delta x'}{c^{2}} \right) \ . \\
\end{array}
ftr said:I am substituting the ratio of delta x/delta t in equation 2 into v of equation 1
It is clear that you will see v again, and substituting for that you get v's again and so on.
Nugatory said:Now I'm not sure what you're trying to show here...
DaleSpam said:Why would you do that?Why are you doing any recursion?
robphy said:Note, in general, these [point]events A and B need not have anything to do with v (the [slope]velocity of the worldline of the other observer in the diagram of the first observer).
ftr said:I just did the manipulation to see what results I will get. Obviuosly it was something not clear in my understanding. Of course I do understand the standard transformation.
I was not trying to do recursions, only the the manipulation seemed to suggest it.
Thanks. I think this is a bit clearer. However, it is still unclear somewhat. I have to think it over.
Sure. No problem.ftr said:Thank you all for your help. I need to understand before I reply.
@Chestermiller
Yes indeed, you are very close to understanding my problem. Can you show that the two expressions you gave are equivalent, if it is not too much of a burden. Thanks in advance.
V represents the relative velocity between two frames of reference in special relativity. It is a measure of how fast one frame is moving with respect to the other.
V appears in the transformation equations in SR because it is a crucial factor in calculating the differences in measurements between two frames of reference that are moving at different velocities.
The value of v directly affects the values of time, length, and momentum in the transformation equations in SR. As v increases, these values change according to the principles of special relativity.
No, v cannot be greater than the speed of light in the transformation equations in SR. According to the laws of special relativity, the speed of light is the maximum speed that any object can travel, and therefore v cannot exceed this value.
V in the transformation equations in SR is different from the concept of velocity in classical mechanics. In classical mechanics, velocity is an absolute quantity, while in special relativity, it is a relative quantity that depends on the frame of reference. Additionally, the laws of special relativity apply to high speeds and account for the effects of time dilation and length contraction, which are not considered in classical mechanics.