# An equation for special relativity?

While surfing the internet, I came across a statement that this is the equation for special relativity:

Line 1: x = a + b
Line 2: x = a + b (c2/c2) with c = speed of light
Line 3: x = a + (y/c2) if y = b(c2)

Is this really the one? If not, is it relevant at all?

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Matterwave
Gold Member
I have no idea what those equations are, I have never seen them before. Also, they seem to all be the same since the c's will cancel from top to bottom and you'll just get x=a+b for all 3 "lines".

pervect
Staff Emeritus
While surfing the internet, I came across a statement that this is the equation for special relativity:

Line 1: x = a + b
Line 2: x = a + b (c2/c2) with c = speed of light
Line 3: x = a + (y/c2) if y = b(c2)

Is this really the one? If not, is it relevant at all?
This seems to be some garbled version of the Lorentz transform, but it's not coherent enough for me to be to be sure, as there is no explanation of what the equations mean. For more details on the Lorentz transform, see for instance the wiki article at http://en.wikipedia.org/w/index.php?title=Lorentz_transformation&oldid=628048814

The Lorentz transform provides a transformation between the coordinates in two different inertial frames, moving relative to each other with velocity v. Because every event in space-time has one and only one set of coordinates, there is a 1:1 mapping between events and their coordinates. This implies there is also a 1:1 mapping between the coordinates between any two inertial frames, including the particular case we are interested in where the two inertial frames are in relative motion. The Lorentz transform provides this 1:1 mapping explicitly. Letting the coordinates in the first inertial frame (presumed stationary) be (t, x,y,z), and the coordinates in the second inertial frame (assumed to be moving with velocity v relative to the first inertial frame) be (t', x' y', z'), we can write the Lorentz transform as:

##t' = \gamma \left(t - vx/c^2\right) \quad x' = \gamma \left(x - vt \right) \quad y' = y \quad z'=z##

Here v is the velocity between frames, and ##\gamma = 1 / \sqrt{1 - v^2/c^2}##

Last edited:
ghwellsjr