If you multiply the matrix by the 4-vector (t', x', y', z') it should result in the 4-vector (t, x, y, z) as set out on the left side of the arrow. I think the matrix is wrong, though. The numerator of the second term in the top row should be v/c^2 and the numerator of the first term in the second row should be v.Thrice said:It's a really easy question, I know, but I must be doing something stupid. Can someone please spell out how to get the right hand side matrix form out of the individual equations?
http://img234.imageshack.us/img234/8497/lorentz25wv.jpg
See I thought that as well, but they have the inverse of that matrix in the book too & it matches up with the one on http://en.wikipedia.org/wiki/Lorent...rmation_for_frames_in_standard_configuration". Apparently it's gotten by switching V for (-V). Does it work out if you use the 4 vector (ct', x', y', z') & (ct, x, y, z)?Andrew Mason said:If you multiply the matrix by the 4-vector (t', x', y', z') it should result in the 4-vector (t, x, y, z) as set out on the left side of the arrow. I think the matrix is wrong, though. The numerator of the second term in the top row should be v/c^2 and the numerator of the first term in the second row should be v.
AM
Thrice said:K got it. Why does that work? Something to do with the symmetry of the metric...
The Lorentz transforms, also known as the Lorentz transformations, are a set of equations that describe the relationship between space and time in Einstein's theory of special relativity. They are used to calculate how measurements of space and time change for observers in different frames of reference.
The Lorentz transforms were first discovered by the Dutch physicist Hendrik Lorentz in the late 19th century. However, they were later incorporated into Albert Einstein's theory of special relativity, which revolutionized our understanding of space and time.
The Lorentz transforms are significant because they helped to explain the results of a famous experiment by Michelson and Morley, which showed that the speed of light is constant in all inertial frames of reference. This led to the development of special relativity and laid the foundation for our modern understanding of space and time.
The Lorentz transforms consist of a set of equations that relate measurements of space and time in one frame of reference to those in another frame of reference that is moving at a constant velocity relative to the first. By applying these equations, we can calculate how measurements such as length and time intervals change between frames of reference.
The Lorentz transforms are useful in situations where objects are moving at high speeds, close to the speed of light. They are also used in many areas of physics, including particle physics, astrophysics, and cosmology, to accurately describe the behavior of objects and phenomena in the universe.