We have seen that space and time are merged into the spacetime in Special Relativity (SR). Morever, in a similar way, we have also deduced that momentum and energy are merged into an analogue concept: the momenergy. Mathematically, it … Continue reading
Suppose we get a beam made of massive particles. The rest mass (the names invariant mass or proper mass are also popular) is . The particle travels a distance L in its inertial frame. The particle has an energy E … Continue reading
We are going to develop the mathematical framework of vectors in (Minkowski) spacetime. Vectors are familiar oriented lines in 3d calculus courses. However, mathematically are a more general abstract entity: you can add, substract and multiply vectors by some number. … Continue reading
“(…)The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to … Continue reading
During the 19th century, the electromagnetic theory of Maxwell assumed that electromagnetic waves travelled in a medium called ether. The Michelson-Morley experiment was an experiment devoted to detect the ether. We can think about the electromagnetic waves like an analogue … Continue reading
Imagine the S’-frame moves at constant velocity (see the frames above this line): relative to the S-frame. In the S’-frame an object moves with acceleration QUESTION: What is the acceleration in the S-frame? Of course it … Continue reading
In our daily experience, we live in a “non-relativistic” world with a very high degree of accuracy. Thus, if you see a train departing from you ( you are at rest relative to it) with speed (in the positive direction … Continue reading
Other striking consequence of Lorentz transformations and then, of the special theory of relativity arises when explore the concept of simultaneity. Accordingly to the postulates of relativity, and the structure of Lorentz transformations we can understand the following statement: … Continue reading
Once we introduce the postulates of special relativity and we have deduced the generalization of galilean transformations for electromagnetism and mechanics, the Lorentz transformation. We can deduce some interesting results. Suppose we have two events and , whose coordinates of … Continue reading
Suppose two events happening in the S’-frame at the same point at different times. and . What is the temporal separation in the S-frame? According to Lorentz transformations, it is: (1) or equivalently (2) i.e. Of course, in … Continue reading