When high-energy cosmic rays hit Earth’s upper atmosphere, new particles including muons are created. These particles are often unstable and decay in a known short amount time. The decay of muons travelling through our atmosphere was used in 1962 to confirm the relativistic concepts of time dilation and length contraction. “Detectors are set up high […]
Category Archives: Lorentz Transformations
Time Dilation and Length Contraction
Both space and time require modification with Lorentz’s gamma factor in order to keep the speed of light invariant. Space modification is known as length contraction, and time modification is known as time dilation. Instead of being intrinsic physical properties of a moving object, time dilation and length contraction are symmetric properties, being applicable to […]
Spacetime Intervals
We have already discussed the invariability of the speed of light. Some other concepts in relativity are invariant, or unchanged by relative motion or position, including the charge of an electron, proper length and time, and rest mass. Spacetime intervals, defined as for 1D motion in a reference frame , is also an invariant quantity. […]
Velocity Addition
Because of the postulates of relativity, it is impossible to reach the speed of light, so the Galilean velocity equations and cannot be used on light. Note that velocity values are vectors, and that the speed , is always with respect to where is in relative motion to . The Galilean equations are modified as […]
Lorentz Transformations
20th century Dutch physicist Hendrik Lorentz came up with an arbitrary factor, called gamma (), to make for different IRFs, thereby keeping classical physics equations valid across spacetime. Note that time doesn’t have to be equal in 2 reference frames. It will be denoted in reference frames and as and . The gamma factor is […]
Clock Synchronization
The reason we need to synchronize clocks is that in physics, we need clocks that keep accurate and precise time. We might want to make measurements of time intervals in two reference frames in relative motion with each other, and we generally want coordinate transformation equations to be consistent with the two postulates of relativity. […]
Postulates of Relativity
Einstein changed the assumptions of absolute space and time with his 2 postulates of relativity. Postulate 1: Laws of physics are same in all IRFs. This means that there is no preferred frame of reference, no absolute or unique position in the universe, and no experiment that can show that an observer is at rest […]