1 / 24

The Lorentz Transformation

The Lorentz Transformation. Section 4. An event has coordinates. x ,y,z,t in the K system x ’,y’,z’,t ’ in the K’ system What is the formula that transforms from one set to the other?. Transformation must leave interval s unchanged. s = interval between world points (events) in 4 space.

jelani-simmons
Télécharger la présentation

The Lorentz Transformation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Lorentz Transformation Section 4

  2. An event has coordinates • x,y,z,t in the K system • x’,y’,z’,t’ in the K’ system What is the formula that transforms from one set to the other?

  3. Transformation must leave interval s unchanged. • s = interval between world points (events) in 4 space. • Such transformation is a rotation in 4-D x,y,z,ct coordinate system. • Every rotation can be resolved into six rotations in planes xy, yz, zx, tx, ty, tz.

  4. Consider tx plane • y,z, coordinates don’t change. • Transform must leave (ct)2 – x2 unchanged • That is the square of interval from origin in tx plane to point (ct,x) ct x

  5. Lorentz transformation • To obtain the inverse formula, V-> -V and swap primes.

  6. In limit c -> infinity, we recover the Galileo transform with absolute time.

  7. For V>c, coordinates and time are imaginary. • Denominators go to zero if V = c.

  8. Small velocities, V<<c

  9. Lorentz Contraction If rod is moving, it will appear shorter to an observer at rest.

More Related