Einstein Relatively Easy

User Rating: 5 / 5

Star ActiveStar ActiveStar ActiveStar ActiveStar Active
 
fShare
0
Pin It

 

Note: the presentation of the Lorentz transformation is done by Einstein in chapter 11 of his book Relativity

Remember that since the beginning, we are trying to find the relationships between the coordinates of an event in two inertial frames R and R', with R' moving with a velocity v with respect to R.

After having spent time giving some insight into the strange nature of the spacetime and of his contruitive effects, it is now time to give a more precise algebraic formulation of how coordinates change for different inertial observers.

This set of equations are called the Lorentz transformations, named after the Dutch physicist Hendrik Lorentz (Nobel Prize 1902)

Given the assumptions that R and R' are in standard configuration, i.e:

  • - An observer in frame of reference R defines events with coordinates t, x, y, z
  • - Another frame R' moves with velocity v relative to R, with an observer in this moving frame R' defining events using coordinates t', x', y', z'
  • - The coordinate axes in each frame of reference are parallel
  • - The relative motion is along the coincident xx' axes
  • - At time t = t' =0, the origins of both coordinate systems are the same

 

  If an observer in R records an event t, x, y, , then an observer in R' records the same event with coordinates t', x', y', z' defined as below:

 

 

With y = Lorentz factor having been already defined in the previous article Constant Speed of light - Introduction to Time Dilation and Lorentz factor

 According to principle of relativity, there is no privileged frame of reference, so that the transformations from R to R' must take exactly the same form as the transformation from R' to R.

The only difference is R' moves with velocity -v relative to R (same magnitude but is oppositely directed). So that if an observer in R' records an event in t', x', y',z' then an observer in R records the same event with coordinates

 

 

 

The reciprocal transformations from each referential relative to the other coud be visualised in a synthetic manner as follow:

 

source wikipedia Maschen

 

Remark 1: Compared to the classical Galilean physics with absolute time, we begin to understand what Minkowski meant by the union of the two concepts.

Galiean transformations

 

Remark 2: When v<<c, i.e when the relativistic effects fade away, we can verify that the Galilean transformation can be derived from the Lorentz transormations.

 

People in this conversation

  • Guest - chris

    This is quite educational post,you have researched a lot before writing the article.I appreciate your efforts in making this post.I will come back to read more.

    Comment last edited on about 1 year ago by Cyril
    0 Like Short URL:

Leave your comments

Post comment as a guest

0
Your comments are subjected to administrator's moderation.

Language

Breadcrumbs

Quotes

"Five or six weeks elapsed between the conception of the idea for the special theory of relativity and the completion of the relevant publication" Einstein to Carl Seeling on March 11, 1952

"Every boy in the streets of Göttingen understands more about four-dimensional geometry than Einstein. Yet, in spite of that, Einstein did the work and not the mathematicians."
David Hilbert

RSS Feed

feed-imageRSS

Who is online

We have 47 guests and no members online