Special relativity
This presentation is the property of its rightful owner.
Sponsored Links
1 / 19

Special Relativity PowerPoint PPT Presentation


  • 95 Views
  • Uploaded on
  • Presentation posted in: General

The Failure of Galilean Transformations The Lorentz Transformation Time and Space in Special Relativity Relativistic Momentum and Energy. Special Relativity. The Galilean Transformations.

Download Presentation

Special Relativity

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Special relativity

  • The Failure of Galilean Transformations

  • The Lorentz Transformation

  • Time and Space in Special Relativity

  • Relativistic Momentum and Energy

Special Relativity


The galilean transformations

The Galilean Transformations

Consider the primed coordinate system moving along the x-axis at speed u. Consider events where clocks record the time at the location of the event.

Galilean Transformation between coordinate systems

x’=x-ut

y’=y

z’=z

t’=t

vx’=vx-u

vy’=vy

vz’=vz


The ether and the michelson morley experiment

“The Ether” and the Michelson-Morley Experiment

  • What about light? Waves must be waving something…

  • The Ether…An absolute reference frame?

  • Should be able to detect and measure Earth’s motion through the ether by detecting an “ether wind” that should modify the speed of light along and transverse to the “wind” direction.


The ether and the michelson morley experiment1

“The Ether” and the Michelson-Morley Experiment

  • Michelson-Morley detected no change in speed of light…

Galilean Transformations not correct for light !!!!


Einstein s postulates of special relativity

Einstein’s Postulates of Special Relativity

A reference frame in which a mass point thrown from the same point in three different (non co-planar) directions follows rectilinear paths each time it is thrown, is called an inertial frame.

– L. Lange (1885) as quoted by Max von Laue in his book (1921) Die Relativitätstheorie, p. 34, and translated by Iro).

  • The Principle of Relativity. The laws of physics are the same in all inertial reference frames.

  • The Constancy of the Speed of Light. Light moves through vacuum at a constant speed c that is independent of the motion of the light source.


The lorentz transformations

The Lorentz Transformations


The lorentz transformations1

The Lorentz Transformations

  • Constancy of speed of light can be satisfied if space-time coordinates satisfy the linear Lorentz-Transformation equations…

Lengths perpendicular toare unchanged

Coefficients determined by invoking symmetry arguments and Einstein’s postulates ….


The lorentz transformations time coordinate

The Lorentz TransformationsTime coordinate

Invoking the constancy of speed of light. Consider flash of light set off at t’=t=0 at common origins. At a later time t an observer in frame S will measure a spherical wavefront of light with radius ct, moving away from the origin and satisfying:

Similarly, at a time t’, an observer in frame S’ will measure a spherical wavefront of light with radius ct’, moving away from the origin O’ with speed c and satisfying :

Inserting equations 4.10-4.13 into 4.15 and comparing with 4.14

t’ should be the same if y-->-y or z-->-z.

Consider motion of the origin O’ of frame S’. Synchronized at t=t’=0. x-coordinate of O’ is given by x=ut in frame S, and x’=0 in frame S’.

At this point:


The lorentz transformations2

The Lorentz Transformations

Lorentz Factor

  • Reveal that

Thus the Lorentz transformations linking the space and time coordinates (x,y,z,t) and (x’,y’,z’,t’) of the same event measured from S and S’ are

When ,relativistic formulas must agree with Newtonian equations….


The lorentz transformations3

The Lorentz Transformations

Four-dimensional space-time

Space and time “mix” !!!!

for light wave x=ct,x’=ct’,x”=ct”,….

Array Representation:

Minkowski Diagram


Special relativity

Electromagnetic Wave Equation

Galilean Transformation

Lorentz Transformation


Space time interval

Space-Time Interval

(interval)2=(separation in time)2-(separation in space)2

Space-time interval is invariant

Time-like interval

Space-like interval

Light-Like Interval

Causality


Space time diagrams

Space-Time Diagrams


Relativity of simultaneity

Relativity of Simultaneity

Observer in S measures two flash-bulbs going off at same time t but at different locations x1and x2. Then an observer in S’ would measure the time interval between the two flashes as:

Events that occur in simultaneously in one inertial frame do NOT occur simultaneously in all other inertial reference frames


Proper time and time dilation

Proper Time And Time Dilation


Proper length and length contraction

Proper Length and Length Contraction

  • Measure positions at endpoints at same time in frame S’ and in frame S, L’=x2’-x1’


Example of time dilation and length contraction cosmic ray muons

Example of Time Dilation and Length Contraction: Cosmic Ray Muons


  • Login