Physics - Special Relativity

The postulates of Special Relativiy

• (1) The laws of physics will always apply for all inertial observers

• (2) All inertial observers will measure the same value of the speed of light in a vacuum, iresspective of their own relative velocities to the source.

Simultaneity

• The concept that two events that are simultaneous in one frame of reference are often not simultaneous in a second frame of reference moving w/ respect to the first; simultaneity is not an absolute concept.

Time Dilation

• The duration of an event as measured by a moving observer relative to the event.

• This is often found to be greater than the proper time.

Proper Time

• The duration of event as measured by an observer stationary relative to the timed event.

Twins Paradox

• The Twin on the ship must accelerate (slow down, turn around, accelerate again), they leave the inertial FoR and their view isn’t valid.

  • Time passed more slowly for the twin on the ship / time passed more quickly for the twin on earth

• Result: Time dilation is only valid for an observer in an inertial FoR

Proper Length

• The length that is measured from the Frame of Reference where the object is at rest or having the space time coordinates.

• The proper length is always the max length of the object.

Length contraction

• The length of an object measured by an observer with relative motion to the frame of reference.

• This is always a shorter length measured in the direction of motion.

Space time interval

• The space time interval is the representation of motion using a coordinate system spanning both space and time.

• This is four dimensional coordinates, with three dimensions representing space and one representing time

• The space time is invariant: every observer regardless of their motion will measure the same value for the combined space and time separation between two events.

Rest Mass (proper mass)

• The measured mass of an object in the frame of reference where the object is at rest.

• The rest mass is always the lowest possible mass of the object.

Michelson-Morely Experiment

• Goal of the experiment was to measure the luminiferous ether and establish a universal frame of reference

• Design: sending light along two paths: parallel and perpendicular to the earth’s movement to see if a path difference exists.

• Result: Path difference didn’t exist, determining the arm length must have contracted.

  • proved 2nd postulate

  • disproved ether

Muon Decay Experiment

• Muons have a half life of 3.1 × 10⁶ at rest. Muons that travel down a mountain at velocity of 0.98c should have experienced about 10 half-lives

• Hypothesis: the number of muons that reached the bottom of the mountain should have been very few.

• Experimental Evidence: shows that a lot of muons survive to reach the surface

• Explanation of results:

  • Earth’s FoR: they experience time dilation, and so the half-life takes more time and they live longer

  • Muon FoR: the Earth’s distance is length contracted, so they have less distance to travel

  • Proved Length Contraction and Time Dilation

Hafele-Keating Experiment

• Two clocks were sent around the World in oppositve directions in airliners

• Result: The one going with the turn of the Earth (Eastbound) were moving faster than the clocks left behind).

• The predicted results was that Eastbound clocks should lost 40ns and the westbound gain 275ns, but the actual results were 59ns and 273ns

  • Proved Time Dilation

  • Resolved the twin paradox

Gamma Ray Bursts Experiment

• Gamma Ray Bursts from a collapsed Neutron star that is rapidly rotation come to the Earth from the near and far fringes of the object as it expands and collapses at near the velocity of light.

• If the speed of light were to be dependent on the speed of the sourcem there should be a separation in the pulses, but to within 1 part in 10²⁰, no separation has been observed

• Results

  • No change in velocity of light

  • 2nd postulate

Galilean Transformations

• Equations that translate measurements made in one frame of reference to another frame of reference without taking into account the theory of relativity

Inertial Frame of reference

• A frame of reference that is not accelerating, but is at rest or moving with a constant velocity

• a frame of reference in which Newton’s law of inertia is valid, that is, a frame of reference in which an object with no unbalanced forces will remain at rest or move at a constant velocity

Pole and Barn Paradox

• ADD HERE