Special relativity

Inertial reference frame

  • Motion of an object is typically described relative to a reference frame
  • If the reference frame does not accelerate, and is therefore stopped or moving at a constant speed, it is called an inertial reference
  • In this reference frame, Newton’s Law of Inertia holds – things will keep on moving at a constant velocity unless acted upon by a net external force
  • Projectile motion is example (e.g. displacement from the origin)

Newtonian relativity

Postulates:

  • All uniform motion is relative and there is no absolute and well defined state of rest
  • i.e there is no absolute standard to which everything moves; an absolute inertial reference frame
  • All inertia reference frames share a universal time

Maxwell’s equations

  • Derived equations that describe the behaviour of light
  • But require speed of light to be constant

Scientists at the time believed that c was only constant relative to a hypothesised medium called the aether, which was theorised to be the absolute unique frame of reference which light needs to travel in.

Experiments failed to detect the aether, and so c must be constant. See book for a bit more detail.

Special Theory of Relativity

Postulates:

  • The principle of relativity. The laws of physics (Newton’s laws) are the same for objects moving in inertial frames of reference
  • The principle of the speed of light. The speed of light is the same of all observers, regardless of their motion relative to the source of light.

Time dilation

time dilation equation

Where t = time measured by a stationary observer on Earth

t0 = time measured by an observer at rest relative to the object travelling at v (in the same inertial reference frame)

  • The faster the object goes, the smaller¬†t0 gets, relative to t
  • The faster the object goes, t would increase or dilate relative to t0
  • Both observers would observe that the other’s time has slowed down (or theirs has sped up)

Proper time is the time measured by an observer in their own reference frame.

Length contraction

length contraction equation

Where L is the length of an object measured by a stationary observer on Earth

L0 is the length measured by an observer travelling at rest relative to the object

  • As v increases, L decreases relative to L0
  • The stationary observer only observes contraction in the direction on motion. All other dimensions stay the same.
  • Again, both observers would see length contraction on each other.

Simultaneity

  • Due to the fact that time is different to two different observers, the order of events may be different as well
  • What occurs simultaneously to one person, may not be simultaneous to another person moving relative to him

 Relativistic Mass

  • As an object approaches the speed of light, it gains mass
  • This is due to mass-energy equivalence
  • Some of the energy used to accelerate the object converts to mass
  • Hence, it would require infinite energy to accelerate an object to the speed of light

 

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