Lecture 18 General relativity I: Is mass and mass the same thing

1
Lecture 18General relativity I Is mass and
mass the same thing ?
2
Special Relativity

• All inertial frames of reference are equivalent
• The speed of light is absolute (invariant)
• Maxwells equations are invariant under Lorentz
  transformation
• Newtons laws, which are based on absolute space
  and time, need to be modified

3
Some open problems

• How to treat accelerations ?
• How to deal with gravity ?
• Newtons gravity acts instantaneously, i.e. it is
  inconsistent with special relativitys conclusion
  that information cannot be communicated faster
  than the speed of light.
• Distance is relative, so which distance to use in
  computing the gravitational force ?

4
Non-inertial reference frame

• Non-inertial frames ? fictitious forces
• centrifugal force
• Coriolis force

5
Why is the Space Shuttle orbiting?

• The space Shuttle is continuously falling
  towards the Earth

6
Is there no gravity in space ?
No, there is gravity (actu- ally Earths gravity
at the orbit of the Shuttle is still 80-90 of
its strength on the ground

• So why do astronauts appear to be weightless ?

7
What effect does mass have?

• Gravity tendency of massive bodies to attract
  each other
• Inertia resistance of a body against changes of
  its current state of motion

8
Is gravity and inertia the same thing ?

• No. They are completely different physical
  concepts.
• There is no a priori reason, why they should be
  identical. In fact, for the electromagnetic force
  (Coulomb force), the source (the charge Q) and
  inertia (m) are indeed different.
• But for gravity they appear to be identical
• ? Equivalence Principle

9
Eötvös experiment
Coriolis
Gravity
10
Result of the Eötvös experiment

• Gravitational and inertial mass are identical to
  one part in a billion
• modern experiments identical to one part in a
  hundred billion

11
What effect does mass have?

• Source of gravity
• Inertia

12
Principle of Equivalence
13
Weak equivalence principle

• The laws of mechanics are precisely
• the same in all inertial and freely
• falling frames. In particular, gravity is
• completely indistinguishable from
• any other acceleration.

14
Consequences of the equivalenceprinciple mass
bends light
Observer in freely falling reference frame
15
Consequences of the equivalenceprinciple mass
bends light
Outside Observer
16
Examples for light bending