General Relativity: The Small Print
● We need to add some important caveats to our definitions of inertial and non-
inertial frames of reference, and equivalence principles.
● The sea comes in and washes away your sand castle because the size of the
Earth is significantly large in relation to the scales over which the gravitational
forces of the Sun and the Moon decrease with increasing distance away from
them.
● The Earth's average diameter is 12,742 km, and the average Earth-Moon
distance is 384,402 km. A 1 kg rock at the Earth's sub-lunar point will be
attracted towards the Moon by the Moon's gravity by a force of 34.4 N, and vice
versa.
PAGE 18
● The tidal force on the Earth is 2.2 N, and the force on the Earth's crust is 250
mm. The force on the Earth's crust is directed away from the centre of the Earth,
and so the Earth bulges on both sides.
● The sideways force of the tides is due to the fact that the Earth's centre of gravity
orbits around the Moon every 27.3 days, and so the tides slow down the sub-
lunar rock and speed up the anti-lunar rock.
● When liquids or gases are pulled towards or away from the Moon in radial
directions, they flow across the Earth's surface, creating tidal flows. Land masses
projecting above the oceans' surfaces channel the tidal flows, creating tidal bores
racing up the rivers at speeds of up to 25 km/hour.
PAGE 19
● If the size of the Earth was reduced, the magnitude of the tidal effects would
reduce, and the sea and ocean tides would become negligible for everyday
purposes.
, ● Tidal effects that are significant in large systems may become negligible in
equivalent but smaller systems, though the definitions of 'significant' and
'negligible' will depend upon the context and circumstances.
● Loose objects falling inside a large laboratory at rest with respect to the Earth will
not have parallel accelerations and their resulting velocities will converge towards
the centre of the Earth.
PAGE 20
● The statement that forms the basis for Einstein's equivalence principle has now
to be modified to read: "If the duration of any measurements being made of the
loose objects' positions inside the laboratory is short enough, then those
systematic movements will be too small to be detected".
PAGE 21
General Relativity: The Nitty Gritty
● Einstein developed our present and still most successful theory of gravity using
these concepts.
PAGE 22
● General Relativity adds constant acceleration to the definition of natural motion,
and develops the notion of a four-dimensional Space-Time.
● Space-time is probably the one concept of General Relativity that does have
some widespread popular currency, since many people have heard that
somehow it includes time as a fourth dimension. However, everybody does have
experience of 4D objects where the fourth dimension is time. A point has
dimensions of the order of the Planck length, which is regarded as the minimum
length possible within the Universe.
● To describe a point in 4D space-time, let us imagine a 3D object with only a
single coordinate, such as a coffee pot, and a physical position adjacent to our
thermometer.
PAGE 23
● We need to add some important caveats to our definitions of inertial and non-
inertial frames of reference, and equivalence principles.
● The sea comes in and washes away your sand castle because the size of the
Earth is significantly large in relation to the scales over which the gravitational
forces of the Sun and the Moon decrease with increasing distance away from
them.
● The Earth's average diameter is 12,742 km, and the average Earth-Moon
distance is 384,402 km. A 1 kg rock at the Earth's sub-lunar point will be
attracted towards the Moon by the Moon's gravity by a force of 34.4 N, and vice
versa.
PAGE 18
● The tidal force on the Earth is 2.2 N, and the force on the Earth's crust is 250
mm. The force on the Earth's crust is directed away from the centre of the Earth,
and so the Earth bulges on both sides.
● The sideways force of the tides is due to the fact that the Earth's centre of gravity
orbits around the Moon every 27.3 days, and so the tides slow down the sub-
lunar rock and speed up the anti-lunar rock.
● When liquids or gases are pulled towards or away from the Moon in radial
directions, they flow across the Earth's surface, creating tidal flows. Land masses
projecting above the oceans' surfaces channel the tidal flows, creating tidal bores
racing up the rivers at speeds of up to 25 km/hour.
PAGE 19
● If the size of the Earth was reduced, the magnitude of the tidal effects would
reduce, and the sea and ocean tides would become negligible for everyday
purposes.
, ● Tidal effects that are significant in large systems may become negligible in
equivalent but smaller systems, though the definitions of 'significant' and
'negligible' will depend upon the context and circumstances.
● Loose objects falling inside a large laboratory at rest with respect to the Earth will
not have parallel accelerations and their resulting velocities will converge towards
the centre of the Earth.
PAGE 20
● The statement that forms the basis for Einstein's equivalence principle has now
to be modified to read: "If the duration of any measurements being made of the
loose objects' positions inside the laboratory is short enough, then those
systematic movements will be too small to be detected".
PAGE 21
General Relativity: The Nitty Gritty
● Einstein developed our present and still most successful theory of gravity using
these concepts.
PAGE 22
● General Relativity adds constant acceleration to the definition of natural motion,
and develops the notion of a four-dimensional Space-Time.
● Space-time is probably the one concept of General Relativity that does have
some widespread popular currency, since many people have heard that
somehow it includes time as a fourth dimension. However, everybody does have
experience of 4D objects where the fourth dimension is time. A point has
dimensions of the order of the Planck length, which is regarded as the minimum
length possible within the Universe.
● To describe a point in 4D space-time, let us imagine a 3D object with only a
single coordinate, such as a coffee pot, and a physical position adjacent to our
thermometer.
PAGE 23
