The search for an absolute reference frame © D Hoult 2011
The search for an absolute reference frame Looking for the “Aether”
dolphin speed relative to water = vd
dolphin speed relative to water = vd boat speed relative to water = v
dolphin speed relative to water = vd boat speed relative to water = v time for dolphin to go from O to A =
dolphin speed relative to water = vd boat speed relative to water = v time for dolphin to go from O to A = L/(vd – v)
dolphin speed relative to water = vd boat speed relative to water = v time for dolphin to go from O to A = L/(vd – v) time for dolphin to go from A to B =
dolphin speed relative to water = vd boat speed relative to water = v time for dolphin to go from O to A = L/(vd – v) time for dolphin to go from A to B = L/(vd + v)
dolphin speed relative to water = vd boat speed relative to water = v time for dolphin to go from O to A = L/(vd – v) time for dolphin to go from A to B = L/(vd + v) so, time for dolphin to go from O to B is
dolphin speed relative to water = vd boat speed relative to water = v time for dolphin to go from O to A = L/(vd – v) time for dolphin to go from A to B = L/(vd + v) so, time for dolphin to go from O to B is L/(vd – v) + L/(vd + v)
dolphin speed relative to water = vd boat speed relative to water = v which is equal to
dolphin speed relative to water = vd boat speed relative to water = v which is equal to 2L / (vd2 – v2)
L2 =
L2 = b2 – a2
L2 = b2 – a2 if time for dolphin to go from A to B = t then L2 =
L2 = b2 – a2 if time for dolphin to go from A to B = t then L2 = (vdt)2 – (vt)2
L2 = b2 – a2 if time for dolphin to go from A to B = t then L2 = (vdt)2 – (vt)2 which means that the time taken to go from O to B in this case is
L2 = b2 – a2 if time for dolphin to go from A to B = t then L2 = (vdt)2 – (vt)2 which means that the time taken to go from O to B in this case is 2 L / (vd2 – v2)1/2
2L / (vd2 – v2)
2 L / (vd2 – v2)1/2 2L / (vd2 – v2)
2 L / (vd2 – v2)1/2 these times are clearly NOT equal 2L / (vd2 – v2)
Dolphin moving parallel to the direction of v tpar = 2L / (vd2 – v2)
Dolphin moving parallel to the direction of v tpar = 2L / (vd2 – v2) Dolphin moving perpendicular to the direction of v tperp = 2 L / (vd2 – v2)1/2
Dolphin moving parallel to the direction of v tpar = 2L / (vd2 – v2) Dolphin moving perpendicular to the direction of v tperp = 2 L / (vd2 – v2)1/2 If we know the speed of the dolphins (relative to the water) and these two times are measured, we can find the speed of the boat (relative to the water)
The Michelson Morley Experiment
Beam 1 is like the dolphin moving perpendicular to the direction of v
Beam 2 is like the dolphin moving parallel to the direction of v
M and M thought that by examining the change in the interference pattern when the whole apparatus was rotated through 90°, they would be able to detect the motion of the Earth relative to the aether.
M and M thought that by examining the change in the interference pattern when the whole apparatus was rotated through 90°, they would be able to detect the motion of the Earth relative to the aether. When the apparatus was turned through 90° they found…
M and M thought that by examining the change in the interference pattern when the whole apparatus was rotated through 90°, they would be able to detect the motion of the Earth relative to the aether. When the apparatus was turned through 90° they found… no change in the interference pattern