cosmic adventure episode 2.05 michelson's river analogy
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ABCC Australia 2015 new-physics.com
MICHELSONS RIVER ANALOGYCosmic Adventure: Episode 2.05
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ABCC Australia 2015 new-physics.com
Albert Michelson
Maxwells idea came to the attention of a brilliant naval instructor named Albert Michelson (1852-1931). With his great success and fame in accurately measuring the speed of light, he considered the detection of motion through the aether to be measurable.This is an epoch-making decision because what then followed became to be known as the most famous experimental observation that had changed the course of science.
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ABCC Australia 2015 new-physics.com
The Michelson-Morley Equipment
The splitter
Mirror A
Mirror BLight source
Analyser or viewer
In 1881 Michelson built an equipment more or less in line with Maxwells proposals. It could be rotated on a pedestal to accommodate angular compensations.
Movement of Earth
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ABCC Australia 2015 new-physics.com
Simplified Diagram
The splitter
Mirror A
Light source
Analyser or viewer
Mirror B
The splitter
Mirror A
Light source
Analyser or viewer
Mirror B
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ABCC Australia 2015 new-physics.com
The Pathways of the Light Beam
The basic idea of Michelsons experiment was to split a light beam by a semi-transparent plate into two separate beams: one laid in the direction of the earths motion, the other perpendicular to that motion.These two beams followed their separate paths and were reflected by mirrors and returned to the plates. We can see this in more details in four stages.
The splitter
Mirror A
Light source
Analyser or viewer
Mirror B
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ABCC Australia 2015 new-physics.com
Splitter
A monochromatic beam is issued from the light source. Nothing happens because there is only one beam which moves with the earth.
Beam of monochromatic light
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ABCC Australia 2015 new-physics.com
Beam 1
Upon arriving the splitter, the single beam is being split into two and they move separately.One (Beam 1) is in line with the motion of the earth. The other (beam 2) is perpendicular to it.
Beam 2
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Splitter
The beams are reflected by the mirrors back to the splitter.
Beam 1
Beam 2
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ABCC Australia 2015 new-physics.com
Splitter
The returned beams recombine at the beam splitter. They will be collected by the telescope or observer. Their subsequent difference in path could be measured precisely using very sensitive interferometers.
Waves in phase.No fringes when motion is considered
Beam 1 Beam 2
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ABCC Australia 2015 new-physics.com
System in Motion
The foregoing is what happens when the whole system is at rest. When the system is adjusted to have the longitudinal beam in line with the motion of the earth, it becomes mobile (with the earth) and the positions of the components will change accordingly.
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ABCC Australia 2015 new-physics.com
Michelsons Idea
Before he started the project, Michelson had a clever idea for detecting the aether wind.
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ABCC Australia 2015 new-physics.com
Aether Wind
The earth is passing the aether at +30 km per second. So the aether wind created is -30 km per second in the opposite direction.
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ABCC Australia 2015 new-physics.com
Two Swimmers
The aether wind is like the flow of a river with speed . The split beams are like two swimmer and both can swim with speed . is trying to swim right across the river while is heading upstream.
B
A
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ABCC Australia 2015 new-physics.com
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ABCC Australia 2015 new-physics.com
SWIMMER A
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ABCC Australia 2015 new-physics.com
Swimmer A
For swimmer . He first swims upstream and his velocity will be his swimming speed minus that of the river, that is:
Upstream Speed:
Upstream Time
1 =
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ABCC Australia 2015 new-physics.com
Swimmer A
But when he returns, he is aided by the river and ended up in gaining speed at the same time, that is:
Downstream Speed:
+
Downstream Time:
1 = / +
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ABCC Australia 2015 new-physics.com
Swimmer A
The result is the same as if he is swimming all by his own speed all the way.
Total Time = Upstream time + Downstream time
1 + 1 =
+
+
= + +
+
=2
2 2
=2
1 2/2
2 1 2/2
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ABCC Australia 2015 new-physics.com
SWIMMER B
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ABCC Australia 2015 new-physics.com
Swimmer B
For swimmer B, the situation is a bit more complicated.If swimmer B wishes to go straight across, he will be brought down by the river and miss the right spot.
B
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ABCC Australia 2015 new-physics.com
Straight across river [wish] River flow
speedRiver flow +Swimmer speed
Swimmer miss landing spot
Landing spot
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ABCC Australia 2015 new-physics.com
Swimming Across River
To succeed in going across to the right spot, swimmer A must actually swim at an angle upstream.If he chooses the correct angle, the flow will redirect him downstream and his resultant movement will be that directly across the river.
Upstream
Flow
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ABCC Australia 2015 new-physics.com
Straight across river River flow speed River flow +Swimmer speed Resultant speed
& direction
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ABCC Australia 2015 new-physics.com
If is the width of the river, then, by the simple geometry of Pythagoras theorem:
2 = 222 222
= 22 2 2
22 =2
2 2
2 =
2 2
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ABCC Australia 2015 new-physics.com
It happens to the return trip as well:
2 =
2 2
So the total trip becomes twice 2:
22 =2
2 2
=2
1 2/2
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ABCC Australia 2015 new-physics.com
Conclusion
Thus Michelsons conclusion was that:For swimmer , the time is:
1 + 1 =2
1 2/2
For swimmer , the time is:
1 =2
1 2/2
2 1 2/2
2 1 2/2
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ABCC Australia 2015 new-physics.com
THE MICHELSON-MORLEY EXPERIMENTTo be continued in Episode 2.06
Let us see how the aether wind concept applies to the actual situation with the instruments in place.
Michelsons river analogyAlbert MichelsonThe Michelson-Morley EquipmentSimplified DiagramThe Pathways of the Light BeamSystem in MotionMichelsons IdeaAether WindTwo SwimmersSlide Number 14Swimmer ASwimmer ASwimmer ASwimmer ASwimmer BSwimmer BSlide Number 21Swimming Across RiverSlide Number 23Slide Number 24Slide Number 25ConclusionThe Michelson-morley Experiment
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