Cosmic Adventure Episode 2.05 Michelson's River Analogy

ABCC Australia 2015 new-physics.com

MICHELSONS RIVER ANALOGYCosmic Adventure: Episode 2.05


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.


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


Simplified Diagram

The splitter

Mirror A

Light source

Analyser or viewer

Mirror B

The splitter

Mirror A

Light source

Analyser or viewer

Mirror B


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


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


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


Splitter

The beams are reflected by the mirrors back to the splitter.

Beam 1

Beam 2


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


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.


Michelsons Idea

Before he started the project, Michelson had a clever idea for detecting the aether wind.


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.


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


SWIMMER A


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 =


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 = / +


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


SWIMMER B


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


Straight across river [wish] River flow

speedRiver flow +Swimmer speed

Swimmer miss landing spot

Landing spot


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


Straight across river River flow speed River flow +Swimmer speed Resultant speed

& direction


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


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


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


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

Science

Cosmic Adventure Episode 2.05 Michelson's River Analogy