Chemistry, Mathematics, Physics

Special Relativity – Part 1

[latexpage]

Luminiferous ether

Mid-ninteenth century: mainstream science believed light particles were (mechanical) waves traveling through a medium called the luminiferous ether

Mid-ninteenth century definition of a wave:

  • Waves = a disturbance traveling through a medium 
    • Note: this is essentially what our current definition of a mechanical wave is today
    • Medium = the material or substance through which a wave is traveling
  • Example 1: a dewdrop falling into a pond (Figure 1)
    water dropplet
    Figure 1
    • Here, the medium is the water in the pond
    • The initial disburbance is the dewdrop landing in the water
      • The water particles initially disturbed by the dewdrop further disturbs the position of surrounding water particles
      • This disturbance is further propagated throughout the medium (i.e., the pond)
  • Example 2: sound waves from clapping
    • Medium = air
    • Initial disturbance = compression of air molecules
      • Compressed air molecules causes them to collide with one another and generate sound waves
  • Note: both of these examples are mechanical waves

We knew from research such as Young’s double-slit experiment (1801) that light has wave-like properties

  • Specifically, it showed one of the hallmark signs of wave behavior: interference
  • Some unaswered questions of the mid-19th century
    • How could they define light in terms of its wave-like properties?
      • Note: they were trying to define light in terms of mehcanical waves (they didn’t know about electromagntic waves back then)
    • They theorized that light (e.g., light traveling from the Earth to the Sun) could be explained as a disturbance propagating through a medium
      • People called this medium the luminiferous ether
    • Big question: does the luminferous ether exist?

Luminiferous ether = medium through which light (supposedly) propogates

  • One major goal of mainstream science back then was to detect/validate the existence of this medium
  •  Note: if there is a luminiferous ether, the Earth must be traveling fast relative to it
    • Not only is the Earth rotating on its own axis, but is also treaveling along an elliptical orbit around the Sun at $\approx 30 \mathrm{km/s}$
    • Moreover, the Sun is estimated to orbit around the center of the galaxy at $\approx 200 \mathrm{km/s}$
    • As far as our galaxy is concerned, we don’t really know what it’s doing, we just know its moving
      • Most scientists theorize our galaxy is rotating around a black hole
    • Take-home-message: if the luminiferous ether exists, Earth’s position should be constantly changing relative to it
      • Reasoning behing this:
        • The odds of us being stationary relative to such a medium are essentially zero
        • We should either be moving relative to the ether or the ether should be moving relative to us
          • Thus, we should be able to detect some sort of “ether wind” or the “current” associated with the luminiferous ether
  • Aside: waves propagate faster in the direction which current is moving
    • Example: a dew drop falling in a stream with a current flowing (Figure 2)
      water dropplet 2
      Figure 2
      • Here, the medium is the water in the stream and the initial disturbance is the dewdrop falling into the stream
      • Propagation of medium distortion (i.e., the waves/ripples in the stream) will occur more quickly in the direction of current (i.e., movment to the left)

 

The Michelson-Morely Experiment:

Experiment Background

Assuming there did exist a luminiferous ether, let $\overrightarrow{s}$ be the velocity of the its ether wind

  • From our dicussion on wave propogation speed and currents, light that is propagated in the same direction as $\overrightarrow{s}$ show travel at a faster velocity than light propagated in the $-\overrightarrow{s}$ direction
  • For a while, no one could figure out how to test this because the tools/technology did not yet exist that could detect velocities near the speed of light (thus, any differences they would have expected to find were inmeasureable)

Eventually Michelson and Morely designed an experiment that was able to work around this issue using wave interference

  • Recall: interference is a hallmark behavior of waves
  • Instead of attempting to measure the speed of light emitted in different directions, they split light into two different directions, recombined them, and observed the interference patterns
    • They reasoned, that if light emitted in different directions traveled at different speeds, then different interference patterns would result
    • However, this isn’t what happened!!
  • No matter how they oriented the apparatus (no matter the time of day and/or year), they always observed the same interference pattern
    • Conclusion: the luminiferous ether doesn’t seem to affect light waves ⇒ breakdown of the idea behind a luminiferous ether and/or an “absolute” inertial frame of reference through which light traveles
  • Titled one of “the most famous failed experiments”
    • Note: there were other experiments besides this one at the time that were also causing people to question the existence of a luminiferous ether

As it turns out, no matter the reference frame, light always travels at a constant speed!

 

Sources

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