Null result of the michelson morley experiment

In summary: T2 - T1 becomes 0. This means that there is no time difference between the perpendicular and parallel paths, resulting in a null effect in the Michelson Morley experiment.
  • #1
Benzoate
422
0

Homework Statement



Show that the null effect of the michelson morley experiment can be accounted for if the interferometer arm parallel to motion is shortened by a factor of
(1-v^2/c^2)^.5

Homework Equations



V(earth)=29.8 km/s , fringe in MM experiment is .4 ; gamma =sqrt(1-v^2/c^2)

The Attempt at a Solution



In the MM original experiment , .4 fringe/(29.8 km/s)^2 = .00045043

I was supposed to show that the fringe effect from the original experiment is still the same even if I used lorentz transformations right?>

.4 fringe/(v(earth) * gamma)=.4 fringe/((29.5)*^2*sqrt(1-(29.5)^2/c^2))= .00045043

My calculator approximates sqrt(1-v^2/c^2 ) to 1
 
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  • #2
You can use a binomial approximation to calculate sqrt(1-v^2/c^2)=1-1/2*v^2/c^2+...
 
  • #3
genneth said:
You can use a binomial approximation to calculate sqrt(1-v^2/c^2)=1-1/2*v^2/c^2+...

you kinda didn't answer my first question

Original question:
I was supposed to show that the fringe effect from the original experiment is still the same even if I used lorentz transformations right?>

Other than that, Is everything else I solved correct
 
  • #4
The total time taken light was expected to take, in the path perpendicular to Earth's motion was:

[tex]T_1 = \frac{2L}{\sqrt{1-v^2/c^2}}[/tex]

The total time expected parallel to Earth's motion was:

[tex]T_2 = \frac{2Lc}{c^2-v^2}[/tex]

So if length contraction happens during the parallel path, what happens T2... and hence what does T2 - T1 become?
 
  • #5
learningphysics said:
The total time taken light was expected to take, in the path perpendicular to Earth's motion was:

[tex]T_1 = \frac{2L}{\sqrt{1-v^2/c^2}}[/tex]

The total time expected parallel to Earth's motion was:

[tex]T_2 = \frac{2Lc}{c^2-v^2}[/tex]

So if length contraction happens during the parallel path, what happens T2... and hence what does T2 - T1 become?

if length is contracted during parrallel path, would L = L(0)/gamma ?
 
  • #6
Yes, the length along the parallel path would be L/gamma. So substitue L/gamma instead of L in the T2 formula...
 

What is the Michelson Morley experiment?

The Michelson Morley experiment was a scientific experiment conducted in the late 19th century to measure the relative motion between the Earth and the hypothetical "ether" that was thought to permeate all of space.

What was the purpose of the Michelson Morley experiment?

The purpose of the Michelson Morley experiment was to test the prevailing theory of the "ether" and its effects on the speed of light. This was important because the speed of light was thought to be constant and the existence of the ether would explain the observed discrepancies in the speed of light in different directions.

What was the null result of the Michelson Morley experiment?

The null result of the Michelson Morley experiment was that the speed of light was found to be constant in all directions, regardless of the Earth's motion through the ether. This contradicted the prevailing theory of the ether and led to the development of Albert Einstein's theory of special relativity.

Why is the null result of the Michelson Morley experiment significant?

The null result of the Michelson Morley experiment was significant because it challenged the prevailing theories of the time and ultimately led to the development of a new understanding of the nature of space and time. It also paved the way for further experiments and advancements in physics, including the theory of relativity.

What impact did the null result of the Michelson Morley experiment have on science?

The null result of the Michelson Morley experiment had a significant impact on science by challenging long-held beliefs and leading to the development of new theories and understandings. It also helped to lay the foundation for modern physics and our understanding of the fundamental laws of the universe.

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