Relativity and Michelson-Morley experiment

[relativemuon]

Hello, I have two physics problems I'm having difficulty with. Can someone help me?
1) A shift of one fringe in the Michelson-Morley experiment would result from a difference of one wavelength or a change of one period of vibration in the round-trip travel of the light when the interferometer is rotated by 90°. What speed would Michelson have computed for Earth's motion through the ether had the experiment seen a shift of one fringe?
2) Consider two inertial reference frames. When an observer in each frame measures the following quantities, which measurements made by the two observers must yield the same results? (Select all that apply.)
the distance between two events
the value of the mass of a proton
the speed of light
the time interval between two events
Newton's first law
the order of the elements in the periodic table
the value of the electron charge

Thank you for your help!

 

[HallsofIvy]

This question looks to me like just giving definitions or quoting from a textbook. What do you KNOW about this and what have you done on it so far?

 

[relativemuon]

For the second problem, by Einstein's first and second postulates (the laws of physics are true for all intertial frames and the speed of light is constant for all inertial frames) I've narrowed out the distance and the time interval between two events and the order of the elements in the period table because order isn't a quantity. Are these fair assumptions?

For the Michelson-Morley question, I know the fringes are caused by the two beams of light returning out of phase. But the guys were never able to dectect a significant fringe, so I'm confused as to how to calculate the Earth's motion through the ether if it was there. I was able to find out that that Michelson and Morley expected a fringe of 0.4 when assuming the Earth's speed through the ether was 29.8 km/h. Is the answer just a simple porportion?

I apologize for not including my work in my original post, I am new to this forum.

 

[Doc Al]

For the second problem, by Einstein's first and second postulates (the laws of physics are true for all intertial frames and the speed of light is constant for all inertial frames) I've narrowed out the distance and the time interval between two events and the order of the elements in the period table because order isn't a quantity. Are these fair assumptions?

What I presume they are looking for is which of those listed "quantities" are frame independent. I'm not sure how you reasoned from Einstein's postulates, but you are on the right track if you eliminated those three quantities as being frame dependent. (By the way, "time order" is as much a "quantity" as is Newton's first law or the order of the elements. )

For the Michelson-Morley question, I know the fringes are caused by the two beams of light returning out of phase. But the guys were never able to dectect a significant fringe, so I'm confused as to how to calculate the Earth's motion through the ether if it was there. I was able to find out that that Michelson and Morley expected a fringe of 0.4 when assuming the Earth's speed through the ether was 29.8 km/h. Is the answer just a simple porportion?

The expected fringe shift is due to the change in phase difference (between the arms of the interferometer) when the set up is rotated 90 degrees. It depends on the expected speed of the Earth through the ether, but it is not a simple proportion. Look up the details of the M-M experiment.

 

[Chronos]

The second question is a test of how well you understand the axioms [premises/assumptions] Einstein used in formulating the theory of relativity. To rephrase what Doc said, what things are 'relative' according to relativity and what are not.

 

[relativemuon]

Update

Alright I figured out the Michelson-Morley experiment question. The equation they used to calculate the fringes was delta N = (2L/lamda)(v^2/c^2), where 2L is the distance each light beam travels, lamda is the wavelength of sodium light source they used was 590 nm, c is the speed of light, and v is the Earth's speed relative to the ether. This means that the fringes were porportional to the Earth's speed relative to the ether SQUARED (v^2). So the answer wasn't exactly a direct porportion(delta N = v); ithe fringes were porportion to Earth's relative speed sqaured (delta N = v^2).

Now as for invariants in the inertial frames question, can you clarify what you mean by "time order" of the elements in the periodic table? Mass, time, and length can change in intertial frames moving relative to another. I googled the elementary charge, and I found that electric charge q is a scalar that is invariant and won't change for different observers. So all that's left to consider is the order of the elements in the periodic table. I don't even see this as a quantity, perhaps you can clarify what you meant in your previous post.

Thank you for help!

 

[Doc Al]

This means that the fringes were porportional to the Earth's speed relative to the ether SQUARED (v^2). So the answer wasn't exactly a direct porportion(delta N = v); ithe fringes were porportion to Earth's relative speed sqaured (delta N = v^2).

Right! $\Delta N \propto v^2$

Now as for invariants in the inertial frames question, can you clarify what you mean by "time order" of the elements in the periodic table?

The question is not "time order" of the elements, just order of the elements. What determines the order of the elements in the periodic table? Is that frame dependent?

The time order (sequence) of two events can certainly be frame dependent, depending upon the relationship of the events. Two unconnected events can happen in reverse order to different observers. Of course, if they are causally connected the order will be invariant.

Mass, time, and length can change in intertial frames moving relative to another.

Whether mass is an invariant depends on how you define it. Most treatments of SR today take mass as an invariant, but some find it useful to use "mass" to mean the so-called "relativistic mass", which does depend on the frame doing the measuring.

I googled the elementary charge, and I found that electric charge q is a scalar that is invariant and won't change for different observers.

Right.

 

[Alkatran]

Whether mass is an invariant depends on how you define it. Most treatments of SR today take mass as an invariant, but some find it useful to use "mass" to mean the so-called "relativistic mass", which does depend on the frame doing the measuring.

For wether or not the mass of a proton changes, it wouldn't matter which definition you took.