Doubt in Michelson Morley experiment

[arka.sharma]

Hi All,

I studied about Michelson Morley experiment in my graduation in the compulsory Physics paper. I had Computer Science major(not a Physics guy), anyways this question came in my mind during my graduation time and may be because of my misinterpretation however couple of days ago in some discussion that question again came back and it is as follows

In the Michelson Morley experiment we have two mirrors(you can refer to http://en.wikipedia.org/wiki/File:Michelson-morley_calculations.png for picture as attachment not working) in the transverse direction how light ray is taking the dotted path (shown in the picture) instead of path along "L" (shown in the picture) is somehow Earth's velocity affecting the light beam's trajectory or it is the relative velocity of aether. If it is the relative velocity of aether respect to Earth then it should be the opposite direction of Earth velocity in the picture "v" is pointed as Earth's velocity.

Regards,
Arka

 

[Enigman]

http://upload.wikimedia.org/wikipedia/en/3/34/Michelson-morley_calculations.png

 

[ghwellsjr]

Hi All,

I studied about Michelson Morley experiment in my graduation in the compulsory Physics paper. I had Computer Science major(not a Physics guy), anyways this question came in my mind during my graduation time and may be because of my misinterpretation however couple of days ago in some discussion that question again came back and it is as follows

In the Michelson Morley experiment we have two mirrors(you can refer to http://en.wikipedia.org/wiki/File:Michelson-morley_calculations.png for picture as attachment not working) in the transverse direction how light ray is taking the dotted path (shown in the picture) instead of path along "L" (shown in the picture) is somehow Earth's velocity affecting the light beam's trajectory or it is the relative velocity of aether. If it is the relative velocity of aether respect to Earth then it should be the opposite direction of Earth velocity in the picture "v" is pointed as Earth's velocity.

Regards,
Arka

That is correct. If you define v to be the velocity of A with respect to B, then the velocity of B with respect to A is -v.

So if v is the velocity of Earth with respect to the aether, then -v is the velocity of the aether with respect to the earth.

Is that the only doubt you have in MMX?

 

[arka.sharma]

Thanks for your reply. My question is how light beam is taking the dotted path as shown in the picture.Is it aether velocity 'v' opposite to the pointed direction in the picture that is causing light beam to follow the dotted line instead of the bold line of distance 'L'.

 

[ghwellsjr]

Thanks for your reply. My question is how light beam is taking the dotted path as shown in the picture.Is it aether velocity 'v' opposite to the pointed direction in the picture that is causing light beam to follow the dotted line instead of the bold line of distance 'L'.

That picture portrays what Michelson and Morley expected would happen when they did their experiment. See the note in the lower right corner?

However, whenever they repeated the experiment, it behaved as if the velocity, v, of Earth relative to the aether was 0, even though they knew that the Earth had accelerated between the different experimental trials.

Since many of the scientists of the day continued to believe that light traveled at c only with respect to an immovable aether, they explained the null result of MMX by assuming that the length of their apparatus along the direction of motion through the aether contracted by just the right amount so that the total path length of the light for the transverse and longitudinal directions remained the same.

I made an animation that might help you to understand how they explained this and also how Einstein came up with an alternative explanation. Have a look at this thread and let me know if it helps:

www.physicsforums.com/showthread.php?t=626807

 

[arka.sharma]

Thanks for the link.I will surely go through the link because right now I can't install the plugins. My question was why the trajectory of light beam was expected along the dotted line is because it is being emitted from a source which is having a velocity v or is there some other reason ? Does velocity of light source perpendicular to the direction of emission affect the light beam's path ?(Forgive my ignorance) May be this is already covered in the link and I shouldn't ask this.

 

[ghwellsjr]

Thanks for the link.I will surely go through the link because right now I can't install the plugins. My question was why the trajectory of light beam was expected along the dotted line is because it is being emitted from a source which is having a velocity v or is there some other reason ? Does velocity of light source perpendicular to the direction of emission affect the light beam's path ?(Forgive my ignorance) May be this is already covered in the link and I shouldn't ask this.

As I said in post #5, they believed that light traveled at c only with respect to an immovable aether. So they believed that the velocity of the light source would have no bearing on the propagation of the light. Once emitted, they believed the light would propagate according to the rest state of the aether, not according to the velocity of the light source. In other words, they believed that light would behave similarly to the way that water waves or sound waves would propagate according to the rest state of the medium carrying the waves and not according to the relative velocity of the source emitting the waves.

They had no idea if the Earth was moving with respect to this immovable aether at any particular time but since they knew that the surface of the Earth where they conducted the experiment kept changing its motion with respect to this presumed immovable aether, they expected that at least some time during the day, they would be moving with respect to the aether.

Maybe I'm not understanding your question. Are you clear that if there were an immovable aether, then the surface of the Earth would sometime be moving with respect to it? Or is your question why the path of the light would be shifted when the surface of the Earth was moving with respect to the aether?

In any case, if you are having trouble viewing the animations on your computer, can you find another computer, maybe at a library or school or a friend that would have the correct plugins installed so that you could view the animations? It might be that your question will be resolved when you study the thread along with the animations. Just be aware that it is not following exactly the experiment of Michelson and Morley, just the principles involved.

 

[jtbell]

AThey had no idea if the Earth was moving with respect to this immovable aether at any particular time but since they knew that the surface of the Earth where they conducted the experiment kept changing its motion with respect to this presumed immovable aether, they expected that at least some time during the day, they would be moving with respect to the aether.

They also did the experiment at different times of the year, to take advantage of the Earth's orbital velocity being in different directions; e.g. in opposite directions at six-month intervals.

 

[Dale]

My question was why the trajectory of light beam was expected along the dotted line is because it is being emitted from a source which is having a velocity v or is there some other reason ?

Yes. We know that the light hits the bottom mirror, then the top mirror, and then the bottom mirror. That is an experimentally observed fact. So if the bottom mirror moved during the two strikes then the light must have followed the dotted path. If it didn't then it would have missed the mirror.

 

[Zee99]

Not mentioned was that MMX requires that the Earth plow through the ether somewhat like a submerged submarine plows through water. If the ether is attached to the earth, we should expect a null result, which was what was observed. Then, when Lorentz applied his logic, he also assumed that the Earth was plowing through the ether. Once again, if the ether was attached to the earth, Lorentz's contraction fails.
So, I have two questions:
1). Could the ether be attached to the earth?
2). What independent evidence is there that Lorentz's contraction actually exists? I looked but found only poor agreement with the theory. Elsewhere on Wikipedia (search for length contraction) it is stated that length contraction is not a physical phenomena, but only the mathematical consequence of assumptions.

 

[ghwellsjr]

Not mentioned was that MMX requires that the Earth plow through the ether somewhat like a submerged submarine plows through water.

It would be more like the ether plows through the Earth as opposed to it being dragged by the earth.

If the ether is attached to the earth, we should expect a null result, which was what was observed. Then, when Lorentz applied his logic, he also assumed that the Earth was plowing through the ether. Once again, if the ether was attached to the earth, Lorentz's contraction fails.
So, I have two questions:
1). Could the ether be attached to the earth?

That's exactly what Michelson believed was the reason for the null result and he proposed in his paper describing the experiment and its result that the experiment be repeated at the top of a high mountain to minimize the effect.

2). What independent evidence is there that Lorentz's contraction actually exists? I looked but found only poor agreement with the theory.

You found poor agreement with the theory? Really? Where? Please provide us some of the places where you looked and found this poor agreement with the theory.

Elsewhere on Wikipedia (search for length contraction) it is stated that length contraction is not a physical phenomena, but only the mathematical consequence of assumptions.

I couldn't find anything like that in wikipedia's article on length contraction. Could you please provide an exact quote?

 

[Zee99]

Ether

It would be more like the ether plows through the Earth as opposed to it being dragged by the earth.

I didn't say the ether was dragged. All explanations of the MMX tell of the Earth plowing through the ether, and Lorentz assumed the same. Could you provide a quote stating that the ether plows through the earth? First time I've heard that one.

That's exactly what Michelson believed was the reason for the null result and he proposed in his paper describing the experiment and its result that the experiment be repeated at the top of a high mountain to minimize the effect.

First time I heard the mountain-top theory. Was that a paper other than the 1887 one? Why didn't he or Dayton Miller move to a mountain top?

You found poor agreement with the theory? Really? Where? Please provide us some of the places where you looked and found this poor agreement with the theory.

Sorry to disappoint you, but I'm not going to repeat the effort. There is a list of experiments done in Wikipedia's description of length contraction. As I recall the assessment, none of these provided compelling proof of the existence of length contraction. They were, within experimental error, consistent with the theory. That was what prompted my question in the first place. I also remember an experiment years ago where a beam of low-energy particles was broad-sided with another beam. Then the energy of the first beam was increased to relativistic speeds, and again broad-sided with another beam. It was argued that by increasing the energy, spherical particles would supposedly turn pancaked shape, and more of the broadsiding particles would penetrate the beam. This likewise gave results that were, within experimental error, consistent with the theory.

I couldn't find anything like that in wikipedia's article on length contraction. Could you please provide an exact quote?

I remember it from sometime back, and I think it was in Wikipedia's assessment of length contraction.

I ask again, is there any experimental evidence that provides compelling proof that length contraction exists?

 

[Dale]

Yes. MMX, cosmic ray muons, and particle accelerator bunches. Furthermore, MMX, Ives and Stillwell, and Kennedy and Thorndike together can be used to derive the Lorentz transform, even without assuming the postulates of relativity. So there is no rational objection to the measurable consequences of length contraction given experimental data.

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

 

[ghwellsjr]

It would be more like the ether plows through the Earth as opposed to it being dragged by the earth.

I didn't say the ether was dragged. All explanations of the MMX tell of the Earth plowing through the ether, and Lorentz assumed the same. Could you provide a quote stating that the ether plows through the earth? First time I've heard that one.

"Dragged" was probably a poor choice of words on my part. I was really trying to point out that the ether was immovable and that it would not flow around the Earth like water around a submarine.

That's exactly what Michelson believed was the reason for the null result and he proposed in his paper describing the experiment and its result that the experiment be repeated at the top of a high mountain to minimize the effect.

First time I heard the mountain-top theory. Was that a paper other than the 1887 one? Why didn't he or Dayton Miller move to a mountain top?.

It was the 1887 paper. Look down about 2/3 of the way to the first paragraph of the Supplement. I can't tell you why they didn't repeat the experiment "at the top of an isolated mountain peak". Maybe other explanations were offered or maybe the expense and logistics didn't warrant it.

 

[Zee99]

Thank you, DaleSpam:
I apologize, but I am struggling with the notion that length contraction is more than a mathematical artifact. Regarding evidence that it is real, let's examine the examples you cited.(1) Muons. Their penetration through the atmosphere before decaying is well explained with the Lorentz transformation for time intervals. However, in order to use the length contraction equation, one must assume that the Earth has been accelerated to high speed, and, if we consider all the mesons penetrating the atmosphere, we must assume that the Earth is being accelerated at high speed in all those directions simultaneously. Now that sounds a bit illogical to me, and I must reject length contraction explaining how the muons reach Earth's surface. (2) Particle beams. Are you referring to the experiment where one beam broadsides a low energy beam of ions, then the ion energy is increased, and it is broadsided again? I examined that data and found that it "barely" confirmed the contraction equation predictions. There was a lot of scatter in the data, and, yes, it could be interpreted that contraction might exist. But that was not compelling evidence. (3) MMX. I've been through their equations, and it was there that I noted how they assumed the presence of an ether. I understand that AE showed it didn't matter, but it did matter in explaining the null result. Especially what happen when the ether is attached to the earth. If the null result can be explained by attaching ether to the earth, then I don't think we should point to the MMX and say that is compelling evidence of the proof of the contraction equation. NOW having said all that, I think I can show evidence that the ether exists and is attached to mass because the ether is none other than gravitational field material. By considering ether of this nature, we can explain the constancy in the speed of light as well as Dark Energy wherein photons pass through vast expanses of space having minimal gravitational field material. There is another proof that I'm working on. More later.

 

[arka.sharma]

Thanks ghwellsjr. I am having difficulty in understanding the following fact.According to the picture that posted by
Enigman the experiment setup/earth is moving right which results aether to move left with velocity 'v' with respect to earth.The light came from the source reflected at first mirror and was supposed to go along vertical path if Earth had no relative velocity with aether.Now aether is moving left relative to Earth and if we draw an analogy with crossing a river having a current leftwards for example.But if this is the case then why that beam slanted right after reflecting to the first mirror instead of slanting left.Like if someone tries to cross a river straight which is having a current towards left his path should slant leftwards correct ? Am I missing some point here or something I misunderstood or is that analogy of a swimmer trying to cross a river straight with current towards left is valid here ? Please let me know if I am able to put my question correctly ?

 

[TumblingDice]

According to the picture that posted by Enigman the experiment setup/earth is moving right which results aether to move left with velocity 'v' with respect to earth.

I read the 'v' arrow in the diagram as indicating the aether's velocity and direction, not the Earth's. The left result (straight path) indicates v=0, and that wouldn't make sense for the Earth. So the angled path result would be in the direction of the aether flow. (I think...)

 

[ghwellsjr]

Thanks ghwellsjr. I am having difficulty in understanding the following fact.According to the picture that posted by
Enigman the experiment setup/earth is moving right which results aether to move left with velocity 'v' with respect to earth.The light came from the source reflected at first mirror and was supposed to go along vertical path if Earth had no relative velocity with aether.Now aether is moving left relative to Earth and if we draw an analogy with crossing a river having a current leftwards for example.But if this is the case then why that beam slanted right after reflecting to the first mirror instead of slanting left.Like if someone tries to cross a river straight which is having a current towards left his path should slant leftwards correct ? Am I missing some point here or something I misunderstood or is that analogy of a swimmer trying to cross a river straight with current towards left is valid here ? Please let me know if I am able to put my question correctly ?

The analogy with the swimmer crossing a river is correct. If you were on the shore watching the swimmer with the water flowing to the left, you would see things floating on the water moving to the left but you would see the swimmer's body slanted to the right in order to swim slightly upstream so that he can go straight across the river. If he wasn't watching where he was going and just aimed his body straight ahead, he would end up going towards the left, just like the other things floating on the water. So if his body was aimed straight, his path would be slanted left but if his body is aimed to the right, then his path would be straight.

 

[Dale]

in order to use the length contraction equation, one must assume that the Earth has been accelerated to high speed

Nonsense. I don't know why you would believe that. If an object is inertial (has not accelerated) in one frame then it is inertial (has not accelerated) in all frames. All frames will agree on the proper acceleration. Ignoring the orbital acceleration around the sun, which is negligible over the life of a muon, the Earth is not accelerated in any inertial reference frame.

Take an arbitrary inertial object in an arbitrary inertial frame and it will have a worldline like $(t,x)=(t,vt+d)$ which clearly has no acceleration. Now, transform that worldline to another frame and after some simplification you get $(t',x')=(t',v't'+d')$ which also clearly has no acceleration.

, and, if we consider all the mesons penetrating the atmosphere, we must assume that the Earth is being accelerated at high speed in all those directions simultaneously. Now that sounds a bit illogical to me, and I must reject length contraction explaining how the muons reach Earth's surface.

It is indeed illogical, however your strange misunderstanding about the basic mathematics of inertial frames in no way constitutes a valid rebuttal of length contraction.

(2) Particle beams. Are you referring to the experiment where one beam broadsides a low energy beam of ions, then the ion energy is increased, and it is broadsided again?

No, I specifically mean the length of a bunch in a particle accelerator. They must be designed with length contraction in mind. If you did not consider length contraction then you would get less charge in a bunch than is actually the case. The fact that we get the designed amount of charge in a bunch confirms that length contraction has occured.

(3) MMX. I've been through their equations, and it was there that I noted how they assumed the presence of an ether. I understand that AE showed it didn't matter, but it did matter in explaining the null result.

No, it didn't. All that mattered is that there exist some frame in which Maxwell's equations hold and that the apparatus length contracted in that frame. In any frame in which Maxwell's equations hold, there is no other explanation for the null result of the MMX other than length contraction.

As I said above, there is no rational objection to length contraction, given the evidence. You can choose to be irrational, if you wish, or you can choose to ignore the evidence, but such choices do not change the facts. Again, I would point out that Michelson Morely, Ives Stilwell, and Kennedy Thorndike together confirm experimentally the Lorentz transform without assuming the postulates of relativity, which means that Maxwells equations hold in all inertial frames. Given that, the experimental consequences of length contraction are an unavoidable logical result.

 

[PeterDonis]

in order to use the length contraction equation, one must assume that the Earth has been accelerated to high speed, and, if we consider all the mesons penetrating the atmosphere, we must assume that the Earth is being accelerated at high speed in all those directions simultaneously.

No, you don't. You only need to apply the length contraction argument in each muon's individual rest frame, one at a time. There is no need to apply it to all the muons "simultaneously"; that doesn't make sense anyway since the muons are in motion relative to each other, so there is no such thing as a single inertial frame in which they are all at rest, and therefore no need to assume that the Earth is somehow moving in all directions simultaneously.

 

[Zee99]

First of all, let's throttle back.
Let's start off with mesons and examine them in their "at rest" frame. In order for them to have the length from a meson to the Earth contracted, the Earth must move toward them. Do we agree on this point?

 

[Nugatory]

First of all, let's throttle back.
Let's start off with mesons and examine them in their "at rest" frame. In order for them to have the length from a meson to the Earth contracted, the Earth must move toward them. Do we agree on this point?

In a frame in which any given meson is at rest, the Earth is moving towards that meson.

That is not, however, the only frame in which the distance between the Earth and the meson is contracted relative to a frame in which the Earth is at rest. In any frame in which the Earth is moving, that distance will be contracted relative to a frame in which the Earth is at rest.

 

[PeterDonis]

Let's start off with mesons and examine them in their "at rest" frame.

Which rest frame? The muons are moving relative to each other, not just relative to the Earth, so as I pointed out in my previous post, there is no single frame in which "they" are at rest. You have to pick some particular muon and do the analysis in its rest frame.

In order for them to have the length from a meson to the Earth contracted, the Earth must move toward them. Do we agree on this point?

Since the muons are moving relative to the Earth, then in the rest frame of a particular muon, of course the Earth is moving.

 

[arka.sharma]

The analogy with the swimmer crossing a river is correct. If you were on the shore watching the swimmer with the water flowing to the left, you would see things floating on the water moving to the left but you would see the swimmer's body slanted to the right in order to swim slightly upstream so that he can go straight across the river.

Now this is completely clear and well understood. So if we compare the river's flow to left as ether's relative velocity with Earth and the swimmer with the path of light towards the top mirror then is the path towards 'b' in fig 2 of http://en.wikisource.org/wiki/On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether then is the first mirror adjusted such a way that after reflection light will take a path slanted more rightwards to the 'ab' but since ether is moving left light beam will be adjusted towards left to reach at 'b' as you told in the previous post "you would see the swimmer's body slanted to the right in order to swim slightly upstream so that he can go straight across the river"

Or is the relative velocity of light beam respect to ether ? Because ether is moving left and light's path is vertical then I understand this.

Or as TumblingDice said

I read the 'v' arrow in the diagram as indicating the aether's velocity and direction, not the Earth's.

But I am not sure this is correct.

Sorry to drag this for so long but I want to make it clear.

Thanks & Regards,
Arka

 

[ghwellsjr]

The analogy with the swimmer crossing a river is correct. If you were on the shore watching the swimmer with the water flowing to the left, you would see things floating on the water moving to the left but you would see the swimmer's body slanted to the right in order to swim slightly upstream so that he can go straight across the river.

Now this is completely clear and well understood. So if we compare the river's flow to left as ether's relative velocity with Earth and the swimmer with the path of light towards the top mirror then is the path towards 'b' in fig 2 of http://en.wikisource.org/wiki/On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether then is the first mirror adjusted such a way that after reflection light will take a path slanted more rightwards to the 'ab' but since ether is moving left light beam will be adjusted towards left to reach at 'b' as you told in the previous post "you would see the swimmer's body slanted to the right in order to swim slightly upstream so that he can go straight across the river"

Or is the relative velocity of light beam respect to ether ? Because ether is moving left and light's path is vertical then I understand this.

You keep switching between two views of the scenario.

Here's View 1: The ether is moving to the left and the experimental apparatus is stationary. This is the view that the analogy to the swimmer applies. The river is moving to the left and the swimmer has to aim to the right to compensate for the motion of the river. If you had asked Michelson and Morley if they would have to aim their mirror slightly to the right, they would have said, "in principle, yes" but they would have also added that since the presumed speed of the ether with respect to the Earth compared to the speed of light was so small that the amount of adjustment would also be too small to make any difference.

Here's View 2: The ether is stationary and the experimental apparatus is moving to the right. The is the view that is depicted in the drawings because it is very difficult to depict View 1 in a drawing. We can visualize the flow of water in a river if there are objects floating in the water and being carried down stream (that's why I mentioned things floating in the water) but we can't visualize things being carried along by the ether. So when in the drawings, View 2 is always used because we can just say that the ether is stationary and it's easy for us to imagine the experimental apparatus moving to the right. But again, if you asked the experimenters if they would have to aim the first mirror slightly to the right, they would have given you the same answer as in View 1 because if it weren't, they would expect the light to go straight up as in the case where the experiment is not moving.

But let's be clear about one thing: it turns out that it is not necessary to aim the mirror to the right in order for the light to hit the mirror, no matter how fast the Earth is traveling relative to any presumed ether. Length Contraction will re-aim the mirror for us by just the right amount to keep the light on target.

By the way, the picture that you linked to in your first post is used in wikipedia's article on the Michelson Morley experiment and all these issues are discussed there.

Or as TumblingDice said But I am not sure this is correct.

Sorry to drag this for so long but I want to make it clear.

Thanks & Regards,
Arka

He didn't sound to sure of himself and if you look in the article, you will see that it is the mirrors that are moving at v in the x direction.

 

[TumblingDice]

He didn't sound to sure of himself and if you look in the article, you will see that it is the mirrors that are moving at v in the x direction.

You're absolutely right, George. I just read the article and it's quite clear that v is the relative velocity of the mirrors in the direction of the arrow. THANK YOU for pointing this out. This thread was beginning to make me dizzy.