Question on Michelson Morley experiment and length contraction

[mangaroosh]

I'm a lay person who is interested in developing a better understanding of science in general, as well as specific theories.

I'm just wondering if someone would be able to help me understand how Length contraction explains the null set of the Michelson Morley experiment?

Hopefully this thread is in the right place and someone can help me with this - cheers.

 

[ghwellsjr]

I uploaded a series of animations that I thought might help people understand this question. Look at posts #78 and #79 on this thread:

https://www.physicsforums.com/showthread.php?p=3059029&highlight=youtube#post3059029

 

[mangaroosh]

I uploaded a series of animations that I thought might help people understand this question. Look at posts #78 and #79 on this thread:

https://www.physicsforums.com/showthread.php?p=3059029&highlight=youtube#post3059029

thanks ghwellsjr

 

[mangaroosh]

I uploaded a series of animations that I thought might help people understand this question. Look at posts #78 and #79 on this thread:

https://www.physicsforums.com/showthread.php?p=3059029&highlight=youtube#post3059029

I had a quick read of the posts, thanks for that, and I will go through them again to try and get a better understanding; but there was just one thing that wasn't immediately clear - to me - and that was how the interference pattern on the interferometer shows that the length is contracted.

If the light is traveling at the same speed along both arms of the interferometer, would it not have the same wave length and so cause no interference pattern (or the null set, if I have that correct)?

 

[HallsofIvy]

Here's an interesting calculation related to this:

Suppose you are swimming in a river which flows at speed v relative to the bank. You can swim at speed c relative to the water. If you are swimming downstream your speed, relative to the bank is c+ v so you could swim distance L in time L/(c+ v). If you are swimming upstream your speed is c- v so could swim back upstream a distance L/(c- v). You swim both legs in time L/(c- v)+ L/(c+ vf)= (Lc+ Lv)/(c-v)(c+v)+ (Lc-Lv)/(c-v)(c+v)= 2Lc/(c^2- v^2)= 2L/[c(1- L^2/c^2)].

If, instead, you were to swim across the river, you would have to "point" slightly up stream so that your speed across the river would be \sqrt{c^2- v^2} (Imagine a right triangle with hypotenuse of length c and one leg (up river) of length v. The length of the other leg (across the river) is \sqrt{c^2- v^2}.) So you go across the river a distance L' and back, for a total distance of 2L' is 2L'/\sqrt{c^2- v^2}.

If it takes the same time to swim both laps,
2L/c(c^2- v^2)= 2L'/\sqrt{c^2- v^2}
so that
L= \frac{L'\sqrt{c^2- v^2}}{c}= L'\sqrt{1- \frac{v^2}{c^2}}

 

[ghwellsjr]

You always get an interference pattern with a properly constructed and operating interferometer (not a trivial task) but the question is whether that pattern changes as the apparatus is rotated. But Michelson and Morley were expecting the light to take longer along one arm during some part of the day and/or season when rotated to the correct orientation. The fact that it didn't meant their understanding of how light propagated had to be modified.

Since the scientists prior to Einstein were unwilling to give up on the notion of a fixed ether medium in which the speed of light is exclusively a constant, they explained the null result as the arms changing length as the apparatus was rotated so that the changing speed of light was exactly compensated and made it look like they were stationary in the ether.

In fact, Michelson thought the Earth was dragging the ether along with it to give the null result and suggested that the experiment be repeated at the top of a high mountain to reduce the dragging.

 

[mangaroosh]

Here's an interesting calculation related to this:

Suppose you are swimming in a river which flows at speed v relative to the bank. You can swim at speed c relative to the water. If you are swimming downstream your speed, relative to the bank is c+ v so you could swim distance L in time L/(c+ v). If you are swimming upstream your speed is c- v so could swim back upstream a distance L/(c- v). You swim both legs in time L/(c- v)+ L/(c+ vf)= (Lc+ Lv)/(c-v)(c+v)+ (Lc-Lv)/(c-v)(c+v)= 2Lc/(c^2- v^2)= 2L/[c(1- L^2/c^2)].

If, instead, you were to swim across the river, you would have to "point" slightly up stream so that your speed across the river would be \sqrt{c^2- v^2} (Imagine a right triangle with hypotenuse of length c and one leg (up river) of length v. The length of the other leg (across the river) is \sqrt{c^2- v^2}.) So you go across the river a distance L' and back, for a total distance of 2L' is 2L'/\sqrt{c^2- v^2}.

If it takes the same time to swim both laps,
2L/c(c^2- v^2)= 2L'/\sqrt{c^2- v^2}
so that
L= \frac{L'\sqrt{c^2- v^2}}{c}= L'\sqrt{1- \frac{v^2}{c^2}}

I'm assuming that c is the speed of light? Does that not mean that the emboldened sentence above could not be possible, because nothing can travel faster than the speed of light?

 

[mangaroosh]

You always get an interference pattern with a properly constructed and operating interferometer (not a trivial task) but the question is whether that pattern changes as the apparatus is rotated. But Michelson and Morley were expecting the light to take longer along one arm during some part of the day and/or season when rotated to the correct orientation. The fact that it didn't meant their understanding of how light propagated had to be modified.

Since the scientists prior to Einstein were unwilling to give up on the notion of a fixed ether medium in which the speed of light is exclusively a constant, they explained the null result as the arms changing length as the apparatus was rotated so that the changing speed of light was exactly compensated and made it look like they were stationary in the ether.

In fact, Michelson thought the Earth was dragging the ether along with it to give the null result and suggested that the experiment be repeated at the top of a high mountain to reduce the dragging.

Does that not mean that the concept of Lenght contraction preserves the idea of an aether?

I'm just having trouble understanding how a non-changing interference pattern indicates, or suggests, that length contraction has occurred.

Could the non-changing interference pattern, or the null result, not be explained by two beams of light [possibly] traveling different distances but arriving in phase, without the necessity of length contraction?

Is there a difference between this kind of length contraction and that of Special Relativity?

 

[HallsofIvy]

I'm assuming that c is the speed of light? Does that not mean that the emboldened sentence above could not be possible, because nothing can travel faster than the speed of light?

No "c" is not the speed of light- it is exactly what I said- the speed with which you swim relative to the water.

 

[mangaroosh]

No "c" is not the speed of light- it is exactly what I said- the speed with which you swim relative to the water.

OK, you'll forgive the confusion surely.

In the equation you posted above, does c not usually represent the speed of light?

 

[ghwellsjr]

Does that not mean that the concept of Lenght contraction preserves the idea of an aether?

Yes, that is why those early scientists came up with the concept.

I'm just having trouble understanding how a non-changing interference pattern indicates, or suggests, that length contraction has occurred.

If they only performed the experiment one time, then they could have jumped to the conclusion that they just happened to be at rest with the aether and that is why their apparatus showed no difference in the round-trip speed of light for all directions. But they weren't that naive and so they repeated the experiment many times during the day and during the year. Since the motion of the Earth's surface is constantly changing and they always detected that they were at rest with respect to the aether, they could only conclude, as Michelson did, that the Earth was dragging the aether along with it, or they could conclude, as the other scientists did, that the appartus was getting modified by the motion of it through the aether so that it only appeared that they were stationary in the aether.

Could the non-changing interference pattern, or the null result, not be explained by two beams of light [possibly] traveling different distances but arriving in phase, without the necessity of length contraction?

The issue is whether the physical apparatus is changing its dimensions so that the positioning of the mirrors rigidly attached to it are also changing their distance apart and thereby the path length of the light along the two directions at right angles is changing. So I don't understand how you could suggest that the two beams of light are traveling different distances without the lengths of their path not also changing.

Is there a difference between this kind of length contraction and that of Special Relativity?

No difference at all. They are exactly the same. The only difference between the interpretation of those early scientists and Einstein is that they believed in a single absolute aether rest state and that the apparatus was experiencing changing lengths whereas Einstein turned it around and said they could consider their state to be at rest and everyone else moving with respect to them have their lengths contracted. That's what Einstein's concept of a Frame of Reference is.

 

[mangaroosh]

Yes, that is why those early scientists came up with the concept.

Apologies, I'm sure my questions are coming across as very basic, but I think there are probably a few things which are preventing me from understanding this - not suggesting that it is your job to help me understand, but I do appreciate your taking the time.

Firstly, is the assumption that some medium is required for the propagation of light waves?

If they only performed the experiment one time, then they could have jumped to the conclusion that they just happened to be at rest with the aether and that is why their apparatus showed no difference in the round-trip speed of light for all directions. But they weren't that naive and so they repeated the experiment many times during the day and during the year. Since the motion of the Earth's surface is constantly changing and they always detected that they were at rest with respect to the aether, they could only conclude, as Michelson did, that the Earth was dragging the aether along with it, or they could conclude, as the other scientists did, that the appartus was getting modified by the motion of it through the aether so that it only appeared that they were stationary in the aether.

Could they not simply have concluded that the aether didn't exist, without the need to postulate that the apparatus was getting modified?

The issue is whether the physical apparatus is changing its dimensions so that the positioning of the mirrors rigidly attached to it are also changing their distance apart and thereby the path length of the light along the two directions at right angles is changing. So I don't understand how you could suggest that the two beams of light are traveling different distances without the lengths of their path not also changing.

Could the distance not simply be measured, to determine if it is actually changing dimensions?

No difference at all. They are exactly the same. The only difference between the interpretation of those early scientists and Einstein is that they believed in a single absolute aether rest state and that the apparatus was experiencing changing lengths whereas Einstein turned it around and said they could consider their state to be at rest and everyone else moving with respect to them have their lengths contracted. That's what Einstein's concept of a Frame of Reference is.

Does this mean that with two reference frames moving relative to each other, that from the perspective of both reference frames, the other one would have it's length contracted i.e. both would have their lengths contracted?

 

[ghwellsjr]

Apologies, I'm sure my questions are coming across as very basic, but I think there are probably a few things which are preventing me from understanding this - not suggesting that it is your job to help me understand, but I do appreciate your taking the time.

That's the purpose of this forum--to help people understand. I'm glad to help--as are many other people who have previously helped me.

Firstly, is the assumption that some medium is required for the propagation of light waves?

Special Relativity is not concerned with the mechanism of light propagation--whether it is photons or waves--what is important is that there is no requirement for a medium, even if it were to exist, it serves no useful purpose in the Theory.

Could they not simply have concluded that the aether didn't exist, without the need to postulate that the apparatus was getting modified?

Just saying the aether doesn't exist doesn't solve the problem of how to reconcile that the speed of light always seems to be c, independent of your motion. In particular, if two observers are measuring the same flash of light, like I show in my animations, how can you understand that they both think they are in the center of the expanding sphere of light when they are in different locations? Can you think of a way to reconcile that without postulating length contraction?

Could the distance not simply be measured, to determine if it is actually changing dimensions?

Yes, but your rulers will get contracted by exactly the same amount so you cannot tell that any dimensions are changing.

Does this mean that with two reference frames moving relative to each other, that from the perspective of both reference frames, the other one would have it's length contracted i.e. both would have their lengths contracted?

Yes, but only one at a time. It's just like relative speeds. From each one's perspective, the other one is moving but you would never think that the real speed was double the perceived speed. Same with length contraction--you pick a Frame of Reference and any objects moving in that frame are length contracted along the direction of motion and the objects that are at rest in that FoR are not contracted. You can even pick a FoR where both objects/observers are moving at the same speed in opposite directions so they are both contracted by the same amount but not the same amount as when you pick a FoR where one of them is stationary.

 

[mangaroosh]

if two observers are measuring the same flash of light, like I show in my animations, how can you understand that they both think they are in the center of the expanding sphere of light when they are in different locations? Can you think of a way to reconcile that without postulating length contraction?

is that definitively the case?

 

[ghwellsjr]

Yes, they both will have an identical experience with regard to the expanding sphere of light.

 

[mangaroosh]

Yes, they both will have an identical experience with regard to the expanding sphere of light.

How do we know this to be the case?

 

[ghwellsjr]

All experiments measuring the round trip speed of light, starting with Michelson and Morley's, indicate that they yield the same constant value c. Do you doubt this?

 

[mangaroosh]

All experiments measuring the round trip speed of light, starting with Michelson and Morley's, indicate that they yield the same constant value c. Do you doubt this?

I don't doubt the constancy of the speed of light, it's just that when someone posted a video explanation of SR, on another forum, there was another video critiquing the thought experiment used by Einstein. In that video was a link to a website which outlines a critique of SR & the MMX, in which a number of issues are raised.

Unfortunately, I'm not well up enough on either to determine the accuracy of the respective theories, so I'm in the position of trying to wade through both of them.

 

[ghwellsjr]

There's another theory? I'm only aware of Einstein's Theory of Special Relativity and Lorentz's Ether Theory as fitting all the experimental facts. I didn't know anyone questioned the experimental facts. Why would you entertain a critique that questions the experimental evidence? There's a lot of people out there that don't understand relativity and so they bash it without first trying to understand it. I hope you stay motivated to understand it before you try to decide between it and what the bashers are saying.

Have you gone through my animations in an attempt to understand them? Do you have any questions about them?

 

[mangaroosh]

There's another theory? I'm only aware of Einstein's Theory of Special Relativity and Lorentz's Ether Theory as fitting all the experimental facts. I didn't know anyone questioned the experimental facts. Why would you entertain a critique that questions the experimental evidence? There's a lot of people out there that don't understand relativity and so they bash it without first trying to understand it. I hope you stay motivated to understand it before you try to decide between it and what the bashers are saying.

Have you gone through my animations in an attempt to understand them? Do you have any questions about them?

Apologies, I used the term "theory" very loosely there, I should have said an alternative interpretation.

I have gone through the animations - thanks for those - and I have been discussing it elsewhere. Ultimately I understand it - to a degree - but it ultimately comes down to the issue of length contraction, which the author of the video and the website has questioned. The challenge, to my mind, appears to be relatively sound, but, as mentioned, I'm not really well up enough on either to say for definite.

Now, I am wary of the fact that there are "bashers" out there and so I try to avoid simply believing what they say, opting instead to try and understand it and see why it is either true or false; the same applies to established scientific theories - I try to opt for understanding over belief, or acceptance.

There is also, however, the unfortunate issue of confirmation bias, and the author's critique of SR and the MMX confirmed, to a certain extent, what I thought seemed intuitively true. Now, I know "intuition" doesn't form the basis of scientific enquiry, but that doesn't necessarily invalidate it; and finding something which confirms existing beliefs, not doesn't it make true, just as it doesn't necessarily invaldiate it either.

I find that discussing them is a very useful way of getting to understand them better; I often tend to fluctuate betweeen challenging and questioning because I reach a point where I think I spot a flaw in the reasoning and so challenge, but then there are times when things are more complex and I question to try and build a better pictur for myself.

 

[ghwellsjr]

So, do you have a question?

 

[harrylin]

I'm assuming that c is the speed of light? Does that not mean that the emboldened sentence above could not be possible, because nothing can travel faster than the speed of light?

Applying the illustration to light, then c is the speed of light. Now, if the one-way speed relative to a "stationary" reference is taken to be c as measured with the stationary reference system, then by mathematical necessarily the velocity of a light ray relative to a moving object (with its speed v<c) can be anything between -2c and +2c. This "closing speed" is the direct consequence of the assumption that nothing can travel faster than the speed of light.

 

[mangaroosh]

So, do you have a question?

the problem with having a lack of understanding is not knowing the right questions to ask, so I generally have to ask a few questions to build an understanding first.

I was hoping that asking how the notion of length contraction was a suitable explanation for the null result, of the MMX, would give me the answer which clarified it for me, but unfortunately it didn't - not saying that the answer was deficient, rather that the question may not have been.

I'm trying to figure out how the interference pattern observed, led to the conclusion that the dimensions of the interferometer contracted in the direction of motion.

I'm also wondering why that couldn't simply be measured using a measuring device? I know that the measuring device would also be contracted but does that mean that our everyday measuring devices are contracted depending on how we hold them i.e. if they are in the direction of motion?

That may appear like a very basic question, but the image I have is of the apparatus floating on a bed of mercury, in a room that anyone could enter, so the same contraction effects would be felt by someone in the room.

 

[mangaroosh]

Applying the illustration to light, then c is the speed of light. Now, if the one-way speed relative to a "stationary" reference is taken to be c as measured with the stationary reference system, then by mathematical necessarily the velocity of a light ray relative to a moving object (with its speed v<c) can be anything between -2c and +2c. This "closing speed" is the direct consequence of the assumption that nothing can travel faster than the speed of light.

Pardon my obvious ignorance, but what do you mean by: by mathematical necessity the speed of light can be +/- 2; and "closing speed"?

 

[ghwellsjr]

the problem with having a lack of understanding is not knowing the right questions to ask, so I generally have to ask a few questions to build an understanding first.

I was hoping that asking how the notion of length contraction was a suitable explanation for the null result, of the MMX, would give me the answer which clarified it for me, but unfortunately it didn't - not saying that the answer was deficient, rather that the question may not have been.

I'm trying to figure out how the interference pattern observed, led to the conclusion that the dimensions of the interferometer contracted in the direction of motion.

I'm also wondering why that couldn't simply be measured using a measuring device? I know that the measuring device would also be contracted but does that mean that our everyday measuring devices are contracted depending on how we hold them i.e. if they are in the direction of motion?

That may appear like a very basic question, but the image I have is of the apparatus floating on a bed of mercury, in a room that anyone could enter, so the same contraction effects would be felt by someone in the room.

You have asked more than once about how the interference pattern leads to length contraction so let me just make sure you understand that the interferometer is basically a techinique to monitor a change in the distances between a source of light, two different paths the light can take and a target on which the two light beams interfere with each other. If the interference pattern remains identical, then that means the difference in the measured distances the light took didn't change. Now if we look at the two paths in MMX, we will see that they are both a round trip (actually back and forth several times to increase the effect) at ninty degrees to each other.

Do you understand that if there were an absolute ether rest state and no length contraction, then as the Earth moved through the ether (the medium that propagates light) then MMX would have detected a change in the interference pattern as the apparatus was rotated on the bed of mercury? That is what I'm attempting to show in this animation which includes four mirrors instead of just two like MMX:

https://www.youtube.com/watch?v=U625Pjm9M-I

But instead they got what appeared to be this animation:

https://www.youtube.com/watch?v=ygvY4AjwPmE

Notice how in the second animation, the reflected light from all four mirrors arrives at the observer at the same time but in the first animation, the light from the top and bottom mirrors arrives before the light from the left and right mirrors.

So in order to make the first situation look like the second situation, Lorentz theorized that the left and right mirrors were really closer than they thought they were. Can you see how if those two mirrors were actually closer, then the reflected light from all four mirrors would arrive at the observer at the same time?

And yes, Lorentz also believed "that our everyday measuring devices are contracted depending on how we hold them i.e. if they are in the direction of motion", but only in the direction of motion with regard to the absolute rest state of the ether. So we have no idea what direction that is, everything seems perfectly normal to us. The point is, if the ether is absolutely at rest, and we change our speed, then our rulers must be changing in length but for all we know, they might actually be getting longer if we happen to start out going fast with respect to the ether and then change our speed so that we are now going slower with respect to the ether. Remember, I am describing what scientists prior to Einstein believed.

 

[harrylin]

Pardon my obvious ignorance, but what do you mean by: by mathematical necessity the speed of light can be +/- 2; and "closing speed"?

That's not exactly what I wrote.
Mathematically, if you measure the speed of one object (the swimmer) to be +c in one direction, and the speed of another object (the river bank) -v (thus in opposite direction), then their relative speed as determined by you is c+v. That is basic vector algebra and in modern jargon such relative speeds are often called "closing speed".

Thus, if the swimmer swims at c while the speed of the river bank v is less than c, then their relative speed as determined in this manner (their "closing speed") is not c but still less than 2c.

Hopefully, if you understand that, you'll next understand #22.

 

[harrylin]

[..] I'm trying to figure out how the interference pattern observed, led to the conclusion that the dimensions of the interferometer contracted in the direction of motion.

It took years of reflection by several people, based on a number of experiments. I doubt that there is a good shortcut for reading up on the history of science...

I'm also wondering why that couldn't simply be measured using a measuring device? I know that the measuring device would also be contracted but does that mean that our everyday measuring devices are contracted depending on how we hold them i.e. if they are in the direction of motion?

That may appear like a very basic question, but the image I have is of the apparatus floating on a bed of mercury, in a room that anyone could enter, so the same contraction effects would be felt by someone in the room.

That makes me think of the following which I'll give as illustration:
an other image, of a space shuttle floating in space, with astronauts inside, so the same gravitation effects would be felt by someone in the shuttle. Thus the astronaut feels the gravity?

 

[mangaroosh]

You have asked more than once about how the interference pattern leads to length contraction so let me just make sure you understand that the interferometer is basically a techinique to monitor a change in the distances between a source of light, two different paths the light can take and a target on which the two light beams interfere with each other. If the interference pattern remains identical, then that means the difference in the measured distances the light took didn't change. Now if we look at the two paths in MMX, we will see that they are both a round trip (actually back and forth several times to increase the effect) at ninty degrees to each other.

Do you understand that if there were an absolute ether rest state and no length contraction, then as the Earth moved through the ether (the medium that propagates light) then MMX would have detected a change in the interference pattern as the apparatus was rotated on the bed of mercury? That is what I'm attempting to show in this animation which includes four mirrors instead of just two like MMX:

https://www.youtube.com/watch?v=U625Pjm9M-I

But instead they got what appeared to be this animation:

https://www.youtube.com/watch?v=ygvY4AjwPmE

Notice how in the second animation, the reflected light from all four mirrors arrives at the observer at the same time but in the first animation, the light from the top and bottom mirrors arrives before the light from the left and right mirrors.

So in order to make the first situation look like the second situation, Lorentz theorized that the left and right mirrors were really closer than they thought they were. Can you see how if those two mirrors were actually closer, then the reflected light from all four mirrors would arrive at the observer at the same time?

And yes, Lorentz also believed "that our everyday measuring devices are contracted depending on how we hold them i.e. if they are in the direction of motion", but only in the direction of motion with regard to the absolute rest state of the ether. So we have no idea what direction that is, everything seems perfectly normal to us. The point is, if the ether is absolutely at rest, and we change our speed, then our rulers must be changing in length but for all we know, they might actually be getting longer if we happen to start out going fast with respect to the ether and then change our speed so that we are now going slower with respect to the ether. Remember, I am describing what scientists prior to Einstein believed.

thanks for that, I wasn't sure what they believed the conditions to be i.e. an aether and no length contraction, and what the corresponding expectations were i.e. animation 1 - that was made very clear, cheers.

Now I know the question I wanted to ask; if the first animation was what they expected with an aether and no length contraction, but the second one was what appeared to happen - which suggested length contraction occurred - what would be the expected case with no aether and no length contraction?

 

[ghwellsjr]

Now I know the question I wanted to ask; if the first animation was what they expected with an aether and no length contraction, but the second one was what appeared to happen - which suggested length contraction occurred - what would be the expected case with no aether and no length contraction?

That is exactly what Einstein proposed that any inertial (non-accelerating) observer would do in order to define a Frame of Reference in which that observer would be stationary. But this meant that any other observer or objects moving in that FoR will experience length contraction and time dilation in order that they, too, would measure the round-trip speed of light to be the constant value, c. Do you follow that?

 

[mangaroosh]

That's not exactly what I wrote.
Mathematically, if you measure the speed of one object (the swimmer) to be +c in one direction, and the speed of another object (the river bank) -v (thus in opposite direction), then their relative speed as determined by you is c+v. That is basic vector algebra and in modern jargon such relative speeds are often called "closing speed".

Thus, if the swimmer swims at c while the speed of the river bank v is less than c, then their relative speed as determined in this manner (their "closing speed") is not c but still less than 2c.

Hopefully, if you understand that, you'll next understand #22.

cheers. I understand all that, I just thought that the speed of light was the upper limit, so thought the c+v wouldn't apply because you could only ever measure the speed of light as c, regardless of the relative movement of objects.