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 occured.

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 occured.

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.

 

[harrylin]

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.

This is simply 1+1=2; the basic rules of mathematics always apply, a theory of physics cannot make 1+1=2 wrong; and it is based on the assumption that you measure the speed of light to be c and not 2c.

What you probably did not discern (indeed, many textbooks gloss over it) is that a vector sum (such as the one you asked about and understand) is fundamentally different from a frame transformation. And when we talk about a measurement of the speed of light, we always mean the speed of light relative to a system as measured with respect to that system, so that v-system=0.

In classical mechanics that makes no difference: there a frame transformation may be confounded with a closing speed because the "Galilean" frame transformation uses the same equations as the vector sum. It is different in relativity: there you must use the Lorentz transformation when you switch reference system.

 

[mangaroosh]

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 sure that over that time the cumulative effect of information being passed on will have lead to more concise explanations, and explanations that suit a wider variety of learning types - such as ghwellsjr's animations.

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?

But would the effect of gravity change depending on what direction your are moving in the shuttle?

 

[mangaroosh]

This is simply 1+1=2; the basic rules of mathematics always apply, a theory of physics cannot make 1+1=2 wrong; and it is based on the assumption that you measure the speed of light to be c and not 2c.

OK, I was thinking of a 1:1 correlation with reality, where c+v wouldn't make sense.

What you probably did not discern (indeed, many textbooks gloss over it) is that a vector sum (such as the one you asked about and understand) is fundamentally different from a frame transformation. And when we talk about a measurement of the speed of light, we always mean the speed of light relative to a system as measured with respect to that system, so that v-system=0.

In classical mechanics that makes no difference: there a frame transformation may be confounded with a closing speed because the "Galilean" frame transformation uses the same equations as the vector sum. It is different in relativity: there you must use the Lorentz transformation when you switch reference system.

cheers. I have absolutely no background in any of that to be honest, and don't really understand what a vector is, or anything like that.

 

[harrylin]

[..]
cheers. I have absolutely no background in any of that to be honest, and don't really understand what a vector is, or anything like that.

OK, I'll try to make it as simple possible.

1. Suppose that the high speed TGV train has a max. speed of 300 km/h (in fact that's in practice the case). And you measure two TGV's pass each other, each at 300 km/h. They have the same speed, but in opposite directions. A vector means simply that you account for both the magnitude and the direction.

Now if we define relative speed (or closing speed) as [change of distance] / [time]; then what is the relative speed of the trains according to your measurements?

2. However, it is altogether a different question what the machinist of a train will measure, if he uses his own, fully independent measurement system. According to classical mechanics he will measure exactly the same relative velocity as you; therefore in classical mechanics we don't care if we stick to one reference system or not. Such a switching of reference systems is mathematically a "frame transformation".

According to relativity however, the machinist will measure a very slightly different speed relative to the other train (although the effect is still negligible at that speed). And if the trains could go at almost the speed of light you would measure their relative speeds to be almost 2c, while each train machinist would measure their relative speeds to be almost c: also according to measurements with his reference frame, a train can not go as fast as the speed of light.

This can be understood by accounting for the combined effects of length contraction, time dilation and relativity of simultaneity (compare with post #29).

 

[harrylin]

[..] But would the effect of gravity change depending on what direction your are moving in the shuttle?

No, you won't notice anything, at least not to very good approximation. It's similar with length contraction etc.: you cannot detect if you are "really" moving (or not).

Now, there is a small imperfection due to gravity getting less at greater distance; and some people have thought that there could be similar imperfections with relativity, for example perhaps wood contracts less than steel and so it would be possible to detect "absolute motion". But all such tests failed to demonstrate any effect of linear motion.

 

[mangaroosh]

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?

The author of the website has an explanation for that, which doesn't involve length contraction. He claims to have carried out an experiment which shows that a "beam of light" would be displaced by something like 2mm for a path length of 20m, which would then be amplified by "bouncing" the beam back and forth in an interferometer, which, he says, would account for the null result of the MMX; something he says isn't accounted for.

I'll have to have another read of the website just to get a better understanding, before I can discuss it. Like I say, I'm not in a position to scrutinise it to any reasonable degree, hence why I'm trying to fumble my way around to getting a better understanding of the MMX

 

[mangaroosh]

hey guys,

have another [what might seem like a basic] question; it's with regard to the idea that two observers moving relative to each other, who see a flash of light, will both remain at the centre of the expanding sphere; I'm just wondering how this has been tested experimentally?

 

[harrylin]

hey guys,

have another [what might seem like a basic] question; it's with regard to the idea that two observers moving relative to each other, who see a flash of light, will both remain at the centre of the expanding sphere; I'm just wondering how this has been tested experimentally?

First of all, that idea as you reproduce it can easily be misunderstood. According to each measurement system, the observer in rest will remain at the centre of the expanding sphere while the other will not.
That effect follows directly and with necessity from the relativistic effects (length contraction, time dilation and relativity of clock synchronization), which were derived in order to explain how such observations can be possible. Thus, only those effects need to be tested experimentally. And the only thing that could not been tested "directly" so far (because of technical limits) is length contraction.

Indirectly it has been tested by positive time dilation experiments in combination with a variant of the Michelson-Morley experiment that demonstrated that if time dilation is real, then also length contraction must be real (its original purpose was just the opposite).
See: http://en.wikipedia.org/wiki/Kennedy–Thorndike_experiment

 

[mangaroosh]

First of all, that idea as you reproduce it can easily be misunderstood. According to each measurement system, the observer in rest will remain at the centre of the expanding sphere while the other will not

but both observers will think that it is they that is at rest won't they?

 

[ghwellsjr]

but both observers will think that it is they that is at rest won't they?

It doesn't matter what they think, it only matters what they measure, and they both will measure that they are in the center of the expanding sphere of light, even if one (or both) of them are moving with respect to the source and to each other. Obviously, they cannot both be at rest with respect to each other and yet their measurements are identical.

The idea of representing the essential characteristic of the principle of relativity (part of Einstein's first postulate--that every inertial observer will measure the round-trip speed of light to be the same constant value in all directions) is this thought experiment of an expanding sphere of light because it makes it very obvious what that principle is saying. There is an abundance of evidence that every inertial observer measures the speed of light to be the same. My animations are intended to help people understand how length contraction explains this evidence.

 

[harrylin]

but both observers will think that it is they that is at rest won't they?

Only if they choose their reference systems accordingly. That is an obvious choice but it's not always the most convenient. For example, astronauts (and even the space centre on the Earth) typically think that they are moving.

 

[mangaroosh]

It doesn't matter what they think, it only matters what they measure, and they both will measure that they are in the center of the expanding sphere of light, even if one (or both) of them are moving with respect to the source and to each other. Obviously, they cannot both be at rest with respect to each other and yet their measurements are identical.

The idea of representing the essential characteristic of the principle of relativity (part of Einstein's first postulate--that every inertial observer will measure the round-trip speed of light to be the same constant value in all directions) is this thought experiment of an expanding sphere of light because it makes it very obvious what that principle is saying. There is an abundance of evidence that every inertial observer measures the speed of light to be the same. My animations are intended to help people understand how length contraction explains this evidence.

again, thanks for taking the time to go through the explanations, and the animations are very helpful for explaining how length contraction explains the evidence. I suppose the position I'm in is that I am new to most of this, and am trying to develop an understanding of it. That means that things which are experimentally supported appear as assumptions to me, until I understand how the evidence supports the assumption; whereas others, like yourself, who understand the evidence see them not as assumptions but evidentially supported postulates.

At present, I'm just trying to wade through the evidence.

 

[mangaroosh]

another basic question here guys, but how is time measured in the time dilation experiments? I'm presuming it is some form of a clock; I'm just wondering what kind of clocks they are?

 

[ghwellsjr]

Take three very stable atomic clocks, leave one on the ground, fly one around the world in an easterly direction, fly the other one around the world in a westerly direction, compare their elapsed times when they come back together.

Or the original famous muon half-life experiment which showed that even though they have a relatively short life time, they survive much longer when traveling at very high speeds.

 

[mangaroosh]

Take three very stable atomic clocks, leave one on the ground, fly one around the world in an easterly direction, fly the other one around the world in a westerly direction, compare their elapsed times when they come back together.

Or the original famous muon half-life experiment which showed that even though they have a relatively short life time, they survive much longer when traveling at very high speeds.

I know this is a very crude explanation, but am I anywhere near right in the understanding that the, let's say, "tick" of an atomic clock is measured from the detection of microwave emissions of changing electrons, or something along those lines? Is it the emissions as they change energy, or how does it work?

Is it an atomic clock that is used in the muon half-life experiment as well, to measure the decay time?

 

[harrylin]

I know this is a very crude explanation, but am I anywhere near right in the understanding that the, let's say, "tick" of an atomic clock is measured from the detection of microwave emissions of changing electrons, or something along those lines? Is it the emissions as they change energy, or how does it work?

Quite so.

Is it an atomic clock that is used in the muon half-life experiment as well, to measure the decay time?

No, it's the fraction of muons that arrive on Earth that is measured. That together with their speed (nearly c) tells us that they "live" longer.

The first experiments to measure time dilation were done by means of the Doppler effect. See:
http://en.wikipedia.org/wiki/Ives–Stilwell_experiment

 

[mangaroosh]

Quite so.

No, it's the fraction of muons that arrive on Earth that is measured. That together with their speed (nearly c) tells us that they "live" longer.

The first experiments to measure time dilation were done by means of the Doppler effect. See:
http://en.wikipedia.org/wiki/Ives–Stilwell_experiment

cheers.

 

[mangaroosh]

I have another pretty basic question.

How does a clock measure the property known as time?

I see time more as a system of measurement as opposed to a property to be measured.

 

[ghwellsjr]

I have another pretty basic question.

How does a clock measure the property known as time?

Any device that operates with a repetitive process and provides a mechanism to count those repetitions can be used as a clock.

A metronome is a device that operates with a repetitive process but it lacks a counter mechanism so it is not a clock. Old mechanical clocks had a similar repetitive process but added a counter consisting of gears and dials to keep track of the repetitions. Normally, an actual clock hides the repetitive process and just displays the result of the counter in some convenient manner. A stopwatch provides a mechanism to display elapsed repetitions between two events. A timer is similar in that it counts backwards from a preset number of repetitions and provides an alert when the count reaches zero. A watch provides a mechanism to set it to some arbitrarily established convention for keeping track of absolute time.

When discussing relativity, we often imagine an ideal clock that keeps perfect time such as a light clock where an imagined packet of light energy bounces back and forth between two rigidly fixed mirrors but this is really a metronome because it lacks a counter. It also lacks a mechanism for the light to continue forever so we really need a mechanism to regenerate the light at the location of one mirror. But we imagine that somehow these devicits are taking care of and we don't worry about it.

I see time more as a system of measurement as opposed to a property to be measured.

If you couldn't measure the property of time with some system, then it wouldn't be a characteristic qualifying to be dealt with by science.

 

[mangaroosh]

Any device that operates with a repetitive process and provides a mechanism to count those repetitions can be used as a clock.

A metronome is a device that operates with a repetitive process but it lacks a counter mechanism so it is not a clock. Old mechanical clocks had a similar repetitive process but added a counter consisting of gears and dials to keep track of the repetitions. Normally, an actual clock hides the repetitive process and just displays the result of the counter in some convenient manner. A stopwatch provides a mechanism to display elapsed repetitions between two events. A timer is similar in that it counts backwards from a preset number of repetitions and provides an alert when the count reaches zero. A watch provides a mechanism to set it to some arbitrarily established convention for keeping track of absolute time.

When discussing relativity, we often imagine an ideal clock that keeps perfect time such as a light clock where an imagined packet of light energy bounces back and forth between two rigidly fixed mirrors but this is really a metronome because it lacks a counter. It also lacks a mechanism for the light to continue forever so we really need a mechanism to regenerate the light at the location of one mirror. But we imagine that somehow these devicits are taking care of and we don't worry about it.

I understand that a "device that operates with a repetitive process and provides a mechanism to count those repetitions can be used as a clock", but I don't see how that repetitive process measures the propery called time; that is, I don't see how a clock measures the property called time.

I can see that the repetitive process can be used as a unit of comparison, but can't see how it is a unit of the property called time.

If you couldn't measure the property of time with some system, then it wouldn't be a characteristic qualifying to be dealt with by science.

That's what I was thinking.