Michelson experiment

[Lammaite2]

Can someone explain, please. I stuck on some problem related to Michelson Morley experiment.

 

The transverse signal travel time was initially calculated by Michelson as 2L/c and later corrected as if the signal travelled along the arms of a triangle: start point – mirror – new position of start point. This correction adds further to expected time difference of light signals: the transverse and the parallel to Michleson’s apparatus movement direction. This is also explained on animated graphic on Wikipedia http://en.wikipedia.org/wiki/Michelson_Morley_Experiment

 

It is presented as a missile (red dot) travelling transverse to the direction of Michelson’s apparatus. It shows speed transverse to apparatus direction © as well as … speed the same as the speed of the apparatus (!).

 

I do not understand that. The prime assumption of the Michelson’s experiment was the light travels with constant speed c (as a wave in a medium, e.g. sound in the air) in the eather (eather is the reference). From that, I would think the signal (missile, red dot) should not have any speed parallel to the speed vector of the apparatus. It was expected independent from the speed of the emitter.

 

If the light was reflected on the first mirror (the splitting mirror) in every direction than the particular signal travelling at certain angle would arrive at “meeting point” in its new location (with a phase delay of course). Yet, as I understand the light was a beam (could be a laser now) directed transverse to apparatus speed vector.

 

 

[swansont]

The apparatus is not assumed to be traveling at c. It's traveling at some speed v << c.

[Lammaite2]

The apparatus is not assumed to be traveling at c. It's traveling at some speed v << c.

 

I said that. Tha apparatus is travelling with some speed v (in relation to the hypothetical aether) much lower than c. My question was why on the Wikipedia animated explanation of the time delay between the transverse and parallel signals the transverse signal is shown as having this speed v? Generally, I do not understand your answer. Please be patient in explaining to me.

[swansont]

OK, I misunderstood your objection that "the signal (missile, red dot) should not have any speed parallel to the speed vector of the apparatus."

 

It is assumed in the diagram that one arm is perpendicular and one along the direction of motion wrt the ether. If the ether exists, the light will have different speeds in each direction, because the light will change speed relative to the apparatus in the motion along the parallel arm (the diagram on top of the animated gif), or, looking at it in the ether frame, the travel distance is different owing to the motion (shown in the gif). The math is worked out on the wikipedia page.

[derek w]

I am not sure that I understand the thinking behind the michelson-morley experiment?

If all sub-atomic particles display wave/particle duality in the double slit experiment,why would light be assumed to be travelling across space or an aether differently to any thing else?

[Lammaite2]

OK, I misunderstood your objection that "the signal (missile, red dot) should not have any speed parallel to the speed vector of the apparatus."

 

It is assumed in the diagram that one arm is perpendicular and one along the direction of motion wrt the ether. If the ether exists, the light will have different speeds in each direction, because the light will change speed relative to the apparatus in the motion along the parallel arm (the diagram on top of the animated gif), or, looking at it in the ether frame, the travel distance is different owing to the motion (shown in the gif). The math is worked out on the wikipedia page.

 

Thank you very much. If you still have some patience.... As you see the question still remains unanswered. Why the "red spot" speeds together with the apparatus? I do not have problem with the maths. I have problems with the assumption related to the transverse signal. Let me try again. The propagation of wave (light) is independant on the source both speed and direction. This is how I understand constant c. Similar to the water wave from any disturbance: e.g. fast ship or slow ship does not matter. The wave speed is related to properties of the medium (water, aether, space itself as suggested by some). So, once the light wave is reflected from the splitting mirror it should be "left behind" because the mirror travels with the speed v. This is not what is shown on the Wikipedia gif. Apparently the red dot acquired the additional speed equal (magnitude and vector) to the speed of the apparatus in addition to the speed c transverse to the apparatus movement. Rightly, the blue dot travelling parallel to the apparaus direction did not acquire any additional speed. This is why t1*c=L+t1*v (forward) and t2*c=L-t2*v (back).

 

From that point of view also the further reasoning of the path of the transverse signal along the arms of the triangle is unclear to me. On other forum someone suggested the light signal travels at angle. In that case I would accept that some signal travelling at certain particular angle will reach the "meeting point" in its new position. However, this does not convince me because I understood the light was a beam, or even a laser beam in modern versions of the experiment. I would appreciate from you some comment on that. Was the light signal limited just to transverse beam or it can be assumed as propagating radially from the reflecting mirror?

 

I do not think the whole thing is erroneous. I am just trying to comprehend this in details instead taking for granted. Also, there must some deal of difficulty with the transverse signal since the initial time of that signal was 2L/c (by Michelson) and later changed to 2l/(c(sqrt(1-v2/c2)).

[swansont]

 

Let me try again. The propagation of wave (light) is independant on the source both speed and direction. This is how I understand constant c.

When the M-M experiment was conducted, that was not the assumption. It was assumed that light had a speed relative to the ether, which was the preferred rest frame of the universe. The gif is showing what should happen if that view were correct: it predicts a fringe shift, which we do not see.

[Janus]

 

Thank you very much. If you still have some patience.... As you see the question still remains unanswered. Why the "red spot" speeds together with the apparatus? I do not have problem with the maths. I have problems with the assumption related to the transverse signal. Let me try again. The propagation of wave (light) is independant on the source both speed and direction. This is how I understand constant c. Similar to the water wave from any disturbance: e.g. fast ship or slow ship does not matter. The wave speed is related to properties of the medium (water, aether, space itself as suggested by some). So, once the light wave is reflected from the splitting mirror it should be "left behind" because the mirror travels with the speed v. This is not what is shown on the Wikipedia gif. Apparently the red dot acquired the additional speed equal (magnitude and vector) to the speed of the apparatus in addition to the speed c transverse to the apparatus movement. Rightly, the blue dot travelling parallel to the apparaus direction did not acquire any additional speed. This is why t1*c=L+t1*v (forward) and t2*c=L-t2*v (back).

 

From that point of view also the further reasoning of the path of the transverse signal along the arms of the triangle is unclear to me. On other forum someone suggested the light signal travels at angle. In that case I would accept that some signal travelling at certain particular angle will reach the "meeting point" in its new position. However, this does not convince me because I understood the light was a beam, or even a laser beam in modern versions of the experiment. I would appreciate from you some comment on that. Was the light signal limited just to transverse beam or it can be assumed as propagating radially from the reflecting mirror?

 

I do not think the whole thing is erroneous. I am just trying to comprehend this in details instead taking for granted. Also, there must some deal of difficulty with the transverse signal since the initial time of that signal was 2L/c (by Michelson) and later changed to 2l/(c(sqrt(1-v2/c2)).

Okay, I think I know what you are getting at. In the animation showing what one would expect if there was an aether, it shows the red dot moving to the right with the apparatus instead of just straight up and down in the image frame. You are correct that this is what would happen in this situation. The animation does not show this because at the relative apparatus speed to light speed used, it would show the red and blue dots offset considerably and this is not the point they were trying to demonstrate. If you were to actually run this experiment at that high a fraction of c, and there was an aether to measure, the mere fact that the transverse beam misses its mirrors would be evidence of the Aether

 

With the actual M&M experiment, the speed of the apparatus with respect to the expected aether was small enough that it wasn't expected to have an appreciable effect. The offset caused by the movement of the apparatus would have been so little that the two beams would have still overlapped for the most part and produced an interference pattern.

 

Of course, the real experiment showed no offset or phase shift.

[Lammaite2]

If you were to actually run this experiment at that high a fraction of c, and there was an aether to measure, the mere fact that the transverse beam misses its mirrors would be evidence of the Aether

Thanks again. This explains very much. Unfortunately the animated gif in Wikipedia actually is confusing and contradicting the experiment assumptions.

 

This is the same as with the disturbance (say a point) on the water surface. The wave (in that case radial) moves in all directions with the same speed never mind what is the speed and direction of the disturbance point. The same should be with the red dot once it is generated (reflected) as a disturbance in the aether.

 

Your statement (quote) is what I thought. The red dot actually would never be able to reach the "meeting point" with the blue dot.

 

As I remember one of the proposed explanation of the paradoxical result of MM experiment was a "drag of the aether together with the Earth (MM apparatus)". In such a case both the red and blue dots would acquire additional speed equal to the speed of aether.

 

Please correct me if I am wrong. From what you are saying I understand the width of the transverse signal (width of the beam) causes that its relative movement backward from the apparatus is negligible. Also, the light reflects from the mirrors at range of angles (not just one missile - red dot on a transverse trajectory), hence a signal that reflects at very certain angle travels along arms of the triangle to hit the mirror in its new position, hence the mathematics behind 2*L/(c*sqrt(1-v2/c2)) instead of 2*L/c? How is that all working with laser beam? I would appreciate your help. That would be the last bit that is tormenting me.

[swansont]

Your statement (quote) is what I thought. The red dot actually would never be able to reach the "meeting point" with the blue dot.

 

It's not supposed to. The difference in their position is indicative of a phase difference between the two beams, i.e. one has a longer path than the other.

[phyti]

Doubting my own interpretation, my question is the same as the op. If light speed is independent of the source, how does it aquire a horizontal v component when it's directed in a transverse/perpendicular direction?

[swansont]

Doubting my own interpretation, my question is the same as the op. If light speed is independent of the source, how does it aquire a horizontal v component when it's directed in a transverse/perpendicular direction?

 

Same answer as above: the gif represents what would be correct if there were an ether, where light does not have a constant speed independent of the source.

[Lammaite2]

 

Same answer as above: the gif represents what would be correct if there were an ether, where light does not have a constant speed independent of the source.

That answer turns upside down all my understanding. Please help. Here is a quote from Richard Feynman:

"If the apparatus is at rest in the ether, the times should be precisely equal, but if its moving toward the right with velocity u, there should be a difference in times. Lets see why..." And then is the whole simple mathematics based on assumption: light moves in ether with speed c independently to the speed of source both as to magnitude and direction. I.e. the times in horizontal direction come from reasoning ct1=L+ut1 and ct2=L+ut2. So, the gif provided to explain the reasoning to calculate the transverse time shows the same situation when: there is ether and the light has constant speed in relation to ether.

 

The reasoning for the parallel direction is easy. The transverse is still unclear to me. The explanation that light reflects at a range of angles appeals to me yet I am not sure this is the case (can someone recommend some books). I can not agree with the gif showing horizontal component speed of the red dot (light signal) if it is meant as if acquired because the source is speeding.

[swansont]

Reread the explanation given by Janus — if the speed were high enough, you would see an issue, but for an apparatus with a size of order 3m, the offset in the ~10ns of travel time is negligible. At 30 km/sec, that's 0.3mm of offset, i.e. much smaller than the spot.

[Lammaite2]

Reread the explanation given by Janus — if the speed were high enough, you would see an issue, but for an apparatus with a size of order 3m, the offset in the ~10ns of travel time is negligible. At 30 km/sec, that's 0.3mm of offset, i.e. much smaller than the spot.

 

I still do not understand. What you are saying is OK but the experiment should show the same if the Earth travelled with say 200000 km/s. Than the offset would not be a "spot" anymore.

 

I try formulate my question other way;

Looks like the concept behind MM experiment was:

1. calculate time parallel and time transverse like if there was ether, hence the difference

2. compare to the results

 

while the explanation provided looks like is (or I may missed something):

1. calculate the parallel time like if there was ether, and calculate transverse time like there was no ether and assume c is constant for some other reasons and travels the arms of triangle, hence the difference

3. compare to the results

 

Don't shoot me

[swansont]

 

I still do not understand. What you are saying is OK but the experiment should show the same if the Earth travelled with say 200000 km/s. Than the offset would not be a "spot" anymore.

 

No, and you'd have to realign the mirrors, which would be evidence of an ether. But the expected value of our speed was not 200,000 km/s.

 

 

I try formulate my question other way;

Looks like the concept behind MM experiment was:

1. calculate time parallel and time transverse like if there was ether, hence the difference

2. compare to the results

 

while the explanation provided looks like is (or I may missed something):

1. calculate the parallel time like if there was ether, and calculate transverse time like there was no ether and assume c is constant for some other reasons and travels the arms of triangle, hence the difference

3. compare to the results

 

At the time of the MM experiment, the option of no ether wasn't being considered. The experiment was to confirm our motion through it, and the experiment was designed to measure the speed. Both the parallel and transverse motions in the example assume an ether.

[phyti]

If a passenger in a static capsule points a laser vertically, it reflects from the ceiling vertically. If the capsule is moving at .5c, the laser is still supposed to reflect in the same manner per the 1st postulate of SR. The posts I've read say the beam moves at an angle to accomplish this, as viewed by a static observer. I've never seen an explanation as to what causes the angular deflection in terms of physics. As the op says, it is contrary to constant independent light speed, which has much experimental verification.
The question: Is the angle of the beam (or single photon) dependent on speed?

[swansont]

Is the drawing above the animated gif confusing in some way, or are you asking about something else?

[Lammaite2]

 

No, and you'd have to realign the mirrors, which would be evidence of an ether. But the expected value of our speed was not 200,000 km/s.

 

 

At the time of the MM experiment, the option of no ether wasn't being considered. The experiment was to confirm our motion through it, and the experiment was designed to measure the speed. Both the parallel and transverse motions in the example assume an ether.

 

I am risking more and more you will use your big pistol....

Of course, the option of no ether wasn't considered - that means it was assumed for pre-experiment predictions of time travel (both parallel and transverse) like if the light travelled with c independantly from the source speed. Then, why there is the parallel component of speed of the transverse signal shown on the gif and used to formulate the equation? Michelson calculated the transverse time 2L/c and later corrected based on the zig-zag path. What am I missing in reading this explanation both on Wikipedia and in Feynman's lecture?

[swansont]

 

I am risking more and more you will use your big pistol....

Of course, the option of no ether wasn't considered - that means it was assumed for pre-experiment predictions of time travel (both parallel and transverse) like if the light travelled with c independantly from the source speed. Then, why there is the parallel component of speed of the transverse signal shown on the gif and used to formulate the equation? Michelson calculated the transverse time 2L/c and later corrected based on the zig-zag path. What am I missing in reading this explanation both on Wikipedia and in Feynman's lecture?

 

Light was NOT assumed to travel at c independent of the source, it was assumed to travel at c wrt the ether, so if you were in absolute motion then light traveled at some other speed with respect to you. There is a parallel component of the transverse speed because the device is moving wrt the ether.

[altergnostic]

The gif to the right would be true if there was an aether. That was the expectation. That is not what occured. Both beams described their paths at c as if the setup was at rest, like the gif to the left. Both beams were detected at the same instant, so they described their paths at the same speed relative to the detector, not relative to some hypothetical aether, hence different aether theories had to be proposed until Einstein (and others) showed that we didn't need an aether at all.

 

The animation to the right is a false visualization.

[Lammaite2]

"The gif to the right would be true if there was an aether. That was the expectation."

Again, I have difficulty to agree with this statement. If there was an ether, and this was the initial assumption, the speed of light was constant c with reference to ether, and it was independant to the speed of source. This was why the journey to the mirror of the "ahead" signal is calculated c*t1=L+v*t1. It was not calculated (c+v)*t1=L. The signal ahead did not acquire additional speed v.

The same should apply to transverse beam so it could not have any speed parallel to the apparatus. So it could not be "the expectation". The expectation could be the light beam lagging behind and actually never meeting the returning "ahead" signal.

So I still do not understand what is shown on the right gif.

 

I noticed from the posts also confusion of "constant speed of light c" and "independant from speed of the source". I think both of the features are unseparable. Please correct me in my learning. I am taking my understanding from great lecture by Feynman. He says the speed of light is constant and independant form speed of source as much as any other wave e.g. sound in the air. That is why there was expected a delay of the signals in Michelson's experiment. Kill me, but I do not understand how the predicted travel time for the transverse signal was calculated, or rather why the zig-zag path was assumed (as Feynman and Wikipedia say). This important because it looks like all later mathematics in SR is based on that (Lorentz correction and transformation of time) once the predicted times (hence delay) was confronted with the fact of no delay.

 

[swansont]

"The gif to the right would be true if there was an aether. That was the expectation."

Again, I have difficulty to agree with this statement. If there was an ether, and this was the initial assumption, the speed of light was constant c with reference to ether, and it was independant to the speed of source. This was why the journey to the mirror of the "ahead" signal is calculated c*t1=L+v*t1. It was not calculated (c+v)*t1=L. The signal ahead did not acquire additional speed v.

The same should apply to transverse beam so it could not have any speed parallel to the apparatus. So it could not be "the expectation". The expectation could be the light beam lagging behind and actually never meeting the returning "ahead" signal.

So I still do not understand what is shown on the right gif.

 

 

The diagram is pretty clear that the transit time is calculated with c+v and c-v, meaning the signal ahead did acquire the additional speed v when traveling in that direction. In the opposite direction, it is retarded by v.

 

The geometry shows the speed of the transverse beam having both transverse and longitudinal components, with a resultant of c.

 

I noticed from the posts also confusion of "constant speed of light c" and "independant from speed of the source". I think both of the features are unseparable. Please correct me in my learning. I am taking my understanding from great lecture by Feynman. He says the speed of light is constant and independant form speed of source as much as any other wave e.g. sound in the air. That is why there was expected a delay of the signals in Michelson's experiment. Kill me, but I do not understand how the predicted travel time for the transverse signal was calculated, or rather why the zig-zag path was assumed (as Feynman and Wikipedia say). This important because it looks like all later mathematics in SR is based on that (Lorentz correction and transformation of time) once the predicted times (hence delay) was confronted with the fact of no delay.

 

It was calculated using t = distance/speed The distance is L, and the speed is c+v or c-v, depending on the direction of travel.

[phyti]

Accepting length contraction as an explanation for equal transit times in x and y, and no ether influence, consider the light clock. Observer A sees/is aware the photon oscillates vertically between mirrors. If the clock moves horizontally relative to A, and the clock continues to work for B who moves with the clock, how does the light/photon aquire a horizontal speed component (the zigzag path)? The 1st postulate states that B should see the same result as A for all speeds less than c.

Edited December 11, 2012 by phyti

[altergnostic]

We can't bring length contraction to this thread because this would be a post hoc solution, and the op seems concerned about the expectations at the time of the experiment, even before the experiment was even performed.

 

I have to agree with the crticism... It seems that the animation doesn't follow from the assumption that light travels at c relative to the aether.

 

Here is the original paper from Michelson:

http://www.aip.org/history/gap/Michelson/Michelson.html

 

On page 5, I think we can find where the problem comes from. There we find the times being calculated by dividing the distance (as measured from the interferometer's frame) over the addition of velocities (as measured from the aether's frame). They were conflating numbers from different frames! The distance D should be a distance as seen from the aether, which should be D +- Vt !!!

 

Holy s***!