Very precise Michelson-Morley experiments

[wmikewells]

I have read that very high precision attempts to confirm the constant speed of light in all directions have been successful. For example in 2009, Stephan Schiller's lab was able to achieve a precision level that was one hundred millions times more precise than the original Michelson Morley experiment. Here is the link to the article:

http://physicsworld.com/cws/article/news/2009/sep/14/michelson-morley-experiment-is-best-yet

I am trying to understand the level of precision the article talks about. I am assuming that improvements have been made in the last six years, but I wanted to convert the numbers into velocity. For example,

"Schiller's experiment is sensitive to eight of these parameters and the team was able to show that four are zero to about two parts in 10^17; one is zero to about one part in 10^16; and three are zero to about two parts in 10^13. According to Schiller, this represents a factor of more than 10 improvement over previous measurements of these parameters and a factor of about 100 million better than Michelson and Morley's original experiment"

According to the article, such precision is important to test some quantum gravity theories and to detect dark energy. The parameters talked about in the above quote refer to nineteen measurable Lorentz symmetry parameters (not that I know what those are).

So here are my questions:

1. Is it a simple matter of dividing the speed of light by the factors such as 10^17 to get the precision in terms of velocity?
2. Schiller's apparatus was suspended on air, so I assume that both light rays remained parallel to the Earth's surface during rotation. Have similar attempts at precision been made for light rays that rotate between horizontal and vertical?
3. If so, what precision was attained in those experiments?

I know that the orientation shouldn't matter. I have seen a Youtube video that purports to show a change in the speed of light for a vertical orientation using off the shelf equipment, but another Youtube video showed that the flimsiness of the equipment was to blame. So the lesson there is that only professionals should make the attempt. However, it just seems that to be thorough, both orientations should be tested.

 

[SlowThinker]

1. The precision would be better viewed as ##10^{-12}##. Also it does not really measure the speed of light. It measures the difference in speed between 2 directions - and finds that they are the same to at least 12 decimal places.
2. We know the vertical speed is different, because the time runs faster at higher altitudes. But we can repeat the experiment at different times of the day or year, so we can explore the Universe in any direction.

 

[wmikewells]

Quote from SlowThinker:
"1. The precision would be better viewed as 10−12. Also it does not really measure the speed of light. It measures the difference in speed between 2 directions - and finds that they are the same to at least 12 decimal places."

That is what I figured. So if the factor is 10^-12, then the speed of light would be precise to plus or minus 3.0 mm/s in perpendicular directions.

Quote from SlowThinker:
"2. We know the vertical speed is different, because the time runs faster at higher altitudes. But we can repeat the experiment at different times of the day or year, so we can explore the Universe in any direction."

Are you sure about the speed being different at different altitudes? I may have understood what your are trying to say, but even in a gravitational field, the speed of light is constant no matter what direction the light is going in. Rotating the apparatus in the horizontal plane at different times of the day or year would be useful for testing the constant speed of light relative to the universe. However, rotating in the vertical plane would be useful to make the test relative to the Earth. I would think that both tests would shed light on alternative theories and could be used to either confirm or invalidate them.

 

[SlowThinker]

Are you sure about the speed being different at different altitudes? I may have understood what your are trying to say, but even in a gravitational field, the speed of light is constant no matter what direction the light is going in.

The speed of light is constant locally (close to you), not when viewed from a distance.
Say we set a series of beacons in a straight line, and each of them flashes when the light from the previous beacon reaches it. To us, it will look as if the flash travels with the speed of light.
But if this is done in a strong gravity field, and viewed from far above, the flash will seem to travel slower - because the time runs slower down there.
Another situation is 2 parallel photons, one passing through a hole in a planet, the other going far away. The one passing through the hole (higher gravitational potential) will need more time than the one going through the weak field.

Now it goes like this. Let's have a tall tower, with a long horizontal arm. First, the arm is at Earth surface, and we send 2 rays.
One goes to the arm, hits a mirror and comes back. The other goes straight up, hits a mirror and comes down. We find the height where the times are equal. Then the height is, in fact, higher than the length of the arm, because the vertical ray spends some time at higher altitude.
Now we move the arm up to this altitude, and put a mirror at the tower's base. Now the time through the arm will be shorter than the time down and up. This is because the vertical ray spends some time at lower altitudes.
That experiment is similar to 2 arms being rotated, except it's better. So even in principle, we know that the results will be different. The difference can be computed, but that defeats the purpose of the experiment...

 

[wmikewells]

Let me get this straight. Are you saying that a Michelson Morley experiment rotated in the vertical plane will show a difference in the speed of light (the interference fringe will move if lasers are used) even in a low precision case?

 

[Dale]

However, rotating in the vertical plane would be useful to make the test relative to the Earth. I would think that both tests would shed light on alternative theories and could be used to either confirm or invalidate them.

Earth centered theories have been out of favor since the days of Copernicus.

 

[SlowThinker]

Let me get this straight. Are you saying that a Michelson Morley experiment rotated in the vertical plane will show a difference in the speed of light (the interference fringe will move if lasers are used) even in a low precision case?

Yes, but... the actual difference is about 10^-15 in a 20-meter tower, so perhaps it's more of a technical problem to rotate the device without deformation.

Also note that if you had small speedometers measuring the speed of light along the vertical path, they would all show ##c##.

 

[jtbell]

Note that here we're getting into the realm of General Relativity (spacetime curvature associated with gravity), in which the "average" speed of light between two points is not necessarily c, even though the "local" speed of light is c at all points.

 

[wmikewells]

Earth centered theories have been out of favor since the days of Copernicus.

I hope you don't think that I believe in Earth centered theories. Any planet would do (that is poor attempt at a joke). My expectation would be that a Michelson-Morley experiment rotated on the vertical would not show a differential. I was just wondering if any more precise experiments have been done than what I saw on Youtube (I can find the link if need be). My guess is that none have been performed because no one would take them seriously. But if anyone has heard of one, that would be great too.

And just to be clear, I am not a proponent of what you call the Lorentz Ether Theory (LET) in your insight article. The alternative theories I was referring to in my original post above were string theory, loop quantum gravity theory, and possibly shape dynamics. There are probably a few others that I have not heard of that could be considered serious candidates for unifying quantum mechanics and gravity.

I figure that something in GR has got to give in order to make the unification. So why not look in places nobody has looked before to try and find anomalies.

 

[Nugatory]

I don't see that we need to invoke general relativity to have an interesting question. All we need is the equivalence principle: what are the results of an M-M experiment conducted in a spaceship accelerating at 1g, when the arms are oriented parallel to and perpendicular to the direction of acceleration?

I would expect the tidal effects from the non-uniformity of the Earth's gravity to be well and thoroughly negligible on the scale of a M-M experiment performed in a lab on the Earth's surface. Thus, we can safely rely on the equivalence principle here and treat this as a flat spacetime problem.

 

[SlowThinker]

While the tidal effects are negligible (so we don't need GR), the time dilation is quite close to the precision of the experiment.

The altitude-dependent time dilation happens even in the accelerating spaceship: it's easy to see that there is Doppler shift in the rocket, and that implies time dilation.

 

[Nugatory]

The altitude-dependent time dilation happens even in the accelerating spaceship: it's easy to see that there is Doppler shift in the rocket, and that implies time dilation.

Of course the altitude-dependent time dilation happens in the accelerating spaceship; that application of the equivalence principle is how gravitational time dilation was discovered in the first place.

But because this is an M-M experiment it's a round trip, with redshift happening on the upwards leg and blueshift happening on the downwards leg. Which effect dominates, or do they cancel? Time to calculate...

 

[wmikewells]

Yes, but... the actual difference is about 10^-15 in a 20-meter tower, so perhaps it's more of a technical problem to rotate the device without deformation.

Also note that if you had small speedometers measuring the speed of light along the vertical path, they would all show ##c##.

Boy, am I glad I asked my question. I thought it would be a trivial "no" and that you were pulling my leg. I will have to re-read your comments and the others to see if I can understand what is going on.

 

[DrGreg]

Here is a spacetime diagram to show why accelerated observers don't measure the correct value for the "vertical" (2-way) speed of light, when averaged over too long a distance.

The solid red line is the observer, the solid blue line a mirror vertically above, the green line is light reflected off the mirror. It is viewed from the inertial frame in which the mirror is momentarily at rest at the time of reflection. The pink lines are the observer's Rindler coordinates.

The dotted lines indicate the same experiment carried out by an inertial observer. It should be clear from the diagram that the light takes a shorter time for the accelerated observer compared with the inertial observer, to cover the same distance according to the respective observers.

The difference in times tends to zero as the distance between the red and the blue tends to zero, so the accelerated observer will get the correct value for c in the limit.

All of the above is in flat spacetime, i.e. no gravity other than the "pseudogravity" caused by acceleration. In the presence of gravitation there will be some additional tidal effects.

 

[Dale]

My expectation would be that a Michelson-Morley experiment rotated on the vertical would not show a differential.

My expectation would be the opposite. You have to realize that at the incredible precision of current experiments, even very small deformations in the apparatus can skew the results.

So when you are designing the equipment for such experiments you have to think of them as though they were made of Jello. I would expect that any non horizontal arrangement would squeeze the Jello into a distorted shape.

Anyway, the test theory used in this experiment, the SME, already includes all possible Lorentz violating terms. This one experiment cannot fix all of the SME parameters, but I believe that all of them have been investigated by one experiment or another at this point. I tried to look up a list of all of the parameters and their current constraints, but couldn't find one.

 

[wmikewells]

Anyway, the test theory used in this experiment, the SME, already includes all possible Lorentz violating terms. This one experiment cannot fix all of the SME parameters, but I believe that all of them have been investigated by one experiment or another at this point. I tried to look up a list of all of the parameters and their current constraints, but couldn't find one.

Thanks for trying. The SME (standard model extension) parameters are a little too esoteric for me anyways. I tried to read an introductory paper on SME, but got lost after the first paragraph. The only thing I understand is the difference in velocity. I did some quick math to get a feeling for the sort of scale that is being talked about. If we are talking about a 10^-15 precision factor (and my math is correct), that is like traveling 7.5 times around the Earth (I am partial to Earth) and detecting a difference in length of a small bacteria, ten times smaller than a human blood cell. That is truly amazing. I could see how that sort of precision could be used to test alternative theories.

 

[wmikewells]

I did a little searching around and may have gotten lucky. Here is a paper with a bunch of precision tables in it that relate to SME. It is a little old (2010), but better than nothing. The article is titled "Data Tables for Lorentz and CPT Violation" by V. Alan Kosteleck and Neil Russell. Here is the link:

http://arxiv.org/pdf/0801.0287v3.pdf

"This work tabulates measured and derived values of coefficients for Lorentz and CPT violation in the Standard-Model Extension. Summary tables are extracted listing maximal attained sensitivitiesin the matter, photon, and gravity sectors. Tables presenting definitions and properties are also compiled."

The internet is a wonderful thing. Please don't ask me to translate any of it to plain English.

 

[wmikewells]

That experiment is similar to 2 arms being rotated, except it's better. So even in principle, we know that the results will be different. The difference can be computed, but that defeats the purpose of the experiment...

So when you are designing the equipment for such experiments you have to think of them as though they were made of Jello. I would expect that any non horizontal arrangement would squeeze the Jello into a distorted shape.

In theory, would the experiment SlowThinker proposed several posts back, get around the "Jello" effect and still validate (or invalidate) the calculated difference DrGreg's diagram above illustrates? Not that the experiment would ever get beyond a thought experiment stage.

 

[wmikewells]

Yes, but... the actual difference is about 10^-15 in a 20-meter tower, so perhaps it's more of a technical problem to rotate the device without deformation.
.

Just one more post of thinking out loud, and then I am done.

In thinking about SlowThinker's experiment, I was coming up with ways to make it less Jello-like. If a horizontal arm was added to the top, would it be possible to sync it up with the horizontal arm at the bottom, so they are to a high degree of precision the same length? That way the bottom arm would not need to be moved, which would most likely mess things up and introduce error. Probably not, though, since the syncing up process would probably also introduce error. Oh well.

 

[SlowThinker]

If you tried really hard, it would probably be possible to measure the low arm and the high arm at the same time, perhaps using two colors of light.
But I don't really see how it could result in not confirming the expected result: We can measure the Universe in any direction, and the change in vertical speed has been confirmed many times since Pound-Rebka experiment. Combining the two leaves little room for surprise.

 

[wmikewells]

If you tried really hard, it would probably be possible to measure the low arm and the high arm at the same time, perhaps using two colors of light.
But I don't really see how it could result in not confirming the expected result: We can measure the Universe in any direction, and the change in vertical speed has been confirmed many times since Pound-Rebka experiment. Combining the two leaves little room for surprise.

Adding an extra arm was just my naive way to reduce the amount of movement that would be required to complete the experiment. I am guessing that the more movement there is (rotation or re-positioning), the more error that would be introduced that would have to be accounted for. I didn't have any great insight that led me to that idea.

Thanks for the reference to Pound-Rebka. I did a quick read to see if I could understand it. I guess I am more of a nuts and bolts kind of guy. I could understand what they were going for. The hard part was isolating the gravitational part from the special relativity part to get a good read on the gravitational red-shift. I can see that the experiment you proposed was along similar lines - to measure the time difference between the ground level and the twenty meter high platform.

So, with a little more under my belt, I am able to ask my original question more intelligently.

Has anyone attempted to precisely measure the difference in the local speed of light between horizontal and vertical orientations and was a difference found?

That experiment would be the exact opposite of Pound-Rebka. Instead of trying to isolate and measure the general relativity effects, the general relativity effects would have to be eliminated to get an accurate read. Also, a large tower would not be needed. I am guessing that yes someone has performed this experiment to a high degree of precision (<10^-14) and that no a difference in the local speed of light was not found.

Thanks for putting up with my learning curve and thanks everyone with providing some great examples and a concise diagram.

 

[Dale]

Has anyone attempted to precisely measure the difference in the local speed of light between horizontal and vertical orientations and was a difference found?

How would you do that? Specifically, how would you determine the height of your apparatus ?

 

[wmikewells]

How would you do that? Specifically, how would you determine the height of your apparatus ?

I am not sure what you are asking. However, if I were to design the experiment (which is a scary thought), I would shorten the arms to reduce the effect of the gravitational red-shift. I would think there might be a sweet spot where the effects of the gravitational red-shift would be negligible (one meter?), and the arms would be long enough to still get a useful reading from whatever M-M apparatus was used. Or maybe the red-shift would not even need to be considered because it is a round trip, so it does not matter how long the arms are. And instead of putting the experiment on an air-elevated horizontal flat slab, I would put it on a huge stone ball larger than a meter across. I saw such a ball at the Seattle science museum. Granite was used in that case. Pumped in water was used to suspend the ball in a shallow cup that holds the ball in place and makes it roll nearly friction-less. I suppose air could be used but the cup would probably have to be deeper. A sturdy flat platform would also have to be attached to one side to hold the M-M apparatus along with a corresponding counter weight. That way the M-M experiment could be mounted vertically and rotated in the vertical plane. This is probably not what you were asking for, though, so I will stop here. It sounds as if I am missing something crucial.