B Measuring Michelson–Morley light beams

[P J Strydom]

I was away for a few months and thought I might pose this thought I am working on, on this forum when I return.
There was a very help full person who assisted me in the finer explanation of the Lorenz transformation a few months ago, and I really learned a lot about SR and GR.
A few weeks ago, I thought to myself, Myself, can one measure the path the light beams on the Michelson Morley inferometer?
I played on Google and found some beautiful mathematical equations that could actually show the expected difference in length if a light beam when split and sent in opposing directions as what MM at first anticipated.

Then I thought, what if I follow the paths and measure the length and time and see if I can get a difference that might explain why MM did not find the fringe interference.

Now, it is a fact that I am not a scientist, but I would like to know what you guys think about my calculations.
The simple way math of coarse.
Michelson Morley's contraption allowed a 11 m path for the light to travel.
I decided to make it 12 m for ease.
This will give us a pathway for Beam A to travel 3m up to the beam splitter, 3m Left to the mirror, 3m right to the beam splitter again, and 3 m right to get to the end.
Beam B will travel 3 M Up, and 3 m up, and 3m down, and 3m right.
Therefore, if there is no (theoretical) movement on the contraption, the beams A and B will travel 12m each.
this will result in each beam traveling at 0.00000001 sec from start to finish.

However, when we assume that the contraption is moving at say 340Km/sec (Earth moving in space)in the parallel direction of Beam B, things started to get interesting.
Beam A was traveling Up = 340000m/s+3m/s
This gave a time of 0.00113334333 UP
I had to calculate using Pythagoras the distance of 3m sq+340000m sq= sqr root to get the distance the light would travel from the splitter mirror to the left mirror
this gave a distance of left=340000.000013235 m
Time traveled = 0.00113333333 sec.
The same distance will go for the Right and Right to arrive at the end.
The totals is as such for A
Up = 340003m/s time 0.00113334333s
Left = 340000.000013235 m time = 0.00113333333 sec
Right = 340000.000013235 m time = 0.00113333333 sec
Right = 340000.000013235 m time = 0.00113333333 sec

Therefore, the total time traveled for A was
1 360 003.00 m 0.00453334333 sec

B traveled
Up = 340003m/s time 0.00113334333s
Up = 340003m/s time 0.00113334333s
Down = -339 997.00 m time -0.00113332333 (this is a huge mistake because it would mean that the light beam arrives at the mirror, before it was reflected from the splitter)
Right = 340000.000013235 m time = 0.00113333333 sec

Therefore B traveled 680 009.00 m Time 0.00226669667 sec.
But looking at the problem we have on beam B when it reached the top of the path, and had to return back to the splitter to deflect it to the end, I decided to increase Michelson Morley's contraption to one c.
We made it 300 000 (theoretical c for this purpose)Km wide.

This made it work much better.
Beam A traveled
Up 1.00113333333 Sec 300 340 000.00 m
Horizontal 1.00000064222 Sec 300 000 192.67 m
Horizontal 1.00000064222 Sec 300 000 192.67 m
Horizontal 1.00000064222 Sec 300 000 192.67 m
Total 4.00113526000 Sec 1 200 340 578.00 m

Beam B traveled
Up 1.00113333333 Sec 300 340 000.00 m
Up 1.00113333333 Sec 300 340 000.00 m
Down 0.99886666667 Sec 299 660 000.00 m
Horizontal 1.00000064222 Sec 300 000 192.67 m
Total 4.00113397556 Sec 1 200 340 192.67 m

Now I am thinking.
If I worked the path and time out correct, using an inferometer with a width of 600 000 Km, and there is a difference of 0.0000012844 sec, will there be any fringe interference visible?
This is a addition of 0.0000000007645500% on yellow light at 540THz.

I then thought, let's go for 0.5c on the movement of the Earth and look at that difference.
The difference between A and B is now 0.2360679775 sec.
This will give a difference of 0.0001405166532737% on the wave of 540THz.

I explicitly wanted to get away from well known formulas, and do it as simple as possible.

Does this not say that MM would not have seen interference at all?
I hope my thinking was correct.

 

[Nugatory]

In problems of this sort, it's a good idea to do the algebra first to get the general formula (in this case, the travel times and distances for the two paths as functions of $D$ (the arm length), $v$ (the hypothetical speed through the ether) and $c$. You can check that for reasonableness (for example, does your formula show the travel time increasing with $D$?) and dimensional consistency, and only after you're sure you have the formula right should you plug in numbers to get a quantitative result.

Google for "Michelson Morley calculations" and you'll find several good examples of this problem being worked. Bear in mind that an interferometer will easily detect differences that are a fraction of a single wavelength, and you'll find that the MM experiment is quite sensitive enough to justify the claim of a negative result.

 

[P J Strydom]

I explicitly tried to work around mathematical formulas, and thought that if I could calculate the path of a beam split as the MM experiment, by actually measuring each increment from the beam to splitter, and splitter to mirror, and along the 2 different paths, back to the splitter and ending in the interference splits, I might see the picture on the reason why the inferometer did not show deviations.

Please, I might be a fool in science, but I just love these scientific interpretations on the speed of light and time dilation etc.
This is why I want to see the calculations in a more practical format.

Perhaps you might be able to tell me if I was wrong with my measurements?
Thank you for your input.

 

[P J Strydom]

(for example, does your formula show the travel time increasing with DDD?)

What I did was to take the distance to the left and right, squared it, and added it to the distance of movement ahead, squared, and with square root came to the distance the beam supposedly had to travel to get to the reflecting mirror, and back to the splitter, and then to the end.
a normal Pythagoras calculation.
Am I correct in my assumption?

 

[Nugatory]

a normal Pythagoras calculation.
Am I correct in my assumption?

That's the right general approach.

If you work through the algebra instead of plugging in the numbers from the start you will find that the difference in the length of the two paths is approximately $Dv^2/c^2$. With $D$ equal to 11 meters and $v$ set to the orbital speed of the Earth that works out to about 100 nanometers, easily detectable by an interferometer working with visible light. https://hepweb.ucsd.edu/ph110b/110b_notes/node40.html is a pretty good explanation.

 

[P J Strydom]

Thank you.
I will go and learn more.

 

[P J Strydom]

I see the assumption in this experimental measurement is to only measure from the splitter mirror to the reflecting mirror and back.
There is no measurements for
1. the light source to the splitter,
2. and a measurement from the splitter mirror to the telescope.
This simplifies the measurements a great deal.
Am I correct?
(Sorry, I will be a pesky itch until I feel I mastered the Lorenz transformation, and the MM experiment is the foundation to it all.)

 

[Nugatory]

I see the assumption in this experimental measurement is to only measure from the splitter mirror to the reflecting mirror and back.

Yes, because those are the only distances that affect the difference between the lengths of the two paths.

until I feel I mastered the Lorenz transformation, and the MM experiment is the foundation to it all.

The Lorentz transforms folllow from the invariance of the speed of light. The MM experiment is just one of many that demonstrate that invariance. For more, you can try section 3 of http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html (which is also linked in a sticky post at the top of this forum).

 

[P J Strydom]

I spent some of my private time and went through the calculations on the expected Aether difference MM thought they would be able to measure, between a light beam traveling parallel to supposed Aether, and again a light beam traveling perpendicular to the Aether.

Now, there are a few thoughts I would like to clarify before I can continue.

1. the beam traveling parallel will take longer to return, than the beam traveling perpendicular to the Aether.
----this means the beam traveling perpendicular to the aether, was expected to arrive back on position first. followed by the one in parallel to the aether.
2. the difference is canceled out due to the length that contracts as the Michelson Morley inferometer travels against the aether, thereby squeezing the length of the parallel distance into itself equal to the difference between the beam traveling lengths. This difference is the calculation factor of Lorenz.
3. Due to this Length contraction, a clock that travels parallel with this light beam against the supposed Aether wind, will also run slower. otherwise we will measure the distance to be shorter that the time traveled. Time should also be adjusted accordingly.

It took me a while to summarize it this way.
If I am wrong, please tell me where.

 

[Ibix]

1. the beam traveling parallel will take longer to return, than the beam traveling perpendicular to the Aether.
----this means the beam traveling perpendicular to the aether, was expected to arrive back on position first. followed by the one in parallel to the aether.

Yes

2. the difference is canceled out due to the length that contracts as the Michelson Morley inferometer travels against the aether, thereby squeezing the length of the parallel distance into itself equal to the difference between the beam traveling lengths. This difference is the calculation factor of Lorenz.

This is written with the assumption that the ether exists and awareness of the null result of Michelson-Morley. So this is basically Lorentz and Fitzgerald's explanation for the result. It's not what Michelson and Morley expected, nor is it Einstein's complete understanding. It's relevant to a long-abandoned phenomenological patch to ether theory that ether somehow contracts material bodies passing through it.

3. Due to this Length contraction, a clock that travels parallel with this light beam against the supposed Aether wind, will also run slower. otherwise we will measure the distance to be shorter that the time traveled. Time should also be adjusted accordingly.

I don't think this is correct. In an ether model, I don't think one can naively build a light clock and expect it to keep time except in the ether rest frame. And I don't think it's immediately obvious that all clocks will be affected the same way by motion through the ether. So I'd be inclined to think that trying to bring time dilation into this is opening an enormous can of worms to no purpose. You'd have to end up with something mathematically identical to relativity, which is perfectly happy without an ether.

 

[P J Strydom]

Thank you for your input.
if I may elaborate on my poor understanding of the movement of light through a split mirror as MM did.
1. Why did they claim that the light moving parallel (with the direction of the Earth against supposed Aether) will travel slower to the reflecting mirror and back to the splitter mirror, than the one perpendicular with this movement?
...The way I see it is that the light will travel slower towards the reflecting mirror as it has to work against the Aether, but the return stroke will be quicker and will actually cancel this delay out.
2. I have been thinking about this for a long time and did quite a few measurements, and find that as the retarded length took longer, the advanced length is shorter by the exact time, but averages out equally to if the time it took to travel longer to the mirror, is equal to the time the return stroke took to travel shorter.

3. In my mind, If I may commute my thoughts, the light beam traveling at an angle perpendicular to the "aether movement" is the one that will take longer to return to the splitter mirror.

Shaacks, why do I have it the wrong way around?

 

[jbriggs444]

he way I see it is that the light will travel slower towards the reflecting mirror as it has to work against the Aether, but the return stroke will be quicker and will actually cancel this delay out.

If you want to drive from Chicago to Des Moines (call it 300 miles) at speed of 30 miles per hour for half the trip and 60 miles an hour for the other half, what is your average speed for the entire trip?

[Or to phrase it differently: "trust the math, not your intuition"]

 

[P J Strydom]

If you want to drive from Chicago to Des Moines (call it 300 miles) at speed of 30 miles per hour for half the trip and 60 miles an hour for the other half, what is your average speed for the entire trip?

[Or to phrase it differently: "trust the math, not your intuition"]

OK, I think I lost your explanation, but let's see if I understand your explanation if I work through it.
1. I will travel 150 miles at 30 miles an hr Westerly direction.
2. then east to Chicago another 150 miles, but this time at 60 miles per hour.

Answer:
West traveling time = time 5 hrs
East traveling time = 2.5 Hrs.
Total traveling time = 7.5 hours
Average speed 40 miles per hour.

Perhaps I got lost in the understanding of your experiment.

Should you not have said,
1. I will travel in the direction of Des Moines (300 miles away West) at an average speed of 40 miles an hour, but only for 150 miles.
2. and return to direction Chicago (East) which is now 150 miles away at an average speed of 40 Miles an hour?
Now I traveled 300 miles at an average of 40 miles an hour.
I traveled 7.5 hours.

But relative to a satellite observer over the North pole, who observes my position as when I left Chicago...
I will travel West from Chicago's position, but should include the rotation of the Earth.
1. Therefore, I am traveling at 1000 + 40 Miles an hour in an westerly direction.
2. Then back to Chicago at 1000 - 40 Miles an hour in an eastern direction.

Conclusion.
The satellite saw me traveling West as if I was traveling East at 1000-40 Miles per hour.
And when I traveled back to Chicago, It saw me traveling East at 1000+40 miles an hour.
I still traveled 300 miles, even if I was observed from the satellite.

Why will it be different than If I was traveling due south for 300 Miles to Highway 69?
Both will be the same distance, and the speed will also be the same.

Therefore, If I drove west and east, and you south to north, we will arrive at the same time upon return.
If there was this huge wind at 5 miles an hour pushing me back as I drove West and my energy was such that I could only deliver 40 miles an hour, I will slow down to 35 miles an hour, but it will assist me to achieve 45 miles an hour on my return.
You on the other hand will experience no drag or assistance on your speed for the entire journey.
In this instance we will again arrive together.

But this speeds we are talking about is very slow, compared to c, but to me it explains the result.

From the perspective of the satellite, There was a clear difference in the speed I traveled west and east, but the satellite will see us both arrive together.

The question is, if the cars were light beams, what would we see?

 

[jbriggs444]

Conclusion.
The satellite saw me traveling West as if I was traveling East at 1000-40 Miles per hour.
And when I traveled back to Chicago, It saw me traveling East at 1000+40 miles an hour.
I still traveled 300 miles, even if I was observed from the satellite.

OK, let us use your version. How long does it take for the round trip at 1000-40 one way and 1000+40 the other way.
How long does it take for the round trip at 1000 one way and 1000 the other way?

 

[P J Strydom]

In short, it took me longer to travel west, but less to travel east.
If the wind blew east, the reverse will be the result, but the time traveled the same.

Then I thought about the following.
It there was an aether wind interfering with the parallel light beam, the theory would be that the light traveled faster with it in the same direction, and slower upon return.
It will not show any difference when measured with the perpendicular light beam.

Someone that travels on the Michelson Morley inferometer on its "North pole" will also observe that the 2 beams arrived at the same time, even if there was an Aether wind.

I still don't understand why the calculations would say the parallel beam will arrive after the perpendicular beam.

Thanks for your patience.

 

[P J Strydom]

OK, let us use your version. How long does it take for the round trip at 1000-40 one way and 1000+40 the other way.
How long does it take for the round trip at 1000 one way and 1000 the other way?

Are you messing with me?
Please explain why the light beam parallel with the Aether wind would have traveled longer than the one traveling at 90 deg?
I have it the other way around.

 

[jbriggs444]

No, I am not messing with you. I am asking you to do a simple calculation. How much time elapses for a round trip which is slow by 40 mph one way and fast by 40 mph the other way? Does it match with the elapsed time for a round trip which is the same speed both ways?

Possibly we are talking at cross purposes, but I think you are trying to determine round trip time.

 

[Ibix]

The way I see it is that the light will travel slower towards the reflecting mirror as it has to work against the Aether, but the return stroke will be quicker and will actually cancel this delay out.

As @jbriggs444 is trying to get you to calculate, the difference doesn't cancel exactly.

2. I have been thinking about this for a long time and did quite a few measurements, and find that as the retarded length took longer, the advanced length is shorter by the exact time, but averages out equally to if the time it took to travel longer to the mirror, is equal to the time the return stroke took to travel shorter.

Recheck your maths (or post it). You've gone wrong somewhere.

3. In my mind, If I may commute my thoughts, the light beam traveling at an angle perpendicular to the "aether movement" is the one that will take longer to return to the splitter mirror.

Both take longer. The parallel beam takes more longer - a factor of $\gamma^2$ for the parallel beam versus $\gamma$ for the perpendicular one, if my maths is correct.

 

[jbriggs444]

Average speed 40 miles per hour.

Note that 40 is not the average of 60 (45 + 15) and 30 (45 - 15).

 

[P J Strydom]

Damn, I get confused.
Perhaps it is due to me not discussing one point at a time.
Please permit me to do the following.
First, the MM experiment standing still, then influenced by Aether wind.
Which beam will arrive first.

1. Now, if this inferometer is at rest.
And we will assume there is no influence on the light beam such as na aether wind.
= the light beams will arrive at the same time back to the beam splitter.

However, If there is an aether wind and if it blows parallel from the right hand to the left,
2. The light beam will travel against the aether wind to the mirror at c-velocity of aether.
3. but upon its return it will travel at c +Velocity of the aether.
4. but the beam traveling up to the mirror perpendicular to the aether, will be affected by a triangular distance it has to travel, and the same when it travels down to the splitter.
= this is where I might be making my error.
To me it seems as if the beam parallel will travel at the same time as it did when if there was no aether wind.
But the beam crossing the aether wind will take longer.

This is where I am missing out on the logic.
I get the Up-Down beam arriving later, and not before the Left-Right beam.

Jeeeeez I hope you can grasp my stupidity in this thought.
because, everytime I check animations on You tube about this description, they say the Left-Right beam will arrive later.

 

[Ibix]

The travel time for the parallel beam assuming an ether wind of speed $v$ is $$t=\frac{d}{c+v}+\frac{d}{c-v}$$Algebra should give you $$t=\frac{2dc}{c^2-v^2}=2d\gamma^2/c$$Therefore the travel time is longer for all non-zero $v$, since $\gamma$ takes its minimum value when $v=0$.

 

[P J Strydom]

Nice, eventually I got it.
If I was traveling East to West for 150 miles at 50 miles and hour, and back, it will normally take me 6 Hours.
However, if a wind blew at 5 Miles an hour I will be traveling With it for 2.7272...Hours, but Against it for 3.3333...Hours.
Total is 6.0606...
I was silly.
$$t=\frac{d}{c+v}$$ Plus
$$t=\frac{d}{c-v}$$
TNX Ibix

I did not comprehend that the distance will stay the same, due to me thinking in a framework of continious movement of both co ordinates.
I will explain later.
Guys you helped me a lot.

 

[P J Strydom]

And if I work out a traveling distance where I travel perpendicular to the wind,
I will travel a length of 150 Miles square, and 5 miles length square, at the square root of the sum.
Times 2 for the return.
This will result in a total time traveled 6.00332 Hrs.
Shorter than the parallel traveling time of 6.0606...
Great stuff.
Hope I am correct now.

 

[P J Strydom]

Now I am again thinking.
If we change the scenario to no aether wind but we measure the movement of the Earth in relation to the MM inferometer, will the result be the same?

lets call beam A the one parallel with the movement of the Earth around it's axis. (so from the splitter to the mirror, the Earth will move towards the splitter against the light beam.
And Beam B the beam perpendicular to the Earths movement around its axis.

Now we have the light beam traveling to the Mirror, but the mirror moves closer to the light beam shortening the distance.
Once the light beam reflects back, the splitter will move away from the light beam, lengthening the distance to the splitter for the Light beam.
on the beam, B, it will now travel to its mirror and back in a triangular Pythagoras calculation.
Will they arrive at the same time, if not, which one will arrive first?

 

[jbriggs444]

Now I am again thinking.
If we change the scenario to no aether wind but we measure the movement of the Earth in relation to the MM inferometer, will the result be the same?

First of all, you are not measuring the movement of the Earth in relation to the interferometer. You are attempting to measure the motion of the interferometer relative to the Ether.

Now then, why would you expect a moving interferometer in a stationary Ether to behave any differently from a stationary interferometer in a moving Ether?

 

[P J Strydom]

You are right.
I forgot to state that I am stepping away from the assumption that there are an Aether wind.
I am quite contend with that scientific proof.
But then I wondered about the following.

If we were to place an inferometer on the earth, knowing there is no Aether, and we think about the following points.
The Inferometer will move with the Earth with beam A traveling against the rotational speed, but upon return will travel with the rotational speed.
In other words, traveling to the mirror will take longer because the mirror moves away,
But traveling towards the splitter, the beam will meet the splitter as it advanced towards the beam.

I just wonder if this will have the same observation measuring the Earths rotation around the axis, or even around the Sun, or even around the center of the Milky way.

In short, will there be a difference in beam A and B due to the speed of the Inferometer traveling through space?

 

[jbriggs444]

So you have decided to do away with Ether and call it space instead. A distinction without a difference.

Again, I ask: what difference do you imagine between moving in space and space moving past you?

 

[P J Strydom]

If I am correct, it will mean that me moving in space, and space moving past me is one and the same.

However, if the Inferometer was not affected by Aether, will it be affected by its movement through space?
I think of it this way.
If there was Aether, and the inferometer was set up on the afternoon of 21 June, and we take a reading exactly 12 hours later, there would have been double the difference in detecting the aether due to the Earth's rotation. If we wait exactly 6 months later, we would have seen the aether wind at 2X the speed of the Earth around the Sun.
This was not discovered.
Then I thought, if I am allowed to, will we be able to detect the movement of the inferometer through space?
Say as it moves around the Earths' axis, or even around the earth?

We could not detect Aether, but will we detect the advance and retardation of the inferometer through space if light travels within it?
Anyhow, Merry Christmas to everyone.

 

[jbriggs444]

If I am correct, it will mean that me moving in space, and space moving past me is one and the same.

That is the expected Newtonian behavior, yes.

However, if the Inferometer was not affected by Aether, will it be affected by its movement through space?

Are you proposing a thought experiment or a real experiment?

If it is a real experiment, it is pointless. We already know that special relativity works.
If it is a thought experiment, you have to explain the model you are using. That's your responsibility, not ours.

Then I thought, if I am allowed to, will we be able to detect the movement of the inferometer through space?

You have agreed that the interferometer does not detect motion through ether but you still want to use it to detect motion through space? You are going to have to explain how your model for "space" differs from the model of Newtonian mechanics + luminiferous ether. If there is no difference then the negative result has already been obtained and dooms the model.

 

[Herman Trivilino]

If there was Aether, and the intferometer was set up on the afternoon of 21 June, and we take a reading exactly 12 hours later, there would have been double the difference in detecting the aether due to the Earth's rotation. If we wait exactly 6 months later, we would have seen the aether wind at 2X the speed of the Earth around the Sun.
This was not discovered.

There was no observed difference. Whether you include an "aether" or a "space" in the way you explain those observations is up to you. Einstein was able to do it without either. Why anyone would be interested in creating a more-complicated-than-necessary explanation seems to always be traced back to a prejudice about the way Nature ought to behave. It's apparently part of being human, because we've seen even the best of us do it.

Nature dictates how the light beams behave in the interferometer. Humans dictate how to explain the behavior. You cannot affect Nature's behavior by altering an explanation.

 

[Ibix]

If I am correct, it will mean that me moving in space, and space moving past me is one and the same.

True.

However, if the Inferometer was not affected by Aether, will it be affected by its movement through space?

No. Why do I say that? You said it yourself (with two minor changes):

If I am correct, it will mean that methe interferometer moving in space, and space moving past methe interferometer is one and the same.

 

[P J Strydom]

There was no observed difference. Whether you include an "aether" or a "space" in the way you explain those observations is up to you. Einstein was able to do it without either. Why anyone would be interested in creating a more-complicated-than-necessary explanation seems to always be traced back to a prejudice about the way Nature ought to behave. It's apparently part of being human, because we've seen even the best of us do it.

Nature dictates how the light beams behave in the interferometer. Humans dictate how to explain the behavior. You cannot affect Nature's behavior by altering an explanation.

Naw, please note that I find these observations and calculations very interesting, and had huge difficuilties having it explained.
And as I said, I am not the cleverest peanut in the package.
And it is also not a situation where I am attempting to prove or disprove anything.

Look at what I achieved up to so far.
1. I was able to find out that.
a beam traveling into supposed aether, and then with it upon return, will take longer on this round trip than a beam traveling perpendicular to this aether.
2. The distance the "horisontal beam" traveled, will stay the same, no matter how fast the inferometer travels through space, or through this aether.
The beam that traveled perpendicular to the direction of movement of the inferometer, will travel longer distances as speed increases.
3. However, the time the 2 beams will take to do their round trips, will be the same, no matter what speed it travels.
I hope my second and 3rd point of observation is correct.

Note: Now, by asking you simple questions, I learned things I never knew, no, I actually discovered it for myself as we went along.

The next thing that I am still confused about is:
...If the inferometer moves through space.
...the "Horizontal beam" travels at first with the direction of the Earths movement (for instance), then return against this movement.
...and the "Perpendicular beam" traveling across this movement (as we explained)
we know that the "Perpendicular beam" will travel a longer distance than the "Horizontal beam".

Q...(removing all notions of aether) is it true that there will be a difference in arrival times of the light beams, but due to the speed light travels at, it will be a difference of less than a 1% of a fringe, not noticeable by an inferometer?
MM did say he found a difference, but not what he expected.
if I may elaborate on how I came to this.
I took an Excel spreadsheet and entered the distance of MM's inferometer of 12 Meters, the speed of light, the speed of the Earth around its axis, and around the sun, and through space, and it shows that the perpendicular beam will be the retarded one, but by such a small amount, MM would not have seen it.

hey guys, I love this thing called relativity.
I hope I am not boring you all.

 

[Ibix]

Q...(removing all notions of aether) is it true that there will be a difference in arrival times of the light beams, but due to the speed light travels at, it will be a difference of less than a 1% of a fringe, not noticeable by an inferometer?

No. In an ideal experiment, analysed in a frame in which it is moving, both beams will return at the same time. If they do not then there is a way to detect absolute motion and therefore the principle of relativity should not be useful. But it is.

Real experiments do show fringe shifts due to things like temperature variation. Experimentalists control for this kind of thing as best they can, but inevitably there are imperfections. Michelson-Morley showed a slight sinusoidal variation of this type. They reported it, but note that it's not consistent with an ether model given the known speed of light. The kind of statistical analysis to estimate noise levels that is routine today wasn't done back then.

 

[Herman Trivilino]

The next thing that I am still confused about is:
...If the inferometer moves through space.

There is no experiment ever performed or observation made that can distinguish between a state of uniform motion and a state of rest. To say something moves through space is the same as saying it doesn't. A meaningless distinction.

Q...(removing all notions of aether) is it true that there will be a difference in arrival times of the light beams, but due to the speed light travels at, it will be a difference of less than a 1% of a fringe, not noticeable by an inferometer?

Every experiment or observation produces a result that may be off by a small but undetectable amount. But in the case of the MM experiment and its countless variations that amount is far less than 1%.

You do realize that a study of the MM experiment reveals how our ancestors came to their conclusions. Since that time so many more experiments have been performed and observations made that MM is just a drop in the bucket.

I took an Excel spreadsheet and entered the distance of MM's inferometer of 12 Meters, the speed of light, the speed of the Earth around its axis, and around the sun, and through space, and it shows that the perpendicular beam will be the retarded one, but by such a small amount, MM would not have seen it.

If you did it correctly any discrepancies must be due to round off error.

 

[P J Strydom]

No. In an ideal experiment, analysed in a frame in which it is moving, both beams will return at the same time. If they do not then there is a way to detect absolute motion and therefore the principle of relativity should not be useful. But it is.

Real experiments do show fringe shifts due to things like temperature variation. Experimentalists control for this kind of thing as best they can, but inevitably there are imperfections. Michelson-Morley showed a slight sinusoidal variation of this type. They reported it, but note that it's not consistent with an ether model given the known speed of light. The kind of statistical analysis to estimate noise levels that is routine today wasn't done back then.

Thanks.

 

[P J Strydom]

There is no experiment ever performed or observation made that can distinguish between a state of uniform motion and a state of rest. To say something moves through space is the same as saying it doesn't. A meaningless distinction.
Every experiment or observation produces a result that may be off by a small but undetectable amount. But in the case of the MM experiment and its countless variations that amount is far less than 1%.

You do realize that a study of the MM experiment reveals how our ancestors came to their conclusions. Since that time so many more experiments have been performed and observations made that MM is just a drop in the bucket.
If you did it correctly any discrepancies must be due to round off error.

This is why I am taking time to go through my thinking again.
The wonderful thing about the use of Excel, is that the fractions one can work with is immensely valued and eliminates any errors in calculations.

For instance, I took the values of c,
the speed of the Earth at 460 m/sec through space in the milky way,
and a length of an inferometer at 11 meters.

The beam traveling parallel to the Horizontal beam will arrive at
0.00000007333333334963 secs versus
0.00000007333333336593 secs.
in meters this is 0.00000000048889.
If I am correct, yellow light fringe is
0.00000054m
The light arriving later will have an effect of less than 0.905% of the sine wave of yellow light.
this will not show any interference.

This made me wonder about the observations.
1. that the parallel beam will travel slower, when clearly the perpendicular beam travels a longer distance.
2. that in relation to the Earths' axis, or even the position of the Earth around the Sun in 6 months will yield a minute result about measuring the position of the Earth, and the speed it travels at.

But as this may mean nothing, it is just some interesting knowledge I love thinking about.

The next thing that bothers me about the MM experiment is that all the physicists I know of, even Neil de grase Tyson, continuously state that due to the MM experiment, Einstein developed the theory of Special and General relativity.
So far, to me, they do not connect.
I will later on post what I don't understand, and perhaps you guys can explain it practical mechanics of this statement.

prosperous new year to you all.
May you guys get a flash of thought, and publish one heck of a paper.

 

[jbriggs444]

the speed of the Earth at 460 m/sec through space in the milky way

Yes, the rotation of the Earth on its axis produces a motion of plus or minus 460 meters per second depending on whether you sample at noon or midnight. But that is just the tip of the iceberg.

The orbital motion of the Earth about the sun is plus or minus 30,000 meters per second depending on whether you sample during summer or winter. But that again is small potatoes.

The orbital motion of the Solar system within the Milky way is 230,000 meters per second.

Until you have a test theory in mind to compare with the predictions of Special Relativity, you will not know which of these velocities, if any, is relevant. If, for instance, the test theory included a non-rotating ether which is dragged along with the Earth in its orbit about the sun then the expectation for a fringe shift corresponding to the Earth's 460 m/s rotational velocity would be correct. But other experiments rule out such a theory.

 

[Ibix]

The wonderful thing about the use of Excel, is that the fractions one can work with is immensely valued and eliminates any errors in calculations.

I hope you are joking. I don't think Excel goes beyond single precision. And I've found circumstances where it'll tell you that two values are equal, but if you subtract one from the other the answer isn't zero (probably an effect of it trying not to scare business users with the details of finite precision arithmetic in binary). Excel is one giant rounding error waiting to happen.

This is almost certainly why you have different answers for the travel time along the two paths - different cumulative rounding errors from different calculation orders. It's trivial to show algebraically that the difference is zero assuming the Lorentz transforms. If you get a different answer you must be making a mistake.

 

[jbriggs444]

I hope you are joking. I don't think Excel goes beyond single precision.

I just created a cell containing =1.0000000000001 + 1.0000000000001 and set the display format to 20 decimal places. The result displays as: 2.00000000000020000000

It looks to me like at least double precision. Wiki confirms.

"Excel calculates in double-precision floating-point format from the IEEE 754 specification[1] (besides numbers, Excel uses a few other data types[2]). Although Excel can display 30 decimal places, its precision for a specified number is confined to 15 significant figures, and calculations may have an accuracy that is even less due to three issues: round off,[3] truncation, and binary storage."

Edit: I found a more definitive test case...

The neatly rounded off decimal 2.000000000000020000000 did not smell right. That is not the result that one would naively expect from a double precision implementation. There had to be something more going on. And there is.

=sqrt(2) with a 20 digit display format yields 1.41421356237310000000
The correct result is 1.4142135623730950488016887242097

What Excel appears to do is to round displayed results at 14 sig figs even when the display format is set wider than that. Since double precision is good to 15 digits, this will [often] yield the expected result and will suppress meaningless trailing digits that might otherwise be inserted.

Even more interesting is the following spreadsheet containing:

=sqrt(2)             =a1*a1
=1.4142135623731     =a2*a2

Which displays as

1.41421356237310000000 2.00000000000000000000
1.41421356237310000000 2.00000000000001000000

 

[Ibix]

It looks to me like at least double precision. Wiki confirms.

"Excel calculates in double-precision floating-point format from the IEEE 754 specification[1] (besides numbers, Excel uses a few other data types[2]). Although Excel can display 30 decimal places, its precision for a specified number is confined to 15 significant figures, and calculations may have an accuracy that is even less due to three issues: round off,[3] truncation, and binary storage."

Ok - I'm over-estimating its awfulness. I've been bitten by being forced to use it as a semi-serious analytical tool too many times to trust it.

Since the differences seem to be arising on the 10th significant figure, I'm still betting on rounding error.

 

[vanhees71]

Well, according to Einstein himself, it's a fairy tail that he came to his special theory of relativity by thinking about the Michelson-Morley experiment. Indeed, when reading his famous 1905 paper "On electrodynamics of moving bodies", nothing the like is mentioned but a much more important way of thought was brought forward: The aim of writing this paper was to understand apparent asymmetries in the theory of electromagnetic phenomena (Einstein brings the example of a moving magnet inducing a current in a conducting loop at rest vs. the same situation in the reference frame, where the magnet is at rest and the loop moving). Of course, famously his solution was a revision of the very foundation of physics in terms of the description of space and time, introducing de facto the notion of "space-time".

The great genius of Einstein was to derive this revision of the space-time structure using the most simple facts of Maxwell's theory of electromagnetism together with the special principle of relativity, namely that if the special principle holds, then the speed of light in vacuo must be independent of the light-sources motion relative to any inertial observer. Indeed, as we know now, the only two space-time models consistent with the special theory of relativity and the usual symmetry assumptions ("Euclidicity" (homogeneity and isotropy) of space relative to any inertial observer as well as time-translation invariance of the natural laws for any inertial observer) leads to only two possible space-time models, namely the Galilean and the Minkowskian space-time manifolds. Only the latter involves a fundamental "limiting speed", which as far as we know today is the speed of light (i.e., the phase velocity of electromagnetic waves).

 

[P J Strydom]

Amaizing.! (The accuracy of excel)
This now forces me to go an work it out manually by hand.
I also made a practical drawing, measuring a theoretical moving diagram

The blue lines show the distance traveled perpendicular to movement of the Earth, and the red lines the parallel movement.
The first circle shows the initial departing positions, the second the point of reflection, and the 3rd the point of return to the splitter beam.
I simply increased the distance between the circles imitating an increase in speed
I copied the lines and changed the angles to horizontal, placed both lines next to each other, and measured the distance between the parallell lines and the angular lines.
I then moved the outer circles further away, thereby imitating an increase in speed, and did the measurements again, a few times.
What I found is that the return distance for the horizontal lines remains the same. But, the lines perpendicular increases in length as speed increases.
Now, this is highly exaggerated (to the effect of about 50% and 75% the speed of light), and if we were to use c as c, and v as 460 Km/sec, the difference will be very small, especially if we measure the distance of the light beams traveling over 11 Meters, as the MM inferometer.

I am sure that there must be a difference between the 2 beams arrival times.
Simply because one beam is traveling further.

 

[P J Strydom]

special principle holds, then the speed of light in vacuo must be independent of the light-sources motion relative to any inertial observer.

This makes absolute sense.
So, if a beam of light gets shot from a moving body, the speed of c will remain at c, and not c+v.
This will also mean, and this is the crucial point which is stuck in my head, that we will be able to detect if something is actually moving in relation to a fired light beam.
If we detect a red, or blue shift, it will mean that the object firing the light is either moving away from us, or advancing towards us.
Does this mean that if we fire a pulse of light in space, the light beam will spread out in a 3D ball, in relation to its point of origin?
this whilst the source of the light moves on?
Thinking of it this way opens another thought in my mind.
We will be able to detect which object is moving in relation to another, if both fires a pulse of light.
The one standing still, will not detect a fringe shift, whilst the object moving will.

Is this not what we see if we look at distant stars?
If we can see a red shift from a far off star, we must be able to see a shift in light on our inferometer.
it will however be very small indeed.
It is exactly the same as the 3 circle diagram I drew.
Anyhow,
lets get back to the "Audi" circle diagram.
Am I correct to say that the angular beam will travel a longer distance, than the horizontal one?
How big is the difference?

 

[vanhees71]

The redshift of stars is of course due to both relative motion to us and (for far distant ones) the gravitational Hubble-Lemaitre redshift. For this you need GR of course.

 

[Ibix]

I am sure that there must be a difference between the 2 beams arrival times.
Simply because one beam is traveling further.

You forgot about length contraction - the circles should be length contracted into ellipses. Please remember that relativity has been thoroughly picked over by literally thousands of people over the last century, and thoroughly tested. Any mistakes are your own.

Let the length of the transverse arm be $l$, and let the velocity of the apparatus be $v$. The time, $t_\bot$, for a pulse to return in this arm can be found by applying Pythagoras' theorem to the outbound path (or the inbound path, since both take the same time $t_\bot/2$):$$(ct_\bot/2)^2=(vt_\bot/2)^2+l^2$$This solves easily to give$$t_\bot=\frac{2l}{\sqrt{c^2-v^2}}=\frac{2l}{c\gamma}$$

Let the parallel arm have length $L$. The travel time in the outbound direction is $t_o$ and satisfies $ct_o=L+vt_o$, which gives $t_o=L/(c-v)$. The time in the inbound direction is $t_i$ and satisfies $ct_i=L-vt_i$, which gives $t_i=L/(c+v)$. The total time, $t_\parallel$, is the sum of these two. A little bit of algebra gives$$t_\parallel=\frac{2Lc}{c^2-v^2}=\frac{2L}{c\gamma^2}$$

So the two return times, $t_\bot=2l/c\gamma$ and $t_\parallel=2L/c\gamma^2$, are equal if $L=l/\gamma$ - i.e. if the parallel arm is length contracted in accordance with relativity.

 

[vanhees71]

For a very nice discussion of the MM experiment using the full SRT (also in frames, where the apparatus is moving!) to analyse the null result, see

https://doi.org/10.1119/1.17535

 

[Ibix]

We will be able to detect which object is moving in relation to another, if both fires a pulse of light.
The one standing still, will not detect a fringe shift, whilst the object moving will.

Are you describing three objects, two emitting pulses and the third receiving them? If so, yes, this is essentially how Doppler radar works. Or are you describing two objects exchanging pulses? In that case, both will see the other's pulse Doppler shifted.

 

[P J Strydom]

Ibex,
I agree with it all.
But keep in mind that I am not so intelligent as you scientists are.
To me something must be a mechanical entity.
What I mean by that is simply that one can look at any machine, and the rules of its design will dictate the outcome of what it is supposed to do.
A can opener will need its shortened blade to perce the lid, a fulcrum and lever, and energy to move the lever to cut the lid open.
The corkscrew was designed to remove a corkscrew.

Now, I can go and use Newtons' calculations to show that it is possible to open the can,
or I can take a can and open it.

Now, if I go through the calculations of Lorenz and I will determine the time and length of specific entities.
But why can I not simply draw the unit on paper, and measure what MM saw?

I am always feeling as if I am told, shutup and look at the maths.
I took a lot of time and I did the maths.
I agree with the maths, no question.

Then I went and look at why my logical mechanical explanation don't add up.
The only difference I find is the following.

1. Length contraction! Time dilation!.

What we all proved is that there will be a difference in the arrival of the light beams, but it will be such a negligent effect, that it is almost immeasurable.
We know there are a difference, but we will write it off with an explanation of length contraction.

And this is what I want to know...is length contraction and time dilation a theory, or experimental fact.
If fact, how do we prove with experiment that length contracts

 

[Ibix]

What we all proved is that there will be a difference in the arrival of the light beams, but it will be such a negligent effect, that it is almost immeasurable.

No. We've proved there is no effect. Without length contraction there would be an effect that would be easily within the detection range of Michelson and Morley's experiment.

And this is what I want to know...is length contraction and time dilation a theory, or experimental fact.

Time dilation has been directly observed many times - see cosmic ray muons, Hafele-Keating experiment, and pretty much every experiment run at CERN. Whether or not length contraction has been observed is a matter of opinion. We can't explain hordes of experiments without it (Michelson-Morley, any experiment in electromagnetism), and it's clearly implied by the invariance of lightspeed, which is also thoroughly tested. So I'd describe it as an experimental fact. But we've never literally photographed two rods side by side while one moved fast enough for length contraction to be visible.

But why can I not simply draw the unit on paper, and measure what MM saw?

Because you neglect effects like length contraction. So you are not modelling the world as it is. You would need to draw a Minkowski diagram to show the effects.

I am always feeling as if I am told, shutup and look at the maths.

The maths accurately describes the real world. It enables us to make precise numerical predictions that can be compared to the outcomes of experiments. And an accurate diagram expresses that maths somehow. Your "Audi" diagram is expressing a Newton+ether model, which is why it gives results consistent with that. If you shorten the parallel arm in accordance with relativity then you are expressing a relativistic model and you'll get a relativistic answer.

It won't tell you why lengthn contraction happens. I'd suggest you learn how to draw Minkowski diagrams for that.

 

[jbriggs444]

Does this mean that if we fire a pulse of light in space, the light beam will spread out in a 3D ball, in relation to its point of origin?
this whilst the source of the light moves on?

Not a 3-D ball. A spherical shell that expands over time.

Surprisingly, the invariance of light speed means that we can adopt the frame of reference where the source is at rest and observe an expanding spherical shell always centered on the source. It also means that we can adopt a frame of reference where the source is moving and observe an expanding spherical shell always centered on the place where the source was when it emitted the pulse. Both descriptions are correct!

The resolution to this seeming contradiction is the relativity of simultaneity. Each spherical shell is a snapshot at an particular instant in time. But time and, in particular, simultaneity, is judged differently from different reference frames.