Why Haven't Two Clocks on a Table Been Used to Measure Light's One-Way Speed?

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The discussion centers on the challenge of measuring the one-way speed of light using two clocks placed on a table, questioning why this straightforward experiment has not been conducted. Participants argue that existing methods, like GPS, assume light speed invariance without directly testing it. The conversation highlights the synchronization issues inherent in using spatially separated clocks, with some asserting that absolute simultaneity is necessary for accurate measurements. Critics of special relativity (SR) express skepticism about the validity of current theories, suggesting that Einstein's framework relies on unproven assumptions. Ultimately, the thread emphasizes the need for a clean, direct experiment to resolve these fundamental questions about light's speed and the nature of simultaneity.
  • #151
Nereid said:
2) ring lasers are the heart of many modern gyroscopes, including those in commercial airliners. To underline outandbeyond2004's point, if there were any anisotropies, or other deviations of the kind that wisp and Eyesaw have described, it would seem remarkable that they'd cancel out perfectly in devices like ring lasers. But maybe that's exactly what wisp et al expect?

The principle on which the ring laser gyroscope works is due to an effect that SR cannot explain clearly.

The Sagnac Effect
An article that explains this clearly, but from relativity's viewpoint is given at http://www.mathpages.com/rr/s2-07/2-07.htm.
The first few paragraphs explain the Sagnac effect (you can ignore the section showing loop and area calculations). The argument in support of relativity's explanation is summed up on the basis that the device centres around one particular system of inertial coordinates (centre of circle), and all other inertial coordinate systems are related to it by Lorentz transformations.

But the flaw in this argument is simply this: What happens to the measuring clock when the radius of the circle becomes very large and the clock's velocity small - a limit process?
The Sagnac effect still applies and the clock's motion becomes more linear. In this limit process it is not unreasonable to treat the moving clock as an inertial reference frame in its own right (the Sagnac effect has been tested to great accuracy and so it perfectly reasonable to use a limit process to make the moving clock's frame inertial). Now according to relativity, since this is an inertial frame, light must travel at speed c in both directions. But the Sagnac effect requires that the speed of light must be c+v and c-v respectively, and not c! This limit process shows that relativity contradicts itself, as the real measurements are made in the moving clock frame and not at the centre of the circle. An argument that focuses on one inertial frame that is the centre of the circle is the only way relativity can explain this effect, and so the case for relativity is very weak.

wisp

"particles of nothingness"
 
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  • #152
outandbeyond2004 said:
A ringlaser project that is able to detect the anistropy of the sort theorized by Wisp? http://www.wettzell.ifag.de/LKREISEL/CII/precise.htm

This group says it hopes to achieve resolution of the Earth's rotation to a few parts in a billion! That's much more than we need, if the wisp ether speed of the ring laser on the equator is totally due to Earth's rotation. speed of the r.l/c is about 1 per million or maybe much more. I forgot what the speed of the solar system (divide by c) is wrt the CRB, but it must be much more, I think.

I don't believe that this experiment will detect any galactic ether flow, because it will be affected by "jiggle effect" (wisp theory). It will suffer the same fate of the MM experiment carried out on the surface of the earth.

However, it will measure the rotation of the Earth with incredible accuracy.

wisp

"particles of nothingness"
 
  • #153
wisp said:
But the flaw in this argument is simply this: What happens to the measuring clock when the radius of the circle becomes very large and the clock's velocity small - a limit process?

You mean relativity isn't preserved by limits? *gasp* Guess what? Neither is mathematics.

Besides, if v is negligably small, then c - v and c + v are negligably different. :biggrin:
 
  • #154
Exactly how does this limit process that wisp writes about in post #151 work? It seems as though as the circle gets larger, the angular speed gets slower proportionally, so as to keep the linear velocity the same. If that is correct -- so what? The rotating frame becomes more and more like a inertial frame -- neglecting gravitational effects of course. If you keep the measurement time small enough, the rotating frame is indistinguishable from an inertial frame beyond the limits of instrumental technology, and that's far easier to do that with a huge and s-l-o-w-l-y rotating r.l.

One has to be careful in applying SR to situations where the curvature of spacetime cannot be neglected. The huge ringlaser is simply in reality not a subject for SR anyway.

There may be some worth in wisp theory, the explantion of how gravitational effects may arise from wisps is intriguing. However, I am less enthusiatic than before. I will continue to skim wisp's future posts to see if there is any significant change of some nature, but except for one thing, I do not think I will post any more on wisp theory.
 
  • #155
Hurkyl said:
Besides, if v is negligably small, then c - v and c + v are negligably different. :biggrin:
Cute, isn't it - wisp declares negligible the most important piece of the model in order to disprove the validity of the model.
 
  • #156
The problem is that as the ring's radius grows to infinity, so does the amount of time it takes for the light to travel around the ring. An infinite amount of time is plenty of time for those negligable errors to build up. :smile:

Basically, he's neglecting the fact that 0 * ∞ and ∞ - ∞ are indeterminate forms.
 
  • #157
I propose to derive the Sagnac effect from classical physics for the benefit of readers not familiar with the effect. I want then to incorporate reasonable wisp-theory changes. I hope to go on from there and then to show that we have reasonable grounds to expect that wisp theory does predict time-varying signals that ringlasers can detect, contrary to wisp's dismissal of them (post #151).

If my derivations pass muster (e.g. nobody can show any error or show that an assumption is unreasonable), I am going to unsubscribe this thread. Look for the next post . . . (How's that for salesmanship? <smile> )
 
  • #158
If wisp ever thought that my last post (#157) was an April Fool joke, no, he fooled himself.

The link that wisp gave in #151 on the Sagnac Effect would be helpful tho not necessary.

A laser can be viewed as a chamber that creates conditions for resonance. There must be a positive integer number, called the mode number, N, of whole cycles (no partial cycles) between the ends of the chamber:

N\lambda = L, _________ EQUATION 1

where L is the "optical length" between the ends of the chamber, and \lambda is the wavelength. That is the resonance condition for lasing.

A ringlaser is two chambers, one for counterclockwise traveling photons, and the other for cw photons. Let's consider in this thread only a circular ringlaser of radius R. Let it be at rest in an inertial frame of reference whose origin is at the center of the circle. On a point of the circle is a device that does several things:

1. shoot out photons of the same mode number in either end equally (often many modes appear in the ringlaser, but we can assume just one mode is excited);
2. combine the ccw signal with the cw signal to form a beat frequency;
3. and measure the beat frequency.

Experimentalists would see the above description as an overly simple and impractical model of the laser, but it should suffice for order-of-magnitude estimates.

Let's modify Equation 1 to get the frequency:

f = N/T, _____________ EQUATION 2

where T is the time for a photon to go around the ring from the device and back to it.

Given T_+ for the trip time of a ccw photon, and T_- for that of a cw photon, we have for the beat frequency f_b:

f_b = N|\frac{1}{T_+} - \frac{1}{T_-}|. ________________ EQUATION 3

Of course if no anisotropy existed in the two chambers, and the ringlaser was still at rest ia inertial rf, the beat would be zero. Suppose the irf moved through wisp space at speed v, it will still not change anything. For every ccw photon going at c + w
we also have, on the other side of the circle, a cw photon going c + w; and likewise for photons going c - w, for any speed w <= v.

However, the situation changes when you rotate the ringlaser at a constant angular speed of \omega wrttirf. Then the photon speeds cannot be matched up that way, canceling out all the w's.

Readers may find it helpful for later posts to derive the Sagnac Effect beat frequency.
 
  • #159
Hurkyl said:
Besides, if v is negligably small, then c - v and c + v are negligably different. :biggrin:

No, the radius of the ring increases, but v stays the same. So c - v and c + v are not negligibly different.
And if the radius were very large, why should errors come into this argument!

wisp

"particles of nothingness"
 
  • #160
outandbeyond2004 said:
However, the situation changes when you rotate the ringlaser at a constant angular speed of \omega wrttirf. Then the photon speeds cannot be matched up that way, canceling out all the w's.

Your reasoning is OK, but if no change occurs due to a galactic ether flow, SR supporters would argue that this was expected - just like in the MM experiment.

But wisp theory also predicts a no change. The argument is similar to that used in the MM experiment and is due to jiggle dilation effect.

So SR and Wisp predict no change due to an ether flow component.

However, if the device were operated away from the Earth's surface things would be different. SR would again predict no change, whereas wisp theory would predict change due to the reduced jiggle effect.

See section 7.7 / equation set 7.7 for the affect of jiggle on the MM experiment.
http://www.kevin.harkess.btinternet.co.uk/wisp_ch_7/wisp_ch_7.html

wisp

"particles of nothingness"
 
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  • #161
Response to wisp's post #159:

I am sorry that other people misread your prior post. However, your infinitely large ringlaser hardly disproves SR. Did you indeed get the point that SR is only of limited validity (the spatio-temporal dimensions of the irf must be small enough that our instruments cannot detect gravitational/acceleration effects)? Your monstrous rl pushes poor SR out of its limits, shivering and shivering. O! Cruel Wisp!
 
  • #162
I think that the main problem of SR is the clock traveling together with light.
Any object cannot travel in c except of light. Including the clock.
 
  • #163
Just to make sure, Wisp: you think that your theory predicts that the motion of the rl through wisp space will not produce any beat whatsoever? No matter how fast it may be rotating and how it is oriented to the motion? If yes, I am surprised that jiggle would cancel things out or balance out so neatly. Oh well, we'll see. . .

You realize, of course, that if you just say that jiggle does this or that so that a null effect ALWAYS occurs, it is just too convenient an ad hoc hypothesis. Your only possible justification for this wondrous pheonomenon is experimental verification. I doubt you can get people to spend scarce time and money on ad hoc experiments to find jiggle without some substantial theoretical foundation.

One correction: I will ignore SR corrections to my calculations. Keep in mind that I specified "optical length." That is not necessarily the same as the circumference of the at-rest, nonrotating rl. That is about all the concession to SR that I have made and that I think I will make. Perhaps after I have presented my theory including the effects of jiggle as I understand it, we can discuss the effects of SR corrections.
 
  • #164
No, the radius of the ring increases, but v stays the same.

The argument to which I responded said that v was small. :smile:


Anyways, how did you manage to conclude that if R is large enough so that the observer is in an essentially inertial frame, then the speed of light around the ring was c+v or c-v?
 
  • #165
Here a ringlaser rotating at angular speed w is moving through the ether at velocity v. Jiggle and wisp space will be considered in later posts but not here.

Source independence is assumed, i.e. EM signals travel through empty ether at c. At the outset of calculating the modified SE beat frequency, let's try to get a clear picture of what is going on. In ether space, each ringlaser photon travels in ether space what we might call pseudo cycloids, but the photon generator/beater travels a true cycloid. It is worth noting that no ringlaser photon travels the same path in ether space as any other; in that sense we do have one-way travel (if this is not acceptable to MM et al. -- why not?).

The following point is not one I am sure ought to be made, but I will make it nevertheless. The photons that beat together in the beater are not photons that start out together, at the same time. Instead of my drawing a diagram, why don't you draw it following these instructions: Draw the following on a piece of paper:
A circle about the size of your fist on a piece of paper.
About the center of the circle, draw a curved arrow going ccw and label it w for angular speed.
A vertical arrow starting near the right side of the circle and label it v for the ring's velocity wrt the ether.
On the circle make a tick somewhere between zero and pi/2 from the direction of v (which we can take to be the x-axis also). Label the tick thetab, for the point on the circle where a ccw photon and a cw photon meet in the beater to create the beat frequency.

Now, the ccw photon had to have started earlier than the cw photon, so you have to draw their respective ticks on the circle as follows:
For the cw photon, simply go a little cw from the first tick and between that and zero angle, draw a tick. Label that theta-.
Again go a little cw and so on except label *that* theta+.

The ccw photon leaves theta+, goes through theta- and then thetab and on all around the circle, ending at thetab. The cw photon goes the other way and on *almost* all around the circle, ending at thetab.

I want to do the math in the ether frame of reference, and am finding it tough going. I never got really good at problems like that. It might be several days before I decide it is good enough to present. Or maybe I will decide on another approach.
 
  • #166
outandbeyond2004

No, it is not acceptable. The ring laser device that controls the motion of the photons is moving through the ether at speed v.
To mimic the pseudo cycloid motion from the ether frame, a device would have to be made that could accelerate and decelerate the photons, which would make the photons feel forces that were variable.
In the moving frame the forces are of constant acceleration only.
Also in ether frames force devices operate differently, as force dilates as the speed v increases (but, Lorentz symmetry stays the same).
With SR you can swap frames about, but you cannot do this with ether frames.

To start of with a simple model, why not make a square sided laser device, which rotates by pi/2. The sides can be the x-y-axes, and later the model can be made circular.

wisp

"particles of nothingness"
 
  • #167
wisp, I do not understand your post, but I did imply that I will not consider wisp theory for now. Later I will consider it. Then I probably will need considerable amounts of discussion. Got the time for that?

I think I am getting the hang of the problem, anyway. In truth, I caught a blooper. The motion of the beater is pseudo cycloid, not true, because its rotation does not necessarily have the proper relationship to the velocity.
 
  • #168
My calculations made it obvious to me that the theory of linear addition of speeds plus the postulate of constant speed of light in the ether predicts a modification of the Sagnac Effect:

Multiply it by a factor like

sqrt ( 1 - (gamma*cos(theta))^2 ) - gamma sin(theta),

where theta is the angular position of the beater measured at the center of the ringlaser from the velocity direction and gamma = v/c, v being the speed of the ringlaser wrt the ether.

I am confident that if some ringlasers can resolve the modified Sagnac Effect to better than the order of gamma (v/c), they would disprove SR, provided gamma is known.

My calculations did not reach the point where the Sagnac Effect is modified, but surely time varying signals in it are obviously demonstratable. The calculations are now presented (skip to --------------- if you want) and some discussion follows.

The position P(vector) of a photon at time t starting from theta0 at t = 0 in the ether frame, given

R = radius of the ring
v = speed of the ring wrt the ether, in the x direction
theta = angular position, = theta0 at t = 0, measured at the center of the ring from the x direction:

P = (vt + R cos(theta) , R sin(theta))

Take the derivative wrt t:

dP/dt (vector) = (v - Rsin(theta)*dtheta/dt, Rcos(theta)*dtheta/dt)

Because the photon is supposed to move at the speed of light in the ether frame,

c^2 = |dP(vector)/dt| (square of the magnitude) =
v^2 + (R*dtheta/dt)^2 -2vRsin(theta)*dtheta/dt

Let w = angular speed = dtheta/dt, and solve for it:

w = (c/R)(+/-sqrt(1-(gamma*cos(theta))^2) -gamma*sin(theta))

The ccw photon requires the plus sign in the above equation; the cw photon the minus sign.
-------------------------

Note that the formula given above does not apply to a ringlaser attached to the surface of Earth, if gamma = Earth rotation speed/c, because the ringlaser does not go in a line, rather it revolves in a circle. I don't see, however, that the qualitative picture is any different.

The factor after c/R in the above equation does approximate 1 - gamma*sin(theta) for gamma << 1, but if you take gamma = 0.9 it is obviously asymmetric as a plot shows. Not that we would ever have ringlasers hurtling through ether at speeds like that, but it was interesting at least to me.

Remember the ringlaser that claimed to be able to resolve Earth's rotation to a few parts in a billion? I do not know the particulars of its design, so I cannot really say 100% positively that its operators ought to see ether anistropy effects generated by Earth's motion and rotation like predicted above, but I would be amazed if it were not so. If my calculations and conclusion are correct, I believe we would have seen reports of anisotropy in ringlaser experiments by now if gamma ~ 1/1000 as per Nereid. MM et al would have been happy. Happy now? :smile:
 
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  • #169
outandbeyond2004 said:
Let w = angular speed = dtheta/dt, and solve for it:

w = (c/R)(+/-sqrt(1-(gamma*cos(theta))) -gamma*sin(theta))

The ccw photon requires the plus sign in the above equation; the cw photon the minus sign.

I got a quadratic, which gives
w=(v*sin(theta)/R)+/-sqrt((v^2*sin^2(theta)-(v^2)+(c^2))/R)

Anyway, with the jiggle factor (slows light in the perpendicular direction to the Earth's motion through the ether) the v terms will cancel. It did exactly this with the MM formula, which had v terms.
I will use your formula and add in the wisp bits. It should give a formula for w without any v term.
 
  • #170
Wisp's quadratic result is correct. However, v^2 -(v^2)sin^2 = (v^2)cos^2. My result is the same.

edit - I did leave out the factor ^2, sorry, while copying from my paper. I edited it into that previous post.
 
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  • #171
Anybody know how to solve this analytically?

\int \frac{d\theta}{\pm \sqrt{1-(\gamma cos\theta)^2} - \gamma sin\theta}
 
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  • #172
The readers who want a neat formula for the modified Sagnac Effect:

There is not any, generally speaking. Numerical approximation looks necessary. This post assumes that you have followed the directions in post #165 https://www.physicsforums.com/showpost.php?p=177177&postcount=165

A general procedure goes as follows:

Obtain a formula relating initial angle and final angle for the ccw photon to the trip time:

T_+ = T_+(\theta_+, \theta_b)

Likewise for the cw photon:

T_- = T_-(\theta_-, \theta_b)

We also have

\omega_bT_+ = \theta_b - \theta_+

and

\omega_bT_- = \theta_b - \theta_-

where omega_b is the rotation speed of the beater.

Even if we had analytic formulas for the trip times as functions of the initial and final angles, these equations must still be solved simultaneously. This is in general impossible to do so analytically. I fear this is the case for the rotating ringlaser in translational motion. I am not sure whether I will do the numerical work necessary to show a time-varying signal. I can program my computer, but I must learn how to solve these equations simulataneously on it. I don't know how much time that would take.

It might be worth doing if it were original work and would be accepted in a journal like Physics Review.
 
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  • #173
outandbeyond2004

I can’t see a simple solution either, but I will use your formula to input into mathcad and calculate a set of series equations that will give an approximation answer.
I will do this with and without jiggle.
Jiggle slows light on the Earth's surface in the perpendicular direction to ether motion by
\gamma \equiv \frac{1}{\sqrt{1 - v^2/c^2}}

Initial mathcad plots (without jiggle) of w against theta show that it is affected by the ether flow and varies in a sinusoidal pattern.
I haven’t added the jiggle effect yet, and initially said that the results would cancel any ether flow effect. However, there is a small asymmetry to the jiggle cancellation effect due to device rotation, which will result in an extremely small variation in w, which will be dependant on the ether flow, but its value may be too small to detected.
 
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  • #174
Mathcad! O, you lucky fellow. What I was planning to do is simply to calculate the photon trajectories backwards until omega_b*deltatime = deltaangle for both photons. Probably have to do this several times, a few times integrating forwards rather than backwards like above, until you find a good step size that minimizes numerical error. Then run with the optimal step size for all theta_b. I guess the angle that would give the most trouble is when cos(theta) = 1, i.e. theta ~ pi/2. That's where I would look for optimal step size. No, come to think of it, I'd try pi/4, because the cos term is only of second order in gamma.

I cannot believe the jiggle only operates in the peripendicular direction. I think it has something like a sine dependence. Let v be the velocity (vector) of the rl and n be an unit vector in the peripendicular direction to c travel. then

\gamma_{jiggle} = \frac{1}{\sqrt{1-(v\cdot n)^2}}

Possibly wrong formula, but you get the idea.
 
  • #175
I looked at the case of a circular ringlaser attached to the spinning earth, ignoring Earth's revolution about the Sun.

Let

v_L =
velocity of photon measured in ether space;
v_E =
velocity of ringlaser center wrt inertial frame centered on Earth's center of mass or in ether space; both velocities are fractions of the inertial speed of light in vacuo.

For the case of a ringlaser on the equator, with its plane parallel to the equatorial plane, let

\theta_L =
angle of photon position measured wrt x-axis of the inertial frame of Earth used above at the center of the rl;
\theta_E =
angle of rl position measured wrt x-axis of the same irf at the Earth center of mass;

So,

v_L^2 + 2v_E cos(\theta_E + \theta_L)v_L - c^2 + v_E^2 = 0

Surprisingly simple. I am not sure what the cos term would lead to in the beat frequency.
 
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  • #176
If we take the beat frequency from a ringlaser like in the last post and that of a same rl but twice as big, that would be more than three x the fun <wild and insane laughter>.
 
  • #177
The beat frequency from a combination of Earth revolution (orbit about Sun) and Earth rotation is certainly going to be much more complex. I will just await wisp's numerical results for this (Earth rotation only) case before considering the revolution + rotation case, if that's OK.

edit - the position of the beater of the equatorial ringlaser is fixed wrt the Earth, so the rotational modification to the Sagnac effect is constant. To measure that, one needs to know the other contributions to the overall effect, such as that of Earth's revolution about the sun. So, it would be better to look at that instead. But, why not consider the Sun's "orbit" about the Milky Way center? Even better, the Milky Way galaxy's orbit about the barycenter of the local group of galaxies . . . the motion wrt the CRB?

In the next post, I will just consider a simple case to see if it's all right to calculcate each effect separately and add 'em up afterwards (principle of superposition).
 
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  • #178
Outandbeyond2004

I've done some calculations using mathcad and thought on how jiggle affects light in the ring laser. Two things happen:

1. Light is slowed by jiggle in the perpendicular direction and this slows light in all directions by the same amount because, light cannot change its path (unlike its affect on the MM experiment where it can change its path). The result is that all light slows in the ring laser by a factor of jiggle.
2. We must apply the "rules for time dilation compensation" (wisp theory 7.15.4). An observer moving with the ring laser records the speed of light in the ring laser as being increased by gamma (gamma has the same value as jiggle). The result is that the speed of light will be measured as being unaffected by jiggle.


(We ignoring the refractive index for glass and will consider the motion of the Earth through the cosmic ether - not its orbit around the sun).
If we assume that the ring laser moves thought the ether at 340km/s in the direction suggested in your message #165. Then the speed of light will slow by 1 part in 1038422 according to your classical ether calculations. And because jiggle and time dilation cancel out, I see no reason to doubt that this does happen.
If the ring laser is perpendicular to the ether flow then the speed of light will remain fixed at c.
If the tilt of the Earth causes the a component of the perpendicular ether flow to move in the x-axis direction by [sin (35.5) = 0.4] then the variation in light speed is 0.4*(1 part in 1038422) or 1 part in 4153689.

The question that I feel needs answering is:
How does the speed of the Earth through the ether combined with the Earth's tilt affect the beat frequency?
I believe that a very sensitive laser ring device will detect a small sidereal variation in beat frequency.

I will do some calculations using your formula.
 
  • #179
Whoa, wisp! (1)Either you are getting something wrong, or I am. I don't see how you get the 1 in 1038422 thing. I would have thought it was more like 340e3/c ~ 1.1/1000. See, expand in powers of v/c and sort of use the principle of superposition for the first power. I suspect you assumed that the rl does not rotate to produce the Sagnac effect. You merely assumed zero rotation, did you? If so, well it would indeed be something for the rl to produce a difference in trip time of even that relative size, all right. However zero or very small rotation is simply not practical for at least one technical reason that I won't go into here. You must let the rl rotate with the earth. Not at the equator, either. See (2) please.

(2) To be practical, you have to consider ringlasers lying flat on the ground of the spinning AND moving earth. I have been struggling to get results, and I am getting there. I was never good with multiple reference frames, especially this: One is moving wrt another, which is moving wrt yet another. Right now I am going over the calculations several times to be sure I have everything straight. I can't say when I feel confident enough to post the results here. Maybe Monday evening, if not sooner. Would you wait until then?
 
  • #180
This is the first part of a three-part post.

A spherical planet of radius R_p (p for planet) hurtles through ether space with velocity \vec v_e (e for ether -- not Ethel!), which is treated as constant for sufficiently brief intervals of time. The planet's angular velocity wrt ether space is \vec\omega_e, also treated as constant. Attached flat to the planet's surface is a circular ringlaser of radius R_L (L for laser). The ringlaser's center is represented by location \vec P_p. The location of a photon in the rl is represented by \vec P_L.
 
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  • #181
Second part of a three-part post

Wrt a particular rf attached to the rl,

\vec P_L = R_L(cos\phi, sin\phi, 0)

where \phi = \phi_0 at time t = 0.

If we orient a reference frame attached to the planet (rfP) so that its z axis runs through \vec\omega_e and the angle from \vec\omega_e to \vec P_p is \theta_p, then wrt rfP

\vec P_L = R_L(cos\theta_p cos\phi, sin\phi, -sin\theta_p cos\phi) + \vec P_p

Let us orient a reference frame attached to ether space (rfE) so that its x-axis runs through \vec v_e and its y-axis points in the direction of \vec \omega_e \times \vec v_e . Let the angle from the z axis to the angular velocity be \theta_e . Then wrt rfE,

\vec P_L = R_L( (cos\theta_e cos\theta_p - sin\theta_e sin\theta_p)cos\phi,
sin\phi,
-(sin\theta_e cos\theta_p + cos\theta_e sin\theta_p)cos\phi )
+ \vec P_p + \vec P_e


where \vec P_e is the position of the planet's center wrt rfE.
 
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  • #182
Third part of a three-part post

Let

v_L = \mbox{velocity of photon in rl}

\phi = \frac{v_L}{R_L}t + \phi_0
where \phi_0 = constant

\vec Y = ((-cos\theta_e cos\theta_p + sin\theta_esin\theta_p)sin\phi ,
cos\phi,
(sin\theta_e cos\theta_p + cos\theta_e sin\theta_p)sin\phi )

\phi_p = \omega_e t + \phi_{p0}
where \phi_{p0} = constant

\vec P_p = R_p(cos\theta_e cos\phi_p ,
sin\phi_p ,
-sin\theta_e cos\phi_p )

\vec \omega_e = \omega_e (sin\theta_e,0,cos\theta_e ); \omega_e = |\vec \omega_e |

\vec v_e = v_e(1,0,0); v_e = |\vec v_e|

Now we can write

v_L^2 + Av_L - B = 0

where we take all velocities to be in units of c ( = 1; e.g. if you have a velocity in m/s, divide by c = 299 etc m/s) and

A = 2\vec Y \cdot ((\vec \omega_e \times \vec P_p) + \vec v_e ),

B = 1 - v_e^2 - 2(\vec \omega_e \times \vec P_p)\cdot \vec v_e

Note that B is an approximation, a constant term was omitted as being small compared to 1.

This is such a complex formula that computer simulation is necessary to comprehend fully what happens in the beat frequency. I still hope to see a nicely complex time-varying signal in it of the order of v_e.
 
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  • #183
Outandbeyond2004

Your right, my calculation on the variation on light speed around the ring laser didn't take rotation into account. I was interested in seeing how light speed varied before taking things further.
The ether flow will alter the speed of light moving in the ring laser, but the effect will be too small to be detected by measuring changes in the time interval.
A variation in light speed of 1 part in 4153689 will result in a time variation of 10^-24 second or less – too small to be detected.

Taking rotation into account, you end up with the standard sagnac equation for time delay in the ring laser. And even though the ether does affect the speed of light slightly, the affect of the rotation dominates the final time delay by many orders of magnitude. I don’t think the results will show up any differences that can be experimentally checked. :frown:
 
  • #184
Wisp, you seem to have forgotten this group thinks it can resolve the sagnac effect of Earth's rotation to 1 part in a billion:
https://www.physicsforums.com/showpost.php?p=173214&postcount=149

I don't pretend to know what "resolution" in this case means exactly, but I hope it means that the group can detect time-varying signals in the beat frequency even though they may be several orders of magntitude smaller than the main effect. What I would like to do is to calculcate what the time varying signals should be if Galilean R is correct blah blah, then write the group to ask, can you detect such signals?

I suspect you, wisp, are correct. They probably would say, no, they cannot. But I think the possibility is there. It is somewhat like a mom managing to hear her child in a noisy room full of dozens of squalling tots.
 
  • #185
Given the following equation:

d\phi/dt = 1/R + f(\phi, t)

and

f &lt;&lt; 1/ R

how would one obtain the "corrections" to the solution of the following equation that the f term gives rise to?

d\phi/dt = 1/ R
?
 
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  • #186
This talks about detecting the motion of the solar system relative to the CRB! (Scroll to the last paragraph):
http://www.phys.canterbury.ac.nz/research/ring_laser/ring_open.html

It also talks about special relativity tests. If Gal R were right and SR incorrect, would we know about them?

In the ringlaser, Gal R and SR agree to zero order. However, in the second order (v/c)^2, they disagree. Gal R does not demand that a factor be included to account for the slow rate of the beat detector's proper time compared to the time in an inertial frame whose center is momentarily at rest at the center of the ringlaser's center.

I will continue to work on my theory. Unfortunately, my three-part posts contain errors, which I will not (as of now) bother to edit.

Let the ringlaser be at the North Pole of Earth, and let there be no motion relative to ether space otherwise. Then

2\pi = (\frac{c}{R} - \omega_e)T_+

2\pi = (\frac{c}{R} + \omega_e)T_-

Rearrangement leads to this equation:

T_+ - T_- = 4\pi \frac{R}{c}\frac{\omega_e\frac{R}{c}}{1-(\omega_e\frac{R}{c})^2}
 
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  • #187
That is a very cool set of experiments outandbeyond2004! :cool:

I particularly like the idea of a 'new' instrument/technique - ring lasers - being used to test GR (and be of use in other areas of physics and geophysics too).

The webpage has a 1997 date on it; do you know if they have published much of their results yet?
 
  • #188
By honey, I didn't know it was that old! I sort of assumed that it was much more recent than that. I looked up the list of collaborators, and guess what, Okla State University Hans R. Bilger is my thesis prof! I will write him as soon as I get his address. i am sorry to say that we have been out of touch for decades.

Incidentally, if anyone wants a copy of my PhD thesis, The Generalized Sagnac Effect in the PPN [Parameterized Post Newtonian] Formalism, just pm me. Gravitational effects on the ringlaser, published 1976.

Thank you, Nereid, for your kind remarks.
 
  • #189
Outandbeyond2004

All the work I have done on mathcad relates to a circular ring laser on the Earth's surface, in which light is forced into a circular path. Because of this, the effects of jiggle and time dilation cancel each other out, and I believe that the change in the result cause by ether flow is too small to be detected.
Your last link show four mirrors arranged in a square, and so the path light takes is dependent on the velocity of the ether flow. In this case the jiggle and time dilation effects should not fully cancel out.
I will rework my mathcad equations and see if it produces a change that can be detected experimentally.
With SR there is no difference between a square and circular paths. But things should be different for ether theories. And I believe there is a difference in results between circular and square laser devices.
:smile:
 
  • #190
Not only do we have to apply a time dilation factor for the velocity of the beat detector relative to the central irf, we have to apply another for the centrifugal force + gravitational force on the detector (General Relativity "gravitational redshift") as well.

People using mathematics more sophisticated than that in my PhD thesis have come up with General Relativity formulas for the Sagnac Effect, which are claimed to be experimentally verified. Since I already have shown ether theory yields a formula different from GenR, . . .
 
  • #191
Hi there guys, sorry I took so long getting here. Acording to meemoe_uk's time theory, the clocks will behave in accordance with SR even if the trip is one way. Glad I could clear up any uncertaintys you had about it.
 
  • #192
Because you must first synchronise the two clocks and then move them apart. This process of motion causes a discrepancy which means that you are always measuring half of the two way effect.
 
  • #193
Ray Tomes, is that a summary of what meemoe's theory really is? If it always makes the same predictions that SR does, why should we be interested in it?
 
  • #194
No it isn`t. People should be interested in my theory because it's a quantum theory of relativity aimed at the layman.
 
  • #195
mee_moe, I am mildly curious, but I am skeptical because you say it is aimed at the layman! Not ducking the real pros, are we? Theory Development is a free for all anyway, so feel free to expound on your theory here or just start a new thread. And, wisp & you ought to get together sometime, you are fellow theorizing countrymateys.
 
  • #196
Readers know already that a irf theoretically consist of a rigid lattice of clocks, one at each point of the rf. The problem is, what procedure should the experimentalist follow to ensure that all these clocks are synchronized, especially in the light (pun not intended) of Einstein's conclusion in SR that there is no such thing as universal time? The following paper disucsses this problem and gives two conditions.
http://faculty.luther.edu/~macdonal/Synch.pdf
As far as I can tell, the paper is sound. Still, I would appreciate your reading it for errors.

If an experiment that should be affected by the anisotropy of light propagation is analyzed in SR with irfs set up as prescribed in the paper and yet shows no evidence of anisotropy beyond experimental uncertainity, I would consider it evidence that Martin Miller is wrong, even if we should be yet unable to meet his demand for direct one-way speed of light measurements.
 
  • #197
outandbeyond2004 said:
Readers know already that a irf theoretically consist of a rigid lattice of clocks, one at each point of the rf. The problem is, what procedure should the experimentalist follow to ensure that all these clocks are synchronized, especially in the light (pun not intended) of Einstein's conclusion in SR that there is no such thing as universal time? The following paper disucsses this problem and gives two conditions.
http://faculty.luther.edu/~macdonal/Synch.pdf
As far as I can tell, the paper is sound. Still, I would appreciate your reading it for errors.

If an experiment that should be affected by the anisotropy of light propagation is analyzed in SR with irfs set up as prescribed in the paper and yet shows no evidence of anisotropy beyond experimental uncertainity, I would consider it evidence that Martin Miller is wrong, even if we should be yet unable to meet his demand for direct one-way speed of light measurements.


He made some errors in his referencing to the equations and I can't figure out what he's trying to say in the last paragraph. I like his way of synchronizing the two clocks using one way light flashes- the process is basically a way to ensure the two clocks are at rest with respect to one another. If light is source independent though, and propagates at c relative to the vacuum, I don't see how it's possible for him to synchronize the clocks using equation 1 or 3 if the two clock-system were moving relative to the vacuum in which light propagates at a constant c. tp-to will never equal to tp'-to' since light will have traveled a longer path from one clock to the other in one direction than the trip back. Einstein called this effect "the relativity of simultaneity"- this is actually anisotropy inside an inertial frame (moving relative to the vacuum) due to light being source independent.
 
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  • #198
[outandbeyond2004 noted:]
If an experiment that should be affected by the anisotropy of
light propagation is analyzed in SR with irfs set up as prescribed
in the paper and yet shows no evidence of anisotropy beyond
experimental uncertainity, I would consider it evidence that
Martin Miller is wrong, even if we should be yet unable to meet
his demand for direct one-way speed of light measurements.

[Martin Miller replies:]
The cited work actually pertains experimentally only to light's
round-trip speed, which, as we all know, is invariant & isotropic.

Here is what the author himself stated:
Conversely, the results of these experiments provide strong
motivation for our definition of "synchronized" clocks: if
the twoway speed of light has always the same value, what
could be more natural than to _define_ "synchronized" clocks
so that the one-way speed has always this value?
[from page 4 of the cited paper][my quotes][my underscore]

Not only has no experiment shown one-way isotropy/invariance, but
it is easy to show that experiment proves just the opposite, as
in the case of the following extremely simple experiment:

Inertial observers Oa and Ob meet in passing as a single
light ray approaches them.

-----Oa
------------------------------------<~~~~~light ray
-----Ob

----------Oa
-----------<~~~~~~~~~~~~~~~~~~~~~
Ob

For simplicity, we let each observer be at his frame's origin.
Given this, anything at any point common to both frames' X axis as
the observers meet in passing will be the same distance from both
observers in terms of each observer's own ruler. In other words, as
the observers meet in passing, the tip of the approaching light ray
must be the same frame distance X from both observers per their own
on-board rulers. (Xa = Xb = X)

However, since nothing, including the leading edge of a light ray,
can be in two places at once, it is clear that the ray arrives at
the observers at absolutely different times. We can (qualitatively)
label these times Ta and Tb.

Here are the experimental results:

Light's one-way speed per Oa = X/Ta

Light's one-way speed per Ob = X/Tb

This very simple experiment shows that light's one-way speed varies
directly with frame velocity, contrary to Einstein's claim of one-way
invariance, which of course was the basis of SR.
 
  • #199
Martin Miller said:
This very simple experiment shows that light's one-way speed varies
directly with frame velocity, contrary to Einstein's claim of one-way
invariance, which of course was the basis of SR.
Certainly, if you don't conform to the theory, it is simple to prove it doesn't work. Try the math again using the framework of relativity and see if the results make any sense. Even better, get some experimental evidence and see that the math you did wouldn't fit the data collected in a real experiment.
 
  • #200
[russ_watters noted:]
Certainly, if you don't conform to the theory, it is simple
to prove it doesn't work. Try the math again using the
framework of relativity and see if the results make any sense.
Even better, get some experimental evidence and see that the
math you did wouldn't fit the data collected in a real experiment

[MM replies:]
Hmmm...
Uhhhh...
Ehhhh...
Duhhhh...
Well, yes, if you use clocks which have been forced by
Einstein's definition to obtain one-way invariance, then,
by George, I agree that you will certainly obtain one-way
invariance, but, as my simple experiment showed, one does
not even need clocks to simply qualitatively compare light's
one-way speed in different frames.

For those who may be lost, my above paragraph is making fun of
watters' absurd demand that I "conform to the theory" in order
to have a valid disproof of it.

And as for his claim that my experiment is not a "real" one,
which part of it does he think is not real?
 
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