A Progress Report on Replicating An Experiment to Measure the Absolute Motion of the Earth

C. Michael Edwards

Upon reading the results of Dr. Lance Osadchey's “An Experiment to Measure the Absolute Motion of the Earth,” (The Citizen Scientist, 2 Feb. 2007), I decided to attempt to verify his claim of a measurable absolute vector reference. I duplicated his apparatus (called a “Velador”), and set to work. Since Dr. Osadchey had already discovered this vector reference, I was absolved of that responsibility. Instead, I focused on known phenomena that could explain the reported result without a previously unknown vector field.

Phenomena Investigated

I identified four candidates for false signals:

1. Inherent image noise – Electronic noise in the camera circuitry can cause CCD cells to register higher than actual intensity, and partially illuminated cells may not register, introducing measurement errors.

2. Thermal refraction – Thermal gradients across the air of the light path can refract the light beam, deflecting it.

3. Bending of the support beam under load – The support is already bent under its own weight, and tiny shifts in its weight will change the angle of bending, moving the camera and laser.

4. Thermal bending of the support beam – Uneven expansion of the support as its temperature changes will cause it to bend and twist, moving the camera and laser.

These were all observed to some extent. My goal was to find if one or more could explain Dr. Osadchey's observations.

My Velador

I designed my apparatus along the same lines as Dr. Osadchey's. There are four important design changes:

1. The support beam is hollow, allowing a light path through its center.

2. The support beam is made of an insulating material which isolates the light path air from the surrounding room.

3. The support beam is suspended, allowing it to remain aligned with the direction of gravity rather than being coupled to a rigid mount.

4. The camera power supply, adjustments and shutter switch are externally wired, allowing use without touching the camera or requiring removal for maintenance.

The basic component parts are:

The assembled support beam is suspended on S-hooks beneath a 2”x 4” board, which is affixed to a mount with bolts. My mount is a wheeled oscilloscope table, propped at the desired angle with scrap lumber from the support beam's construction, holding the Velador at fixed attitude. This is shown in Fig. 1 and Fig. 2. The uninstalled camera and laser cells are shown in Fig. 3.

Figure 1. Schematic of my Velador design.

Figure 2. Photo of my Velador before a trial.

Figure 3. The laser cell (bottom) and camera cell (top), with springs and mounting brackets installed prior to final assembly.

The design does not have an adjustable elevation.

Measuring Image Position

I wrote a program to compute statistical measures of position for each image and to append that data to a spreadsheet for each experimental trial. My programming skills were insufficient to analyze images right from the camera. Each had to be converted to bitmap format first, but this process is still faster and more reliable than manual measurements.

The average position coordinates of the image, X and Y, were computed as:

(Eq. 1)

Standard deviations of size in the horizontal and vertical directions were calculated. These values are measures of image size, and are not a standard deviation of position.

(Eq. 2)

I also planned how many images to take for each trial. Using the reported results as a guide, I estimated the effect I would see using my camera. Using a linear motion approximation (which was adequate for planning but which I eventually abandoned), I expected roughly 3 km/s lateral motion. My camera CCD is 4 mm vertical x 5 mm horizontal, +/- 0.5 mm, with 1054 pixels vertical by 1250 pixels horizontal. This corresponds to 4.0 microns +/- 0.4 µm per pixel. The expected lateral deflection, d, for a beam length L is computed using the ratio of lateral motion, v, to the speed of light, c.

(Eq. 3)

I assumed the image noise to be +/-1 pixel (+/- 492m/s) per image, making the expected peak-to-trough noise +/- 2 pixels, and assumed a standard deviation of position of 2 pixels. This suggested a minimum reliable measurement of 3 pixels (+/-1475m/s) peak-to-trough for each trial. I chose this as a rejection criterion, being the (assumed) limit of the instrument's accuracy. Similarly, measured deflections of more than double the expected value are rejected, too.

For a statistical confidence of 99%, the sample size required is:

(Eq. 4)

Where µ LOWER is the lower bound for an acceptable signal; µ UPPER is the upper bound; s is the standard deviation of position; a and ß are the probabilities of Type I and Type II statistical error, respectively; and z a and z ß are the normalized test values corresponding to a and ß, respectively.

Since thermal bending is non-linear, I expected non-linear drift (motion due to an accumulating error such as gradual bending). Three points are needed for a useful fit, so I needed at least three data points at the same angle to correct for drift. The minimum acceptable sample size was two complete turns with a final measurement at the starting position. I chose three turns.

Statistical confidence is only probability that the measurement is not random noise. A non-random false signal has statistical confidence, too. Since I did not plan sufficient sample size for Fourier analysis, isolating a false signal required recognizing characteristic patterns for the expected errors.

Models of False Signals

Theoretical models of each error source revealed that each has a unique signature.

Inherent noise in the camera circuitry causes increased standard deviation of position and image distortion (manifesting as mode and median changes not corresponding to image motion, and changes in the image size).

Thermal refraction is a three dimensional phenomenon. Equation 5 gives the dependence of the index of refraction, n, on temperature, T, and Eq. 6 describes the deflection of the light, but the transition between angles ? 1 and ? 2 is not instantaneous. The transition causes uneven image distortion in proportion to the image motion (reflected in the image mode, median, and size). Because refraction is temperature dependent, image motion due to refraction can be increased by increasing the temperature.

(Eq. 5)

(Eq. 6)

Figure 4 shows a photo of the laser beam illuminating a wall, and Fig. 5 is a photo of the same area with the laser intentionally distorted by a large thermal gradient.

Figure 4. A webcam close-up of the laser beam on a wall. Note the ghost image to the right due to internal reflection.

Figure 5. A webcam closeup of the incident laser after refraction by a candle flame. The image is visibly smeared in comparison to Fig. 4.


Shifts in the beam's weight will most likely be caused by pendular motion or variations in the floor slope. This will show up in control experiments, for which the observed amplitude will vary for different positions on the floor, as in Fig. 6.

Figure 6. Two patterns of motion for the Velador with the same orientations but moving over different floor positions.


Temperature changes causing refraction and thermal deformation will be time dependent, and image motion due to heat transfer can be exaggerated by increasing the time interval between measurements. Also, drift will tend to wash out a real signal over time. Equation 7 is an approximation for thermal bending of a thin beam, d, where d is beam thickness, l is length and a TE is the thermal expansion coefficient of the material. Figure 7 shows a simulated false signal created by evenly rotating the Velador near a heat source.

(Eq. 7)

Figure 7. A position chart for a simulated false signal caused by alternating thermal bending. The overall motion follows a curve.

My analysis method can also introduce error. Thermal deformation can vary in rate. Subtracting out a polynomial fit for drift can exaggerate these changes in rate and make them appear to be oscillating motion. However, the uncorrected motion will not oscillate. The reported effect is characterized by reversal of uncorrected image motion.

Observed Behavior

I have observed image motion varying predictably with orientation as reported, with approximately similar amplitude. Furthermore, although the assumptions used to derive my experimental plan suggested statistical inadequacy in Dr. Osadchey's trials, my experiment shows that the average noise level and standard deviations of position are lower than assumed (0.75 pixel per image and 0.6 pixel over 4 turns, respectively). A single sample is adequate to differentiate from random noise at this level. I retain a minimum sample size of two turns, due to the large observed drift in my own measurements.

Observations of average error and standard deviations lead me to reject inherent image noise as an explanation of the observed effect. Noise levels are simply not large enough to explain the effect, even if it could be made to respond to orientation.

My measured amplitude has consistently tended toward 2.1 +/- 0.6 times less than Dr. Osadchey's, and varies during the day by a factor of at least 2. Because the amplitude regularly and predictably decreases to less than 3 pixels on a daily basis, I am able to actively test the effect of floor surface variations. I have experimentally verified that variations due to floor surface do not exceed 2 pixels with household foundation tolerances (1 cm per 3 m), and are thus insufficient to explain my observations.

This daily variation places geometric constraints on any real reference vector, which can be used for additional testing. I have not yet conducted sufficient trials to determine if the variation is dependent on sidereal time or diurnal time.

I have observed thermal refraction, both during trials and with the use of a webcam, and it's magnitude is large enough to account for the observed amplitude. Because refraction angle will vary slightly across the width of the laser, not all portions of the laser beam are refracted equally, and this manifests as stretching of the image in the direction of motion.

However, observations of refraction demonstrate that it is too variable to explain the observed dependence on orientation. Further, refraction of the required magnitude is relatively infrequent. Most measurements show no evidence of the image distortion predicted by my theoretical model and observed during both induced and spontaneous refraction. I must reject refraction as a cause.

That leaves thermal deformation of the beam, which can mimic a real signal as the beam is alternately heated and cooled by rotating relative to a nearby heat source.

I deliberately conducted the majority of my experiment without air conditioning to induce thermal drift, and I found it. Figure 8 shows a typical trial without climate control.

Figure 8. A typical observed position chart for an actual trial. The overall motion follows a curve, with the effect of interest superimposed.


Unlike mine, the drift in Dr. Osadchey's results is sufficiently small that the motion in his measurements is nominally circular. I deliberately sought circumstances with drift outside that regime because the characteristic patterns of thermal drift do not manifest for small drift rates. This data can be corrected for drift by subtracting out a polynomial fit for measurements at the 0 degree orientation. Figure 9 shows adjusted coordinate values for this case, corrected for drift.

Figure 9. A graph of adjusted coordinates vs. angle for the trial shown in Figure 8. Estimated drift is subtracted out.


This pattern can be imitated by alternating heat flow as the Velador rotates. However, increasing the time interval will increase the drift. A false signal will increase in amplitude with longer intervals, while a real signal will have a relatively constant amplitude, or decrease in amplitude as it is washed out by the larger drift. Figure 10 shows the results of a trial and an accompanying control conducted with double the interval between measurements. There is no noticeable increase in the adjusted x coordinate, and the vertical amplitude has been overwhelmed to the point that its angle dependence is longer apparent. The unadjusted data in Fig. 11 shows evidence of a cooling curve in the overall drift. However, there is no corresponding increase in amplitude for the oscillating component.

Figure 10. Two graphs of adjusted coordinates vs. angle for two sequential trials. Measurement intervals are 40 seconds for Trial 15 and 20 seconds for trial 16. The adjusted X amplitude and phase remains approximately the same for both.

Figure 11. Position charts for the observed motion of trials 15 and 16. Trial 15 needs double the scale of Trial 16, because it has double the drift.

The amplitude is not related to the drift rate. Increased heat input (same heat flow over longer time) at each angle does not increase the measured amplitude despite the fact that it clearly increases the drift.

The drift is likely a manifestation of thermal bending. Since the oscillations appear independent of drift rate, they are unlikely to be due to thermal bending.

My model for thermal deformation cannot explain my observations. Also, Dr. Osadchey's experiments – with more stringent temperature controls – indicate that drift can be reliably reduced to a level insufficient to explain his observations.

Conclusion

I eliminated three of my four alternate explanations for the reported observations, and made significant progress toward excluding thermal deformation.

My test of thermal deformation was guided by a specific theoretical model rather than the general case, but that model describes the observed drift relatively well. The observed effect does not match my predictions for a false signal due to varying drift, because the amplitude is independent of the measurement interval. Thermal deformation is still a candidate explanation, because the behavior is time variable over the course of a day. However, continued experimentation can resolve the involvement of thermal deformation, since thermal deformation will be dependent on diurnal time.

I cannot reject an absolute vector reference based on my initial results. Thus, I am planning another phase of my experiment. I will modify my Velador for variable elevation, check for dependence on sidereal time, and change to a camera compatible with a regulated power supply to record enough cycles for Fourier analysis. It is my opinion that my results allow for a phenomenon new to science, and I want to see where continuing this experiment takes me.

I will continue posting collected data and reports to my web site: http://hearth2.50megs.com and to my experimental journal at the SAS web site.

References and Recommended Reading :

Beer, F.P., Johnston, Jr., E.R. and DeWolf, J.T. Mechanics of Materials, Fourth Edition . McGraw Hill Publishing, 2005.

Devore, J.L., Probability and Statistics for Engineers and the Sciences, Third Edition. Brooks/Cole Publishing Co., 1991.

Serway, R.A. and Faughn, J.S., College Physics, Third Edition . Saunders College Publishing, 1991.

Osadchey, L., “An Experiment to Measure the Absolute Motion of the Earth,” The Citizen Scientist, 2 Feb. 2007, http://www.sas.org/tcs/weeklyIssues_2007/2007-03-03/project1/index.html. Last Accessed 6/24/07.

Osadchey, L., “Update and Comments about An Experiment to Measure the Absolute Motion of the Earth,” The Citizen Scientist, 6 Apr, 2007, http://www.sas.org/tcs/weeklyIssues_2007/2007-04-06/project2/index.html. Last Accessed 6/24/07.

Osadchey, L., “The Velador Series”, http://www.lanceosadchey.com/. Last Accessed 6/24/07.