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Nuclear Analysis of the Shroud of Turin part 2

After some time without being able to publish due to different problems, we continue with the activity of the web. We upload the rest of Robert Rucker's article to make up for the time we have not been able to publish. Although it is a bit long, it is worth reading.


4. Mystery 2. Carbon Dating of the Shroud

The process of carbon dating an object is performed by first taking one or more small samples from the object, because the material to be carbon dated must be burned. After the samples have been burned to reduce them to carbon, the ratio of C-14 to C-12 in the carbon is measured. A standard equation is then used to calculate the date based on the measured C14/C12 ratio. This equation assumes that the C14/C12 ratio could only change due to the decay of the C-14, which has a half-life of 5730 years. Based on the analysis below, it is believed that new C-14 was produced on the Shroud, so the assumption that the C14/C12 ratio could only change due to the decay of the C-14 is not valid. Thus, if new C-14 was produced on the Shroud, then this equation is not valid for calculating the date for the Shroud from the measured C14/C12 ratio.

In 1988, a thin strip was cut from the corner of the Shroud for dating (Figure 1). Samples were cut from this strip and sent to three carbon dating laboratories: Tucson in Arizona, Zurich in Switzerland, and Oxford in England (Figure 2). These laboratories cut their samples into smaller pieces so that ultimately 12 subsamples were carbon dated with each of the twelve dates having an uncertainty based on counting statistics and other considerations. The dates and uncertainties obtained for these 12 subsamples were reported by Damon, et al. in the British journal Nature in 1989 [4]. This paper concluded that the Shroud dates to 1260 to 1390 AD, though most Shroud researchers believe this date should be rejected, i.e., given no credibility [5, 6], because: 1) they did not have the technology to produce the images in 1260-1390, 2) there are many other date indicators that contradict the carbon dating to 1260-1390 AD [7, 16], and 3) because of the statistical analysis of the measurement data discussed below.

Table 2 shows the dates and uncertainties for the 12 subsamples from Damon [4] in black. These value are uncorrected values, i.e., not corrected for the changing concentration of C-14 in the atmosphere. They are also dates AD, whereas the dates in Damon [4] are Years Before Present (YBP), where the present is defined as 1950. Thus, the dates AD in Table 2 equals 1950 minus

the date (YBP) given in Damon. In Table 2, the values in red are the author’s calculated values starting from Damon’s reported values. The values in red display one additional digit to the right of the decimal point to prevent propagating a round-off error to the next step. The weighted average or mean value of these three laboratory weighted mean values is in red at 1277.8  12.6 AD. Instead of this value, Damon [4] chose to report an unweighted mean of 1260  31, which was then corrected for the changing C-14 concentration in the atmosphere to produce a range of 1260 to 1390 AD for the date of the Shroud. It was claimed in Damon [4] that the true value had a 95% probability of being within this range of 1260 to 1390 AD. The average of the 1260-1390 range is 1325 AD, so it is often assumed that carbon dating proved the Shroud dates to the Middle Ages. However, the calculation of this 1260-1390 range and the 95% probability that the true value falls within this range assumed that the uncorrected mean value of 1260  31 was known with certainty. Subsequent statistical analysis of the subsample data in Damon has indicated that this 1260  31 value should be rejected, i.e., given no credibility (see below).


5. Analysis of the Data from Carbon Dating

The difference between the Arizona date (1303.6  17.1) and the Oxford date (1200.8  30.7) is 102.8  35.1 years (square root of 17.12 + 30.72 = 35.1), which means that the dates from Arizona and Oxford are different by 2.93 standard deviations (102.8 / 35.1 = 2.93). This is greater than the usually allowed two standard deviations so it should be concluded these laboratories obtained statistically different dates. This should not be the case since all samples were cut from the same cloth and next to each other. The average dates from the three laboratories can also be correlated to the positions of their samples relative to each other. From left to right on the strip cut from the Shroud (Figure 2), the samples were sent to Oxford, Zurich, and Arizona (Arizona did not date sample A2), but in this same sequence the carbon dates are increasing. This spatial dependence of the measured carbon date is plotted in Figure 3 with the three laboratories, Oxford, Zurich, and Arizona plotted from left to right. The vertical bars indicate the one standard deviation range. The y-axis is the carbon date AD and the x-axis is the distance of the center of the sample from the left edge of the Shroud when it is displayed horizontally as in Figures 1 and 2. This plot shows that the uncorrected average value of 1260 AD claimed in Damon [4], represented by the horizontal black dashed line in Figure 3 only goes through the date from Zurich but not the dates from Oxford or Arizona. The best fit to the three laboratory average values is the red dashed line, which has a slope of about 36 years per cm, which is about 91 years per inch. This is very significant because if the sample point were moved 25.4 cm (10 inches) further from the short edge of the cloth and thus closer to the center of the body, then at this rate (36 years per cm) the measured carbon date would increase by about 910 years from 1260 AD to 2170 AD, which is a date to the future. This data indicates that an unknown factor appears to be causing the measured carbon date to be a function of the distance from the short edge of the cloth. This is equivalent to stating it to be a function of the distance from the center of the body.

Further analysis of the data can be done using a Chi-squared statistical analysis technique to determine whether the 12 subsample dates and their uncertainties for the Shroud are consistent with each other, as they should be. This statistical analysis on the data obtained from the Shroud is in Table 1, which is a copy of Table 5 in [8]. In this table, the Shroud samples are called material one on the top row and the three standards are called materials 2, 3, and 4 on the top row. The three standards discussed in Damon [4] are pieces of fabric taken from sources with known historical dates. They were carbon dated at the same time as the subsamples from the Shroud to confirm the accuracy of the carbon dating equipment and procedures. The result of this analysis is shown on the bottom row in Table 1 which gives the significance level for each of the four materials. This calculated significance level is the probability, in percent, of obtaining the magnitude of the scatter in the data that would have been obtained by random measurement errors alone. The usual criterion is a significance level of 5%, so if the significance level is 5% or above then the scatter in the data is normally accepted to be the result of random measurement errors alone, whereas if the significance level is below 5% then the magnitude of the scatter of the data is unlikely to be explained by random measurement errors alone so that a systematic measurement error is also likely present. As shown in the bottom row of this table, the significance levels for the three standards (materials 2, 3, and 4 in Table 1) are 90.1%, 28.0% and 13.9% which are all greater than 5% so the scatter in the data for the three standards is likely due to random measurement errors alone. However, the significance level for the subsamples from the Shroud, which is material 1 in Table 1, is only 1.4% and thus less than the criterion of 5%. This means that a systematic error was also likely affecting the measurements. Since it is not possible to determine the magnitude of this systematic measurement error, the only option is to reject the data, i.e., give no credibility to the measured carbon dates of the 12 subsamples or the alleged carbon date range of 1260 to 1390. This result is confirmed by four recent papers in peer-reviewed journals [9, 10, 11, and 12] which concluded that the subsamples from the Shroud are heterogeneous – fundamentally different from each other, so it is not correct to calculate an average value by adding the individual values and dividing by the number of values. Thus, it is not correct to arrive at a range of 1260 to 1390 AD. This conclusion is consistent with previous statistical analyses of the measurement data [8, 13].

The carbon dating of the corner of the Shroud produces three types of data: 1) the average value is about 1325, which is the midpoint of the range of 1260-1390 AD, 2) the change in the measured carbon date as a function of the distance from the short side of the cloth is about 36 years per cm, and 3) the measured carbon dates and uncertainties for the twelve subsamples are specified in Damon [4]. There is one additional evidence: 4) the carbon date for the Sudarium of Oviedo, which is believed to be Jesus’ face cloth, was measured to be about 700 AD. This 700 AD date for the Sudarium is significant for the study of the Shroud because Jesus’ face cloth (Sudarium) is closely related to Jesus’ body cloth, which is believed to be the Shroud of Turin. For a hypothesis to be correct in explaining the carbon dating of the Shroud, it must be consistent with these four evidences. To assume that the Shroud was made in 1260-1390 is only consistent with the first of these four evidences, so this assumption should be rejected.

6. Explanations for the Carbon Dating

The concepts that have been proposed to explain the measured carbon date of 1260-1390 are the following, in their approximate order of being proposed:


1. The neutron absorption hypothesis was proposed in 1989 by particle physicist Dr. Tom Phillips [14] in the same edition of Nature that contained the paper [4] by Damon, et al. Phillips proposed that neutrons absorbed in the Shroud would produce new C-14 on the fibers that would shift the carbon date measurement forward from the true date. No further work was done on this concept until nuclear analysis computer calculations were performed by the author in 2014.


2. Contamination due to handling of the Shroud during exhibitions.


3. Contamination due to intentionally putting materials such as wax or talc onto the Shroud to strengthen it.


4. Bioplastic film left on the fibers due to the normal action of bacteria. Concepts 2, 3, and 4 are not commonly advocated now because these forms of contamination would have to be over 65% of the mass of the samples to produce a measured carbon date of 1260-1390, and because visual inspection indicates these sources of contamination are not present in anywhere near this amount.


5. The invisible reweave hypothesis was proposed by Joe Marino [15] in 2000. In this hypothesis, French “invisible” reweave technology was used in the early 1500s, i.e., probably about 1520, to repair the corner of the Shroud where in 1988 the samples were cut from the Shroud for carbon dating. This involved weaving dyed cotton into the original linen fabric at the corner in such a careful manner that the resulting reweave cannot be seen. Thus, the samples that were carbon dated consisted of a mixture of new (about 1520 AD) and old (about 33 AD) material, resulting in the 1260-1390 carbon date. This hypothesis is currently the most common explanation for the 1260-1390 carbon date.


6. Carbon monoxide absorption hypothesis proposed by Dr. John Jackson. This hypothesis has largely been dropped due to lack of evidence for this mechanism, and other fabrics not being affected by it.


Since the measured carbon dates for the three standards were determined with reasonable accuracy, it should be accepted that the C14/C12 ratio measurements for the twelve Shroud subsamples were likely correct. As a result, the spatial dependence of the carbon dates for the Shroud must result, not from an error in the measurements of the C14/C12 ratio, but from something that altered the C14/C12 ratios in the twelve subsamples as a function of the distance from the short side of the cloth. As discussed above, of the above six proposed options for explaining the carbon dating of the Shroud, only the neutron absorption hypothesis (#1) and the invisible reweave hypothesis (#5) are now considered to be viable options by Shroud researchers. Probably most Shroud researchers now believe an “invisible” reweave occurred in the early 1500s when new cotton thread and cloth was dyed and interwoven into the older linen cloth of the Shroud [6, 15] using French “invisible” reweaving technology, but there are multiple objections against this hypothesis as discussed in section 10 of [17]. Due to these objections, the neutron absorption hypothesis (#1) deserves further consideration.


7. Nuclear Analysis Computer Calculations

Due to his extensive experience in calculating neutron distributions in nuclear reactors, the author recognized that the spatial dependence of the carbon date measurements for the Shroud (Figure 3) is similar to the neutron distribution that would occur if neutrons were emitted from the body. If neutrons were emitted from the body, a small fraction of these neutrons would have been absorbed in the trace amount of N-14 in the linen. When a N-14 nucleus absorbs a neutron,

it ejects a proton, thus becoming a new C-14 atom [N14 + neutron  C14 + proton]. This production of new C-14 atoms in the samples will shift the measured carbon date to the future relative to the true date. For example, if the C-14 concentration were increased by 16.9%, it would shift the carbon date from 33 AD to 1325 AD.

To determine whether this could be the explanation for the carbon dates obtained in 1988, nuclear analysis computer calculations were performed using the MCNP computer code. MCNP is an acronym for Monte Carlo N-Particle where “N” stands for neutron. MCNP was developed at the Los Alamos National Laboratory over many decades by a team of people. It is considered by US government agencies to be fully verified and validated for general nuclear calculations based on comparison of MCNP calculations with thousands of experiments in nuclear facilities.

In these MCNP calculations, for simplicity, a human body was modeled using simple geometrical volumes. The body was then surrounded by thin linen in the shape of a rectangular box to represent his burial cloth. Both were modeled with the head to the right on the back bench in a limestone tomb as it probably would have been designed in first century Jerusalem with a back bench and left and right-side benches (Figure 4). It was assumed that the neutrons were emitted homogeneously (uniformly) from within the body. Uncertainties in the assumptions had to be investigated using over 400 MCNP calculations run over a five-month period in 2014. To obtain good statistics, each MCNP calculation usually followed 30 million neutrons one at a time, which took between six and thirteen hours on a desktop computer. One set of assumptions had to be chosen from among these many calculations to facilitate communication of the results. For this set of assumptions, Figure 5 shows the MCNP predicted carbon date along the centerline of the body, i.e., along the backbone, on the section of the cloth that would have been under the body, where the dorsal image is now located. The output from MCNP is normalized to one neutron produced in the entire model. To make the calculated neutron distribution useful, it had to be renormalized to the only experimental data available, i.e., to the average experimental value obtained by the three laboratories for the location where the samples were cut from the Shroud. For convenience, it was also assumed that the area on the Shroud from which the samples were cut was folded under the feet so that the sample area was assumed to be on the centerline of the body just under the section of the cloth that was under the body. Thus, the carbon date distribution in Figure 5 was normalized to a total neutron emission from the body of about 2 x 1018 neutrons so that the second point from the left in Figure 5 would have a carbon date of 1260 AD, which is the uncorrected average value from the three laboratories. The question then is whether this hypothesis to explain the carbon dating of the Shroud is consistent with the above four evidences which it must be consistent with to be true.


1. Is the average date at the sample location 1260 to 1390? The answer is yes, but this is the result of the normalization process that forced the second point from the left to be the uncorrected average value of 1260 AD. The merit to this normalization is that it tells us how many neutrons would have to be emitted from the body, about 2 x 1018 neutrons, to produce the average carbon date at the sample location. This number is about one neutron for every ten billion neutrons that would have been in the body.


2. Is the change of the carbon date, as a function of the distance from the short edge of the cloth, about 36 years per cm? The answer is yes, the slope across the second point from the left in Figure 5, in comparison to the first and third points from the left, is close to a slope of 36 years per cm. Nothing was input to MCNP to force this slope to be correct. The MCNP computer code calculates this slope (about 36 years per cm) to be consistent with the experimental measurements of the three laboratories based on two assumptions: 1) the neutrons were emitted homogeneously within the body, and 2) the modeling of the limestone tomb was close enough to reality.


3. Is the distribution and range of the calculated carbon dates for the twelve subsamples consistent with the measured carbon dates and their uncertainties listed in Table 2? To answer this question, acceleration techniques must be added to the previous MCNP calculations to improve the spatial resolution so that calculated carbon dates can be obtained for areas on the cloth as small as the subsamples that were submitted for carbon dating. These calculations will be done in the future.


4. Is the carbon date for the Sudarium of Oviedo, Jesus’ face cloth, about 700 AD? We have no direct evidence of where the Sudarium was placed in the tomb other than the statement in John 20:7 that it was “folded up in a place by itself”, but the most likely location for the Sudarium can be predicted based on normal human behavior. It is unlikely the Sudarium would have been placed on the back bench where Jesus’ body and burial cloth were located, or dropped on the floor of the pit area, or placed on the walls or ceiling of the tomb. The only remaining areas are the left and right-side benches. Most people are right-handed, so the face cloth probably would have been dropped on the right-side bench. The person doing the burial would have been standing at the front of the pit or stand-up area in the tomb facing the body that he was working on, so he probably would have dropped the face cloth next to his own body onto the right-side bench in front of the back bench, i.e., in the direction of the entrance into the tomb. Based on this, it was predicted that the Sudarium was most likely located on the right bench about 35 to 45 cm (14 to 18 inches) in front of the back bench. MCNP was then rerun to include locations on the left and right benches. For the predicted location on the right bench, MCNP calculated a date of 700 ± 50 AD, in excellent agreement with the experimental results. The carbon date for the Sudarium would have been shifted less (from about 33 AD to 700 AD) than for the Shroud (from about 33 AD to 1260 AD) because the Sudarium was further from the body where a lower neutron density would have created fewer new C-14 atoms in the fabric.

The above indicates that the neutron absorption hypothesis is in good agreement with evidence related to the slope of the carbon date, i.e., the increase in the carbon date as the distance increases from the short edge of the Shroud, and the carbon date for the Sudarium, but that additional MCNP calculations should be performed to determine the agreement with the dates and uncertainties from the twelve subsamples. Due to problems with other explanations for the 1988 carbon dating of the Shroud to 1260-1390, it appears that the neutron absorption hypothesis [17] is the best explanation. The neutron absorption hypothesis proposes that if about 2 x 1018 neutrons were emitted homogeneously within the body, then a small fraction of them would have created enough new C-14 atoms in the linen fibers (a 16.9% increase in the C-14 density is required) at the 1988 sample location to shift the measured carbon date from 33 AD to about 1325 AD, which is the mid-point of the range of 1260-1390. About 96% of the new C-14 atoms would have been produced by a [N14 + neutron  C14 + proton] reaction. The other 4% of the new C-14 atoms would have been produced by two other reactions: C13 + neutron  C14 + gamma, and O17 + neutron  C14 + alpha (He4). The man that was wrapped in the Shroud has

been estimated to weigh about 78 kg (170 to 175 pounds). A person of this weight would have about 2 x 1028 neutrons in his body, so emission of 2 x 1018 neutrons is only one neutron for every ten billion neutrons in the body. The results of the MCNP calculations have also received significant confirmation from the position dependence of the fluorescence on the Shroud [18] based on photos taken by STURP in 1978. This is indicated in Table 3, which is from section 13 of [17].

The credibility of a hypothesis is not only determined by its consistency with the current evidence but also by testing its predictions. Predictions made by the neutron absorption hypothesis are testable, falsifiable, and unique, including: 1) Every location on the Shroud will date differently as determined by nuclear analysis computer calculations. 2) Using the usual equation for calculating a date from a measured C14/C12 ratio, about 75% of the area of the Shroud will date to the future relative to today, since it will contain a higher C14/C12 ratio than in our environment today. 3) Neutron absorption in Cl-35 in the Shroud and in the Sudarium will produce new Cl-36. Neutron absorption in Ca-40 in the limestone of the tomb will produce new Ca-41. There are naturally only trace amounts of Cl-36 and Ca-41 present in these materials, so a significant ratio of Cl-36/Cl-35 or Ca-41/Ca-40 should be easily measurable. The half-life of Cl-36 is about 301,000 years and the half-life of Ca-41 is about 99,400 years, so if Cl-36 or Ca-41 were formed by neutron absorption, they should still be present and measurable. Distributions of these isotopes can be predicted by nuclear analysis computer calculations.


8. Mystery 3#: Blood

The third mystery is related to the blood that is on the Shroud. About a dozen tests have been performed on the blood that is on the Shroud. Results of these tests proved that what appears to be blood is blood. All results are also consistent with it being human blood, though further testing is needed to exclude other possible options. Blood could have drained from the body onto the cloth where there were open wounds in the scalp, wrists, side, and feet. However, the problem is regarding the blood that would have dried on the skin before the body was wrapped in the cloth. Examples are the blood that drained from the wrist wounds and ran down the arms, and the blood from the scourging.

Since dried blood does not absorb into cloth, why is the blood that would have dried on the body now on the cloth? The hypothesis of an extremely brief intense burst of radiation emitted in the body offers a possible explanation. If the vertically collimated radiation burst within the body were sufficiently brief and sufficiently intense, it might have forced the wet or dried blood vertically off the body onto the cloth. This concept is suggested by our common experience of one object hitting another object causing the second object to accelerate away from the point of collision, as when one ball hits another ball on a pool table. If wet or dry blood is hit by particles in a sufficiently brief burst of radiation, then the blood will be hit with particles within this extremely brief time interval. If this time interval is brief enough, then the cohesive forces that normally hold the wet or dry blood together perhaps could continue to hold the blood together as it is accelerated, both vertically up and vertically down, away from the body toward the cloth. In this concept, the blood must not be excessively heated, so that the radiation would have to be particle radiation. Examples of particle radiation include neutrons, protons, and electrons.

Electromagnetic radiation such as ultraviolet light would vaporize the blood before it caused the blood to move significantly. This is based on the different equations for momentum and kinetic energy of particles compared to photons of electromagnetic energy. An example of particles accelerating an object is a man being hit by bird-shot from a shotgun. His body will continue to hold together as it is accelerated away from the shotgun. Experimental evidence for blood being thrust off fabric by an extremely brief burst of particles would probably require use of a particle accelerator, but this experiment has not yet been done. However, this concept of particles forcing the blood off the body onto the cloth should be considered to be a possibility, and results in predictions that should be tested.


9. The Vertically Collimated Radiation Burst (VCRB) Hypothesis

The author’s effort to solve the mysteries of the Shroud started with a scientific analysis of the 1988 carbon dating of the Shroud, as discussed in sections 4 to 7. The conclusions of this analysis is that: 1) the stated average carbon date of 1260 to 1390 is to be rejected, i.e. given no credibility, due to the presence of a systematic measurement error that caused the twelve subsample dates to be heterogeneous, as though they were not related to one another, and 2) the best explanation for the carbon dating of the Shroud is that neutrons were emitted from the body, with a small fraction of them being absorbed in N-14 to produce new C-14 atoms [N14 + neutron  C14 + proton] on the cloth that shifted the measured carbon date forward from the true date to the range of 1260-1390. This production of new C-14 atoms on the cloth by neutron absorption caused the systematic measurement error that is evident in the measurement data from carbon dating. This explanation is called the neutron absorption hypothesis. This explanation is the only hypothesis that could be consistent with the four things we know to be true about carbon dating related to the Shroud: 1) the average carbon date of 1260-1390 AD, 2) the change in the carbon date as a function of the distance from the short edge of the Shroud is about 36 years per cm, 3) the distribution and range (1155 to 1410 AD) of the measured carbon dates for the twelve subsamples, and 4) the measured carbon date for the Sudarium of Oviedo, which is believed to be Jesus’ face cloth, of about 700 AD. The neutron absorption hypothesis is consistent with #1, #2, and #4 above, but additional MCNP calculations will be needed to prove it is consistent with #3. The invisible reweave hypothesis is consistent with #1 above, can be consistent with #2 under the right assumptions, is unlikely to be consistent with #3, and cannot explain #4.

Scientific evidence related to how the images of a crucified man were formed on the Shroud is discussed in section 3 based on [3]. The process was to follow the scientific evidence where it led. The conclusion of this analysis is that the images could probably have been formed by an extremely brief intense burst of vertically collimated low energy charged particles, probably protons, which were emitted in the body. These charged particles, when absorbed on the cloth, caused electrical currents in the fibers which produced extremely localized electrical heating which produced extremely localized discoloration of the fibers which caused the images. These charged particles could also have formed ozone in the air that could have chemically altered the thin circumferential region of the fibers. This charged particle radiation had to carry the information from the body to the cloth that was required to discolor the correct fibers to form the images of a crucified man. This information, in the form of the number of particles , was deposited on the cloth when the radiation was absorbed on the cloth. The basis for believing this

hypothesis could be true is its consistency with the scientific evidence related to the nature of the images.

These explanations for the image formation and the carbon dating both depend on particles being emitted from the dead body that was wrapped in the Shroud. Thus, both explanations are beyond or outside of our current understanding of the laws of physics, but this is consistent with the unique qualities of the Shroud. The Shroud is the only cloth in existence in which the dead body that was wrapped within it produced full-size front and dorsal images of itself on the cloth. In this situation, it is probably reasonable to assume that the charged particle emission that caused the images and the neutron emission that shifted the measured carbon date forward are both part of the same event. When these two explanations are combined, the result is the Vertically Collimated Radiation Burst (VCRB) hypothesis.

The VCRB hypothesis proposes that radiation was emitted from within the body in an extremely brief intense burst of low energy radiation. Charged particles such as protons in this radiation produced the images whereas neutrons in this radiation shifted the measured carbon date in the forward direction. For the protons to form good resolution images of the front and dorsal images without images of the sides of the body, they had to be vertically collimated. The protons and neutrons were probably emitted in the body by nuclei in the body that released their component parts by fission or splitting. The isotope that requires the least energy to fission and is thus the most likely to fission is deuterium, also called heavy hydrogen because it not only contains a proton in its nucleus but also a neutron, thus making it about twice as heavy as a normal hydrogen atom.

The discolored outer layer less than 0.2 micrometers thick around the outer circumference of the fiber was probably produced by a “skin-effect” of a high frequency alternating current in the fibers, which was most likely produced by proton emission that oscillated between vertically up and vertically down directions. Due to conservation of momentum, when a deuterium nucleus emitted a proton vertically up, the neutron would have been emitted vertically down. And when a deuterium nucleus emitted a proton vertically down, the neutron would have been emitted vertically up. Perhaps this process could have been produced by a vertical oscillation of nuclei in the body that caused about 0.0004% of the deuterium nuclei to split. This 0.0004% value is obtained from the requirement that about 2 x 1018 neutrons be emitted from the body to shift the measured carbon date for the corner of the Shroud from about 33 AD to 1325 AD.

To understand what could have caused such a vertical oscillation of the deuterium nuclei will probably require considerations in advanced modern physics such as particle physics, quantum field theory (QCD, QED, QFD, and EWT), super symmetry, and string theory. Many questions would arise in such considerations. For example, could the deuterium nuclei fission due to vertically oriented fluctuations in one of the quantum fields that permeates space-time, such as the quark field that gives rise to the up and down quarks that compose protons and neutrons, or the gluon field by which protons and neutrons are held together in the nucleus? In the standard model of modern physics consisting of 12 particle fields, four force fields, and the Higgs field, why would a gluon field fluctuate in the direction of the gradient in the gravity field? Could these vertical fluctuations be related to the alternate dimensions hypothesized by the various string theories? And could this be related to transfer of matter between dimensions, as suggested

by the Biblical evidence for the disappearance of Jesus’ body from within his burial cloth [19, John 20:8-9]. Progress in better understanding this radiation process can hopefully be made by these considerations and future testing of the Shroud.

The VCRB hypothesis has the qualities of a very good hypothesis: 1) It can be consistent with the scientific evidence related to image formation and carbon dating since it was derived from this evidence, 2) it makes predictions that are testable, falsifiable, and some of which are unique, and 3) it offers explanations for multiple mysteries of the Shroud related to image formation, carbon dating, and the blood on the Shroud. Scientists are generally more attracted to a hypothesis that could explain multiple mysteries of a phenomenon. No other hypothesis attempts to explain more than one mystery of the Shroud. Predictions of the VCRB hypothesis include the following:

Image Formation:


 A very high frequency alternating current in a flax fiber will discolor the outer circumference of a fiber to a thickness of less than 0.2 micrometers.

 An extremely rapid pulse of charged particles such as protons hitting a linen cloth will produce a mottled pattern of discolored fibers only two or three layers deep in the thread that is like the fiber discoloration on the Shroud.

 If protons were emitted in a human body in an extremely brief burst, the number of protons will diminish due to scattering and absorption as they pass through the air that is between the body and the cloth, consistent with evidence on the Shroud. This effect is necessary to explain the images on the Shroud being negative images with light and dark area reversed, and the presence of 3D or topographical information encoded into the images related to the vertical distance between the body and the cloth. This will probably have to be investigated using computer calculations such as the MCNP computer code.


Carbon dating:

 Every location on the Shroud will carbon date differently as determined by nuclear analysis computer calculations, as in Figure 14 of [20].

 Using the usual equation for calculating a date from a measured C14/C12 ratio, about 75% of the area of the Shroud will carbon date to the future relative to today, since it will contain a higher C14/C12 ratio than in our environment today.

 Neutron absorption in Cl-35 on the Shroud and in Ca-40 in the limestone of the tomb will produce Cl-36 and Ca-41. These isotopes have half-lives of 300 thousand years and 99 thousand years, so if they were formed by neutron absorption, they will still be present and should be measurable.

 The distribution of neutrons hitting the Shroud calculated by MCNP will cause measurable differences in the fluorescence from the Shroud. This was tested by McAvoy [18] and found to be true.


Blood on the Shroud:

 If a radiation burst is sufficiently brief and intense, it will force wet or dry blood off a surface such as skin onto another surface such as linen.


10. Future Testing of the Shroud

The Shroud was owned by the Savoy family in Italy starting about 1453, but in 1983 the Shroud was willed to the reigning pope so he will make the final decision regarding future testing of the Shroud. The last extensive testing was performed in 1978 immediately after an exhibition of the Shroud in Turin. Future testing of the Shroud should take advantage of the significant advances in nondestructive testing (NDT) technology since the last extensive testing in 1978. Predictions of the VCRB hypothesis that should be tested are discussed in the previous section. The following are some of the questions that should guide future testing of the Shroud.

Image Formation:

Nature & location of discoloration?

Evidence of bones, backside image, coins over the eyes?

Cause of banding and mottling?

Distribution of fluorescence on the Shroud?

Other evidence of radiation on the Shroud?

Dating:

Carbon dates for other locations? [21]

Other long-lived isotopes produced by neutron absorption, such as Cl36 and Ca41, on the Shroud, on the Sudarium, or in the tomb?

Evidence of an invisible reweave at the 1988 sample location? [6, 15]

Other dating methods: reflectance, tensile strength, etc.?

Blood:

Location, shape, composition, serum rings?

Is blood human, male, type AB?

DNA genome? What race?

Why is it reddish? What are the possible explanations?

Has the blood been retouched with paint?

History:

Pollen?

Limestone chips, dust, debris?

Side piece and stitch?

The following have been suggested for future testing of the Shroud.

 Light and electron microscopy

 Multispectral & Hyperspectral imaging

 X-ray fluorescence

 Fourier Transform Infrared Spectroscopy

 Raman and Energy Dispersive Spectroscopy

 Atom probe tomography

 Nuclear Activation Analysis

 Radiation detection methods


11. Conclusion

The main mysteries of the Shroud are image formation, carbon dating, and the blood that is now on the cloth. Hypotheses to explain these mysteries should be developed by following the scientific evidence where it leads. This should be done with a neutral mindset that is not restricted by presuppositions. According to the scientific process, for such a hypothesis to be credible, it must be consistent with the evidence and make predictions that are testable and falsifiable, and when tested the predictions are found to be true.

Consideration of the scientific evidence related to the images indicates that the images appear to have been formed by an extremely brief intense burst of vertically collimated low energy charged particles such as protons emitted in the body. When these particles were absorbed on the cloth, they caused electrical currents in the fibers that produced extremely localized heating which produced extremely localized discoloration of the fibers that made the front and dorsal images. The charged particle emission from the body could have also produced ozone in the air that chemically altered the thin discolored region around the circumference of the fibers. Consideration of evidence related to the carbon dating indicates that about 2 x 1018 neutrons were probably emitted in the body that produced new C-14 atoms on the Shroud primarily by a [N14 + neutron  C14 + proton] reaction. These new C-14 atoms would have shifted the measured carbon date forward relative to the true date. It is reasonable to conclude that the image formation and the carbon dating are related to each other since they are both the result of radiation emitted from the body. When these two explanations are combined, the result is the Vertically Collimated Radiation Burst (VCRB) hypothesis. The VCRB hypothesis proposes that an extremely brief intense burst of vertically collimated low energy particles were emitted in the body, with protons causing the images and neutrons shifting the carbon date forward from the true date. The source for these protons and neutrons could possibly have been the splitting of 0.0004% of the deuterium nuclei in the body. What would cause deuterium nuclei to split is not currently understood but might be investigated by future testing of the Shroud and by various considerations in modern physics. If this burst of radiation from the body were sufficiently brief and sufficiently intense, it could possibly have thrust wet or dry blood off the body onto the cloth.

The VCRB hypothesis has the qualities of a very good hypothesis: 1) Since the VCRB hypothesis was derived from the scientific evidence, it is possible for it to be consistent with the scientific evidence related to image formation and carbon dating, 2) it makes predictions that are testable, falsifiable, and some of which are unique, and 3) it offers explanations for multiple mysteries of the Shroud related to image formation, carbon dating, and the blood on the Shroud. No other hypothesis attempts to explain more than one mystery of the Shroud. For there to be a general consensus among Shroud researchers that the VCRB hypothesis is probably true will require: : 1) time to build a consensus that the VCRB hypothesis is consistent with the evidence from the Shroud, and 2) time to test the predictions in section 9 to determine whether they are true. To the extent that the VCRB hypothesis is accepted as true, it leads to two criteria that can be used to determine whose image is on the Shroud of Turin: 1) He was crucified exactly as Jesus was crucified according to the New Testament, and 2) His dead body emitted an extremely brief intense burst of radiation that encoded an image of his body onto the Shroud and shifted the measured carbon date of the Shroud to the future relative to the true date. In all the historic

documents available to humanity, the only person and event that satisfies these two criteria is Jesus in his resurrection.

There is no known example of a human body producing an image of itself on a piece of cloth, except for the Shroud of Turin. This unique encoding event appears to require a unique mechanism that is beyond our current understanding of physics. There has been extensive progress in testing procedures since the last systematic testing of the Shroud in 1978. Testing should again be allowed on the Shroud to further mankind’s understanding of reality.


12. References

1. Websites include shroud.com, which includes an extensive list of papers on the Shroud, as well as shroudencounter.com, shroudresearch.net, and testtheshroud.org. Recommended books include “Report on the Shroud of Turin” by John Heller (1983), “The Blood and the Shroud” (1998) and “The Shroud, Fresh Light on the 2000-Year-Old Mystery” (2010) by Ian Wilson, “Resurrection of the Shroud” (2000) and “Test the Shroud” (2015) by Mark Antonacci, “The Shroud of Turin” (2015) by Giulio Fanti & P. Malfi, “The Hidden History of the Shroud of Turin” (2021) by Jack Markwardt, and “The Shroud of Christ, Evidence of a 2,000 Year Antiquity” (2023) by Michael Kowalski.

2. Robert A. Rucker, “Holistic Solution to the Mysteries of the Shroud of Turin”

3. Robert A. Rucker, “Image Formation on the Shroud of Turin”

4. P.E. Damon, and 20 others, “Radiocarbon Dating of the Shroud of Turin”

5. Mark Antonacci, “Test the Shroud’, 2015, Chapter 14 “Nine year Carbon Dating Fiasco”

6. Joseph G. Marino, “The 1988 C-14 Dating of the Shroud of Turin: A stunning Expose”

7. Robert A. Rucker, “Date of the Shroud of Turin”

8. Robert A. Rucker, “The Carbon Dating Problem for the Shroud of Turin, Part 2: Statistical Analysis”

9. T. Casabianca, E. Marinelli, G. Pernagallo, and B. Torrisi, “Radiocarbon Dating of the Turin Shroud: New Evidence from Raw Data”

10. Paolo Di Lazzaro, Anthony C. Atkinson, Paola Iacomussi, Marco Riani, Marco Ricci, and Peter Wadhams, “Statistical and Proactive Analysis of an Inter-Laboratory Comparison: The Radiocarbon Dating of the Shroud of Turin”

11. Bryan Walsh and Larry Schwalbe, “An Instructive Inter-Laboratory Comparison: The 1988 Radiocarbon Dating of the Shroud of Turin”

12. Bryan Walsh and Larry Schwalbe, “On Cleaning Methods and the Raw Radiocarbon Data from the Shroud of Turin”

13. Remi Van Haelst, “Radiocarbon Dating the Shroud of Turin, A critical review of the Nature report (authored by Damon, et al.) with a complete unbiased statistical analysis” and “A critical review of the radiocarbon dating of the Shroud of Turin. ANOVA – a useful method to evaluate sets of high precision AMS radiocarbon measurements”

14. Thomas J. Phillips, “Shroud Irradiated with Neutrons?”

15. Joseph G. Marino and M. Sue Benford,"Evidence for the Skewing of the C-14 Dating of the Shroud of Turin Due to Repairs"

16. Michael Kowalski, “The Shroud of Christ, Evidence of a 2,000 Year Antiquity”

17. Robert A. Rucker, “Solving the Carbon Dating Problem for the Shroud of Turin”

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18. Thomas McAvoy, “On Radiocarbon Dating of the Shroud of Turin”

19. Robert A. Rucker, “The Disappearance of Jesus’ Body Part 2: Physical Considerations”

20. Robert A. Rucker, “The Carbon Dating Problem for the Shroud of Turin, Part 3: The Neutron Absorption Hypothesis”

21. Robert A. Rucker, “Proposal for C14 Dating of Charred Material Removed from the Shroud”

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