Ladies and Gentlemen, Dear Colleagues!
I am very grateful to the organizers of the conference for the invitation. It is a pleasure and a great honor for me to speak before you here, in Italy, where the great Christian relic - the Shroud of Jesus Christ - is stored. Excuse, please, my emotion, because I know there are many experts and scientific researchers here, who contributed a lot to investigations of the Shroud. In spite of the great interest in the Shroud among Christians and other people in Russia, there were no explorations of the Shroud up to now in our country. The reason is the presence of the prevailing atheistic ideology. Now the situation has changed, and the Patriarch of Moscow and all Russia, Aleksii, has pointed out in a letter to Dr. J. Jackson, " ...in Russia and Russian Orthodox Church there is a great interest to the Shroud of Turin".
Due to the efforts of Dr. Jackson from the Turin Shroud Center of Colorado and Dr. Dmitrii Kuznetsov (Moscow), research of the Shroud has now started in Moscow. Dr. Jackson initiated the opening of the Branch of the Turin Shroud Center in Moscow, which will coordinate research and distribute knowledge about the Shroud in Russia. I hope it will be interesting for you to learn that the Patriarch of Moscow and all Russia, Aleksii, has given his blessings for the opening of a small museum devoted to the Shroud of Turin in Moscow, in the Sretenskii Monastery. It is planned that the exact, full-sized copy of the Shroud, prepared for public demonstration by Dr.Jackson, will be exhibited there. I hope that the Moscow Turin Shroud Center and the museum could involve Russian orthodox scientists and other researchers in the investigation of the Turin Shroud in various directions, starting from a history of the church and iconography up to physics and chemistry. I hope that the participation of the Russian Orthodox Church could be very fruitful in this area and contribute much to the research of the Shroud.
For me, as a physicist, the most intriguing puzzle raised by the Shroud is the question about the mechanism of the image formation. The problem is that not one of the available mechanisms of image formation could explain the high degree of resolution of details observed on the Shroud.
Dr. Jackson applied computer programs for the investigation of the Shroud, developed previously for reconstruction of three-dimentional objects utilising aerophotographs . Working with a model of the Shroud, he measured experimentally (with the help of volunteers) the distance between the Shroud and human body, and obtained data he has compared with the Turin Shroud photographs. As a result of this research he found that the opacity on the Shroud is in a simple functional dependence on the distance between the Shroud and the surface of the body. Thus, the statement that on the Shroud we have a negative image is only the first approximation to reality. More strictly, the image is a record of the distance between a body and the Shroud, written by means of opacity. Knowing this functional dependence and using the image on the Shroud, Dr. Jackson was able to reconstruct the three-dimensional shape of a human body.
The modern level of investigation of the Turin Shroud and the accumulated knowledge about it allows us to reject all previously proposed hypotheses for the explanation of the image formation. It is possible to separate the available hypotheses into four classes:
1) The image is simply painted on the Shroud;
2) The image is result of a direct contact with the body;
3) The image appeared as a result of diffusion processes;
4) The image arose due to some radiation processes.
These hypotheses were investigated theoretically and experimentally and thoroughly tested, in particular, by Dr. Jackson. It was shown, that the "direct contact" mechanism and a hand painter may reproduce tiny details of the object, but they are not able (to create) an image with the opacity related to the distance between the Shroud and the body. On the other hand, diffusion and radiation processes may give rise to the images which contain information on smoothly varied distance between the object and the Shroud, but they could not give the needed resolution (i.e. rather high degree in reproduction of details, which we find in the image on the Shroud).
In remarkable and extended investigations of Dr. Jackson's work along this problem, as to my mind, some factors were not taken into account, which could explain the rather high degree of resolution of the image. It could be that in experiments with sculptures, painted with phosphorus and placed on a semi-transparent medium with absorption, the surface radiation may have another angular dependence (other) than the radiation, (and) created the image on the Shroud. If the radiation outgoing from Christ's body was created not on its surface, but inside the body, radiation will become anisotropic on a surface of the body, i.e. dependent vs the direction of radiation. In the theoretical investigation of the resolution of the anisotropic radiation, Dr. Jackson considered the resolution of two point sources, instead of the resolution from a radiating body of a complicated geometrical form.
From the dependence of the opacity on the Shroud versus the distance to the body, obtained by Dr. Jackson, it follows that a light outside the body has to be appreciably absorbed in air on characteristic distances of about one centimeter. Otherwise, inside the body the radiation should be absorbed on distances of order 0.01 mm, because the density of the body is three orders higher than the density of air. Thus, the radiation intensity in each point of a surface of the body should be identical, but the radiation at different directions will be different (anisotropic). In the theoretical work  devoted to investigation of resolution of anisotropic radiation, Dr. Jackson considered the resolution of two point sources, lying on a non-radiating surface. However, it is necessary to consider the resolution from some details, lying on a uniformly radiating substrate, having a complicated geometrical form.
Therefore, for me the first task was an investigation of the resolution of the anisotropic radiation from two hemicylinders lying close to each other on a plane, taking into account possible partial absorption in surrounding medium. Radiation from the plane outside the cylinders was also included. Such a geometrical shape of the body was chosen as the most closest for simulation of lips, fingers and legs. As were shown in theoretical calculations and computer simulations (programmer - Sergey Stepanov), such an anisotropic radiation gives better resolution then the isotropic one, but does not lead to the degree of resolution needed to explain the appearance of the image on the Shroud. For the illustration of the obtained results I'll show later two figures to compare the results, obtained in different models.
Thus, we come to the conclusion, made earlier by Dr. Jackson, that for the explanation of the appearance of the image on the Shroud we must address not to the "traditional, old" physics, but a "new" one. However, the difference between these concepts in our case is not well defined. For example, the radiation in the model considered above propagates according to the conventional laws of "old" physics, but it is difficult to explain the nature of the body source of this X-ray radiation, having the shape of a human, remaining within the framework of old physics.
For explanation of a high degree of the resolution of the image on the Turin Shroud we should make one step more toward the new physics. It is an assumption, that during the resurrection of Jesus Christ his body was surrounded by a light-like energy. An intensity of this luminescence decreases with the distance from the body. Probably, this luminescence was similar to that "fire", by means of which the power of God was usually appeared (we read about it in the Old Testament). When God appeared to Moses on Sinai mountain, Moses saw burning but the fire did not damage the bush. When Elijah was taken to havens, Elisha saw something like a fiery chariot, picking Elijah up and carrying him away. It should be noted, that the resurrection of Jesus Christ was not like other known cases of resurrections of people, described in Old and New Testaments. More likely this Resurrection was similar to that described by the apostle Paul: "it is sown a natural body; it is raised a spiritual body". Maybe this fire was a direct action of God, creating something in our world. In front of God anything "melteth as wax before the fire", but this fire does not expand or flow arbitrarily, and does not obey the laws of physics. This fire itself could be the law of creation in this world.
Contact of this fire with the Shroud initiated chemical changes of the Shroud fabric and its opacity, similar to that which can take place from action of a strong radiation. The unique difference with external, traditional physical standpoint was that the radiation does not propagate according to known physical equations of physical light. However, it surrounds a body, reproducing its shape, and the intensity of this radiation ("firing body") decreases versus the distance from the surface of the natural body. Therefore the Shroud got more opaque in the regions which were closer to the body. Maximal opacity was in the places which were in a direct contact with the Shroud.
We may learn something about the type of the decrease of this intensity, basing on the relative opacity of the Shroud, which changes depending on the distance up to the body of Jesus. This functional dependence was investigated by Dr. Jackson and other scientists (see fig.1). Using these data now we can calculate the resolution obtained within this new model. According to Jackson's estimations the mechanism of image formation should satisfy to the following criterion. On a distance of 1.1 cm from the surface of a body, such small-sized details as lips must be resolved on the image. Thus, distances up to 1.2 cm between the Shroud and the body are of interest for us.
The experimental curve (solid line in fig.1) in the range from 0 cm to 12 cm was obtained in the work  and may be expressed by the following equation:
Relative opacity = 9 + 46 exp(-1.03 d), (1)
where d is the distance between the body and the Shroud in centimeters. However, for d less then 1.2 cm the behavior of the experimental data can be approximated by another relationship:
Relative opacity = 3 + 52 exp(-d/0.7). (2)
Here, 3 is a background or the value of natural opacity of the Shroud. Extraction of the external background is needed for proper separation of the effect of radiation from initial conditions. Exponential form of the above equations allows to compare the resolutions within two discussed models: model of the radiating body and model of the firing body. The last formula would correspond (in the frame of the first model) to the absorption of radiation with a characteristic absorption length 0.7 cm in the air. X-ray radiation with the energy about 3.5 keV has just the same absorption length. Within the frame of the first model we may explain the functional dependence in fig.1, taking into account the presence of radiation with different absorption lengths in the radiation spectrum. The radiation with energy 3.5 keV would be responsible for the presence of the fine structure of the image at distances about 1 cm from the surface of the body. It would be possible to accept this point of view, if the resolution of the first model would be sufficient to satisfy with Jackson's criterion. However, within the framework of the first model it is impossible to reach the observable resolution.
The resolutions reached within these two models are displayed in fig.2, where the degree of resolution k (in %)
k = ( E2 - E1 ) / E1, (k>0),
is plotted versus the radius R of hemicylinders. Here E1 is the intensity on a distance 1.1 cm from middle point between the tops of two hemicylinders, and E2 is maximal intensity on a distance 1.1 cm (just above of one of hemicylinders). E2 must be much more then E1 for the images of the hemicylinders remain separate. The value of k characterizes the relative difference in E1 and E2.
It is seen that the first model does not satisfy Jackson's criterion and, therefore, must be rejected. It should be noted, that in the first model the initial opacity of the Shroud was not taken into account, and only monochromatic radiation with the energy of 3.5 keV was considered. Account of the initial opacity of the Shroud and the real spectrum of radiation will lead to an increase of a background and make the resolution even worse.
In frame of the second model we may get the necessary resolution. The resolution with k = 6% is quite sufficient for observation. Such a resolution from two hemicylinders with the radius R=0.4 cm on the distance of 1.1 cm from their surface may be obtained and interpreted using the second model. This number of R corresponds to the geometry of lips. Thus, the second model can be considered as a reasonable hypothesis for explanation of a mechanism of the image formation on the Turin Shroud and stimulate further research of the problem.
Our investigation demonstrates, that the proposed model is able to explain the image formation of the Shroud. To prove that our model is quite sufficient for the explanation of the mechanism of the image formation, additional research has to be done. Their main trends are the following:
1. One may try to obtain more strict functional dependence of the opacity versus the distance between the Shroud and the body. We must distinguish between the error of measurement and the uncertainty, which is caused by the unknown position of the Shroud on the body and the shape of the body as well. First of all, one must find those points on the Shroud which are separated from it by a well-determined distance. For other points one should measure the value of uncertainty in the Shroud-to-body distance. Then we will have some freedom to vary the opacity vs distance within some limits. In the frame of the hypothesis of the firing body we can reduce an uncertainty of the definition of the distance between the body and the Shroud, restricting the variation of the data along the X axis. This variation should be chosen in such a manner as to minimize the deviation of experimental data from the continuous curve. On the other hand, in this way we shall also specify the functional dependence of the opacity versus Shroud-to-body distance, reducing a spread from a smooth continuous curve.
2. When the more rigorous functional dependence of the opacity on the Shroud versus Shroud-to-body distance is obtained, we must reconstruct the image of the whole human body by means of mathematical simulations in the frame of the discussed hypothesis. The degree of opacity in each point will be calculated according to the above written formula, where the distance involved will be the distance from a given point to the nearest point on a body. We do not need any assumptions about a preference of the vertical direction, as was used by Dr. Jackson . The obtained image should coincide within error limits with the image on the Shroud. This problem, in essence, is an inverse one to the problem (previously solved by Dr. Jackson) of a reconstruction of the shape of the body, basing the image on the Turin Shroud.
3. Within the frame of the first model a type of the functional dependence of opacity versus Shroud-to-body distance depends on the spectrum of radiation. Low energy radiation is strongly absorbed in air and does not extend far. On the contrary, high energy radiation is slightly absorbed and may act on a textile at larger distances. Thus, knowing the dependence of the opacity versus distance, we can conclude about the energy of radiation. Such a dependence does not enter to the second model and the firing body energy, irradiating the Shroud, remains unknown for us. It is possible to try to find out this energy, investigating chemical and nuclear changes in textile. For this purpose it is necessary first to investigate experimentally the effect of radiation on a textile in a wide energy range, from strong ultraviolet up to X-rays. Also the structure changes in various points inside cellulose versus the distance from the surface of the textile should be investigated. As a result of this research it would be possible to obtain a scale which allows us to determine the energy (or energy spectrum) of radiation, knowing the structure of the previously irradiated cellulose. This scale must be developed in such a way to be applicable to the Turin Shroud. Optical response of a textile on the radiation of a different energy should also be under investigation in this research.
4. A textile chemically modified as a result of irradiation may have very different chemical activity. Time variation of this activity with respect to the processes of carbon (or carbon groups) attachment and substitution should also be investigated in view of the fire in the year 1532, when the Shroud was damaged.
The last two items are directly related with the problem of the dating of the Turin Shroud.
This research was done in the Moscow Turin Shroud Center (Branch of the Turin Shroud Center of Colorado) and under financial support of Dr. D. Kuznetsov.
1. John P. Jackson et al., The three dimensional image on Jesus' burial cloth, 1977 United States Conference of Research on the Turin Shroud.
2. John P. Jackson et al., Correlation of image intensity on the Turin Shroud with the 3-D structure of human body shape, Applied Optics, Vol. 23, p.2244, July 15, 1984.
3. John P. Jackson, A problem of resolution posed by the existence of a three dimensional image on the Shroud, 1977 United States Conference of Research on the Turin Shroud, New Mexico, USA, p.223.
4. John P. Jackson, Is the image on the Shroud due to a process heretofore unknown to modern science?, Shroud Spectrum International, No 34 March, 1990, p.3.
5. John D. German, An electronic technique for constructing an accurate three-dimensional shroud Image, 1977 United States Conference of Research on the Turin Shroud New Mexico, USA, p.234.
Editor's Note: The following is the text of a short presentation made by Dr. Belyakov to a church group in Rome.
According to interdisciplinary research which has been performed by historians (including Dr. Ian Wilson), the Shroud of Turin and the orthodox Mandylion of Edessa are the same items. As seen from historical records, the Mandylion was kept in Constantinople in X-Xll centuries, i.e. prior to its disappearance in 1204. Starting in Xl-th century, the tradition to demonstrate the Mandylion during the Passion Week in Constantinople was started. There are serious reasons to believe that during this time a special liturgical rite was developed in the Orthodox Church. This rite consists of veneration to the Holy Shroud on Good Friday.
At the present time, each one of the Orthodox cathedrals or chapels has a so-called "Holy Shroud of Jesus Christ" inside the altar. This liturgical item, 'the Shroud", is used for decoration and then for demonstration and veneration during a special ceremony on Good Friday. This size of this piece of cloth, "the Holy Shroud", is about 1 x 1.5 meters. This Shroud has an image of the whole body of the deceased Jesus Christ. In Xl-Xll centuries, the connections between Eastern and Western Churches were broken and the Orthodox liturgical rite mentioned above was not adopted in the West. Perhaps, a careful investigation of the Orthodox tradition will help us to learn more about the history of the Holy Shroud.
As you know, the Orthodox Church has a deep worship to icons in both prayer and liturgical ways. The icons differ from the Church art not only because some of the icons are miraculous ones and not only because they were naturally incorporated into the liturgy. Canons, or in other words, SPECIAL RULES FOR ICON PAINTING, are very old, conservative, and these CANONS are very different from the rules of common art. In particular, there is a special rule called "REVERSED PERSPECTIVE" in icon painting. According to this rule, the closer objects look smaller than those objects (or their parts) which are situated farther away. The perspective lines cross each other NOT ON THE HORIZON (like in common art) but in front of the objects in Orthodox icons. So if the image on the Shroud of Turin appeared when the cloth surrounded the body of Christ, the unfolding of the Shroud on the plate desk should deform the image exactly in accordance with the LAW OF THE REVERSE PERSPECTIVE. Indeed, this type of the "image deformation" has been remarked by Dr. John Jackson, a famous scholar of the Shroud of Turin from the US Air Force Academy at Colorado Springs, CO, USA. The reversed perspective has a deep theological basis in the Orthodox iconography. On other hand, it is very likely that the reversed perspective rule in Orthodox icons has a "genealogical" link with the Turin Shroud image.Alexander Belyakov