Synchronization Gauges and the Principles of Special Relativity

The axiomatic bases of Special Relativity Theory (SRT) are thoroughly re-examined from an operational point of view, with particular emphasis on the status of Einstein synchronization in the light of the possibility of arbitrary synchronization procedures in inertial reference frames. Once correctly and explicitly phrased, the principles of SRT allow for a wide range of `theories' that differ from the standard SRT only for the difference in the chosen synchronization procedures, but are wholly equivalent to SRT in predicting empirical facts. This results in the introduction, in the full background of SRT, of a suitable synchronization gauge. A complete hierarchy of synchronization gauges is introduced and elucidated, ranging from the useful Selleri synchronization gauge (which should lead, according to Selleri, to a multiplicity of theories alternative to SRT) to the more general Mansouri-Sexl synchronization gauge and, finally, to the even more general Anderson-Vetharaniam-Stedman's synchronization gauge. It is showed that all these gauges do not challenge the SRT, as claimed by Selleri, but simply lead to a number of formalisms which leave the geometrical structure of Minkowski spacetime unchanged. Several aspects of fundamental and applied interest related to the conventional aspect of the synchronization choice are discussed, encompassing the issue of the one-way velocity of light on inertial and rotating reference frames, the GPS's working, and the recasting of Maxwell equations in generic synchronizations. Finally, it is showed how the gauge freedom introduced in SRT can be exploited in order to give a clear explanation of the Sagnac effect for counter-propagating matter beams.Comment: 56 pages, 3 eps figures, invited paper; to appear in Foundations of Physics (Special Issue to honor Prof. Franco Selleri on his 70th birthday

Integrability and chaos: the classical uncertainty

In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now named by the more fashionable term of deterministic chaos. There is still substantial interest in a matter that is included in many graduate and even undergraduate courses on classical mechanics. Based on the Hamiltonian formalism, the main objective of this article is to provide, from the physicist's point of view, an overall and intuitive review of this broad subject (with some emphasis on the KAM theorem and the stability of planetary motions) which may be useful to both students and instructors.Comment: 24 pages, 10 figure

The Sagnac Phase Shift suggested by the Aharonov-Bohm effect for relativistic matter beams

The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a a formal analogy with the the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.Comment: 18 pages, LaTeX, 2 EPS figures. To appear in General Relativity and Gravitatio

The relativistic Sagnac Effect: two derivations

The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in this way the universality of the effect. Another derivation is based on a formal analogy with the phase shift induced by the magnetic potential for charged particles travelling in a region where a constant vector potential is present: this is the so called Aharonov-Bohm effect. Both derivations are carried out in a fully relativistic context, using a suitable 1+3 splitting that allows us to recognize and define the space where electromagnetic and matter waves propagate: this is an extended 3-space, which we call "relative space". It is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform': the geometry of this space turns out to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also http://digilander.libero.it/solciclo

Force Spectroscopy Study of the Coordination Bond Between a His-Tag and the (Ni2+-NTA) Group.

A number of extensively used methods employed in the purification of recombinant proteins are based on the formation of a coordination bond between the nickel(II)-nitrilotriacetate (NTA) group present on a chromatographic matrix and a stretch of six consecutive histidine residues (6XHis-tag) appended to the primary sequence of the protein. Force spectroscopy studies performed in the past by different groups on the Ni2+-NTA-(His)6 bond gave rise to very different results 1, 2, 3. In order to have an internal control on the value of the experimentally determined force, we thought to insert the Ni2+-NTA group into a polymer with known mechanical properties, such as DNA 4. A DNA molecule presenting a Ni2+-NTA group at one end and a thiol group at the other end was attached to a gold surface via a thiol-gold bond. Force spectroscopy experiments were performed bringing a gold-coated AFM tip functionalized with a CG6H6 peptide into proximity to the NTA-DNA gold substrate. Whenever the 6XHis-tag of the peptide formed a chelate with a Ni2+-NTA group appended at the end of the DNA linker, a molecular bridge was established between the tip and the substrate. The tip was subsequently retracted until the bridge broke and the resulting force/distance curve was collected. The identification of the formation of the desired coordination bond is easy since it leads to a force curve in which the overstretching transition of the DNA linker generates a plateau whose length must be equal to 70% of the length of the DNA. In the preliminary experiments performed, the mean breaking force or the Ni2+-NTA bond resulted to be 172 pN. This value is comparable to what found by the group of Hinterdorfer et al. 2. 1 M. Conti, G. Falini and B. Samori (2000) Angew. Chem. Int. Ed., 39 (1): 215-218, 2 F. Kienberger, G. Kada, H. J. Gruber, V. P. Pastushenko, C. Reiner, M. Trieb, H.-G. Knaus, H. Schindler and P. Hinterdorfer (2000) Single Mol., 1: 59-65. 3 Schmitt L., M. Ludwig, H. E. Gaub and R. Tampe (2000) Biophys J., 78 (6): 3275-3285. 4 Smith, S. B., Y. Cui and C. Bustamante (1996) Science. 271 (5250): 795-799

Structural Biology Meets Nanoscience at the Interface: the Nanoscale Structure of DNA and the Interactions of Single Molecules of DNA with Surfaces.

DNA has been selected by millennia of evolution as the primary molecule that carries, preserves and uses information for the great majority of the living organisms. The structure of DNA is the basis for the astonishingly complex functions that DNA accomplishes very efficiently. A sugar-phosphate backbone solubilizes a double helix of paired and stacked aromatic bases that are so shielded by the aqueous environment. In this hydrophobic environment, bases also find the specific interactions that are the foundation of the chemical recognition between the two chains, the essential informational content for the replication of life itself, the other major discovery of James Watson and Francis Crick\u2019s, together with the unveiling of the helical structure. The chemical specificity of the DNA recognition code is so stringent that is can be used to prepare artificial constructs that take advantage of the information code to easily and purposely auto-assemble structures of unprecedented complexity. Nanoscale objects of very complex topology and geometry have been prepared by mastering the art of oligonucleotide sequence selection and design; the recognition process has been used as an add-in feature to drive recognition processes in systems that would not display it, and so achieve self-assembly, proximity, order. The pairing of DNA bases into a double helix, and the additional recognition properties that DNA normally employs in the living cell has been shown to be valuable for the assembly of electronic circuit elements, possibly a starting step towards a totally new electronic architecture.[1] On a size-scale that is one order of magnitude larger than that relevant for base-pairing and recognition, a DNA double-helix displays a whole new set of properties, derived from the chemical inhomogeneity along the chain, and from the helical nature itself. These properties have been the object of the studies of our group in the last years. With scanning force microscopy experiments, we have directly measured how a double-stranded DNA helix can be intrinsically curved, though being fairly flexible, and how its flexibility can be modulated along the chain.[2,3] We have shown that the dynamics of the different sections of the chain can be studied directly, and we have found them to depend on the sequence too.[4] These Nanoscale properties of DNA are known to have a paramount effect on DNA-protein interactions in the living organisms. We have recently shown that they can also affect the way DNA also interacts with non-biological objects, like crystalline surfaces, all the way to the point of representing an example of nanoscale recognition between DNA and non-biological objects.[5] The understanding of these long-range nanoscale properties of DNA could lay the groundwork of a new generation of recognition processes that might be used in nanoscience. 1. Keren, K., Krueger, M., Gilad, R., Ben-Yoseph, G., Sivan, U., and Braun, E., Science 297, 72-75 (2002). 2. Zuccheri, G., Scipioni, A., Cavaliere, V., Gargiulo, G., De Santis, P., and Samor\uec, B., Proc. Natl. Acad. Sci. USA 98, 3074-3079. (2001). 3. Scipioni, A., Anselmi, C., Zuccheri, G., Samor\uec, B., and De Santis, P., Biophys. J. 83, 2408-2418 (2002). 4. Scipioni, A., Zuccheri, G., Anselmi, C., Bergia, A., Samor\uec, B., and De Santis, P., Chemistry & Biology 9, 1315-1321 (2002). 5. Sampaolese, B., Bergia, A., Scipioni, A., Zuccheri, G., Savino, M., Samor\uec, B., and De Santis, P., Proc Natl. Acad. Sci. USA 99, 13566-13570 (2002)

Force Spectroscopy Study of the Coordination Bond Between a Histidine Tag and the Nickel-Nitrilotriacetate Group (Ni2+-NTA).

Several molecular biology techniques nowadays employed in the purification and immobilization of recombinant proteins are based on the formation of a coordination bond between a Ni(2+)-NTA group present on a chromatographic matrix and a stretch of six consecutive histidines (6XHis-tag) appended to the primary sequence of the protein (1). The stability of the anchoring of the His-tagged proteins on Ni(2+)-NTA functionalized matrices is challenged by the frictional force exerted on them by the flow. Such interplay between external forces and chemical processes can now be studied at the single-molecule level, thanks to the recent development in nanoscale manipulation techniques. Force spectroscopy studies performed in the past by different groups on the Ni(2+)-NTA-(His)6 bond gave rise to highly variable results (2, 3, 4). Probably, these differences derived from the different experimental setups used. We thought to overcome this problem by inserting the Ni(2+)-NTA group into a polymer with known mechanical properties, in order to have an internal control on the value of the experimentally determined force. To this aim, we thought to use ds-DNA, whose mechanical behavior has been thoroughly investigated by different authors (5, 6). We constructed a DNA molecule presenting a Ni(2+)-NTA group at one end and a thiol group at the other end. This latter group allows the attachment of the molecule to a gold-coated SFM tip via a thiol-gold bond. Force spectroscopy experiments were performed bringing the functionalized tip into proximity to a gold substrate functionalized with a CG6H6 peptide. Whenever the 6XHis-tag of the peptide formed a chelate with a Ni(2+)-NTA group appended at the end of the DNA linker, a molecular bridge was established between the tip and the substrate. The tip was subsequently retracted until the bridge broke and the resulting force/distance curve was collected. The identification of the formation of the desired coordination bond is easy since it leads to a force curve constituted by 3 phases: (a) entropic stretching of the DNA linker; (b) overstretching transition of the linker, generating a plateau whose length must be equal to 70% of the length of the employed DNA; (c) detachment of the probe, which corresponds to the breaking of the coordination bond. In the preliminary experiments performed, the mean overstretching force resulted to be 50 pN, a value comparable to what found by other groups, while the mean length of the overstretching transition resulted 280 nm, in accordance to what expected for the DNA molecule we employed. The mean breaking force or the Ni(2+)-NTA bond resulted to be 172 pN. This value is comparable to what found by the group of Hinterdorfer et al. (3). (1) Hochuli E., H. Nobeli and A. Schacher (1987) J. Chromatogr., 411: 177-184. (2) Conti M., G. Falini and B. Samori (2000) Angew. Chem. Int. Ed., 39 (1): 215-218, (3) Kienberger F., G. Kada, H. J. Gruber, V. P. Pastushenko, C. Reiner, M. Trieb, H.-G. Knaus, H. Schindler and P. Hinterdorfer (2000) Single Mol., 1: 59-65. (4) Schmitt L., M. Ludwig, H. E. Gaub and R. Tampe (2000) Biophys J., 78 (6): 3275-3285. (5) Smith, S. B., Y. Cui and C. Bustamante (1996) Science. 271 (5250): 795-799. (6) Rief, M., H. Clause-Schaumann and H. E. Gaub (1999) Nature Struct. Biol. 6 (4): 346-349