Theoretical  Physics  Research  Institute

Home    About    Research   Publications   News   Contact

  Research areas


Testing Newton's second law


Small statistics violation


Do fundamental constants change?


Millicharged particles


Foundations of quantum mechanics


Theoretical physics


Testing Newton's second law


NewtonÕs second law was proposed by Sir Isaac Newton back in 1687 and is the foundation of classical mechanics and the whole of physics. It relates 3 basic quantities: force, mass, and acceleration.


The relationship is always true except two cases: when the velocities are very large and when the masses are very small. The first exception is due to special relativity, the second is about quantum mechanics. Apart from these two areas, the law is supposed to be absolutely correct.


But here we are talking about the third area which has nothing to do with either special relativity or quantum mechanics. And this is the case of small--- extremely small---accelerations: about one-hundred-billionth of the acceleration of the free fall on the Earth.


A natural question is why are we interested in considering these tiny accelerations. The reason is that we usually assume that the laws that we know from our laboratories must be valid up to very large astronomical distances. That is, we assume normally that the laws that we learn and test in our laboratories are valid, basically, for the whole of Universe.


But because we donÕt have the opportunity to experiment somewhere very far from us---in some far away galaxy---we cannot be hundred percent sure that the laws stay the same. We  canÕt be sure that the laws that we know from our everyday experience would be valid under very different physical conditions.


And these small accelerations that we are talking about  are practically never encountered in everyday or laboratory conditions. So to learn about these accelerations so far we needed to look into astronomical data. And when people looked at these data, they saw an amazing thing.


So basically we have some data and we can try to understand these data first time around assuming that NewtonÕs law is absolutely correct. And we get some picture. Now, we see some deviations. We see that the data that we have from astronomy and what we should have seen if NewtonÕs law was correct, these are two different pictures. So the ends donÕt meet. And now, if we assume that the second NewtonÕs law is slightly corrected when the accelerations are very small then the theoretical picture and the observed picture fit together perfectly.


And this is why we are interested to know if this law should indeed be modified. And so far weÕve had only astrophysical evidence and this astrophysical evidence and the whole idea of changing the NewtonÕs second law got the name of MOND (M.Milgrom). This abbreviation stands for Modified Newtonian Dynamics.

(Actually, there are 2 versions of MOND: one is to modify the universal gravitational law, and the other is to change NewtonÕs second  law. Here, we are only talking about the latter.)


So this whole idea was discussed and tested and checked within astrophysical context. People looked into astronomy data. And what was  suggested recently, is that we should look at the laboratory experiment (A.Yu.Ignatiev). We should look at how to test this idea in an ordinary experimental way that we test other similar ideas.


Because this acceleration is much smaller than any acceleration due to many forces that act on a body under laboratory conditions. Under ordinary conditions every physical body is under the action of many, many forces and these forces give this body an acceleration that is much larger that this one-hundred-billionth of g.


And because of that, it was considered very close to impossible. But recently it was found that the effect known as ŌSHLEMÕ allows us to test  the hypothesis in a normal terrestrial laboratory.


And to do this, we have to provide such conditions that would lead to cancellation of all big forces, all these big forces that act on our test body should cancel almost exactly, leaving only this small, small, tiny residue. ThatÕs the idea.


And to do that is of course not easy. Basically, it could be explained by this. When we are on the Earth, on each body there are forces due to the fact that the Earth rotates around its axis and due to the fact that the Earth orbits around the Sun. These are so-called centrifugal forces. These forces are similar to when you sit on the merry-go-round and everyone feels that  there is some force that pushes you away from the centre. So because the Earth rotates around its axis and also orbits around the Sun, we have 2 forces. And the main problem is how to make these 2 forces cancel?


This is exactly what we are interested in. It appears that when we do all calculations---and calculations are quite difficult in the sense that they have to take into account all kinds of forces, all kinds of small things, but the net result that this cancellation can be realized but not always and not everywhere, but only at a certain time and at a certain place on the Earth. And that looks like very lucky circumstances. But these are very rare and special occasions.


This places lie on the latitude about 80 degrees to the north or to the south. The southern circle is in Antarctica and the northern one goes through such places as Greenland or northern islands of Russia or Canada. So these are not the places where you normally go for a holiday.


But this place is not new for physicists: in the 90Õs they drilled a borehole in Greenland to see if there are deviations from the gravitation law. It is the so-called ``fifth forceÕÕ.


However, we may prefer to perform the experiment in the comfort of our laboratory at home. Then, we still have to exploit the same idea of cancellation of forces, but in this case different forces will be involved. This leads to the so-called ŅCCC setupÓ   where CCC symbolizes the Cancellation between the Coriolis and Centrifugal forces.


In this case, there is no restriction on the laboratory location. But the restriction on time (only twice a year) remains. Technically, this stems from the fact that the centrifugal forces are due to the EarthÕs spin.


Finally, there are at least two approaches to doing the test at any time and any place. One is to move a test body along a special trajectory with a prescribed speed and acceleration (A.Yu.Ignatiev).


Another approach (due to V.A. de Lorenci, M.Faundez-Abans and J.P.Pereira) exploits the same basic idea of cancellation, but in a different experimental set-up. The key point is to introduce extra, man-made centrifugal forces into play (in addition to the usual, terrestrial ones). To realize this, a spinning object, such as a ring is needed. If the rotation of the ring is carefully  controlled, then there is a chance to achieve the desired cancellation at any time and any place.


The improvement comes at a cost, though: the time window for the effect to show up becomes reduced from  ~ 1 millisecond to ~ 1 microsecond.


All four setups proposed so far are technically challenging and it is hard to predict the winner. But the game is exciting: itÕs not every day that a 300-year old law can be challenged!




Small statistics violation



The Pauli Exclusion Principle (PEP) is a cornerstone of modern physics and chemistry. At all levels---from quarks to nuclei to metals to stars---PEP tells the matter how to behave. If not for this principle, the periodic table of elements and life itself would not exist as chaos would engulf cosmos.


The fundamental principles of physics govern the world as we know it, but not all of them are equally well understood. For some, there are clear-cut theoretical schemes describing possible small deviations from the principle and experimental ways to place upper bounds on those deviations. Others are still resistant to that kind of treatment. To this latter category belong the principles governing strict correspondence between spin and statistics such as PEP (or Fermi statistics) and Bose symmetry.


For a long time, it was believed that small violation of statistics is impossible in much the same way as "you can't be a little bit pregnant". However, this view was challenged when A.Yu.Ignatiev and V.A.Kuzmin constructed a simple quantum-mechanical model exhibiting PEP violation controlled by a small parameter &beta.


The physics community, both theorists and experimenters, took up the idea with great enthusiasm. Scientific American published an article titled "Roll Over, Wolfgang?'' that described the model and its subsequent theoretical development by O.W.Greenberg and R.N.Mohapatra as well as plans to look for small PEP violations experimentally. These experimental efforts were ongoing soon after the appearance of the theory papers.


Alternative generalization of the model was attempted by L.B.Okun who also pointed out some challenges it brings.


Thus a new and active area of research had been established. The number of papers on small statistics violation leapt from about a dozen during 30 previous years to over 300 in the subsequent decade. In May 2000, the first ever international conference entirely devoted to the subject of small statistics violation and related areas was held in Italy. It was followed by the Workshop on theoretical and experimental aspects of the spin-statistics connection in Trieste (October 2008).


Recently, new searches for PEP-forbidden transitions have been performed at leading institutions world-wide including major underground laboratories such as Gran Sasso (VIP, Borexino, and DAMA/LIBRA), Frejus (NEMO-2), and Kamiokande (ELEGANTS V). Alternatively, one has looked for anomalous, PEP-forbidden elements using accelerator mass spectrometry, laser spectroscopy and other methods, many of which are based on the ideas of L.B.Okun, the proposal of A.Yu.Ignatiev and V.A.Kuzmin and its later versions . This review of both experiment and theory contains a detailed bibliography.


Models of the small deviations from PEP have led naturally to studying theories with small violation of Bose statistics for photons. Research on this topic builds on the ground-breaking work of A.Yu.Ignatiev, G.C.Joshi and M.Matsuda who proposed that the normally forbidden decay Z into 2 photons could occur if Bose symmetry were broken.


This idea was further developed in two directions:


In atomic physics, a similar experiment was carried out by D.DeMille, D.Budker, N.Derr, and E.Deveney which involved a pair of photons which could violate Bose symmetry.


In 2011, S.N.Gninenko, A.Yu.Ignatiev, and V.A.Matveev suggested looking for Bose symmetry violation at the highest energy via the decay process Z' into 2 photons at the CERN LHC.


Violating statistics slightly turns out not to be an easy task, and in trying to do this we learn a lot about how the fundamental principles work. We also get new, ever more stringent constraints on the violation parameters. This is what makes this subject an on-going, fascinating field of inquiry.




Do fundamental constants change?


Recently evidence has been sought for a possible time evolution of the basic constants of physics such as the fine structure constant, mass ratios of elementary particles and others. If existent, the effect must be rather small. According to the Nobel laureate S.Glashow, Ņeven that small change would rock physics and cosmology. The importance of such a discovery would rank 10 on a scale of 1 to 10Ó.


Variation of fundamental constants cannot be accommodated in the Standard Model of particle physics, which therefore would need to be extended if the evolution is observed and independently confirmed. The possible extensions are Kaluza-Klein theories, superstring theories, and other models.


One striking implication of the constants evolution is that the basic units of measurement (such as metre, second, etc.) would also become time-varying due to their dependence on the fundamental constants. It follows that the evolving constants and units cannot be considered separately from each other. Both constants and units form one interdependent set of quantities.


This fundamental fact calls for construction of a new theory of measurements ("the metrological approach") that takes into account the variability of constants and units in a self-consistent and systematic way. The basis for such a theory was laid by A.Yu.Ignatiev and B.J.Carson. The referee of their paper reported that Ņit brings welcome clarity to this rather confused subjectÓ.


Suppose the Žne structure constant (&alpha) is indeed evolving over the cosmological timescale. This raises a much debated question: is &alpha variation due to the variation of the speed of light (c), elementary electric charge (e), or the Planck constant (h)? The metrological approach offers a clear and convincing answer to this question.


Another issue of contention is the variation of dimensional quantities. On the one hand it is claimed that time variation of dimensional constants is a meaningless concept. On the other hand, a number of proposals have been made in which one (or more) dimensional constants (such as G, e, c or h) are varying.


The above analysis explicitly shows in what sense and to what extent the variation of dimensional constants is meaningful and when it becomes misleading; hence bringing the two points of view closer to each other and eliminating some controversy in this area. As it often happened in the past, the truth lies in the middle.


The next steps in constructing the new theory of measurement consist in addressing the following issues:


    What are the implications of the metrological approach for the currently accepted procedures for establishing evolution of the fundamental constants?


    Can one extend the metrological approach to the case with multiple varying constants? This question is motivated by the prediction of modern theories (such as Grand Unified Theories) that along with the variation of the fine structure constant other fundamental constants (such as mass rations or magnetic moment ratios) are also likely to vary.



Millicharged particles


All known elementary particles fall into two groups: electrically charged and electrically neutral. But here we deal with hypothetical "intermediate" particles which are charged, but at the same time very close to neutral, because their electric charge is a very small fraction of the electronic charge e.


They were first introduced and studied by A.Yu.Ignatiev, V.A.Kuzmin and M.E.Shaposhnikov while investigating the problem of possible electric charge non-conservation. Millicharged particles became popular after a paper of that title appeared in Physical Review Letters where the accelerator search for such particles was proposed by M.I. Dobroliubov and A.Yu.Ignatiev. This was based on the comprehensive study of constraints on such particles undertaken in the paper. It was featured in New Scientist.


A bit later, a number of Canadian and U.S. physicists obtained similar results (see papers by S. Davidson, B. Campbell, and D. Bailey, by R.N. Mohapatra and I.Z. Rothstein, and by R.N. Mohapatra and S. Nussinov).


The experimental realisation of the above proposal at the Stanford Linear Accelerator Centre (SLAC)  was initiated by the Nobel Prize winner M. Perl. It took six years of work involving 17 physicists to complete the experiment. This subject has been highlighted in Science and Physics Today.


Today, this is a lively and exciting research area counting hundreds of papers and lots of new ideas being tossed around both in theory and experiment.


What is the motivation behind these developments?


The absolute values of the electric charges of the known elementary particles can be 1/3, 2/3 or 1 (in terms of the electron's charge). If we compare charge with similar quantities such as mass then the difference is astonishing. The masses of elementary particles can take up hugely different values spanning many orders of magnitude. Can something similar happen to the charge as well? In other words, can there exist particles with the electric charges much smaller than the known ones?


The answer is yet to be found.



Foundations of quantum mechanics


From its beginnings, Quantum Mechanics raised a lot of interesting   if puzzling questions. Does an electron have a definite position when no-one looks at it? Does the Moon have a definite position when no-one looks at it? What is the nature of reality?


To many of these issues there are still no answers that all physicists can agree on. The subject is as challenging as it is exciting and future surprises are to be expected.


Theoretical physics


A theoretical physicist operates with pen and paper, not pumps and power plants. This occupation is barely hundred years old. Before the 20th century, all physicists were supposed to perform experiments and do the theory by themselves. But the complexity of experimental as well as theoretical work grows so much that it is no longer possible for one person to do both. Hence, the division of labour between specialists in experiment and in theory.


But physics is still one science, not two. Whatever is being done on one side should eventually be supported by the other. We need both legs to stand and walk on the ground. The collaboration between theory and experiment is what drives physics forward.

© TPRI 2006-2012