• William Snyder added an answer:
    Is there any rule how many degrees of freedom are needed in order to allow an Interpretation of the partial correlation coefficient?

    I did partial correlations on a relatively small sample. As a result the degrees of freedom are partly below 4. Is there any rule how many degrees of freedom are needed in order to allow an Interpretation of the partial correlation coefficient?

    William Snyder · University of Connecticut

    One simple rule of thumb is that the absolute *minimum* number of observations should be at least five times the number of factors you're correlating. Below that point, it often becomes too easy to fit a linear model to the data, and the p-values are completely unreliable. (Obviously, much larger numbers of observations are far better, whenever this is practically feasible.)

    In simple linear correlation of two factors, the df is N-2. If you partial out another factor, the df should be N-3. Thus, if I understand you correctly, it sounds like you're already below the bare minimum number of observations.

  • Han Geurdes added an answer:
    How did Schrodinger concluded that adding a complex number to wave function is important? What's the physics behind that?

    The wave function is complex, Why? Can the time and position for elementary particles have a complex relation (transformation) relative to our time and position?

    Han Geurdes · CGI plc.

    In Jagdish Mehra's and Helmut Rechenberg's  "The Historical Development of Quantum Theory" (Springer, ~ 1989) one can read how Schroedinger derived his equation from the Hamiltonian.  He failed to get relativity in but was struck by the eigenvalue structure of the partial differential euqation he got for the Hydrogen atom. 

  • V. Krasnoholovets added an answer:
    Survey: what topics should be covered in Scholarpedia's encyclopedia of space-time and gravitation?

    Although Scholarpedia's encyclopedia of space-time and gravitation is constantly growing, numerous subjects are still missing.

    Being one of the editors of the encyclopedia, I would like to have your opinion about subjects that should be covered by the encyclopedia.

    I will then relay your suggestions to the editorial team in order to decide whether or not the suggested topics should be covered (and even sometimes be given the priority).

    Thank you for your help.

    PS: Please click on the link associated to the question in order to be directed to the encyclopedia. Thank you.

    V. Krasnoholovets · Institute of Physics of the National Academy of Science of Ukraine

    I would recommend articles from my very short Encyclopedia of Fundamentals   (further reading especially about gravity, cosmology, dark matter and dark energy, as well as the Casimir effect see in my web site

  • Tolga Yarman added an answer:
    An old question that is still fresh: Is gravity a Newtonian force or Einstein space-time curvature?
    No gravitational wave was measured yet, no graviton was detected accordingly. On the other hand no space- time curvature was observable. There is no successful experiment to validate the current theories. What is the nature of the mysterious gravity? What is the velocity of this effect ?
    Tolga Yarman · Okan Universitesi

    This ( is a huge work you have achieved, Dear Setve, and Bravo to you... I have read it with great profit...

    All the best to you, and to all of Colleagues present with us here......  

  • Sheng Yang asked a question:
    Applying for a postdoc job

    Hi, everyone. i am applying for a postdoc job now.Does anyone have a vacancy in relative project? Many thanks if you give me a reply in your free time.

  • Abdolhalim Rajabi asked a question:
    When adjusted relative risk in the report, what type of analysis used?


    I wish calculate relative risk adjusted for other risk factors caesarean. Given that caesarean is a common outcome, so use the adjusted odds ratio is over estimated.

    So how do I calculate adjusted relative risk?
    Can the Generalized linear models(GLMs) be used?(in stata)

     thank you

  • Pierre Bergey added an answer:
    The trend of the curve for effective permeability vs saturation and rel. permeability vs saturation remains the same then why don't we use first one?

    Relative permeability importance and physical significance

    Pierre Bergey · TOTAL

    What matters is effective permeability vs. saturation, true. This is what is is actually represented in models. The reasons people actually deal with K and Kr vs. Sw derive are twofolds. First, one does not measure directly effective permeability and saturation, those quantities are interpreted from pressure and volumetric measurements. Second, effective properties are more costly and henceforth rare than absolute values; there is a need to extrapolate. In both cases, the framework people operate within assumes that the relatve permeability is, within a certain domain, independent of absolute permeability. It is, to date, the most convenient one use for both the laboratory person and the geo-modeller and for all I know data supported to a good (but not perfect) extent. 

    Sorry, I don't have pointer to bibliographic ressources, just summing up a generalist viewpoint on this. 

  • Charles Francis added an answer:
    How can the units of a velocity (vector) be cancelled by speed (scalar)?

    The Lorentz equation is a good example.  I've always thought the use of that factor in time dilation should use speed rather than velocity.

    Once, while reading about "turn-around effects", I actually looked at the date on the journal to see if it was April 1.

    Charles Francis · Jesus College, Cambridge

    since the Lorentz transformation is expressed in terms of a velocity, it is natural to talk of the magnitude of velocity. Speed means the same thing, but it is a less technical word and so less appropriate in a scientific context.

  • How can I calculate the enzymatic relative activity?

    How can I calculate the enzymatic relative activity?

  • Samuel Picton Drake added an answer:
    How to make interesting Special Theory of Relativity unit for engineering students?
    20% of students seem to be confused with velocity addition topic based numerical problems.
    Samuel Picton Drake · University of Adelaide

    Ring laser gyroscopes are an excellent example of the application of the Einstein velocity addition formula. That should get the engineers interested.

  • Petrus Marques added an answer:
    In enzyme characterization, what is difference between Residual enzyme activity and relative enzyme activity?

    In enzyme characterization, what is difference between Residual enzyme activity and relative enzyme activity?

    Petrus Marques · University of Campinas

    When comparing diferente conditions of na enzymatic activity, you can express the highest value as 100% and the other values accordingly. This is residual activity.

    I believe relative activity is a contrast to an absolute quantification, where you don't have exact values, but can know if a specific result is higher or lower then another one.

  • Arno Gorgels added an answer:
    Can one use the relation between the area of a triangle and its apollonius circle's radius to represent the length contraction in general relativity?

    here, we try to use the relation between the circumcircle and the apollonius circle to study the length contraction.

    see: the ptolemy theorem in conics (1) (page 13-17)

    our steps are : technique handling the equation of special relativity, we can get the discriminant,that is:

    $\Delta=\sqrt{(vt)^2+4x(x-vt)}$ we realize that the crucial point in the relation between the circumcircle and the apollonius circle is, we can select the angles of the triangle as :


    which allow us to handle the determinant as (page 4)

    3.consequently,we can introduce the result for the orthocenter (see :how to use the vector method to study the apollonius problem?) to handle the determinant above . then we can use the results above to calcular the lorentz parameter as (page 5,formula (28) (29) (30))

    the orthocenter of a triangle with vector method:

    see: application of the ptolemy theorem (3) (section 1.1)

    lastly,we obtain our estimate for the length contraction:


    where, the constant $C$ can be found in the relation between the area of a triangle and its apollonius circle's radius.

    see: application of the ptolemy theorem (1)  (section 2)

    for more detail, you can refer to:

    From Ptolemy theorem to non-euclidean geometry (1) (page 1-6)

    Arno Gorgels · Principia Naturae

    Length contraction is imho a matter of Special Relativity, not of General Relativity?

  • Jilan Gaskarth added an answer:
    What are the most promising theories that can explain the dielectric permittivity of free space?
    Permittivity of free space
    Jilan Gaskarth · rpc group

    Hi John, I am familiar with your website. I will take another look. Thanks for responding.

  • Cheng Tianren asked a question:
    What are your thoughts about the relation between the radius of the apollonius circle and the speed of light under the effect of relativistic ?

    In this topic, our main idea is to introduce the apollonius problem into general relativity. firstly, by the discriminant we get in section 1 (page 2) and the angle we select in section 2 (page 3). it stimulate us to use the symmetry property of the relation between the lester circle and the apollonius circle to handle the determinat in section 2 (page 3), and the last estimate imply that the limit of speed in relativity ,that is the speed of light ,which can be represented as the radius of its apollonius circle. and our trial to relate the apollonius problem with relativity is finished. and the relation can be seen clearly now:


    the lester circle and the apollonius circle :

    the ptolemy theorem in conics (1) (section 3)

    for more detail, please go to:

    From Ptolemy theorem to non-euclidean geometry (1)  (page 6-8)

  • Robert Shuler added an answer:
    Is it possible to derive the constant & uniform velocity of light & the Lorentz transform without starting from the principle of relativity?
    Originally the Lorentz transform was developed to explain the Michelson-Morley experiment in terms of length contraction due to motion through an ether. Some work was done on how this might produce distortions of electromagnetic forces and interatomic bonds to produce length contraction. Einstein postulated a fully symmetric (i.e. relative) form with no preferred frame of reference, and gave a different derivation based on the principle of relativity, that the laws of physics including the velocity of light should be the same in all inertial frames. It is a pretty large assumption and gives no insight into mechanisms.

    In years of searching I've found only two papers that claim to derive something like the relativistic Lorentz (not the ether one) from more fundamental principles, one by Yilmaz using de Broglie waves which has received no follow up discussion that I can find, and one by Matthew Brown using pseudo-measurement interaction counting which is only on arXiv (and RG in his profile). Are there any others?

    Does it make any difference if relativity can be derived from some mechanism-like postulates? Does it have any implications for understanding things like spooky action at a distance (entanglement)? Or inertia/gravity?
    Robert Shuler · NASA

    In my view, time is controlled by inertia, and whatever interaction determines inertia is more likely to be akin to entanglement than to QFT.  While QFT interactions are limited to lightspeed, it is well known that entanglement interactions have no regard for relativistic limits.  Think of inertia as position entanglement of multiple masses. 

    Over the course of several papers which I have referenced variously in these discussions, I have shown how gravity can be formulated as emergent from inertia, explaining its weakness.  That implies gravity is probably not a QFT type of force (and therefore there are no conventional gravitons).  Direct evidence for this comes from the way the strength of gravity varies in relation to relativist quantities.  Recall the discussions of the sonic world and the characterization of what an effect with Lorentz stiffness greater than c would look like.  It would not be subject to relativistic slowdowns and limits.  Therefore it could maintain a constant acceleration in spite of relativistic time slowdown (which gravity exactly does, and this amount of acceleration leads to the correct orbit for mercury) and it would be able to push things beyond relativistic limits, or horizons, which depending on the views of Stephen Hawking at any given moment, gravity may or may not be able to do (you couldn't actually push sonic objects beyond their limits, but if there were other objects not made of sound, or EM waves, gravity could push them further than sonic or EM forces in whichever case).

    Thanks for bringing this up.  I forgot to include this very important conclusion (about the Lorentz stiffness of gravity) in my summary.

  • Vikram Zaveri added an answer:
    What is a simple procedure for calculating trajectory in a given metric?

    I am looking for a way to take a particle position, mass and velocity (including both regular particles and photons), and calculate an integrable delta V, delta position increment, given a simple metric, particularly the Schwarzschild metric. While I'm willing to accept this in any coordinate system, I'd prefer it in the coordinates of a remote observer.

    I have seen this question in many discussion boards.  A lot of people would like to know exactly how spatial-temporal curvature is supposed to affect trajectory. The answer I always get is "read a textbook."  I have read many. They don't really answer the question. Textbooks are concerned with the Einstein field equations and many other complex topics.  A metric is a particular solution and the Schwarzschild metric a particularly simple and symmetric one. This does not need to get into the complexity of the why and wherefore of the field equation.

    Vikram Zaveri · Independent Researcher

    Periodic relativity proposes an alternative to Schwarzschild metric which satisfies Einstein's field equations but does not depend on geodesic trajectories or weak filed approximation. The theory gives primary importance to two body systems and the multibody systems are of secondary importance.

  • Philip Machanick added an answer:
    A new take on relativity: does a complex analog of c work for an infinitely expanding pre-universe, or is it just a crazy idea?

    I developed this alternative take on how a pre-universe could expand infinitely fast by postulating an imaginary equivalent of c in the Lorenz transformation. Since I am not a physicist and do not have the resources to test predictions, I am putting this out for anyone interested to review. If it’s a good idea, it would be great to get expert opinion confirming. If bad, I can always write an SF novel based on it.

    Philip Machanick · Rhodes University

    Stephen: no, I don’t have time to look at all these alternatives. No doubt others reading this thread will be happy to have further reading. Thanks.

  • Luis Felipe Ateca Torres added an answer:
    Could the spin be related with the destruction of matter?

    Suppose a matter A with mass, m1, and spin up. Suppose a second matter B with mass,m2 and spin down. If both particles have the same mass, m1=m2. Is this a particle-antiparticle reaction?  That is:

    for m1=m2=m, the reaction A Sup + B Sdown --> 0



    A Sup + B Sdown --> (A+B) with S = 0


    Luis Felipe Ateca Torres · University of Puerto Rico at Mayagüez


  • Carringtone Kinyanjui asked a question:
    Treatment of charged particles in General Relativity

    If,say a lump of electrons were in a free falling lift and an observer(Alice) was in the lift,invoking classical electrodynamics she would not see any radiation by the electrons because the electrons are stationary in her frane of reference.However Bob who is on the ground will measure the electrons radiating energy because of CED.How do we nontrivially explain the inconsistency in the observations of alice and bob?

  • Ilja Schmelzer added an answer:
    Why do we always discuss the origin of the universe and its fate in terms of the general theory of relativity? Is it the only suitable theory?
    It is well known in physics that most theories are good and suitable for certain circumstances, for example Newton’s laws (i.e. classical mechanics) are suitable for classical system (macroscopic systems), Quantum mechanics is suitable for atomic systems (microscopic system). Also, Charles' law, which describes how gases tend to expand when heated, is suitable for certain temperature ranges.
    Ilja Schmelzer · Independent Researcher
    Carlos, what do you mean with RTG "extends Einstein's special relativity to accelerated systems"? There has never been a problem with accelerated or other coordinate systems in SR, they are simply not preferred as inertial systems.

    What do you think are the problems of RTG? IMHO, the main problem is the causality condition, which is not compatible with the equations: Even if initial values fulfill the causality condition, it may later be violated. What happens then? (The other one is a history of incorrect criticism of GR, but this is not a problem of the theory itself.)

    This is an advantage of my ether variant of RTG - it does not need the RTG causality condition, replaces it by another one, which has a clear physical meaning: The ether density should be greater zero.
  • Luis Felipe Ateca Torres added an answer:
    Do you believe that the General Theory of Gravitation of Einstein could be taught in High Schools?
    Luis Felipe Ateca Torres · University of Puerto Rico at Mayagüez
    Robert J. I like the lecture you gave me, Thank you. It will help me when teach this.
  • Sergey Shevchenko added an answer:
    Is the flow of time an illusion?
    This has been discussed on ResearchGate in a rather ad hoc way in relation to another question about the absolute immutability of some physical laws but it really deserves its own separate discussion. Below I summarise the arguments in favour.
    The philosophers
    The nature of time has been the subject of discussion by philosophers for 2000 years or more. In the last two decades their views have crystallised. If time flows - (1) How do we know? and (2) How do we measure its speed? In other words - what frame of reference can we use to measure time?
    The philosophers' conclusion is that they would have to invent another time dimension for the purpose but this would then need a third time dimension and so on ad infinitum. This would be absurd and so they conclude that the flow of time is an illusion.
    Relativity, Einstein and Godel (A World Without Time - Palle Yourgrau - Penguin Books, 2005)
    According to the theories of relativity two observers can never agree on the simultaneity of two events that both witness and neither has a "preferred" position that makes one of them correct. This implies that all events already exist and that what we perceive as the flow of time is an illusion.
    Godel showed that rotating universes were consistent with relativity and proved that in them it was possible to travel back in time. He immediately realised that this implied that the past must still exist and that what he called "intuitive time" is therefore an illusion. In 1949 he published a formal proof that time (in our intuitive sense) cannot exist in any universe. This uncomfortable discovery was ignored for nearly half a century but was revived by Julian Barbour in "The End of Time" and is now widely discussed and accepted by many physicists.
    The Laws of Physics
    The fundamental laws of physics describing the forces are time-symmetric.
    What can we say about the time dimension?
    Time still exists but only as a chronological map in which events are located;
    Time is not in any way like the spatial dimensions because:
    It is anisotropic and contains an entropy gradient;
    If we exist in more than one location in any of the spatial dimensions then we will also always then be in different locations in the time dimension;
    Separations in 4 dimensions are extensions of Pythagoras's Theorem but have the form:
    separation = √[x2 + y2 + z2 - (ct)2], which means that time measurements are imaginary (ict) where i=√(-1), as Hawking suggests in "A Brief History of Time".
    Free will is also an illusion
    We live all our lives all the time but every instant feels like "now"
    Time travel is impossible because (a) there is no dimension in which travel is possible, (b) we occupy all the spacetime of our lives and cannot take back to an earlier time our memories of a later time.
    Sergey Shevchenko · Institute of Physics of the National Academy of Science of Ukraine
    Is the flow of time an illusion?

    - see “Space and Time”
  • Sergey Shevchenko added an answer:
    Is it possible to construct a time machine?
    A hundred years ago, few people believed it was possible for humans to travel through outer space. Time travel, like space travel, was merely science fiction. Today, spaceflight is also commonplace. Might time travel one day become commonplace too?
    Sergey Shevchenko · Institute of Physics of the National Academy of Science of Ukraine
    To “construct a time machine” is necessary to understand – what is “time”? (And, of course – what is space, since any material object, including, hope, a “time machine”, operates in the 4D spacetime.) Mainstream physics doesn’t answer on this question, in spite of some declarations that the “fundamental properties of space and time are explained in the relativity theory”. Including the assertion that real spacetime in Matter is Minkowski pseudoeuclidian continuum, where space and time depend, in certain sense, from each other. All that is evidently incorrect – nobody observed till now, e.g., imaginary space or time, as well as didn’t observe imaginary distance between a couple 4D spacetime points, etc.
    In reality the Space and the Time are some independent logical Rules that control (govern by) the informational structures: Space establishes that different fixed informational patterns must be separated by something what in Matter a human calls “space (spatial) interval”; Time Space establishes that different states of changing informational patterns must be separated by something what in Matter a human calls “time (temporal) interval”. Both Rules are universal in the Set “Information”, when all/ everything what exist, including material objects, is/are some informational structures; Matter is some subset of the Set.
    So for any changing in some structure “time” – or more correct “time interval” – is always additive (positive by convention); there principally doesn’t exist of any logical step that make the “changing of the time” negative. “Time machine” cannot exist principally.
    Besides, Matter in our Universe consists of uninterruptedly operating automata; when their algorithms are, as a rule, reversible. That is, in spite of automata states are uninterruptedly changing “in same time direction”, the results of running, for example two of algorithms with relatively reverse command orders, are reverse, it seems as one automate “runs in positive time direction”, when the other one runs “in negative time direction”. Such organization of the informational patterns (first of all – elementary particles) is critically necessary for existence of our Matter. So in Matter besides “true time (above) Rule” acts other “time Rule” that allows (controls, govern by) reversible processes.
    Next – it is clear from above that the Rules themselves are universal and act in whole Set, they don’t determine totally how they should be realized in concrete cases. In our Matter, as it seems, the Rules act as rigid 4D (3D “space” and 1D “time”; but this “time” isn’t true time, that is “coordinate time” ) dense lattice of “material” (Rules, since they are rules, aren’t, of course ,“material”) fundamental logical elements (aether), when any elementary particle and any system of particles is/ are some disturbances of the aether. At that, for example, antiparticles move
    in negative “time direction”, when particles – in the positive one, by convention. But the movement in the negative temporal dimension 4D Matter’s spacetime by no means is a “travel into the past”, for any step in the spacetime is necessary to spend [positive] true time interval. So, for example, if somebody meets some “scientific” new that other somebody found a method – often such a methods appear as some sequence of general relativity (wormholes, etc.), then with a great probability that is a next fantasy…
    More – see “Space and Time”
  • Moataz Emam added an answer:
    How do I compute spin-connection and vielbein (tetrad) fields from a metric using Mathematica?
    Want to write Mathematica code that computes these things.
    Moataz Emam · State University of New York College at Cortland
    Thank you both for your discussion. I also downloaded your notebook Martin and plan to adapt it to my work as well. Truly appreciate it.
  • Charles Francis added an answer:
    Why is the Lorentz factor assumed to be a constant under a constant relative velocity between two inertial systems?
    In the deduction of Lorentz transformation, why is Lorentz factor assumed to be a constant under a constant relative velocity between two inertial systems? Should Lorentz factor be assumed to be a function of the velocity of observed event? By assuming Lorentz factor to be not only a function of the velocity of inertial systems, but also the velocity of observed event, a new transformation can be deduced. This new transformation keeps the constant velocity of light without introducing time dilation. Can someone give some comments about this paper?
    Charles Francis · Jesus College, Cambridge
    There are two ways of looking at it. One is simply tautology; a ruler must have the same length with respect to itself. That is how it works for local law. The other is when we are able to compare a ruler (or preferably a clock) from one frame to the other. I only made two points, first that this is part of gr, but the discussion only referenced sr, and second that for a connection we only need talk about the effect of infinitesimal parallel displacements - an entire trajectory is a more sophisticated notion which must come later in the development of the theory. Apart from such details, I think we were in agreement.
  • Demetris Christopoulos added an answer:
    Does the assumption that the speed of light is changed with changing gravitational potential represent reality or an assumption?
    One of the most important assumptions in general relativity is assuming that the speed of light changes with gravitational potential change. Is this assumption proved experimentally? Is it valid and consistent with physical laws and phenomena?
    Demetris Christopoulos · National and Kapodistrian University of Athens
    So, we can agree that no kind of 'a step forward' will be done in near future, just for scientific political reasons. Our hope is that after so many years and by using open platforms like RG, all past theories that are still on 'use' (usage and GR are incompatible words), will be rejected from scientific community and the strong political support for them will start to decrease...
    Meanwhile, I don't think that it is good idea for somebody to work in GR field and try to publish his/her negative arguments against GR... He/she will never be published in a serious journal...
  • Srikar Phani Kumar Marti added an answer:
    Does anti-matter exist in our universe? Is positron a reality?
    If positron is a reality, then, if we bombard the positron with electrons, is a black hole formed or into which form of energy is it transformed?
    Srikar Phani Kumar Marti · Vignana Bharathi Institute of Technology
    Yes sir Arnaud Chapon.......i was also asking the same question! if the matte annihilates the is black hole an obvious phenomenon?? When the LARGE HADRON COLLIDER experiment was being experimented, formation of black hole was one of their expected that true??
  • Vikram Zaveri added an answer:
    Where is the boundary of space-time?
    Quantum mechanics can answer this question. Relativity defines the differential structure of space-time (metric) without giving any indications about the boundary. This suggests that relativity is a correct but not a complete theory (a well-formulated mathematical problem, i.e. Dirichlet problem, needs differential equations and boundary conditions). Is it possible that quantum mechanics is the manifestation of microscopic boundary conditions of space-time? Recent papers, e.g. see attached "Elementary space-time cycles" , absolutely confirm the viability of this unified description of quantum and relativistic mechanics.
    Vikram Zaveri · Independent Researcher
    The idea of space-time arise in the human mind by way of delusion. This is identical to mistaking a rope for a snake. The human mind superimposes the idea of snake on a rope and behaves exactly as if it has seen a snake. We can present this argument in a little more scientific language. When a particle wave is presented to a physicist, instead of seeing the oscillating energy, what he does is, superimposes the idea of wavelength and period on this wave and sees the space-time. All the geometrical theories in physics are founded upon such delusion. So the boundary of space-time is determined by the extent of the oscillating energy you are looking at.

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