thegoodfellas/blogset-br huggingface dataset:
carried by the test particle, t = the coordinate time as measured on the different clocks (the coordinate clocks) as the test particle passes them. If we substitute , the above equation can be written as dtdrv/= dtd=t., (6) the time-dilation formula of SR. Since the proper time is measured at one position on one body it will be the same for all observers, whether they are fixed at various points in the coordinate frame or moving with the proper clock. We call such a quantity an invariant. The energy E in (2) is similarly an invariant. In Fig. 1 the coordinate clocks A and B are fixed in some reference frame, whereas the proper clock moves from one coordinate clock to the other. SR states that the time interval 12ttt-=., as measured on the proper clock, will be shorter than the time interval 12ttt-=. between the two coordinate clocks. For infinitesimal small intervals the difference is given by (6), where v is the relative velocity between the proper and coordinate clocks. coordinate clock A coordinate clock B Figure 1: Proper clock passing coordinate clocks. A fundamental requirement of SR is that the relative velocity between the coordinate and proper clocks must be constant, which also implies motion along a straight line. The description of such motion, as well as any others, is called kinematics. Kinematics only tells us how a particle moves in space with time, without referring to the forces giving rise to the motion. SR is a pure kinematical theory. The early challenge of gravitation theory was to incorporate the results of SR into the dynamics of gravitation. Einstein's first efforts were along this line.5 In this paper we shall show how such incorporation can be achieved. 5. The red-shift formula SR is not only a kinematical theory; it is also a theory of electromagnetism. This is indicated by the title of Einsteins paper: Zur Elektrodynamik bewegter Korper. Incorporating SR into our theory of gravitation will then provide the link between gravitation and electromagnetism. For this we need the red-shift formula. Frequency is the inverse of time, so that the inverses of (6) give the Doppler shift for frequency: p...=, (7) where . and .p are respectively the frequencies of a coordinate clock and a proper clock. By substituting for . from (2) we find rRpeA2/-=.., (8) where 20/cmEA=. (9) Since both A and .p are invariants we may define another invariant frequency as pA..=0. (10) Equation (8) can then be written as , (11) rRevv2/0-= )2/1(0rR- ., (12) which gives the observed values for gravitational redshift. One of the perplexities of astrophysics is the relation between Doppler shift and gravitational redshift. The above relations clarify this relation. Multiplying (11) by Plancks constant h on both sides gives an energy equation, rRehE/0~-=., where .hE=~ (13) has the form for the energy of a photon. A significant aspect of the equation is that it contains the quantum mechanical h and the gravitational G in one equation. Since both E and h.0 are invariants, they are related by a constant. Since
these invariants do not have any absolute values at this stage, we may set the constant equal to unity. Therefore rReEE/~=. (14) With the foregoing in mind we now formulate our second postulate: Postulate 2: Special Relativity is valid instantaneously and locally at all points in the reference system of the central massive body. This is also a standard assumption in relativity theory. It implies that the time-dilation formula of (6) is valid locally at all points in space. The time difference between the proper clock and the coordinate clocks varies with ., or equivalently, with the velocity. But, since . is related to the gravitational potential according to (3), the time differences also depend on the gravitational potential at the point where the measurement is made. 6. The photo-electric effect Einstein received the Nobel Prize for his 1905 paper on the photo-electric effect. This relation relates the kinematical energyE~ of SR to the frequency of a photon: .hcmE==2~~, (15) where 0~~mm.=. (16) The quantitym~is the electromagnetic mass of a particle, and it varies relative to its rest mass 0~maccording to (16). The difference between the gravitational mass m and the electromagnetic mass0~mis fundamental to our theory. The above relations forE~, as well as the link between electromagnetism and the kinematics of SR, persuades us to associateE~with the electromagnetic energy of a system. From (14), (15) and (16) we get rRrRecmcvecmE2/2222/20~/1~=-=, (17) or, in terms of, F 22/22/20~/1~cceEcvecmEFF=-=. (18) The corresponding Lagrangian for the above energy can be derived as 3 2/2220/1~cecvcmLF--=. (19) 7. The Hydrogen atom Expanding (18) gives K+F+F+F+F++=4220220220020204/~2/~2/~~2/~~cvmcmcvmmvmcmE (20) Consider the first three terms on the right-hand side (RHS) of the above equation: . (21) F++=020202/mvmcmEIn order for the motion of the system to be bounded, the last term must not only be inversely proportional to r, but also negative. To ensure this we let rem/~20-=F , (22) where e is an arbitrary constant. This is a significant result as the constant e eventually turns out to be the charge on an electron. Its existence is a mathematical requirement for bound motion. Alternately, a positive sign in (22) results in unbounded, repulsive motion. Since , (22) can also be written as rRc2/2=F erecm/~220-=, (23) where 2/Rre=. (24) In this case R is the Schwarzschild radius of the proton. Eq. (23) has the same form as the expression for the classical electron radius. In standard physics this expression is an ad hoc defined quantity, whereas in our model it is derived from the properties of the system. Eq. (17) can now be written as rreecmE/20~=. (25) 8. Hydrogen spectrum In mathematical physics we use a perturbation method when a quantity, such as the energy above, is expressed in a convergent series. To apply this method to E above, we need to express the energy in terms of the momentum. From SR, 224202~cpcmE+= , (26) where vmprr~= is the classical momentum of a particle. Substituting this expression in (18), we get . (27) 2/2/142022)(cecmcpEF+=We take the finite radius of the proton into account by changing r to egrr-, where g has
equations of motion. In particular, we can derive the paths of planets and the spectrum of the hydrogen atom from this fundamental Lagrangian. The model is further confirmed from the fact that both the classical electron radius and Diracs Large Number Relations are inherently part of the model. The distinguishing feature from other attempts to unification is the distinction between the gravitational mass m and the electromagnetic mass m~ of a particle. This distinction is discussed further in section 14. The Lorentz-type force offers a description of higher order gravitational properties such as geodetic precession and frame dragging of binary pulsars. 12. The nuclear (strong) force Any theory of the nuclear, or strong interaction, must satisfy certain basic requirements concerning the properties of the force. They are briefly (see Ch.17 of Ref. 8): (a) The force is charge independent, (b) it only acts over a range ~ 10-13 cm, (c) the form of its potential is )/, exp(/2qrrrQ--(d) where the coupling constant h/2Q could range from 1 to 15, (e) qris related to the mass pmof a pion by cmh rqp/~. At the gravitational energy equation (5) can be rearranged in a unique form as:3 rR . (39) /exp()/(2RrrRmcE Repeating the same procedure for the electrodynamic energy (25) we find that at , err /exp()/~(2eerrrrcmE . (40) Both (39) and (40) are accommodated in the model for a deuteron as depicted in Fig. 2. We also use for . qm%m% Fig. 2: Model of a deuteron. Two protons are separated at a distance R from each other. A particle of mass qm~and charge e moves in a figure eight pattern about each of them, alternately at a radius of r = rq =|re| from each proton. For this case we write (23) as eerecm/~220-= , (23) where 0~emis the electromagnetic rest mass of the electron. Substituting (23) in (40) gives [])~//(exp1~~2022022cmerrcmecmEee-........- . (41) Defining eqrr= , (42) (41) can be written as )/exp(~2qqrrrrcmE-- , (43) )/exp(2qrrrQ--=, (44) where Q2 is defined as qqrErcmQ~~22==. (45) Eq. (44) has the form of the Yukawa potential. The mass qmm~~= is then equal to the pion mass . pm Property (e) for the pion mass can be derived from the above relations by assuming property (d) as a boundary condition (see Ch.7 of Ref. 3). 13. The weak force The weak force cannot yet be incorporated explicitly in the model as no classical equivalent of this force exists. This force gives rise to radioactivity, in particular -decay. It acts over distances r < R = 2re and we therefore expect that our Lagrangian (1) must be adapted for this range. 14. Possible implications for cosmology Einstein was deeply influenced by the ideas of Ernest Mach (1838-1916), in particular that the local properties of matter should be determined by the properties of the distant, massive stars. He wrote:9 But in the second place the theory of relativity makes it appear probable that Mach was on the right road in his thought that inertia depends upon a mutual action of matter. For we will show in the following
that, according to our equations, inert masses do act upon each other in the sense of the relativity of inertia, even if only very feeble. What is to be expected along the lines of Mach's thought? The principle implies that changes in the distant universe will cause changes in local properties, such, for example, as the mass of an electron. We shall not be able to measure this change as it is a relative change, and our measuring apparatus will be changed equivalently. This effect has become known as the Mach effect. Dennis Sciama (1926-1999) proposed an ad hoc formulation for this effect as10 . (46) /2MLcG.where L = radius of the universe, M = mass of the universe . mass of the distant stars. This relation can be found (see Ch.10 of Ref. 3) by applying the energy relation of (2) to the system of Fig. 3: Fig. 3: Mutual gravitational interaction between a central mass M1 and the distant stars of total mass M2. The potential at due to is and the potential of the shell atis . Furthermore, since and are in relative motion, the value of . will be the same for both of them. Applying (2) then gives 2M1MLcRLGM2//2111==F1MLcRLGM2//2222==F1M2M . /exp()/exp(122221LRcMLRcME== Since L > R2 >> R1 we can realistically approximate the exponential to first order in R2/L. After some algebra we then get R2 L, which gives the Mach relation 2GM2/Lc2 1. One of the mysteries of modern astrophysics is the accelerating expansion of the universe. This can be explained in terms of the conversion of radiation energy into mass. We note from (4) that m decreases with increasing velocity, implying that mass is converted into kinetic energy. Alternatively, if the masses m of two bodies are increased through the conversion of radiation energy into mass, then the masses will repel each other according to (5). For example, if the mass m of a test body in the vicinity of a central mass M is increased, then the distance r between them will increase equivalently to keep E constant. The rate of repulsion will depend on the rate of conversion of energy into mass. This conversion is the opposite to the conversion of mass into energy as is found in nuclear fission. At the Big Bang the universe consisted of radiation only. As this radiation was converted into mass, the masses repelled each other. This process is still continuing, and according to our model, accounts for the accelerating expansion of the universe. Higher order gravitational effects are becoming increasingly relevant in the study of binary pulsars.11 12 Astrophysicists are looking for confirmation of the Einstein-Mach effects predicted by General Relativity theory. These effects include geodetic precession and frame dragging, or Thirring effect. We are presently looking at applying (36) to calculate these effects. 15. Conclusion The equivalence of planetary and atomic motion is in accord with the axiom of As above, so below. Similarly, Machs Principle also appeals to the mystical scientist. Changes in the universe cause changes in the locally small. Since we are part
of this change, we are not aware of it. This also casts light on the meaning of absolute time. Absolute time is the time interval between two coordinate clocks fixed in the reference frame of the universe. This interval will change according to the properties of the universe, or equivalently, to those of the distant stars. A fundamental feature of the model is the distinction between the dynamics and kinematics of a system. This is reflected in the two postulates. The Lagrangian of (1) specifies the dynamics of a system. It describes a gravitational force that causes particles to move, specifically in accelerated motion. The way the particles move is described by the kinematics of the system. There is no reference to forces. Kinematics is described by special relativity, which, at speeds much less than that of light, gives the classical Newtonian equations of motion. Special relativity also describes the electrodynamics of a system, which depends on the velocities of the particles. The velocity of a particle changes according to the magnitude of the force acting on it, but our postulate 2 stipulates that the velocity remains constant within infinitesimally small intervals of time and space. This is a standard assumption in physics. It allows the global validity of special relativity, and therefore also that of the Maxwell equations of electrodynamics at all points in space under the influence of gravitation. The electrodynamical force therefore results from the motion induced by the gravitational force determined by the Lagrangian. The two forces are linked by the relations of the LNH. Postulates 1 and 2, therefore, form the foundation of a unified model of gravitation and electrodynamics. The model is also characterized by two different types of masses: a gravitational mass m and an electromagnetic massm~. These two masses are related by the relations of the LNH. Different types of masses for the electron are not unusual in modern physics. Quantum electrodynamics, the theory of the electron and photon, is plagued by conceptual problems of mass renormalization (see p. 217 of Ref. 13). It must still be seen to what extent our model could resolve the ambiguities of this procedure. We have mentioned that m decreases with velocity, and it is well known that increases with velocity. The first effect is consistent with our closed particle model of gravitation. As velocity, or kinetic energy, increases, it must be at the expense of mass, which is converted into energy. This does not apply to electrodynamic systems that are not closed: energy is applied from an outside source, and part of the energy is converted into mass to impede the acceleration of a charged particle. This is equivalent to the Lenz effect. m% An intriguing aspect is the possibility of demonstrating gravitational repulsion in the laboratory. The theoretical mechanism is explained in section 14. A suggestion of how this can be applied appears in the work of Roger Jennison.14 The paper shows that there is possibly only one force in nature, that of gravitation. The electromagnetic force arises from the kinematics induced by the gravitational force,
and the strong force is a unique form for gravitation at a separation equal to the Schwarzschild radius of a nucleon. No expression has yet been found for the weak force, but we can deduce that it would have a form for the gravitational force in a region smaller than the Schwarzschild radius of a nucleon. The proposed Lagrangian is general enough to be applied, in principle, to all dynamical systems. Equivalently, the Lorentz-type force of (36) offers more direct applications. It should simplify the present mathematical formulations to describe the higher order gravitational effects of binary pulsars. The proposed model has a rigid structure with a consistent mathematical formulation. Change the form of the classical electron radius and the perihelion precession of Mercury is affected. All assumptions are well established in physics and all predictions, with the exception of the Lamb shift, agree with observation. The discrepancy of the Lamb shift should be resolvable with a closer look at the effective nuclear radius of the hydrogen atom. Taking all these conditions into consideration we must conclude that the proposed model satisfies the basic requirements for a unified model of forces. REFERENCES 1. Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions and the Quest for the Ultimate Theory (Vintage, 2000). 2. P.C. Wagener, Newton and the international year of physics, The Rose+Croix Journal 2 (2005): 63-77 http://www.rosecroixjournal.org/issues/2005/articles/vol2_63_77_wagener.pdf. 3. P.C. Wagener, Principles of a Theory of General Interaction, PhD thesis, University of South Africa, 1987. Published as a book in January 2004. 4. Richard Feynman. Quoted in http://www.imdb.com. Search for Feynman. 5. A. Pais, Subtle is the Lord ... (Oxford, UK: Oxford Univ. Press, 1982). 6. Randal C. Telfer, Everything you always wanted to know about the hydrogen atom but were afraid to ask. http://www.pha.jhu.edu/. May 1996. 7. E.R. Harrison, Physics Today 12 (1972):30. 8. Robert Eisberg and Robert Resnick. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (New York: John Wiley & Sons, 1974). 9. A. Einstein, The Meaning of Relativity (Princeton: Princeton Univ. Press, 1955). 10. D.W. Sciama, The Physical Foundations of General Relativity (Doubleday, 1969). 11. Michael H. Soffel, Relativity in Astrometry, Celestial Mechanics and Geodesy (New York: Springer-Verlag, 1989). 12. F. Curtis Michel, Theory of Neutron Star Magnetospheres (Chicago: University of Chicago Press, 1991). 13. Walter T. Grandy, Introduction to Electrodynamics and Radiation (New York: Academic Press, 1970). 14. R.C. Jennison and A.J. Drinkwater, An approach to the understanding of inertia from the physics of the experimental method, J. Phys. A: Math. Gen. 10 (1977): 167-179.
Some Thoughts on Reality, Actuality, Presumptuousness, and Tolerance Fallibility is part of the human condition. Unfortunately, we often seem to disregard this fundamental truth. Though we might agree with it when pinned down, we often act contrary to it in our daily interchange with others. We simply let our egos lead us astray when we fail to properly consider the others point and insist that were right and theyre wrong. Permitting a little bit of humility to temper our behavior here, we could go a long way in making the world a better place.Some Thoughts on Reality, Actuality, Presumptuousness, and Tolerance"True wisdom is less presuming than folly.The wise man doubteth often, and changeth his mind;the fool is obstinate and doubteth not;he knoweth all things but his own ignorance."-- Unto Thee I GrantListening to much of todays political debate, the thoughtful person cannot help but be struck by the obnoxious tone of it. Far from respectfully disagreeing, the rivaling factions battle with such hateful anger as if locked in mortal combat. This is particularly evident in the banter that occurs on the many talk shows that are broadcasting across the country. The arguments are mostly along the lines of the two major ideologies that make up American political thinkingliberalism and conservatism. Fired on by the often radical pronouncements of the talk show hosts, the callers are ranting about the evils of the other side with a degree of contempt and odium that has led to the point where some of these shows have actually been labeled Hate Radio.Striking too, is the widespread preoccupation with the words true and truth that is exhibited by the proponents of the respective sides. They never seem to miss an opportunity in using those terms to label their own beliefs. Perhaps, this is what is at the core of what is troubling to the more circumspect listener, particularly the student of Rosicrucian principles. The terms reality and truth are commonly considered interchangeable, even synonymous. The word reality and its derivatives permeate everyday usage of the language. Phrases like get real and the reality of it is..., or reality check are part of everyones conversation. They are used in response to the perceived nonsensical, the phony, the mythical, and the false. A commercial somewhere admonishes that perception is not always reality. Rosicrucians go further in equating perception with reality and in pointing out that the difference is between reality and actuality. Reality is what we realize through our perception. It is what we perceive through our, somewhat fallible, five senses and our far from perfect minds. Actuality is what describes the true, the actual nature of things and events. We humans are not always able to discern the difference. Once we understand this we become a lot less reckless in our employment of the word truth. Philosophies and ideologies, also political and even religions views, while often formulated by folks of superior intelligence, are all prone to be flawed and subject to debate. They all originate in human thinking. Great and respected philosophers clash in their views and ideas,
which are often diametrically opposed to one another. In view of this, it would seem an astonishing presumptuousness for a person to lay claim to the absolute truth in an argument.Differences of opinion are natural. Moreover, in the light of Hegelian dialectics they are beneficial in the search for agreement and resolution of conflict. If one starts with the idea that either side of an argument is rarely ever entirely correct, the resolution is greater in value than the sum of the arguments. Inflexibility and stubborn insistence on the validity of ones own views are often counterproductive and even foolish. This is not to say that there are not great controversies that have deep rooted beliefs at their foundation on both sides. Those beliefs may compel the holder to fight to the death in defense of them. Two examples of such divisive issues are the bitter disagreements over the issues of abortion and capital punishment. Abortion is held to be the inalienable right of the mother by the proponents of the pro-choice side, who say that it is her right to decide on matters concerning her body. The pro-life faction on the other hand, holds that abortion is the taking of the life of a human being. Both have compelling and honestly felt arguments. In the case of the death penalty the arguments are perhaps more complex, if only because they cross the line of religious belief. There are religious as well as non-religious followers on both sides of the capital punishment issue with both sides bringing compelling arguments to the table. If a criminal commits a capital crime, gets convicted and sentenced to life in prison, then gets paroled and kills again, a very strong case can be made that, had he been executed, society would have been acting in self defense and an innocent life would have been saved. On the other hand, opponents could argue that the blame should be placed with the faulty justice system that granted parole to a murderer. These opponents point to the many false convictions that have placed innocent people on death row. This time supporters will blame the imperfect system. The point is that, while it may be easy to come out on either side of the line for those prone to make snap decisions based on visceral or emotional reaction, the more thoughtful will find those decisions much more difficult. And they will be much less likely to condemn the other side for their opinion.To make things even tougher for the thoughtful amongst us, such reluctance to clearly come out for or against an issue is often treated less than kindly by a society that places great value on taking a stand. It is considered weak and derided as wishy-washy. Steadfastness of views is considered a virtue and desirable, particularly in those seeking leadership positions in life. Whether these views are of proven value often seems of secondary importance. Similarly, changing ones mind is viewed with great prejudice. The proverbial right to change ones mind is chauvinistically reserved for the female sex.