Essay Abstract

An investigation is undertaken of the basis and implications of space-time kinematics. An understanding of the drawbacks and limitations of their use is sought. The possibility of addressing the same problems using the classical methodology of dynamics in rigorous terms is evaluated and the necessary means to make the Maxwell equations invariant in situations of moving bodies or across moving frames is explored. Further exploration leads to a derivation of the relativistic energy-momentum relations within purely 3 dimensional space and independent time using only the Maxwell equations and the Lorentz force equation.

Author Bio

The author studied Mathematics, Physics and Computer Science at Western Washington University. After graduation, he decided to pursue an independent path of the study with a focus on an understanding of the underpinnings of physical theory and practice across disciplines. A book and papers are being prepared which present some initial results of the study as it applies to Electrodynamics, Relativity and Quantum Mechanics. Historical factors are considered and an attempt is made to develop new mathematical models and procedures and to unify the use of models in areas where they are current held to be disparate.

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Stephen

I found little ontological basis for resolution of some of the knottier problems in rationalising observation, and am unable to comment on the veracity of your maths, but the brilliance and veracity of your findings as far as they went shone out so brightly that the above fell into the shadows. I sense a high score coming on!

You will find an ontological analogue of your essay in mine, from a slightly different vista (and language) and lacking most of the essential mathematical basis you provide, though extending to address matters of Unification, Space-Time etc. As an astronomer I also find significant astrophysical falsification.

You'll find a number of other consistent essays here, including Kingsley-Nixey who reviews and lists others.

I critically agree your observation that "Lorentz covariance applied to time and spatial relationships is too restrictive as a constraint to be generally applied to field expressions for elementary particles or to serve as an underlying basis for their determination."

You may not recognise the view from my approach immediately, but quickly will. I use Proper Time rules and delta lambda on detection, analysing frequency from different observer frames and deriving two distinct cases instead of the assumed one, of more than one phenomena.

I'm very interested in whether you found the same commonality as I, and of my own basic formula conserving c, energy, (and the wave'function') locally via the Doppler formulations. I'd also like to identify any present divergence.

I hope you don't mind Shakespeare!

Best wishes

Peter

    Hi Peter, Shakespeare sounds intriguing. I'll take a look at your paper and see what I can make out of it.

    I was almost going to buy a small refracting scope this spring, being inspired by the beauty of Venus as it swung near Jupiter, even from just the naked eye.

    Thanks for your interest and cheers!

    Steve

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    • Post #4

    There are many paths to a realization that the Lorentz transformations (LT) have fatal flaws as physics. This essay provides one of the more mathematically sophisticated ways. A central point brought out here is that Maxwell's equations, modified by the replacement of partial time derivatives with total time derivatives, become invariant under the Galilean inertial transformation, so that covariance under the LT is not the only way to express a relativity principle for inertial motions. Einstein's approach, based on rigorous preservation of Maxwell's unmodified equations, has long needed a rival, in order to correct the false impression, widespread among physical theorists, that no rival is possible.

      I need to clarify a potential point of confusion. The velocity variable v has an entirely different meaning in section 4 than it does in section 5. In section 4, where the Doppler effect is determined, v is the relative velocity between the emitting and receiving particles. I say "receiving" rather than "absorbing" because although "absorbing" applies to the case of radiation, the equations hold true for Maxwell's displacement current as well which occurs in situations with no radiation, such as the charging of capacitors.

      In section 5, v is the velocity of the receiving electron in the inertial frame where the electron was initially at rest before it encountered the incident electric and magnetic fields. The text "and v is the relative velocity between the emitting or disturbing particle particle and that of the particle involved in a measurement" in the sentence "The force on the electron

      is F = me dv/dt = e (E + v ﾃ-- B) where me and e are the mass and charge of the

      electron and v is the relative velocity between the emitting or disturbing particle particle and that of the particle involved in a measurement." needs to be removed as it is not correct. The later sentence "We will assume that the measurement particle is initially at rest." sets the frame of reference to the inertial frame of the electron before it started moving in response to the incident fields. Unfortunately there was not enough time to do a more thorough check of the essay before it was submitted.

      hello to all,

      It is relevant when the velocities of rotations of physical quantum and cosmological spheres is correlated with the harmonic osccillators.The planck constant of course is relevant like always..If now we consider an uniquen quantum state in a pure BEC for example, we can see that the lattices between spheres disappear due to the perfect entanglement where the volumes increase towards the main central sphere, the biggest volume, see that the singularities and their binar correspondance is relevant when we differenciate the bosons and the fermions.Indeed they turn in opposite sense logically.The real ask is binar or fusioned. The volumes so can answer.The vibrations and rotations more the volumes can converge whent he groups are finite and precise.

      The frequences and periodicity can be universally linked with the maxwell equations.Even Debye is ok and Stirling also.Now of course Clausius said that all is unified. They turn so they are ...E=m(c³o³s³) don't forget that the fermions encode the bosons ......and that these bosons turn in opposite sense than fermions. The steps of energies can be seen with thje volumes and the stabilities implied !

      We can substituate with the kinetic energy and the potential energy correlated with the entropical evolution and its heat. If we consider that it exists a force between all spheres, so we can correlate with the pure newtonian dynamic.So F=Gm1m2/r² , with F=S s1s2/r². It is relevant when the real universal number is found.and its finite and precise serie of uniqueness.The substitutions are very relevant!!!Of course the time is purely irreversible in its pure universal meaning.

      Regards

        Hello Steve,

        Thanks for that intriguing post. Do you have a reference or two with more details? Yes, Debye and in particular Brillouin were also masters of certain phases of Wave Mechanics and dispersion. I'm not familiar with Sterling's work. As for modeling fermions and bosons, the expressions for field interactions when the particles are moving or spinning become so much simpler in SU(n) with use of dynamics.

        Steve Sycamore

        5 days later

        Hello all,

        I've received some probing questions and comments about the essay by email from a person who doesn't have the time to participate in this forum but has granted the posting of those remarks here. I'll post them under auspices of the anonymous user.

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        • Post #10

        > orthochronous etc: sorry I never heard those words.

        > Note: I'm afraid that many readers don't know that stuff!

        > Probably your background is mathematics, and mine isn't, so that I can't comment on those issues...

        That could well be. They are specialized words and concepts that you find in post-graduate, post-doctorate literature when group representations are being discussed. But it's really not as complex or mysterious as it sounds.

        Wikipedia on the Lorentz group has this to say

        Lorentz transformations which preserve the direction of time are called orthochronous. Those which preserve orientation are called proper, and as linear transformations they have determinant +1.

        and this (which parallels what I wrote)

        Wikipedia on the Lorentz transformation

        Proper Lorentz transformations have det(Auv) = +1, and form a subgroup called the special orthogonal group SO(1,3).

        Improper Lorentz transformations are det(Auv) = -1, which do not form a subgroup, as the product of any two improper Lorentz transformations will be a proper Lorentz transformation.

        From the above definition of A it can be shown that (A00)2 >= 1, so either A00 >= 1 or A00

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        • Post #12

        > The "Lorentz group" isn't a pure part of SR. Does the Lorentz transformation have the same problem? If not, then it's an artificial one. Parity is not part of SR.

        Strictly speaking, what you say is true. Parity relations would seem to be the extension of SR or the application of its definitions and methodologies where those particular difficulties crop up. There are several steps in the entire chain:

        LT -> SR -> Minkowski space -> Lorentz and Poincare groups (from which the subgroups or classifications of the LT are observed) -> generation of Parity rules

        I believe it's generally understood in the professional Physics community that the term "spacetime" encompasses the whole ball of wax - everything in the sequence above.

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        • Post #14

        > - The meaning of the symbols of the Voigt transformation is subtly different from that of the Lorentz transformation.

        >

        > - how is it "more general"? It has a different application... no abrogation of the universality of time or distance was invoked!

        As Voigt himself pointed out in a postscript addendum to his paper, his transformation can be normalized (not his words but mine) to be equivalent to the LT.

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        • Post #16

        > I did not read that he stated that - if he did, then I think that it was dishonest, or due to confusion, because his theory was very different. It was a successful "me too"!

        That could be. Of course it was a bit unfair of Lorentz to not cite Voigt's work he as it has been shown he clearly read and considered it.

        Also what Voigt did that Lorentz did not do was to explicitly consider how the transformation works when the relative velocity is not aligned along the x, y or z axis. Furthermore, he showed the transformation's effect on the wave equation which Lorentz didn't really follow up on and used his transformation for several examples in his paper. His use of symbols is difficult to follow though. That could be the reason that there are very. very few studies of his transformation.

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        • Post #18

        > - It's unclear how to interpret your finding that "we have apparently discovered the origin of the Lorentz gamma factor", referring to the "plasma frequency". It is present all-over wave mechanics.

        Historically, de Broglie worked out the mathematics of wave mechanics based on some aspects of SR. But now, we can see that the physical situation is the other way around. SR is a particular interpretation or application of the outworking of wave mechanics.

        That is the result I wished to portray in the paper! Because of that we can show that all mathematical relations described in SR or Minkowski space are a homomorphism to the relations described in the paper using 3-vectors in the Newtonian-Galilean framework. If you look at the second image attached in this forum you can see that the homomorphism is

        [math]\Delta E = f(t, x, y, z, q, m) \qquad \qquad = \qquad \qquad \Delta E \rightarrow f(-ct, x, y, z)[/math]

        Where the left hand side could be called the Maxwell-Thomson-de Broglie relations in which the effects of charge q and mass m are accounted for in the function f(). The right hand side could be called the Poincare-Einstein-Minkowski relations which employ the Lorentz transformation. The numerical results for a problem expressed in one system are equivalent to the results for the problem expressed in the other system.

        J. J. Thomson is the only physicist I know of who has made the direct connection between plasma frequency and wave mechanics. But he didn't actually know of or use the term "plasma frequency" as far as I can see. Normally it seems plasma physicists don't talk to quantum physicists and vice versa. Or they don't mutually understand each other. Which is a shame because this homomorphism could have been discovered long ago.

        Sorry, the equation above has a misplaced equal sign and arrow. It should be

        [math]\Delta E = f(t, x, y, z, q, m) \qquad \qquad \rightarrow \qquad \qquad \Delta E = f(-ct, x, y, z)[/math]