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Correction to length contraction equation

  1. Jul 26, 2004 #1
    Suppose an electron has a small radius and we look at its radius and
    mass from the point of view of special relativity.

    Let's use the idea of (mass x length) = constant.
    No quantization.

    Is the contraction to zero radius at c a problem?
    If so then we can guess how to stop it.
    One way would be just to write:

    LENGTH = Rest Length x ( 1-v^2/c^2 + small constant)^1/2

    if mass = m0 / ( 1-v^2/c^2 + small constant)^1/2

    then:
    (mass x length) = m0 / ( 1-v^2/c^2 + small constant) x

    Rest Length x ( 1-v^2/c^2 + small constant)^1/2

    = constant = m0 x Rest length

    Perhaps we can use this as a basis for a field theory with
    an electron that has a radius and that is not point-like.

    The small constant would mean that mass does not become infinite
    but that it reaches a finite value and so rest masses can,in principle be accelerated to the speed of light.
    If time dilation is considered then the maximum speed a clock on Earth can run compared to a clock at the visible horizon of the universe where v =c is
    10^19 seconds ( about the current age of the universe) per second that passes on the horizon.This means that the small constant has a value of 10^ - 38 metres.So if an electron at rest had a radius of 10^ - 18 metres,
    at the speed of light it would have a radius of 10^-19 x 10^-18 = 10^-37 metres.
     
  2. jcsd
  3. Jul 26, 2004 #2
    I think that is your first mistake right there.
     
  4. Jul 26, 2004 #3
    Hi Locrian;

    Could you explain why? Or point out where the answer might be found.

    Thanks
     
  5. Jul 27, 2004 #4
    I'm not aware of any evidence to suggest electrons have a radius; a wavelength, and a probability distribution of where you might find one, but not a radius. You wave away quantization to avoid QM issues, but your final value for the radius of an electron is so small it cannot avoid QM effects.

    I don't feel the measurable you are suggesting with which to test your theory is measurable in the language you are using.
     
  6. Jul 29, 2004 #5
    I also think the vision of Locrian is correct. In the model proposed by kurious, QM-effects at very small scale are not taken into account, right ??? Correct me if i am wrong. Besides I still have some difficulties with your concept of this restmass you are using. Given the fact that this proposal is to be used for QFT-like-models. How is this mass generated for the electron. I remember you saying, kurious, that this concept was needed for the elektromagnetic-massgiving-system. Using two new models at once with no correlation to the existing theories is a bit to faroff for me.

    But let us ignore all this and be positive. What about this ? What would be the influence of this extra number, used to keep the mass from blowing up to infinity, on the metric of space time. I mean, we get this factor 1/(1-v²/c²)^1/2 from the fact that c is an universal constant. We take two equations of a sferical wave and state that x²+y²+z²-c²t²=x'²+y'²+z'²-c²t'²

    Is this still going to be valid when this extra term is taken into account, i don't know. I will, do the reverse calculations and see what the implications are... to be continued...
     
  7. Jul 30, 2004 #6
    It is interesting to note that if we let a proton fall into a black hole and assume it reaches the speed of light near the singularity, then,taking the rest diameter of a proton as 10^-15 metres, the small constant would say that at the singularity
    the proton ha s a diameter of 10^ - 19 x 10^ -15 = 10^ -34 metres.
    This is the minimum length of a string in string theory. But could it be the minimum size of the "singularity" in a black hole?
     
  8. Jul 30, 2004 #7

    russ_watters

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    Staff: Mentor

    I'm not seeing the relevance of the electron there, but in any case, you can't change the laws of the unvierse by changing equations. You change your equations to match the laws of the universe. Your equation does not match the laws of the universe.
     
  9. Jul 30, 2004 #8
    Russ Waters:
    Your equation does not match the laws of the universe.

    Kurious:
    In what way is this true? Nobody can know that the original Lorentz transformations are accurate to 19 decimal places - they have never been derived-they were arrived at by trial and error and experiment has not proved them correct to 19 decimal places.
     
  10. Jul 30, 2004 #9
    T ab would still equal T ba?The magnitude of the four-momentum of a photon would still be zero.Where would the problems arise?
    Would there be any problems caused by the small constant for general relativity?
    Wouldn't it be the case that the energy density of the universe at the time of the Big Bang would not be allowed to be infinite because of the small constant? The curvature of space-time would also not be infinite and so
    we would have a calculable theory from which the universe could have expanded.
     
    Last edited: Jul 30, 2004
  11. Jul 30, 2004 #10

    russ_watters

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    You mean like THIS. That's Apppendix I to Einstein's "Relativity." The title of the appendix is: "Simple Derivation of the Lorentz Transformation."

    What you are doing here is hoping that just beyond our current measurement ability lies a piece of data that doesn't fit the current theory and adding that piece of data to an equation. I don't know where you would have gotten the idea that that's acceptable - it is absurdly unscientific.
     
    Last edited: Jul 30, 2004
  12. Jul 30, 2004 #11
    Russ Waters:
    What you are doing here is hoping that just beyond our current measurement ability lies a piece of data that doesn't fit the current theory

    Kurious:
    No, the idea of the small constant is to stop infinities forming and singularities.
    Most physicists agree that these two things are bad news in a physical theory.
    It is not unscientific to propose a modification to a theory and then
    see if the modification is useful in practice - which is why I am on this forum proposing the idea to other people like yourself.The aim is to see if my idea can make a prediction that matches experiment.I have guessed the magnitude of the constant but even Einstein made guesses.It is possible to guess right! Most of the time one will guess incorrectly.I do not see the small
    constant as an attack on special or general relativity but just as a helpful modification if it turns out to be right.By Occam's razor it's more likely than string theory to be the right way of removing a singularity because it's simpler
    and keeps the current theory - relativity - intact.

    A proton reaching the centre of a black hole would have a diameter of
    10^19 x 10^-15 metres = 10^ -34 metres- relative to an outside observer at rest - according to my equation for length contraction.
    If a neutron has a similar diameter, then given that there are about
    10^ 57 neutrons which go into making a black hole,this would mean that
    all the neutrons could fit into a sphere of radius 10^19 x 10^-34 =
    10^ -15 metres.A photon (electric force mediator) or a gluon (colour force)
    would take 10^-23 seconds to cross 10^-15 metres.
    Using E x t = hbar, we find that the energy of a photon or gluon over this distance is 10^-11 Joules.This corresponds to a mass of 10^-28 kg per neutron.But if we wnat to know the vacuum energy density in 10^-15 m^3 how do we calculate the number of force-mediators present at one instant of time? How do the coupling constants relate to time?
     
    Last edited: Jul 30, 2004
  13. Jul 30, 2004 #12
    Kurious:
    In what way is this true? Nobody can know that the original Lorentz transformations are accurate to 19 decimal places - they have never been derived-they were arrived at by trial and error and experiment has not proved them correct to 19 decimal places. [emphasis added]

    Russ Waters:
    You mean like THIS. That's Apppendix I to Einstein's "Relativity." The title of the appendix is: "Simple Derivation of the Lorentz Transformation."

    Kurious:
    A paper just out this month:

    Mathematical Error in Lorentz Transformation

    http://www.newtonphysics.on.ca/lorentz-light/light.html

    Though I'm not saying the transformation is wrong - perhaps it's just not complete.
     
  14. Aug 1, 2004 #13
    If there are masses that can move faster than light then this must be reflected in the
    Lorentz transformations.This can be done as follows:

    mass = m0 / ( 1-v^2/c^2 + small constant)^1/2

    becomes:

    m = m0 / [ (1 - v^2/ Vfast^2) - (1 - v^2/ Vfast^2) v^2/c^2 + constant)]^1/2
    Once again Tab = Tba and the magnitude of the four momentum of a photon is zero.
     
    Last edited: Aug 1, 2004
  15. Aug 1, 2004 #14
    If there are masses that can move faster than light then this must be reflected in the
    Lorentz transformations.This can be done as follows:

    mass = m0 / ( 1-v^2/c^2 + small constant)^1/2

    becomes:

    m = m0 / [ (1 - v^2/ Vfast^2) - (1 - v^2/ Vfast^2) v^2/c^2 + constant)]^1/2

    Once again Tab = Tba and the magnitude of the four momentum of a photon is zero.
     
  16. Aug 1, 2004 #15

    russ_watters

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    Staff: Mentor

    Since there is no data which matches what you predict, how is your modification "useful in practice?"
    The transformation works. It makes accurate predictions and has never been wrong. There is no other critereon by which theories are measured. Again, you're approaching science backwards: you don't write theories based on how you want the universe to work, you find out how the universe works and write theories that reflect it.
    What have particle accelerators shown us about this?
     
    Last edited: Aug 1, 2004
  17. Aug 2, 2004 #16
    Russ Waters:
    >What have particle accelerators shown us about this?

    Particle accelerators can say nothing on this at the moment.I see the speed of a mass as depending on the ratio of E/B which I have proposed in another thread on theory development - Higgs Particle and Electromagnetism - can account for THE SPEED OF EVEN SUPPOSEDLY ELECTRONICALLY NEUTRAL PARTICLES (I am saying all particles have very short range electric and magnetic field interactions with a charge that fills space).The motivation for superluminal speed is to give gravitons a speed that allows them to come and go from black holes freely,and to account for instantaneous action at a distance.My transforms are useful because they stop singularities from forming in a black hole with no quantum theory required.
    The fact is my transforms work so they show that in principle relativity theory can be altered but still be virtually what it originally was.
    I am not an enemy of relativity theory - I am a fan of it!
     
    Last edited: Aug 2, 2004
  18. Aug 2, 2004 #17
    mass = m0 / ( 1-v^2/c^2 + small constant)^1/2

    Having checked out Einstein's original derivation, I think the small constant
    could have its origins (assuming it really exists!) in the term c x t
    (speed of light x time).It seems to me that c x t would have to be bigger than expected.This means that in special relativity a clock at rest in an inertial reference frame is ticking faster than it should. A gravitational
    field slows down a clock. There must be a field that causes
    a clock to tick ever so slightly faster than usual - a field that exists throughout the universe.A field associated with dark energy perhaps?
     
    Last edited: Aug 2, 2004
  19. Aug 2, 2004 #18

    russ_watters

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    Staff: Mentor

    Are you saying the particles in accelerators are not reaching C because the energy doesn't reach them due to magnetism not working the way we think it does? Before we go any further, is there anything about accepted physics that you do accept or are you just making everything up from scratch?
     
  20. Aug 2, 2004 #19
    Russ Waters:
    Are you saying the particles in accelerators are not reaching C because the energy doesn't reach them due to magnetism not working the way we think it does? Before we go any further, is there anything about accepted physics that you do accept or are you just making everything up from scratch?

    Kurious:

    They're not reaching c in this case because the energy required is
    the energy required to get a particle to 99.9999999999999999999 per cent the speed of light.(I think the small constant has a maximum value proportional to 1/age of universe so time dilation can never be greater than age of universe).
    But much less energy may be required if the ratio of E/B can be increased for
    the short range fields of the particle.I think that this can be done by using a
    strong magnetic field (probably going to need more advanced superconductor technology) to decrease the local density of magnetic charges in space ( yes monopoles-I don't believe in inflationary theory: I think the universe has never been smaller than 10^25 metres and this explains why dark energy density and baryonic matter density are of similar magnitudes today.Also I don't think the universe will get bigger than about 10^27 metres.
    The universe is a harmonic oscillator and oscillates between big bangs and big crunches:


    If I take two spherical regions of space about one metre in radius,
    they would contain about 10 ^ - 27 kg of dark energy each.
    If I now say that the centres of these regions are one metre apart,
    and assume that there is rest mass associated with dark energy (this rest mass being uniformly distributed in each of the spherical regions),
    then using Force = G m1 m2 / r^ 2 I would get a force of attraction
    for the spheres of 10^ -11 x 10^ -27 x 10^ - 27 / 1 x1 = 10^ -65 Newtons.

    If these two spherical regions obeyed Hooke's law F = - constant x extension
    then 10^ - 65 = k x 1 (I am assuming that earlier in the universe when it was smaller the centres of the spheres converged and at equilibrium there was no distance between them)
    k = 10^ -65
    Let's postulate that the universe oscillates regularly between a big bang and a big crunch.

    The frequency of a harmonic oscillator is given by:

    w = ( k/m)^1/2

    w = ( 10^ -65 / 10^ -27) ^ 1/2

    w = 10^ -19 s^-1.

    I accept that the mathematics of physics is in general correct
    but I do think that there must be some modifications for progress to be made.
    I do not accept the Higgs theory of mass creation because without even knowing the full details of it,I do get the impression that the Higgs theory and standard model are only giving each other moral support!
    Until there is a theory that includes gravity too - gravity being a theory that involves mass in a big way - it does not seem to me that the Higgs theory can be right and be linked to the standard model ( in my opinion gravity is an electromagnetic phenomenon and the gravitational force-carrier an electromagnetic wave!).
    And there is nothing wrong with making some educated guesses and then seeing if we can work backwards and produce a reasonable theory from them - by reasonable I mean a theory that is still by and large the old one.
     
    Last edited: Aug 2, 2004
  21. Aug 3, 2004 #20
    What kind of field would make a clock tick faster than it would if the field was not present? If every particle in the universe is swimming in a sea of mass-giving particles,
    and a gravitational field slows a clock by causing the sea to become more dense,near to a large mass like the Sun,perhaps a clock runs faster than it
    should if the particles it is made from can make the sea less dense - by repelling the sea.A fast moving clock would collide with the sea of mass-giving particles and cause the density of mass-giving particles to increase and the clock would tick more slowly.
     
    Last edited: Aug 3, 2004
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