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    Zoran S. D.'s picture
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    Joined: Jan 14 2014

    Hello!
    I join the revolution, with a contribution. :)

    -----------------------------------------------------------------------------------------------------------------------------------------------

    The year 1900.

    1) Planck made the crucial discovery: 
    ( means that this energy is the elementary energy which is finite)


    2) In the same year, Henry Poincare wrote and published the paper 
    http://fr.wikisource.org/wiki/La_th%C3%A9orie_de_Lorentz_et_le_principe_...
    where he derived the equation for mass-energy relation
    arxiv.org/ftp/physics/papers/0608/0608289.pdf (page 2)
    http://en.wikipedia.org/wiki/Henri_Poincar%C3%A9#Mass.E2.80.93energy_rel...
    “Poincaré concluded that the electromagnetic field energy of an electromagnetic wave behaves like a fictitious fluid ("fluide fictif") with a mass density of E/c2.”
    http://en.wikipedia.org/wiki/Henri_Poincar%C3%A9#Poincar.C3.A9_and_Einstein
    “A few years before his death, Einstein commented on Poincaré as being one of the pioneers of relativity, saying "Lorentz had already recognised that the transformation named after him is essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further ...." [35] ”

    3) Newton’s law of gravitation was known for a long time already.

    (According to GR, the Newton’s law of gravitation is just an approximation. But, during the course of these posts, it will become completely clear  that the situation is exactly opposite, namely, that the GR equations are approximations of reality, which are good in the area which is far away from the Schwarzschild radius

    and become more and more wrong as we approach the Schwarzschild radius, and, finally, become totally wrong at the Schwarzschild radius.)



    So, if I were Poincare, or somebody else who lived then, I would have tried the following theoretical investigation/derivation about how would an EM quantum energy (which, a few years later, will be named as “a photon”) behave in the gravitational field.


    The intensity of the gravitational force is


    where   is, for example, the Earth’s mass, and    is the mass of an entity within the Earth’s gravitational field.

    The amount of work which has to be done in order to move the mass  infinitesimally radially away from Earth,  , is




    In the case of a photon which moves radially away from Earth, and according to the energy conservation principle, and according to the equation which Poincare had derived, we would have



    from which we easily obtain the Pound-Rebka experiment result:



    The height of the Pound-Rebka measurement platform was 22.5m. 
    That is much, much less than the Earth's radius, so we can use the approximations





    and we get that the ratio of the photon's energy change and the photon's energy is



    We could also obtain the exact equation for calculation of the red-shift.
    From the equation



    we first derive the equation which describes the behavior of photon's energy in the gravitational field:



    where is energy of the photon when it is infinitely away from the gravitation source (or, practically, when it so far that the gravitational influence is neglectable).
    And, the exact equation for red-shift calculation would be



    So, we can use this equation to calculate the exact red-shift, but the result will be practically the same as the result which we have already obtained, using the previous approximative calculation. Or, if we use the following approximation:
    Since the exponent is very small, we have



    Hence, we get again





    A photon is an elementary EM-oscillation which propagates linearly through the space.
    An oscillation has the frequency. Frequency is the reciprocal value of the time period in which one full oscillation is performed.
    So, 


    which means: the frequency of some oscillation is 1 full oscillation in the time period during which that oscillation completes.
    Also, during the time period , the photon travels the distance which is equal to its (wave)length.


    The least amount of energy for some given frequency is



    The least amount of energy means: the energy can be equal to or greater than that least amount, and the mathematical notion for that is 



    that is,



    that is,




    For a single photon we have


    This equation universally defines/determinates the state of each and every photon:
    - for some given energy, photon's EM-oscillation-period has to be such that the product of that energy and that time period is equal to h.
    Or:
    - for some given EM-oscillation-period, photon's energy has to be such that the product of that energy and that time period is equal to h.


    Hence,
    If the energy of a photon does change (i.e. as the photon moves away from the gravitational source), then the photon's EM-oscillation-period does change too, in the way that the product of their current values is equal to h:









    where   is the oscillation-time-period of the photon when it is infinitely away from the gravitation source (or, practically, when it so far that the gravitational influence is neglectable).

    Through some fixed point which is infinitely far from the gravitation-source (or, practically, which so far that the gravitational influence is neglectable), the photon would pass in

     time units.

    Through some fixed point which is in the vicinity of the gravitation source (i.e. Earth), that same photon would pass in

      time units.


    In that given, observed, fixed point, which our photon is passing through, an infinitesimal time-fraction of the photon's oscillation-period would be




    An infinitesimal time-fraction of the photon's oscillation-period is, generally, an infinitesimal time, so




    Knowing that the gravitational acceleration is

    ,

    and that

    ,

    we will derive the velocity-equation of a photon which moves through the gravitational 
    field:



    So,



    Or,



    The differential of the   is:



    Hence,




    And, the length element of the photon’s path would be




    So, the single photon, that tiniest and most fundamental entity in universe, we have used as – so to say – the finest “litmus-paper” for discovering the space- and time- “flavors” of gravitational field:






    Here we’ve introduced



    It has the dimension of length, and it depends on M. Since it is, so to say, the normalization factor for the radial coordinate r (or, for the radius r), we can call it “the characteristic radius of the body whose mass is M”. (That is how Planck, or Poincare would have probably named it, if they would had been those who did the previous derivations, in the year 1900.)


    So, all this could had been derived in 1900 – from the existing knowledge at that time.
    What we know now is that the Newton’s law of gravitation is very, very accurate:
    http://physics.aps.org/story/v7/st8
    http://arxiv.org/pdf/hep-ph/0405262.pdf
    Hence, according to everything presented so far, the equations





    are logically, mathematically, and physically quite correct.
    In the next post, we will use them to calculate the precession of planetary orbits, Shapiro time delay, gravitational deflection of light.

    Comments

    The Stand-Up Physicist's picture
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    Joined: Mar 10 2011
    Hello Zoran:
    I am a skeptic.  That means I expend some effort to understand a new proposal.  I then say why I think the proposal may or may not be true.  You are then free to continue working as you wish.

    I have spent a long time playing with curved metrics written as exponentials. One basic criteria is that any such metric must agree with Taylor series expansion of Schwarzschild solution of general relativity to first order Parameterized Post-Newtonian (PPN) accuracy.  That sounds fancy, but it is not - it is just 5 terms found in "Gravitation" by Misner, Thorne, and Wheeler, equation 40.1:




    They both start with a one.  That is good because when M goes to zero or R goes to infinity, this goes one like space-time is flat with no gravitational mass. When there is a mass, the dt term gets smaller while the dR term gets bigger.  I think of this in two setting.

    Imagine 2 firecrackers explode.  There is a reference observer with a super accurate ruler and clock measuring it on the surface of Earth.  There is also a girl in a balloon measuring it.  Since she feels less gravity, her heart beats faster while her meter stick expands.  With a faster clock, the time between the firecrackers will be larger while the distance measured with the meter sticks will be smaller.

    In special relativity, the changes in measurements happen the same way.  If one is walking toward the reference observer, the time between the explosions and the distances will both appear smaller.  If one is walking away from the reference observer, the time and distance between the explosions will both be larger.

    If someone is in the basement of a building watching the firecrackers, then they will be closer to the gravity source.  That makes their heart beat slower and makes their meter stick smaller.  Thus their measurement of dt will be smaller with the slow beat but the dR will be larger with the mini meter stick.

    In SR, the dt, dR move in unison, while in GR they move in opposite ways.  That is standard physics as I understand it.

    Now you have a new proposal.  The final two equations are:




    This appears a little garbled to my eye.  I have only seen ds^2 = dR^2 - dt^2 c^2.  There is no need to use the "dot" because the exponential is just a scalar and dots are usually reserved for vector dot products.  These are minor things I point out but do not consider a big deal for a blog.

    What matters to me is that I see two things wrong.  First, these both change in the same way as M gets bigger or smaller.  In my opinion, that is 100% wrong.  I know you did a total of 9 blogs in this series and did a lot of math, but cannot get past this blocker.  The second issue is that the changes in space are twice as large as changes in time.  That is not what equation 40.1 in Misner, Thorne, and Wheeler says - the first order changes are of the same size and opposite directions due to a mass instead of your proposal where changes are the same way but twice as big for space.

    I hope I have been clear as to why I don't think your GEM proposal is of lasting value.

    Zoran S. D.'s picture
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    Joined: Jan 14 2014

    Hello Doug,

     

    Lemaitre once said to Einstein (at a conference in Solvay, Belgium):

    “Your math is correct, but your grasp of physics is abominable”.

    And, he was right, but yet, Lemaitre’s grasp of physics was incomparably more abominable.

    In the Einstein’s case, I would have never used the word “abominable”. “Abominable” is insulting. “Wrong” is appropriate. Einstein’s mistakes were the kind of the so called honest mistakes.

    But, the word(s) “abominable/hideous/bawdy” essentially properly describe the physicses which emerged after that conference in Solvay.

    Einstein’s postulations were wrong, unphysical, but the Heisenberg’s were far worse. Both the Relativity theories and QM, turned physics into mathematical mysticism, essentially based on religious foundations (Lemaitre's "Big bang", that is "God creates the Universe out of nothing", and Heisenberg's "uncertainty principle", that is "inconceivable/mysterious are the God's ways"). Into the worst kind, the most perfidious kind, of mind-deviation in the history of mankind. The heaven for vanity and conceit of “elevated minds”, minds of the “chosen ones”. Minds which try to play Gods: to invent the world(s).

    I am simply totally disappointed (more appropriate description would be that I feel soul-pain, I feel sadly hopeless) with the “discussions” of “crème-de-la-crème of human minds”, that is, with the vanity/conceit driven “outwitting” among the QM-ers and string-ers/brane-rs, and among promoters of the too many variations of relativisms. In short: I am disappointed with the super-stupidity (vanity/conceit driven intelligence) of human species. I am disappointed by the indication which becomes more and more confirmed as the time goes by: that the super-stupidity of human species is incurable. In other words, that our species is doomed to destroy itself, and if it does not, that it will be destroyed by some extraterrestrial civilization, because they cannot allow that the super-stupid human species starts to spread through universe. Human species will be destroyed from human reasons. Somewhat like human species is dealing with the pandemic diseases. “Somewhat” is used because the human species does that driven by fear, by the survival urge. And, some reasonable extraterrestrial species would destroy us driven by sorrow, sadness, about the fact that we are incurably evil. Evil in the most perfidious way: humans are able to, occasionally, be reasonable, but, most of the time, they just act/pretend to be reasonable, in order to pursue their hidden evil plans. Human species is hypocrite-species. And, the most hypocrite part is exposed in the way they call themselves: they call themselves humans. The devils which perfidiously present themselves as angels.

     

    If your true intention is to really understand the world you live in, please read everything what is offered for reading at

    http://www.science20.com/the_answer_to_why_does_photonpath_bends_and_beyond-172180

     

    You wrote:

    I have spent a long time playing with curved metrics written as exponentials. One basic criteria is that any such metric must agree with Taylor series expansion of Schwarzschild solution of general relativity to first order Parameterized Post-Newtonian (PPN) accuracy.

     

    Now, if you are a true sceptic, try to set aside Einstein’s and Minkowski’s postulations, and Schwarzschild solution of the Einstein’s postulation.

    The Taylor series expansion of the Minkowski’s postulation is wrong, because his postulate is wrong – it is mathematically valid, but it is not physically valid.

    And, the Schwarzschild solution is composed only of the first two terms of the Taylor series. So, it is actually, the first order approximation of reality. It is the exact solution of Einstein’s postulation. So, Einstein’s postulation is just the fancy tensorial generalization of that first order approximation of reality.

    So, ultimately, it is both incorrect and superfluous/unnecessary.

    And, actually, the Schwarzschild solution would be correct approximation if instead of 8pi, there would be the 4pi in Einstein’s equation (in front of the energy-tensor-flux). And, 8pi stands because that solution is then applied in the Minkowski’s square-root-postulate. And gives the result which is the very good approximation of reality outside the Schwarzschild radius. Which becomes more and more wrong approximation as one approaches the Schwarzschild radius, and becomes complete nonsense at the Schwarzschild radius.

     

    What I had done/wrote, is not a proposal. It is the true physics. For example, just like the Newton’s laws are not the proposals, but the facts.

    In that what I wrote, you will not find any idea, but only the basic reality facts, and unambiguous, rational, reasonable, comprehensible, simple conclusions.

    If you take some time to read all that patiently, and using your capability for reasonable thinking, you will see that there is nothing wrong there.

    It would take less than a week.

     

    But, I doubt that you will do that. The only reason you took some time to read The gem (1) (and The gem (1) only), is that you have felt a bit frightened that someone else came up with the same/similar equations, but in a different way, and you have a bit examined that “threat” to “your emancipation”, and felt relief when you saw the “100% wrong thing” in it. And, then, when you felt safe, you felt safe to be good (people are usually good only when they feel safe and happy), and you tried to friendly warn me about my “mistake”.

    There is no mistake, Doug.

    It is you who is wrong. You build up the wrong postulations, you try to make mathematical variations of mathematical postulations which are mathematically valid, but physically invalid. You try to introduce/propose “new idea”.

    You feel safe, because you think that “you are standing on the shoulders of giants”. Concerning the basics, the majority of the scientific community has nothing against your approach. And, that is why you think that you are on a good track. And that I am definitely wrong.

    The true physics has nothing to do with ideas, but only with the facts. True scientist does not try to invent the world – the true scientist tries to discover it. Using only the rational, comprehensible reasoning. Everything beyond that is the mysticism, the vanity driven self-deceiving.

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