Mössbauer, Pound & Snider, Einstein - Principle of Equivalence

Rudolf Mössbauer received the Nobel Prize37 in 1961 for his work on “Recoilless nuclear resonance absorption of gamma radiation”. He investigated the optical type of resonance fluorescence, a phenomenon in which the re-emitted and the incident radiation are both of the same wavelength, and selected light sources in which the atoms undergo transitions from excited states to their ground states. The light quanta emitted in these transitions are used to initiate the inverse process of resonance absorption in the atoms of an absorber which are identical with the radiating atoms.


The successful discovery of his effect was used by Pound & Snider in their experiment reported in the Physical Review in 1965 that produced a very accurate result in agreement with the prediction of Einstein’s principle of equivalence. The introduction of the Pound & Snider paper38 provides a useful starting point for this topic: “More than fifty years have elapsed since Einstein proposed what has come to be called the "principle of equivalence", a generalisation of the results of the experiments of Eötvös on the proportionality of mass and weight. Einstein39 proposed that no local experiment of any kind could distinguish between the effects of a gravitational field, on the one hand, and the effects of a uniform acceleration of the laboratory with respect to an inertial frame, on the other. In particular, if a source of radiation were to be viewed from a distance h below it, in a region having a uniform gravitational field of such strength that the acceleration of bodies in free fall were g, the observer should find the same properties that would be found if the whole laboratory were free of gravitation but were accelerating upward at the rate g. In this latter situation the velocity change taking place during the time of transmission of a given part of the radiation puts the observer at an effective velocity ΔV = gh/c. Therefore, one predicts that if a source of radiation at a height h above an observer were given an upward velocity gh/c, the effect of gravity would be cancelled40".


The Pound & Snider Experiment was the first experimental proof of Einstein’s principle of equivalence. The high accuracy achieved based on the use of the Mossbauer Effect makes the experiment an excellent test bed of all new theories of physics and was used as a detailed check of my own theory of Physics in 5 Dimensions41


With Physics in 5 Dimensions, the motion of all particles and bodies in 5-dimensional space follow their own closed path (e.g. an elliptical or circular orbit) with a common radial constant velocity c, the speed of light. The closed path is fundamental to the existence of matter created from electro-magnetic-radiation acting as de Broglie matter waves forming wave groups with the properties of mass and energy of classical physics in 4-dimensional space. Therefore in 5-dimensional space particles & larger bodies (matter) are always subject to an acceleration g arising from their own fundamental motion in a closed path. This motion has nothing to do with the attractive force of gravity of classical physics in 4-dimensional space.


With v4 defined as the velocity vector of a body as viewed by an observer in classical physics, the relative velocity v4 between two different particles or bodies in 5-dimensional space is dependent on the angle θ subtended between the two respective planes of orbit with velocity c. As well as the fundamental plane of motion with radial velocity c on radius Rc, all bodies also have planes of motion with radial velocity v4 on radius R4 and their matter waves have a radial velocity w4 on radius R5, where from de Broglie’s postulate42 we have v4 w4=c2.


Two key aspects of Physics in 5 Dimensions are that:  

  1. All objects and particles of have a constant mass m (not varying with v4) and a constant energy E = m c2
  2. All bodies have three velocity vectors, namely v4, v5 and c, the speed of light, with the scalar relationship c2=v42+v52. It follows that all changes of energy43 can only be an exchange between kinetic energy K=m v4 c and potential energy V=m v5 c where E2=K2+V2; which represents absolute conservation of energy.

In the Pound & Snider experiment we look at the emission of a gamma ray (g) from a single free standing Iridium 77Ir191 nucleus (n) and are interested in the recoil velocity v4n of the nucleus and the resulting momentum and energy distribution between the gamma ray (g) and the nucleus (n). We find that as predicted by Einstein, when the source of radiation, the emitter nucleus, at a height h above the absorbing nucleus is given an upward velocity of v4n = g h/ c the effect of gravity is cancelled. 


In 5-dimensional space the following velocity relationships apply to the experiment: v4= g h / c = c - v4g. These relationships apply to all photons and bodies subject to a uniform acceleration g acting over a distance h. As illustrated opposite, from a frame of reference rigidly fixed to the absorber nucleus, the expression (c–v4g) applies to photons starting an experiment with the velocity of light c and where the instantaneous velocity of the gamma particle after travelling the distance h is v4g


This leads to the following 5-dimensional space view of the Pound & Snider experiment. With the emitter nucleus at a height h above the absorber nucleus, the gamma ray emitted at the nucleus has a wavelength λg and a measured wavelength λg’ at the absorber due the instantaneous velocity v4g of the gamma particle after travelling the distance h. In this case we find that44 Δλg = λg’ – λg = λg (c-v4g) /c. 


The gamma ray has a velocity v4g <c and this is comparable to the optical case of light passing through a material of refractive index n. The refractive index n is defined as n = c/v where c is the velocity of light in a vacuum and v is the velocity of light in the medium of refractive index n. Photons travel slower in a material with refractive index n>1 and we find that this effect causes light passing close to the sun to be deflected, which idea was revived by Einstein in in 1911.


The wavelength λg’ observed is larger than λand so we have a shift of wavelength to “red”. Moving the emitter away from the absorber creates a wavelength change at the absorber due to the Doppler Effect and in this case the wavelength observed is smaller. We have an apparent shift of wavelength to “blue”. The Pound & Snider experiment proves to a high level of accuracy that the movement of the emitter away from the absorber with velocity v4n = g h/c = c–v4g does compensate for the effect of the acceleration g.


The Doppler Effect relates to the relative velocity v4n between the nucleus emitting the gamma ray (a photon) and the nucleus absorbing the gamma ray and can only be associated with an increase of kinetic energy of the nucleus emitting the photon. In order to conserve kinetic and potential energy, the resulting effect on the photon must be an equivalent increase in potential energy and decrease in photon kinetic energy.


The treatment of a gamma ray as a particle of energy Eg with implied mass mg = Eg/c2 is compatible with the results of the Pound & Snider experiment. With the theory of Physics in 5 Dimensions photons can be treated in the same way as any other particle or object, where the detectable mass m is zero when v4=c, the speed of light.



(37) Rudolf Mössbauer –Recoilless nuclear resonance absorption of gamma radiation, Nobel Lecture Dec. 1961 https://www.nobelprize.org/uploads/2018/06/mossbauer-lecture.pdf

(38) Effect of Gravity on Gamma Radiation, R.V. Pound and J.L. Snider, Physical Review Vol. 140, Number 3B, 3. Nov. 1965

(39) A short description of this experiment and its results has been published in Phys. Rev. Letters 13, 539 (1964).

(40) Time taken for a gamma ray to travel the distance h is t = h/c and the velocity ΔV reached by any object subject to an accelerating force g for the time t is given by ΔV = g t = gh/c

(41) Physics in 5 Dimensions – ISBN: 978-3-96014-233-1 / PDF at https://www.researchgate.net/publication/266794606_Physics_in_5_Dimensions_Bye_bye_Big_Bang

(42) de Broglie’s “ The wave nature of the electron” – Nobel Lecture December 12, 1929 https://www.nobelprize.org/uploads/2018/06/broglie-lecture.pdf

(43) See pages 42-46 - Physics in 5 Dimensions ISBN: 978-3-96014-233-1

(44) See pages 415 - Physics in 5 Dimensions ISBN: 978-3-96014-233-1


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