Mass Increase with Speed Explained as a Relativistic Doppler Effect

4702 | P a g e M a r c h , 2 0 1 7 w w w . c i r w o r l d . c o m Mass Increase with Speed Explained as a Relativistic Doppler Effect Constantin SANDU, Dan BRASOVEANU 1 Romanian Research and Development Institute for Gas Turbines-COMOTI, 220D, Iuliu Maniu Bvd., Sector 6, OP76, CP174, Bucharest, Romania constantin.sandu@comoti.ro 2 Systems Engineering Group Inc. (SEG), USA 9861 Broken Land Pkwy, suite 350, Columbia, MD, 21046, USA brasovdx@yahoo.com ABSTRACT


INTRODUCTION
The Special Theory of Relativity (STR) states that the mass varies with speed and this prediction was experimentally validated. After over 100 years of relativity, this increase is still considered a weird thing because this phenomenon did not yet received an intuitive demonstration.
The phenomenon of mass contraction can be easily accepted by intuition if the wave feature of micro-components of body is considered. The Doppler effect for sound sources is easily understood by everybody: The frequency of sound heard by an observer increases when the sound source approaches by observer and decreases when the sound source departs by observer. Similar, the frequency of associated waves of micro-components of a body are subject to the Doppler relativistic effect when they are perceived by an external observer, i.e. the frequency of wave (of microcomponent) which moves towards the observer is perceived as been higher than the frequency of the same wave (of micro-component) when it departs by observer. But the observer perceives only an average frequency. According to Doppler relativistic effect this average frequency is inversely proportional with the number 2 2 c / V 1 because the terms containing speed of body at the power of 1 disappear. The mass of a body at rest is proportional with the frequencies of the associated waves of its micro-components. When the body is moving with a given speed V, the average frequency 'seen' by observer increases and that observer must perceive accordingly that mass of body increases in the same proportion as the average frequency.

DEMONSTRATION
Assume that a massless reflective sphere contains a number of photons, n, which reflects inside forming stationary waves having frequency ν0 (see Figure 1; for simplicity only one stationary wave corresponding to photon no.1 was represented). The angle between the propagation direction of wave and the x-axis is θ. If the sphere begins to move with speed V in the x-direction, the observer will note a shift in the frequency of wave caused by the Relativistic Doppler effect [1]. When the wave propagates from A to B (case 1'), the observed frequency increase is: When the wave propagates from B to A (case 1"), the observed frequency decreases: Equation (1) and (2), provide the average frequency 1  of photon: and the average energy E1 of photon is therefore: Obviously the average mass m1 is: Taking into account that the sphere contains n photons, the total mass mS of sphere moving with velocity V is: The relativistic formula correlating mass and velocity was thereby determined in a manner that clarifies the interdependence 'mechanism'. Similar, for a body composed of condensed matter which is moving with speed V with respect to a fixed observer, mass increase is a natural phenomenon because: 1) waves associated with body particles are subject to the Relativistic Doppler Effect, which causes frequency changes; 2) the observer can detect only the body's inertia, therefore he perceives only the average frequency of these associated waves; 3) the average frequency of associated waves increases with velocity. Therefore, the observer detects increased inertia of body with speed.
In other words, mass increase is a consequence of the Doppler relativistic effect and the wave aspect of its microcomponents, waves which propagate between two positions A and B, which are virtually fixed.

CONCLUSIONS
Increase of body mass with speed is a natural phenomenon, which can be explained as a Doppler relativistic effect applied to the body micro-components seen as stationary waves in the matrix of body.
An external observer perceives the inertia of a body through the average frequencies of stationary waves of its components. When the speed of body increases, those average frequencies increase with speed due to Doppler effect.