CAUSECAUSE of the of the mechanical mechanical andand

electromagneticelectromagnetic equivalency equivalencyof of

inertialinertial systemssystems

MICHELSON EXPERIMENT ANALOGYMICHELSON EXPERIMENT ANALOGY • Elastic ScatteringElastic Scattering

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Beyond the phenomenology of special relativityBeyond the phenomenology of special relativity

• Special relativity stipulates the equivalency (mechanical as Special relativity stipulates the equivalency (mechanical as well as electromagnetic) of inertial systems. It is its starting well as electromagnetic) of inertial systems. It is its starting point. There is no causal justification, it is just a point. There is no causal justification, it is just a phenomenological standpoint.phenomenological standpoint.

• The equivalency of inertial systems is stated in the first The equivalency of inertial systems is stated in the first postulate: “The physical laws of nature are the same in postulate: “The physical laws of nature are the same in every inertial frame of reference”.every inertial frame of reference”.

• But what makes inertial systems to behave identically, But what makes inertial systems to behave identically, independently of their motion, whenever linear and independently of their motion, whenever linear and constant? Is this a primordial property, or is there an constant? Is this a primordial property, or is there an underlying cause that makes them equivalent?underlying cause that makes them equivalent?

• Here, beyond the phenomenology of special relativity, the Here, beyond the phenomenology of special relativity, the cause of equivalency is quested.cause of equivalency is quested.

First and second order equivalencyFirst and second order equivalencyof inertial systemsof inertial systems

• First order equivalencyFirst order equivalency: mechanical and ray : mechanical and ray optic equivalency optic equivalency (on the following animations the (on the following animations the impinging object can equivalently be a ball or a photon)impinging object can equivalently be a ball or a photon)

• Second order equivalencySecond order equivalency: electromagnetic : electromagnetic equivalency equivalency (interferometric invariance)(interferometric invariance)

First order equivalency of inertial systemsFirst order equivalency of inertial systems

Invariance of the observed beam pathInvariance of the observed beam path

Fig.1a: Actual path of the beam through space

(red line)

Scenario of observer

Scenario of actor

Fig.1b: Observed path on the inertial system

(dashed line)

Two different kinematic scenarios, with different Two different kinematic scenarios, with different relative speed. Still, in both cases on each inertial relative speed. Still, in both cases on each inertial

system the ball path appears identicalsystem the ball path appears identical

Two other kinematic scenarios, in which the ball and Two other kinematic scenarios, in which the ball and the system move in opposite directions. On the inertial the system move in opposite directions. On the inertial systems the ball path still appears identicalsystems the ball path still appears identical

Ball and system are moving in the same direction, with respective speed vBall and system are moving in the same direction, with respective speed v11 and v and v22

Their relative speed is: Their relative speed is: δδ11 = = vv11- v- v22

Ball and system are moving in the same direction, with respective speed vBall and system are moving in the same direction, with respective speed v33 and v and v44

Their relative speed is: Their relative speed is: δδ22 = = vv33- v- v44

Speed-induced deflection of the incident beam

• The deflection angle The deflection angle is proportional to the speed of the is proportional to the speed of the inertial system and that of lightinertial system and that of light

• sin(sin()) = v / c= v / c

• V = absolute speed of the inertial systemV = absolute speed of the inertial system

• C = absolute speed of lightC = absolute speed of light

Speed-induced deflection

Beam trajectory vcx

c

Absolute speed stands for the actual speed through space, independently of how any observer may perceive it. Actors (i.e. the moving objects) do not care about observers, they behave independently of them (excepting the quantum ambit)

X

Y

Beam deflection versus inertial system speed

• Deflection angle Deflection angle as a function of the inertial system as a function of the inertial system speed vspeed v

Incidentally, note that Incidentally, note that the beam deflection the beam deflection is identical to the is identical to the relativistic Bradley relativistic Bradley aberration of light:aberration of light:

sinsin(() = v/c) = v/c

The beam deflection as an outcome of the The beam deflection as an outcome of the momentum conservationmomentum conservation

• The deflection angle is ruled The deflection angle is ruled by the law of momentum by the law of momentum conservation and is fixed by conservation and is fixed by the relative speed between the the relative speed between the ball and the inertial systemball and the inertial system

• sin(sin() = v) = v11 /v/v22

• vv11 = = inertial system speedinertial system speed • vv22 = = ball speedball speed

• This implies that the inertial This implies that the inertial system speed and the speed system speed and the speed component of the ball along component of the ball along the X axis are equalthe X axis are equal

Electromagnetic first order equivalencyElectromagnetic first order equivalency

• Equivalency is equally factual in the case of an Equivalency is equally factual in the case of an electromagnetic beam, such as e.g. a laser beamelectromagnetic beam, such as e.g. a laser beam

• vv11 == ccXX == cc sin(sin())

• Hence the projection of each photon on the beam-Hence the projection of each photon on the beam-splitter is invariant. splitter is invariant.

• So, on the beam way back to the beam-splitter, the So, on the beam way back to the beam-splitter, the light spot it makes on it remains still, independently light spot it makes on it remains still, independently of the variance of the kinematic scenariosof the variance of the kinematic scenarios

A few first deductionsA few first deductions

• On any inertial system the ball path appears to be invariant, On any inertial system the ball path appears to be invariant, independently of the variance of kinematic scenariosindependently of the variance of kinematic scenarios

• So, it is said that inertial systems are equivalentSo, it is said that inertial systems are equivalent

• However, this fact actually reflects a lack of accessible information, However, this fact actually reflects a lack of accessible information, due to the inability of inertial observers to detect their spatial due to the inability of inertial observers to detect their spatial kinematics without external referenceskinematics without external references

• The emerging point is thus that any observer is blind to its own The emerging point is thus that any observer is blind to its own kinematic scenario and to any variance of it (except during kinematic scenario and to any variance of it (except during acceleration)acceleration)

• The coarse stipulation that inertial systems are equivalent, without The coarse stipulation that inertial systems are equivalent, without causal concern, has led to misleading conceptual standpointscausal concern, has led to misleading conceptual standpoints

Electromagnetic wave equivalency along the Y Electromagnetic wave equivalency along the Y axisaxis

The apparatus measures the paths length in number of The apparatus measures the paths length in number of and the time and the time in number of T. Using arbitrary units, such as m and t (SI), which are in number of T. Using arbitrary units, such as m and t (SI), which are foreign to the measuring system, requires an ad hoc manipulation by foreign to the measuring system, requires an ad hoc manipulation by means of the Lorentz transformation. This becomes superfluous when means of the Lorentz transformation. This becomes superfluous when using the system proper units, since the Doppler effect acts on themusing the system proper units, since the Doppler effect acts on them

On the Y axis the wavelength λOn the Y axis the wavelength λ appears contracted, such that appears contracted, such that the number of λthe number of λ along it is always equal to that along the actual beam pathalong it is always equal to that along the actual beam path

Electromagnetic wave equivalency along the X Electromagnetic wave equivalency along the X axisaxis

On the inertial system the observed number of λλ appears always equal to that of the actual beam path into space

(Observe that on the beam actual round trip there are 3 λ and the λ and the observed one there are also 3 λ)observed one there are also 3 λ)

• Whatever the variation of the speed of the inertial Whatever the variation of the speed of the inertial system, the path of the reflected beam as seen on the system, the path of the reflected beam as seen on the proper system is invariant, even though the actual spatial proper system is invariant, even though the actual spatial path of the beam is different in each case. This path of the beam is different in each case. This incapacity to observe the effective path of the beam, and incapacity to observe the effective path of the beam, and the fact of seeing instead an invariant deceptive path, the fact of seeing instead an invariant deceptive path, makes inertial systems behave in an equivalent waymakes inertial systems behave in an equivalent way

• Due to the Doppler effect the wavelength along the Due to the Doppler effect the wavelength along the interferometer arms varies in the same proportion as interferometer arms varies in the same proportion as does the actual beam path length. This makes the does the actual beam path length. This makes the number of wavelength along each arm to be invariant, number of wavelength along each arm to be invariant, and therefore the phase stays stiffand therefore the phase stays stiff

Comparison of the two approachesComparison of the two approaches

• Classical Model (Newtonian)Classical Model (Newtonian)

• Natural units: Natural units: and T and T • (system operating units) (system operating units)

• Doppler effectDoppler effect

• Length and time measured in terms of Length and time measured in terms of and T are invariantand T are invariant

• The invariance of the measured length The invariance of the measured length and time just relies on a metric based on and time just relies on a metric based on and T as units and T as units

• This metric does not need to be This metric does not need to be artificially manipulated by means of the artificially manipulated by means of the Lorentz transformation. Instead it Lorentz transformation. Instead it naturally obeys to the Doppler effectnaturally obeys to the Doppler effect

• Natural metric Natural metric

• Relativistic ModelRelativistic Model

• Arbitrary units (SI): m and sArbitrary units (SI): m and s• (foreign to those used by the set-up) (foreign to those used by the set-up)

• Lorentz transformationLorentz transformation

• The groundwork of special relativity The groundwork of special relativity requires an illusive contraction of space and requires an illusive contraction of space and the dilation of timethe dilation of time

• The relativistic metric needs an ad hoc The relativistic metric needs an ad hoc manipulation by means of the Lorentz manipulation by means of the Lorentz transformationtransformation

• The contraction of space is an unphysical The contraction of space is an unphysical effect, it is just a mathematical need of a effect, it is just a mathematical need of a counterfeit metriccounterfeit metric

• Artificial metricArtificial metric

ConclusionConclusion

• SRT invokes the contraction of space itself and the dilation of time. Instead our approach relies on the SRT invokes the contraction of space itself and the dilation of time. Instead our approach relies on the wavelength and the period, avoiding the use of an arbitrary metric and its manipulation through the Lorentz wavelength and the period, avoiding the use of an arbitrary metric and its manipulation through the Lorentz transformationtransformation

• In fact, the Lorentz transformation derives from the Doppler effect and applies exclusively to In fact, the Lorentz transformation derives from the Doppler effect and applies exclusively to and T, and not and T, and not to space itself neither to time itselfto space itself neither to time itself

• We take the contraction of space as a fictitious effect, and as an irrational concept. It is just a mathematical We take the contraction of space as a fictitious effect, and as an irrational concept. It is just a mathematical joker that is void of any physical reality, and derives from the use of an artificial metric, foreign to that used joker that is void of any physical reality, and derives from the use of an artificial metric, foreign to that used by the measuring systemby the measuring system

• Inattention to the origin of the equivalency of inertial systems has promoted the absurd and irrational belief Inattention to the origin of the equivalency of inertial systems has promoted the absurd and irrational belief in space contraction induced by speed, which is as irrational as or even more than the old belief in in space contraction induced by speed, which is as irrational as or even more than the old belief in geocentrism. It derives this time from a gauche direct mathematical reading of physical reality geocentrism. It derives this time from a gauche direct mathematical reading of physical reality

• The scarcity of a critical search for the physical cause of the equivalency of inertial systems, in favour of the The scarcity of a critical search for the physical cause of the equivalency of inertial systems, in favour of the sole search for a mathematical solution, has led to conceptual aberrations. A workable mathematical sole search for a mathematical solution, has led to conceptual aberrations. A workable mathematical formulation does not necessarily imply an accurate apprehension of the actual physical reality formulation does not necessarily imply an accurate apprehension of the actual physical reality

• The cause of the constancy of the speed of light stands in the inaptitude of inertial observers to detect their The cause of the constancy of the speed of light stands in the inaptitude of inertial observers to detect their proper motion, so they end up inexorably getting the intrinsic speed of light, which is constant proper motion, so they end up inexorably getting the intrinsic speed of light, which is constant

• The major conceptual flaw of SRT arises from its assimilation of appearance to actual reality. Its inability to The major conceptual flaw of SRT arises from its assimilation of appearance to actual reality. Its inability to discern them has led to quite a few inner conceptual incoherencies and irrationalities, some of them pointed discern them has led to quite a few inner conceptual incoherencies and irrationalities, some of them pointed out as paradoxesout as paradoxes

More information in the following links:More information in the following links:

• (1) (1) First and second order electromagnetic equivalency of inertial First and second order electromagnetic equivalency of inertial systems, based on the wavelength and the period as speed-depsystems, based on the wavelength and the period as speed-dependant units of length and timeendant units of length and time

• (2) (2) A causal approach to first-order optical equivalency of inertial A causal approach to first-order optical equivalency of inertial systems, by means of a beam-pointing test-experiment based osystems, by means of a beam-pointing test-experiment based on speed-induced deflection of lightn speed-induced deflection of light

• (3) (3) HomepageHomepage