Qualitative evaluation on time dilation in Einstein's theory of relativity
Time dilation in special relativity
"In special relativity, clocks that are moving with respect to an inertial system of observation are measured to be running slower. This effect is described precisely by the Lorentz transformation.", "In special relativity, the time dilation effect is reciprocal: as observed from the point of view of any two clocks which are in motion with respect to each other, it will be the other party's clock that is time dilated. (This presumes that the relative motion of both parties is uniform; that is, they do not accelerate with respect to one another during the course of the observations.)" - Excerpts from Wikipedia on Time dilation.
“Time and space are modes in which we think and not conditions in which we live.” - Albert Einstein
In the philosophical idea of absolute time and space, at any instant during the course of the observations when observing the phenomenon of time dilation effect on the other party's clock, the coordinate time is identical for the two clocks that are in uniform velocity motion with respect to each other.
The other clock that are moving with respect to an inertial system of observation merely appears to be slower as a result of the image of the relatively moving away clock takes increasing time at the speed of light to reach the inertial observer, the moving away clock would therefore appear to be slowing down perpetually; the phenomenon of time dilation effect in special relativity is merely an optical illusion of relative motion in uniform velocity that corresponds to the speed of light. This resolution resolves the artificial cognitive paradox of special relativity and elucidates that time has not physically transformed at all; time dilation is merely an apparent effect in special relativity.
Although it is a fallacy in classical physics for its a priori assumption on the speed of light is infinite, it is also fallacious in modern physics with its current form of mathematical relativism for its a priori assumption of reified time, which postulates time could be physically transformed in its hypothetical construct after it has factored in the finite speed for light. This is a consequence as a result of the scientific consensus on luminiferous aether does not exist, which was fallaciously based on a null hypothesis with the null result obtained by the Michelson-Morley experiment.
See a UVS topic on "Michelson-Morley experiment reviewed with UVS" for further elaboration.
"Larmor and Lorentz, who believed the luminiferous aether hypothesis, were seeking the transformations under which Maxwell's equations were invariant when transformed from the ether to a moving frame.", "In early 1889, Heaviside had shown from Maxwell's equations that the electric field surrounding a spherical distribution of charge should cease to have spherical symmetry once the charge is in motion relative to the ether. FitzGerald then conjectured that Heaviside’s distortion result might be applied to a theory of intermolecular forces. Some months later, FitzGerald published his conjecture in Science to explain the baffling outcome of the 1887 ether-wind experiment of Michelson and Morley. This became known as the FitzGerald-Lorentz explanation of the Michelson-Morley null result, known early on through the writings of Lodge, Lorentz, Larmor, and FitzGerald. Their explanation was widely accepted as correct before 1905.", "Michelson and Morley in 1887 designed an experiment, which employed an interferometer and a half-silvered mirror, that was accurate enough to detect aether flow. The mirror system reflected the light back into the interferometer. If there were an aether drift, it would produce a phase shift and a change in the interference that would be detected. However, given the results were negative, rather than validating the aether, based upon the findings aether was not confirmed. This was a major step in science that eventually resulted in Einstein's Special Theory of Relativity.". - Excerpts from Wikipedia on Lorentz transformation under the "History" section.
The original idea for Lorentz transformation was based on existence of luminiferous aether in absolute time and space (one temporal dimension of time and three-dimensional Euclidean space); it is the Poincaré's Lorentz transformation that had eliminated the existence of aether with pure mathematics. After the existence of aether was falsified with negative result of the Michelson and Morley experiment, this theory was then modified with mathematical treatments to adapt to non-existence of aether that can be considered as a rotation of Minkowski space with four-dimensional real vector space in its hypothetical construct.
See a section on "Four-dimensional spacetime continuum in mathematical construct for sound wave".
Galileo's principle of relativity in inertial frame of reference based on absolute space and time had suffered its foundational crisis with a wrong a priori assumption in an era when the speed of light was dominantly assumed to be infinite. Whereas Lorentz transformation that had factored in a finite speed for light, it therefore could quantitatively predict the passive transformation precisely, and it is applicable to all relative velocities. Lorentz transformation in Euclidean space is merely the Doppler effect of a moving object at uniform velocity with direct or reflected radiation of light waves; it is an optical phenomenon of passive transformation in a coordinate system that is subjected to the speed of light. Although Galileo had also suspected there is a limit for light speed and was the first person known to have scientifically tried to measure the speed of light, his lanterns experiment at then could not be conclusive on the upper limit of light speed, and therefore could not rule out the infinite speed of light. By factoring in the speed of light has limit into Galilean transformation, it could be analytically visualized to correctly describe astronomical phenomena coherently without any contradiction.
From the perspective of classical physics in absolute time and space with limited speed for light, when an observer on Earth is looking at a moving away galaxy cluster that is 100 million light years away and appears to be five million light years in length in the moving away direction, the nearer end of the moving away galaxy cluster is a time-dilated image that is also time delayed by 100 million light years while the further end is a time-dilated image that is delayed by 105 million light years, the actual length of the observed galaxy cluster would be longer than the optically observed length of five million light years and the actual location of the galaxy cluster would have traveled a distance according to its trajectory. This is a uniform velocity motion phenomenon of length contraction that is merely an optical illusion caused by time dilation effect and time delay effect.
If a non elastic rod of one light-year long is moved away from an observer by a distance of z in space in the direction of the rod over a period of time t at speed v, although the rod from end to end would move instantaneously by a distance of z, the observer would see that the rod is contracted by the length of z, the image of the rod at the far end that had moved to the distance of z would take one year to reach the observer. This simple thought experiment demonstrates that this phenomena of length contraction and length extension are optical illusions caused by the combinations of time dilation effect and primarily the time delay effect over the entire length of the rod; these are cognitive paradoxes. Another observer at the opposite end of the rod would observe that this rod is being extended by the length of z instead. These transformation phenomena of the very long non elastic rod moving at a uniform velocity is a passive transformation of no physical significance.
If this no elastic rod moves from rest and then move past an observe at the speed of light, its entire length observed would appear to be gradually contracted over a period of one year to eventually become zero in length; this phenomenon is merely an optical illusion that is subjected to the speed of light.
If synchronized clocks are placed along the rod at equal distance apart, the observer observing the rod moving away from him would observe all these clocks to be dynamically time-dilated according to their individual time delay factors. This would depend on the distance of the clocks from the observer that would be observed to be dynamically changing in the motion with a dynamical effect of distance over time. The observer at the other end of the rod would observe an inverse scenario of the clocks indicating their time in a combined function of dynamic reverse time dilation effect and dynamic reverse time delay effect, this would also depend on the distance of the clocks from the observer that would be dynamically changing in the motion with a dynamical effect of distance over time in a reverse manner.
Note: An animation to illustrate this dynamically time-related phenomenon would be ideal, however this was not satisfactorily produced as yet.
See an externally linked topic on "Ladder paradox" that elaborates it is an apparent effect for the transformation of length contraction in SR.
"The relativity of simultaneity is the concept that simultaneity is not absolute, but dependent on the observer. That is, according to the special theory of relativity formulated by Albert Einstein in 1905, it is impossible to say in an absolute sense whether two events occur at the same time if those events are separated in space." - Excerpts from Wikipedia on relativity of simultaneity.
To understand relativity of simultaneity from the platform of classical physics, do a thought experiment to simultaneously fire one laser pulse from two locations with their clocks synchronized to a coordinate time, one laser pulse is fired on Earth and the other laser pulse is fired on Moon at the same time. As a result of time delay cause by the limit of light speed, a natural negation that causes a cognitive paradox would occur to the observers. The observer on Earth would see the laser pulse on Earth was fired first and the laser pulse on Moon was fired later, while the observer on Moon would see the laser pulse on Moon was fired first and the laser pulse on Earth was fired later. The time delay of slightly more than one second as locally observed in the sequence of these laser pulse firing events is identical for both observers is because the distance between them is the same. When two supernovae separated in space are observed to be simultaneously exploding in the night sky, without knowing their locations, it would be impossible to say in an absolute sense whether the two events have occurred at the same time like they are observed. However, in absolute time and space, it is possible to measure in an absolute sense whether these two events separated in space that are observed in the celestial sphere have occurred at the same time if their locations are known; the effect of time delay that is subjected to the speed of light over distance would render optical illusion for the observer.
'If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by "time". We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, "That train arrives here at 7 o'clock,'' I mean something like this: "The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.' - Excerpt from "Electrodynamics of Moving Bodies" by Albert Einstein in 1905, at a section in "Definition of Simultaneity".
Do a thought experiment with an observer moving away at almost the speed of light from the train station just seconds before the train arrives at 7 o'clock. For a long period of time (could be hours or longer depending on the Lorentz factor) that is measured with the observer's clock, the moving away observer would observe time dilation effect in the observation of the train station and therefore would be observing a slowed down scenario for the events occurring at the train station. Although seconds later in coordinate time at 7 o'clock the train would have arrived on schedule, the observer would take a long period of time to observe this past event of train arrival in slow motion with a simultaneous event of a clock there indicating 7 o'clock in the correspondingly slower process. The instances of these past events are observed when the time-dilated image of the train station reaches him while he is moving away. This thought experiment illustrates that time dilation effect is an optical illusion.
When an observer on Earth see a star that is supposedly twenty light-years away, what the observer is seeing is the image of the star that has took a time of twenty years to reach him at the speed of light (barring the gravitational effect of nearby celestial objects on speed of light and negligible relative motions that would cause some minute variations). In a thought experiment with a clock observed on this star from Earth, what observed is the optical time-delay image of this clock, if this clock on the star is synchronized and has started together with a clock on Earth, the clock on the star when observed from Earth would appear to be approximately slowed by twenty years. In the observer's frame of reference, the actual location for the observed star would have further traveled twenty years in distance according to its trajectory, its synchronized clock accounted for gravitational time dilation when observed on the star would indicate a time that is exactly the same as the clock on Earth that can be theoretically verified with Einstein synchronisation.
time in three-dimensional invariant space is a concept
Time has never began, neither would it end, there is no smallest limit of a shortest moment nor is there a finite limit of longest period for time.
Time without motion is meaningless, but nothing in the observable universe is without motion, time is a concept of measurement for the motion of physical entity in the three-dimensional physical space. Time does not exist physically at all and therefore would not be subjected to any physical interaction. Time as a dimension merely exist in a conceptual system as a scalar field of a hypothetical construct in the physical space, and it is regardless of all physical elements. Absolute time in the coordinate system is universally synchronized throughout the observable universe.
“Not everything that can be counted counts, and not everything that counts can be counted.” - Albert Einstein
Time as a concept of defined interval can be counted in a physical event for its period with a clock, but it itself cannot be counted. Although variation of time in relative motion illusion or time delay effect does not physically occur at all as it could be empirically observed in such physical events, time paradoxically exists in the coordinate system of physical space and therefore these variations of time in passive transformation can be quantitatively accounted for. Time is merely a dimension created for the task of measurement as per se, and it is not something that arises to naturally exist in the objective reality.
To give time a physical identity in a different frame of reference is to introduce dualism, this would create a logical paradox in its mathematical construct, it would have contradicting definitions inevitably that can lock a theory in circular logic to render it paradoxical in its delusion; giving identity to time to express that it physically exists is an abuse of logic. Any statement that describe a concept of time has motion in a three-dimensional physical framework of space is a fallacy, such as time (concept) can move from one location to another. Any identity that exists (material or non-material such as optical phenomenon) must also be qualified with shape, volume and location; time cannot be qualified at all in such manners.
Consequently, any theory extrapolated from this foundation that was based on the false fact that time exist would be fallacious, this is despite it could paradoxically work in the conceptual framework of its relativist model; it does not refer to reality.
See a section on "Reviews on time dilation effect in Einstein's special theory of relativity" that illustrates on the artificial cognitive paradoxes of mathematical physics with foundational crisis.
"In general relativity, clocks at lower potentials in a gravitational field — such as in proximity to a planet — are found to be running slower.", "gravitational time dilation (as treated in general relativity) is not reciprocal: an observer at the top of a tower will observe that clocks at ground level tick slower, and observers on the ground will agree. Thus gravitational time dilation is agreed upon by all observers, independent of their altitude." - Excerpts from Wikipedia on time dilation.
"Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the higher the local distortion of spacetime due to gravity, the more slowly time passes. Albert Einstein originally predicted this effect in his theory of relativity and it has since been confirmed by tests of general relativity.", "Gravitational time dilation has been experimentally measured using atomic clocks on airplanes. The clocks that traveled aboard the airplanes upon return were slightly fast with respect to clocks on the ground. The effect is significant enough that the Global Positioning System needs to correct for its effect on clocks aboard artificial satellites, providing a further experimental confirmation of the effect.". - Excerpts from Wikipedia on Gravitational time dilation.
From the perspective of classical physics that time is merely a concept and it is invariant, it suggests that the proposition of active transformation of time for gravitational time dilation in GR as advocated with mathematical relativism, is fundamentally erroneous. The philosophical idea of absolute time in three-dimensional Euclidean space is synchronized throughout the observable universe would simply suggest it is the atomic clock that is affected in different gravitational potential; the atomic clock when subjected to stronger gravitational field has physically become slower. In a delusion with the a priori assumption that the radiation count of atomic clock is consistence in different gravitational potential, it paradoxically renders the illusion that time is physically transformed.
There was no direct proof that the electron vibration frequency of the caesium-133 atom used in atomic clock would remain stable when it is subjected to different inertial accelerations. But assumed to be stable in the mathematical constructs of modern physics, thereon by self-referencing with its quantitative proofs that were boasted to have ten-digit precision of a second, and asserts with its quantitative predictions that have been overwhelmingly successful for technological achievements, it was misleadingly used with such conviction to conclude that transformation of time occurs; the postulation for time is physically transformable as posited in modern physics was fallaciously proven in its artificial cognitive paradox with circular reasoning. This is as fallacious as the claim of proof for geocentrism with self-fulfilling prophecy by using its successful quantitative predictions that were validated with its hardcore belief, which has had insidiously corrupted all its perceptions in its reality that are perceived in its topsy-turvy delusion.
Intrinsically, a quantitative proof of a scientific theory, is not the proof for the scientific theory.
Specifically, the empirical observations for transformed time in the relativistic experiments, are paradoxically rendered by the physical paradox of the scientific theory with its fallacious a priori posits for time is variant; it circularly proves what it postulates by self-referencing. Qualitatively, despite the transformation of time is a valid conclusion in the abstract of relativism with the posit of variant time, in reality this is a myth.
The claims of scientific proof for gravitational time dilation was stemmed from delusional observations with it foundational crisis, and therefore the postulated transformation of time is a cognitive paradox fallacy in the objective reality.
"The principle of operation of an atomic clock is not based on nuclear physics, but rather on the microwave signal that electrons in atoms emit when they change energy levels. Early atomic clocks were masers with attached equipment. Currently the most accurate atomic clocks are based on absorption spectroscopy of cold atoms in atomic fountains.", "Since 1967, the International System of Units (SI) has defined the second as the duration of 9,192,631,770 cycles of radiation corresponding to the transition between two energy levels of the ground state of the caesium-133 atom.". - Excerpts from Wikipedia on atomic clock.
"An atomic fountain is a cloud of atoms that are tossed upwards by lasers in the Earth's gravitational field. If visible, it would resemble the water in a fountain. While weightless in the toss, the atoms are measured to set the frequency of an atomic clock. This eliminates the effects of the Earth's gravity on the frequency." - Excerpt from Wikipedia on atomic fountain.
Although the microwave signal that electrons in atoms emit when they change energy levels in an atomic fountain can be very stable, it is a spurious assumption that in weightless condition when the atoms are measured to set the frequency of an atomic clock would eliminate all the effects of the Earth's gravity on the frequency of the electrons; weightless condition of an atom would not eliminate the effect of Earth's gravity acting on it.
A freefalling object in the atmosphere would experience weightlessness but it is still subjected to the effect of different air density in different region that is caused by the effect of gravity. Gravitational potential of Earth following the principle of inverse-square law with varying potential density at different altitude and latitude would behave like fluid density that can affect the electron vibration frequency of the caesium-133 atoms used in atomic clock; it is matter that undergoes the active transformation in varying potential density, not time.
Gravitational potential of Earth following the approximate principle of inverse-square law with varying potential density at different altitude and latitude, would behave like fluid density that can affect the electron vibration frequency of the caesium-133 atoms used in atomic clock; it is matter that undergoes the active transformation in varying potential density, not time.
UVS predicates that the spin frequency of an electron can be affected by gravitational potential of Earth that has varying potential density at different altitude and latitude.
Ironically, the atomic clocks that have traveled aboard the airplanes upon return were slightly faster with respect to atomic clocks on the ground, is therefore the independent qualitative proof that atomic clock is not consistence when it is in different gravitational potential.
As a metaphor, do a thought experiment with a propeller rotating in deep water with constant power input such that it has a constant rotating speed, maintain the power input and lift the propeller to near the surface of water in water that its mean density is slightly lowered at near the surface. The propeller with a same driving force uses less torque to overcome water that has lower mean density, would therefore spin at a slightly faster speed. Lift the propeller out of water into air that has much lower density, and we could expect the propeller to spin at a much faster speed. Using as a comparative analysis for stationary clocks placed at different altitude, this thought experiment elaborates that the rotating speed of the propeller (driven with a constant power input) is subjective to the density of the medium.
The propositions for physical transformation of time with gravitational time dilation in general relativity of the mathematical relativistism that posit variant time, is a qualitative fallacy as a result of the artificial cognitive paradox that is simply as a result of an incorrect a priori assumption for its posit. Consequently, any extrapolation from gravitational time dilation (such as the time-dilated space flight, time travel and the likes) with variant time as its basis would be fallacious in its slippery slope fallacy.
"Time dilation is the phenomenon whereby an observer finds that another's clock, which is physically identical to their own, is ticking at a slower rate as measured by their own clock." - Excerpts from Wikipedia on Time dilation.
'If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by "time". We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, "That train arrives here at 7 o'clock,'' I mean something like this: "The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.' - Albert Einstein, excerpt from "Definition of Simultaneity" on "Electrodynamics of Moving Bodies", 1905.
When Einstein mentioned in his above paper that "the time marked by the clock (viewed in the stationary system) is slow by T seconds per second.", he specifically mentioned that the factor T in time dilation refers to the position of the clock; it should not be assumed that he meant time itself is being physically transformed.
In Einstein's examples of time dilation effect in SR, Einstein had clearly illustrated that the phenomenon of time dilation as observed by the two inertial observers in relative motion of uniform velocity is a passive transformation in symmetrical situation with no absolute reference frame. In the Einstein’s 1907 version of relativity, which was formulated to explain the redshift of moving canal rays, it asserts that both the Lorentz contraction and the slowing of clocks are apparent; the effect of optical illusion.
See an externally linked topic on "Ladder paradox" that elaborates on an apparent effect of transformation in SR.
Although Einstein had illustrated with GR that in gravitational time dilation there is an active transformation involved and this has physical significance, he specifically mentioned slower ticking clock at a particular rate that in proper time it records lesser time in comparison to coordinate time for all his examples; he did not specifically mention that time itself in time dilation phenomenon would physically pass slower in higher gravitational potential or when it is experiencing inertial acceleration.
In the address delivered on May 5th, 1920, in the University of Leyden, Einstein categorically mentioned "Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time". He also categorically mentioned space is his measuring rod (invariant) and time is his measuring clock (invariant). In GR where aether was supposedly swapped with absolute space or absolute time, an ambiguity in circular logic would occur in linguistic manner and when aether was treated as an invariant scalar field therefore Einstein further mentioned "this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.".
It was not like a third party trying to interpret what it meant by the term “spacetime” that was originally coined by Einstein, it was the author of "Theory of relativity" who had published his papers since 1905 through 1915, which had thus began the era of modern physics, and Einstein by himself, not through another party, after 1919 with the world famous initial successful test of general relativity, was trying to tell the world in 1920 with his definitions to clarify what he meant by spacetime.
“Time and space are modes in which we think and not conditions in which we live.” - Albert Einstein
It is the mathematical relativists whom had made the claim through hypothetical constructs by analytically conclude with quantitative predictions that time passes at different rates in regions of a different gravitational potential; the higher the local distortion of spacetime due to gravity, the slower time passes. In the examples of mathematical relativism for time dilation effect in SR, active transformations of time in non-symmetrical situations for the phenomena are illustrated instead.
In this context, mathematical relativism refers to the studies in the current form of relativistic theory that adopts mathematical physics with the postulation of reified time for Einstein’s theory of relativity. The research in mathematical constructs inspired by theoretical physics with scientific consensus, emphasizes on quantitative analysis through deductive reasoning with mathematical rigors. Most problems and theorems come from within mathematics itself, and the conclusions are purely based on deductions with its mathematical constructs to explain, predict and describe any natural phenomenon. Science practices by such mathematicians who omit qualitative analysis, and engage analytical methods to investigate, evaluate and deduce with its mathematical construct to conclude any perceived natural phenomenon, are very much relied on a supra sense of belief with varying degree of uncertainties for their references to reality.
Mathematical relativism could be traced to be championed by David Hilbert in "Einstein–Hilbert action" as "The sixth problem" with an axiomatic approach to physics through mathematical construct he had introduced. Although David Hilbert had made the distinction between mathematics and unassailable metamathematics, his abstract concept of variant space and time without qualitative proof is fallacious; this a priori fallacy has had led to the conclusion of false facts in the illusion of knowledge that causes the delusions with modern physics in all sorts of cognitive paradox fallacies.
Intrinsically, a quantitative proof of a scientific theory, is not the proof for the scientific theory.
To perceive any natural phenomenon with its scientific hypothesis thar refers to reality, the epistemic process with qualitative rigors for its correspondence theory of truth to evaluate at its fundamental level, is the foremost. Despite quantitative research with truth value is an essential aspect for scientific studies, qualitative analysis must precede quantitative analysis. Without qualitative proof, it cannot be certain that the quantitative proof of a scientific theory is true.
Physics should adopt the qualitative studies of natural phenomena as the primary discipline for perceiving natural phenomena that refer to reality, and then their quantitative studies follow as the secondary discipline for developing their a posteriori knowledge.
the mathematicians have invaded the theory of relativity,
this Einstein's thought experiment for time dilation effect on him receding
from a clock tower at the speed of light is based on unrealistic assumptions,
it is a valid intellectual platform to comprehensively understand the
fundamental of time dilation effect qualitatively. In realistic situation,
to reach light speed for a rest mass it has to involve acceleration, and
by the time when Einstein is receding at light speed (if
it is possible) and even if he could do that in a few seconds time
he would have travel away from the clock tower on Earth where he had originally
stood and reached a distance beyond the orbit of the Moon, by then the
flat spacetime of equal gravitational potential is no longer valid, the
gradient for gravitational potential would be involved. In geodesic
motion there is also inertial acceleration involved that would result
in active transformation. Also, after the first pulse of light from the
clock touches his eye’s cortex when he has reached the speed of
light, biologically he would see nothing thereafter; he could never see
a clock that freezes in a time dilation effect in a relative motion at
the speed of light. Then there are also atmospheric layers involved with
varying refractive index that would affect the accuracy of the result,
friction would also involve in realistic situation. However, the unreal
situations in this Einstein's thought experiment would not change the
fundamental for the illustration of time dilation effect qualitatively.
This reverse time dilation effect conflicts with the mathematical relativism version of SR for its time dilation effect that postulates active transformation of time and the transformed time in uniform velocity motion can only become slower.
When an observer sees a star that is ten light years away, he is seeing a ten year time delayed image of the star. If he observe a starspot event on the star (similar to sunspot that occurs on the Sun), that event had actually occurred ten years ago, this is as a result of the distant apart that takes light to travel ten years from the star to reach the observer; the observer is observing a past event. A starspot event can be very temporal that might last only for less than an hour, a particular starspot event on the star could be long gone in real time when he is observing the time delay image of the event through his telescope.
If the observer has moved halfway toward the star in uniform velocity, he would see the image of the star that is five years time delayed. In uniform velocity moving towards the star, the ten years time delayed image of the star would be gradually transformed to the five years time delayed image. During the course of uniform velocity motion to reach the halfway distant, the observer catches up five year of time delay image in a speed up manner; he would literally observe the events on the star to have sped up. If there is an identical atomic clock on the star that ticks at the same rate as the atomic clock with the observer when he is in rest frame, he would see the clock on the star speed up while he approaches the halfway point, and when he reached the halfway point, the clock on the star would be observed to record five years of time more than the clock with him (adjusted for gravitational time dilation) that records coordinate time. If he move at 50% of light speed (c) in uniform velocity to travel five light years it would take him approximately 10 years (5c years / 0.5c) to reach there, and his clock would record this approximately 10 years of time that is identical to coordinate time. At that halfway location the clock on the star would be observed to become five years time delayed instead of ten years, and he would observe this clock on the star to record 5 years more of time with a total of approximately 15 years while his clock records approximately 10 years of time. This progressive decreasing of time delay effect is a passive transformation that is caused by the speed of light over distance; it is merely a relative motion illusion of no physical significance that is rendered by the limit of light speed and it requires a period of time for the light wave of an image to travel in space. This illustration also elucidates that although the speed of light in vacuum is the same for all inertial observers regardless of the state of motion of the source, the image it carries in the propagating light would be time-varied to the observer according to the relavtive motion of the source.
“Not everything that can be counted counts, and not everything that counts can be counted.” - Albert Einstein
Although time dilation effect in Einstein's SR refers to relative motion of uniform velocity in symmetrical situation with no absolute reference frame, in mathematical relativism it is deduced with Lorentz transformation that time dilation effect in absolute motion undergoes an active transformation of time. With pure mathematical deduction for the twin paradox example that only involves uniform velocity motion, mathematical relativists analytically deduced that time dilation effect is an active transformation of dilated time with reference to coordinate time. Einstein did not endorse the SR solution for the twin paradox example provided by mathematical relativists, he instead had provided a GR solution to the twin paradox problem that involves active transformation to cause the shorter proper time for the accelerated traveling twin and therefore the said paradox in the example does not exist with his relativistic solution.
In mathematical relativism, it is claimed that in SR an observer moving in uniform velocity would undergo active transformation in time dilation effect, time is elastic and passes at a slower rate under such circumstances. This violates the principle of time dilation effect of Einstein's SR that it is reciprocal for both inertial observers in relative motion; the claim in mathematical relativism is simply a logical fallacy. It is therefore fallacious that the a priori assumption of elastic time in Minkowski space is extrapolated as the foundation of GR under an umbrella concept to maintain uniformity in the mathematical relativism version of its "Theory of relativity" with mathematical logic; this is merely a self-reference tautology. The tautology with circular definition in mathematical relativism is merely a mathematical verification with self-referential equations by using its inverse function for deductive inference that is defined by the rule if (x) = y, then (y) = x.
“I don't believe in mathematics.” - Albert Einstein
A self-reference mathematical construct, will create a mathematical paradox with self-referential equations derived from a dichotomy (defined by the rule if (x) = y, then (y) = x) that would be jointly exhaustive to infinitely regress in its manifold of mathematical logic. Consequently, in its paradox with circular logic, all the problems it attempts to solve as they are with the ambiguities tof their interchangeable mathematically idealized objects, such as transformable space or reified time, it therefore could irrefutably deduce to infallibly conclude its propositions in the delusion of its mathematically defined realm based on its fundamental a priori assumption.
Without qualitative proof for the a priori assumption, all its validated a posteriori deductive proofs substantiated with precise and consistent quantitative predictions, are not conclusive at all when referred to reality.
A hypothetical a priori assumption, cannot be validated with mathematical logic or equations in a self-reference construct with its duality. Examples of such tautology in mathematical relativism, are atomic clock experiment, Einstein's light clock and Muon experiment.
The Einstein's light clock example is a simple inference to illustrate time dilation effect of SR; this hypothetical clock is fiddled to quantitatively illustrate the phenomenon of time dilation effect. It illustrates how this light clock when it is moving in uniform velocity would physically slow and this phenomenon could be analytically observed by an inertial observer. This Einstein's light clock example is merely used to comprehensively illustrate on how the proper time with the moving observer could be analytically understood to be time-dilated in the manner it is being observed by an inertial observer.
See an externally linked topic on "Relativistic time dilation" that illustrates a time dilation effect example with animated Einstein's light clock.
However, mathematical relativism assumed that this light clock is equivalent to all types of electromagnetic clock and therefore has claimed that time passes slower for the observer in motion of uniform velocity. Qualitatively, this a priori assumption is incorrect; it is logically fallacious to conclude that time dilation effect is an active transformation with the behavior of this light clock moving in uniform velocity has physically shown to be traveling a longer light path.
For the light clock that is fiddled in this manner to illustrate the time dilation effect in SR, physical change for this clock has occurred and it would tic-tock slower in a physically lengthened zigzag light path ( l > y ) as a result of its motion in uniform velocity, but the observer in the uniform velocity motion would not be able to notice the zigzag light path of his light clock. The light beam does travel a longer path when the light clock is in motion even though this is not apparent to the observer who is moving in the same motion; this is merely a cognitive paradox in the effect of its relative motion illusion.
In this Einstein's light clock example, both observers in relative motion would still observe it is the other party’s clock that is time-dilated if their light clocks are calibrated to indicate coordinate time (time interval for one cycle is 2y/c for stationary clock and 2l/c for moving clock assuming no gravitational time dilation is involved); symmetric time dilation does occur for this light clock example. This example of time dilation effect in SR is similar with Einstein's thought experiment of him receding from a clock at the speed of light; they are merely different types of hypothetical construct to illustrate qualitatively with one example and quantitatively with the other example for passive transformation of time dilation effect.
Einstein's light clock is a fiddled clock can be comprehensively understood through the following illustration by modifying the light clock. Rotate the light clock (as illustrated below) so that the mirrors are arranged in a manner for the light beam to move in a parallel direction of the motion instead of the perpendicular setup used in the Einstein's light clock example. This modified ligth clock is rotated with a 90 degree change in angle for the path of the light beam bouncing between the mirrors, the “tick” of the light beam when moving in the direction of its motion would take a longer period in an extended light path, while the “tock” of the light beam when moving against the direction of the motion would take a correspondingly shorter period to travel to the other mirror in a correspondingly contracted light path, therefore the full clock cycle of the light beam in tick-tock motion in this rotated light clock setup would not physically travel a longer light path while moving in uniform velocity at below half of light speed; this rotated light clock would not change physically to tick-tock at a different clock rate when it is at rest or it is in uniform velocity motion. Note: The uniform velocity of the rotated light clock in motion has to be below half of light speed to accomodate its half clock cycle in order to maintain a constant wavelength for a full tick-tock clock cycle, otherwise, variable wavelength for a full tick-tock cycle of the rotated light clock has to be accounted for in the case study if it moves with a velocity at half or above half the speed of light.
The pulse-train ratio adjusted to be equal for the rotated light clock when it is at rest would be different when this rotated light clock is in motion moving in the same direction as the light path, but the period for a full tick-tock cycle of this rotated light clock would remain constant for its fixed wavelength when it is at rest or it is in uniform velocity motion; λ = p + t = λ2 = p2 + t2.
This illustration with the moving rotated light clock has maintained a constant tick-tock period qualitatively proves that Einstein's light clock is a fiddled clock; Einstein's light clock would be physically slowed in uniform velocity motion is therefore not a standard clock.
Both inertial observers in this example with modified light clocks would still observe that it is the other party's rotated light clock in relative motion of uniform velocity is time-dilated and tick-tock at a slower clock rate when it is compared with their rotated light clock; the phenomenon of time dilation effect in SR is a passive transformation that has no physical significance.
Although Einstein's light clock is a better mechanism to illustrate time dilation effect in SR for this specific example, it cannot be assumed that the light clock is a standard clock. And just because Einstein's light clock quantitatively correlates with Lorentz transformation in the example therefore in mathematical relativism it further concludes with self-reference that time dilation effect in SR is an active transformation of time. The a priori assumptions and a posteriori conclusions in mathematical relativism are logically fallacious.
Einstein's light clock is not a standard clock can also be illustrated with an example in symmetrical situation by comparing it with standard clock in a comparison analysis. In this symmetrical situation example, presumes that two identical standard clock A and standard clock B are moving away in opposite direction from a location x in uniform motion at a velocity of v = 0.49 in flat spacetime ( is the speed of light).
An inertial observer at location x would see both standard clocks to be symmetrically time-dilated to a Lorentz factor ( γ ) of approximately 1.147 when he compares these two clocks to his standard clock. Both observers with clock A and clock B in their inertial reference frames would also observe that the clock at location x to be apparently time-dilated to the identical Lorentz factor of approximately 1.147 when they compare it with their clocks. The observer with clock A in his inertial reference frame would see that clock B is time-dilated to a Lorentz factor of 5.025 at a relative velocity of 2 x 0.49 when comparing with clock A, and in symmetrical situation the observer with clock B in his inertial reference frame would also see that clock A is time-dilated to the identical Lorentz factor of 5.025 when comparing with clock B. This example maintaining a symmetry situation for both standard clocks that are in motion quantitatively illustrates that time dilation effect in SR is an optical illusion of relative motion in uniform velocity.
Nevertheless, the observer with light clock A would see that light clock B is still time-dilated to the Lorentz factor of 5.025 when comparing with light clock A and this phenomenal of time dilation effect in SR is symmetrical for the other observer with light clock B. This is because both light clocks in motion of similar velocity moving in opposite direction are under the same flat spacetime circumstances and therefore in symmetry both light clocks are physically ticking at a same slower rate. If the light clock in uniform motion is compared to a standard clock next to it, it would be observed that the light clock is physically slowed by a function of Lorentz factor.
The two inertial observers in this situation with two identical light clocks that are in motion would symmetrically observe the time dilation effect of the other party to a function of Lorentz factor in comparision with their light clocks and this conforms with Lorentz transformation.
The comparison analysis for the above cases in symmetrical situation illustrates that Einstein’s light clock is not a standard clock.
"We do not know why the meson disintegrates of what its machinery is, but we know its behaviours satisfies the principle of relativity. That is the utility of the principle of relativity - it permits us to make predictions, even about things that otherwise we do not know much about. For example, before we have any idea at all about what makes the meson disintegrate, we can still predict that when it is moving at nine-tenths of the speed of light, the apparent length of time it lasts is ( 2.2 x 10^-6 ) / √( 1 - 9²/10² ) sec; and our prediction works - that is the good thing about it." - Excerpt from "The Feynman Lectures on Physics" Vol I, page 15-7.
In mathematical relativism, the muon experiments are claimed as the scientific proofs for active transformation of time that correlates with the phenomenon of time dilation effect in SR. However, barring the understanding for the machinery of muon, it cannot be conclusive on what causes the observed mean lifespan of muon to be extended in uniform velocity motion that has corresponded with Lorentz factor according to its speed. The claim in mathematical relativism that time is physically dilated for muon in high velocity motion is simply absurd in a double standard of the objective reality; it is a myth illustrated with moot reasoning in mathematical abstract in two reference frames that do not correlate with the objective reality. Although the math for time dilation effect has worked for these muon experiments in applied science, there could be other scientific reasons that would account for the physical change of properties for muon according to the function of Lorentz factor, and thus muon could extend its mean lifespan that corresponds to different velocity of its motion related to the speed of light.
far as the laws of mathematics refer to reality, they are not certain,
Note: It is also postulated in mathematical relativistic theory for the muon experiment that in the muon's frame the Earth (and it's atmosphere) are length contracted in an interchangable manner with time dilation effect in SR. This theory posits that space in complex conjugation is physically transformed in the muon's frame, and this is claimed with deductive proofs of precise and consistence quantitative predictions through rigorous experiments. However, this postulation is simply absurd.
The relativistic theory in mathematical relativism that has successfully predicted the experiments on high velocity moving muon could fit the observation results and therefore concluded that time is dilated or length is contracted in an interchangeable manner is as a result of a delusion. Although active transformation for the muon in vortical wave function is involved and it correlerates with the time dilation effect in SR, empirically it is not time or length that has undergone active transformation in the objective reality; evidently the muon itself is physically transformed to extend its lifespan through its motion that corresponds with a function of its velocity.
There should be other secondary active transformations as a result of gravitational time dilation for the muon particle that are caused by different factors, such as different gravitational potential when the projected muon particle moves toward the Earth from a higher altitude, and inertial acceleration that is associated with geodesic or curvilinear motion in its projected path. These secondary active transformations should also contribute to extend the lifespan of muon.
“If there is a God, he's a great mathematician.” - Paul Dirac
“God does not care about our mathematical difficulties. He integrates empirically.” - Albert Einstein
A very interesting aspect demonstrated with the Moun experiment is the active transformation that extends the lifespan of muon particle is conjugated with the passive transformation of time dilation effect in SR; perhaps this is the evidence that objective reality is merely a conceptualized structure of nature that is weaved in vortical motion.
See an externally linked topic on "Measurements of relativistic time dilatation".
"Spinning objects such as merry-go-rounds and ferris wheels are subjected to gravitational time dilation as an effect of their angular spin.", "The equation is Td = √(1 -r² ω² / c² ), where Td is the total time dilation at a distant position, r is the radius, ω is the angular velocity and c is the speed of light.", "It is no accident that in an inertial frame of reference this becomes the familiar velocity time dilation √(1 - v² /c² ).". - Excerpts from Wikipedia on Gravitational time dilation.
For this experiment at CERN by Bailey et al. projecting muons at a velocity of 0.9994c to orbit in the 14 meter diameter CERN Muon Storage Ring, there is curvilinear motion involved for the mouns a result of the circular path and there would be significant inertial acceleration experienced by the muons at such high speed projection; in circular orbit it would incur gravitational time dilation through centripetal acceleration and this is an active transformation that has physical significance.
From the UVS perspective, the vortical effect is similar for a vortically coalesced moun moving in rectilinear motion or curvilinear motion to physically interact in a vortically intensified process that increases its lifespan through conservation of energy in vortical motion.
However, in the experiment it was the mouns that were observed to have somehow extended their mean lifespan through active transformation; as empirical observed, in reality it was not time that has physically transformed at all.
By reifying time with such mathematical constructs for their time dilation analyses, it will lead to all sorts of mythology that can be quantitatively valid in the realm of their models.
Although Einstein had mentioned a phenomenon of time dilation with active transformation in his 1905 SR paper as quoted above, it must not be assumed that this is the typical time dilation effect in SR of a symmetrical situation with no absolute reference frame. The typical time dilation effect in SR refers to the phenomenon of a reciprocal time-dilated observation that is identical for two inertial observers who are relatively moving away from each other in uniform velocity motion with no preferred frame. Einstein specifically stated that this uniform velocity motion of the moving clock is in a circumstance of moving on a continuously curved line; there is angular displacement in geodesic motion and this is an accelerated frame of reference.
An object moving at uniform velocity on a continuously curved line would experience a centripetal acceleration; this is an inertial acceleration. This geodesic motion phenomenon raised in Einstein's 1905 SR paper was later elucidated in general relativity that angular displacement would incur an active transformation of gravitational time dilation to physically slow down the ticking of the clock; inertial acceleration is experienced by the clock when it moves at uniform velocity in curvilinear motion.
The three-dimensional space and time are invariant in the coordinate system of Doppler effect, the volume within the coordinate system is filled with a variant medium with physical properties for light to traverse as wave. In a paradigm shift the wave effect of light is similar to Doppler effect of sound wave traversing in the elastic medium of air at lower velocities in absolute space and time. From the perspective of UVS, these phenomena in vortical motions of different bandwidths are compatible in the UVS model.
One can also tweak the coordinate system of sound wave in air by interchanging variant time and variant 3D to replace air in a volume therefore this space is void of air, but the transformation result in motion for the source of sound wave with the different posits would still be equivalent to Doppler effect of sound. This is a four-dimensional spacetime continuum in a hypothetical construct for sound wave in a vector space void of medium. Under such tweaked setting, one can say time dilation has occurred or length is contracted that is equivalent in principle when the source of the sound in flat spacetime is moving at speeds near to the speed of sound, and the four-dimensional spacetime continuum for sound can be physically distorted in inertial acceleration according to pressure tensor of potential density.
In reality, sound cannot propagate in a vacuum; in a vacuum void of medium there is nothing to vibrate for creating audible sound wave.
“Pure mathematics is, in its way, the poetry of logical ideas.” - Albert Einstein
Nevertheless, one can visualize with this hypothetical construct that the source of sound wave can travel faster than the speed of sound without problem. This could provide a hypothetical model to infer the behavior for superluminal speed of matter in order to understand uncharted phenomena in the observable universe.
~ With thanks to Graham Burnett for his email with a link to "The sixth problem".
~ With thanks to Max from the ToeQuest forum for his very engaged discussions on time dilation and several interesting point of views raised.
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