By David William Jedell UPDATED November 20, 2025
(From Philosophy of Time, Space and Now (With A.I. Review) https://thejedellreport.blogspot.com/2025/11/philosophy-of-time-space-and-now-with.html
Section Three: Theory of Relativity "Time" Dilation
The Following Shall Be known as the Relativistic "Time" dimension which has only been verified by the dilations of quantum particles (so is really a part of quantum mechanics and not at all related to the human perception of normal existence). There has been no confirmation of Special Relativity Time Dilation on a macro scale, only aberrations of the relative motions of quantum particles with respect to speed or gravitational field intensity.
Albert Einstein
Special Relativity
The thought experiment of Albert Einstein to explain time dilation is a space ship traveling at relativistic speeds (close to the speed of light 'c') with a photon moving up and down, from side to side, in a straight line within the space ship, from the emitter to the receiver and back. Relative to an outside stationary observer on earth, the photon is moving over a greater distance than just up and down (it is traveling twice the hypotenuse of a right triangle because of the space ship's motion and length in the x-direction), but because light travels at 'c' in every reference frame, the photon must still travel at the same speed 'c' relative to the outside observer. Hence, according to the theory, because it travels a greater distance with the same speed, it must take longer to do so and hence time will appear to be running slower within the rocket relative to the observer outside. (It should be noted that there is no convincing evidence that a material light emitter could ever reach a speed that would cause the practically instantaneous quantum particle photon to appear to divert even to a small hypotenuse of a right triangle.) It will be shown that Special Relativity "Time" dilation has only been experimentally verified by relative movement and pulses of quantum particles on a nanosecond scale, just like the whole theory initially is based on the purported displacement of the natural path of a quantum particle (photon), which uses a leap of logic to claim that the "Time" in the space ship as whole is dilated.
Moreover, in accordance with Einstein's Special Relativity, light always moves in a straight line. In his famous thought experiment, the light leaves the emitter and heads straight up towards the receiver at an angle. This is impossible. Actually, the beam must be moving straight up and down. It is the space ship that is moving, that's all, and in the opposite direction, the "proper" frame is also "moving." Clocks are not "Time" itself, but rather, they measure and compare relative motions. The use of light (which is not "Time" either), with its constant speed in all reference frames, to measure the rate of clicks, is simply a convenient way to exactly compare the so-called proper frame number of clicks with the relativistic frame number of clicks. Even if Special Relativity did elongate clicks of a light clock, why does this prove time dilation, especially on a macro scale? Time does not tell the clock to change its frequency of clicks once the gears are set. Conversely, a clock moving at longer intervals does not tell time how to behave.
Quantum particles evidently exist in their own strange dimension separate from NOW, but also might move in a strange way within universal Now.
Spacetime Physics is counterintuitive, inconsistent and practically incomprehensible and will keep you up at night, for what, if you are not a physicist working on GPS or the dimension of quantum mechanics?: For nothing as a normal human being! Quantum particles exist in their own strange dimension separate from NOW as evidenced further by, as Einstein called it, the "spooky action at a distance" of quantum paired particles that can instantaneously affect each other no matter how great the distance is between them, violating the Now postulate that light speed "c" is the maximum speed possible for one particle to send information to another.
Note: in his paper on Special Relativity, even Einstein says, "We will raise this conjecture (whose intent will from now on be referred to as the "Principle of Relativity") to a postulate ... "Is the Principle of Relativity just a postulate? All of special relativity rests on it. How do we know it is true? What lies behind the Principle of Relativity? This is a philosophical question not a scientific one. You will have your own opinion; here is ours..." See, Taylor, Edwin F., and Wheeler, John Archibold, Spacetime Physices, MIT, https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/03%3A_Same_Laws_for_All/3.01%3A_The_Principle_of_Relativity , p. 3.1
Special Relativity "Time" Dilation Formula (as Part of Its Own Dimension)
At most, each photon in the Einstein rocket time dilation thought experiment has a sideways velocity (vΔt' forward in the rocket frame) in addition to its forward velocity (2L/c side to side, back and forth) according to the view of an outside observer. Sideways velocity does not change the back and forth velocity "2L/c". Velocity is not just change of end position, displacemet is, and in the case of the rocket, the rocket is totally responsible for the displacement of the photon receiver position. Exactly why is this situation any different from Galilean Relativity, albeit with a speed limit?
In SR, a spacecraft carries the space inside with it while moving at a constant speed, because everything inside is moving along with it at the same velocity due to inertia. Since there is no friction or other unbalanced force to change the motion of the objects inside, they remain at rest relative to the spacecraft, just as if the spacecraft were stationary. Inertia An object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Relative motion: Because the spacecraft and everything inside it are moving together at the same constant velocity, the objects inside do not "feel" the motion. Their relative velocity to each other is zero, making them appear "at rest" relative to one another.
The expansion of space is exempt from the speed of light limit because it is not an object moving through space, but rather the fabric of space itself expanding, like the space inside the spacecraft with the photon is moving through the outside space. Einstein's theory of relativity states that nothing can travel faster than light through space, but this limit does not apply to the expansion of space itself, which can cause distant galaxies to recede from us at speeds exceeding the speed of light. This presents a question of the actual "speed" of the photon inside the spacecraft and whether, combined with the movement of space, is moving faster than the speed of light in is's distance travelled with respect to the outside space.
Special relativity time dilation equation
Special Relativity "Time" Dilation Graph Due to Speed
It should be noted that it is an unjustified fallacious leap of logic to assume that "Time" slows down for everything (on the macro level) within the (impossible) space ship, simply because the completely untested impossible and imaginary speeding space ship causes displacement of the photon. Moreover, Einstein doesn't apply his own postulate that all inertial frames are equivalent. So, the observer on the (impossible, moving close to "c") space ship sees the clock on earth going symmetrically slower while the observer on earth sees the clock on the space ship going slower at the exact same rate. Since all inertial frames are equivalent, when the two observers are joined back together, the number of clicks of their clocks are physically the same. Otherwise, the observer on the space ship would see the earth spinning like a top. This is symmetry.
Moreover, in accordance with Einstein's Special Relativity, light always moves in a straight line. In his famous thought experiment, the light leaves the emitter and heads straight up towards the receiver from one side of the ship to the other at an angle. This is impossible. Actually, the beam must be moving straight up and down. It is the space ship that is moving, that's all. [4]
Understanding photon (also a quantum particle) behavior on a moving space ship.
When considering a different photon shot straight from the back to the front then reflected straight back to the back of a space ship traveling at high speeds, the principles of special relativity become contradictory. Einstein says the speed of light in a vacuum is constant for all observers, regardless of their own motion.
Here's a breakdown of what happens from different perspectives:
1. From the perspective of an observer on the space ship, the photon travels from the back to the front at the speed of light, c. To the observer on the ship, everything appears normal, just as if the space ship were stationary.
2. From the perspective of a stationary observer outside, the space ship is moving, so during the time it takes the photon to travel the length of the ship, the front of the ship will have moved further forward. However, the external observer will still measure the speed of the photon as c. This is because to maintain the constant speed of light, the stationary observer will perceive length contraction of the ship appearing shorter in the direction of motion, according to Lorentz. The contradiction lies in considering length contraction at the same moment of the extended light path as a result of a non-contracted ship because the contraction would cancel out the purported time dilation effect. (It should be noted here that light speed and distance cannot be measured one way but only back and forth. So there really is no need for a Lorentz contraction because from back to forward, the photon moves L + Δx, and going back travels L - Δx.)
A stationary "Twin" in the spacecraft is not moving at all; dv/dt = 0 and Δt = 0 except that with respact to the outside space, the twin moves the distance Δx without moving at all. Δx is the dilated displacement of the quantum photon, which is virtually instantaneous. This is a showing that the macro scale object cannot be affected by "Time" dilation.
A clock is made by having a pulse of light bounce back and forth between two parallel mirrors separated by a distance.
Postulated Lorentz Contraction of the Length of the Ship = L’ = L(1-v^2/c^2)^1/2
Time Dilation = t' = t/(1-v^2/c^2)^1/2
The photon is moving within the ship and the "Time" dilation depends on the ship's length insofar as the presumed displacement of the photon moving from the emitter to the opposite side then reflected back to the receiver at a point that was displaced as a result of the length (and speed) of the ship. Thus, the length of the ship cannot be ignored because it is the basis of the claim that the light (photon) moved a greater distance than the speed of light "c" would allow, incorrectly "proving" that time itself had to slow down. Putting these two effects together, the length of the ship and the sideways displacement of the photon, the Lorentz shrinkage and the lengthened "allowable" distance that the photon traveled, the two cancel out time dilation:
T' = T(1 – v^2/c^2)^1/2/(1 – v^2/c^2)^1/2 = T X 1 = T.
At v = c, the photon experiences (in its own "rest" frame) t = o, travelling at an instantaneous speed (per SR)
lim T/(1 − v^2/c^2)^1/2 = 0, if T = 0
v → c−
If T > 0, then → +∞
Only if T = 0 does the limit equal 0.
It should be noted that in the Michelson-Morley experiment, a single light beam was split into two, with each beam traveling back and forth along one of two perpendicular arms of an interferometer before being recombined. The expectation was that the Earth's motion through the hypothesized "ether" would cause a difference in the travel times of the two perpendicular beams, leading to a shift in their interference pattern upon recombination. However, no such shift was detected, indicating that the speed of light was constant regardless of direction, a finding that challenged classical physics and supported the foundations of special relativity.
Assumption: If the Earth were moving through the ether, one arm of the interferometer would be moving with or against the ether wind, while the other would be moving across it. The light traveling with and against the wind was expected to take a different amount of time than the light traveling across the wind. This time difference would cause the two light beams to recombine slightly out of phase. The out-of-phase beams would create a shift in the observable interference pattern (fringe shift). Despite careful measurement and repeated experiments over several months, no fringe shift was detected. To Michelson and Morley, this "null result" meant that the speed of light was the same in both perpendicular directions, regardless of the Earth's motion. This fallaciously contradicted the prevailing ether theory.
To explain this "null result", Lorentz came up with his contraction explanation and formula. It seems totally unnecessary! If a light beam travels at "c", then goes in one direction where the reflecting mirror is located and moving farther away, then the emitter-receiver must be moving precisely the same distance in the same direction. The overall speed back and forth is "c", but on the initial trip the light travels L + Δx (further), while on the return trip travels L - Δx (shorter). Thus, the overall speed is still "c" in either frame of reference. The Michelson-Morely interpretation supported Einstein's idea that the speed of light is constant for all observers, a fundamental postulate of Einstein's theory of special relativity. Special Relativity is thus on shaky ground because you cannot measure the speed of light solely in one direction because of the principle of relativity of simultaneity. It's generally considered impossible to directly measure the one-way speed of light, as it requires two precisely synchronized clocks at two spatially separated points, and synchronizing these clocks necessitates knowing the one-way speed of light in the first place.
Special Relativity Postulated Mass Increase Formula
Special Relativity Mass Increae Graph
Objective Experimental Confirmation of Quantum Particle "Time" Dilation
Muon Decay:
In special relativity, the proper time in the muon’s frame is dilated in the Earth frame (t = γt). For v = 0.999cv = 0.999cv = 0.999c, γ ≈ 22.4 nanoseconds, so the half-life appears as 2.2 × 22.4 ≈ 49.3 μs, allowing more muons to reach Earth’s surface.
Experimental Evidence: Cosmic ray experiments (e.g., Rossi-Hall, 1941) and accelerator tests (e.g., CERN muon storage rings, 1970s) show muon lifetimes extended by exactly γ, matching time dilation predictions. Other quantum particles (e.g., pions, kaons) show similar lifetime extensions at relativistic speeds, proportional to γ, regardless of their rest mass.
If mass increase altered decay, we’d expect different quantum particles (e.g., muons vs. pions) to show different decay behaviors at the same velocity, due to their different rest masses. Instead, all unstable particles show lifetime extensions proportional to γ, consistent with time dilation. Muons have a short mean lifetime (~2.2 µs in their rest frame) before decaying into other particles. At non-relativistic speeds, they wouldn't travel far enough to reach Earth's surface from the upper atmosphere.
Another explanation is proposed based on the CERN results: muons' lifetime would be proportional to gamma factor, indirectly to their speed or energy level. It is then shown that restless muons can reach ground level. This explanation registers within the framework of neo-Newtonian mechanics, which makes it possible to explain phenomena at a very high speed and which is compatible with Quantum Mechanics. [8]
Pedro H. Morais analyzed Planck scale induced modifications of the relativistic time dilation using data from the Muon Storage Ring experiment at CERN. By examining the lifetimes of muons, Pedro H. Morais established, for the first time, a constraint on such quantum gravity-inspired deformations using this channel. The magnitude of the effect indicates that the study of cosmic rays is a well suited arena for this scenario. Pedro H. Morais showed that the spectrum of muons would be significantly affected for particles at the PeV scale. Since this later observation of the effect of time dilation is more indirect compared to a direct lifetime measurement, we encourage to perform a high precision measurement of the muon lifetime as a function of the muon’s energy. [9]
These facts present another question Muon • Gravity's role: Gravity is a force that can change the muon's's velocity, so any movement at a constant velocity would be maintained only in the absence of gravitational forces or other external forces. So, in the particle accelerator and in the gravitational field of earth's atmosphere, GR acceleration produces some of the time dilation.
General Relativity Space Curvature
Spacetime curvature accounts for tidal accelerations of objects.
Local curvature adding up to the appearance of long-range gravitation. The shortening of distance between any one pair of ball bearings is small when the distance itself is small. However, small separation between each ball bearing and its partner demands many pairs to encompass Earth. The totalized shortening of the circumference in any given time - the shortening of one separation times the number of separations - is independent of the fineness of the subdivision. That totalized pulling in of the circumference carries the whole necklace of masses inward. This is free fall, this is gravity, this is a large scale motion interpreted as a consequence of local curvature. Above example:
Original separation between A and B -and every other pair: 20 meters
Time of observation: 8 seconds
Shortening of separation in that time: 1 millimeter
Fractional shortening: 1 millimeter/20 meters = 1/20,000
Circumference of Earth (length of airy necklace of ball bearings): 4.0030 X 10^7 meters
Shrinkage of this circumference in 8 seconds: 1/20,000 X 4.0030 X 10^7 meters = 2001.5 meters
Decrease in the distance from the center of Earth (drops by the same factor 1/20,000):
1/20,000 X 6.371 X 10^7 meters = 315 meters.
This apparently large-scale effect is caused - in Einstein’s picture - by the addition of a multitude of small-scale effects: the changes in the local dimensions associated with the curvature of geometry (failure of to remain at rest as observed in the free-float frame associated with A).
Curvature of spacetime and nothing more is all that is required to describe the millimeter or two change in separation in 8 seconds of two ball bearings, originally 20 meters apart in space above Earth, and endowed at the start with zero relative velocity. Moreover, this curvature completely accounts for gravitation.
See, Taylor, Edwin F., and Wheeler, John Archibold, Spacetime Physics, https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/09%3A_Gravity_-_Curved_Spacetime_in_Action/9.06%3A_Gravitation_as_Curvature_of_Spacetime
Many local reference frames, fitted together, make up the global structure of spacetime. Each local Lorentz frame can be regarded as having one of the ball bearings at its center. The ball bearings all simultaneously approach their neighbors (curvature). Then the large-scale structure of spacetime bends and pulls nearer to Earth (illustration shown above). In this way many local manifestations of curvature add up to give the appearance of long-range gravitation originating from Earth as a whole.
"
Space tells matter how to move; matter tells space how to curve."
- John Archibald Wheeler
Einstein 1n 1915 When he Completed the Theory of General Relativity
The Einstein field equation (EFE) of General Relativity:
where Rμν is the Ricci curvature tensor, R is the scalar curvature, gμν is the metric tensor, Λ is the cosmological constant, G is Newton's gravitational constant, c is the speed of light in vacuum, and Tμν is the stress–energy tensor.
Confirmation that Mass Curves Space
There is no explicit time parameter in the Einstein Field Equations (EFE) of General Relativity (GR). The EFE is written in a fully covariant, coordinate-independent form and treat time and space on equal footing within 4-dimensional spacetime.
All indices μ
ν = 0, 1, 2, 3 run over all four spacetime coordinates.
The metric tensor gμ
ν encodes both spatial and temporal geometry.
There is no distinguished "time" coordinate in the equations themselves.
Key Point: Coordinate Independence: Time appears only when you choose a coordinate system (e.g., x^0 = ct), but this is arbitrary.
The GR EFE does not contain a time parameter.
Time is not privileged — it is just one coordinate in a 4D Lorentzian manifold.
The equations are timeless in form; dynamics arise from geometry and matter.
The 1919 Solar Eclipse Eddington/Einstein Experiment
Gravity as the curvature of space was experimentally verified in 1919 during a solar eclipse, where stars behind the sun appeared to be aside the sun.
The Equation That Described the Photon Path is:
(dr/d𝜙)^2 = r^4/b^2[1 − b^2/r^2 (1 − 2M/r)]
or in inverse radius form: (d^2u/d𝜙^2) + u = 3Mu^2 (GR correction term)
The Schwarzschild Metric
Karl Schwarzschild
The differential equation, derived from the geodesic equation in the Schwarzschild metric, was used to compute the deflection of starlight in the 1919 experiment as follows:
Here’s the direct chain from the above EFE equation for the photon deflection in 1919
EFE in vacuum (Λ = 0) → Rμν = 0 → Birkhoff’s theorem → Schwarzschild metric,
Rμν = 0
Assume spherical symmetry → Schwarzschild, EFE: Produces the Schwarzschild metric (when solved in vacuum)
ds^2 = -A(r)dt^2 + B(r)dr^2 + r^2Ω^2 =? A = 1 - 2M/r, B = A^-1
Null geodesic (ds^2 = 0), (1 - 2M/r)(dt/dλ)^2 = (1 - 2M/r)^-1(dr/dλ)^2 + r^2(d𝜙/dλ)^2
Describes: Motion of light (null geodesic 1st order ODE in r(𝜙)) in a fixed spacetime. EFE (2nd order PDEs in gμν): Describes: How matter/energy curve spacetime
Conserved quantities → (dr/d𝜙)^2 = r^4/b^2[1 − b^2/r^2 (1 − 2M/r)], This is a geodesic equation in curved spacetime (Schwarzschild metric, General Relativity). Applies to massless particles (light, photons). It Answers "How does light move in already-curved spacetime?
This Geodesic equation: Analogy: Trajectory of a puck on curved ice. EFE Analogy: How heavy objects warp the ice ("How does mass curve spacetime?")
This is the null geodesic equation for light rays (photons) in Schwarzschild spacetime (general relativity, around a non-rotating, spherically symmetric mass). Here is a complete, term-by-term definition of every symbol in the equation:
Term Definition - Without time as a dimension, it’s not spacetime. It’s space. No (t) appears.
Left Side => (dr/dϕ)^2
(r) Radial coordinate (areal radius). Distance from the center of the mass in Schwarzschild coordinates. Units: length (e.g., meters)
𝜙 Azimuthal angle in the orbital plane (like longitude). Unitless (radians)
(dr/d𝜙) Rate of change of radius with angle. How fast the distance from the center changes as the light ray turns
(dr/d𝜙)^2 Squared radial velocity per unit angle. Always non-negative. Zero at closest approach (pericenter)
Physical meaning: Describes the shape of the light ray’s path in polar coordinates (r, 𝜙)
Right Side => r^4/b^2[1 − b^2/r^2 (1 − 2M/r)]
r^4 = fourth power of the radial coordinate. Comes from (r^2dϕ/dλ)^2 in the geodesic derivation
(b) Impact parameter: Definition: The perpendicular distance from the central mass to the asymptotic incoming ray (in flat space limit); Units: length (same as (r).
Formula: b = L/E, where (L) = specific angular momentum, E = specific energy at infinityr^4/b^2 = Scaling factor; Ensures dimensions match (both sides are dimensionless when squared); Large when r≫b, (far away), small near closest approach
[1 − b^2/r^2 (1 − 2M/r)] => This is the effective potential term for null geodesics
Inside the Brackets: Term-by-Term
(1) Flat-space (SR) contribution from E^2 in energy conservation
b^2/r^2 => Centrifugal barrier from angular momentum L^2/r^2
(1 − 2M/r) = > Gravitational redshift potential, from Schwarzschild metric coefficient gtt = −(1 − 2M/r)
2M/r => Gravitational correction proportional to GM/c^2r (Schwarzschild radius over distance)
Physical Interpretation of Key Terms
1 − b^r2 => Flat-space (SR) limit: light travels in straight line, zero at closest approach
−b^2r^2 X 2M/r => GR correction: gravity pulls inward, allowing light to get closer than (b) and bend
2M/r => Strength of gravity at radius (r). Vanishes far away, strongest near horizon (r =2M)
Units (with (G, c) restored)
(r) => meters
𝜙 => radians
(b) => meters
(M) => GM/c^2 => Schwarzschild radius in meters, e.g., Sun: M ≈ 1.47 km
2M/r => dimensionless => 2GM/c^2r
Real-World Example: Light Grazing the Sun
(M) = 1.477 km; (b) => R⊙ = 696,000 km; 2M/b ≈ 4.24×10^−6; Deflection = Δϕ ≈ 4M/b = 1.75′′ (arcseconds)
Argument
The shape of the light path is determined empirically
Empirical measurement requires traveling the path
Traveling the path requires time
Therefore, time is essential to knowing the shape
Thus, the orbital equation — which claims to describe the shape — must include time as a parameter (but it doesn't)
famous observation by Sir Arthur Eddington (and echoed by others like Hermann Weyl) about the geodesic equation in general relativity specifically, that when written in terms of coordinate time (t) as the parameter (as is common in orbital mechanics), the resulting effective 3D equation of motion appears to treat time differently from space, undermining the full 4D symmetry of spacetime.
Light from a star grazes the Sun. Its path is deflected by 1.75 arcseconds. The calculation uses only spatial geometry — no explicit time, no cause-and-effect in the equation. Yet we say “cause and effect requires time” — but time is not in the deflection formula. Deflection uses no time in equation:
d𝜙 = 4GM/c^2b is pure spatial
Start and finish imply cause and effect even at τ = 0
GR Explanation:
The equation is a timeless pattern extracted from time-dependent data
It is validated by time, but defined without it (questionable!)
Light from a star grazes the Sun. Its path is deflected by 1.75 arcseconds. The calculation uses only spatial geometry — no explicit time, no cause-and-effect in the equation. Yet GR says “cause and effect requires time” — but time is not in the deflection formula.
Cause and effect requires 4D spacetime — but the actual prediction throws time away. This is the fatal crack in the standard narrative. • GR textbooks: “Causality needs 4D light cones.” • GR prediction: “Here’s the number — no time needed.” They cannot both be true without sleight of hand
If we remove time as a coordinate dimension and treat it only as a parameter, then: "Spacetime" is a misnomer. It should be called "space" or more precisely, "spatially curved 3D space evolving with a parameter called time." This is exactly the philosophical and practical tension Eddington, Weyl, and others pointed out.
Historical Voices
Hermann Weyl
Hermann Weyl (1918): "The world is a 3D manifold of space bounded by two instants."
Arthur Eddington
Arthur Eddington (1923): "The time coordinate does not appear in the description of the orbit in the same way as the space coordinates."
Kurt Gödel
Kurt Gödel (1949): "In rotating universes, time can lose its global meaning — reinforcing that "time" is not always a dimension."
The Orbital Deodesic Equation Shows:
“Now” is a 3D space filled with moving matter and energy, evolving through a sequence of such spaces.
However, quote "The curvature of rays of light is nothing but the curvature of time."
= Einstein, 1911
Bending, Warping and Flexing of Space
Thus, bending, warping and flexing of space goes on to tell matter how to move. In general relativity, everything from bits of light to speeding bullets to blasting spaceships want to travel in straight lines. But the space around them is warped, forcing them all to follow curved trajectories; like trying to cross a mountain pass in a straight line, but following the peaks and valleys of the topography. So-called gravitational time dilation (slowing relative to an outside observer somewhere else) in a strong gravitational field is as follows:
Gravitational Time Dialation GR Equation
Einstein concluded gravitational time dilation by imagining an accelerating rocket with a man inside. If the rocket accelerated at 9.8 m/s^2, then the man would feel the equivalent of gravity. So Einstein postulated that gravity is equivalent to acceleration. Since a photon emitted up from the back of the space ship would reach the person slower (because the person is moving away from that photon) then the photon emitted from the top (which moves towards the man) would get to the man first. This is Einstein's "Equivalence Principle."
This acceleration not gravity. It is not equal to gravity because objects in a gravitational field will move closer to each other because their space is curved. This is what the above General Relativity Space Curvature diagram by Einstein shows.
Hafele-Keating Experiment
The Hafele-Keating Experiment: The Airplane Test of Time with Cesium-133 Atomic Clocks. The "airplane test of time" refers to the famous Hafele-Keating experiment conducted in 1971, which tested Albert Einstein's theories of special and general relativity using cesium atomic clocks aboard four commercial airliners plus one in the "proper frame" on earth to compare with. Military GPS adjust for time dilation caused by both special (speed time dilation) and general (gravitational time dilation) relativity, as this correction is crucial for accuracy; the adjustment is made by pre-launch atomic clock frequency adjustments and ongoing recalibrations performed by ground control centers to compensate for the differing effects of speed and gravity on the satellites' atomic clocks. Without these adjustments, positioning errors would accumulate rapidly, rendering the system useless.
Cesium oscillates 9,192,631,770 times per second
Cesium clock = 9.19 X 10⁹ Hz, Accuracy is 1 second in 300 million years
Normal human experience is rooted in Earth’s rotation (day/night), not cesium oscillations
The muon traveled 15 km in 0.00017 earth rotations
However, there is cause to doubt the accuracy of the Hafele-Keating Experiment. The accuracy of the clocks might have needed to be two orders of magnitude better to give confidence in the results. The actual test results, which were not published, may have been changed by H & K to give the impression that they confirm the theory. Probably only one clock had a failry steady performance over the whole test period; taking its results may show no difference for the Eastward and the Westward tests. [5, 6, 7]
E = mc^2
E = mc^2 is a direct consequence of the full relativistic energy-momentum relation E^2 = (pc)^2 + (m_{0}c^2)^2 under the condition that an object is at rest (p = 0).
Derivation from the Relativistic Energy-Momentum Relation
The mass-energy equivalence equation E = mc^2 is derived by considering the specific case of an object with no momentum (i.e., stationary) within the broader framework of special relativity.
Start with the relativistic energy-momentum relation: This fundamental equation from special relativity describes the total energy (E) of any particle in terms of its momentum (p), its invariant rest mass (m_{0}), and the speed of light (c):
E^2 = 0 + m_{0}^2 X c^4.
This equation is universally applicable to all particles, whether massive or massless, moving or stationary.
Consider a particle at rest: The equation E = mc^2 specifically relates to the rest energy of a particle. For a particle that is stationary relative to an observer, its momentum (p) is zero (p = 0).
Substitute zero momentum into the equation: By setting p = 0 in the energy-momentum relation, the momentum term (pc)^2 becomes zero:
E^2 = (0 X c)^2 + (m_{0}c^2)^2
E^2 = 0 + m_{0}^2 X c^4
E^2 = (m_{0}c^2)^2
Solve for E: Taking the square root of both sides (and considering only the positive energy solution) yields:
E = m_{0}c^2
Alternate Derivation
The relativistic kinetic energy is defined as the total energy minus the rest energy: KE = E(total) − E(rest)
The rest energy (energy when v = 0, so γ = 1) is E_rest = m c². Therefore, the standard relativistic kinetic energy is: KE = γmc2 − mc2
So, E = γmc^2
This immediately tells us that the
total energy must be: E(total) = KE + mc^2 = (γmc^2 −mc^2) + mc^2 = γmc^2
Now, when the particle is at rest (v = 0), γ = 1, so the total energy simplifies to:E = mc^2
That is,
even a particle at rest has energy E = m c². This is the famous mass–energy equivalence.
Starting from the relativistic expression for kinetic energy
KE = γ m c² − m c²,
adding the rest energy to both sides immediately gives the total energy as
E = γ m c²,
and in the rest frame (γ = 1) this becomes the famous
E = m c².
Second Alternative low-speed derivation, shows consistency with the Newtonian classical limit. If you expand γ for small v/c (« 1): γ = 1/(1 − v^2/c^2)^1/2
≈ (1 + [1 X v^2/2 X c^2]) + ⋯
Then
KE ≈ 1 + 1/2 X [v^2/c^2]) X mc^2 − mc2 =
(1/2)mv^2
which recovers the classical Newtonian kinetic energy. The remaining term m c² is a constant (rest energy) that doesn’t appear in classical mechanics but is always present in relativity.
This is Einstein's famous mass-energy equivalence equation. It indicates that even a stationary object with mass possesses an inherent amount of energy, known as rest energy. In modern notation, m is used to represent the rest mass (m_{0}),
Third Alternative Historical Derivation (Thought Experiment)
Albert Einstein's original 1905 paper did not use the four-momentum approach, which was developed later. Instead, he used a thought experiment involving a box emitting two flashes of light in opposite directions to show the link between energy emission and a change in mass.
Conservation Laws: Einstein applied the principles of conservation of energy and conservation of momentum.Change in Mass: By observing the system from two different reference frames (one at rest, one moving at a low velocity), he reasoned that for momentum to be conserved, the mass of the object must decrease when it emits energy (light).
Result: This thought experiment concluded that the change in a body's mass (Δm) is directly related to the energy (ΔE) it emits, resulting in the relationship (ΔE = Δmc^2). This established that mass and energy are interchangeable forms of the same physical quantity.
Lise Meitner (center), Otto Hahn (right) and Fritz Strassmann (left)
Lise Meitner was the first to provide the theoretical explanation for nuclear fission and used Einstein's E = mc^2 equation to calculate the immense energy released. The experimental work that showed uranium nuclei could be split was conducted by her colleagues, the chemists Otto Hahn and Fritz Strassmann, in Berlin in late 1938.
Hahn wrote to Meitner for help in explaining the puzzling results, as the production of a much lighter element, barium, seemed impossible based on the physics theories of the time. Her nephew, physicist Otto Robert Frisch, suggested thay Meitner use the "liquid drop" model of the atomic nucleus to hypothesize that the nucleus had indeed split into two smaller nuclei. She then applied Einstein's famous equation, E = m c², to calculate that the mass difference between the original uranium nucleus and the resulting lighter nuclei (barium and krypton) was converted into a massive amount of energy (approximately 200 million electron volts).
Otto Robert Frisch
Today we know the average total energy released in U-235 fission is ~202–205 MeV (including prompt neutrons, gamma rays, and later beta decay of fragments), of which about 168–175 MeV is recoverable kinetic energy of the fragments. Meitner’s quick 1938–39 calculation was astonishingly close using only pencil, paper, and the semi-empirical mass tables of the day; however, it was the first quantitative proof that splitting the atom releases an enormous amount of energy.
Bikini A-Bomb Tests July 1946
J. Robert Oppenheimer (1904–1967) was a prominent American theoretical physicist widely recognized as the "father of the atomic bomb" for his pivotal role as the director of the Los Alamos Laboratory during the Manhattan Project in World War II.
E = mc^2 existed before Einstein.
Olinto De Pretto: Some sources claim that Italian industrialist Olinto De Pretto published E = mc^2 in 1903. However, his work was not fully understood at the time, lacked a theory of relativity to give it context, and did not receive scientific recognition. Henri Poincaré: In 1900, Poincaré suggested that the momentum of electromagnetic radiation implied a relationship between energy and mass, leading to a conceptual version of the formula. Fritz Hasenöhrl: In 1904, Hasenöhrl used a thought experiment involving a moving cavity and derived an equation for the energy of heat radiation, which was E = (3/8)mc^2. J.J. Thomson (1881): Suggested that a moving charged body's mass increases due to its own electromagnetic field. The work was later simplified by Oliver Heaviside to m = (4/3)E/c^2, a precursor formula.
David Hilbert
David Hilbert was a leading mathematician who worked alongside and corresponded with Albert Einstein during the development of Einstein's General Theory of Relativity in 1915. While Einstein conceived the core physical ideas, Hilbert developed rigorous mathematical foundations, even publishing his version of the field equations around the same time as Einstein's final paper. Einstein acknowledged Hilbert's mathematical genius and the resulting priority dispute was resolved by Einstein's gracious letter and a shared understanding that both were vital contributors to the theory's development.
The photoelectric effect (For which Einstein won a Nobel Prize)
German physicist Heinrich Hertz
The photoelectric effect was discovered in 1887 by German physicist Heinrich Hertz in 1887 when he observed that shining ultraviolet light on a metal could cause it to release sparks. While Hertz made the initial discovery, it was Albert Einstein who provided the theoretical explanation in 1905, introducing the concept of photons and earning a Nobel Prize for his work on the photoelectric effect.
Heinrich Hertz
French physicist Jean Perrin and Brownian Movement
The person who helped confirm Albert Einstein's theory of Brownian motion and used it to determine the size of atoms was French physicist Jean Perrin. The conclusive experimental evidence provided by Perrin's work ended the long-standing scientific skepticism about the physical reality of atoms. For this achievement, Perrin was awarded the Nobel Prize in Physics in 1926.
Jean Perrin
Reinterpreting "Time" as a Measure of Dilated Displacement.
If we assume there is no fundamental time dimension and that what we perceive as time is a measure of the "dilated displacement" of quantum particles through space, we’re effectively proposing that time is merely a measurement that emerges from the dynamics of particles in a purely spatial framework.
Dilated Displacement: The term "dilated displacement" suggests that the motion of quantum particles (e.g., photons or in cesium atoms) is altered in a way that mimics time dilation, possibly due to interactions with space itself. You can liken SR’s time dilation to GR’s spacetime warping, so let’s interpret this as the displacement of particles being stretched or modified by some property of space, which we mistakenly measure as time as a dimension in and of itself.
No Time Dimension: In standard collectivist physics, time is a coordinate in four-dimensional spacetime (three spatial dimensions plus one temporal dimension). "Time" is thus viewed as an emergent measurement, tied to the relative positions, velocities, or interactions of quantum particles.
Quantum Particles: Photons (massless particles) behave differently in relativistic contexts because they are very small and can be experimentally verified, without macro systems being affected whatsoever. Photons travel at the speed of light (c), and their proper time is zero in SR and GR. Cesium atoms, used in atomic clocks, have measurable proper "Time" affected by both relative velocity (SR) and gravitational fields (GR).
"Time" Dilation in SR
If time is not a fundamental dimension but a measure of "dilated displacement" of quantum particles, we need to reinterpret what (t) represents; i.e., that (t) is a proxy for the cumulative displacement of a quantum particle (e.g., a photon) through space, modified by some interaction or property of space that depends on relative velocity. For a photon in SR: Photons move at (c) along null geodesics (ds^2 = 0ds^2 = 0).
Their displacement in space is straightforward, they travel at "< ct" within the space carried by the inertial frame from within the spacecraft. SR postulates that "c" is the maximum speed through space according to an "outside observer". This is why Einstein used a photon example in SR rather than, say, a baseball, which could simply be said to pick up speed pwithin the spacecraft as it travels, so would not prove "Time Dilation" when its path is displaced.
c = light distance/fraction of Earth rotation
c = 7.5 X 40,000 km/fraction of day = 3 X 10^8 m/s
Earth rotates approximately once per 86,164 seconds
The word "Time" is just a measure of this displacement, the "dilated displacement" means the observed path length or frequency of a photon appears stretched when measured by observers in relative motion within the space outside the spacecraft. Outside space is moving in the opposite direction of the spacecraft also at "< ct", creating a sideways vector for the photon without affecting the straight line up and down movement of the photon within the space inside the inertial frame of the space inside and carried along with the spacecraft.
In GR, the quantum particle emissions from the cesium atoms (used to define the nanosecond dilated displacement) involve quantum energy level changes, which occur at regular intervals in the atom’s rest frame on the surface of the earth in a strong gravitational field. Their paths are warped just like the photons from the star behind the sun in the 1919 Eddington verification of space curvature.
In SR, an observer in the outside space, spatial displacement of the photon's path is being "stretched" (like the photon in the 1919 observation of the star behind the sun) due to relative motion through outside space and the warp created by the quantum particle being in two places at once as a result of the difference between the photon's "undisplaced" path in the spacecraft's internal inertial space inside and the backwards very fast movement of the outside space.
In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. They are minute random fluctuations in the values of the fields which represent elementary particles, such as electric and magnetic fields which represent the electromagnetic force carried by photons, W and Z fields which carry the weak force, and gluon fields which carry the strong force
Werner Heisenberg
Where "Time" is not a dimension in and of itself but a mathematical place holder representing the fractional relative rotational motion of earth in relation to the sun, and measure of dilated displacement, the curvature of space in GR could be reinterpreted as a modification of the spatial paths or interactions of quantum particles (e.g., photons). For example: In GR, photons follow curved geodesics due to space curvature. If time is just a measure of their displacement, the "dilated displacement" could mean their paths through space are longer or their frequencies are redshifted (gravitational redshift), which we interpret as "Time" slowing down, when in fact, the photon's path is merely stretched and curved.
Cesium Atoms: The hyperfine transitions in cesium atoms occur at a lower frequency in stronger gravitational fields. If time is not fundamental, this is seen as the spatial displacement of the atom’s internal quantum states being stretched by the warped geometry of space around the massive object of Earth, and the relative backwards speed of the space outside the surface of the Muon.
The "warping of space" affects the displacement of quantum particles, which are mistakenly measured as "Time" dilation. Some speculative theories, like causal dynamical triangulation or certain quantum gravity models, explore time as an emergent phenomenon, but these are not "mainstream". (Emergent Time: In some quantum gravity theories (e.g., loop quantum gravity), time might not be fundamental but emerge from quantum entanglement or geometric structures in space. "Dilated displacement" could align with ideas where time is a measure of changes in quantum states across space.)
Quantum Mechanics in Curved Space: In GR, quantum particles like photons propagate in curved space, and their wave functions are affected by the metric. If you reinterpret the temporal part of the metric as a spatial effect, time dilation is a stretching of quantum particle paths, purely spatial not temporal.
Copyright © 2025 David William Jedell
Email: d.w.jedell@gmail.com
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