Clock in Accelerated Motion Slowing down is Necessity of Newton's Law
| Scientific Paper | |
|---|---|
| Title | Clock in Accelerated Motion Slowing down is Necessity of Newton's Law |
| Read in full | Link to paper |
| Author(s) | Qing Zeng |
| Keywords | constant velocity, accelerated velocity, relativity, Newton's law, clock slows down |
| Published | 2010 |
| No. of pages | 10 |
Read the full paper here
Abstract
According to the special relativity, clock will slow down due to its motion. So, someone took the clock into the flight capsule in the earth equator line, and measured the clock in the airplane slowing down, and then they got the conclusion "moving clock will slow down". This article will analyze this kind of physical phenomenon. Is Newton's law right or relativity right? This article obtains the result through theoretical arithmetic: clock in the equator line slowing down is necessity of Newton's law; it is caused by accelerated motion, not constant motion. Therefore, this article is challenging the relativity.
Overview
Zeng Qingping, writing from the Air Force Radar Academy, takes up the best-known popular argument for relativistic time dilation: clocks carried around the Earth were found to run slow, therefore "moving clocks slow down". His counter-claim is that the slowing is entirely a Newtonian effect and has nothing to do with uniform velocity. What actually changes a clock's rate, he argues, is acceleration — and acceleration is available to Newtonian mechanics without any modification of time itself. His slogan is that "the clock's speed depends on acceleration, not the constant linear motion."
Behind this sits a stronger metaphysical commitment, which the second half of the paper develops: a clock is a "man-made measure attribute" that "depends on measure tool and environment", whereas time is a "nature attribute", absolute and one-dimensional. On this view relativity commits a category error, reading a property of instruments into the structure of the world. The paper closes by arguing that inertia — Foucault's pendulum, the Coriolis force, the eastward deflection of falling bodies — is the direct experimental signature of Newton's absolute space, and that the space of relativity is "mathematic space" rather than physical space. The author's own reference list shows this is one instalment of a long programme against Maxwell's equations and the Lorentz transformation.
The argument
The pendulum as the model clock
Zeng's chosen clock is the simple pendulum, on the grounds that "the clocks made at the beginning of last century were all mechanical clocks, and mainly famous for pendulum clocks". He derives its period from scratch in the natural coordinate system, with deflection angle θ as the single generalised coordinate and suspension length l, obtaining the equation of motion
- θ̇̇ = −(g/l) sin θ
Multiplying by θ̇ and integrating gives the energy integral, and with the pendulum released from rest at θ0 he obtains θ̇2 = (2g/l)(cos θ − cos θ0). The same integral yields the constraint force in the suspension,
- N = mg(3 cos θ − 2 cos θ0)
from which he notes the standard result that N vanishes at a critical angle θM = cos−1(2cos θ0/3): a rigid rod can then push instead of pull, while a soft rope cannot, so the bob goes into free flight.
The elliptic integral and the two approximations
Substituting cos θ = 1 − 2sin2(θ/2) and introducing k = sin(θ0/2) with sin(θ/2) = k sin φ, the quarter-period becomes the complete elliptic integral of the first kind. Zeng gives the first two terms:
- T = 2π √(l/g)
- T = 2π √(l/g) (1 + θ02/16)
This is textbook, and correct as far as it goes; it is included to establish that the period depends on g and on nothing else that motion could change.
The equatorial correction
The step the paper's title rests on is the next one. At the equator the bob co-rotates with the Earth, so in the rotating frame an inertial centrifugal force appears, directed opposite to gravity. Zeng quotes its magnitude as f = 3.39 × 10−2 m newtons, i.e. a centrifugal acceleration acen = 3.39 × 10−2 m/s2. The equatorial period is therefore
- T = 2π √(l/(g − acen))
which exceeds the polar period 2π√(l/g). "The clock in the earth pole goes faster, and the clock in the equator line goes slower." The elevator analogy is offered as the general principle: a pendulum in an upward-accelerating lift speeds up, in a downward-accelerating lift slows down, and "all the clocks generated by object's motion (including particle's motion) will be influenced by acceleration."
Inertia as the signature of absolute space
Section 3 argues that because inertial forces can be felt and measured, absolute space can be detected mechanically. Foucault's 1851 pendulum is presented as the earliest such experiment; Zeng writes the linearised equations of motion at latitude φ with Earth angular velocity ω and gives the solution as a precessing ellipse with p = √(g/l) and precession rate ω sin φ. He then rederives the Coriolis acceleration by an unusual route: instead of transforming coordinates, he treats a particle moving radially outward along a narrow slot in a rotating disc as undergoing repeated oblique collisions with the slot wall, applies the elastic-collision formula with restitution coefficient k = 1, takes the limits of a narrow slot and a disc mass much greater than the particle mass, and recovers
- ay = 2ω × ur
and hence Fc = 2m ω × ur. The point of the construction is that the curved trajectory is "overlaid by several linear lines": inertia is fundamentally rectilinear, so the space it reveals is "linear type" Euclidean space, isotropic and indifferent to the motion of bodies in it.
Why mechanics rather than optics
The conclusion explains the choice of arena. Zeng holds that "the mass of electric field, magnetic field and optical field is zero, and they do not have inertia or occupy absolute space", so electromagnetic and optical experiments cannot detect absolute space at all — with the reservation of stellar aberration. Mechanics, having inertia, can.
Assessment
Two things in the paper are simply right, and should be said plainly. The pendulum derivation is standard analytical mechanics carried out correctly, including the constraint force, the critical angle, and the elliptic-integral amplitude correction. And the equatorial number checks out: with ω = 7.292 × 10−5 rad/s and R = 6.378 × 106 m, ω2R = 3.392 × 10−2 m/s2, exactly Zeng's figure. A pendulum clock does run slow at the equator, and the reason is Newtonian. This is in fact one of the oldest quantitative results in physics — Jean Richer found in 1672 that his pendulum clock lost time at Cayenne relative to Paris, and Newton used it in the Principia to argue for the Earth's oblateness. Zeng's Section 2 is a careful rederivation of a 350-year-old effect.
The difficulty is that this effect is not the one the relativistic claim is about, and the paper's own numbers make the mismatch impossible to paper over. The clock experiment alluded to in the abstract — Hafele and Keating's 1971 flights — used caesium beam standards, whose rate is set by a hyperfine transition frequency in the free atom. That frequency does not contain g, does not contain l, and is unaffected by a 3.4 × 10−2 m/s2 centrifugal acceleration; the pendulum period is not a model of it in any respect. Worse, the size is wrong by nine orders of magnitude in the direction that refutes rather than explains. Zeng's own formula gives a fractional rate change acen/2g ≈ 1.7 × 10−3, which is about 150 seconds per day. The discrepancies actually measured in the 1971 flights were of order 10−7 seconds. A mechanism roughly 5 × 108 times too large is not an alternative explanation of the observation; if it applied to the flown clocks they would have been useless as clocks.
There is a second, sharper problem, and it is a case of the paper unknowingly proving the opposite of its thesis. Zeng's centrifugal term and the special-relativistic velocity term at the equator are not competing accounts of one number: they are both real, and they very nearly cancel. The kinematic term is v2/2c2 with v = ωR = 465 m/s, giving 1.2 × 10−12 — and the gravitational potential difference between equator and pole, which exists precisely because the centrifugal acceleration Zeng computes has deformed the Earth into its equilibrium shape, contributes an equal and opposite amount. That is the definition of the geoid: clocks at mean sea level run at the same rate everywhere, equator and pole alike, to about a part in 1017. The equatorial centrifugal effect is therefore already inside the relativistic account, not outside it. A pendulum at sea level does run slow at the equator; a caesium clock at sea level does not.
Third, the framing "acceleration, not constant motion" cannot be maintained even within the paper's own examples. Zeng's argument for acceleration is that it changes the effective g of a gravity-driven oscillator. But a clock with no restoring force set by gravity — a caesium atom, a muon lifetime, a light-clock — has no g to change, so the mechanism has no purchase on the very cases where time dilation is claimed. The muon lifetime measurements, and the storage-ring experiments in which muons circulate at accelerations of order 1018 g with lifetimes depending only on the Lorentz factor and not at all on the acceleration, are the direct test of exactly this proposition, and they come out the other way.
The Coriolis rederivation in Section 3 is ingenious and, as a piece of physical intuition about why the fictitious force has the form 2ω × u, instructive. But it establishes only what standard mechanics already grants: that in a rotating frame the inertial forces are real, measurable and calculable. That was never in dispute, and it does not distinguish Newton's absolute space from the local inertial frames of general relativity, which also give a rotating Earth a Foucault precession of ω sin φ. The final claim, that fields have zero mass and therefore "do not occupy absolute space" so that optical experiments cannot bear on the question, is asserted rather than argued, and it is the assumption that allows the Michelson–Morley experiment to be set aside without discussion. Readers should also note that some of the paper's remarks — the reading of Einstein's 1905 opening paragraph as a concealed admission about absolute space, and the closing rhetorical passage about Newton — are interpretive rather than physical, and carry no weight in the argument.