Absolute simultaneity and invariant lengths: Special Relativity without light signals or synchronised clocks
J. H. Field
备注：
16 pages, 6 figures. v2 has 19 pages, changed title, abstract, references and added appendix. Important conceptual error in v1 is corrected. v3 Appendix and one equation corrected. Minor text addition. Conclusions unchanged
It is demonstrated that the measured spatial separation of two objects, at rest in some inertial frame, is invariant under space-time transformations. This result holds in both Galilean and Special Relativity. A corollary is that there are no `length contraction' or associated 'relativity of simultaneity' effects in the latter theory. A thought experiment employing four unsynchronised clocks and a single measuring rod reveals that the physical basis of the time dilatation effect is a relative velocity transformation law, not `length contraction'. Time dilatation, which is universal and translation invariant for all synchronised clocks at rest in any inertial frame, is the unique space-time phenomenon discriminating Special from Galilean Relativity.
The Lorentz transformation is used to analyse space and time coordinates corresponding to two spatially-separated clocks in the same inertial frame. The time dilatation effect is confirmed, but not `relativity of simultaneity' or `relativistic length contraction'. How these latter, spurious, effects arise from misuse of the Lorentz transformation is also explained.
An orbiting `photon clock' is proposed to test directly the relativity of simultaneity effect of special relativity. This is done by exchanging microwave signals between two satellites in low Earth orbit carrying clocks that have previously been synchronised in the Earth-centered inertial system. A similar experiment using synchronised signals from two GPS satellites with the receiver on a single satellite in low Earth orbit, is also proposed.
Time-like and space-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances defined by two spatially-separated clocks. The time dilatation effect is confirmed, but not `relativity of simultaneity' or `relativistic length contraction'. How these latter, spurious, effects arise from misuse of the Lorentz transformation is also explained.
The theory of special relativity derives from the Lorentz transformation. The Lorentz transformation implies differential simultaneity and light speed isotropy. Experiments to probe differential simultaneity should be able to distinguish the Lorentz transformation from a kinematically-similar alternate transformation that predicts absolute simultaneity, the absolute Lorentz transformation. Here, we describe how published optical tests of light speed isotropy/anisotropy cannot distinguish between the two transformations. We show that the shared equations of the two transformations, from the per…
We present a relativistic space-time diagram that displays in true magnitudes the readings (daytimes) of two inertial reference frames clocks. One reference frame is the rest frame for one clock. This diagram shows that two events simultaneous in one reference frames are not compulsory simultaneous in the other frame. This approach has a bi-dimensional character.
Observations of the apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not spatial intervals, so breaking space time exchange symmetry and forbidding relativity of simultaneity and length contraction. A satellite cesium clock experiment to test these predictions is proposed.
An orbiting `photon clock' is proposed to test directly the relativity of simultaneity of special relativity. This is done by comparison of the arrival times at a ground station of three microwave signals transmitted by two satellites following the same low Earth orbit.
Space-like and time-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances. The former are found to be Lorentz invariant --there is no `relativistic length contraction', whereas the latter exhibit the experimentally confirmed `time dilatation' effect, without, however, `relativity of simultaneity'. It is shown how the spurious predictions of length contraction and relativity of simultaneity arise from the use of inconsistent synchronisation procedures for spatially separated clocks.
The simultaneity framework describes the relativistic interaction of time with space. The two major proposed simultaneity frameworks are differential simultaneity, in which time is offset with distance in "moving" or rotating frames for each "stationary" observer, and absolute simultaneity, in which time is not offset with distance. We use the Mansouri and Sexl test theory to analyze the simultaneity framework in rotating frames in the absence of spacetime curvature. The Mansouri and Sexl test theory has four parameters. Three parameters describe relativistic effects. The fourth parameter, $ε(…
Evaluation of the additive constants in the space-time Lorentz transformation equations required, according to Einstein, to correctly describe synchronised clocks at different spatial locations, reveals the spurious and unphysical nature of the 'relativity of simultaneity' and 'length contraction' effects of conventional special relativity. Unlike time dilation, there is no experimental evidence for these putative effects. Only a universal (position independent) time dilation effect for different inertial frames distinguishes special from Galilean relativity.
A sign error in an angle while drawing the original Minkowski plot has persisted for a century in text books and the pedagogical literature. When it is corrected, the `length contraction' effect derived from the geometry of the plot disappears. It is also shown how the `relativity of simultaneity' effect that has been derived from the plot results from a lack of correspondence between certain geometrical projections on the plot and the properties of the physical system --two spatially separated and synchronised clocks in a common inertial frame-- that they are purported to describe.
A careful study is made of the operational meaning of the time symbols appearing in the space-time Lorentz transformation. Four distinct symbols, with different physical meanings, are needed to describe reciprocal measurements involving stationary and uniformly-moving clocks. Physical predictions concern only the observed rate of a clock as a function of its relative speed, not its setting. How the failure to make this distinction leads to the conventional predictions of spurious `relativity of simultaneity' and `length contraction' effects in special relativity is explained.
Basic for the definition of 'time' are clocks operating under stationary conditions. The periods of two clocks can be compared with each other via two return experiments. The central clock mediates between the rotating and the inertial frame. Dimensional arguments and a detailed deduction show that the period of a rotating clock, measured externally in the inertial system, is the same as the internally defined one. There is a common synchron-time, especially 'absolute' simultaneity and invariance of flight times hold. This allows a new discussion of the twin problem. The invariance of a rotati…
A calculus based on pointer-mark coincidences is proposed to define, in a mathematically rigorous way, measurements of space and time intervals. The connection between such measurements in different inertial frames according to the Galilean or Lorentz transformations is then studied using new, simple, and practical clock synchronisation procedures. It is found that measured length intervals are Lorentz invariant, whereas moving clocks show a universal time dilatation effect. The `relativistic length contraction' and `relativity of simultaneity' effects of conventional special relativity theory…
Space-time intervals corresponding to different events on the worldline of any ponderable object (for example a clock) are time-like. In consequence, in the analysis of any space-time experiment involving clocks only the region for $cΔt \ge 0$ between the line $Δx = 0$ and the light cone projection $cΔt = Δx$ of the $cΔt$ versus $Δx$ Minkowski plot is physically relevant. This breaks the manifest space-time symmetry of the plot. A further consequence is the unphysical nature of the `relativity of simultaneity' and `length contraction' effects of conventional special relativity theory. The only…
In this paper, Lorentz Transformation(LT) is derived by an alternate method, using photon clocks, placed at the locations of the concerned events, which are initially synchronised using a light signal(Einstein synchrony). Then, it is shown that the second term in the time dilation equation of the LT, is the term responsible for time travel and further it is shown that this term arises merely due to non-simultaneous initial clock synchronisation and that this term does not correspond to any actual time elapsed while timing events, thus ruling out the possibility of time travel, from the framewo…
Translational invariance requires that physical predictions are independent of the choice of spatial coordinate system used. The time dilatation effect of special relativity is shown to manifestly respect this invariance. Consideration of the space-time Lorentz transformation with arbitrary spatial coordinates shows that the spurious `length contraction' and `relativity of simultaneity' effects --the latter violating translational invariance-- result from the use of a different spatial coordinate system to describe each of two spatially separated clocks at rest in a common inertial frame
The apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not spatial intervals, so breaking space-time exchange symmetry and forbidding relativity of simultaneity and length contraction. Two satellite-borne experiments to test these predictions are proposed.
The concepts of primary and reciprocal experiments and base and travelling frames in special relativity are concisely described and applied to several different space-time experiments. These include Einstein's train/embankment thought experiment and a related thought experiment, due to Sartori, involving two trains in parallel motion with different speeds. Spatially separated clocks which are synchronised in their common proper frame are shown to be so in all inertial frames and their spatial separation to be Lorentz invariant. The interpretions given by Einstein and Sartori of their experimen…
The conventional discussion of the observed distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations, from a stationary frame, of : (i) objects moving with constant velocity and uniformly illuminated during a short time $τ_L$ (their `Luminous Proper Time') in their rest frame; these may be called `Transient Luminous Objects' and (ii) a moving, extended, array of synchronised `equivalent clocks' in a common inertial frame. Application of the Lorentz Transformation to (i) shows that such objects, observed…
To consider a medium carrying light and electromagnetic waves is impossible, when this medium shall have properties according to the principle of constant speed of light, that is, isotropy of speed of light in every system of reference. Therefore, with principle of constant speed of light abandoned, the so-called medium synchronization of clocks is defined, yielding isotropy solely in the system at rest and anisotropy in all moving systems. From medium synchronization the appropriate coordinate transformation is developed, the so-called medium transformation, a Galilean type of transformation,…
This work deals with the questions of absolute space and relativity. In particular, an alternative derivation of the effects described by special relativity is provided, which is based on a description that assumes a privileged reference frame. The present theory follows the ideas of Lorentz and Poincare, abandoning a strict view of Einstein's "equivalence" of all inertial frames. The meaning of the Principle of Relativity is discussed and elucidated, and it is shown that it is not incompatible with the existence of a preferred, absolute, frame. Most scientists nowadays still consider the basi…
