Ion-Vlad/Time-vs.-Duration-Lorentz-Consistent-Minkowski-Diagrams: Time vs. Duration: A Reinterpretation of Special Relativity v1.5

Uploaded Time vs Duration_v1.5.pdf and Time vs Duration_v1.5.tex.
Replaced Figures 3 and 4 and added the following explanation to Section 2.1 on page 6: " In this representation, points P and P' lie on the same horizontal line, indicating that they correspond to the same event. The temporal coordinate of P is identical to the temporal coordinate of T' (ct′ = 5). Because the Lorentz transformation is embedded in the S' grid but is not applied to the S grid, P appears on the ct-axis with coordinate

ctP = ctT′ ′ = 3. Therefore, a correction must be applied to the ct coordinate. Consequently, the γ projection of T' onto the S grid initially appears at (x = 2.4, ; ct = 3). It is important to recognise that these coordinates do not correspond to a single event in S. Rather, they arise from separate projections onto the x and ct axes and therefore cannot be combined into a unique spacetime point. A consistent event representation is recovered only after the appropriate Lorentz transformation is applied. Once the Lorentz-consistent correction is applied, the coordinates of P become (x = 0, ct = 5), and the projection of T' is correspondingly located at (x = 4, ct = 5), thereby preserving the coordinate relationships between the two frames. Moreover, the coordinate time associated with the ct axis appears dilated when viewed from the non-inertial frame, with ct5′ < ct5, while the spatial units in S' are contracted compared with those in S, in agreement with the predictions of Special Relativity. This difference reflects the distinction between coordinate time and elapsed proper time, which underlies the standard interpretation of "time dilation". Consider 1 kg of water at 4°C, which occupies approximately 1 L. When the same quantity of water is cooled to 0°C or below, its volume changes, even though its mass remains constant. The underlying physical entity is unchanged, while its measured properties depend on the conditions of observation. Importantly, the quantity of water itself has not changed; only the conditions under which it is observed have been altered. When the temperature is restored, the volume returns to its original value while the mass remains unchanged throughout. The analogy is not exact, but it illustrates a general principle: changes in observational or measurement conditions can modify the numerical values assigned to certain properties without altering the underlying physical entity. Similarly, in relativity, changes in relative motion affect the measured duration associated with an event, while the event itself remains the same physical occurrence across all reference frames."