Abstract
The mechanical motion of a system consisting of simple springs is investigated from the viewpoint of two inertial observers with a relativistic relative velocity. It is shown that the final displacement of the springs is not measured the same by the observers. Indeed, it is demonstrated that there is an incompatibility between kinematics and dynamics in Einstein’s relativity regarding the force transformation.
Highlights
It is worthwhile to note that some other works show paradoxes of special relativity regarding rotating reference systems for only kinematic effects [3], which is related to the subject of this article
The analysis demonstrated in the article is based on the well-known dynamics of special relativity, other dynamics have been introduced in some references of the literature
It has been shown that different dynamics can be derived for the kinematics of special relativity [4], and our multispring system paradox analysis can be performed under other dynamics too
Summary
Too many very thin identical springs, each with a similar constant of kP′′, are attached at one end to the circumference of a thin solid cylindrical plate, all being perpendicular to the plane that passes through the plate, and in the other end, the springs touch the floor. The net constant of the P springs is equal to that of S, and it is anticipated that the upward forces of the P springs and the downward force of S are balanced, so that, from the viewpoint of the lab observer M, the thin plate remains motionless at a distance d0′/2 from the ceiling as well as the floor level (see Figure 2(a)). The above formula is not always valid for all arbitrary values of u′ and v, and it seems that relativity includes a null result, at least, in this example To prove, it suffices to substitute v 0.6c and u′ 0.8c and do the calculations numerically. An important point with this problem is that if the forces are transmitted via some sort of signaling from the P springs towards the center of rotation of the plate to which one end of S is attached, the arrival of the signals to the center is simultaneous from the viewpoint of both M and N. is simultaneity makes the spring S react to all of the signals sent by the P springs instantly as viewed by both of the observers; otherwise, it is expected that the plate is deformed in shape due to the signal delays
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematics and Mathematical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
