Information transmittal and time uncertainty, measuring the speed of light and time of reflection, representations of Newton's second law and related problems

• Authors: E. A. Galperin
• Venue: Computers & Mathematics with Applications
• Year: 2008

Some physical and computational aspects related to the intuitive notion of time in its connection with natural and technological processes are considered. The phenomenon of finite speed of information transmittal relative to measurement and computation is analyzed. It is argued that this phenomenon creates inevitable and irreversible time delays (uncertainties) that affect all measurements and computations, makes the exact synchronization of clocks impossible, shifts our knowledge to the past, and limits the accuracy of experiments. Some past experiments for the measurement of the speed of light are revisited, the possibility of a finite time of mirror reflection is discussed, and a stand for the experimental measurement of time spent in mirror reflection is proposed by a modification of Fizeau experiments. The positive orientation of the flow of time in its relation to the mathematical concept of time derivative is considered. It is demonstrated that right time-derivatives normally used to describe physical processes actually set forth non-causal representations of physical realities and may severely restrict the possibility of control and optimization in real life systems. The use of (causal) left time-derivatives produced by measurements and computations and consideration of variable masses lead to new representations of the second Newton's law of motion where forces may contain controls depending on accelerations and higher order left time-derivatives of velocity. Such controls are actually required in jet-propelled space vehicles with variable masses, as demonstrated in the space shuttle example. The parallelogram rule does not apply to forces depending on higher order derivatives, so the concept of effective forces is considered within original Newton's representation in which effective forces can be recovered in the process of integration; thereby the parallelogram law stays intact for effective forces. Consideration of forces with left higher order time derivatives alters classical methods in mechanics that were developed on the basis of absolute time and assuming no higher order derivatives in the forces of Newtonian equations of motion. Inclusion of such forces and consideration of natural time delays and time orientation opens new avenues for investigation and control of processes in physics, economy, medicine and mechanics. It is demonstrated that Lagrange and Hamilton equations stay intact in some generalized forms which forms can be used to derive higher order dynamical equations that exclude geometric constraints, thus having the minimum number of independent generalized coordinates.