Inertial Frame R: Persisting Relationships of Particles' Positions & Velocities

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SUMMARY

The discussion focuses on the relationships between the positions and velocities of particles in an inertial frame R, defined by the equations A1 = -m2(A2) / m1 and V1 = -m2(V2) / m1 at time t = 0. It is established that these relationships persist over time due to the conservation laws governing inertial frames. The mathematical derivation confirms that the relationships hold true for all subsequent times, reinforcing the principles of classical mechanics.

PREREQUISITES
  • Understanding of classical mechanics principles
  • Familiarity with inertial frames of reference
  • Basic knowledge of particle dynamics
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the conservation laws in classical mechanics
  • Learn about inertial and non-inertial frames
  • Explore the implications of Newton's laws on particle interactions
  • Investigate advanced topics in dynamics, such as Lagrangian mechanics
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Students of physics, educators teaching classical mechanics, and anyone interested in the mathematical foundations of particle dynamics in inertial frames.

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Suppose that we choose an inertial frame R in which the particles’ positions and velocities are related by

A1= - m2 (A2) / m1


V1 = - m2(V2) / m1

at time t = 0. Show that these relationships persist at all subsequent times.
 
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Thread 'EPR revisited'

In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
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