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What is phase space in classical mechanics?
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An abstract space representing all possible states of a system.
What is meant by conservation of information in classical physics?
Knowing the current state of a system provides knowledge of both past and future states.
What additional information is needed to define the state of a moving particle in continuous time systems?
Both position and velocity
What is the difference between Newton's equations that are first order and second order?
First order equations involve velocities, second order involve accelerations.
What is an example of a system with more states beyond heads or tails?
A die with 6 sides, where various laws can define its state transitions.
What are the two basic principles of classical mechanics?
Conservation of energy and momentum
What does stroboscopic world refer to in classical mechanics?
Time evaluated in discrete intervals
What does a deterministic law mean in classical mechanics?
It allows for the consistent prediction of future states if the current state is known.
Why are both position and velocity needed to predict the future state in classical mechanics?
Because Newton’s equations describe particle motion and involve second order (accelerations) versus first order (velocities).
Describe a non-allowable law in classical mechanics.
A law that is irreversible, such as having multiple arrows leading into a single state, is not allowed.
What is the basis of all physics and fundamental in describing the motion of objects?
Classical mechanics
Give an example of a deterministic law for a coin.
Law 1: Heads stays Heads, Tails stays Tails OR Law 2: Heads becomes Tails, Tails becomes Heads.
What does Newton's Second Law state?
Force equals mass times acceleration (f = m * acceleration)
Why must every state in classical mechanics have a unique in and out path?
To maintain determinism and reversibility.
What is one key takeaway about phase space from classical mechanics?
Phase space must include all necessary information to determine future states.
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