20 questions linked to/from Norton's dome and its equation
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### Ball spontaneously rolling down hill [duplicate]

I'm trying to remember a problem in classical mechanics involving a special surface that allows a ball to roll to the top and lose all it's momentum in finite time. This leads to some interesting ...
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### Do identical starting conditions always lead to identical outcomes?

My friend and I are discussing whether or not physical phenomena are deterministic. Let's say, for example, that we have a 3-dimensional box with balls inside of it upon which no gravitational forces ...
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### How can the solutions to equations of motion be unique if it seems the same state can be arrived at through different histories?

Let's assume we have a container, a jar, a can or whatever, which has a hole at its end. If there were water inside, via a differential equation we could calculate the time by which the container is ...
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### History of interpretation of Newton's first law

Nowadays it seems to be popular among physics educators to present Newton's first law as a definition of inertial frames and/or a statement that such frames exist. This is clearly a modern overlay. ...
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### What situations in classical physics are non-deterministic?

In Sean Carroll's book "The Big Picture," he states (chapter 4, page 35): Classical mechanics, the system of equations studied by Newton and Laplace, isn't perfectly deterministic. There are ...
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### Infinite series of derivatives of position when starting from rest

Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
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### Reversibility = non-causality. Can this be right?

I read yesterday the Norton Dome's paper, which shows that some Newtonian systems can be non-causal, based on specific solutions of Newton's laws. The author justifies the solutions in very nice, ...
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### What's the intuitive reason that phase space flow is incompressible in Classical Mechanics but compressible in Quantum Mechanics?

One of the most important results of Classical Mechanics is Liouville's theorem, which tells us that the flow in phase space is like an incompressible fluid. However, in the phase space formulation ...
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