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Even a high school level equation of motion has a t squared term in it. Classical mechanics is not linear. And even if it were, the real world is obviously not.

Even a high school level equation of motion has a t squared term in it. Classical mechanics is not linear. And even if it were, the real world is obviously not. The basket ball will stop bouncing at some point, even though the model for the bouncing movement is an infinite exponentially decaying curve. After it stops bouncing it will stay there, resting, for ever. Good luck trying to determine when and if it moved at all. The fact that you have to invoke God to reverse a system back into its initial conditions proves my initial point. Remember, my whole point was the current state of a system does not necessarily encode its past. You cannot know where or when a particle with constant velocity started or will stop moving. Unless you are God, of course. And you cannot know when a particle hit a wall. All you can know is that it happened some time in the past. What did I say that made you think that initial conditions are not "physical" and what does that even mean? I feel like we are talking about different things...

lisper 9y ago
You don't understand what a linear theory means. It does not mean that higher order polynomials don't exist in the theory, it means that the dynamics of the system are described by linear differential equations. And your bouncing basketball example is dissipative (look it up). > Remember, my whole point was the current state of a system does not necessarily encode its past. Yes, I know. You're wrong about that. The state of a bouncing basketball is not described by the position and velocity of the basketball, it's described in classical mechanics by the position and velocity of every elementary particle that the basketball comprises, and in quantum mechanics by the wave function of every such particle. That information, together with the same information about the environment, encodes the basketball's past and its future.
- leovailati 9y ago
  I feel like we are not gaining anything from this discussion. Here are some references to back my point: "Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system." https://en.wikipedia.org/wiki/State_variable https://en.wikipedia.org/wiki/State_variable "State functions do not depend on the path by which the system arrived at its present state." https://en.wikipedia.org/wiki/State_function https://en.wikipedia.org/wiki/State_function MIT lecture on state representation of linear systems: http://web.mit.edu/2.14/www/Handouts/StateSpace.pdf http://web.mit.edu/2.14/www/Handouts/StateSpace.pdf - see Section 1.1. I got my "Linear Systems and Signals" B.P. Lathi 2nd ed from my shelf and found similar information. See section 10.1 if you have access to that book. > The state of a bouncing basketball is not described by the position and velocity of the basketball, it's described in classical mechanics by the position and velocity of every elementary particle that the basketball comprises I'm no physicist, but I think you might run into problems with the Heisenberg uncertainty principle when you try to determine the state of your system. Even if you are just mentioning that as a mental exercise and we assume that we can in fact determine everything there is to know about every particle in a basketball, your theory still won't hold. When your system reaches an equilibrium state (i.e., minimal energy state) it will rest there forever and you will lose the ability to reverse it. In other words: "The science of thermodynamics is able to capture these generalizations as consequences of its claim that systems spontaneously evolve to future equilibrium states but do not spontaneously evolve away from equilibrium states." Obtained from the first paragraph of the original article.
  - lisper 9y ago
    > I feel like we are not gaining anything from this discussion Sorry about that. I'm frustrated, but I really am trying to be constructive here. > "Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system." Right. So if your state describes the whole universe, that provides enough information to determine its future behavior because there is nothing external to the universe (by definition!) > "State functions do not depend on the path by which the system arrived at its present state." Right. However, because the dynamics of both classical and quantum mechanics are reversible, you can determine the past states of a closed system (like the universe) in exactly the same way you can determine its future states. (That's how we know, for example, that the big bang happened.) > I think you might run into problems with the Heisenberg uncertainty principle when you try to determine the state of your system. Right. That's why it's important to distinguish between classical and quantum mechanics. In classical mechanics there is a mystery about where the arrow of time comes from because the fundamental equations are all time-symmetric. Quantum mechanics (and more specifically QIT - quantum information theory) solves that mystery. > "The science of thermodynamics is able to capture these generalizations as consequences of its claim that systems spontaneously evolve to future equilibrium states but do not spontaneously evolve away from equilibrium states." This is not a solution to the mystery because it has to introduce this extra axiom about equilibrium states, which does not follow from Newton's equations. QIT is a better solution because the (practical) irreversibility of measurements can be derived from the basic axioms of QM. It doesn't have to be assumed.

lisper 9y ago

You don't understand what a linear theory means. It does not mean that higher order polynomials don't exist in the theory, it means that the dynamics of the system are described by linear differential equations. And your bouncing basketball example is dissipative (look it up). > Remember, my whole point was the current state of a system does not necessarily encode its past. Yes, I know. You're wrong about that. The state of a bouncing basketball is not described by the position and velocity of the basketball, it's described in classical mechanics by the position and velocity of every elementary particle that the basketball comprises, and in quantum mechanics by the wave function of every such particle. That information, together with the same information about the environment, encodes the basketball's past and its future.

leovailati 9y ago
I feel like we are not gaining anything from this discussion. Here are some references to back my point: "Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system." https://en.wikipedia.org/wiki/State_variable https://en.wikipedia.org/wiki/State_variable "State functions do not depend on the path by which the system arrived at its present state." https://en.wikipedia.org/wiki/State_function https://en.wikipedia.org/wiki/State_function MIT lecture on state representation of linear systems: http://web.mit.edu/2.14/www/Handouts/StateSpace.pdf http://web.mit.edu/2.14/www/Handouts/StateSpace.pdf - see Section 1.1. I got my "Linear Systems and Signals" B.P. Lathi 2nd ed from my shelf and found similar information. See section 10.1 if you have access to that book. > The state of a bouncing basketball is not described by the position and velocity of the basketball, it's described in classical mechanics by the position and velocity of every elementary particle that the basketball comprises I'm no physicist, but I think you might run into problems with the Heisenberg uncertainty principle when you try to determine the state of your system. Even if you are just mentioning that as a mental exercise and we assume that we can in fact determine everything there is to know about every particle in a basketball, your theory still won't hold. When your system reaches an equilibrium state (i.e., minimal energy state) it will rest there forever and you will lose the ability to reverse it. In other words: "The science of thermodynamics is able to capture these generalizations as consequences of its claim that systems spontaneously evolve to future equilibrium states but do not spontaneously evolve away from equilibrium states." Obtained from the first paragraph of the original article.
- lisper 9y ago
  > I feel like we are not gaining anything from this discussion Sorry about that. I'm frustrated, but I really am trying to be constructive here. > "Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system." Right. So if your state describes the whole universe, that provides enough information to determine its future behavior because there is nothing external to the universe (by definition!) > "State functions do not depend on the path by which the system arrived at its present state." Right. However, because the dynamics of both classical and quantum mechanics are reversible, you can determine the past states of a closed system (like the universe) in exactly the same way you can determine its future states. (That's how we know, for example, that the big bang happened.) > I think you might run into problems with the Heisenberg uncertainty principle when you try to determine the state of your system. Right. That's why it's important to distinguish between classical and quantum mechanics. In classical mechanics there is a mystery about where the arrow of time comes from because the fundamental equations are all time-symmetric. Quantum mechanics (and more specifically QIT - quantum information theory) solves that mystery. > "The science of thermodynamics is able to capture these generalizations as consequences of its claim that systems spontaneously evolve to future equilibrium states but do not spontaneously evolve away from equilibrium states." This is not a solution to the mystery because it has to introduce this extra axiom about equilibrium states, which does not follow from Newton's equations. QIT is a better solution because the (practical) irreversibility of measurements can be derived from the basic axioms of QM. It doesn't have to be assumed.