4 ms·

Right, but that was not my point. I said two things: you can't always know the initial conditions and you can't transpose non-linearities. Yes, you can invert t

Right, but that was not my point. I said two things: you can't always know the initial conditions and you can't transpose non-linearities. Yes, you can invert the sign of all velocities and trace the path of a particle in reverse, but can you tell where it started moving if its current velocity is constant? What if that particle hits a wall and stays there? How can you know when in the past it stopped moving?

lisper 9y ago
> you can't always know the initial conditions Just because you can't know them doesn't mean they aren't physical. God can know the initial conditions. In a classical world, that's good enough. > and you can't transpose non-linearities So? Classical mechanics is linear. > can you tell where it started moving if its current velocity is constant? Yes, of course. Just as easily -- and by the exact same method -- as you can tell where it will stop moving. > What if that particle hits a wall and stays there? How can you know when in the past it stopped moving? That's a question that is answered in a first-year physics course, but the TL;DR is that any collision must conserve both momentum and energy. If a ball hits a wall and "sticks" then some of its energy must be dissipated as heat. That is the thermodynamic arrow of time, which is exactly what the original post was about.
- posterboy 9y ago
  > God https://en.wikipedia.org/wiki/Laplace's_demon https://en.wikipedia.org/wiki/Laplace's_demon
  - leovailati 9y ago
    This is a great link, thank you for the reference. @lisper, check this out.
- leovailati 9y ago
  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

> you can't always know the initial conditions Just because you can't know them doesn't mean they aren't physical. God can know the initial conditions. In a classical world, that's good enough. > and you can't transpose non-linearities So? Classical mechanics is linear. > can you tell where it started moving if its current velocity is constant? Yes, of course. Just as easily -- and by the exact same method -- as you can tell where it will stop moving. > What if that particle hits a wall and stays there? How can you know when in the past it stopped moving? That's a question that is answered in a first-year physics course, but the TL;DR is that any collision must conserve both momentum and energy. If a ball hits a wall and "sticks" then some of its energy must be dissipated as heat. That is the thermodynamic arrow of time, which is exactly what the original post was about.

posterboy 9y ago
> God https://en.wikipedia.org/wiki/Laplace's_demon https://en.wikipedia.org/wiki/Laplace's_demon
- leovailati 9y ago
  This is a great link, thank you for the reference. @lisper, check this out.
leovailati 9y ago
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.