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Is it a fair summary of your rebuttal to say that its not permissible to speak of the probability distribution of past events, because the past just is what it

by o_nate 4y ago

Is it a fair summary of your rebuttal to say that its not permissible to speak of the probability distribution of past events, because the past just is what it is?

lisper 4y ago
No. Probability is something that arises from incomplete knowledge, not the actual state of affairs (except in quantum mechanics). In a classical universe both the past and future are fully determined by the present. But our knowledge of the present is limited, and that is why we have to introduce probabilities. Because it is possible to have incomplete knowledge of the present (and hence incomplete knowledge of the past), it makes sense to speak of the probability distribution of past events. If I flip a coin but don't look at it, then I can fairly say that the probability of heads (with respect to my knowledge state) is 0.5 despite the fact that the coin definitely, in point of actual fact, either landed heads up or it did not.
- effie 4y ago
  Probability is useful also when we have complete knowledge of the state of a model involving many particles (e.g. gas), but can't reliably integrate equations of motions. This lack of skill is the same towards the future as towards the past, at least in the context of reversible theories of motion like classical mechanics or evolution governed purely by Schroedinger's equation. Flip a coin, do not look at it, and make a short video of the coin from above when it is at the top position. This video provides us with details of state of the coin. Assuming a fair coin and a strong enough flip, from this state of things we can't predict the resulting face, and also can't predict the starting face on the thumb. This problem is symmetric towards the future and towards the past. The same argument holds for knowledge of one microstate of gas at single time instant. Past and future are equally undetermined, and all probabilities are the same towards the future as towards the past. To get 2nd law, we need to assume the asymmetry in addition, and it's best if it is explicit. E.g a process connecting two equilibrium macrostates, where the two states aren't defined in a symmetric way. For example, as Jaynes does, we define B as the reliable result of autonomous evolution after manual intervention in A. This makes A,B asymmetric, because it is not stated in the assumptions (and usually not considered possible) that also A is the reliable result of autonomous evolution after intervention in B. This asymmetry is what allows us to derive 2nd law. See e.g. this Jaynes' paper, Section IV The 2nd Law. https://github.com/lawrennd/jaynes/blob/main/gibbs-vs-boltzmann-entropies.pdf https://github.com/lawrennd/jaynes/blob/main/gibbs-vs-boltzm... It is interesting that this derives asymmetric 2nd law from symmetric (reversible) underlying microscopic model. The asymmetry comes in exclusively due to the assumption of B being the reliable result of intervention in A.
  - lisper 4y ago
    > when we have complete knowledge of the state of a model involving many particles (e.g. gas) We cannot have complete knowledge of the state of a gas. We cannot even have complete knowledge of the state of a single particle because the positions and velocities of classical particles are real numbers but our knowledge is constrained to be finite, so there will always be some measurement error, and so chaos theory applies. (And physical reality is actually quantum, so we have the uncertainty principle at work as well.) > This problem is symmetric towards the future and towards the past. Only because you've carefully crafted this example to have this property; it is not true in general. You have constrained your knowledge of the present to exclude that which is needed to reliably extrapolate into the past. But it is possible to change your scenario and collect data that allows reliable extrapolation into the past, for example, by looking at the coin before it is flipped and remembering (or writing down) what you saw. But for the future this is not possible. That is the essential asymmetry. > See e.g. this Jaynes' paper I have a lot of respect for Jaynes so I'll take a look but it may be a while before I have the time to give it the attention it deserves. One thing I see right away that he gets right (well, mostly): in section 6 he observes that there is no such thing as "the entropy" of a system, which is correct. Entropy can only be measured relative to a state of incomplete knowledge. But calling it "anthropomorphic" is not right. It's not a function of human ignorance specifically, it's a function of ignorance in general.
    - effie 4y ago
      > ...it is not true in general. Agreed. But it is true for your original argument applied to a non-equilibrium state at any single time instant, while not assuming any more on the past or the future states. If we adopt further assumptions about the past states, but not about the future states, then we agree this problem of prediction/retrodiction is asymmetric between past and future and this may be the reason why the multiplicity argument does not have to result in past entropy being higher. In particular, there may be other facts on record about the past states and that would override/modify the multiplicity argument for the past. > it is possible to change your scenario and collect data that allows reliable extrapolation into the past, for example, by looking at the coin before it is flipped and remembering (or writing down) what you saw. But for the future this is not possible. That is the essential asymmetry. Yes, in any realistic scenario involving prediction and retrodiction at any time, we have some data on the past states (in some lucky cases, enough data for having certainty), but never data on the future states (we may have predictions, but those are not of the same quality as data). I agree. But in addition, you seem to argue that this asymmetry of availability of data is an essential fact to derivations of the 2nd law. Consider a scenario where we have an isolated system that is a mixture of miscible liquids that exists for ages but we have data on its state only for the last 2 years, and that data says its entropy was steadily rising the whole time. Now, given this data, was entropy increasing before the collection of data started, or was it decreasing? For short enough times around the edges, we can extrapolate the entropy curve based on collected data, but for long enough times, we can't. Using the multiplicity argument, including the data, we get that entropy of very distant past states was much larger than entropy of the first recorded state. Which contradicts 2nd law. Effect of that "essential asymmetry" has a time span that is not universal, but limited to times where collection of data was happening. Outside it vanishes, and using only that data and the multiplicity argument, the distant past becomes as cloudy(highly entropic) as the distant future is.

by o_nate 4y ago

Is it a fair summary of your rebuttal to say that its not permissible to speak of the probability distribution of past events, because the past just is what it is?

lisper 4y ago

No. Probability is something that arises from incomplete knowledge, not the actual state of affairs (except in quantum mechanics). In a classical universe both the past and future are fully determined by the present. But our knowledge of the present is limited, and that is why we have to introduce probabilities. Because it is possible to have incomplete knowledge of the present (and hence incomplete knowledge of the past), it makes sense to speak of the probability distribution of past events. If I flip a coin but don't look at it, then I can fairly say that the probability of heads (with respect to my knowledge state) is 0.5 despite the fact that the coin definitely, in point of actual fact, either landed heads up or it did not.

effie 4y ago
Probability is useful also when we have complete knowledge of the state of a model involving many particles (e.g. gas), but can't reliably integrate equations of motions. This lack of skill is the same towards the future as towards the past, at least in the context of reversible theories of motion like classical mechanics or evolution governed purely by Schroedinger's equation. Flip a coin, do not look at it, and make a short video of the coin from above when it is at the top position. This video provides us with details of state of the coin. Assuming a fair coin and a strong enough flip, from this state of things we can't predict the resulting face, and also can't predict the starting face on the thumb. This problem is symmetric towards the future and towards the past. The same argument holds for knowledge of one microstate of gas at single time instant. Past and future are equally undetermined, and all probabilities are the same towards the future as towards the past. To get 2nd law, we need to assume the asymmetry in addition, and it's best if it is explicit. E.g a process connecting two equilibrium macrostates, where the two states aren't defined in a symmetric way. For example, as Jaynes does, we define B as the reliable result of autonomous evolution after manual intervention in A. This makes A,B asymmetric, because it is not stated in the assumptions (and usually not considered possible) that also A is the reliable result of autonomous evolution after intervention in B. This asymmetry is what allows us to derive 2nd law. See e.g. this Jaynes' paper, Section IV The 2nd Law. https://github.com/lawrennd/jaynes/blob/main/gibbs-vs-boltzmann-entropies.pdf https://github.com/lawrennd/jaynes/blob/main/gibbs-vs-boltzm... It is interesting that this derives asymmetric 2nd law from symmetric (reversible) underlying microscopic model. The asymmetry comes in exclusively due to the assumption of B being the reliable result of intervention in A.
- lisper 4y ago
  > when we have complete knowledge of the state of a model involving many particles (e.g. gas) We cannot have complete knowledge of the state of a gas. We cannot even have complete knowledge of the state of a single particle because the positions and velocities of classical particles are real numbers but our knowledge is constrained to be finite, so there will always be some measurement error, and so chaos theory applies. (And physical reality is actually quantum, so we have the uncertainty principle at work as well.) > This problem is symmetric towards the future and towards the past. Only because you've carefully crafted this example to have this property; it is not true in general. You have constrained your knowledge of the present to exclude that which is needed to reliably extrapolate into the past. But it is possible to change your scenario and collect data that allows reliable extrapolation into the past, for example, by looking at the coin before it is flipped and remembering (or writing down) what you saw. But for the future this is not possible. That is the essential asymmetry. > See e.g. this Jaynes' paper I have a lot of respect for Jaynes so I'll take a look but it may be a while before I have the time to give it the attention it deserves. One thing I see right away that he gets right (well, mostly): in section 6 he observes that there is no such thing as "the entropy" of a system, which is correct. Entropy can only be measured relative to a state of incomplete knowledge. But calling it "anthropomorphic" is not right. It's not a function of human ignorance specifically, it's a function of ignorance in general.
  - effie 4y ago
    > ...it is not true in general. Agreed. But it is true for your original argument applied to a non-equilibrium state at any single time instant, while not assuming any more on the past or the future states. If we adopt further assumptions about the past states, but not about the future states, then we agree this problem of prediction/retrodiction is asymmetric between past and future and this may be the reason why the multiplicity argument does not have to result in past entropy being higher. In particular, there may be other facts on record about the past states and that would override/modify the multiplicity argument for the past. > it is possible to change your scenario and collect data that allows reliable extrapolation into the past, for example, by looking at the coin before it is flipped and remembering (or writing down) what you saw. But for the future this is not possible. That is the essential asymmetry. Yes, in any realistic scenario involving prediction and retrodiction at any time, we have some data on the past states (in some lucky cases, enough data for having certainty), but never data on the future states (we may have predictions, but those are not of the same quality as data). I agree. But in addition, you seem to argue that this asymmetry of availability of data is an essential fact to derivations of the 2nd law. Consider a scenario where we have an isolated system that is a mixture of miscible liquids that exists for ages but we have data on its state only for the last 2 years, and that data says its entropy was steadily rising the whole time. Now, given this data, was entropy increasing before the collection of data started, or was it decreasing? For short enough times around the edges, we can extrapolate the entropy curve based on collected data, but for long enough times, we can't. Using the multiplicity argument, including the data, we get that entropy of very distant past states was much larger than entropy of the first recorded state. Which contradicts 2nd law. Effect of that "essential asymmetry" has a time span that is not universal, but limited to times where collection of data was happening. Outside it vanishes, and using only that data and the multiplicity argument, the distant past becomes as cloudy(highly entropic) as the distant future is.