3 ms·
>The intuitive answer is that it's the time reversed situation to a ball being carefully rolled UP the dome so that it stops and comes to rest on the apex. Tha
by moralestapia 2y ago
>The intuitive answer is that it's the time reversed situation to a ball being carefully rolled UP the dome so that it stops and comes to rest on the apex.
That's nonsense. The arrow of entropy always goes forward. Sure, the ball comes to the top of the dome to rest but it also carries direction, momentum and a lot of other properties that you have to put in as well in your hypothetical entropy-arrow-now-goes-back scenario.
This is high-school grade physics, come on. It's surprising some people still take John Norton seriously, not because of the dome, but because of his many other "controversial" takes on physics that fail miserably on their foundations.
- ajross 2y ago> The arrow of entropy always goes forward. The arrow of what now?[1] This is classical dynamics we're doing. I repeat, this is a math result, not an argument about physical systems. [1] Edit as this was clearly missed: THIS IS SARCASM. Thermodynamics and statistical mechanics are excellent theories and worth studying as they tell us deep and profound things about the natural world. This particular novelty is a result from classical dynamics where they don't apply. The "arrow of time" in Newtonian mechanics is absolutely reversible, and there is no Newtonian idea of "entropy".
- moralestapia 2y agohttps://en.wikipedia.org/wiki/Entropy_as_an_arrow_of_time https://en.wikipedia.org/wiki/Entropy_as_an_arrow_of_time Read. Then post. >I repeat, this is a math result, not an argument about physical systems. Did you even care to read the title of the post?
- pxx 2y agodid you? the title and content of this post is about math results. you should really consider the possibility that you're very wrong here. the discussion is about hypothetical results from classical mechanics, which, along with the rest of physics, is a mathematical model that may be incongruous with observations.
- aipatselarom 2y ago>What situations in classical physics are non-deterministic? Sorry, I didn't take my crazy pills today. To me it is very clear that the question involves physics from the start.
- cycomanic 2y agoI suggest you read the HN guidelines, you are quite abrasive and aggressive in your posts. Regarding your post about entropy. The reason it does not apply is because entropy is a concept from statistical mechanics which is about the statistics of ensembles of many (even non-classical) particles. It's a concept invented after Newton dynamics, but does not apply to describing the equations of motion of a single particle (try to define the entropy of the single particle system). Time reversal is a core tenent of Newton dynamics.
- aipatselarom 2y agoRead the title of this post, and the title of the question in the exchange, I will post it yet again, *sigh* >What situations in classical physics are non-deterministic? Is "statistical mechanics" contained within "classical physics"? Yes or no? No need for a nonsensical philosophical essay.
- cycomanic 2y agoMaybe you should read my most, I didn't say that statistical mechanics is nonclassical. I said statistical mechanics does not apply to the discussion of a single particle rolling up or down a slope. Tell me which of the states has more entropy the one with the particle at the top od the Norton dome or the one at the bottom?
- Certhas 2y agoSeriously, you don't seem to know much about things you speak confidently about. Norton's dome is a surprising mathematical situation in very conventional classical mechanics. It doesn't matter what else Norton has done, this observation is trivial to verify for every undergrad maths/physics student. This has absolutely nothing to do with entropy or the arrow of time. The mathematical situation is of no practical relevance because it's "density zero": Generic deviations will destroy this peculiar behaviour.
- moralestapia 2y ago>you don't seem to know much about things you speak confidently about Good one, chap! How about you argue with substance instead ... Explain, what makes the ball suddenly start rolling down the dome? Do not hand-wave, just give a direct answer to this question, based on your purported understanding of the problem.
- Certhas 2y agoNothing. The Newton equations predict that, given the Norton potential, there are two possible trajectories that solve them. The next state is not uniquely determined by the prior state, so asking what makes the ball roll shows that you don't understand the claim (non-determinism ) at hand.
- aipatselarom 2y agoI'm trying to wrap my head around your logic. So, I'll go step by step to make sure I get it. If you were able to perfectly balance the ball on a perfectly constructed dome, blah blah, would the ball stay static indefinitely or would it start rolling down some arbitrary path?
- Certhas 2y agoThe point is that the equations don't tell you what would happen. Both options would be valid according to the equations. This is completely contrary to our intuition about Newtonian mechanics. The question "given this situation, what would happen?" typically has a unique answer is typical. If it does, we have determinism. The observation of Norton's dome is that mathematically this question does not have a unique answer in all situations.
- RHSeeger 2y ago> This is high-school grade physics, come on. And yet, the video in question seems to make it _very_ clear that this has been debated over and over, across various papers and people, and _nobody_ has been able to provide proof as to why it's wrong.
- moralestapia 2y agoIf you even knew the least bit about math and its history, you would know that "no proof given by anyone in 500 years" doesn't mean a thing.