4mo ago

The Dome Paradox: A Loophole in Newton's Laws

TLDW

A paper, by philosopher of physics John Norton, describes a scenario in which a ball is placed at the apex of a perfectly smooth and frictionless dome. The paper argues that, according to Newton's laws, the ball will spontaneously start rolling down the dome at some random time, without any external force acting on it. Norton's claim suggests that Newtonian mechanics may not a deterministic theory or that there are multiple possible interpretations.

https://sites.pitt.edu/~jdnorton/papers/DomePSA2006.pdf

23 comments

I don’t watch YouTube videos with those stupid clickbait thumbnails out of principle, if it was a serious video worth watching they wouldn’t resort to that.
- 1000% agreed
  The thumbnail also indicates it's 95% waffle and 5% info
- you must be fun at parties
  
  You must waste literally years of your life listening to someone pad out a video for clicks

As a total amateur my instinctive response to the "unexpected" result is to validate that apply Newtonian physic is appropriate, and if not, we should look for an explanation at a level where the unexpected phenomenon becomes possible, aka non-Newtonian physics. We know that Newtonian physics works fine until we try to explain things at the atomic or subatomic level, or under extreme gravity, or close to the speed of light. Why not the same at extremely small points on a dome?
The dome used is the same shape as the graph she showed. The closer to zero you get on the graph the more vertical the line "looks", but with enough resolution in the data it becomes clear line is never vertical except at the starting position of zero. When you make a dome based on the same curve the zero point is so small that it falls into the realm of non-Newtonian physics where you run into uncertainty. I can't do the maths myself but I'm going to guess the zero point needs to be subatomic in size for the "unexpected" excitation event to have an impact. If true, and the zero point is too large, the ball is going to remain stationary until an explainable force acts on it.
I'm guessing the ball needs to be a perfect sphere. Does the maths incorrectly neglect the ball?
Edit - I feel like I used non-Newtonian wrong when I should have used quantum or something instead. But hopefully it made sense enough to see my point.
- Yes, it is actually stated in the paper. This is a result about newtonian theory, not about real world physics
- It's nothing so obvious given that plenty of people tried to point out holes in the logic. The issue is with the notion of causality and there being multiple possible future states that are all equally valid.
  
  My point is, the zero point has to be so small it becomes subject to the uncertainty principle, which is not a Newtonian law. So while the maths might resolve to the unexpected excitation event it doesn't make sense in reality because we don't apply Newton's laws at the tiny point sizes needed here?
  When you plug crazy small numbers into Newton's laws don't the answers stop making sense, so you have to use Einstein rather than Newton's physics?
  So frequently, philosophy forces us to think about wonderful ideas that lead us to amazing realisations, but so often those same ideas breakdown when applied to reality. This is where physics steps in.

What? An object at rest stays at rest unless acted upon by an outside force. If there are no outside forces, there is no reason for it to roll off.
- This wouldn't be an open debate in the scientific community if there was a clear cut answer. You should let all the experts know you've figured it out though.
  
  I've never heard of this being an open debate, and I don't see anything in the paper that explains why this would be a "loophole" in Newton's laws. What am I missing here?

I see some people are having issues with the scenario, but it's not as impossible as it seems. The key is that Newtonian mechanics are in principle time-reversible. If a system got to a state one way, it can get back to the state it was by running it backwards, so to speak. A ball going down an inclined plain with a given kinetic energy could be going up that inclined plain up to the top with that same amount of energy.
The problem with these systems is, it's possible to impel the right amount of force on a mobile so that it goes through a path and then stops. But since there is time reversibility, it should be possible for the mobile to spontaneously start moving from that stopping point and draw the same path.
Other weird similar cases are the so-called space invader (particle going to infinity, and therefore spontaneously appearing in reverse) and some strange n-body problem cases.
- It's not spontaneously starting to move from rest. There was a force exerted on it to cause it to stop. That force will cause it to start moving in time-reversal.
  
  The loophole here is that the motion starts so smoothly from rest that there is still no force at the starting point, but that it rather appears simulatneously with the motion

This was a very interesting read !
I get the impression that the author considers Newtonian theory as completely disconnected from reality just because we know it to not hold in every context, and hence practical considerations should not be used to call the apex motion unphysical.
However, the needed infinite precision would make the experiment impossible to set up even if Newtonian mechanics held at microscopic level, just because of measurement erros, as well as wind, earth shaking, ...
- The discussion about whether Newton's first law actually states that the forces are first causes for the motion is very interesting. However, I do not find the comparison with the harmonic oscillator appropriate : vanishing instantaneous acceleration at one point in time (like in the harmonic oscillator) is not the same thing as an inertial motion.

Math is an approximation, when applied to physics. Sometimes the approximation is useful, sometimes it is not useful.
Math, by itself, does not care about physical realities, it just provides a model that may or may not be helpful to approximate reality

23 comments