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Is Newtonian physics nondeterministic? http://personal.lse.ac.uk/robert49/teaching/methodologies/pdf/Norton.pdf http://personal.lse.ac.uk/robert49/teaching/met

Is Newtonian physics nondeterministic? http://personal.lse.ac.uk/robert49/teaching/methodologies/pdf/Norton.pdf http://personal.lse.ac.uk/robert49/teaching/methodologies/pd...

Koshkin 10y ago
Newtonian mechanics does not support the idea of a "spontaneous movement". On the other hand, the theory is incomplete (by Goedel), so it is inevitable that there are assertions that cannot be proved (or disproved) based on just Newton's Laws.
- tgb 10y ago
  It's incomplete not by Godel, it's incomplete because Newtonian mechanics doesn't even attempt to describe most forces. It describes what forces are and how they act, but then it is left up to the reader to experimentally determine what forces there are in the universe. The only specified forces are gravitational.
  - lisper 10y ago
    That's not quite true. The third law (every action has an equal and opposite reaction) places hard constraints on what forces are possible. For example, if there is an apple resting on the table in front of me I can observe that it is not accelerating despite being in a gravitational field. I can deduce therefore that something must be exerting an upward force to counter the force of gravity, and that it's probably the table. Of course, Newton doesn't let me prove it's the table. It could be, for example, an apple-suspending demon which only acts in the presence of tables (and other solid objects). Newton does not allow me to eliminate that possibility (but Occam does).
  - Koshkin 10y ago
    > doesn't even attempt to describe most forces Well, in a way it does, as long as these forces are "conservative", which includes gravitational field that you mentioned as well as (static) electric field. On the other hand, you are correct, it is not a goal of classical mechanics as a mathematical theory to describe any specific physical force in particular. In that sense it can be seen as "incomplete" - as a physical theory. But classical mechanics as a (modern) physical theory is not only "incomplete", it is also plain "wrong"! (But that is a topic for another time, perhaps.)
danbruc 10y ago
No, it is not. I can not exactly pin down where the mistake in the linked paper is after looking at it for five minutes but I am pretty sure it is related to his choice of r(t) in equation 4 as a piecewise polynomial so that a t = T there is a discontinuity in the 4th derivative which is non-physical, i.e. without a force tangential to the dome at the apex the object would never move away from the apex of the dome. If you only look at lower order derivatives like velocity and acceleration, then there is no discontinuity and everything seem superficially fine.
- kurthr 10y ago
  I agree, this is likely a joke paper. I find it fairly hilarious since at it looks like the standard Divide by Zero algebra problem, but then error after error compounds the result. The first error appears to be in an un-numbered equation: sin(theta)=dh/dr which is equal to 0 at r=0!! which is then substituted into the differential equation: F=g dh/dr = sqrt(r) = d^2r/dt^2 again equal to ZERO at r=0 Of course this is also an abuse of Leibniz notation (mathematicians squirm whenever physicists do this sort of "algebra" on differentials) which is then integrated twice and then differentiated twice (ignoring constants of integration) to get the equations for r(t) and a(t). The second key is the square root, which allows for multiple solutions of the differential equation (one of which is the normal r=a=0), but that's just part of the side show. Physics has all sorts of "non-physical" results from integrations, DiffEq, etc. A classic being a negative time solution to parabolic trajectories. I would add the use the statistics of continuos probability distributions to say that there is in fact ZERO probability that any ball is at r=0 just to complete the silliness. Perhaps he's willing to co-author a follow up?

Is Newtonian physics nondeterministic? http://personal.lse.ac.uk/robert49/teaching/methodologies/pdf/Norton.pdf http://personal.lse.ac.uk/robert49/teaching/methodologies/pd...

Koshkin 10y ago

Newtonian mechanics does not support the idea of a "spontaneous movement". On the other hand, the theory is incomplete (by Goedel), so it is inevitable that there are assertions that cannot be proved (or disproved) based on just Newton's Laws.

tgb 10y ago
It's incomplete not by Godel, it's incomplete because Newtonian mechanics doesn't even attempt to describe most forces. It describes what forces are and how they act, but then it is left up to the reader to experimentally determine what forces there are in the universe. The only specified forces are gravitational.
- lisper 10y ago
  That's not quite true. The third law (every action has an equal and opposite reaction) places hard constraints on what forces are possible. For example, if there is an apple resting on the table in front of me I can observe that it is not accelerating despite being in a gravitational field. I can deduce therefore that something must be exerting an upward force to counter the force of gravity, and that it's probably the table. Of course, Newton doesn't let me prove it's the table. It could be, for example, an apple-suspending demon which only acts in the presence of tables (and other solid objects). Newton does not allow me to eliminate that possibility (but Occam does).
- Koshkin 10y ago
  > doesn't even attempt to describe most forces Well, in a way it does, as long as these forces are "conservative", which includes gravitational field that you mentioned as well as (static) electric field. On the other hand, you are correct, it is not a goal of classical mechanics as a mathematical theory to describe any specific physical force in particular. In that sense it can be seen as "incomplete" - as a physical theory. But classical mechanics as a (modern) physical theory is not only "incomplete", it is also plain "wrong"! (But that is a topic for another time, perhaps.)

danbruc 10y ago

No, it is not. I can not exactly pin down where the mistake in the linked paper is after looking at it for five minutes but I am pretty sure it is related to his choice of r(t) in equation 4 as a piecewise polynomial so that a t = T there is a discontinuity in the 4th derivative which is non-physical, i.e. without a force tangential to the dome at the apex the object would never move away from the apex of the dome. If you only look at lower order derivatives like velocity and acceleration, then there is no discontinuity and everything seem superficially fine.

kurthr 10y ago
I agree, this is likely a joke paper. I find it fairly hilarious since at it looks like the standard Divide by Zero algebra problem, but then error after error compounds the result. The first error appears to be in an un-numbered equation: sin(theta)=dh/dr which is equal to 0 at r=0!! which is then substituted into the differential equation: F=g dh/dr = sqrt(r) = d^2r/dt^2 again equal to ZERO at r=0 Of course this is also an abuse of Leibniz notation (mathematicians squirm whenever physicists do this sort of "algebra" on differentials) which is then integrated twice and then differentiated twice (ignoring constants of integration) to get the equations for r(t) and a(t). The second key is the square root, which allows for multiple solutions of the differential equation (one of which is the normal r=a=0), but that's just part of the side show. Physics has all sorts of "non-physical" results from integrations, DiffEq, etc. A classic being a negative time solution to parabolic trajectories. I would add the use the statistics of continuos probability distributions to say that there is in fact ZERO probability that any ball is at r=0 just to complete the silliness. Perhaps he's willing to co-author a follow up?