Conservation of momentum - problem?

[two-penneth]

Can't remember the formula, but it does occur to me that, for instance, a bee hitting a train coming in the opposite direction has at some point to change direction as it is carried with the train. if I remember correctly, this would mean that one side of the equation is 'zero', therefore so must the other side. In effect, has the bee stopped the train, even for a fraction of a second? If so, how does anything move anywhere?

[jake-the-peg]

I think you're confusing maths and physics vascop.

You can't apply Newtonian ideas of physics to indefinately small intervals.

At some point you will come smack into the Heisenberg uncertainty principal and Quantum mechanics will cause your nice little deterministic Universe fall apart.

[Symmetryigr8]

The equations imply states
momentum train + momentum bee = a constant number
So if train has +10 and bee has -1 to start then the constant =9
So after bee stops and has momentum=0 then
momentum train + momentum bee=momentum train+0=9
New momentum train=9
Therefore the train has a smaller momentum and assuming a constant mass has a lower velocity.

jake and vascop i think you are confusing practicality with pedantry, yes calculus does work on the approximation that values like time,area or speed can be infinitely small and yes quantum mechanics does say this approximation has limits. But the fact remains that calculus is used in dynamics and does an excellent job of describing instantaneous velocities and positions. largely because the quantum mechanical disturbances decay very rapidly over time. Imagine a time distance plot, gradient is velocity. At the most accurate the line would be very jagged as QM changes the velocity by introducing an error in certainty. But calculus treats the line by extrapolating the trend to a new point, at a new point beyond the end of the line both lines are stupidly close because the random changes and statistical approximation of calculus cause the same fuzziness in the exact position of the line. For these purposes calculus is instantaneous.

[Symmetryigr8]

Although to go back a step in the discussion jake was right about not being able to tell from a photo, Hamilton cracked this when he sussed Xeno's paradox.

[schonovic]

even the weakest photons warp space to a degree so there is an interchange of movement warpage which requires a momentary freeze of time between both objects.

[schonovic]

even the weakest photon warps space to some degree or there would be no movement; so there is a moment of time dilation, in acordance to relativity,between the two objects before the weaker photons of the bee could change directions.

[schonovic]

even the weakest photons warp space (or there would be no movement) so there has to bee a moment of transfer of warp momentum between the two objects where time is zero.

[Rev. Green]

Sorry folks, I don't see the problem here. When the bee stops dead a tiny piece of the train also stops dead. Most of the train continues as before. Immediately afterwards, the small piece of train, and the remnents of fly, move at almost the original speed of the train.