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How does anything change?

  1. Jan 18, 2015 #1
    If a ball is held at rest on a slope and then released what is it's next velocity? How can it's velocity change from nothing to something ?If the change from zero is infinitesimally small would this contradict the Quantum Theory as it's change of energy would be continuous.
     
  2. jcsd
  3. Jan 18, 2015 #2
    I don't think this has anything to do with quantum mechanics. By placing the ball onto the ramp, you've inserted potential energy into that system. When you release it, Gravity converts that potential energy to kinetic energy, and it starts to slide down. That is experimentally verifiable.
     
  4. Jan 18, 2015 #3
    The fundamental question is how does the ball change from zero velocity to some velocity ie. from nothing to something .I am aware that the total energy of the system is conserved.Thanks for your reply ,but it has not answered my question.
     
  5. Jan 18, 2015 #4

    DrClaude

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    Energy is only quantized for bound systems. Free particles can have any energy continously. And for a macroscopic object, the spacing between energy levels in the quantized case would be so small as to be unobservable: it would look continuous.
     
  6. Jan 18, 2015 #5

    DrClaude

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    I don't see how this is a problem. Care to expand on what you find difficult to understand?
     
  7. Jan 18, 2015 #6
    Hi thanks for your reply ,I'd like to repeat my fundamental question of what is the ball's next velocity after zero it does change from nothing(zero) to something.Could you tell me if kinetic energy is quantized ,thanks again.
     
  8. Jan 18, 2015 #7

    DrClaude

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    For a free particle, kinetic energy is not quantized. But I don't understand your obsession here with QM: the problem you describe in the OP is classical. For a quantum system, you would have to define what you mean by "held then released" and by a quantum particle "at rest."
     
  9. Jan 18, 2015 #8
    I think the OP is stuck up on Zeno's paradox right now. I.e. What is the first velocity after being at rest? Is it .01? .001? .00000001? .000...? But if it's .000..., then that's just a rest state.
     
  10. Jan 18, 2015 #9

    russ_watters

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    Sure it does -- why wouldn't it?
    As far as is known, the universe is not quantized, so there is no identifiable "next velocity". You have to pick what time interval you want to look at -- the universe doesn't decide for you.
     
  11. Jan 18, 2015 #10

    Dale

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    Energy is quantized in bound systems, but what you describe seems to be a free system where energy would not be quantized. You would have to solve the time independent Schrödinger's equation and see if the solutions are discrete, but I don't think they would be.
     
  12. Jan 18, 2015 #11
    Thanks for your answer to my kinetic energy question.I still would like to know how the ball initially at rest can "jump" to some velocity,it is a similar problem to Zeno's paradox but I still cannot see how the ball can go from no velocity to some velocity.PS.is a "free particle" one that is in equilibrium? if so the ball in question is not a free particle and it's it's kinetic energy that I was referring to.
     
  13. Jan 18, 2015 #12

    Dale

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    Eddie, you have to decide if you want an answer according to classical mechanics or quantum mechanics.

    Why not? What would prevent it from moving?
     
  14. Jan 18, 2015 #13
    Thanks for your reply ,the kinetic energy I was referring to was that of the ball.If it's increase in velocity could be infinitely small then it's kinetic energy would be continuous.
     
  15. Jan 18, 2015 #14

    Dale

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    Yes.
     
  16. Jan 18, 2015 #15
    Nothing so what would be it's first velocity?
     
  17. Jan 18, 2015 #16
    Why,would the answers be different?
     
  18. Jan 18, 2015 #17
    So what are they?
     
  19. Jan 18, 2015 #18

    DaveC426913

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    1] Any object with mass is, in essence, always moving. It's made of atoms and atoms bounce around. It is really meaningless to say that the object's velocity is ever zero. You'd have to average the Brownian motion of every atom in it.

    2] Its "first" velocity will depend on how long you wait to measure it. Since a force is being applied to it, you will have to calculate what its velocity is after a non-zero length of time. So, pick a time. 0.00000000000000000001 seconds? OK, well, after that length of time you can easily calculate its velocity based on F=ma. Too long a delay? try 1x10-20 seconds. Shorter time = smaller velocity. But it'll always be >0 as long as the time is > 0.
     
  20. Jan 18, 2015 #19
    Hi Mr Watters thanks for your excellent answer at last I've got an answer that I understand.I asked the same question of Professor Hawking years ago ,the answer that I got was that he was too busy to give me an answer.
     
  21. Jan 18, 2015 #20
    Thank you Dave for your reply ,my question has been answered by Russ Watters.
     
  22. Jan 18, 2015 #21

    Dale

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    See: http://hyperphysics.phy-astr.gsu.edu/hbase/sphinc.html

    Taking that and solving for velocity we get ##v=\frac{5}{7} g \sin(\theta) t##

    If you want the "first" v then all you have to do is plug in ##g##, ##\theta##, and the "first" ##t##.
     
  23. Jan 18, 2015 #22

    sophiecentaur

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    It is a shame that QM was brought into this so early on. The number of quantum states for a massive ball is huge and that number would actually depend upon the mass / size of the ball. That would make it impossible to answer such a question with a definite number - plus the fact that we are really talking in terms of a 'drift velocity' - just as with electrons in an electric current. If we're not talking about individual atoms / molecules in the gaseous state, then quantum levels are really just a distraction.
     
  24. Jan 18, 2015 #23
    Hi thanks for the effort you have made to answer my question ,I know the answer to what v equals at t=0 but what I'm asking is what v equals next.I think you will find there is no answer to this question at the present time ,russ watters has stated there is no "next" velocity as the energy of the universe is not quantized
     
  25. Jan 18, 2015 #24
    Hi Sophiecentaur thanks for your reply, the partial answer was given to me by russ watters stating that the energyy of the universe is not quantized and hence there was no "next velocity" after zero time .But the problem is that there is
     
  26. Jan 18, 2015 #25

    Dale

    Staff: Mentor

    I understand your question. My question back to you is "which t is next?".
     
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