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.axmls said: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.
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.eddie said:would this contradict the Quantum Theory as it's change of energy would be continuous.
I don't see how this is a problem. Care to expand on what you find difficult to understand?eddie said:The fundamental question is how does the ball change from zero velocity to some velocity ie. from nothing to something.
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.DrClaude said:I don't see how this is a problem. Care to expand on what you find difficult to understand?
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."eddie said: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.
Sure it does -- why wouldn't it?eddie said:The fundamental question is how does the ball change from zero velocity to some velocity ie. from nothing to something ...
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....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.
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.eddie said:.Could you tell me if kinetic energy is quantized ,thanks again.
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.DrClaude said: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."
Why not? What would prevent it from moving?eddie said:I still cannot see how the ball can go from no velocity to some velocity.
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.DaleSpam said: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.
Nothing so what would be it's first velocity?DaleSpam said: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?
Why,would the answers be different?eddie said:Nothing so what would be it's first velocity?
So what are they?DaleSpam said:Yes.
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.russ_watters said: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.
Thank you Dave for your reply ,my question has been answered by Russ Watters.DaveC426913 said: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.
See: http://hyperphysics.phy-astr.gsu.edu/hbase/sphinc.htmleddie said:Nothing so what would be it's first velocity?
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 quantizedDaleSpam said: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##.
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 issophiecentaur said: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.
I understand your question. My question back to you is "which t is next?".eddie said:I know the answer to what v equals at t=0 but what I'm asking is what v equals next
That's a good question ! how about minus infinity.I think we are getting to the crux of the matter.I'm very surprised that you are still helping me with this problem ,thank you.Also thank you for not trying to baffle me.DaleSpam said:I understand your question. My question back to you is "which t is next?".
This is a nonsensical value.eddie said:how about minus infinity.
Yes that is what I wanted to go for .DaveC426913 said:This is a nonsensical value.
We are talking about a lapse of time after t=0. Minus infinity does not make sense.
I wonder if what you were going for was 1 / infinity. i.e. an infinitesimally small lapse of time.