# Topic: Modeling Time and Velocity Using Integers in Relation to the Real Numbers

• eddie
In summary, the conversation discusses the concept of a ball changing from zero velocity to some velocity when released on a slope. The discussion touches on the relationship between potential and kinetic energy, the idea of quantization in free and bound systems, and the difference between classical and quantum mechanics in understanding the ball's motion. The experts mention that the ball's velocity is never truly zero due to atomic motion, and that the first velocity will depend on the time interval chosen for measurement.
eddie
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.

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.

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.
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.

eddie said:
would this contradict the Quantum Theory as it's change of energy would be continuous.
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.

sanpkl
eddie said:
The fundamental question is how does the ball change from zero velocity to some velocity ie. from nothing to something.
I don't see how this is a problem. Care to expand on what you find difficult to understand?

DrClaude said:
I don't see how this is a problem. Care to expand on what you find difficult to understand?
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.

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.
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."

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.

DrewD
eddie said:
The fundamental question is how does the ball change from zero velocity to some velocity ie. from nothing to something ...
Sure it does -- why wouldn't it?
...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.
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.

davenn
eddie said:
.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.

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."
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.

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

eddie said:
I still cannot see how the ball can go from no velocity to some velocity.
Why not? What would prevent it from moving?

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.
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.

Yes.

Bystander
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?
Nothing so what would be it's first velocity?

eddie said:
Nothing so what would be it's first velocity?

DaleSpam said:
Yes.
So what are they?

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.

CWatters
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.
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.

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.

eddie said:
Nothing so what would be it's first velocity?
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##.

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.

DaleSpam 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 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

sophiecentaur 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.
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

eddie said:
I know the answer to what v equals at t=0 but what I'm asking is what v equals next
I understand your question. My question back to you is "which t is next?".

DaleSpam said:
I understand your question. My question back to you is "which t is 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.

eddie 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.

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.
Yes that is what I wanted to go for .

What does it mean for one element of a set to be the next element. Think about mathematical conditions that you could write down to test if something was next.

Several off topic posts and their replies have been deleted. I remind all members to please stay on topic and within PF rules.

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eddie said:
Yes that is what I wanted to go for .

1 / infinity is not a real number, and measurements and their results are described by real numbers. Real numbers form a continuum, and in a continuum there is no "next element" after a given element. So there is no "next instant of time" after ##t = 0##, and therefore no "next velocity" after ##v = 0##. The velocity changes continuously as the time advances continuously.

eddie said:
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 ball is on a flat surface, and I come along and push on it, are you still puzzled that it moves?

Zz.

Excellent answers have been provided, but I just wanted to add one more point.

0 velocity is just a random and arbitrary velocity, and it is relative to some reference frame. If you are traveling in an airplane at 500 mph, you and everything inside the plane have a velocity of 500 mph relative to the ground, yet you might also say that a cup of water on a tray is traveling at 0 velocity relative to you inside the plane. It (the cup of water) has different velocities relative to different frames, and 0 velocity is just 1 of an infinity of choices of reference frames.

So an equivalent to your question of how does an object go from zero velocity to a non-zero velocity might just as well be “How does an object go from say 10 mph to the next higher velocity above 10 mph? or “How does an object go from 2801.63 kilometers per second to some other velocity?” In the end, these and all velocities (less than c) can be considered to be at rest (zero velocity) in some reference frame.

Therefore, due to the relative nature of velocity, in my opinion you are asking in your OP about the nature of acceleration, and in particular what is the smallest increment of acceleration (if any). Perhaps viewing it in this way might help a bit.

CWatters
Closed for moderation due to some recent posts.

EDIT: The thread is reopened after some cleanup. Note, the system described by the OP is not a bound system so, as described in posts 4, 7, and 10, its energy levels are not expected to be quantized.

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DrClaude said:
Energy is only quantized for bound systems. Free particles can have any energy continously.
Can anyone please give simple explanation.

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