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

[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.

 

[axmls]

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.

 

[eddie]

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.

 

[DrClaude]

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.

 

[DrClaude]

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?

 

[eddie]

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.

 

[DrClaude]

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."

 

[axmls]

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.

 

[russ_watters]

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.

 

[Dale]

.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]

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.

 

[Dale]

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

I still cannot see how the ball can go from no velocity to some velocity.

Why not? What would prevent it from moving?

 

[eddie]

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.

 

[Dale]

Yes.

 

[eddie]

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]

Nothing so what would be it's first velocity?

Why,would the answers be different?

 

[eddie]

Yes.

So what are they?

 

[DaveC426913]

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]

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.

 

[eddie]

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.

Thank you Dave for your reply ,my question has been answered by Russ Watters.

 

[Dale]

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" $t$.

 

[sophiecentaur]

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.

 

[eddie]

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

 

[eddie]

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

 

[Dale]

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?".

 

[eddie]

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.

 

[DaveC426913]

how about minus infinity.

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.

 

[eddie]

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 .

 

[Dale]

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.

 

[Drakkith]

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