Is velocity incremental when measured precisely?

[golmschenk]

I know many values become incremental when you go into very precise measurements in quantum physics and whatnot. Angular momentum, spin, etc. When measured very precisely does velocity become incremental? I wouldn't think that would make much sense intuitively, but then again, neither does spin. Or does the uncertainty principle get in the way somehow? Just a random thought. I know it may be a very strange question with a simple explanation, but let me know. Thanks.

 

[Neo_Anderson]

I know many values become incremental when you go into very precise measurements in quantum physics and whatnot. Angular momentum, spin, etc. When measured very precisely does velocity become incremental? I wouldn't think that would make much sense intuitively, but then again, neither does spin. Or does the uncertainty principle get in the way somehow? Just a random thought. I know it may be a very strange question with a simple explanation, but let me know. Thanks.

Mathematically, velocity is a continuous function. For this reason, velocity is not 'incremental' (discreet), but always continuous. As far as I understand, the HUP does not apply to velocities. The HUP does not apply to accelerations (derivative of velocity), thus it must not necessarily apply to velocities.

 

[Danger]

I have no education, so I might be way off-base here. Isn't the Planck length considered the minimum distance that something can move? If so, then speed would have to be incremental in those units.

 

[Char. Limit]

Contrary to statements sometimes found in the popular press, there is no evidence to suggest that distances in space are quantized in units of the Planck length.

Sorry about quoting Wikipedia, but this seems to suggest that distance is not quantized at the Planck length. Heck, "seems to suggest"? The article explicitly states it.

So, if a function, such as distance, is necessarily continuous (and differentiable), than its derivative (velocity here) is also continuous.

I think.

 

[Lsos]

No education here either...but, if not distance, then at least energy is quantisized. Since the motion of an object can be translated into its energy, and energy is quantisized, it follows that its motion must be quantisized, or incremental, as well.

 

[Dale]

No education here either...but, if not distance, then at least energy is quantisized. Since the motion of an object can be translated into its energy, and energy is quantisized, it follows that its motion must be quantisized, or incremental, as well.

I think there is a general misunderstanding of quantization of energy. The quantization of energy only applies to bound states. The energy of a free particle is, in general, not quantized.

Since the energy of a bound state is quantized then I guess you could say something to the effect that the "motion" of a bound state is quantized, but it is hard to speak meaningfully about motion in a bound state anyway. On the scale of a bound state wavefunction it is not as though you have a little billiard ball whipping around with some well defined velocity and position.