# Is velocity incremental when measured precisely?

• golmschenk
In summary: 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. But, if distance is not quantized at the Planck length, then how is energy quantized? Since the energy of a free particle is, in general, not quantized. So, if a function, such as distance, is necessarily continuous (and differentiable), than its derivative (velocity here) is also continuous, but if distance is not quantized at the Planck length
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.

golmschenk said:
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.

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.

Planck length - Wikipedia said:
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.

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.

Lsos said:
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.

## 1. What is velocity?

Velocity is a measure of an object's speed and direction. It is a vector quantity, meaning it has both magnitude (speed) and direction.

## 2. How is velocity different from speed?

While velocity and speed are both measures of how fast an object is moving, velocity also includes the direction of the movement, whereas speed does not.

## 3. How is velocity measured precisely?

Velocity can be measured precisely using a variety of methods, including radar guns, GPS systems, and high-speed cameras. These methods allow for accurate measurement of an object's speed and direction at a specific moment in time.

## 4. Is velocity incremental when measured precisely?

Yes, velocity can be measured incrementally when measured precisely. This means that it can be measured in small, specific intervals, allowing for a more accurate understanding of an object's motion.

## 5. How does precision affect measurements of velocity?

The more precise the measurements are, the more accurate the velocity calculation will be. This is because precise measurements allow for smaller intervals to be measured, resulting in a more accurate average velocity over a given time period.

• Quantum Physics
Replies
25
Views
670
• Introductory Physics Homework Help
Replies
33
Views
557
• Mechanics
Replies
1
Views
321
• Quantum Physics
Replies
3
Views
606
• Mechanics
Replies
42
Views
5K
• Mechanics
Replies
1
Views
4K
• Mechanics
Replies
11
Views
12K
• Quantum Physics
Replies
21
Views
1K
• Quantum Physics
Replies
16
Views
484
• Classical Physics
Replies
9
Views
1K