# What is the slowest Velocity possible?

1. Mar 14, 2006

### Chaos' lil bro Order

This question may sound dumb, but what is the slowest Velocity possible?

Say a car is parked in a parking lot perfectly flat on the concrete ground, is the car perfectly still? Or does the interactions of the cars tire with the concrete produce a tiny flux in movement? I'm guessing that if there is a tiny flux in movement that it cancels out to zero for all macroscopic observations. Lets assume that all background noise is zero for the sake of argument.

2. Mar 14, 2006

### chroot

Staff Emeritus
In classical terms, the minimum possible velocity is quite obviously zero.

In quantum-mechanical terms, the minimum possible momentum is limited by the Heisenberg Uncertainty Principle. If you have no knowledge of where a particle is, you can have compete knowledge of its momentum. In such a situation, it can still be arranged for the particles involved to have zero velocity with respect to some observer.

It doesn't make much sense (i.e. it's not very useful) to describe a car with quantum mechanics; decoherence makes objects like cars behave purely classically.

- Warren

3. Mar 14, 2006

### Chaos' lil bro Order

Ok thanks, guess it was a dumb question.

4. Mar 14, 2006

### vanesch

Staff Emeritus
Well, for fun, you could do an estimation: take a car of 1000 kg, and assume that we know the position up to 10 micrometers.
That gives us an uncertainty on momentum of ~ 10^(-34) Js/ 10^(-5)m = 10^(-29) kg m/s, or an uncertainty in velocity of 10^(-32) m/s (given the mass of 1000 kg).

So, given that we know the position of the car up to 10 micrometers, and that the velocity is uncertain (and hence of the order of) 10^(-32) m/s, in order for us to notice a movement of the car (meaning, that it moves for more than 10 micrometers), we'd have to wait for: 10^(-5)/10^(-32) s = 10^27 seconds, or ~10^19 years, which is about one billion times the age of the universe. In the mean time, probably the car will have evaporated.

5. Mar 14, 2006

### Ivan Seeking

Staff Emeritus
I used to wonder if I might diffract if I walk through a doorway slowly enough.

6. Mar 14, 2006

### Danger

You'll diffracture if you're blocking Tsu's path. :tongue:

7. Mar 14, 2006

### Loren Booda

Could the ratio of Planck length to Hubble time be a significant lower limit for quantized velocity?

8. Mar 14, 2006

### chroot

Staff Emeritus
There's nothing special about the Hubble time. In fact, it's always changing.

As I've said, in both classical and quantum mechanics, there is no lower limit to velocity.

- Warren

9. Mar 14, 2006

### pallidin

Since there is no "universal" referance frame regarding absolute static locality, the question is impossible to answer.
However, it CAN be reasonably inferred that there is no evidence in non-motion.