# B Smallest possible velocity

1. Jul 22, 2017

### Peter88

Hey I wonder if there is a smallest possible velocity. There should be mathematically speaking.

Smallest possible distance: planck unit
Smallest possible time: planck time
Velocity: distance/ time

If we have fundamental distance and time then we have fundamental velocity.

2. Jul 22, 2017

### Staff: Mentor

Planck distance/Planck time = c which is the largest possible speed, not the smallest.

I agree that it is the fundamental velocity

3. Jul 22, 2017

Staff Emeritus
Not true.

There is nothing magical about Planck units. The Planck resistance is 30 ohms. Resistances both above and below this occur all the time.

4. Jul 22, 2017

### Staff: Mentor

5. Jul 23, 2017

### Peter88

But you guys are contradicting my math? Im deriving minimal possible values from other minima.

6. Jul 23, 2017

### lewando

If you are looking for small velocity, then d should be small and t should be large.

7. Jul 23, 2017

### Peter88

But then how do we measure the smallest change in position per unit time aka the smallest velocity?

8. Jul 23, 2017

### weirdoguy

Do you know and understand what things you are using in your math? Planck lenght is not the smallest possible distance. We don't even know if there is one!

9. Jul 23, 2017

### DrGreg

That is simply wrong. Did you not read the following?

10. Jul 23, 2017

### Merlin3189

I've no idea what Plank's units are (I promise I'll read the Insight), but " the smallest change in position per unit time" means simply, the smallest change in position per arbitrary amount of time. So the result could be anything (well, perhaps not zero nor infinite.)
Unit time is a second in SI, but could have been chosen to be a minute, an hour, a year, the time it takes the earth to rotate by one radian, the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of some other atom, etc. The unit of time known as the second can hardly be the shortest possible time if we can divide it into 9 192 631 770 parts.

11. Jul 23, 2017

### weirdoguy

And I would say that the smallest possible speed is 0, in any units you choose

12. Jul 23, 2017

### Staff: Mentor

In addition to what others have said about Planck units not being minima, if you want something small do you want to divide by a large number or a small number?

13. Jul 23, 2017

### Peter88

I did not say I "wanted something small". I mathematically proved a minimum velocity based on minimal distance and time.

14. Jul 23, 2017

### SammyS

Staff Emeritus
A velocity based on minimal distance and time is not a minimum at all. That's what Dale was referring to.

Last edited: Jul 23, 2017
15. Jul 23, 2017

### weirdoguy

Um, no. You did not prove anything. You didn't even finish your calculations! If you did, you would notice that (as Dale said in post #2) what you got is speed of light which is the largest possible speed.

16. Jul 23, 2017

### Staff: Mentor

If there were a minimum distance and a minimum time (and there isn't, because the Planck time and distance aren't what you think they are), you'd be able to prove a maximum velocity, not a minimum. The maximum possible speed would be one minimum distance per minimum time, but nothing would prevent an object from taking longer than the minimum time to cover the minimum distance - and that's a slower speed.

17. Jul 23, 2017

### Staff: Mentor

A minimum is a smallest possible value.

Let me ask this question. If you want to have the minimum monthly payment, do you want to get a (0% interest) loan with the minimum duration or the maximum duration?

Last edited: Jul 23, 2017
18. Jul 23, 2017

### Peter88

That has nothing to do with planck units, correct me if I am wrong. I am talking about the smallest observable change in location per unit time.

19. Jul 23, 2017

### phinds

And you are doing it very badly. It has been pointed out to you that the Plank Length is NOT the smallest unit of distance. Do you not believe this?

20. Jul 23, 2017

### Staff: Mentor

You are wrong and have been corrected multiple times. Please answer the question. Here is the same question in a more relevant form:

If Alice drove 100 km in 1 hour and Bob drove 100 km in 2 hours, then who drove slower?

21. Jul 23, 2017

### Peter88

That has nothing to do with this. What is the smallest change in unit position per unit time? Clearly the value derived from planck units

22. Jul 23, 2017

### phinds

You know, you can keep saying that over and over (in fact you HAVE said it over and over) but that does not make it right. I suspect the mods will just give up on you now, since you clearly aren't listening and we are wasting our time with you.

23. Jul 23, 2017

### SammyS

Staff Emeritus
What is the Planck unit you propose for this ?

24. Jul 23, 2017

### Staff: Mentor

Yes, it does. 100 km / 1 hr = 100 kph and 100 km / 2 hr = 50 kph. 100 kph > 50 kph.

So the smallest velocity is the smallest distance divided by the largest time. Since there is no known smallest distance nor any known largest time there is no known smallest velocity.

25. Jul 24, 2017

### Staff: Mentor

There is no such thing.
You can travel 1 Planck length per 2 Planck times. You can travel 1 Planck length per 100 Planck times. You can travel 1 Planck length per 100 million Planck times. The last one is actually possibly by foot.