What is the smallest possible velocity?

[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.

 

[Dale]

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

I agree that it is the fundamental velocity

 

[Vanadium 50]

Smallest possible distance

Smallest possible time:

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.

 

[Nugatory]

Smallest possible distance: Planck unit
Smallest possible time: Planck time

That's not what the Planck time and distance are, but this misunderstanding is so common that we have an Insights article about it: https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/

 

[Peter88]

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

 

[lewando]

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

 

[Peter88]

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

 

[weirdoguy]

But you guys are contradicting my math?

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

 

[DrGreg]

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

We're not contradicting your maths. We are contradicting your initial assumptions:

Smallest possible distance: Planck unit
Smallest possible time: Planck time.

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

That's not what the Planck time and distance are, but this misunderstanding is so common that we have an Insights article about it: https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/

 

[Merlin3189]

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

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.

 

[weirdoguy]

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

 

[Dale]

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

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?

 

[Peter88]

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?

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?

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

 

[SammyS]

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

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

 

[weirdoguy]

I mathematically proved a minimum velocity based on minimal distance and time.

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.

 

[Nugatory]

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

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.

 

[Dale]

I did not say I "wanted something small".

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?

 

[Peter88]

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 loan with the minimum duration or the maximum duration?

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.

 

[phinds]

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.

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?

 

[Dale]

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.

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?

 

[Peter88]

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?

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

 

[phinds]

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

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.

 

[SammyS]

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

What is the Planck unit you propose for this ?

 

[Dale]

That has nothing to do with this.

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.

 

[mfb]

What is the smallest change in unit position per unit time?

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.

 

[fresh_42]

The question is answered (multiple times) and isn't really of any value. The moment the overall movement of a body is slower than the movement of its outer electrons the question becomes meaningless.

Thread closed.