# B Does c = ℓP/tP ?

1. Nov 13, 2016

### danihel

Hi, i'm no physicist and i have no clue how stupid this question is and i know how it would be possible to verify if its true, knowing 'c' in 'm/s' but the numbers are so huge (or small) i don't think i have a calculator that could do that.

So is the speed of light one Planck length per one Planck time in vacuum?

2. Nov 13, 2016

### PeroK

Who needs a calculator? Just look up the definitions.

3. Nov 13, 2016

### danihel

haha i'm sorry i'm a retard, i thought i read it and just assumed the definition is just something like that those are the smallest units of space-time. Well now i know. Thanks and sorry.

4. Nov 13, 2016

### danihel

So object that constantly moves half the speed of light literally stays every other planck time at the same position, and object that moves third of c changes position on every third tP?
thats weird

5. Nov 13, 2016

### PeroK

What makes you think it does that?

6. Nov 13, 2016

### danihel

Well lP is the smallest distance it can travel, so if it moves 2tP/1lP which is c/2 (if i'm not wrong) then it has to stay at the same spot for two tP units because 1tP/0.5lP doesn't exist. So even when object is pulled by some force or gravity it somehow works only on every n-th time

7. Nov 13, 2016

### PeroK

The Planck length and Planck time have no such relevance to the theory of motion.

8. Nov 13, 2016

### danihel

so is it possible for an object to travel less then one Planck length unit?

9. Nov 13, 2016

### danihel

or does it have to do with the uncertainty principle, that at such small scales the object can't by pinpointed so the idea of how much it moves has no substance?

10. Nov 13, 2016

### PeroK

How would you ever know? Your questions are increasingly mixing up different concepts from different parts of physics and that's making it very difficult to answer.

First, time and space are modelled as a continuum, not as a sequence of discrete steps. In theory, you can pick any time $t$, it doesn't have to be a number of Planck times. And space is not divided up into a grid of discreet Planck lengths.

It may be a common misconception that the Planck units divide up space and time as you thought and somehow enforce a theory of motion as you describe, but there is no evidence (indeed, owing to the scales involved, there can be no evidence) for this.

Last edited: Nov 14, 2016
11. Nov 13, 2016

### danihel

I thought as there is no fluent transition between energy states, there can't be fluent transitions in position when those changes occur and that the lP is the smallest distance a particle can move. I'm sorry, I'm very curious about this, but i don't really understand physics, certainly not most of the math beyond Newton's laws.

12. Nov 13, 2016

### ZapperZ

Staff Emeritus
Why are you "very curious" about, of all things, this?

Zz.

13. Nov 13, 2016

### Staff: Mentor

What makes you think there isn't?

14. Nov 13, 2016

### Staff: Mentor

As far as we know, yes. The Planck length is so small that it's hard to do experiments ("hard" means that no one has come close yet) but there's no reason so far to think that the Planck length is some sort of minimum distance, or that there is any problem with a speed of less than one Planck length per Planck time.

We have an insights article that you might want to read: https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/

15. Nov 14, 2016

### danihel

By “this” I meant more generally, how the world works on a fundamental level.

If I recall well, various popular sources like documentaries and some science podcasts mentioned that particles can occupy only certain energy states derived from the Planck constant.

I was also puzzled by that since if ‘E= hf’ and ‘f’ doesn’t have to be an integer then ‘E’ can be equal to any number anyway.

So it seems like I got it all completely wrong.

16. Nov 14, 2016

### PeroK

To take one point about the energy of a particle. In some systems, like the harmonic oscillator, infinite square well or an electron in the hydrogen atom, a particle can have only certain energy levels. If you measure its energy, you get one of certain discrete values. These energy levels are not multiples of the Planck units, but are determined by the system: e.g. by the width of the well; or by the electric charge on the electron and proton.

But, a free particle, has no such constraint and, when measured, can have any energy level.

The idea, possibly promoted by pop science, that "energy is quantized" and every energy you will ever measure is a number of units of some fundamental "Planck energy" is wrong.

17. Nov 14, 2016

### danihel

Thanks PeroK for making that clear! I guess i'll stop watching documentaries on physics, they just seem to make me dumber.

18. Nov 14, 2016

### Staff: Mentor

There is this problem with popular sources and documentaries.... You can't fit a semester-long intro to QM class into an hour-long documentary so they have to leave a lot of stuff out.

What's really going on here (and of course I can't fit a semester-long intro to QM class into a forum thread so I'm leaving a lot out too) is that the energy states are calculated from Schrodinger's equation. Planck's constant does appear in that equation, and for many important problems (electrons in an atom, for example) the solutions come in discrete steps with no in-between values. That's what the sources you've been reading are talking about. However, in other problems (most notably, a particle moving freely through space) the solutions are continuous.

19. Nov 15, 2016

### danihel

Thanks Nugatory for the explanation! Now i have a clearer picture about the role of Planck constant.