Is the Speed of Light Tied to the Plank Distance and Time?

[Quinzio]

My question is:
since there exists a Plank time and a Plank distance, is it true or false that any speed and the speed of light in particular must be a multiple of (Plank distance)/(Plank time) ?

Am I saying something nonsense ?

 

[Fredrik]

It's not nonsense, but it would be a mistake to think that there's a theory-independent answer. Questions like these can only be answered by theories, and different theories may give you different answers.

SR and GR both say no. The Planck length is just a number like any other, and has no special significance.

In non-relativistic or special relativistic QM, I would have to ask "the speed of what?" since there are no classical point particles. If you're referring to e.g. the speed associated with a momentum eigenstate, then the answer is still no.

A quantum theory of gravity might give you an answer different from no, but I still don't think it would be yes. I think it would be more complicated.

 

[mfb]

The Planck units are defined such that the speed of light is the fraction (Plank distance)/(Plank time), every object with mass has to be slower than that.
Neither of them has to be a "smallest possible unit" of space or time, our current theories are just unable to (properly) describe processes at this scale.

 

[Dale]

is it true or false that any speed and the speed of light in particular must be a multiple of (Plank distance)/(Plank time) ?

It is false. I often travel at 100 kph wrt the surface of the earth, and 100 kph is not an integer multiple of (Plank distance)/(Plank time).

 

[Naty1]

Thank goodness Dalespam just posted...I don't understand the first two posts...

As I understand Planck scale it is where the concepts of size, distance, time, break down as quantum indeterminacy becomes overwhelming. It's a range of values where our current theories no longer are reliable...where we need a theory of quantum gravity to merge GR and QM. This doesn't mean that some new theory might not form some sort of a relation ship as is suggested, but that seems beyond our reach so far.

 

[phinds]

It is false. I often travel at 100 kph wrt the surface of the earth, and 100 kph is not an integer multiple of (Plank distance)/(Plank time).

Dale, I agree w/ your contention that it is false, but I have a quibble about your example and I'm curious if we could come up with a better one.

Here's my problem. "100 MPH" is a measured unit that is SO gross in granularity that it doesn't make sense to say that it is not an integer multiple of Pd/Pt as you've contended since even if we could measure it to 15 decimal places, it still would be VERY gross relatively speaking and COULD in fact be an integer multiple.

Unless you want to posit "100.000MPH out to 50 decimal places" (or thereabouts) it doesn't work and I can't think of anything that does even though I still agree w/ you.

 

[Fredrik]

I think DaleSpam's point (as well as mfb's) was that 1 Planck length per Planck time is the speed of light, 299792458 m/s. So the OP is asking if every speed is an integer multiple of that.

Every speed less than 299792458 m/s is clearly not an integer multiple of 299792458 m/s.

 

[DrewD]

Perhaps the appropriate question is whether every possible speed is a fraction (rational multiple) of c. That would essentially boil down to where distances and times are integer multiples of of Planck dist and time. I don't know enough about this but my understanding is that there is not a definite answer to this (?).

 

[Naty1]

Fredrik:

I think DaleSpam's point (as well as mfb's) was that 1 Planck length per Planck time is the speed of light, 299792458 m/s.

Ah ha!
THAT makes it clear...

 

[phinds]

Fredrik:

Ah ha!
THAT makes it clear...

+1 on that. I clearly wasn't really paying attention to the RESULT of the specified calculation.

 

[Dale]

I think DaleSpam's point (as well as mfb's) was that 1 Planck length per Planck time is the speed of light, 299792458 m/s. So the OP is asking if every speed is an integer multiple of that.

Every speed less than 299792458 m/s is clearly not an integer multiple of 299792458 m/s.

Yes, that was my point. I guess I should have mentioned that the speed in the OP is c.

 

[HomogenousCow]

Sure, you can use "planck speed" if you like, they don't provide any mathematical advantage though.
We usually just set c=1 and work in really long distances and really short times.