Smallest "unit" of space?

[DyslexicHobo]

I was wondering if the fabric of space-time was made of something so when something traveled through it, it always moves at a multiple of some constant; is there a "smallest unit" of space that can not further be sub-divided?

If you're one inch from a tree and you keep moving halfway there, is there a point where you would either need to not move, or actually reach the tree?

I know it's not something useful to think about (at least I can't think of a reason why it'd be useful), but it seems to me like there HAS to be some sort of semi-tangible stuff making up space-time. Therefore there has to be a smallest amount of it (or so my logic tells me).

 

[NikolaeVarius]

Planck Length

1.6 × 10-35

 

[StopSign]

But back to the classic tree example...

Planck Length can't be the limit in this case. The limit, no matter how you look at it, is 0. You would eventually be traveling distances smaller than 1 lp. It is very very close to 0, but it is not 0. You are still moving. You can't stop moving because the only way to stop is to actually reach the tree (distance = 0), which from a mathematical standpoint is impossible.

The OP is asking if there is a discrete and indivisible unit of length in space. I don't know the answer to that.

 

[chcarnage]

I too immediately thought of Planck when reading the question. We can't get meaningful information of an object with less than a Planck mass, or measure a time shorter than Planck time.

http://en.wikipedia.org/wiki/Planck_units

However our world is not a grid and we don't experience only exact multitudes of Planck Units.

 

[DyslexicHobo]

I am somewhat familiar with the Planck length, but can we experience motion in ONLY multiples of the Planck length? I thought this was only used to describe the distance at which quantum foam became noticeable.

Maybe I should better phrase my question: if we were to have a grid for the entirety of space, is there a scale which we could use so that it would be impossible to move less than one unit at a time?

 

[f95toli]

No. For the simple reason that we are not limited to multiples of quanta even when we know for sure that something is quantized.
A good example would be electrical charge which has a quanta of e=1.6022e-19 C.
However, there are plenty of situations where screening (or, even better, quantum interference as in coloumb blockade) allow us to see and measure fractions (real or rational) of e. Hence, while the charge carriers all have a charge of e the effective charge is not neccesarily a multiple of e.

I would expect the same to be true for length.

 

[randumb]

No. We live in continuous space.

 

[silverpig]

Kind of no, kind of yes.

Imagine trying to say exactly when two clouds collide. You can be on the ground looking up and be fairly sure, but when you get up close to the cloud, where does one begin and the other end? Microscopically, can you say that one water vapour molecule belongs to cloud A and not cloud B when they are very close? The same sort of things happens with "solid" objects. They don't have well definied boundaries. Realistically there is no instant of contact.

So, short answer, yes. Shorter answer, no.

 

[lyssword]

smallest so far is thought to be planck lenght, if there is anything smaller they/we don't know about it yet

 

[Rastus]

A point. It has no measurement, kind of like an instant of time.

 

[CycloWizard]

Originally posted by: Rastus
A point. It has no measurement, kind of like an instant of time.

You can always define a point between two other points, so this doesn't really fit his description. A point is more of a mathematical abstraction than a reality.

 

[PowerEngineer]

Originally posted by: tenshodo13
Planck Length

1.6 × 10-35

My understanding of string theory is that the so-called Planck Length does represent the smallest distance you can have in this universe. By establishing this minimum distance, string theory avoids many of the infinities that pop up when trying to solve equations at vanishingly small distances and allows for a linking of relativity (big physics) with quantum mechanics (small physics).

I'm not claiming that string theory is correct. Just pointing out that there are theories out there that suggest that distance might also have a minimum non-zero increment.

 

[Biftheunderstudy]

A more subtle point is that string theory just says that talking about distances less than the plank length is unphysical and impossible to measure. It gets around the quantum gravity by replacing the ill-behaved point particles by 1-D strings, some of them are 2-d membranes and up until 11 dimensions or so.

 

[f95toli]

Originally posted by: Biftheunderstudy
A more subtle point is that string theory just says that talking about distances less than the plank length is unphysical and impossible to measure.

True. However, that does not mean that all lengths have to be multiplies of the Planck lenght. As I pointed out above: The existence of a "quanta" neither precludes the possibility of measuring smaller values than that quanta, nor does it mean that all measurements will show a result which is a multiple of the quanta.