# I Is space infinitesimal? Can it be divided unlimited times?

1. Jul 21, 2016

### Tanelorn

Is space infinitesimal?
By this I mean can it be divided an unlimited number of times?

If we take a 1m ruler and divide it in 2 and we get a 50cm ruler
How many times can we keep doing this? (disregard that the ruler is made of atoms)
So for many years I have been told that the limit is the Plank length, but I want to ask if this is this an established proven fact? Is it even possible to prove?

I think there is a similar concept for time also ie plank time?

Last edited: Jul 21, 2016
2. Jul 21, 2016

### Staff: Mentor

You may have heard that, but as far as we know it's not true - it might be, but there's no particular reason to believe that it is. This is one of the more pervasive misconceptions about the Planck length, so common that have an Insights article: https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/

Same thing - no particular reason to believe that time is granular in units of the Planck time.

3. Jul 21, 2016

### Tanelorn

Thanks for the link Nugatory, actually that is a succinct way of putting it, are space and time granular? Are they even physical at all or just numbers?

Perhaps quantum mechanics considerations in general may have suggested these granular ideas for space and time, but this is not needed if space and time are not physical and are just numbers.

4. Jul 22, 2016

### Justice Hunter

The plank length is the shortest possible distance that we can physically measure. The reason for this is because, when we probe smaller and smaller distances, we need to use more and more energy in order to probe those distances. At the plank length, the amount of energy required to probe it is equal to the collapse ratio that forms a black hole (energy is equivalent to mass via E=mc^2).

In other words, when we probe distances comproble to the plank length, we create a black hole. Black holes are regions of space in which information can not escape, which means no measurements can be made.

Without understanding the inner workings of blackholes, we are left with the conclusion that the plank length is the smallest distance scale we can measure, but by no means is it the smallest distance physically. According to some studies, space-time doesn't appear to be granular, although further experiments are being conducted to get the record straight.

5. Jul 25, 2016

### pBrane

As I see it:

Space and time are just numbers: You, personally, are an expression of energy and maths as it stands in the universal possibility/probability field.

The mathematical 'you' needs a mathematical history to put 'you' where 'it' is in the field. The reason you are reading this is because you came to THIS PAGE and NO other page would lead to your current position in the 'probability field'.
Your history is required to exist, void of energy, but as a mathematical route you have traveled from the past.

Imagine tunneling into a fractal for 30 seconds, set a flashing beacon and freeze frame. Now reverse out and flip the fractal face down so you can see where you have traveled from and to.
You will notice that to be at the beacon's location it is required that the 'numbers' you passed through on your journey must have existed or you could not be at that location. If you deleted any one of those numbers from the fractal your current location would cease to exist within the fractal.

A kind a mathematical scaffold or history is required to allow 'now' to not be the same as a second ago. The maths do not suddenly become nonexistent or impossible. When a 'pixel' of probability maths contains energy it is 3D real, when it doesn't it is either an unselected probability or was selected previously.

I think granular time, recording at the particle interaction scale, is required somehow.

I like to imaging particle events being recorded on old-style paper tape, the tape with all the holes (chads) poked through.
If we read the tape we can see the history, if we read the chads we see the same information from the opposite angle, like a photo negative. The tape and chads complement or complete each other.

If both the interaction and it's compliment are recorded then the net change is nothing.

That is what I think we need granular time for, to store these two things (time and anti-time) which add up to nothing.

Hope that made sense and cleared everything up for you.

6. Jul 25, 2016

### DrChinese

Welcome to PhysicsForums, pBrane!

Personal speculation and general musings are not the stuff of posts on this moderated board. As you are new, you may not be aware of the prohibitions in that regard. That especially applies in the Quantum Physics subforum. A question is welcome, as long as you don't use the question to espouse your own (non-standard) viewpoint.

I would recommend you make statements that are in concert with generally accepted physics. For example, your idea regarding there being a "single" history that led to a current position in n-space is not generally accepted. It is instead a possibility that is accepted in some interpretations (such as Bohmian Mechanics) but not in most others (such as MWI, consistent histories, etc). It is acceptable to discuss interpretations of QM as long as you identify and label the discussion suitably. (Debating interpretations is not particularly useful as there are no known predictive differences between them.)

7. Jul 25, 2016

### pBrane

Thanks for being gentle with me. I can see the need especially on this subforum. Off to dig around in Bohmian Mechanics then.

8. Jul 25, 2016

### DrChinese

There are a number of members here who are extremely well versed in all things Bohmian. If you have questions about it, I would encourage you to ask (a new thread is probably best). Or look for posts and threads by member Demystifier as he often comments in threads about Bohmian Mechanics (a/k/a de Broglie Bohm or dBB).

9. Jul 25, 2016

### Tanelorn

pBrane, thanks for your reply, for which I think I respectfully disagree.

I think you are saying that there is such a thing as granular time and also that the physical state of the entire Universe for every single Planck time interval exists permanently. And not just the information, but also an astronomical amount of permanent energy also, since this is a physical universe. I believe that such a view is not mainstream. I think I also concluded that this is why we will not be able to travel backwards in time, because all past destinations were transitory and no longer exist, only the instantaneous present. It is an interesting idea though, thanks.

Last edited: Jul 25, 2016
10. Jul 25, 2016

### lox_and_whiskey

As far as a ruler, we have found no particles smaller than the so-called elementary particles, but this doesn't absolutely mean they have no subcomponents. However, it's a perfectly practical to assume that they are indivisible.

For space-time itself, there is no evidentiary reason to think it is granular.

11. Jul 25, 2016

### Staff: Mentor

That's not true.

The plank length is about the scale the standard model is thought to break down.

Although you will often read QM and gravity do not mix that is false. We have a quantum theory of gravity valid to the plank scale:
https://arxiv.org/abs/1209.3511

Beyond that is the issue. As far as we can tell today there is no limit to the accuracy we can measure distance in principle, nor is there any 'graininess' to space. Our deepest formalism, QFT, assumes space-time is continuous and at the moment we have no reason to doubt it, although there are all sorts of conjectures about.

Thanks
Bill

Last edited: Jul 25, 2016