# Is matter infinitely divisible?

1. Jan 7, 2010

First things first, so that answers will more closely approach my level of understanding; I have only completed multivariable calculus and linear algebra and haven't yet taken a "real" physics course. I am part-way through Penrose's "Road to Reality" though.

Secondly, this question stems from an argument I was destined to lose on YouTube. I'm not looking for an argument just (hopefully) helpful answers.

The original question (as stated in the title): Is matter infinitely divisible?

I wrote physicists at the top 20 Google-returned sites asking just this question and of those who responded, the overwhelming answer was "No one knows" (<- Verbatim reply from UCSD). (There was also one "No" answer and one "I believe it is.")

1) As I understand it, discounting everything else, Planck's Length is the smallest we could ever hope to zoom in on, not necessarily the smallest there is, is this correct?

2) I have read a few articles from the mid '90's about the possibility of a substructure discovered in quarks, what came of this, was it disproven?

3) If there is a smallest length and corresponding smallest bit of matter, can someone outline motion for me at that level? Below are my general thoughts on the matter and why I have difficulty imagining a smallest subunit.

Assume there is a length which cannot be subdivided; Ill call it k. Take a piece of matter of size k and move it over one k unit. Since k is not divisible anything moving onto k must cover it completely instantly for if it were to at any point cover it partially, you would have subdivision of k. This implies that the movement between the two points takes no time what so ever. But instant is faster than the speed of light and so conflicts with the laws of the physics. (Obviously I really know nothing of physics, but alas I copied this from a different conversation I had in which I pretended to know something and so leave the paragraph as is for completeness sake.)

I'm probably leaving a lot out that I wanted to ask but will stick with this for now. Thanks in advance for all who help.

2. Jan 7, 2010

### espen180

-Is matter indefinately divisible?
The answer you'll get depends on what model you prefer, I beleive. According to the Standard Model, it stops at quarks and leptons. Someone with more expertise might elaborate more on more recent theories.

-Smallest length
Length is an abstract notion, invented to allow us to measure spatial distance. As it is not a physical object in itself, there is nothing stopping you from making arbitrarily short line segments.

3. Jan 7, 2010

### mudderrunner

something not being divisible is hard to conceive.

4. Jan 7, 2010

### FoxCommander

Yes this is true. But what he means is that lets say you take a bit of foam, you start cutting it down smaller and smaller and SMAlLER till you get an atom, then you get protons and neutrons and then you get quarks and leptons and then when you cut those? With the Standard model you wil just cut them into energy because there is no structure inside. But there might be some new studies and research sugesting that there is some sort of structure to quarks and leptons so maybe you can get something else out of them. And yes everything is divisible, once you get to the energy state its just gets infinitly smaller. As with length I also agree, there is not one length that we can reach either long or short.

Sincerely,
FoxCommander

5. Jan 7, 2010

### mudderrunner

^ that makes sense.

6. Jan 7, 2010

### diazona

In the Standard Model, you really can't "cut up" quarks and leptons - they're assumed to be truly fundamental. You can involve them in reactions that might turn them into other particles, but the Standard Model doesn't contain any way to "divide" them into anything smaller. And there's no reason that it should, because as far as I know, there's no solid experimental evidence that these particles have any substructure.

I'm sure there are lots of theories out there (like string theory) but that's all they are, theories.

7. Jan 7, 2010

### rfstanton

Physics will always have something to explore. If we ever figure it all out the MA (master architect) will probably change the rules. Even the known physics that we accept as true is very often revised as more is discovered. Infinitely small, infinitely large? How could we ever hope to know? Thankfully, our best guesses often allow us to make useful gadgets.

RS

8. Jan 8, 2010

### FoxCommander

I dont even know if that is even relevant to this ha ha, And what i mean by cut up is break down into its basic properties, like molecules to atoms to protons neutrons and electrons to quarks and leptons to..... something else? i havent heard of anything but people have sugested that they could have a structure. But if there isnt anything then it just breaks down to energy.

Sincerely,
FoxCommander

9. Jan 8, 2010

### Neo_Anderson

Length isn't any more abstract than the idea of measuring time, though...

10. Jan 8, 2010

### rcgldr

But there's a point where what makes one form of matter unique from another stops at the molecular level.

11. Jan 9, 2010

### Evolver

I think it may help to think of matter as a collection of forces as opposed to physical entities.

12. Jan 9, 2010

### jkerrigan

Hmmm, I was under the impression that plancks length was the absolute smallest size or length recognized because anything smaller than that would be insignificant to any type of manipulation or advancement for us,kind of like an absolute minimum where anything below it we'd just ignore.

13. Jan 10, 2010

### rfstanton

Mathematics and numerology, to me, are the closest thing we have to science with hard fast rules, and even then only probably apply to this physical dimension. Everything else I can think of is our current best guess, and as I said earlier, thankfully allows us to make useful things. I think my best answer to the original question is that for the foreseeable future, we will continue to break matter and energy into smaller and smaller particles and sub-particles just based on what we see so far. FoxCommander, you said something about everything breaking down into energy at some level. Do we know what "energy" is?
RS

14. Jan 10, 2010

### DaveC426913

Numerology?? Numerology isn't even science; it's woo-woo-ism, akin to astrology.

15. Jan 10, 2010

### rfstanton

Why are some musical notes when played together sound pleasant and some don't? This is a commonly accepted phenomenon, yet math cannot explain it. Our science is at a crossroads where we are going to have to start factoring in the long view, way outside the box, and accepting some obvious, real experiences we have as humans as valid parts of the equation in any given area of study. We might then be able to even resolve some of the paradoxes that plague our science. I know that this complicates our beloved scientific method, but maybe this explains why we know far more about what we don't know (for sure) than what we do. (Kind of like studying sea creatures and ignoring the ocean.)
RS

16. Jan 10, 2010

### DaveC426913

It most certainly can. Why would you say such a thing?

Read up on harmonics.

When you say "we don't know stuff" ... maybe you should just speak for yourself... :tongue:

17. Jan 10, 2010

### gmax137

I didn't think "math" had the job of "explaining" anything. Isn't math really a huge web of "if ... then" syllogisms, leading from postulates to conclusions? How could that "explain" why combinations of periodic pressure variations are "pleasant" to a given culture of some species? Why should it need to explain something like that, and why should failure to do so indicate anything?

To DaveC... sorry, but nothing about the mathematics of harmonics has the concept of "pleasant" as a conclusion. Ever heard music you don't like?

18. Jan 10, 2010

### DaveC426913

It has everything to do with it. Aharmonic tones played together jar on the ear.

Is it possible that, by "notes played together" you actually mean "notes played in sequence"? This might explain your otherwise coutnerintuitive claims.

That is a completely different question. See above, "notes played in sequence".

19. Jan 10, 2010

### gmax137

I think you've mistaken some of the text I quoted as being mine.

Anyway, as far as the jarring of the ear, is it possible that some species are wired such that this 'jarring' stimulates their pleasure response? Or that such a pleasant response is present in some cultures? This is my only point, that such a question is not an issue of mathematics, it is physiology and culture.

20. Jan 10, 2010

### DaveC426913

It appears I did. I lazily duplicated the [ quote ] tag. OTOH, it seems you've picked up the ball.

Two harmonic notes played together tend to reinforce each other. This sounds pleasant to the ear.
Two aharmonic notes tend to do unpredictable things to each other, such as setting up unintended and unpredictable pulsing.

(Can I give a scientific, objective definition of "pleasant" and "unpleasant"? I'm not sure.)

There is no question that, when it comes to musicians using these to achieve a desired emotional effect, aharmonic tones can make for enjoyable music. Angst and stress are often important elements of deep music. But that is because the unpleasant qualities of aharmonic tones are known and taken advantage of.

21. Jan 11, 2010

### mikelepore

I think the musical terms you guys are looking for are concord and discord, which frequency ratios can predict. G,C,E notes played simultaneousy together make a chord. C and C-sharp notes played simultaneously produce beats, which most people consider unpleasant, although this is a cultural value judgment.

22. Jan 11, 2010

### mugaliens

Elephants? Just a guess. I wouldn't want to test this theory...

Bingo. My parents don't like rock and roll (they claim it grates), but I do. Math has nothing to do with it.

23. Jan 11, 2010

### Molydood

sorry Dave, but this is just arrogance IMO.
first off, the point rfstanton was making I believe is that 'music' is not explained by science, ie what sounds nice, what doesn't etc... a fairly nice analogy for making his point I believe, but you missed it by taking things too literally.

secondly, in this case I believe you have mistaken literal translation for 'Dave's view'; 'together' does not necessarily mean 'simultaneous', could it not also imply 'in short sequence'? (that was the way I 'read' his post)

I know you know your onions Dave: you usually speak the truth on these forums and I hope you don't take this the wrong way, but I just think a little more open mindedness about other peoples comments would go a long way in this case.

all IMHO of course :-)

24. Jan 11, 2010

### vanesch

Staff Emeritus
What are actually "subjective experiences" such as "pleasantness" is not as such part of science, that's true. It's an old philosophical issue. Of course, science will probably advance to a level where we can find correlations between what a subject claims is a pleasant experience, and certain neurological phenomena in the brain. But even then we wouldn't know what, in all generality, it is for a material object to have "pleasant subjective experiences". You can only rely on the testimony of the material object (in this case a human being) and, very important, the apparent similarity between yourself and that material object (namely, you also have a rather similar body, so chances are that what you intimately know to be "pleasant subjective experience" to yourself, corresponds to the testimony of that other material object, namely the test person). Indeed, once you have hugely different material objects from your own body, there's no way anymore to find out whether any "testimony" corresponds somehow to what you intimately know to be a subjective experience. It is not because a computer prints on its screen "That sounds pleasant!" that something similar to what you would call "pleasant" is actually experienced by that computer object. This is, as I said, an old problem in philosophy.

So, we already found one thing that is not "science's cup of tea": subjective experiences of material objects sufficiently different from ourselves so that the guessed-for 1-1 relationship between their testimonies and our own experiences is not to be taken for granted.

There's another thing that is not science's cup of tea: "what is reallyout there". This brings us back to the OP. Science makes up theories about "what is reasonable to postulate, as a working hypothesis, out there" in such a way that those theories say something about observable phenomena. In as much as what is said about those observable phenomena seems to be in agreement with what is actually observed, we take it that those theories are helpful working hypotheses (and, with a shortcut, we take it that it is a reasonable working hypothesis to imagine that what those theories say is out there, is "really out there" for sake of imagination). If we have a theory about the geometry of the earth as being a sphere, and many things it predicts about the position of the sun and gravity and so on seem to fit with actual observations, we take it as a good working hypothesis to say that the earth is a sphere. We go even imagining it "really is" a sphere. That helps us to think about certain phenomena. So we make the short cut in this case to say that earth IS a sphere, but actually, purely according to the book, this is a bridge too far for science. Probably this theory is so good, that it will never be contradicted, and so we might just as well keep in mind that the earth IS a sphere. In a holographic universe, this is just an illusion, in fact, but you will probably never need to think of earth that way. So for all practical purposes, think of the earth as a sphere. Think it is really one. You won't make any mistakes. It is now very "evident".

However, there are parts of science which are far from being so "evident". In fact, many parts of modern physics are far from giving you a clear, unequivocal, undisputed, and unalienable picture of what is "really out there". Each time, there is some picture you can adhere to for sake of simplicity and ease of mind, but when you think about it, the picture is not unique, and far from absolutely certain. And then you realize that there's no scientific way to find out "for real" what is really out there.

So whether matter is infinitely divisible is not really a question science can address, because it is supposed to say something about what "really is there" instead of "what observable consequences it may have". Only the last bit is what science really addresses.

25. Jan 11, 2010

### gmax137

Thanks, vanesch, I find your post very interesting.

There is a thread in the quantum sub forum (sorry, I don't know how to create a link to another thread) but it is asking about the deBroglie-Bohm interpretation. In there one of the contributors says something like, the difference between Bohr and dBB is that the dBB approach "simply assumes that the electron is *really there* when we are not looking." So, based on your thought above, you think maybe the dBB isn't "science?" I'm not sure I agree with that. But I'm not sure I disagree with that, either. There's some references cited in that other thread that I want to go read.

I'm sure there's some apt quote about physicists, mathematicians, and philosophers.