Is Matter Infinitely Divisible?

[rjmorgalo]

Hello,

This is my first time posting something related to physics. I have never studied physics but I have a question that has been with me since my childhood. When I was about 10 years old, I was sitting alone in my backyard. I had a twig in my hand. I broke the twig in half and was left with two peices in my hand. I then discarded one of the twig halves and took the remaining half and then broke that one in half. I kept doing this over and over. I was determined to see how far I could go with this. It then dawned on me that as long as I have one half left I could continue to divide the piece to infinity. No matter how small the piece was, I will always have two smaller peices when I divide it in two. This may seem simple, but it has weighed heavy on my mind since I was a child. Just as the Universe is considered to be infinite in its magnitude, so is it infinite in its miniscule. This is not like dividing a molecule in half. This is simply dividing a mass in half without disturbing its molecular structure. How would you put this into an equation or formula and what do you make of this?

Thank you for your input.

Robert

 

[diazona]

I'm not sure what to make of this, really... what exactly do you want this equation or formula to express? Just the fact that you can divide a number by two repeatedly?

On a somewhat related note:
http://en.wikipedia.org/wiki/Zeno's_paradox

 

[mikelepore]

Since the question is about "dividing a mass in half without disturbing its molecular structure", that means the process is NOT infinite. When you get down to having one molecule, the process stops.

 

[rjmorgalo]

To: Mikelepre.

How can it Not be infinite? The molecular structure remains the same no matter what the size of the mass. As long as you can divide the mass in half you will always have a remaining mass to infinity. The molecules are untouched. So in this same space and time that we are in there is an infinite space and time that continues to get smaller and smaller. I know this sounds wierd, but ever since I was I child I can actually see this process in my mind. That twig that I had in my had was both a fixed size and infinite.

To:diazona.

I am not too sure what to make of this either, but it has bugged me since I was a child. I am not talking about simply dividing a number in half. I am talking about dividing a mass in half to infinity. The mass remains the same only smaller and at each division it will still be there no matter how small as there will always be a mass remaining. I believe that somehow this formula will open up a new way of looking at quantum physics and how it relates to time and space. Crazy, huh?

 

[diazona]

I am not too sure what to make of this either, but it has bugged me since I was a child. I am not talking about simply dividing a number in half. I am talking about dividing a mass in half to infinity. The mass remains the same only smaller and at each division it will still be there no matter how small as there will always be a mass remaining. I believe that somehow this formula will open up a new way of looking at quantum physics and how it relates to time and space. Crazy, huh?

Nope. It won't. As far as I can tell this really has nothing to do with quantum physics or time and space. As Mikelepre said, matter occurs in discrete units and once you're down to one particle, that's it, you can't divide it any more. (Of course, you can split a molecule in half by chemical processes, or an atom by nuclear processes, but when you do so you no longer have the same substance, and at any rate you still eventually get down to elementary particles at some point)

 

[russ_watters]

To: Mikelepre.

How can it Not be infinite? The molecular structure remains the same no matter what the size of the mass.

That makes no sense. Molecules are objects with a specific mass and structure. You can't divide them. This just sounds like you don't understand what a "molecule" is.

Ie, if a molecule of water is two hydrogen atoms and one oxygen atom, exactly what do you think happens when you divide it in two?

I am not too sure what to make of this either, but it has bugged me since I was a child. I am not talking about simply dividing a number in half. I am talking about dividing a mass in half to infinity. The mass remains the same only smaller and at each division it will still be there no matter how small as there will always be a mass remaining. I believe that somehow this formula will open up a new way of looking at quantum physics and how it relates to time and space. Crazy, huh?

Sorry, no, this is just a simple misunderstanding of chemistry, and an ancient one*. It is not a new way to look at the world, it is what people thought the world looked like until chemists figured out what molecules and atoms were.

Btw, what you are saying can be expressed mathematically as:

m_n=m*1/(2ⁿ)

Where "m" is mass and "n" is the number of times you divide it by 2.

*A brief history is on the wiki page for atoms and atomism. The idea that substances were continuous is one of Aristotles many errors: http://en.wikipedia.org/wiki/Atomism#Greek_atomism

 

[rjmorgalo]

To: diazona.

I respectfully disagree. I know I am a complete novice at this. But I am not talking about changing the chemical properties of the mass, I am talking about the physical properties. If I divide a compound (solid) without changing its chemical structure, then I am left with a smaller version of the original. This CAN continue to infinity as there will always be a smaller version of the original.

To: Russ Watters.

Thank you for the formula. I think we are saying the same thing only I may not be speaking the same language. I undestand that molecules are objects with a specific mass and structure. I am not talking about dividing the molecule just the mass (object). You asked, " If a molucule of water is two hydrogen atoms and one oxygen atom, exactly what do you think happens when you divide it in two?" I am not talking about dividing the molecule of water. I am talking about dividing the volume of water. Correct me if I am wrong but that one molecule of H2O in liquid form has a specific volume. If you divide the volume you still have H2O only in two separate smaller volumes. Correct?

 

[Doc Al]

I respectfully disagree. I know I am a complete novice at this. But I am not talking about changing the chemical properties of the mass, I am talking about the physical properties. If I divide a compound (solid) without changing its chemical structure, then I am left with a smaller version of the original. This CAN continue to infinity as there will always be a smaller version of the original.

Since you're not talking about splitting molecules, only 'volume' of material, why do you think it can go on to 'infinity'? Why don't you estimate how many water molecules are in a glass of water--that might give you an idea of how many times you might divide it into smaller quantities.

I am not talking about dividing the molecule of water. I am talking about dividing the volume of water. Correct me if I am wrong but that one molecule of H2O in liquid form has a specific volume. If you divide the volume you still have H2O only in two separate smaller volumes. Correct?

Again, what happens when you get down to a single molecule of water?

 

[diazona]

Since you're not talking about splitting molecules, only 'volume' of material, why do you think it can go on to 'infinity'? Why don't you estimate how many water molecules are in a glass of water--that might give you an idea of how many times you might divide it into smaller quantities.


Again, what happens when you get down to a single molecule of water?

Yeah. What he said.

A molecule cannot be divided without changing its chemical structure.

 

[russ_watters]

Correct me if I am wrong but that one molecule of H2O in liquid form has a specific volume. If you divide the volume you still have H2O only in two separate smaller volumes. Correct?

No. If you divide a car in half, do you get a smaller car?

 

[rjmorgalo]

No. If you divide a car in half, do you get a smaller car?

Yes you do. I am not talking about the functionality of the car, just the compound of the car. The car is metal in the form of a car. If you divide this metal, regardless of its form or function you will have two smaller versions of the compound. A table for example is made of wood. When you cut the table in half, you still have two halves of a wood table. I understand that when you get to the last molecule of a compound, then you have a choice. You can divide the molecules that form that compound and you are left with two separate elements and not the original compound, thus changing the structure all together. Or you can simply divide the physical property of the volume or mass of the object leaving you with two versions of the same compound. What do you think will happen when you get to the last molecule of a glass of water (H20)? This molecule is still in liquid form with a specific volume. If you divide this volume in half, won’t you still have the physical properties of liquid water only in two smaller volumes?

 

[Doc Al]

I understand that when you get to the last molecule of a compound, then you have a choice. You can divide the molecules that form that compound and you are left with two separate elements and not the original compound, thus changing the structure all together. Or you can simply divide the physical property of the volume or mass of the object leaving you with two versions of the same compound.

Once you get to that last molecule you do not have such a choice. You cannot 'simply divide' that molecule into two smaller versions of the same molecule.

What do you think will happen when you get to the last molecule of a glass of water (H20)? This molecule is still in liquid form with a specific volume. If you divide this volume in half, won’t you still have the physical properties of liquid water only in two smaller volumes?

Of course not. To split that last molecule, you must destroy it.

 

[Dale]

What do you think will happen when you get to the last molecule of a glass of water (H20)? This molecule is still in liquid form with a specific volume. If you divide this volume in half, won’t you still have the physical properties of liquid water only in two smaller volumes?

First of all, it doesn't make any sense to talk about a single molecule being in a solid, liquid, or gas state. A single molecule of water does NOT have "the physical properties of liquid water", and whatever you would get by splitting that in half certainly won't either.

 

[russ_watters]

Yes you do. I am not talking about the functionality of the car, just the compound of the car. The car is metal in the form of a car. If you divide this metal, regardless of its form or function you will have two smaller versions of the compound.

Ah, no. You had 4 wheels, now you have two. Half an engine, fuel tank, etc. But you can't drive it. It isn't a car, it is just pieces of a car. I'm starting to wonder if you're jerking our chains here!

I understand that when you get to the last molecule of a compound, then you have a choice. You can divide the molecules that form that compound and you are left with two separate elements and not the original compound, thus changing the structure all together. Or you can simply divide the physical property of the volume or mass of the object leaving you with two versions of the same compound. What do you think will happen when you get to the last molecule of a glass of water (H20)? This molecule is still in liquid form with a specific volume. If you divide this volume in half, won’t you still have the physical properties of liquid water only in two smaller volumes?

No. This is a very illogical line of reasoning you are on. A water molecule is two atoms of hydrogen and one of oxygen. There is no way to divide it to end up with two atoms of hydrogen and one of oxygen again. What you are saying doesn't make logical sense - the two ideas (that you can continuously divide a substance and that substances are made of descrete objects) are complete opposites of each other and can't both be true!

You do not get to choose how the universe works. The universe is not obliged to conform itslef to how you wish it would work.

 

[rjmorgalo]

I am not trying to be disrespectfull nor am I trying to pull anyone's chain. If this is the impression, please accept my opologies. What I am, is curious about a paradox that I beileve exists and that can be resolved. The argument was given that a single molecule of H20 would not be in a liquid state. My question is what state would it be in? If it will be in a vapor or gas state then what will it take to convert that one molecule of H20 into a liquid state? Is it pressure? Or the loss of Heat? If so how much pressure or how much heat must be released to convert that one molecule of H20 into a liquid form? Then once it is in a liquid state, what would be its volume? That volume, I believe can be divided making it two smaller volumes of H20. Also, the smaller the volume of h20 the greater the pressure/loss of heat that would be required to convert the smaller volume to a liquid state and continue the process. The amount of pressure required increases relative to the decrease in volume. But as long as there is volume, it can be divided without destroying or compromising the integrity of the molecule. This is my argument. I understand that everyone says it cannot be done. But there was a time when people thought the wordl was flat, that atoms could not be split, an so on. This is a ligitimate question that I believe needs some serious thought. What say you?

 

[russ_watters]

Simply put, it doesn't work the way you think it does and YOU are the one holding on to the ancient "flat Earth" idea.

Also, if you can't understand why something that is indivisible can't be divided, you have no hope of understanding the completely separate issue of
why a single molecule can't be a solid or liquid.

 

[Doc Al]

The argument was given that a single molecule of H20 would not be in a liquid state. My question is what state would it be in? If it will be in a vapor or gas state then what will it take to convert that one molecule of H20 into a liquid state?

It is meaningless to ask for the 'state' of a single molecule, since being liquid or solid is a bulk property of many molecules.

Is it pressure? Or the loss of Heat? If so how much pressure or how much heat must be released to convert that one molecule of H20 into a liquid form? Then once it is in a liquid state, what would be its volume? That volume, I believe can be divided making it two smaller volumes of H20. Also, the smaller the volume of h20 the greater the pressure/loss of heat that would be required to convert the smaller volume to a liquid state and continue the process. The amount of pressure required increases relative to the decrease in volume. But as long as there is volume, it can be divided without destroying or compromising the integrity of the molecule. This is my argument.

And, as has been pointed out repeatedly, your 'argument' is wrong. (You haven't really given an argument, you've just stated your claim without providing reasons.) Regardless of the 'volume' a single molecule may inhabit, when you divide that volume what are you dividing if not the molecule itself?

I understand that everyone says it cannot be done. But there was a time when people thought the wordl was flat, that atoms could not be split, an so on. This is a ligitimate question that I believe needs some serious thought. What say you?

I say read up on the atomic & molecular theory of matter, which has been well-established for quite some time. (Funny you should mention atoms being split, since that's just what we're talking about here.)

 

[espen180]

The argument was given that a single molecule of H20 would not be in a liquid state. My question is what state would it be in?

State of matter is only defined for bulks of molecules or atoms. In the case of water, the state is given by the number of hydrogen bonds and dipole bonds between the molecules. If you have only one molecule, there are no intermolecular bonds and therefore no defined state of matter.

 

[rjmorgalo]

I would like to thank each and everyone of you who contributed to this discussion. It is obvious that I am like a 5 year old continuously asking questions that you all may think rediculous. I have found that I am facinated with a subject that I have never thought about. As I have said, I have never taken any physics courses. I will pursue some in hopes of getting answers to my questions. It seems that the more I ask, the more questions I have. It is precicely NOT knowing the answers to those questions that intrigues me. You all are obviously accomplished.

I hope to learn more in this subject that I suddenly found so captivating. I am in the US Army and when I returned from Iraq, I found myself facinated with the subject of the Middle East. I am now completing my BA in Middle Eastern Studies and I start my Graduate studies in March where I am pursuing a Masters in Diplomacy. Perhaps, when I am finished with that, I can start re-inventing the wheel with my crazy theories on Physics. It has been a pleasure discussing this topic with you and, with your permission and indulgence, I will ask more questions as they come up. Happy Holidays to you all.

 

[russ_watters]

As I have said, I have never taken any physics courses. I will pursue some in hopes of getting answers to my questions...

I hope to learn more in this subject that I suddenly found so captivating.

FYI, for the issue in this thread, the subject you'll want to look more into is chemistry, not physics. I'm sure you can pick up a used freshman basic chemistry book for not too much money.

 

[Dale]

The argument was given that a single molecule of H20 would not be in a liquid state. My question is what state would it be in?

That is exactly the correct question. What state is it in? What do we mean by "liquid state"?

A "state" is a complete description of a system. For a single point particle you need 6 numbers to specify its state, 3 numbers for position and 3 for momentum. For a single water molecule you would also add 3 numbers for orientation and 3 for angular momentum. So, those 12 numbers characterize the state of a single water molecule. To fully characterize the state of 18 g of water would thus require approximately 12*Avogadro's number pieces of information, which is a ridiculous amount of information (microstate). So we take averages instead and ignore an enormous number of internal degrees of freedom (macrostate).

When we describe a bunch of water molecules as being in a "liquid state" we are essentially describing things like their spatial separation (nonsensical for a single molecule) and their average kinetic energy and average momentum (indistinguishable for a single molecule). These are properties that only exist as averages, in bulk, when ignoring the details. It just doesn't make sense to talk about the average of a single number, when you have all of the details of the microstate.

One thing is certain, however you define the volume of a single water molecule, if you divided it in half then either one half would contain a single water molecule and the other half would be empty or each half would contain something that is no longer a single water molecule. Either way, you could not continuously divide the water into an infinite number of smaller volumes of water.

I am in the US Army and when I returned from Iraq, I found myself facinated with the subject of the Middle East. I am now completing my BA in Middle Eastern Studies and I start my Graduate studies in March where I am pursuing a Masters in Diplomacy. Perhaps, when I am finished with that, I can start re-inventing the wheel with my crazy theories on Physics.

Thank you for your service, and I hope that you do pursue more in depth studies of chemistry and physics. It is a fascinating subject, but it does require that you be willing to discard many pre-conceived notions and examine the experimental evidence of the universe as it actually is and not as you would expect it to be. This will certainly not be the last surprise you encounter in your studies.