If any part of mass is infinitely divisible, what would that mean?

[Kyriakos]

A question risen out of the seminars, cause that is pretty much the position of the Eleatics. That any part of mass (or other extendable volumes/surfaces/lines) is (mentally, but arguably they claimed the human mental world was closer to the truth than our senses) infinitely divisible, and therefore nothing can actually ever take a different position in any progression.

You can also read the largish spoiler for some background on the presocratic idea of infinite divisibility, but i merely want some guiding to current notions of infinite systems and what is theorised to be the relative position of their distinct particles within them.

Spoiler :

The argument (termed a paradox in Zeno's examples of it, but originally Parmenides did not use this line of presentation) seems (to me, but also others i read a bit) to mostly consist of the following parameters:

1) If something is infinitely divisible then it already can be said to be in all parts of its own divisions, which would likely render it as being tied to other things of its likeness through the same infinite divisions and therefore be in Oneness with all those as well. The Eleatics famously argued that the Cosmos is a Monad (a One) and the senses makes us believe it alters, but they are part of the problem with understanding the actual truth.

2) The senses obviously make us think there is change around us or in us. But if there was change then we would have no notion of infinity given it would be un-natural as an idea. Eg in the paradox with Achilles and the tortoise the latter has a headstart and Achilles can't reach it due to first having to reach the first position of that headstart, upon which the tortoise would have moved slightly more, and so on to infinity. While the senses tell us that regardless of that syllogism a faster runer will overtake a slower one given enough time, this would require the cosmos to operate in a system of finite division, which idealistically is not true. The start of what by now is termed as idealism is argued to be Parmenides (and maybe before him Xenophanes), and Plato regards Parmenides of Elea as the father of his own (platonic) philosophy of ideas as well.

 

[Cheezy the Wiz]

At their smallest, the fundamental pieces of matter are expressed as probabilities and frequencies, not as mass. This is because all mass is commutable to energy, so the question of it's infinitely small "parts" isn't really applicable any more, IMO. Unless you mean to wonder what energy is at its most fundamental level...

 

[warpus]

I think the implications are different depending on your context - mathematical, philosophical,.. quantum physical?

 

[Kyriakos]

At their smallest, the fundamental pieces of matter are expressed as probabilities and frequencies, not as mass. This is because all mass is commutable to energy, so the question of it's infinitely small "parts" isn't really applicable.

A direct reply to Zeno came in the same period (early-mid 5th century BC) by Democritus and his atomic theory, where the divisions are theorised to end at the level of an 'atom' (which just means 'non-divisible') whereby there are only some atoms (particles you could say) moving around in a vastly larger 'void', and so they cannot be further broken down.

But Democritus famously accepted that if the divisions instead never end, then change (for example movement, or erosion, or any other) could not be real (ie it would be entirely an illusion of the senses). I am wondering, therefore, why an infinite division of things would clearly mean that there could not be any change (we only have fragments on this issue, so it is not that easy to guess, which is why i thought i could ask about somewhat similar theories in current physics).

I think the implications are different depending on your context - mathematical, philosophical,.. quantum physical?

Quantum was specifically mentioned by some people in the seminar, and i would like to at least know some introductory stuff about how it ties to the theories i presented by the Eleatics. So that would be a major help

 

[Souron]

Even if matter were infinitely divisible, the laws of nature work differently on different scales. Specifically, the four fundamental forces dominate at different distances. So a galaxy, which is dominated by gravity, cannot be made up of smaller galaxies, but instead is made up of stars and planets, which are nothing like galaxies, and are more dominated by electromagnetic and nuclear forces. And in general an object of a particular size won't behave the same as an object of the same shape, but a different size.

 

[nc-1701]

Quite simply matter isn't infinitely divisible and this has been known for several hundred years.


If it were then perhaps some fun could be had, some of the mechanics probably still need to be ironed out, but we could probably explore this in real life
The Banach-Tarsky "paradox"
Not really a paradox, just a surprising fact about continuous mathematics.

 

[Kyriakos]

^Thank you both for the replies Can you elaborate a bit? Mostly looking for an answer to:

-If matter is in fact no longer divisible upon reaching a very different state (eg particles in a vastly larger than them 'void' - or similar - or objects of clearly a different nature than anything they would add up to in a macrocosm next to their own position) what is the fundamental difference between such a state and one where matter is infinitely divisible while still the microcosmic divisions would be of a very different nature? (eg Souron mentioned the example of galaxies an then idnividual star systems, which too break up to more stuff etc).

In other words: if the particles too break up to other things (just that the next smallest thing is a microcosm next to what they are as well) and this goes on theoretically forever, what would the implications be in regards to the Cosmos being 'in reality' a Oneness or not?

 

[woody60707]

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

the Planck length is the length scale at which the structure of spacetime becomes dominated by quantum effects, and it is impossible to determine the difference between two locations less than one Planck length apart.

In short, your grade school math teacher lied to you when she said there were a infinite number of points between A and B.

 

[Kyriakos]

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



In short, your grade school math teacher lied to you when she said there were a infinite points between A and B.

Damn the liar

Although not really, cause a 'point' is 0dimensional anyway, so it does not have much to do with material divisions

As for Planck length (in an attempt to still avoid reading physics articles) can anyone sort of 'sum up' why after a certain micro/particle size the theory is that those rapidly alterating/moving/other particles cannot be broken up more? (i mean i can get that we don't have the means to examine them as more divisible, but this by itself surely does not mean they have to be non-divisible?).

And you did not answer the main question i posed in my previous post, #7 (which is really all that i am focused on in regards to this!)

 

[timtofly]

The plank length is the barrier standing between dividing something infinitely and the connectedness off things. It is the mathematical theory that all things are connected and cannot be divided any further.

If one day the "math" barrier is broken and we actually can see this plank length, then the theory will change to something more definitive, if it needs to.

According to the wiki entry from above the next step would involve a black hole. This would be where space time and distances are "stretched" past the ability to be observed.

It also points out that a dot would be the half way point between the size of the universe and a plank length.

 

[uppi]

Quite simply matter isn't infinitely divisible and this has been known for several hundred years.

Not really. What was supposed to be indivisible 100 years ago, was found out to be divisible after all. And even now having no evidence for the divisibility of quarks and leptons does not mean we can rule out divisibility. Maybe we just haven't tried hard enough to divide them.

But even if the quanta of matter turn out to be indivisible, their field is divisible. Although we can observe only whole quanta, they can in principle be spread out over the whole universe so that only a very tiny part of it is in one place. So the fields are infinitely divisible - at least for practical purposes (what happens at the Planck length is anybody's guess).

 

[Souron]

If I remember right, I think a problem with leptons being a non-point would be a problem because they spin in ways that a 3D object cannot. Leptons have a component of angular momentum that cannot be emulated with any arrangement of components moving at sub-light speed. Ergo, they must be point particles, with their spin as an inherent property of the one point, instead of a property that results from the arrangement and motion of it's parts.

 

[Kyriakos]

Thanks so much for the three greatly interesting posts

Points do interest me. So many relations there, to other core notions such as 'zero', an origin, a theoretical 0dimensional sole place of linking of 1dimensional forms, and also other stuff such as the center of a spiral.

The leptons and other Physics micro-particle terms posted about also seem hugely interesting.. I will try to start reading some basic stuff about them

 

[uppi]

If I remember right, I think a problem with leptons being a non-point would be a problem because they spin in ways that a 3D object cannot. Leptons have a component of angular momentum that cannot be emulated with any arrangement of components moving at sub-light speed. Ergo, they must be point particles, with their spin as an inherent property of the one point, instead of a property that results from the arrangement and motion of it's parts.

Huh? Leptons have spin 1/2 and protons also have spin 1/2. I am not aware of anything that would cause the spin of leptons to behave differently than the spin of protons. As the latter are clearly a compound particle with finite size, the argument that a spin 1/2 particle cannot be a compound particle cannot be true.

It is true that the spin of electrons cannot be modeled as the rotation of a classical object. But that only means that spin is a quantum property without a classic equivalent, not that the particles cannot have a finite size.