|MadSci Network: Physics|
Our notion of matter and reality are greatly different from those of classical physics, i.e. the paradigm that is taught in schools. I've tried not to use of the word "matter" since classically this excludes light. The division between classical views of light and matter become somewhat blurred in Quantum Theory (QT). Light and Matter are still very different in QT, but QT states that everything exists as wave-particles and since your question is one of existence i feel justified. Question (1) If something has mass must it also take up space? Physicists describe the universe with only a handful of theories. The most fundamental of these, when we are talking of the very small, is Quantum Theory (QT). As such it seems like a good theory to use to answer your first question. In QT (or more Specifically in the Standard Model of Particle physics) all fundamental particles like the electron or quark are considered to be point like particles. That is in all calculations it is assumed that all fundamental particles have zero size or take up zero space. If we were being hasty we may say that the answer to question 1 is that it is possible for an object to have zero size and yet have mass; the electron being an example. This however may not the case. Our most accurate measurement of the size of an electron finds no structure but this is very different from stating that it is a point particle. What if we make a better measurement? In fact in an attempt to understand nature on a deeper level String Theory is being developed. In this theory particles can crudely be thought of as oscillating strings that are admittedly very small, 10^-35 m, but definitely non zero. As an aside for the more clued up; There is a hint of a fundamental limit to how small anything can be said to be in QT. There is a distance known as the Planck length which is believed to be the scale at which Quantum Gravity becomes dominant. Associated with the Planck length is the Planck time, the time taken for light (or rather information) to traverse the planck length. The nature of such things is the answer to a different question so I hope you will forgive me for simply using them. What is important is that there exists a quantity called the Planck length and a quantity called the Planck time collectively they are known as the Planck scale. At the Planck scale space and time lose all meaning. It can be said that NO interval of time exists below the Planck time and NO interval of space below the Planck length. Our best guess is that at this level space-time becomes like an ever changing foam and new theories take over from QT; possibly String theory. Essentially space-time itself does not exist below the Planck scale. If space does not exist on length scales less that the Planck length then how can we claim that something is smaller? Of course we cannot. Extension below the Planck scale becomes as meaningless as time before the beginning of time or south of the south pole. On this level question (1) has no meaning. In summary to answer (1) I hopefully have shown that it is believed that all objects take up space irrespective of mass. Current theories may assume point like particles but this is expected to be an approximation, albeit a fantastically good one! This either appears to be true or at the very least the notion of extension becomes questionable. Either way, it can be said that no object can be observed as having zero size whatever the mass may be. Question (2) If something takes up space must it also have mass? No This ones a lot easier to answer because we have examples. For instance the Photon has zero mass. Part of my answer to question 1 was essentially that no object could be observed with zero size. Consequently the photon can not be observed to have zero size even though QT currently treats it as such. The photon is known to be massless and hence is an example of an object that has extension yet no mass. Incidentally, as a footnote, Rene Descartes defined matter as; "Extension in length, breadth, and thickness constitutes the nature of corporeal substance" he explained: "Everything else that can be ascribed to a body presupposes extension". That is mass, charge, color, texture, motion, or any other property are incidental . Substance can exist without all of these if, and only if it takes up space. It is interesting to find that a seventeenth century philosopher could answer your question in one line where as myself and 300 years of Physics took a page!
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