Can Matter be Infinitely Small?
No matter how small matter is, you could you still zoom in and cut it in half (with the appropiate technology.)
Or, no matter how small matter is, there is always something inside it, that can be taken out, only to find something inside that... and so on...
Is this correct?
Yes
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No
Side Score: 5
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Clearly there is issue with the questions of "matter" and "infinitely small". However: Bose Einstein distributions do not limit the number of particles occupying a particular quantum state - see e.g. p86 here http://books.google.co.uk/ Consider that you can chose a space arbitrarily small and that no matter how many bosons are in the space you can theoretically add additional bosons then the boson must be considered to occupy an increasingly infinitesimal volume (or indeed none). To put it another way, see http://www.stanford.edu/~rsasaki/AP389/ "The pressure of the gas does not depend on the volume in a BEC [Bose-Einstein Condensate] regime so that the compressibility of the BEC phase is infinite." Side: Yes
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What you are essentially touching on here is the infinite divisibility of matter. Could all of matter be infinitely subdivided, if only we had the appropriate technology? The short of it is that from what we understand of modern physical theory, the answer is no. There is a scale known as the Planck scale, where any determinate measurements of space and time (e.g. distance and length) can no longer be made. At the Planck length, spacetime becomes a kind of "foam" where continuity breaks down, and quantum-mechanical uncertainty reigns. At this level, it is speculated that microscopic wormholes come into existence - gateways to other universes in a space of "metaverses." One could entertain the possibility that there is a theory more fundamental than quantum theory, and perhaps this theory would do better in explaining some of its less comfortable results (e.g. violations of the locality principle, the measurement problem, and the theory's myriad interpretations). Interestingly, the concept of a sub-quantum theory was explored in a book entitled "Quanta and Reality: A Symposium." At the current time, however, this is no such theory, and therefore physical theory tells us that any measurements at the Planck scale will necessarily be limited by uncertainty (regardless of the technology). Side: No
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What is matter? stable energy. Is energy infinite? no. If something is infinite, it is infinitely big as well as infinitely small. How do we know energy is finite? - E=MC2 - C is limited - mass is limited. How? the limit is the largest sub atomic particle ever because sub atomic particles are the simplest matter (can't be broken down) -if the two variables are limited, the E is limited - Another reason why energy is limited is because light is the simplest form of energy and it has a speed limit. Side: No
According to two leading fundamental theories in physics, String Theory and Spinfoam Theory (commonly known as Loop Quantum Gravity), matter cannot be made infinitely small. In both theories, matter cannot be compressed into a region smaller than a Planck length, which is roughly a trillionth of a trillionth of a billionth of a centimeter. This is because in both theories, the notion of a length shorter than this does not make physical sense--you cannot, even in principle, measure distances smaller than this length according to both theories. Even if you do not subscribe to these theories, any alternative theory must include a theory of quantum gravity, which is generally expected to be a theory that describes how our usual notions of space and time break down when you do physics over distances comparable to the Planck length, so even then, physicists generally expect distances shorter than the Planck length to be nonsensical. Thus, according to our leading theories, we do not expect that matter can be made infinitely small--regions of space smaller than the Planck length simply don't exist in our current theories. Side: No
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