A math teacher of mine always describes an infinite amount of points in any one area, line, etc. Although I know exactly where her logic is coming from, doesn't quantum theory tell us that she is wrong? Im not exactly the most knowledgeable on the subject, but from what I understand the smallest of anything is known as a the plank length, roughly equal to the size of a photon. Does this mean that if you take any distance and continually divide it by two, you will eventually get to the plank length? Therefore, you will then have nothing smaller to "cut" or "break" this photon because it is the smallest thing that exists. I guess it mostly depends on how one defines a point --In theory or in reality (or in my case, utter confusion). Any comments?
The basic problem in your thinking is equating math and physics. In mathematics, there are in infinite number of points in a line interval, etc. However, when talking about physical reality, the story, as you point out, is quite different. Try to keep this separation (math or physics) in mind.
I agree. That's basically what I meant by "in theory or reality" --Mathematics being theory, and Physics being reality.
Mathman is right. Despite what most people think, mathematics does not describe "the real world". Mathematics is a purely logical construction that just happens to be very useful in modeling real world events.
Hi Possumking, The Planck length is not the size of a photon. The photon doesn't really have a well defined size, but this is a subtle point for another day. Lots of people argue that spacetime will somehow be discretized on the scale of the Planck length, or that the Planck length is somehow a minimum distance, or variations thereof. The important thing to remember is that nobody really has the slightest idea what the universe is like at the Planck scale. We don't know if spacetime is continuous or discrete, or if the notion of spacetime has any meaning at all. If it were discrete, then you're likely right that it wouldn't make sense to talk about lengths less than the Planck length. So, keep exploring this fascinating world, but remember that it's all very loose speculation at this point.
sorry that didn't reply earlier, there is no prove that Planck lenght is the lower limit belows which space and time concepts have no sense, accualy planck lenght contains gravity constant G and has sense as the wave-lenght of a graviton or Schwartshild radius of a graviton, i am not sure about it physical sense but it do not have any direct sense and is very wrong to be stated that the quantum of space is the Planck lenght
Possumking Depending if you're interested, consider the hyperreal number line. Aside from the infinite amount of real numbers on the real number line, you can pick any two real numbers (infinitely close actually) and still fit an infinite number of hypperreal infinitesimals in there. It's a whole another way of deriving the calculus we all know and love. ... and the whole hyperreal deal is just a mathematical construct, just theory, yet calculus is so useful in the real world
