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Fields Vs Dimensions Vs Axes

  1. Mar 16, 2013 #1
    A lot of below might be a question of semantics however it helps to understand better, I am a novice:

    1. What's the difference between a field and a dimension?

    A field is present at all points in time and space, ...so is a dimension.

    why don't we call/label a field as a dimension?

    2. or vice-versa -- Time-space is present at all points in time-space. Time-space can be curved, bent, twisted by matter-energy. So why don't we label space-time as a field?

    3. If we have separate field for electron, photons etc, (i.e. a field for each elementary particle) don't we end up with too many fields? pervading all points in space-time

    4. x,y,z are also called axes, why does the need arise to call them dimensions? so why do we consider space-time as four dimensions when it can be only one (i.e. space-time = one dimension)?

    Does it spoil the mathematics/physics in any way?

    5. We say Hilbert space has infinite dimensions, why not call them axes? that way we have just one dimension = space-time and we can draw as many axes we want in space-time.
    does that cause any problems/conflicts in the mathematics/physics?

    _________________________________________________
    Because we are live, and are trapped, in space-time
    We might be psychologically biased towards the primacy of Space-Time
     
    Last edited: Mar 16, 2013
  2. jcsd
  3. Mar 16, 2013 #2
    By a dimension we generally mean a direction in spacetime.

    A field, by contrast, is quantity that takes on a numerical value at each point in spacetime.

    Spacetime itself isn't a numerical value, so it isn't the sort of thing we mean by a field. But the shape of spacetime is described by the metric tensor (http://en.wikipedia.org/wiki/Metric_tensor). The metric tensor is a quantity that takes on a value at each point in spacetime: that is, the metric tensor is a field. So the properties of spacetime at each point are fields.

    How many fields is too many?

    When we say the spacetime is four-dimensional, we mean the following: to specify a point in spacetime, you need to give four real numbers, for example the point's x-, y-, z-, and t-coordinates.

    When we say that Hilbert space is infinite-dimensional, we mean that in order to specify a vector in Hilbert space you need to give an infinite list of real numbers (for example, the inner product of the vector with each member of a basis of the Hilbert space).
     
  4. Mar 16, 2013 #3
    Thanks The_Duck, Well answered

    Every particle to have a (separate/individual) all pervading field seems inefficient.

    Let's take the case of traffic. While there are cars, trucks, busses they are all on the same road. Each car, truck, bus does not have its own separate road (field).
     
  5. Mar 16, 2013 #4
    Well, God can't please everyone I guess. As the Hitchhiker's Guide puts it: "In the beginning the Universe was created. This has made a lot of people very angry and has been widely regarded as a bad move."

    So-called "grand unified theories" are in part motivated by your concern that it seems inelegant to have all these different fields lying around. In grand unified theories people postulate a much smaller number of fields and try to show how the many standard model fields could arise as separate parts of these "unified" fields. See http://en.wikipedia.org/wiki/Grand_unified_theories
     
  6. Mar 16, 2013 #5
    Agreed The_Duck. Which one is the bad move, though? ;)

    -Universe being created or
    -People getting angry about it? Or
    -Both

    Was Adams referring to the second one?

    Thanks, I will go through it at some point......... in space-time.
     
    Last edited: Mar 16, 2013
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