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A 5th Dimension

Using Vector Maths, could one describe the path of a "elementary" particle
by adding a 5th dimension. The first three dimensions would be the place:
x, y, z (of course relative). The fourth dimension time, when the particle
was where. And the 5th dimension as the Uncertainty Principle (ΔxΔp>ħ/2 and ΔEΔt>ħ/2), defining where the particle roughly was or will be.
So that in the end there are millions of paths that could be gone
with different certainties.

Do not hesitate to ask for clarification

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    Mar 11 2014: A book you might find interesting to put your work in context is Physicist Lisa Randall's book Warped Passages. She articulates how extra dimensions are built into theoretical models in particle physics. I think eleven dimensions is what many scientists in that field are examining, some dimensions being "rolled up."
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      Mar 11 2014: The 11 dimensions of string theory seem to be quite popular. Thank you for the
      suggestion Fritzie! I'll look for the book and see where the pieces fit together. =D
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    Mar 13 2014: My am almost certain the Uncertainty Principle is not a dimension, but is a method to explain how particles act when we cannot actually observe them completely. An explanation for the particles behavior could be another dimension but the equation does not describe it. Equations can be misleading because there is the equation (regarding position, momentum and energy changes and result) and all the possible implications of this equation (such as observation interference, another dimension or even another form of energy etcetera).
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      Mar 14 2014: There is a book for arguments against using equations to solve nature,
      it's by Jim Baggot and called "Farewell to Reality". I would like to add the question,
      which I forgot in the description, "What is a Dimension?"
      Thank you for the reply. =D
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        Mar 14 2014: di·men·sion
        an aspect or feature of a situation, problem, or thing.

        In physics I think of it as something that structures reality.
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          Mar 14 2014: Thank you for your opinion.
          So what is real?
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        Mar 14 2014: IMO something that is real is something that can be continuously validated in some way and stays constant. After all in a seemingly infinite space almost anything can happen, so really real is a collective of perspectives facts and interactions.