Originally Posted by **pittsburghjoe** Is it saying the power of observation/measurement of a quantum object is not enough to make it a fully 3D + 1 space-time object? If something on our scale was partially fuzzy depending on how many measurements you made (at the same time) ..would you say it was a full fledged three dimensional object? No, you'd say isn't fully here. |

(Note: Any particle, such as an electron to be specific, has 6 degrees of freedom in its motion: 3 spatial and 3 momentum. So the electron actually carries 6 dimensions in phase space. It also has spin and if it's a left handed electron it also has weak hyperspin...that's 4 more dimensions. (Right handed electrons have 0 weak hyperspin.) I know this isn't what you are talking about but we have to be clear on just where these dimensions live.)

The Uncertainty Principle says nothing about experimental equipment and how well it measures. It can be best explained using the wave mechanics representation of QM.

Consider a gaussian wavefunction, or more correctly a gaussian wavepacket. (It can be shown that the maximum uncertainty in position can be got from this. The associated momentum wavefunction is a delta function so the uncertainty in the momentum is 0 and hence the uncertainty in position is a maximum.) I've played with the scale to make the wavefunction more "peaked." The blue line represents the "width at half-maximum." This is an average size of the width of the wavefunction and tells us that the particle is generally within that range. This is where the uncertainty in the position as given by the Uncertainty Principle comes from. It has nothing to do with how many dimensions that the particle lives in.

-Dan