What does it actually mean when we talk about “inflating” a wormhole? If we find a Planck-scale natural wormhole, and we cram exotic matter into its two mouths to stretch it up to, say, one metre wide, then the wormhole may nominally now be a metre across … but have we actually added any additional useful space to the throat interior, or have we taken a throat that only has a fixed amount of internal space and "stretched" that fixed space, so that although it's now nominally one metre across, the internal measurement (and the wormhole's “capacity” as measured with internal rulers) might still be Planck-scale?
Would inflation be adding more space and more useful “transit capacity” to the wormhole throat, or would we still have the original Planck-scale throat, inhabiting a distorted and stretched region of space in which everything is rescaled and magnified?
Eric: May be what I will tell you now will give you a bit of "matter" to think. If you scale a quantum black hole, mass, length and time of Planck´s units by a factor of 10^61 then you get the present mass length and age of the visible universe.
Planck´s units: 10^(-5) gr, 10^(-33) cm, time 10^(-44)sec
Universe: 10^56 gr, 10^28 cm, age 4 10^17 sec
All numbers are orders of magnitude
Regards,
Antonio
Do we have the mathematical tools to perform this calculation? How are we to 'scale' the measurements of equations? If we have a measurement that is, say, 10^(-30) cm (with an error term of) +/- 10^(-33) and we want to 'scale up' our measurements to something like 10^0 cm (with an error term of) +/- 10^(-6). How are we to address the extreme difference in error terms? Even if we could get the error term at our scale to 10^(-10) - there is still such a tremendous gap in error terms to make any association between the measurements irrelevant.
Are our mathematical tools adequate to the task - or do we need new tools? Do we have the mathematical tools able to cross vast differences in scale? I think not - and this is a large problem facing science today. We are not able to develop equations that cross significant spans of scale because we do not have adequate mathematical tools.
Further - our concept of space as 3-dimensional (physical - less 'time') does not include scale as a continuum. Any measurement implicitly includes a scale 'measurement' along the continuum of scale (the power of our measurements). This is an implicit 4th continuum (or dimension) required for any measurement of location we make. We should be able to measure the distance between any two objects in 3-D space, yet try measuring the distance between your liver and an atom in your vein. We must limit our measurements to small 'spans' of scale - because our mathematical tools cannot adequately cross spans of scale.
In scale modeling and simulation, crossing 'upward' in scale involves integration across a 3-D space. This integration 'moves' the model 'up' in scale - again suggesting scale is a continuum of space. However, this still only works for scales very 'close' to each other.
I do not think we have the mathematical tools to answer this question.