What the Bleep!!! Down the rabbit hole

G'day Ernie, I missed your prior post - so HI! :-)

Now to task:

#1 With energy there are no absolute levels. Any physical measurement can only ever define the difference between levels, and any of the mathematics gives the same predictive result for a given E versus (E + constant). This behaviour can be related to a deep symmetry in the physical laws that describe nature - that they are constant over time. This seems to be the case for periods studied ( or deduced ) by science thus far. So 'ground state' refers back to an arbitrary, but in practice reasonable, choice of what is meant by 'zero' energy.

#2 Enter Mr Heisenberg, who allows a zero level, but physical systems cannot actually achieve an exact level of any magnitude - zero or otherwise. The Uncertainty Principle implies that any particle must have a minimal product of exactness in its 'conjugate co-ordinates'. These come in pairs like linear position & linear momentum, energy & time, angular position & angular momentum ..... Moreover there is 'orthogonality', such that for instance linear position/momentum have a minimal product in each spatial direction separately. Anyhows, regardless of any choice of 'zero' setting there are irreducible uncertainties. Unfortunately some explanations blur the important distinction between energy level/scale choices and energy level uncertainties, they are distinct concepts.

#3 Let's say you have, even classically, some bucket of gas which you measure all sorts of properties ( pressure/volume/mass ) with respect to it's interior kinetic energy. Take an 'ideal gas'. Then one can define a quantity ( T = PV/nM ) which has values for all manner of choices of gases. If you investigate over a wide range of the P/V/n/M parameters, then after a while you may deduce that one can extrapolate 'back' or 'down' to a hypothetical case where T becomes zero. Now try and achieve that state in practice - you won't. This 'T', as defined by this process, is the 'thermodynamic' temperature and all systems studied to date have never achieved an exact null value. This is explained as the 'ground' state being above zero by a small, but irreducible, gap.

#4 The ground state wave function then represents that bit of mathematics which is used to quantitatively describe said ground energy level. By the machinery of quantum mechanics it also yields the above uncertain behaviours - it falls out at the end - as it was designed to. For any given experiment however the number you get from any measurement process is going to reflect a distribution of results around an average or 'expected value' of that wave function. If you watch the system for a long time then the variation of your numbers around that average will gradually diminish and one's estimate of the energy level under study becomes more exact. This is a pragmatic meaning of energy and time being conjugate co-ordinates.

#5 The Planck scale is typically described as a distance, but can denote an equivalent energy/mass/momentum/time. It corresponds to the smallest theoretically possible uncertainty in position for the largest theoretically allowed momentum known. We're talking momenta for big bang scale energies now ie. corresponding to really massive/energetic events. Even much, much larger than your friendly neighbourhood billion solar mass black hole. If one were to hypothecate a particle accelerator to achieve that, it would span the known universe, and probably take a while to set up ..... :-)

#6 Perhaps the best way to describe the Planck scale therefore is: it is the smallest possible definable distance that could ever possibly be measured/deduced ( if quantum mechanics and other assumptions are true ).

#7 Strings are pretty well defined to have dimensions of about the size of the Planck length. If you subscribe to the idea that a length can only be what you can measure ( fair enough ) then you can't look 'inside' a string. They are truly atoms in the old Greek indivisible sense and we're never going to see them directly. We may construct a theory ( M or whatever ) that forms a unifying basis for other explanations at larger scales ( and lesser energies ).

Cheers, Mike.