I would stay with dimensionless units, which can include qubits etc. The 
Planck mass is m_p = sqrt{ħc/G} and this can be compared to the mass of 
some elementary particle M so that

(M/m_p)^2 = GM^2/ħc,

which looks suspiciously similar to the fine structure constant α_e 
= e^2/(4πεħc) ~ 1/137 and we can call the above ratio α_g. My temptation 
is to put the mass of the Higgs boson in for the mass M = 125GeV and the 
Planck mass is 1.22×10^{19} GeV and we then get α_g = 1.02×10^{-36}. 

I chose the Higgs particle mass because I think the Higgs field is a scalar 
field connected to gravity. Also the masses of all fundamental particles we 
know, not complex bound systems like hadrons with an induced mass gap, is 
given by the Higgs field. The masses of other particles is related to this 
with various Yukawa coupling terms. The Higgs field, along with inflaton 
and related scalar fields (dilatons axions etc) are potentially singlet 
entanglement states of a gauge-like field that in a triplet entanglement is 
equivalent to a graviton. 


On Sunday, January 6, 2019 at 10:10:36 AM UTC-6, Jason wrote:
> I am trying to make a list of what properties are comparable between two 
> universes and which properties are incomparable. I think this has 
> applications regarding what knowledge can be extracted via simulation of 
> (from one's POV) other abstract realities and worlds (which may be actual 
> from someone else's point of view).
> So far this is what I have, but would appreciate other's 
> insights/corrections:
> Incomparable properties:
>    - Sizes (e.g., how big is something in another universe, is a galaxy 
>    in that universe bigger or smaller than a planet in our universe?)
>    - Distances (what possible meaning could a meter have in that other 
>    universe?)
>    - Strength of forces (we could say how particles are affected by these 
>    forces in their universe, but not how they would translate if applied to 
>    our own)
>    - Time (how long it takes for anything to happen in that other 
>    universe)
>    - Age (when it began, how long the universe has existed)
>    - Speeds (given neither distance nor time is comparable)
>    - Present (what the present time is in the other universe)
>    - Position (it has no relative position, or location relative to our 
>    own universe)
> Comparable properties:
>    - Information content (how many bits are needed to describe state)
>    - Computational complexity (how many operations need to be computed to 
>    advance)
>    - Dimensionality of its objects (e.g. spacetime, strings, etc.)
>    - Entropy
>    - Plankian/discrete units (e.g. in terms of smallest physically 
>    meaningful units)
> Unsure:
>    - Mass? (given forces are not comparable, but also related to energy)
>    - Energy (given its relation to both entropy and mass)
> So if we simulate some other universe, we can describe and relate it to 
> our own physical universe in similar terms of information content, 
> computational complexity, dimensionality, discrete units, etc. but many 
> things seem to have no meaning at all: time, distance, size.
> Do these reflect limits of simulation, or are they limits that apply to 
> our own universe itself?  e.g., if everything in this universe was made 
> 100X larger, and all forces similarly scaled, would we notice?  Perhaps 
> incomparable properties are things that are variant (and illusory) in an 
> objective sense.
> A final question, are they truly "causally disconnected" given we can 
> simulate them? E.g. if we can use computers to temporarily compel matter in 
> our universe to behave like things in that simulated universe, then in some 
> sense isn't that a causal interaction?  What things can travel through such 
> portals of simulation beyond information?
> Jason
> P.S.
> It is interesting that when we consider mathematical/platonic objects, we 
> likewise face the same limits in terms of being able to understand them.  
> e.g., we can't point to the Mandlebrot set, nor compare its size in terms 
> of physical units.

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