Lee Smolin tantalizing hint in TTWT

[RandallB]

Lee Smolin tantalizing hint in TTWP

Marcus
You seem to have one of the best reads on Lee Smolin and the points he makes.
I’m hoping you, or someone here, can help make sense of part of his book ‘The Trouble With Physics’.
On page 217 he refers to “another tantalizing hint”, relating the very large (GR scale) with the very small (QM scale).
He is dealing with R_d the distance scale and R_m the mass scale of the universe (my subscripts on R).
I understand arriving at 10^60 of Planck scale for R_d (page 204).
Lee then uses “just the fundamental constants of physics” to covert that to R_m.

Which constants did he apply; and what is R_m?
It would have been simple enough to just list them in his book!

His point is R_m give the same “order of magnitude” as the mass differences between the different types of neutrinos.
What is he talking about?
He could have listed this as well if it is such an important comparison.
I make the mass scale difference between electron and muon neutrinos as 10^5
and between muon and tau neutrinos as 10^2.
Maybe he means the full range for a 10^7 scale, I cannot tell from the book.
He seems about one paragraph short of making himself clear.

Can you, or does anyone, have a reference that might make sense of this.

 

[marcus]

Hi Randall,
I think I can help
No, it turns out I CANT help. I tried and got crazy numbers!

He must be using some way I don't know to get an energy (or mass) corresponding to a length.

====================
HERE IS WHAT I TRIED which didnt work out:
If one is working in Planck units, the distance he is talking about (prob. square root of reciprocal cosm. const) is 10^60 Planck length.

So the mass, again in Planck units, would be (I'll explain later) 10^-60 Planck mass.

But Planck mass is just under 22 micrograms. So the mass he is talking about (the mass equivalent of the cosmo distance scale) is 10^-60 of that, or about 22 x 10^-66 grams...or 22 x 10^-69 kilogram.

THIS IS TOO CRAZY SMALL. So I am missing something. Maybe someone else can explain.
============================

Here is what is going on in the approach I tried. If you look at fundamental constants like h, or h-bar, and c, you find that h-bar c is the product of any photon's (angular) wavelength times its energy
there is a locked in relation between vacuum wavelength and energy----they are reciprocals

so anytime you specify a length, you are simultaneously specifying an energy----and a big length corresp. to a small energy

there is often a little ambiguity because you don't know whether the author is talking h or h-bar.
In my experience they most often mean h-bar-----they think of it as somehow more fundamental
(and they secretly prefer to think of the "angular wavelength" of something which is the length of a full cycle divided by 2 pi)----
but that 2 pi ambiguity only involves some order-one indefiniteness so it does not have much affect on these order-of-magnitude discussions.

 

[marcus]

think of the energy of a photon which has that huge wavelength----it has to be miniscule

this is giving funny answers, I have to check.

==================

LATER: I went and looked at that passage on page 217 that you were asking about. And I can't interpret it.
I will give it another try later, if nobody else shows up and straightens us out.

 

[RandallB]

Well you point me in a better direction for R_m
I had been thinking of a larger number like the total mass, your smaller number makes much better sense.
By taking a broad guesses at neutrino masses, since they are not measured very precisely yet anyway, I think I can define a reasonable Kilo-gram Mass Scale for each neutrino as follows:

[u]Neutrino          eV            Kg-mass     Kg-mass scale[/u]
 electron        1 eV         2x10^-36             ^-36 
  muon          100 KeV       2x10^-31             ^-31
   tau           10 MeV       2x10^-29             ^-29

Now relating those scales I still cannot do,
as you say the numbers seem to be crazy small for R_m.

But since this is related to measurements from WMAP
If we look at the Dipole, Quadra pole and Octa-pole;
Wouldn’t the R_l be getting progressively shorter for each.
Thus the R_m would be progressively larger.
Maybe something here is where he sees a correlation,
if not in direct scale values, maybe it the ratios of the two sets of three?