# Thread: Do you think scientists will ever be able to calculate G from scratch?

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## Do you think scientists will ever be able to calculate G from scratch?

Do you think scientists will ever be able to calculate G from scratch?

6.67408 × 10-11 m3 kg-1 s-2

If anyone could actually come up with a theory of everything, then, in principal, it should be possible to come up with the exact value of G from that theory, or be able to express it in some way, like pi.

2. Originally Posted by WaxRubiks
Do you think scientists will ever be able to calculate G from scratch?

6.67408 × 10-11 m3 kg-1 s-2

If anyone could actually come up with a theory of everything, then, in principal, it should be possible to come up with the exact value of G from that theory, or be able to express it in some way, like pi.

I don't think you can ever calculate something from scratch. But I think what you mean to ask is, will a time ever time when we will be able to find an explanation for why gravity has the value that it has? I guess the answer is yes, but that is just a guess with no good reason to support it.

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I think if someone came up with a TOE that it would just be a model of a universe/reality, there would be no way to really connect it to this reality, it would lie forever on paper.

4. At this point, we can't really determine the value of any of the fundamental constants from first principles. A theory that could do so would indeed be impressive, but seems unlikely to exist.

5. Originally Posted by WaxRubiks
<snip>

If anyone could actually come up with a theory of everything, then, in principal, it should be possible to come up with the exact value of G from that theory, or be able to express it in some way, like pi.
I'm not an expert, but I think your idea about a "Theory of Everything" is incorrect, and it is a mistake I see a lot of people make. A "Theory of Everything" is usually used to name a theory that would combine General Relativity and Quantum Mechanics, and thus describe all the forces in the Universe. But it doesn't mean it would literally describe ever possible aspect of the universe.

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Originally Posted by Swift
I'm not an expert, but I think your idea about a "Theory of Everything" is incorrect, and it is a mistake I see a lot of people make. A "Theory of Everything" is usually used to name a theory that would combine General Relativity and Quantum Mechanics, and thus describe all the forces in the Universe. But it doesn't mean it would literally describe ever possible aspect of the universe.
In the 80s/90s at least there was a general hope that a TOE would explain everything and have one unique solution with no free parameters - a kind of "The universe is how it is because that is the only way it could be". Ideally it would also fit on a T-shirt. Optimism died quite fast on that and these days TOE is used more commonly to mean a quantum gravity theory, as you say. What we now often hear called a TOE is more similar to what used to be a GUT, Grand Unified Theory which was basically a TOE with lots of loose ends (primarily parameters you had to measure and for which there didn't seem to be a reason for the value that they took)

7. Originally Posted by WaxRubiks
I think if someone came up with a TOE that it would just be a model of a universe/reality, there would be no way to really connect it to this reality, it would lie forever on paper.
Maybe you are hinting at goldilocks theories meaning if you wanted to start a universe you would describe certain fundamental things which would allow evolution. The values of fundamentals then on paper produce atoms etc. And people say the values we observe are just right for us to evolve, and if changed a little would make our universe impossible. So on that basis you can play with fundamentals on paper to see what differences would arise. But it is using what we know to lever our assumptions so it becomes kind of circular.

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If this is up for a vote, then I vote yes except, I really think the final theory will, in certain respects, be unit-less, which G is not unit-less. I would be curious how the universe was able to construct units in the first place.

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Originally Posted by Copernicus
If this is up for a vote, then I vote yes except, I really think the final theory will, in certain respects, be unit-less, which G is not unit-less. I would be curious how the universe was able to construct units in the first place.
any self contained theory would have to deal in rations, I think...like 1meter is defined as a ration of other things.

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Originally Posted by WaxRubiks
any self contained theory would have to deal in rations, I think...like 1meter is defined as a ration of other things.
I'm not sure what you mean by rations or ration.

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Originally Posted by Copernicus
I'm not sure what you mean by rations or ration.
I meant 'ratios'...not sure why I typed 'rations'

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Originally Posted by WaxRubiks
I meant 'ratios'...not sure why I typed 'rations'
It could be ratios WaxRubiks. I am very curious to figure out how the Higgs causes mass and what else causes mass.

13. Originally Posted by WaxRubiks
any self contained theory would have to deal in rations, I think...like 1meter is defined as a ration of other things.
The meter is an invented unit of length peculiar to Planet Earth. If I am not mistaken it was intended to be 1/10,000,000 of the distance from the equator to the North Pole along the meridian through Paris. The actual SI length may be slightly off. I see nothing universally fundamental about it.

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Originally Posted by Hornblower
The meter is an invented unit of length peculiar to Planet Earth. If I am not mistaken it was intended to be 1/10,000,000 of the distance from the equator to the North Pole along the meridian through Paris. The actual SI length may be slightly off. I see nothing universally fundamental about it.
oh, it's not fundamental at alll, just a local reference.

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One would need a "Theory of Everything", or at least some theory that unifies gravity and the Standard Model.

To see what would be involved, let us look at the units of measurement in G.
• Second: defined in terms of the frequency of the hyperfine transition of ground-state cesium-133.
• Meter: defined in terms of the second by fixing c, the speed of light in a vacuum.
• Kilogram: defined by an artifact, a platinum-iridium cylinder in a suburb of Paris.

The fixing of c is justified by c being related to the geometry of space-time. In a vacuum, light travels in null space-time lines, lines where the distance and time along them is zero, even if nonzero to outside observers.

The BIPM, which handles measurement units, is planning a meeting in November to decide on some changes to measurement units. In particular, the kilogram will no longer be defined with an artifact, but instead by fixing Planck's constant.

The Cs-133 transition can, in principle, be calculated from the Standard Model, but in practice, it is very difficult. One has to solve three difficult many-body problems: electrons in atoms, quarks in nucleons, and nucleons in nuclei.

So the problem of calculating G from scratch reduces to calculating G in terms of the Standard Model's overall mass scale, however that might be defined.

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The Standard Model is, it must be noted, rather complicated. It has 19 free parameters, and including massive neutrinos, 26 or 28. It also has a rather complicated multiplet structure.

Low-energy (spin, QCD multiplicity, electric charge) mass:
• Higgs (0, 1, 0) 125.09 GeV
• Photon (1, 1, 0) 0
• W (1, 1, +-1) 80.39 GeV
• Z (1, 1, 0) 91.19 GeV
• Gluon (1, 8, 0) 0
• Up, charm, top (1/2, 3, 2/3) / (1/2, 3*, -2/3) 0.0022, 1.28, 173.1 GeV
• Down, strange, bottom (1/2, 3, -1/3) / (1/2, 3*, 1/3) 0.0047, 0.096, 4.18 GeV
• Neutrinos (1/2, 1, 0) / (1/2, 1, 0) ~ 3 * 10^(-11) GeV
• Electron, muon, tau (1/2, 1, -1) / (1/2, 1, 1) 0.000511, 0.10566, 1.7768 GeV

The Minimal Supersymmetric Standard Model (MSSM) adds all these particles:
• Extra Neutral Higgs (2) (0, 1, 0)
• Charged Higgs (0, 1, +-1)
• Neutralinos (4) (1/2, 1, 0)
• Charginos (2) (1/2, 1, +-1)
• Gluino (1/2, 8, 0)
• Up Squark (6) (0, 3, 2/3) / (0, 3*, -2/3)
• Down Squark (6) (0, 3, -1/3) / (0, 3*, 2/3)
• Sneutrino (3) (0, 1, 0) / (0, 1, 0)
• Selectron (6) (0, 1, -1) / (0, 1, 1)

Predictions of these particles' masses depend on the details of supersymmetry breaking.

We still have not observed any of them, even with the LHC, but I think about disproving it what Albert Einstein thought about disproving general relativity: "I would feel sorry for the dear Lord -- the theory is correct."

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Now for the (Minimal Supersymmetric) Standard Model before electroweak symmetry breaking. Quantum numbers are (spin, SUSY-partner spin, QCD multiplicity, weak-isospin multiplicity, weak hypercharge). The paired ones are (left-handed), (right-handed).
• B (1, 1/2, 1, 1, 0)
• W (1, 1/2, 1, 3, 0)
• gluon (1, 1/2, 8, 1, 0)
• Higgs Hu (0, 1/2, 1, 2, 1/2) / (0, 1/2, 1, 2, -1/2)
• Higgs Hd (0, 1/2, 1, 2, -1/2) / (0, 1/2, 1, 2, 1/2)
• Left-handed quarks Q (1/2, 0, 3, 2, 1/6) / (1/2, 0, 3*,2,-1/6)
• Right-handed up quarks U (1/2, 0, 3*, 1, -2/3) / (1/2, 0, 3, 1, 2/3)
• Right-handed down quarks D (1/2, 0, 3*, 1, 1/3) / (1/2, 0, 3, 1, -1/3)
• Left-handed leptons L (1/2, 0, 1, 2, 1/2) / (1/2, 0, 1, 2, -1/2)
• Right-handed electrons E (1/2, 0, 1, 1, 1) / (1/2, 0, 1, 1, -1)

The W is a triplet, with two charged and one neutral. The two charged ones become the low-energy W+- and the neutral one mixed with the B to make the photon and the Z.

"Weak isospin" is something that gets flipped in charged weak interactions, like beta decay. "Weak hypercharge" is the average electric charge of a multiplet.

In the plain Standard Model, Hd is a version of Hu, not a separate particle.

If right-handed neutrinos N exist, they would have quantum numbers (1/2, 0, 1, 1, 0) -- they would be Standard-Model singlets.

The particles' interaction terms look rather simple: U.Hu.Q, D.Hd.Q, N.Hu.L, E.Hd.L, Hu.Hd

The neutrinos' masses are much smaller than the other elementary fermions' masses. There is a theory that explains this called the "seesaw model". It states that right-handed neutrinos have very high masses (interaction term N.N), and that the neutrinos we observe are mostly left-handed ones.

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The patterns in the Standard-Model multiplets have inspired searches for Grand Unified Theories. I will list some of the most straightforward ones.

SU(5) - Georgi-Glashow
• Gauge: G(24) = gluon + W + B + (1,1/2,3,2,-5/6) + (1,1/2,3*,2,5/6)
• Up Higgs: H(5) = Hu + (0,1/2,3,1,-1/3) / H*(5*) = Hu* + (0,1/2,3,-1,1/3)
• Down Higgs: H(5*) = Hd + (0,1/2,3*,1,1/3) / H*(5) = Hd* + (0,1/2,3,1,-1/3)
• Elem Ferm F(1) = N, F*(1) = N*
• Elem Ferm F(10) = Q + U + E, F*(10*) = Q* + U* + E*
• Elem Ferm F(5*) = L + D, F*(5) = L* + D*

Some new particles appear that can cause isolated protons to decay. Proton decay is a prediction of most Grand Unified Theories.

There is an interesting pattern of elementary-fermion multiplets: left 1, right 5, left 10, right 10*, left 5*, right 1 -- the binomial coefficients for power 5. That suggests some further simplicity. Also, as with the MSSM, the SUSY Higgs particles come in mirror-image pairs.

The interaction terms go as
F(10).H(5).F(10) -- U.Hu.Q
F(5*).H(5*).F(10) -- D.Hd.Q, E.Hd.L -- notice the mass unification for the down-like quarks and the charged leptons
F(1).H(5).F(5*) -- N.Hu.L
H(5).H(5*) -- Hu.Hd

-

The next one up is SO(10) -- Georgi-Fritzsch-Minkowski
It contains the SU(5) one, with an extra "charge" related to B-L, baryon number - lepton number
• Gauge: G(45) = (24,0) + (1,0) + (10,-1) + (10*,1) -- more particles that can cause proton decay
• Higgs: H(10) = (5,-1/2) + (5*,1/2) -- the MSSM/SU(5) mirror images are united as one Higgs multiplet
• Elem Ferm F(16) = (1,5/4) + (10,1/4) + (5*,-3/4), F(16*) = (1,-5/4) + (10*,-1/4) + (5,3/4) -- only one multiplet per generation

There are only two interaction terms, F(16).H(10).F(16) and H(10).H(10). The first one unifies all the EF mass terms, but it is too successful: it does not allow cross-generation decay.

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Then one called E6. It contains the SO(10) one, with an extra "charge" that I can't interpret.
• Gauge: G(78) = (45,0) + (1,0) + (16,-1) + (16*,1)
• Others: X(27) = (16,1/3) + (10,-2/3) + (1,4/3), X*(27*) = (16*,-1/3) + (10,2/3) + (1,-4/3)

X includes the elementary fermions and the Higgs particles. It has an additional "Higgs singlet" (rather standoffish particle), S.

Its interactions: X.X.X = F.H.F + S.H.H

The S.H.H replaces the H.H term, and if the S is observable at low energies, it makes two neutral Higgs particle and one neutralino.

-

Finally, E8. It contains the E6 one, with an extra type of multiplet added on called SU(3). It has this breakdown:
Gauge: G(248) = (78,1) + (1,8) + (27,3) + (27*,3*)

So in E8, all of the Standard Model fits into one multiplet, at least if one ignores spins. There are two main theories that features an E8 super GUT: string theory and Garrett Lisi's theory. String theory has a way of getting different spins: shrink six of the dimensions into a teeny tiny Planck-sized ball ("compactification"). However, I don't know how Garrett Lisi's theory does it.

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Although E8 has the simplicity of putting every Standard-Model particle into its fundamental multiplet with room to spare, it requires some complicated cascade of symmetry breaking to get to the Standard Model. One can get part of the way there with string theory, and I don't know how GL's theory does it.

String theory has the virtue of including gravity, meaning that in theory, one can calculate G with it and relate it to the Standard Model's mass scales. I wrote "in theory" because whether or not one gets the Standard Model depends on the topology of space-time, especially the topology of those six small dimensions. And that is far from unique. So while we have essentially one theory, we have a heck of a lot of possible states of that theory. Some estimates go as high as 10^(500) (the "string landscape").

20. Originally Posted by profloater
Maybe you are hinting at goldilocks theories meaning if you wanted to start a universe you would describe certain fundamental things which would allow evolution. The values of fundamentals then on paper produce atoms etc. And people say the values we observe are just right for us to evolve, and if changed a little would make our universe impossible. So on that basis you can play with fundamentals on paper to see what differences would arise. But it is using what we know to lever our assumptions so it becomes kind of circular.
Has there been any work to calculate what universes with different free parameters would look like and if they could support life?

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Originally Posted by Tom Mazanec
Has there been any work to calculate what universes with different free parameters would look like and if they could support life?
Yes, quite a lot. It underpins one of the arguments behind the various levels of anthropic principle that has been resurrected to try to deal with the landscape problem of string theory.

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