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Deriving the Gravitational Constant G

Today we will derive the gravitational constant G, also known as Newton's constant. Here are the variables we will be working with: ...

Tuesday, August 1, 2017

Adding Gravity to the Standard Model Lagrangian

Here is one version of the Standard Model Lagrangian. Click on the image below to learn more details. Lagrangian L =

To read a pretty good outline re: the Standard Model Lagrangian, click here.

Now you have probably been told a gazillion times that the Standard Model does not include gravity, that Einstein's field equations are incompatible with the big messy equation you see above. Let's have a look at the field equations:

The energy-stress tensor (Tij) provides a clue to how we can unify gravity with the Standard Model. Its units are energy density or energy over a volume (V). The Lagrangian has units of energy. Hmmmm ... if we contract the tensor indices and do a little algebra, we get equation 5 below:

Equation 5 shows that the scalar or zero-order tensor T is equivalent to the Lagrangian (L) divided by a volume (V). That leads us to equation 6 below:

We can now see the relationship between gravity and the other forces. If we do a little more algebra, we get an interesting result:

At equation 9 we add the newly-formed gravity Lagrangian to the Standard Model Lagrangian. Doing this yields the ground-state vacuum energy--and this quantity is consistent with the Wilkinson Microwave Anisotropy Probe measurement. So if we add gravity to the Standard Model as illustrated above, we not only get a result that is mathematically consistent, but also consistent with observations.

2 comments:

  1. If gravity is due to the curvature of time (and that's a debatable "if" addmitedly), and time is a wavelike field of energy (another big "if") and I believe these ideas to be true for many reasons, then, I cannot see how we might apply the rules of this cyclical energetic field, the rules of gravity, below the scale of the cycles where the quantum world exists. It's not that gravity nd quantum physics are incompatible but just that their rules apply in different domains. We will never be able to reconcile the two mathematically.

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    Replies
    1. "We will never be able to reconcile the two mathematically."

      See equation 9. To reconcile the two involves an understanding of expectation values and expressing gravity in Lagrangian terms. So it's not impossible.

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