Why the Graviton Can't Be Found

Why hasn't the graviton been discovered yet? A thought experiment could shed some light on this question. Imagine a universe with only a Higgs field and nothing else. No strong, weak or electromagnetic interactions, no spacetime as we understand it. The basis of this universe is just the Higgs, so the only boson available is the Higgs boson. It's true the Higgs can decay into other particles, but let's focus on it while it is a Higgs.

Now, in such a universe, there should be no gravity, since there are no gravitons, right? (We performed a similar thought experiment in a previous post involving photons. Click here to read all about it.) Let's lay out the mathematics and see. First, we define the variables:

If we find gravity in our Higgs-only universe, that would explain why the graviton hasn't been found--it isn't necessary--so let's begin with the Higgs Lagrangian (L) at equation 1 below. At 2 we convert the Lagrangian to the Hamiltonian (H). To make the math less cumbersome we set the kinetic term equal to chi at 3.

We make a substitution at 4. Equation 5 is a Hamiltonian (H') with the same energy as H, but a different mass and kinetic energy. Equations 4 and 5 represent two adjacent fields whose centers of mass are r distance apart. At 6 we show the equality or conserved energy of the two fields. At 7 and 8 we equate the kinetic and potential energy differences.

Here is an overly simplified, crude diagram for illustrative purposes only:

As you can see the two adjacent fields are outlined with imaginary boxes and labeled blue (high kinetic energy/low mass) and red (low kinetic energy/high mass). The white dots represent the masses. Now, equation 8 fails to take into account distance r, so let's convert mass m as follows:

At equation 11 we have distance r where we want it. Equation 11 is the value of the kinetic-energy difference between the two fields. Classical kinetic energy is a function of velocity squared. What we want to know is the value of the velocity squared:

Now that we know the value of velocity squared, we can do one more step and determine the value of the gravitational constant for this Higgs universe (Gh):

We made a substitution at 14 above and end up with Newtonian gravity! And no gravitons! Equation 14 reveals that gravity is the net velocity squared of kinetic energy differences. If we divide both sides by another r, we get gravitational acceleration. Given these results, one could postulate that gravity is the net motion resulting from motion differences. And motion differences are caused by mass differences. Einstein suggested that matter curves spacetime. However, that assertion is very specific to our universe. A more general assertion is mass disturbs the status quo, whatever that may be, and causes kinetic energy variations. At the quantum scale, gravity does not seem to need its own boson. Information is passed using whatever boson is available. In this case, it's the Higgs.

Now, for extra credit, let's derive Einstein's field equations from equation 14:

If you are feeling ambitious, you can work backwards and derive the Higgs Langrangian from Einstein's field equations.

Update: Here is a couple of videos that falsify the graviton:

Unifying Spacetime and the Forces

Let's start with a simple idea and expand on it. Imagine you have a total energy (E) and you subtract from that the energy of the strong, weak and electromagnetic forces. What do you have left? Gravitational energy.

Now we need something that represents the total energy. How about Schrodinger's Hamiltonian?

It's a good idea to express Schrodinger's Hamiltonian in terms of light speed squared (C^2). Why? Because light speed squared connects all the fundamental interactions (forces)--so we will set them all equal to C^2.

If we divide the Hamiltonian by mass (m) we set it equal to C^2. (C^2 = E/m.) Next, let's multiply each C^2 by time squared (t^2). Doing so gives us the spacetime metric. To make the terms equal, we should probably multiply each one by a coefficient K.

As you can see we've unified the forces and spacetime. What better way to spend a Sunday afternoon? The last equation, which is the spacetime metric, is just another way of saying, "Gravitational energy is equal to the total energy minus the other forces' energy."

In case you are curious, here are the variables: s is spacetime; z is the proton number; epsilon is the permittivity of free space; h-bar is Planck's constant; c is light speed; t is time; gij is the metric tensor. E is electricity; B is magnetism; I is current; p is charge density; Gn is Newton's constant; Gij is Einstein's tensor; Tij is the energy-stress tensor; Mh is the Higgs mass; g is the magnitude scaling constant; e is the natural exponent; m is the Yukawa particle mass; r is the particle radial distance; Fw is the weak force.

And let's not forget the equation for the Higgs field energy. The Greek letter there is the complex scalar field. H is its Hamiltonian (energy). The next term is kinetic energy and the last two terms are potential energy.