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:

Why Gravitational Waves Fail to Confirm Extra Dimensions

According to the holographic principle, our four-dimensional universe, consisting of three space dimensions and one time dimension, is a surface area of a five-dimensional spacetime called "the bulk." The remaining dimensions of string theory or M-theory are allegedly compacted and rendered insignificant.

Gravity, compared to the other fundamental interactions, is weak due to the graviton's unique ability to move between the surface area (our spacetime) and the bulk. Other particles remain fully in our spacetime and thus have more intensity. At least that's how the story goes. Unfortunately, the gravitational-wave test described in the above video failed to confirm the existence of "the bulk" or any extra dimensions beyond our four-dimensional spacetime. This does not surprise me, given the problems extra dimensions can cause (click here to read all about it).

So why did the gravitational-wave test fail? Do we really need "the bulk" to explain the nature of gravity? We will explore these questions. First, let's define the variables we will use:

According to general relativity, gravity is a function of energy density, so let's begin with the energy density of an atom. An atom is mostly space, so let's only consider the volume of space taken up my the average nucleus and the electrons. That approximate volume can be found in the denominator of equation 1 below:

Of course if we put that volume in the numerator, we get the energy (E):

If we put a larger volume (V) in the denominator (equation 3), we get a reduced energy (E'). Reduced energy is consistent with weak gravity, so we are on the right track.

We don't want Energy units, so at 5 and 6 we use meters and Newtons to adjust the units:

Now, coincidentally, 10^-45/N is approximately equal to G/c^4, so we make the substitution:

We use distance D and the alpha scale factor to make more substitutions at equation 9. From there we derive equation 12.

Equation 12 is Newton's equation. We were able to derive this equation because we started with the premise that the intensity of gravity is determined by the actual amount of space a particle interacts with. For baryonic matter, that actual amount of space corresponds with the gravitational constant G. Note that no extra dimensions are needed to get equation 12. Our 4D spacetime is sufficient. So why should we be surprised that the gravitational-wave test failed to confirm "the bulk"?

Caveat: the above mathematics may work just fine for ordinary matter such as atoms and molecules, but what about singularities such as black holes? Theoretically, a singularity takes up no space, so there shouldn't be any interaction between the matter and space, but there is! To resolve this conundrum, we first need to establish that light speed is truly the top speed in our universe. Consider the familiar Lorentz equation:

The main problem with this equation is time (t) is arbitrary. Let's make it precise. Let's make time (t) equal to the age of the universe. When I say universe I mean everything including the megaverse if such a thing exists. What we want is the longest time ever lapsed--so we set t accordingly and define the other variables we need:

Now we derive 21 below:

Line 21 shows that no velocity (v) can exceed light speed (c). So what does this have to do with gravity and black holes? Given the fact that light speed is the top speed, we can derive the following:

Take a look at 25 and 26 above. At 25, G stays constant as long as the change in time (delta-t) is equal to or less than the age of the universe. Note that delta-t increases as radius r decreases, so G remains constant. But delta-t has an upper limit of t. If r continues to shrink, G must also shrink. Thus it appears the intensity of gravity is determined by how much space interacts with matter. The smaller the radius r, the smaller the space the matter occupies. Equation 27 shows that the intensity of gravity never exceeds the speed of light squared no matter how much radius r shrinks.

In conclusion, "the bulk" and extra dimensions are completely unnecessary to describe gravity.