The foundation of the Fractal-Holographic Universe is space itself. Space is everywhere, saturating the emptiness between atoms as well as galaxies – yet measurements reveal that space is not empty, but full of energy. When calculating the energy density of the quantum vacuum, physicists find it to be teeming with intensely energetic vibrations, or vacuum fluctuations.

blue grid

1QuantumfoamVacuum fluctuations are actually electromagnetic waves in an absolute vacuum, and they can fill a finite volume of empty space with infinitely finer and finer degrees of electromagnetic vibration (waves). As every single vibration in reality is a tiny expression of energy, logically the vacuum must be said to possess absolute energy. Both laboratory experiments, like the Casimir effect, and mathematical calculations points towards the reality of this subtle ocean of energy, but as its energy level is indefinite – and possibly infinite – physicists are unable to integrate its meaning into a functioning model of our universe. In physics an unlimited value is a somewhat pacifying concept, as it is mathematically impossible to formulate into a valid equation. Thus, in order to formulate meaningful physics, the potential energy of the vacuum must be quantified to a conceivable quantity, a process achieved through renormalization.

To renormalize the vacuum energy physicists utilize the Planck length, the smallest measurable length in our particular universe, to cut the electromagnetic spectrum short at its smallest meaningful distance (to our conceptual world of physics). By cutting off the electromagnetic spectrum at this level a minimum EM vibration frequency is defined, thus the effectual energy level of the vacuum may be appropriately calculated. Notice, however, that the Planck length is a proven, physical constant of nature – not a figment of Man´s imagination. It is derived by three other physical constants of Nature; the Planck constant, the speed of light and the gravitational constant. Interestingly the resulting Planck length closely matches the golden ratio of Phi, providing additional confirmation to its relevance to our universe (Planck length=1.61619926 × 10-35 meters vs. Phi ratio=1,618033989).

To give a mental image of the scales of Planck space, a Planck unit so small that if we expanded it to the size of a grain of sand, a single proton world reach from here to Alpha Centauri, 4.37 light years away! With the Planck length as base unit we may approach the universe as consisting of units, or bits, of information and thus we can identify the relation of the vacuum energy to the forces of nature in a more appropriate (quantified) manner. Equipped with this physical constant, physicists have a definite unit of measurement with which to calculate the vacuum energy within a given volume of space.

universe in a sugar cube

The available vacuum energy within a volume of space equal to a sugar cube is far more than all the matter in the universe combined!

Using Einsteins mass-energy equivalence (E = mc²), the renormalized energy density of the vacuum is calculated simply by counting the number of Planck units you can fill in one cubic centimeter of empty space. The result is a mass-equivalent of 1093 grams per cubic centimeter (10 with 93 zeros after)! So even after this procedure the vacuum seem to contain a tremendous amount of energy (practically infinite, for all conceivable intents and purposes). In fact one cubic centimeter of vacuum energy is far, far more energy than there is in the entire visible universe, in the form of ordinary matter. In comparison, the total mass of the universe is “only” 4.98 x 1055 grams. This result may seem nonsensical and it poses significant explanatory problems within our current theoretical framework. Adding to the confusion, Einsteins field equations state that any given amount of energy results in electromagnetic radiation (light) and/or spacetime curvature (gravity), which we apparently do not observe in the vacuum. As a result, current consensus in physics communities is that the vacuum energy is “incoherent” and that it bears no significant physical meaning at all, other than at macro-cosmic scales (as the cosmological constant) . Yet, rightly so, many physicists are dissatisfied with this ad-hoc conclusion, and the true role of the vacuum energy remains a hot topic of discussion…

To learn just how this conundrum may be solved, proceed to The Quest for Quantum Gravity.

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4 Responses to Renormalization

  1. Ulrik Heger says:

    Hei Amndreas,

    Love reading your posts, keep up the excellent work! 🙂

    Have I missunderstood something or ss there a discrepancey between what you are saying at the beginning of the post:

    Vacuum fluctuations are actually electromagnetic waves in an absolute vacuum, and they can fill a finite volume of empty space with infinitely finer and finer degrees of electromagnetic vibration (waves


    To renormalize the vacuum energy physicists utilize the Planck length, an absolute minimum electromagnetic vibration frequency, to calculate the its effectual energy level.

    To me it seems as though you are saying at first that there is no limmit to the size of an electromagnetic wave whereas the discussion reagrding the plank length suggest that it is not?

    • Takk Ulrik;)

      Thanks for pointing it out – there’s a badly formulated segment there (to be corrected shortly).

      The Planck length does not relate directly to EM waves, of course, but is its own theoretical unit of meassurment, below which physics (concerning our particular universe) becomes meaningless. That is not to say that the EM spectrum ends there – most likely EM wavelenghts can be divided to infinity.

      The Planck length itself is derived from three other constants of nature; the Planck constant, the speed of light and the gravitational constant.

  2. d8_thc says:

    Mis-type here?

    1,093 grams per cc/3.

    Can you superscript that?

    The html tag should allow you to – at the 10^55 gram section as well.

    Love your posts!

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