This three part post is the first chapter of my book, Unraveling the Universe’s Mysteries. Here is part 2. Enjoy!

According to Paul Dirac, a British physicist and Nobel Prize Laureate, who first postulated virtual particles, empty space (a vacuum) consists of a sea of virtual electron-positron pairs, known as the Dirac sea. This is not a historical footnote. Modern-day physicists, familiar with the Dirac-sea theory of virtual particles, claim there is no such thing as empty space. They argue it contains virtual particles.

This raises yet another question. What is a positron? A positron is the mirror image of an electron. It has the same mass as an electron, but the opposite charge. The electron is negatively charged, and the positron is positively charged. If we consider the electron matter, the positron is antimatter. For his theoretical work in this area, science recognizes Paul Dirac for discovering the “antiparticle.” Positrons and antiparticles are all considered antimatter.

Virtual particle-antiparticle pairs pop into existence in empty space for brief periods, in agreement with the Heisenberg uncertainty principle, which gives rise to quantum fluctuations. This may appear highly confusing. A few paragraphs back we said that the Heisenberg uncertainty principle embodies the statistical nature of energy at the quantum level, which implies that energy at the quantum level can vary. Another way to say this is to state the Heisenberg uncertainty principle gives rise to quantum fluctuations.

What is a quantum fluctuation? It is a theory in quantum mechanics that argues there are certain conditions where a point in space can experience a temporary change in energy. Again, this is in accordance with the statistical nature of energy implied by the Heisenberg uncertainty principle. This temporary change in energy gives rise to virtual particles. This may appear to violate the conservation of energy law, arguably the most revered law in physics. It appears that we are getting something from nothing. However, if the virtual particles appear as a matter-antimatter pair, the system remains energy neutral. Therefore, the net increase in the energy of the system is zero, which would argue that the conservation of energy law remains in force.

No consensus exists that virtual particles always appear as a matter-antimatter pair. However, this view is commonly held in quantum mechanics, and this creation state of virtual particles maintains the conservation of energy. Therefore, it is consistent with Occam’s razor, which states that the simplest explanation is the most plausible one, until new data to the contrary becomes available. The lack of consensus about the exact nature of virtual particles arises because we cannot measure them directly. We detect their effects, and infer their existence. For example, they produce the Lamb shift, which is a small difference in energy between two energy levels of the hydrogen atom in a vacuum. They produce the Casimir-Polder force, which is an attraction between a pair of electrically neutral metal plates in a vacuum. These are two well-known effects caused by virtual particles. A laundry list of effects demonstrates that virtual particles are real.

The above discussions distill to three key points. First, in accordance with the Heisenberg uncertainty principle, virtual particles pop in and out of existence in a vacuum. Second, we cannot measure virtual particles directly. Third, modern science believes virtual particles are real because they cause measurable changes to their environment.

This creation of virtual particles is sometimes termed spontaneous particle creation. Spontaneous particle creation raises an intriguing question. Are there hidden dimensions? Assume the Dirac sea model is correct, and that empty space (a vacuum) consists of a sea of virtual electron-positron pairs. If you are willing to accept this assumption, where are they located? It is a reasonable question. We are dealing with a vacuum, and at the same time asserting it contains electron-positron pairs. Where are they located? A possible explanation is they are in another dimension. As mind bending as this sounds, a formidable scientific theory known as M-theory asserts reality consists of eleven dimensions, not simply the four (three spatial, one temporal) we typically encounter. M-theory is “string” theory on steroids. At this point, I suspect you may be ready to blow a time-out whistle. This theory explains one puzzle using another puzzle. Therefore, in the interest of clarity, we will take it one step at a time, and start by explaining more about M-theory. This will be a conceptual modeling of the theory.

In a sense, science has been working its way to M-theory since the discovery of atoms and subatomic particles, culminating in the discovery of the quarks (circa 1970s) as the fundamental building blocks for protons and neutrons. (Protons, neutrons, and electrons are the fundamental building blocks of atoms. Quarks are the fundamental building blocks of protons and neutrons.) In the 1980s, scientists claimed that these fundamental building blocks could be further reduced to infinitely small building blocks of vibrating energy, having only the dimension of length, termed “stings.”

Conceptually, the “strings” vibrate in multiple dimensions. The vibration of the string determines whether it appears as matter or energy. According to string theory, every form of matter or energy is the result of the string’s vibration.

By the 1990s, science recognized five different string theories, each with their own set of equations. The five string theories appeared valid, but scientists became uneasy. Surely, they could not all be right. In 1994, string theorist Edward Witten (Institute for Advanced Study), and other researchers, proposed a unifying theory called “M-theory.” The “M” stands for “membrane.” M-theory asserted that strings are one-dimensional slices of a two-dimensional membrane vibrating in eleven-dimensional space.

I understand it is hard, if not impossible, to picture an eleven-dimensional space because we live in a four-dimensional world. My picture goes something like this. The membrane (referred to as a “brane”) is like a shadow of a million spread-out toothpicks. A shadow has two dimensions, and is the brane in this analogy. Each toothpick represents a string, having only the dimension of length. In this example, we are considering the toothpicks to have no width. Next, I think about this shadow being able to float off the surface and move around the room in three-dimensional space. It continually changes position in time. That is to say at time t1, it is in one place, and at another time t2, it is in another place. In this mind-bending analogy, we have accounted for seven dimensions. A two-dimensional shadow made from one-dimensional toothpicks accounts for three dimensions. The shadow floating in three-dimensional space accounts for three additional dimensions. Now, picture the shadow floating to a specific place at a specific time. When it moves to another place, time will have passed. The shadow, changing positions in time, accounts for one additional dimension (a temporal coordinate). How do I picture the other four? I think of there being small, invisible holes in space. The shadow can slip into, move around in, and disappear from view in these holes. The holes would represent a hidden three-dimensional space accounting for another three dimensions. The shadow moving in the holes would again represent another temporal coordinate. This analogy, which may be difficult to understand, is how I picture eleven-dimensional space. We live in a four-dimensional world. It is difficult to imagine seven other hidden dimensions.

Scientists, too, have a problem with the eleven-dimensional model of reality that M-theory provides. The mathematics of M-theory is elegant, but correlating the mathematics to reality has frustrated numerous scientists. However, M-theory did accomplish one main goal. It unified the previous five spring theories into one. It demonstrated that each of the five was a specific case of M-theory. Well-known scientists, like Michio Kaku, Stephen Hawking, and Leonard Mlodinow, became proponents of M-theory, applauding its mathematical elegance, and suggesting it may be a candidate for The Theory of Everything. (The Theory of Everything would be a comprehensive scientific theory that explains the physical behavior of all matter and energy.) The one thing missing to make this picture perfect is experimental evidence. To date, we have no experimental evidence for M-theory. This does not mean M-theory is wrong or should be dismissed. Scientists continue to work on it, and experimental proof may eventually emerge.

“Fascinating,” as Mr. Spock would say on Star Trek, but where does that leave us? Why am I bringing up M-theory and hidden dimensions? The answer is that spontaneous particle creation may have a connection to the hidden dimensions of M-theory. The entire Dirac sea (a vacuum filled with particle-antiparticle pairs) may exist in the hidden dimensions predicted by M-theory. Of course, it is easy for me, a theoretical physicist, to make this assertion since we have no proof of M-theory. However, we do have experimental evidence that enables us to infer that virtual particles exist. If they do exist, where are they located? Even if they exist as pure packets of energy (quanta), where are they located? One suggestion is to look into the hidden dimensions predicted by M-theory.

Stay tuned for part 3 (conclusion)