Updated 25 June 2020

If you know the answers to any of these questions, then please, please contact me and tell all!

Scientists love to tell us ordinary folk about their great discoveries, and they work hard to dumb it all down for us. But sometimes they go too far and leave little questions unanswered. There are quite a few such questions that I have long wondered about but never found any explanation beyond vague references to incomprehensible equations. My suspicion, borne of long experience as a technical writer, is that physicists don't explain it because they haven't thought about it clearly and don't actually understand the various inconsistencies they have drawn from their equations. They have, perhaps unconsciously, steered past the issue and thus avoided a reality check on their pet theory. Or, am I being unfair? This post raises a few such inconsistencies that spring to mind, I am sure there must be plenty more where these came from.

Contents

- Electricity and magnetism
- Negative energies
- The energy of the Universe
- The manifold shapes of spacetime
- An absorbing corollary
- Information

It has long been known that electricity and magnetism are the two curious partners in electromagnetism. Changing an electric field creates a magnetic field and vice versa. As the two changing fields interact they make each other oscillate to and fro, creating an electromagnetic wave which travels off at the speed of light. And for almost as long we have known that these waves are made of quantum particles called photons.

But we can also have static fields. The field round a magnet is static, it is not radiating off anywhere. The same goes for the static electricity on a balloon that has been rubbed on your hair and stuck to the ceiling. As quantum theory was elaborated, it came to explain these static electric and magnetic fields as special kinds of photon.

And there the popular explanations stop. What kinds of photon? What is so special about them? How come you can trap photon energy like that? I read once that they are polarized in a special way, perhaps in another direction not in ordinary space. What way is that? And I once also read that these are "virtual" photons, continually being emitted but then reabsorbed before they can do anything. Yet, unlike the more usual virtual particles, their lifetime is not limited by Heisenberg's uncertainty principle; these static fields can extend indefinitely. And clearly, when I hold one magnet near another, the field is exerting a force which is many orders of magnitude greater than say the Casimir effect.

Our most sophisticated quantum picture, quantum field theory (QFT) descrbes a zero-point field for each fundamental force, with individual quanta comprising perturbations or disturbances of the zero-point field. But I am told that it has no model of how these electrostatic and magnetostatic perturbations happen, for that one must resort to classical electromagnetic waves. Is that true? If so, then why does everybody pretend we do know and the central mystery is never acknowledged?

It is often explained that gravitational enegry is negative. The argument goes that it increases as two objects fall towards each other and the gravitational field between them intensifies, reaching its strongest just as they collide. But at the same time they have been falling faster and faster, increasing their kinetic energy of motion. But energy must be conserved overall, so the only answer can be that, as the kinetic energy gets more positive, the gravitational energy gets more negative to balance it out. And since the gravitational energy is also getting stronger, the only way it can get both stronger and less positive is by being negative. All this is a consequence of the nature of gravitation as an attractive force.

That is all very well, but it suggests to me that any attractive force should similarly involve negative energy. Consider for example the attractive forces between positive and negative electric charges, or between north and south magnetic poles. These obey much the same laws of attraction that gravity does and they behave in much the same way. Does this mean that the energies stored in these fields is also negative? Yet like charges or poles repel, so these fields must be positive. Does flipping a magnet round really swap all its stored energies between positive and negative? That would surely explain the energy involved in making the flip, another detail at best left barely acknowledged, never properly explained.

Going deeper into the atom, the weak nuclear force attracts protons and neutrons to each other in the atomic nucleus. More negative energy? (The strong nuclear force, which attracts quarks within a single such particle, bizarrely increases with distance and so must presumably have positive energy.)

Yet nobody ever explains that the energies of these attractions are therefore negative, never mind explaining how this works. Or aren't they after all?

Why are we never told the whole story?

It has often been pointed out that the balance of positive and negative energies in the universe is a very close one. We find ourselves on a cusp where either might just dominate. Positive energy such as mass and light causes positive curvature of spacetime, which is associated with the universe eventually collapsing. Negative energy such as gravity causes negative curvature of spacetime, which is assoiated with the universe expanding forever. Since the two so nearly in balance out, the net energy of the universe is close to zero. The law of energy conservation therefore implies that the universe never had much to begin with, if any. It must all have just exploded out of nothing, positive mass and negative gravity appearing side by side. As it expands, the decrease in negative gravitational energy is balanced by an associated slowing of the expansion rate and reduction in kinetic energy of the galaxies flying apart. But other forces are also at work.

We now believe that the early period of inflation was driven by an inpouring of positive "dark" energy, and in recent aeons that expansion has started to speed up again due to more of the same. Today we reckon it to comprise about 70% of the universe's total energy (positive + negative). Scientists are honest enough that they have no idea where this vast inpouring of dark energy is coming from.

But they seem less inclined to talk about what happened to that neat balance between positive and negative. How come, after the arrival of 70% extra positive energy, we are today balanced on that cusp of zero net energy, where spacetime is still flat on the grandest scale we can yet measure it? Startlingly unlikely coincidence? Or are we missing something we don't like to talk about?

Relativity describes reality as inhabiting a four-dimensional spacetime. There are a huge number of shapes that such a spacetime can take, referred to rather abstractly as "solutions to the equations of General Relativity." We do not know which of all these possibilities is the real one. We get glimpses of their properties, such as whether a particular one is expanding or shrinking in space, over time. But these glimpses hide most of the reality. Mathematicians call such shapes "manifolds". A manifold is the idea of a two-dimensional surface, generalised to allow more dimensions. Where space can be thought of as a three-dimensional manifold, spacetime is a four-dimensional one. Such manifolds may be twisted in amazing ways and may or may not have boundaries. For example the outer surface of a ball has no boundaries, while the outer surface of a bottle has a boundary around its rim and a length of pipe has two boundaries, one at each end.

Does spacetime have any boundaries? It is easy enough to talk of the Big Bang, an apparent bounding point where time begins. But General Relativity does not deal in boundaries. Or at least, they are more boundaries to the theory, what are called boundary conditions, than to the spacetime it is describing. Physicists talk of the theory "breaking down" at such points. With no theory left of the physics at such boundaries, it is hard to believe the theorists who talk about what might or might not lie beyond.

Stephen Hawking was among those who explored an alternative interpretation of General Relativity, in which Time is treated slightly differently. He called it "imaginary time" for technical but otherwise meaningless reasons, it is no more nor less in the imagination than "real time." In his model, the theory does not hit the buffers at the Big Bang but is able to negotiate smoothly around it. It's a bit like travelling north to the North Pole. Traditional Relativity breaks down when you reach the pole, because you cannot travel further north. But Hawking's version allows you to just keep on going, where you will find yourself now travelling back south again. He famously suggested that "perhaps the boundary condition of the Universe is that it has no boundary."

There is a mathematical subtlety built into this that the cosmologists never talk about (You will find it discussed elsewhere, for example in Fields Medal-winning mathematician Shing-Tung Yau's popular book on string theory, *The Shape of Inner Space*, just not in relativistic cosmology). A manifold such as a spacetime has two distinct kinds of property, global and local. Its global properties describe its shape in a general kind of way: is it bounded, does it have inherent loops or twists? The study of these properties is called topology. Its local properties, which comprise its geometry, are more concerned with how far one point is from another, how flat or curved it is at some point, and suchlike. To study these local properties you typically have to make maps or charts of it, and to make a chart you have to lay down a coordinate grid, much like the Ordnance Survey grid on maps of the UK. But the old French, Russian and Chinese grids were nothing like the Ordnance Survey's one, the grid you use is arbitrary and chosen only for convenience. What appears as a singularity where one grid hiccups, such as at the north pole, may appear as perfectly smooth in another.

Relativity theory traditionally uses a grid system (called a metric) known as Minkowski spacetime coordinates. Hawking's imaginary-time metric is subtly different but it can be overlaid onto the same topological manifolds as the conventional grid. There is generally little visible difference between them but, from the hints he gave, the two grids differ wildly around the Big Bang. So, it is unhelpful when cosmologists ramble cheerfully on about the beginning and end of the universe, without distinguishing between its assumed global properties and how the chosen local coordinate system relates to them. In particular, is the Big Bang singularity a boundary to the spacetime manifold or is it just an arbitrary "north pole", an artefact of the Minkowski metric?

One of physicist Richard Feynman's many claims to fame is his sum-over-histories approach to quantum theory. He showed that if you take all the possible outcomes of a given initial state, then adding together the probabilities for every individual possibile path to a given outcome should leave you with the probability for that outcome. Some of these paths can be insanely weird, traversing points all over space and, indeed, all over spacetime. In fact, the majority of them are. Remarkably, the weird paths that traverse the past neatly cancel out the weird paths that traverse the future, just leaving the expected ones, so you don't have to make any restrictive assumptions about the final wave of probabilities.

There is no known boundary to space but there is to time. What happens with paths that reach all the way back to the Big Bang? Feynman and his mentor John Wheeler thought it reasonable to assume that if time begins somewhere then it must end somewhere. If we assume the paths just bounce back off the ends, the maths no longer gives sensible answers. So they instead proposed that these ends of time acted as perfect absorbers, that no possbile path could bounce back off them. However nothing can be so easily destroyed, so the possibilities had to somehow be re-emitted. They reappeared with their phases randomised, much like black-body radiation. When they met back in the present, their phases meant that they neatly cancelled each other out again and the theory worked again. This mathematical embellishment became known as Wheeler-Feynman absorber theory.

Fast-forward now to Stephen Hawking's investigations into imaginary time. As mentioned above, one of its more curious consequences is to flatten out the Big Bang so that it is not so much a sharp point as a pole on a gently curved spacetime "surface", much like the South Pole on the surface of the Earth. It did the same for a Big Crunch at the end of time.

In Hawking's universe there is now nowhere for the Wheeler-Feynman absorbers to go. Paths from the future can go back to the Big Bang or forward to a Big Crunch and freely cross over the poles to return to the near-future after all. The mechanism to randomise their phases is no longer there, so are they randomised or mutually cancelled in some other way? Does the maths still hold up?

Some theoretical physicists are so enthusiastic about information theory that they regard it as a fourth pillar of modern physics, following thermodynamics, relativity and quantum theories. But I find a fundamental inconsistency between these theories.

Thermodynamics has a concept called entropy, sometimes characterised as disorder. It is a fundamental law of thermodynamics that entropy never decreases but can only ever increase, which it does inexorably over time. Many physicists treat entropy as the inverse or opposite of information, on the grounds that a high-entropy state is in equilibrium and therfore contains no novel information. For example the size of a black hole, as given by the area of its event horizon, is a measure of both the entropy and the information that the hole has swallowed. The entropy of the universe has vastly increased since the Big Bang and therefore the information it carries must have decreased.

Quantum theory also has a concept of information. The properties of any given quantum naturally carry information, and information is transmitted when a quantum travels from one place to another. Shannon's law describes how much information can be carried by say a beam of light. When two quanta interact, the information may be radically transformed but it is never destroyed. Since quantum mechanics is time-symmetric, information can never be created either. Therefore, throughout any sequence of quantum interactions, the total amount of information in the system must remain constant. The amount of information in the universe must therefore have remained constant since the Big Bang.

There is a glaring contradiction between these two pictures. Is the amount of information in the universe ever-increasing, or is it constant and unchanging? The processes described by thermodynamics are classical processes, but in practice such a process is an aggregate sum of untold numbers of individual quantum events. Consider now some such event where entropy increases, such as dropping a glass on the floor where it shatters into dozens of pieces. According to quantum theory each and every minuscule part of that shattering process conserved information, so the total amount of information can not have changed either. But according to thermodynamic theory, since its entropy has increased then the total information to be gained from all those pieces will have decreased too. A watered-down version of the theory describes entropy as the "capacity to hold" information, so that although a shattered glass can hold more information than a whole one, it does not have to. But that grossly breaks the mathematical relationships between the area of an event horizon, its entropy and its information content. Why should a black hole stuff itself chock full of information when a broken glass does not have to?

There appears to be an obvious difference between the objective total information in a system and any subjectively novel information in that system. Similarly, where entropy is equated with ignorance, that also is subjective. So are the theories, of objective information/entropy on the one hand and their and subjective perceptions on the other, very different? Can information increase or can't it? Is there really a way to resolve this ridiculously glaring anomaly?