The Quantum Thomist

Musings about quantum physics, classical philosophy, and the connection between the two.
Quantum Switches

A Universe from Nothing? Part 1: Introduction
Last modified on Sat Apr 27 23:24:14 2019

This is the first post in a series discussing Professor Lawrence Krauss' work A Universe From Nothing.

Professor Krauss' thesis is that contemporary physics can explain where the universe came from and why there is something rather than nothing. He himself is a top quality physicist. He specialises in cosmology, which is the study of the development of galaxies and the universe as a whole. It looks at the universe at a large scale.

I myself am from a different area of physics, particle physics, which is concerned with the opposite extreme: the smallest things we know about. Progress in particle physics has now largely stalled for about forty years. The standard model of particle physics has been well established since that time. I won't say that there has been no progress in that time. We better understand the consequences of the standard model, have better experimental evidence, and there are a few areas (such as neutrino physics) where exciting discoveries are being made. But, for the most part, an up to date text book from the early 1980s would be almost as relevant today as when it was first written.

Cosmology is again the opposite extreme. There has been a huge leap forward in this time frame. Krauss has personally contributed to that. We have gone from a position where we had little certain knowledge of the structure and evolution of the universe (beyond general relativity) to a model which is very successful in explaining observation, and has been confirmed from multiple viewpoints to a high precision. So I'll begin by giving a quick outline of the current state of cosmology.

The starting point of cosmology is Einstein's theory of general relativity, in particular the Robertson-Walker solution to the field equation. This beautiful theory describes gravity and dynamics. It has been tested to a high precision, and is highly successful. Like quantum field theory, it reduces to Newtonian physics and Newtonian gravity in a particular limit. When you express the solution to the field equation in a series expansion, the leading order term gives you Newtonian gravity and Newton's laws of motion. You then have various corrections, which are important either in the presence of strong gravitational fields, or for very sensitive experiments. Thus all the experimental evidence supporting Newton's theory is also as predicted by General Relativity. But General Relativity continues to give accurate predictions in places where Newton's theory breaks down. There has not been an experiment contradicting the predictions of general relativity. We expect it to break down when it collides with quantum physics, but the energies where these effects are expected to become significant are so absurdly large we are nowhere near seeing that.

The philosophy behind general relativity is, like Newtonian mechanics, mechanistic. However, there are important differences. In particular, gravity is no longer seen as a force in the same sense that Newton used the term. Nor does it rely on the gravitational potential. Instead, it changes our notion of space, time, and what it means for an object to undergo inertial motion. General relativity is the study of more complex coordinate systems geometries than Cartesian in a Euclidean geometry. Indeed, some practical effects of general relativity are well known to us. When you are in an accelerating car, you feel a "force" pushing you backwards against your seat. This force is just an artefact of the coordinate system you use. You place yourself at the origin of your coordinate system. You are always at a location (0,0,0). Somebody walking along the side of the road at a constant speed has their own coordinate system, with themselves at the origin. In their coordinate system, they are always at location (0,0,0), while you are at a position accelerating away from them. We can, of course, convert from one coordinate system to another. But when we do so, we find that the equations of motion are slightly different in each coordinate system. This difference is mathematically equivalent to a gravitational force pulling back the driver of the car. Hence the "fictitious force" that the driver feels.

What the equations tell us is there is a difference in the gravitational force felt between the driver and the person on the side of the road. But why is it the driver who feels this force, and not the person on the road? The natural answer is because he is the one in the accelerating reference frame. But, of course, to him he is in the stationary frame, and the man at the side of the road is accelerating backwards. So there is something a bit more to it than just this going on. In practice, we can highlight a natural local coordinate system as the system which has no fictitious forces.

Einstein realised that one can also switch to a local coordinate system where the "fictitious force" exactly compensates for the force of gravity. If you travel in such a way that you always sit at the origin of this coordinate system, then you won't experience any gravity (think of the weightlessness experienced by astronauts). But I just said that the natural coordinate system is one in which you don't feel any fictitious force. What this means is that our familiar Cartesian coordinate system in Euclidean geometry (where the astronaut is in orbit around the earth) is not the natural coordinate system of the universe. Instead, the natural coordinate system is one which describes an astronaut in orbit as travelling with a constant velocity. (just like the man at the side of the road). In this coordinate system, the astronaut is just undergoing inertial motion. But this isn't a Cartesian coordinate system, and it isn't a Euclidean geometry. We say that space-time has been curved by the matter in the universe. Einstein's field equation provides the key link between the curvature of space time and the matter in the universe. And this means that gravity is another fictitious force, just as experienced in the accelerating car. There is no gravitational force and no gravitational potential. Just inertial motion in curved space time.

Another important difference between Newtonian gravity and general relativity is their view of the history of the universe. This is the next ingredient in the standard model of cosmology. Newtonian gravity is consistent with a static universe. General Relativity is not. In General relativity, the universe is expanding. This might seem a rather strange statement. What can infinity expand into? I usually think of it in a different way. How do we measure the distance between two points? The most natural thing to do is to take a ruler, place one end of the ruler at one point, and count of how many inches or centimetres needed to reach the other point.

Obviously cosmologists use more sophisticated methods to distances than this. In particular, there are certain natural measurements of distance rather than the artificial ruler. For example, today we define the second in terms of the frequency of a certain spectral line of the caesium atom and the speed of light is defined to be a certain number of meters per second. Put these together, and you get a fixed definition of the meter. We can measure the distances of distance stars in different ways. The simplest is to measure the difference in angle to the North Pole between when the earth is at the opposite sides of its orbit. We can then use basic trigonometry to calculate how far away the object is from us. This works for objects reasonably close by. For objects further away, we use other methods. For example, there is a type of star known as a Cepheid. The intensity of the light emitted from a Cepheid varies according to a regular and repeating pattern. The brightness of the star as measured at a point next to that star has been found to depend on the frequency of this oscillation. But when we are a large distance from the star, the intensity varies according to an inverse square law with distance: the further away you are, the dimmer the star is and the harder it is to see. We can measure the frequency of the Cepheid's oscillation, infer its brightness when it is first emitted from the start, and then from the intensity of its light as we receive it compute how far it is from us. At longer distances still, we can do something similar with supernovas (exploding stars). The brightness of the supernova is tied to how long the blast lasts. So we use a falling intensity of light beams instead of ticks on a ruler, but otherwise the principle is the same.

Now suppose that we measure the distance to a particular galaxy. Wait a little while, and then measure it again. We will find that the distance has increased slightly. (In practice, we use special relativistic redshift to calculate the relative velocity between us and the galaxy). We find that the galaxy is moving away from us. This is true for every galaxy we observe. There is nothing special about us: we are not at the centre of the explosion. Every galaxy will observe every other galaxy moving away from it. So what is going on?

Remember that those increasing distances are just ticks on a ruler, or grid lines in a coordinate system. So there are two ways of thinking about this. Either we can say that the ruler remains the same and the spaces between galaxies is increasing, or the galaxies remain the same but the ruler is shrinking.

The spacing between the marks on the ruler is ultimately taken from the natural coordinate system of Einstein's theory, and the geometry of space time. The spacing between galaxies is getting larger on this ruler as we move forwards in time. Look backwards, and we this distance gradually getting smaller. Go back far enough, if this continues, then the space between galaxies will be comparable to the size of an atom. At this point, our current theories break down, since we would need both general relativity and quantum physics working together. But we know enough to say that in the distant past the universe was very dense, very small, and very hot. In classical general relativity, it is inevitable that the universe begins with such a singularity. There are numerous pieces of evidence that this big bang occurred.

The second leg of the standard model of cosmology is thus the big bang. This came as a surprise. Ever since the days of Aristotle, it was assumed that the universe was fundamentally static, at least on the large scale (neglecting the orbits of the planets, and so on). We now know that it is not. The universe had a beginning.

The next question is whether the rate of cosmic expansion is constant. Is the expansion speeding up or slowing down? And what happened in the past? In particular, we know understand that the universe expanded extremely rapidly in its earliest years. While some of the precise details of what caused this inflation are still debated, that it occurred is reasonably certain, since there is no other way to get from the initial big bang to the large scale structure of the universe we observe. This is the third leg of the standard model of cosmology.

One of the effects of general relativity is what is known as gravitational lensing. Large gravitational fields bend the path of light. This allows you to in effect see behind a very massive object, as the light path bends round it. Since the path of the light beam depends on the mass of the object, this gives us a way of calculating different astronomical objects are. So, for example, if we have two galaxies in line with each other, and there is a supernova in the more distant one, then the light from that supernova will bend around the intermediary galaxy creating something similar to a halo around it. By carefully measuring the size of the deviation in each direction, it allows us to not only measure the mass of the galaxy, but also how that mass is distributed within the galaxy. What we find is that while you might think that most of the galaxy's mass would be taken up with stars, in practice a lot of it comes from something else. What that something else is is one of the big remaining mysteries of physics, but we do know that it doesn't interact with light (otherwise we would be able to see its effects). So we just call it dark matter, and fund plenty of research programs trying to figure out what it is.

What about the future fate of the universe? There are three options. Firstly, that it is going to continue to expand forever, on open universe. Secondly, that it the expansion is going to reverse, and the universe will eventually collapse into another singularity: a closed universe. Thirdly, that it is on the knife-edge between the two. This last solution is known as a flat universe. In particular, this distinction describes how light waves propagate through space over large distances. In a flat universe, they do what we are all taught in our school level physics: travel in straight lines. In an open universe, they bend outwards, and a closed universe they bend inwards.

After the big bang, there were a lot of energetic particles. At this time, they hadn't been bound together into nucleons and atoms. Charged particles moving around at high speeds emit and absorb a lot of electromagnetic radiation. At this point, things were so hot that the particles were all more energetic than is required to bind them into atoms and the nuclear particles. Then, as the universe cooled, the particles began to combine into the sort of chemical structures we see today. An atom is electrically neutral, so the electromagnetic radiation was no longer emitted and absorbed. Where did it go? It's still out there, and known as the cosmic microwave background. It provides a snapshot of what the universe was like about 300 000 years after the big bang. The frequencies of the radiation from the background follows the expected pattern emitted from a black body at a fixed temperature. We can thus calculate the temperature of the radiation, and it is about 2.7°K.

The cosmic microwave background is remarkably uniform in temperature. However, there are some small fluctuations in the temperature of the background as we scan across the sky. These are caused by the particles of the initial plasma being attracted together by gravity, creating areas of either denser or less dense material, which would cool at slightly different rates. Since the universe was 300 000 years old at the time the background formed, two bits of matter more than 300 000 light years apart wouldn't be able to interact with each other, so they would fall into different structures. Thus we have a limit on the maximum size of these structures.

This allows us to calculate whether the universe is open, flat or closed. The curvature of the path of the light in an closed universe would have the effect of magnifying the structures in the background. An open universe would reduce the apparent size of the structures. A flat universe keeps them the same size. And our observations of the size of the structures match what we would expect if the universe is flat. So we can tell that the universe as a whole is flat. This is the next leg of the standard model of cosmology.

Whether the universe is flat, curved, or open also depends on the amount of matter in the universe. Einstein's field equation relates the curvature of space time to two things: the first is the stress energy tensor, which describes the energy, mass and momentum of all the particles in the universe, and the second is the cosmological constant. Einstein initially supposed that the cosmological constant was zero, but to get a flat universe you need it to be a very small but non-zero value. This is known as dark energy. Again, it is called dark energy because we can observe its effects but don't yet know what it is. This is the final component of the standard model of cosmology.

By now, you are probably wondering what any of this has to do with a review of Krauss' book.

The heart of the book (chapters 1,2,3,5,6 and 7) outlines the physics I have described above. It gives a generally historical introduction, discussing the people involved in each of these discoveries, and marshalled the evidence well. I found this part of the book very well written, and a good popular introduction to cosmology. I'm not, of course, a cosmologist, and thus not personally an expert on the subject. My knowledge in this area is merely that of the average person you might meet on the street with a doctorate in an unrelated area of physics. I am not the person to turn to if you want a detailed verification of this material. But, that caveat aside, his description of the latest status of cosmology in these chapters was well written and scientifically sound. I would recommend it.

So that just leaves his preface, chapters 4, 8, 9, 10 and 11. And these are considerably more problematic. My intention is to discuss each of these in turn, in subsequent posts. Here I will just offer a quick summary.

His preface outlines the purpose of his book, to answer the question Why is there something rather than nothing? He intends to show that modern science can and is addressing this question. Indeed, he claims that something can arise from nothing, and that this is where modern science leads us to. The question then is what is meant by the term nothing? He dismisses what philosophers and theologians have to say. Recent developments in science have instead shed light on these questions. And science is great.

Chapter 4 ventures into my own field of particle physics. It discusses the cosmological constant, and describes how it can emerge from the quantum vacuum. He relates the cosmological constant to the energy contributed by nothing. If this sounds confusing, then he is quick to clarify:

By nothing, I do not mean nothing, but rather nothing.

He goes on to propose that the uncertainty principle allows nature to borrow a bit of energy over a short period of time, allowing particle-antiparticle pairs to emerge from the vacuum, and then collapse again. He claims that the energies of these virtual particles boiling in and out of the vacuum allows for the cosmological constant. In my view, he gets the physics badly wrong in this chapter, and his interpretation of the physics is off-the-wall. But I'll discuss that in more detail in my detailed review of the chapter.

Chapter 8 discusses anthropic selection. He starts with the small but non-zero value of the cosmological constant, and other parameters of particle physics. He argues that these have to be the way they are in order for human life to emerge. He proposes that this fine tuning is due to a multiverse. The idea here is that our universe is not unique, but that there are numerous different universes each with different values of the physical parameters. It is then inevitable that at least one of them would hit the jackpot. Again, I will critique his presentation here later.

Chapter 9 is where he starts to put things together. The chapter is entitled "Nothing is something," which starts by claiming that science has made religious explanations impotent. The only thing left for theologians is the start of the universe. Here he suggests that science can make it plausible that something came from nothing; and plausibility is enough for us to dismiss the "God" explanation. He argues that in a flat universe, the total gravitational energy (negative) exactly cancels out the energy of matter (positive). The total energy of the universe is zero, which is what we expect from a universe that arise from nothing. His nothing is empty space plus the laws of physics, believing this to be a good approximation of what people like Aquinas and Plato understood by the term. But empty space still undergoes inflation, carries energy, which is converted into the matter we see around us. Thus the universe can start out from being a tiny region of empty space and expand to what we see without costing any energy.

Chapter 10 is titled "Nothing is unstable," where he discusses empty space being a sea of virtual particles popping into and out of existence. Thus nothing always produces something, if even for an instant. But how can these endure? Firstly, in the presence of a large electromagnetic field (the setup he is thinking of here is that related to what is known as the Klein paradox, which is observed). Then he proposes that a strong gravitational field, such as around black holes, can have the same effect. Thus nothing can not only produce something, in certain circumstances it is required to. CP violation in physics is then invoked to explain why there is more matter than antimatter in the universe. This basically means that anti-matter doesn't quite interact with the strong and weak nuclear forces in the same way as matter. Thus one can get a universe which is (for example) dominated by electrons, protons, neutrons and anti-neutrinos. Some CP violation is observed in the standard model of particle physics, and it is hypothesised that extensions to the standard model will lead to a bit more. Thus we can get an imbalance between matter and anti-matter, and the particles and anti-particles won't immediately annihilate each other. He then goes onto discuss how a quantum theory of gravity will allow space itself to pop into existence in the same way. While this can only happen for a short period of time, so these universes would normally appear and then collapse into themselves, if we have a period of inflation we might be able to avoid this.

Chapter 11 discusses where the rules or laws of physics come from. He discusses first cause arguments, and their relevance in the light of his discussion so far. The rule out of nothing, nothing comes has, he claims, no foundation in science. He proposes that the multiverse can avoid the need for invoking a first cause. Finally, he states that the ultimate end of the universe would be to retreat into a different sort of nothingness.

Needless to say, I believe that much of this work which I have summarised in the previous paragraphs is philosophically and scientifically incoherent. Krauss' work is very good when he discusses cosmology, but very bad when he ventures into areas beyond his expertise. In the next posts, I will discuss in detail why I think this and outline (some of) Krauss' mistakes.

A Universe from Nothing? Part 2: Particle Physics

Reader Comments:

1. Scott Lynch
Posted at 09:07:32 Tuesday May 7 2019

Comments on What is Physics - An Excellent Book So Far

Dr. Cundy,

I am reading your book right now. I am on Chapter 7.6 (Classical Physics Comes to Maturity - Noether’s Theorem). So far I like it very much. I am impressed with your background of the medieval scientists and mathematicians. I think it is very helpful in setting the stage.

I have a few constructive criticisms (although since I have yet to finish the book, I will suspend total judgement).

1. There are quite a few typographical errors. Nothing takes away from the meaning of the book, but it is noticeable. I cannot remember if you said whether this book was professionally edited. I think it was independently published, correct? If that makes you the chief editor, I could see why that would be the case. It is impossible for someone to write a work as ambitious as yours without small mistakes here and there.

2. I feel like you are a bit redundant or wordy in some places. I think a good editor could strip out some of that redundancy and shave off some pages.

3. You mover really fast on the mathematics. I think this (plus the history of science) is what separates this book from another pop science book. I am able to follow along for the most part on an engineering background, but I think a reference appendix with additional graphs, figures, and possible examples could be really beneficial to a reader who wants to get up to speed quickly without reading multiple math text books. Another thing I think would be helpful is writing footnotes for how to “say” the equations. This would be helpful for auditory readers to understand what the equation means (in addition to merely defining your variables). For example, when writing dx/dt = v, a footnote saying “this says the change in position (x) with respect to time (t) equals the velocity (v). I know this is not a math textbook, but I think this could be a helpful resource to the initiated non-science major who wants to understand the mathematical concepts better before moving on.

4. In your section on Galileo and the Church, you write that the Church “formally” declared that the Sun revolved around the Earth. “Formally” is somewhat vague and possibly misleading. Some people may take it to mean that it was declared dogma. It was not declared by an Ecumenical Council or an infallible Papal Decree, so what exactly does “formally” mean? I would add a clarifying comment or drop the word “formally”. To say the Church declared it communicates the matter without adding dubious doctrinal authority to the pronouncement.

5. Here is my main criticism. In section 7.5 on special relativity (page 232), you make the conclusion that four dimensional hyperbolic space implies a B-theory of time. You also say that this agrees with the eternity of God (God does not know the future by calculating the future but merely “observes” the future. Many Thomists such as Edward Feser would take serious issue with this (so I believe a footnote stating such would be advisable here). The traditional Thomist belief is that God does not know the future by observing it but rather by knowing Himself and then willing a creation that imitates Him (or participates in Him) in a finite way. To say God “observes” the future is to imply God is an observer inside of time. This would mean that God creates, observes, then learns. Of course this would imply change in God which would cause serious problems for Divine Simplicity and the Principle of Sufficient Reason. Rather God is the creator of all spacetime and this knows everything in Spacetime simultaneously with His creating it (but logically prior to it since God must know what He creates [logically] before He can create it). Many people argue that this leads to fatalism (Thomists would disagree because they would say that God’s knowing the choices of a volitional agent does not contradict said agent choosing freely as long as you have the right understanding of second order causality). Either way, that debate would take you into the weeds. The point is that it is a tenuous statement that should be flagged as such even if you ultimately are unconvinced by my arguments (I would be happy to discuss further). Furthermore, many Thomists and Aristotelian would take issue with the B-theory of time. I do not think the mathematics demands eternalism (though I do not think it demands presentism either). The fact that time seems to dilate based on velocity etc. just means that the rate of succession of causality is affected by these factors. Objects traveling at the speed of light with respect to a “stationary” observer seem to not change at all apart from their location. That is to say, the only potential that is actualized is local motion. For objects traveling near light speed, potentials are actualized much more slowly, and for “ordinary” speeds they are actualized at an “ordinary” rate. Of course this assumes that local motion is a genuine change. I think that at the very least relative motion has to be considered as a genuine change (the actualization of a potential). That time can be treated like space in some ways does not mean that it can be treated like space in all ways (as you even agree that the order of causality, specifically the law of entropy, is conserved). So in all three space dimensions you can rotate or translate the dimensions however you like so that X = -X, Y = -Y, etc. but you cannot rotate your coordinates to make t = -t. Otherwise that would imply that in some reference frames time can move backwards. I do not believe that would make any sense even if it could be done mathematically. I think there is nothing inconsistent with saying that the four dimensional mapping of spacetime represents the four-dimensional set of possible points. The set of all possible points is just the set of all real numbers in each dimension in hyperbolic space. The hyperbolic space represents all potential universes given the current nature of physics (but not all logically possible universes). The function is not the state of the actual universe or even the state of the potential universe. Rather the function is the state of the universe that is, has been, and will be actualized (which is a subset of the potential universe but itself is a set that always contains the actual universe as a member. The fact that the function f(x, y, z, t) always has a value at all t does not mean that everything exists at t1, it merely means that the function at t1 represents the actual universe and all other points represents the past and future. To say that all states of the universe exist actually at t1 would be to say that f(x, y, z, t) = f(x, y, z, t1) for all x, y, z, and t. If anything, this interpretation of the space leads to presentism (although one could argue that the function can be interpreted differently to give credence to eternalism). In any case, I believe the mathematics is philosophically indeterminate at best and can lead to presentism given at least one interpretation. This also implies that since f(x, y, z, t) is not equal to f(x1, y, z, t) for all x, y, z, and t, that not all points in space exist (necessarily). As a matter of fact, many Aristotelians would say that the space between two objects is merely a potency. So if there are no substances (or at least parts of substances) at location x1, then x1 does not exist in actuality. Now in reality, it could be that the nature of space is such that “empty space” can be treated as a substance (in which case f(x, y, z, t) would represent actual values for all x, y, and z, but it is at least possible in principle for f(x, y, z, t) to represent merely potential values. It would seem that the value of the function would be the form of the particle (or lack thereof) at that time and place. This form would include the actual and potential states as well as identify empty space.

Anyway I am really trying to nit pick only because of your old post saying you would like reviews. I think this book is a gold mine and a pleasure to read.

2. Nigel Cundy
Posted at 19:46:46 Wednesday May 8 2019

Thanks for your comment

Thanks for your comments, Scott. I will certainly bear 1-4 in mind the next time I review the text.

You are also right about point 5 -- I just separate it here because it deserves a little bit more attention. I should make more clear the distinction between the A and B theories, and certainly that the traditional position of Thomists is the A theory (presentism). As I noted in the book, I naturally favour a version of the B-theory, but one that allows for change in time (I have never quite understood why the B-theory is said to deny the possibility of change). It's probably worth me taking time to work things out in this blog (and digging up the notes I already have) first before writing it up for publication. Maybe I'll do that after I finish with Krauss.

3. Callum
Posted at 08:22:46 Tuesday May 14 2019

This is a great blog. I'd like to disagree with Scott regarding God's 'observation' of the universe being incompatible with the PSR. I don't see how. Eleonore Stump puts forward a plausible account in her 2003 book. It obviously is a bit testy with the doctrine of impassibility, but neither views are inconsistent with the PSR

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