The Quantum Thomist

Musings about quantum physics, classical philosophy, and the connection between the two.
The A and B Theories of Time

A Universe from Nothing? Part 4: Is Nothing Something?
Last modified on Wed Sep 11 16:50:31 2019

Firstly, I must apologise, since it has been a long time since I wrote one of these posts. Life has just been throwing too much at me. It's now time for me to finish off my earlier discussion of Krauss' Universe from Nothing.

This is the fourth post in a series discussing Professor Lawrence Krauss' work A Universe From Nothing. In the first post, I gave an introduction to the underlying cosmology, and a quick overview of the rest of his work. Since his discussion of the cosmology was broadly correct, and very well presented, I am (largely) skipping over those chapters and concentrating on those parts of the book which I find problematic.

In the second post, I had a look at chapter 4, which is where things start to go awry. The chapter was about particle physics, and Krauss' claim was the uncertainty principle allowed matter to spontaneously emerge from the vacuum, with nothing before it, albeit only for very short periods. I suggested that his arguments for this were poor, and he made a number of mistakes with regards to the physics.

Last time, I had a look at his chapter 8, which discussed the anthropic principle, which Krauss uses to support his contention of a multiverse. He is discussing a real issue, and it is generally recognised that fine tuning rules out the natural atheist approach of a single self-explanatory universe. That leaves two options; that the universe isn't self-explanatory, but depends on an external principle, which would be an external will, which is the solution favoured by theists. Atheists instead have to suppose that there is not a single universe, but many different universes, each with slightly different laws of physics, so that between them the entire possible gauntlet of physical parameters is sampled. Krauss presents a few models of how such a multiverse might work. There can, of course, be no direct experimental evidence for such a picture, while there can be (and theists argue has been) direct observational evidence supporting the existence of God (namely miracles). But whichever of these two solutions is adopted, we are already moving beyond the bounds of the empirical sciences.

So this point marks the end of Krauss' discussion of the physics. It was mostly pretty good. His discussion of particle physics was poor. The issue is around particle creation and annihilation (or generation and corruption). The issue is where do those particles come from? Krauss' answer was the vacuum. This is based, I think, on an assumption left over from mechanism that particles are indestructible. There is simply a storehouse of unobservable particles (the quantum vacuum), and a visible layer on top, and what particles do during quantum events is move from the storehouse to the visible layer and back again. However, if this proposal is true, then the quantum vacuum would contain a great deal of energy. This effect would show up in gravitational models, and would be much larger than is observed. The alternative approach, which I adopt, is to abandon this mechanistic presupposition and say that substantial change can occur. An actual photon can decay into an electron and positron. An actual electron and actual positron together have the potential of becoming a photon. Energy (the quantum rather than the cosmological definition) is conserved when any one of these possible events occurs, so nothing can come from nothing. Krauss also took more from the uncertainty principle than is actually there, and confused the definition of energy used in cosmology (the stress-energy tensor) with the definition used in quantum physics (the eigenvalues of eigenstates of the Hamiltonian operator in jargon, or a label used to distinguish between different possible meta-stable states in a slightly more understandable language).

But now we leave physics behind us, as Krauss tries to pull everything together. This starts with the ninth chapter, with the unfortunate title "Nothing is Something".

This chapter is wide ranging. It partially summarises what went before, and partly prepares for what comes next. My intention is just to go over the chapter, and point out the mistakes that I noticed (and occasionally commend Krauss for getting something important right). I can't say that I have them all, but nonetheless this is going to be a long post. The title of the chapter itself is a contradiction, which gives us some idea of what we are up against. My response is thus going to be a bit disorganised, jumping from one subject to another, mainly because the chapter I am responding to is the same.

Laws and gaps

Newton was a great physicist. That, I think, everyone admits. But what was his greatest achievement? I would personally say the discovery of calculus and its applicability to physics. Krauss argues,

But perhaps the most important contribution he made was to demonstrate the possibility that the entire universe is explicable. With his universal law of gravity, he demonstrated for the first time that even the heavens might bend to the power of natural laws.

Krauss is, of course wrong, to attribute this achievement to Newton. For example, Aristotle and Ptolemy also explained how the heavens obey natural laws. Of course, Ptolemy's description was wrong, but, then, so was Newton's (albeit less wrong than Ptolemy). Even if we discuss Newton's system, then Kepler was there before Newton. And long before any of these, we had the prophet Jeremiah.

Thus says the Lord, who gives the sun for light by day and the fixed order of the moon and the stars for light by night, who stirs up the sea so that its waves roar— the Lord of hosts is his name: "If this fixed order departs from before me, declares the Lord, then shall the offspring of Israel cease from being a nation before me forever."

The words "fixed order" used by the ESV to translate the Hebrew are obviously different from the word "law," but the underlying meaning is similar. The context shows the immutability of this order: the idea is that God's desire for Israel is so strong that it is as likely to broken by Him as the regular motion of the moon and stars, i.e. not at all. Of course, there is one important difference between Krauss' notion of laws and this fixed order, in that the fixed order is dependent on God, while the laws, as Krauss interprets them, are self-sustaining.

Of course, the notion of laws of physics is a fascinating one, and Krauss' brief discussion doesn't do them justice. He reasons that if immutable laws governed the universe, then that would leave the gods of ancient Greece and Rome impotent. I'm not so sure. The Greek gods are created beings, i.e. in the world. One would thus suppose that they would also be bound by some form of law (perhaps the same as the laws we know about from science; perhaps part of a wider set of laws, of which the ones we know about are only a part, applying only to material beings such as ourselves). But that wouldn't render them impotent: they would still be able to act within the context of those laws.

Then Krauss says that the same logic applies to the God of Israel. This, of course, is a category error. The Greek gods, created beings within the order of nature, would, if the existed, be an entirely different order of being to the Christian God. The discussion here involves the nature of the laws of physics. When the concept was originally specified in those terms, it was similar to the "fixed order" of Jeremiah. The movement of the planets is fully within God's control; but God's regularity and rational nature implies that they would behave in a predictable way. We now explain that regularity through the laws of gravity. But general relativity doesn't change the question. It describes how the space time metric interacts with matter and itself, and how matter moves under different curvatures of space and time. The theist would still attribute those interactions to God. The laws of gravity provides no explanation of why the curvature of space time is linked to the stress-energy tensor. That explanation might well be found in some deeper scientific theory (just as Newton's gravity is explained by general relativity), but at some point that sequence of explanation has to terminate, and since scientific law is only a description of how those interactions proceed, the final layer of scientific question must still leave open the question of why those particular interactions. No matter how deep one goes into science, some question like this would remain. The theist has a simple answer for this: the material universe is not complete, and the laws of physics are a description of God's continual sustaining of it. As our understanding of physics increases, all we do is gain a better understanding of how God operates in the world. The atheist, believing that the universe and its laws describe a complete system, needs an alternative answer.

This theist understanding of the laws of physics predates the atheist one. Indeed, the concept of the laws of physics was originally proposed by theists as a consequence of their theology. Krauss recognises this, and states that there are two ways of understanding the laws of physics: the theological one, and the other that states that "the laws themselves are all that exist." The laws themselves require the universe to come into existence and develop. The laws may be eternal, or may themselves have come into existence through some physical process (governed, presumably, by a higher set of laws).

Now, of course, there is a contradiction between the laws being all that exist, and the notion that things in the universe came to exist; but that's a minor quibble. There is also a problem with discussing the laws both creating the universe and coming into existence. Something can only come into existence in time; but time begins with the creation of the universe. Thus to say that the laws come into existence implies the presence of time in something that is outside time. An alternative perspective would be to say that the laws of physics are continuously generated from something else, as a musician generates music while existing simultaneous with the music. But then, one might as well just skip the middle man, and concentrate on those higher laws of physics.

I note that the laws of physics play a very similar role in Krauss' cosmology as God does in the theist's. They have similar properties; eternal, unchanging, they bring the universe into existence and also drive its evolution and changes, nothing is beyond their grasp and so on. This, of course, arises from the theological origin of the concept of laws. The difference would be that theists describe God as a personal being, while Krauss' laws are an impersonal abstraction.

Indeed, we have to ask what we mean by "exist" here. Clearly the laws of physics don't exist in the same sense that the objects of physics do. An alternative is that they exist as something similar to a Platonic form; but then we have the problem of describing how the abstract world of the forms interacts with the real world. The natural explanation would be to say that there is some law connecting the world of abstractions and the physical world -- but then that law needs to be explained, which puts us back where we started. The third option is that they exist in the same way that a relationship exists. And this makes some sense. The laws of physics describe the interactions, or possible interactions, between beings. However, a relationship between two or more beings cannot not exist in itself. It is a derived form of existence, in that it depends on the existence of the beings. If the laws exist in this sense, they cannot be the creator of the universe. A relationship cannot exist prior to the beings that it relates. Once again, the theist has a simple answer to this problem: the laws of physics describe the relationship between God and the universe in the absence of special acts of providence. They depend solely on God, and come into existence at the creation of the universe. The atheist would reject this model, but needs an alternative, and a coherent alternative at that.

The laws of physics are central to Krauss' argument. Yet he gives no indication what he means when he says that they exist (without turning them into or making them dependent on a God-like being), and this makes it difficult to follow his argument.

Krauss stated that philosophers and theologians continue to debate the question of whether the laws are derived from God, or exist independently. Perhaps we will never know, though the answer, if it comes, will arise. from the exploration of nature. The universe is how it is, whether we like it or not (a very true statement).

Krauss thinks it significant that (in his view at least) a universe arising from "nothing" (by which he means the laws of physics and perhaps some primordial vacuum) is consistent with what we have learnt about the world. But why is this significant? Even if true, it says nothing about whether the laws are a description of God's normal way of acting, or independent in themselves. The theist might even say, that given that God created the universe, and the laws describe God's interaction with the universe, we might expect to see some hints about creation in there. We might conclude (as I do) that the nature of the laws of physics implies the existence of God; but we cannot say from the nature of those laws that they imply the non-existence of God. For the theist, everything that the laws describe is the work of God, and there is nothing in the laws themselves that could demand that they are independent of God rather than describing God's interactions. We need to turn to philosophy to make that judgement.

Of course, there is also the possibility of miracles providing direct evidence for God. Krauss has a brief discussion of this.

Of course, supernatural acts are what miracles are all about. They are, after all, precisely those things that circumvent the laws of nature. A god who can create the laws of nature can presumably also circumvent them at will. Although why they would have been circumvented so liberally thousands of years ago, before the invention of modern communication instruments that could have recorded them, and not today, is something to wonder about.

Krauss seems to be discuss a deist perspective of miracles here: note the laws of physics are something created by God. Again this is problematic, since only beings can be created in the sense meant here. But the main problem is Krauss' assertion that claims of miracles stopped in ancient times. That is certainly not the case. I wouldn't say that all of these accounts are true. Not all have been carefully investigated. Others might just have been chance; a rare event mistaken for a divine intervention. But there are those which are documented, and are confirmed to be genuine. Such miracles are well , particularly among known in some Christian circles. Charismatics and , particularly among Pentecostals are well known for the abundance of miracle stories associated with those churches. They are also attested in countries where the gospel is new and the church growing. But miracles certainly aren't exclusive to those churches: one doesn't have to travel far in many evangelical or orthodox Roman Catholic circles to find miracle claims. Of course, miracles tend to be absent in other churches: some orthodox Protestant churches (those which accept cessationism), and also more liberal churches. These, of course are the churches deny the possibility of miracles today. I think that the dominance of liberal Protestantism and liberal Catholicism in "respectable" Western secular society is why knowledge of these miracle accounts has generally escaped the notice of secular society. The prevalence of people who offer first hand accounts of miracles is stronger in those churches that still believe in the miraculous. Of course, there are three explanations for this. Firstly, the standard theist one, that miracles require a certain amount of trust in God among the people involved. Secondly, that the causation is reversed: that the experience of miracles makes peoples and churches more accepting of the miraculous and drives them in a more charismatic direction. Thirdly, the atheist explanation, that charismatic beliefs only appeal to the gullible and easily fooled. But just because the atheists have an explanation doesn't make the explanation correct. For example, the atheist explanation doesn't account for the often strong evidence for the miracles themselves. Of course, I don't want to deny that there are numerous frauds and false flags out there. But that some of the healers are frauds does not mean that they are all frauds; that some stories are untested does not mean that they are all untested. Krauss ought to have done his research before making an undocumented assertion such as this.

The meaning of Nothing

So, we return to the question "Why is there something rather than nothing?" This question has to be informed by science. Krauss admits that he has changed the meaning of the word "nothing" so much that by a linguistic side-step he has convinced himself that he has avoided any theological questions.

Krauss has rejected defining nothingness as non-being (as everyone else does), since that doesn't allow him to give the answer he likes. Imagine an electron positron pair pops out of the vacuum. We have to imagine it because it doesn't happen in reality; there is always a gauge Boson or Higgs Boson that decays into them. Did the electron and positron exist before the decay? No, but that doesn't mean that nothing existed or they came out of nothing.

There was potential for their existence, certainly, but that doesn't define being any more than a potential human being exists because I carry sperm in my testicles.

Of course there is a distinction between potential existence and actual existence. But potential existence only resides in something that exists actually. Potentiality, of course, is traditionally seen as the middle ground between being and non-being; necessary to avoid a wholly static universe.

Krauss attempts to defend his redefinition of the term "nothing" by turning the tables on his attackers, and accuse them of committing the same error that he is accused of. For this, he needs an older authority who would have accepted his definition of Nothing as Empty Space. He cites Aquinas and Plato.

There are two problems with this. Both Aquinas and Plato explicitly defined "Nothing" to mean non-being. Secondly, neither of them even believed that "empty space" is a coherent concept.

I'll focus my discussion on Aquinas. Lecture 10 of his commentary on Aristotle's physics defines the term void along the lines of what Krauss means by empty space,

The void is thought to be place with nothing in it. The reason for this is that people take what exists to be body, and hold that while every body is in place, void is place in which there is no body, so that where there is no body, there must be void. Every body, again, they suppose to be tangible; and of this nature is whatever has weight or lightness. Hence, by a syllogism, what has nothing heavy or light in it, is void. This result, then, as I have said, is reached by syllogism.

But, following Aristotle, Aquinas rejects the notion of the void. He concludes,

Then he [Aristotle] concludes his chief proposition. And he says it is clear from the foregoing that there is no separate empty space: it is not anything existing absolutely outside a body; or in a rarefied thing after the manner of empty holes; or in potency in a rarefied body, according to those who did not posit a void that exists in bodies as something separated from the fullness of the body. Consequently, in no way is there a void, unless someone simply wants to call matter the void, since it is somehow the cause of heaviness and lightness, and consequently the cause of motion in respect of place. For density and rarity are causes of motion according to the contrariety of heavy and light; but in regard to the contrariety of hard and soft, passible and non-passible are the causes: for the soft is that which easily suffers division and the hard contrariwise, as was said. However, this does not pertain to local motion but rather to [the motion called] "alteration."

We can, of course, question Aquinas' (and Aristotle's) reasoning, and much of it needs to be updated at the very least. Although, as Krauss himself would have to acknowledge, their conclusions hit the mark closer than classical physicists would have realised. There are still quantum and gravitational fields in what was previously thought as "empty space," and topological gluonic objects litter the vacuum, so even if one defines "empty" as a quantum field without excitations that doesn't pass muster either. But nonetheless, Aquinas would certainly not have defined "nothing" as empty space because he did not believe that empty space was a coherent concept. Plato, in the Timaeus, also denied the possibility of the void. There were, of course, ancient philosophers (particularly the atomists) who accepted the void (although still had very different understandings of "space" to modern physicists). Krauss could have cited those writers, but instead he picked on two who most definitely would have disagreed with him.

With regards to the actual definition, Aquinas put it plainly,

For "nothing" is the same as "no being".

"No being" is certainly not the same as "Empty space."

It took me about five minutes of googling to find those quotes. Admittedly, I had one advantage over Krauss: I am already familiar with Aquinas' thought, and knew roughly what to look for and where to look for it. So it might have taken him ten minutes. How much effort would it have been for Krauss or his editor to look it up? There is nothing wrong with citing authorities to back up your conclusions and definitions. Indeed, it is good, as long as you don't rely on the argument from authority but separately provide your own arguments and evidence. But one should make sure that those authorities actually said what you are attributing to them.

The meaning of "Why"

Still, redefining the word "Nothing" is not enough for Krauss. He now realises that he must also redefine the word "Why". The reason for this is, I think, straight-forward. Science doesn't easily answer "Why" questions. To do that, you need to turn to explanations in terms of efficient, final, material or formal causes; and Krauss doesn't care much for those. So instead he wants to ask the question "How?" He justifies this by stating that when most people ask "Why" they really mean "How." He must move in different circles to me. Where I come from, when there are two words with clearly distinct meanings, people generally choose the one most in line with what they want to say.

But, in any case, it is clear that asking "How is there something beyond a quantum vacuum and laws of physics rather than only a quantum vacuum and law of physics?" as Krauss has converted the question into, doesn't have any special theological significance. How questions most frequently reduce to a physical answer. The dispute between theists and atheists centres around the nature of the laws of physics. Are they necessarily dependent on God or independent of God? Giving an answer in terms of these laws does nothing to address the question.

When we try to understand the solar system in scientific terms, we do not generally ascribe purpose to it.

If true (and, of course, there are different meanings of the word purpose; a description of the solar system can certainly be made using Aristotelian tendencies), this is again a red herring. It assumes that the only understanding worth having is the scientific one; something which is again a major point of dispute. I would agree that everything should be informed by the scientific explanation, and consistent with it, but that by no means implies that there is nothing except the scientific explanation.

Krauss then breaks down the "How might something arise from the laws of physics acting on a quantum vacuum" question into sub questions. What conditions are needed to bring about what we observe? How might we find out? All good questions, and these certainly should inform our answer to "Why is there something rather than nothing." But neither can questions such as this by themselves be sufficient to answer the question. Ultimately, the question why there is something is a philosophical one. It must be informed by the science, but necessarily goes beyond the science.

The differences between Scientific and Theological method

Krauss also distinguishes this type of enquiry from a theological one. Theological explanations, he asserts, presume their answers. But, this is only the case to the same extent that scientists presume their answers. A theologian will draw from two sources: revelation and philosophy. The existence of God is made clear from direct observation (for example, from miracles). The task of the theologian is then to explain that observation; and deduce which philosophical model best fits it. The expanding universe is made clear from direct observation. The task of the scientist is then to explain that observation, and deduce which theoretical model best fits the data. If the theologian explains the scientific data by saying that ultimately "God did it," that is not a presumption as such, but the result of the desire to maintain consistency with his own data. There is the bigger question, of how to best combine the philosophical model of theism with the scientific model. We are not going to achieve the full truth by dismissing one part of the evidence out of hand and without good reason; whether the scientific evidence (as done by certain religious groups), or the religious evidence (as done by atheists).

Krauss then asks what advance in knowledge theology has provided in the last 500 years, since the dawn of science. He claims that he has received no satisfactory answer. So I will have a go.

Obviously, the study of theology has provided much insight into questions concerning God. It has also driven a lot of useful philosophical research. There is influence in the fields of literary criticism and the historical sciences (where, if nothing else, many methods were developed as useful tools to better understand the Christian sources, before being applied more widely). Even if we reduce the scope of the question to scientific knowledge, then one could argue that theology was nonetheless a great motivation for many of the great thinkers who brought us to this point: they sought to understand the mind of God through understanding His creation. Equally, Christianity gave us the Western European Universities which provided the infrastructure that allowed science to progress.

But unquestionably the biggest contribution of theology to science was the establishment of modern science itself. Take, for example, the following propositions:

  1. There are regularities in how matter evolves which can be understood as laws of physics.
  2. These laws are understandable.
  3. These laws are unchanging in time.
  4. These laws are unchanging in space, and universally applicable.
  5. These laws are in some sense unified.
  6. The universe is not irrational, but everything has a sufficient reason to explain it.

These principles are theological in origin. The laws of physics inherit these attributes from God. There is no reason why things have to be this way; and it is of no coincidence that science arose in a society founded on Christian religion and Greek philosophy. Atheists have tried to take away the foundation, but can only do so by leaving themselves with problems such as explaining why physical objects are bound to obey those laws and why the laws of physics have the nature that they do.

Could theology provide more than just the framework for modern physics? I personally believe (and outlined it in chapter 15 here) that, had the theologians their wits about them, and knew enough twentieth century mathematics, they could have gone further than these basic principles. But this is subtle, requires mathematical skill, and away from the main focus and goals of theology. The majority of theologians have had more important (from the perspective of theology) things to do than worry about science. After all, if we were all scientists, we would still be in the dark about justification; but since we have both scientists and theologians, we can understand both topics. Of course, the exchange is not just one way: scientific knowledge should also be used to inform theological discussion. But as for theology's contribution to science (aside from founding it), why should the success of theology be measured by that? One may as well state that science is a failure because it has contributed next to nothing over the past five hundred years to the art of dance. One must judge the success or failure of any endeavour by its own goals. The goal of theology is to better understand God and His relationship to man. One can debate whether modern theological has contributed to that, or simply clouded the waters. But to class it as a failure because scientists rather than theologians uncovered the Schroedinger equation seems to be a strong case of missing the point.

Newton and God's actions.

Newton's work dramatically reduced the possible domain of God's actions, whether or not you attribute any inherent rationality to the universe. Not only did Newton's laws severely constrain the freedom of action of a deity, they dispensed with various requirements for supernatural intervention. … We can describe the evolution of the universe back to the earliest moments of the big bang without specific need for anything beyond known physical laws.

Rarely do you see the difference between the atheist and theist philosophy of physics put more bluntly than this. The key atheist assumption is that the laws of physics operate independently of God. Theists reject that assumption. If Newton's laws describe God's usual actions, then they don't reduce God's sovereignty. Krauss here is begging the question without providing any evidence for his assumption.

I'll deal with the second point first. Krauss discusses the straw men of planets moving because angels push them around. I'm not quite sure who believed this: certainly not anyone who accepted Greek philosophy, which (in this regard) was pretty much everyone in academia before Newton (or perhaps Kepler). Aristotle's explanation of the orbits of the planets, sun and stars was that they were composed primarily of quintessence or an aether, which was predisposed to circular motion in the absence of an external force, just as terrestrial matter is predisposed to linear motion. There are various variants on this theme (such as from Ptolemy, Copernicus and Tycho), but the underlying principle remained. Obviously this explanation is wrong. Though not as wrong as it seemed in Newton's day. General relativity tells us that, without a non-gravitational force, matter is predisposed to travel along geodesics of the space time metric (obviously there are other interpretations; but it is consistent with the modified Aristotelian view). If that curvature is generated by a large mass, then some of those geodesics are, indeed, circles, while others are straight lines towards the centre. Aristotle's mistake was in dividing terrestrial and earthly matter, and thinking that quintessence was restricted to circular motion. But in any case, there are no angels involved.

But what of the other point; that the laws of motion constrain God's freedom to act? Again, this is making the assumption that the laws are independent of God. For if the laws are shaped by God, and maybe a reflection of His intentions, then clearly they cannot constrain Him. The theist will claim that the motion of the planets is both described by the laws of physics and an example of the continual divine intervention in His upholding of the universe. But even so, is God limited in what He can do? Obviously, there is the possibility of miracles: God choosing to act in a different way in response to a different circumstance. Secondly, we also know that Newton's description of physics is wrong. Quantum physics (most obviously in the path integral formulation) tells us that God is not constrained to evolve the universe in a single fixed way, but has numerous options at each moment of time for each particle.

Given that a "God of the gaps" is unacceptable to both atheists (for obvious reasons) and theists (because it reduces God's sovereignty over what is described by physics), Krauss believes that the only refuge for the theist is that moment where physics must surely break down, namely the beginning of the universe. The something from nothing question.

He views the idea of a deity existing outside the universe and yet governing it as extraordinary, and thus ought to be the last rather than first resort. Krauss' opinion, of course, counts for little. Whether something is extraordinary or not depends on ones prior assumptions. The idea of entanglement and electron diffraction is extraordinary if one accepts Newtonian mechanics; for it not to happen is extraordinary if one accepts quantum physics. For the classical theist, God, being perfectly simple in essence, is the most straight-forward answer to the question. Any physical explanation must be complex; one needs to explain the existence of matter, of physical law, and the relationship between the two. At least three principles before we start.

But, of course, Occam's razor is not a good guide in the first place. Not only because which alternative is simplest depends on one's prior assumptions; but because it is wholly the wrong approach. If one has a firm deductive argument, or a view is ruled out by observation, then that should be used ahead of any appeal to simplicity. If not, then we ought to leave all options open until more evidence comes in. Of course, theists claim to have firm deductive arguments for God; while atheists lack such arguments for an absence of God.

Science as a rival to God

So now we come to the classic problem with atheist scientists. They emphasise how we should not take our world-views on authority or without evidence, and rightly so. And then commit the same mistake themselves. Central to the atheist construction of reality is that God and science offer rival explanations. If there is a scientific explanation, then that means that God didn't do it. This is, of course, a statement that the theist would reject every time. As one notable theist put it,

He upholds the universe by the word of His power.

Elsewhere, God is written as being responsible for the grass growing, or lightning, or the tides. Today, of course, we have scientific explanations for this. But why should that mean that God didn't do it? Only if one assumes that scientific laws operate independently of God. Yet the whole scientific project was founded on the assumption that they don't. Scientific law was constructed to reflect many of the divine attributes because it was seen as a description of God's actions upholding the universe with the word of His power.

Atheists will ask what evidence is there that this understanding of physics is correct. To which the obvious first response is to ask for the evidence that scientific law operates independently of God is correct. The second response is to provide evidence; to show that scientific law is consistent with what we would expect if the theist model is correct, as I have done elsewhere.

So when Krauss starts discussing how he is certain that science will provide an explanation for the origin of life, and how evolution by natural selection explains the complexity of life, he ought not conclude that that removes the need for divine intervention. He has glossed over the main question.

Krauss believes that his arguments make it plausible that scientific law can explain how something can arise out of nothing. As I have explained, his argument is problematic. But for the sake of argument, let us grant him it. Let us grant that plausibility is all he needs to undermine the case for God; that aside from this point the case is firmly on the atheist side (again, something which I vigorously contest). He believes that this shows that there is no need for divine intervention. But, if the theist view of physics is correct, all he has done is offer a scientific proof of Genesis chapter 1 or the first line of the Nicene creed.

Inflation and the rise of the universe from empty space

Krauss goes on to repeat his errors about the Newtonian gravitational energy. As discussed before, it is problematic to talk about gravitational energy in the context of general relativity, and general relativity uses a different definition of energy to quantum physics -- which is what the conservation of energy applies to. However, before, in chapter 6, he made a great fuss over how the negative Newtonian gravitational energy exactly cancelled out the positive energy of all the stuff in the universe. Here he is now basing his argument on the contention that the Newtonian gravitational energy is zero. He is responding to criticisms that the zero point of energy is arbitrary. In most scientific theories, these criticisms are correct: all we measure are energy differences. In quantum physics, this is a bit more complicated, since energy is the eigenstate of the time evolution operator, that implies that a negative energy would imply particles travelling back in time. But Krauss is certainly correct that in general relativity, the zero point of energy is certainly not arbitrary.

So now, finally, we come to Krauss' explanation of how matter can arise from the quantum vacuum. As the universe expands under inflation, it will get flatter. The pressure associated with empty space (which is a component of the stress energy tensor) is negative. We are used to positive pressure, where we have to pump energy into a system in order to compress it. Negative pressure means that energy gets pumped into an expanding system. This energy has to go somewhere, and Krauss suggests that it gets turned into matter. Thus, starting from a small speck of empty space, the universe can grow to an enormous scale, containing vast quantities of matter, and appear to be almost perfectly flat with very little variation, as we observe.

Krauss' problem is, of course, the same as he had in the earlier chapter: quantum physics and general relativity use two different definitions of the energy of matter; and it is not clear that it makes sense to discuss gravitational potential energy in the context of general relativity. Thus the mechanism of how stress-energy can convert into quantum energy is unproven. Granted, it might well be that the true theory of quantum gravity, if we ever discover it, will provide us with that link. At the moment that is just ifs and maybes.

Equally, he relies on empty space containing a vast amount of stored energy. His justification for this is the idea that creation and annihilation events in quantum physics involve particles coming in and out of the vacuum, so the vacuum contains a vast store of particles. This model has been disproved because it predicts a much larger value of the cosmological constant than has been observed.

So Krauss' particular model has its flaws. But, nonetheless, inflation is established. The universe did start small and rapidly expand to become what we see around us. The point of dispute is over whether that starting point is empty space. The standard model of cosmology has the starting point as being very hot (energetic) and dense (i.e. with large numbers of photons and other Bosons packed into a small area). That starting point can't really be described as empty space. But, of course, that point is something we don't know much about: our experimental evidence only takes us back to the formation of the microwave background, and both classical general relativity and the standard model of particle physics will break down in the earliest moments of the universe. But, nonetheless, Krauss' contention that the starting point of inflation was a patch of empty space seems to be a rather non-standard perspective.

Now, Krauss admits that the idea of matter arising spontaneously from empty space seems weird. The beauty of science is that it considers irrelevant our subjective notions of what is and isn't weird. But this does not prove Krauss' argument that something can arise from nothing, since even if he is right, "empty space" in modern physics is not non-being. You still have the gravitational field, and the various matter and gauge Boson fields, and with them the potential for excitation. You still have to explain how that "empty space" came about (since Krauss' vision of "empty space" contains structure and energy). One also has to explain where the laws of physics come from. That Krauss wants to address in the next chapters.

I'll take up his case when I next have time to write a post. Hopefully you won't have as long to wait as you did for this one.

A Universe from Nothing? Part 5: Is Nothing Unstable?

Reader Comments:

1. Scott Lynch
Posted at 01:18:26 Saturday September 14 2019

Ironic Cosmology

It is incredibly ironic that Krauss asks how theology has contributed to science when theology was at the center of the debate of early 20th century cosmology. Isn’t Krauss aware of the belittling comments made to Fr. George Lemaitre for his primeval atom (Big Bang) theory by other experts in the field? Albert Einstein famously said (to paraphrase) that his mathematics was flawless, but his physics was atrocious. The reason experts rejected his theory was because they had an a priori commitment to an eternal universe. Lemaitre, whose spiritual advisor was a famous Thomist (Cardinal Mercier) probably didn’t care one way or the other about what the science pointed to (as Thomists frequently believe that the universe’s beginning cannot be proven, but has been revealed). It is the eternalist, determinist, mechanistic atheism that has consistently been holding back science (in both cosmology and QFT) for the past 100 years.

2. John Not Real Name
Posted at 14:42:43 Saturday September 14 2019

Science and it's Pesky Results

My Email is my schools. Thank You Dr Nigel Cundy as I have now delved into Cosmology and Quantum Physics in discussions with my Physics Teacher who is going to start his Masters on Monday (16.09.19).

The Website ( ) is a link my teacher gave as a different interpretation of Quantum Physics but I am confused with the Physics so if you so wish please help.

I cannot reply but ( ) it is a video from the 2017 conference of the Society of Catholic Scientists about Lemaitre and his achievements and his recognition for them.

I want to ask the difference between the Orthodox or Copenhagen interpretation ( ) and the Thomistic Interpretation ( ).

Thank You!

3. Nigel Cundy
Posted at 20:10:55 Saturday September 14 2019


1. Scott - Good point, and thanks for it.

2. John - I'm travelling at the moment and for the next week. I'll get back to you when I return.

4. Dominik Kowalski
Posted at 10:55:37 Friday September 20 2019

Hello Dr.Cundy!

YOu have said that you are reworking aspects of your book. Admittedly, I´m still not through it, so I judge by the sources in your acknowledgements, but I would recommend a discussion of Quentin Smiths argument that quantum cosmology provides strong arguments for atheism, since it shows that the conditions for life to appear were only probable and not certain, and that would be irrational for a creator. I don´t think its that great of an argument, but it is certainly something you could mention.



5. John Not Real Name
Posted at 11:32:05 Friday September 20 2019

Quantum Cosmology?

(To Dominik) While I also disagree with the idea brought up by Quentin Smith (I am no Scientist) I do not understand how it only being probable would be a problem.

Thank You

John Not Real Name

6. Dominik Kowalski
Posted at 19:41:57 Friday September 20 2019

Hi John!

Basically the argument goes like this: Quantum cosmology shows that the laws of nature are only probable and not certain. This would be an irrational way for a creator who wants to create life, since the life permitting laws of nature are not certain. This supports a random universe where our appearance is an accident.

I´m not really troubled by that argument, especially since it seems to demand something close to necessitarianism. I think it is an "Anti-finetuning"-kind of argument. Howard SObel endorsed it, too, so I think it is worth being responded to. Koons responded that it being probable (<1) is not a problem, since God could intervene to make the probability a certainty. While I agree with Koons, I guess my hope is that Dr. Cundy can provide something, lets say, more elegant.


7. John Not Real Name
Posted at 14:00:10 Saturday September 21 2019

Ahhh Yes it seems we agree.

(To Dominik) Yes, Koons' idea was exactly the same as mine (though a dissection of the Physics and the Philosophy would be appreciated) so it seems I could figure that out. What exactly is Quantum Cosmology?

John Not Real Name

8. James
Posted at 01:16:42 Sunday September 22 2019

It seems to me that an objection like that only works against a deistic hands-off creator. It makes the assumption that God just rolled the dice at the big bang then let the chips fall where they may without any further intervention. Of course it's not an issue for theism because the regularities in the natural world are only regularities because of Gods constant and continual will that the material universe function in the way it does. A theistic God doesn't just create then allow the universe to function based on principles He bakes into the fabric of it, and that's the primary assumption that the argument of probabilities makes.

Koons response seems off the mark as well because he too seems to be working off the assumption that there exists a natural world that functions without Gods intervention. He thinks the answer is that God tipped the scales and made probability a certainty but he's missing the point that without God there is no probability in the first place, and in fact the existence of probability is an illusion created by our incomplete understanding of reality. The truth is that when you throw a ball it arcs in a predictable parabola because God wills it to do that when you throw it. There's no such thing as any natural laws without God because natural laws are in fact the manifestation of the regularities that occur when things behave in the predictable way that God wills them to act, nothing more nothing less.

9. Nigel Cundy
Posted at 22:31:05 Sunday September 22 2019

Quentin Smith

Thanks everyone for your comments. I'm now back, so I'll try to reply. I'll start with Quentin Smith, since that's a bit easier.

I fully agree with James' comment 8. I don't think that the objection makes much sense in the context of theism. I'll also provide my own response, although the below will be a bit confused as I work things out as I type them.

We have to think about what we mean by "random" or "probable." Random means something akin to unpredictable. There are two ways in which something can be random. 1) "True" randomness, which implies some sort of logical jump and breakdown; 2) something that appears random due to our lack of knowledge. For example, if we roll a balanced dice (in a classical mechanics system), we treat the result as random, even though in principle if we knew precisely how it was thrown, and the various coefficients of friction, then we would be able to compute the outcome.

With regards to either quantum uncertainty, or the "selection" of the cosmological constants, the theist will say that it appears to be random in the second sense (I would be surprised if there was randomness in the first sense; it would contradict the PSR). The selection depends on the free decisions of God, which we cannot predict or know in advance. To put it another way, we can know (in principle) the current state of the universe, but that is insufficient data to make the predictions with certainty, because one key factor (God's thinking) is missing.

I also see another issue with saying that "Quantum cosmology shows that the laws of nature are only probable and not certain". Every statement of probability is model-dependent. Since we don't (as far as I know) have a confirmed theory of how the laws of nature are selected, we don't have a model to use to calculate the probability. This is an issue for any argument concerning the anthropic principle. The argument is that the various constants in the laws of nature could in principle take any value, but in practice only a small region within space is consistent with various physical and chemical conditions needed for life to arise. But without knowing how to sample the possible combinations of parameters, it is impossible to unambiguously state precisely how unlikely it is. (This is the measure problem). Every model of how those constants are generated will lead to a different answer for the probability. It might be that for a model in which God's motivations are unknown (or a model where God plays no role in formulating the laws of nature) the probability that the universe is as it is is very small. But then, a different model which takes into account God's motivations might lead to a very high probability (perhaps even 1) that the constants are as they are.

Let L represent the laws of nature, A represent our knowledge of the processes used to select those laws, and B represent God's knowledge of the processes used to select those laws. The argument seems to be that if God exists, then the probability P(L|B) should be 1. However, we know that P(L|A) << 1. Both of these premises look reasonable to me, but I can't see how they lead to the conclusion that God doesn't exist.

10. Nigel Cundy
Posted at 23:35:05 Monday September 23 2019

Super-determinism (part 1)

Sorry again for the long delay in replying, John. I'll probably break down my response into a number of comments. I'll discuss the post on Super-determinism in this one.

First of all, the writer spends a few paragraphs emphasizing how interpreting QM is becoming fashionable again. OK. He mentions a few new (or in progress) technologies based on quantum physics in his third paragraph. I'll just discuss entanglement and Bell's inequalities, which are needed for the rest of the article.

Entanglement is the idea that you can have two individual particles linked together. Suppose, for example, you have a spin zero particle which decays into a spin half particle and its anti-particle. Total spin is conserved, so one of the decay products must have positive spin and the other negative spin. Spin (which is badly named, since it has nothing to do with the particle's internal rotation) must be orientated along a particular axis (in a three dimensional space -- in this sense a picture of a sphere rotating along some axis is useful, but remember it is only a picture and fails in other respects), so, for example, if particle A is spin up along a particular direction, particle B must be spin down along that direction.

That makes sense for classical particles. The complexity is because these are quantum particles. In particular, the spin of the particle along any axis can either be +1/2 or -1/2; it cannot take any other values. The operators representing spin along the different (x,y,z) axes don't commute with each other, meaning that the spin only takes a defined value along one axis at a time. For example, if particle A is spin up along the x axis, then its spin along the y axis is wholly undefined. If you measure the spin along the y axis, then 50% of the time you will measure it as being spin up, and 50% of the time spin down. And if you measure the spin of particle B along the y axis, then you will get the opposite result.

The natural picture (using a classical intuition) is that the Fermions are emitted in a particular spin orientation (say along the x axis). Particle A has spin up along the x axis, particle B has spin down along the x axis. But when you measure the spin of particle A along the y axis, it randomly picks either positive or negative spin, and that's what you observe. But then particle B would also randomly pick either positive or negative spin along the y axis. The classical intuition would be that these two events are wholly independent of each other, so the measurements of the two particles' spins would only disagree 50% of the time. (In practice, one wouldn't know the original orientation, so they would disagree more than this, but still less than 100% of the time.) But in practice, the particles have opposite spin 100% of the time along any axis. The two particles seem to be in some way joined together despite being separated by a large distance. We call this joining together entanglement.

The next classical picture one might consider is that the value you measure for the spin is determined along each axis at the moment of decay. So the particle's spin state is described by three numbers. For example, particle A might have spin (1/2,1/2,1/2) while particle B has spin (-1/2,-1/2,-1/2). It has to be three numbers because there are three independent operators describing the spin. The measurement process would then measure the spin in the appropriate direction, while randomizing the spin in the other directions. This is where Bell's inequality comes in. If, instead of orientating the detectors at 0 degrees or 90 degrees, one chooses an angle in the middle, one gets a different probability of the two spins agreeing between this classical picture and the quantum mechanical picture. If one detector is orientated theta_1 from the axis, and the other detector an angle theta 2 from the axis, the classical picture predicts that the measured spins of particle A and particle B will agree with a frequency that is less than or equal to 2sin^2((theta_1-theta_2)/2), while standard Quantum physics predicts that the frequency of agreement is sin^2(theta_1-theta_2). Experiment agrees with the quantum prediction.

Bell's theorem to calculate the classical probability depends on two assumptions:

1) The rules of standard probability theory apply to the measurement of the two particle's spins, in particular P(A \cup B) \le P(A) + P(B) [The article calls this statistical independence.]

2) The two measurements don't influence each other [The article calls this statistical locality].

Since the equality is violated, one of these assumptions must be incorrect.

I should note that there are also Bell inequalities for many different physical systems, such as photon polarizations.

My own interpretation of quantum physics maintains statistical locality, and violates statistical independence. It does this by assuming a) that the quantum state represents our knowledge of the system; b) this knowledge is uncertain; c) uncertainty for quantum physics ought to be represented by an amplitude rather than a probability, since a probability is too crude a measure to capture the internal degrees of freedom of the quantum particle (this is where I violate statistical independence); d) the particles themselves are always in a definite spin state in a definite direction; e) the apparent randomness in quantum processes arises from the free actions of God [who is outside space and time; thus I here violate statistical locality]; f) calculations in quantum physics compute amplitudes that correspond to the likelihood of each of God's possible choices given a particular individual state and perhaps some later measurements g) our computations of amplitudes in quantum physics are always conditional on our knowledge; h) these amplitudes are only used to predict the results of experiments; i) if we know that particle A and particle B are entangled, and have measured the spin of particle A along one particular axis, we can predict the results of the measurement of the spin of particle B along any axis based on those premises, with the results being in agreement with the predictions of quantum physics.

So while most interpretations of QM violate either assumption 1) or assumption 2), I assume that both are violated (though in such a way that assumption (2) doesn't imply that physical locality is undermined). Most interpretations target assumption 1 as the one that is broken.

The article itself instead proposes a deterministic theorem that breaks statistical independence. Unfortunately, it doesn't go into details on how this is achieved. It mentions that the hidden variables might be contained within the detector itself, rather than the particle. It suggests that the detector depends on a superposition of prepared states. The key point is that these detector states aren't independent of the wider system, but have a common cause (going back to the initial state of the universe). This means that there is a correlation between the detectors and the measured system, which breaks statistical independence. I can sort of see how that might work.

Unfortunately, I have run out of time for this evening, so I'll stop here for now, and continue (hopefully) tomorrow. I see that the article references two papers which outline the model in more details. I'll next review those papers, and then give my comments. I also need to review the Copenhagen interpretation, Bohm's interpretation and so on.

11. Nigel Cundy
Posted at 23:40:28 Tuesday September 24 2019

Super-determinism (part 2)

This will be the second part of my response to the super-determinism article. As before, I'm largely writing this as I go along, and will stop when I run out of time. I'm unlikely to be able to say everything, so I will continue later in the week. I'll get a bit mathematical here.

The blog post in the link proposes that if the hidden variables that define the entangled system are correlated with the set-up of the measurement devices, then one can preserve both statistical locality and determinism. It proposes that the link between these can be from a set of causal chains all going back to the same event, namely the beginning of the universe. As I said above, this seems plausible, but it remains to be seen if a formulation can be produced which produces the correct results.

As an example of a super-deterministic system, the article links to two papers. I'll concentrate on the first of these here, This proposes a few super-deterministic models.

Some definitions: (a,b) correspond to the outcomes of the measurements of the spin of the two particles, which in this case are normalised so they take values +1 or -1. (x,y) correspond to the parameters describing the measurement device, and in particular the directions of the spin axes. B refers to the background physics; which in this case would include the deterministic equations of motion and the initial state of the universe. l refers to the set of hidden variables. (I have changed the notation a bit to make it easier to type in this HTML comment.)

The formal derivation of Bell's inequality is based on three assumptions. Firstly Statistical completeness, defined as

P(a,b|l,x,y,B) = P(a|l,x,y,B) P(b|l,x,y,P).

This means that the outcomes a and b are statistically independent of each other. This is automatically satisfied for a deterministic system, defined as P(a|l,x,y,B) and P(b|l,x,y,B) must be either 0 or 1.

Secondly, statistical locality, where

P(a|l,x,y,B) = P(a|l,x,B)

P(b|l,x,y,B) = P(b|l,y,B)

This implies that the result you get for a is independent of the settings of the detector parametrised by y, and vice versa.

Thirdly, measurement independence, i.e. the hidden variables l are statistically independent of the detector settings

P(l|x,y,B) = P(l,B)

The derivation of the generalised form of Bell's inequalities is based on the decomposition

P(a,b|x,y,B) = integral dl rho(l) P(a,b|l,x,y,B)P(l|x,y,B) = integral dl rho(l) P(l|B)P(a|l,x,B)P(b|l,y,B)

where the measure rho(l) [Not actually specified in the paper, but I think it ought to be there] is defined by

integral dl rho(l) P(l|x,y,B) = 1

The paper shows that one can maintain the first two assumptions (including determinism) and violate the third while implying the standard results of Quantum Mechanics. It provides three choices of P(a,b|l,x,y,B) and P(l|x,y,B) which achieve this.

The first of these (Brans model) uses a two parameter choice of l. This is insufficient to describe the degrees of freedom of a spin half fermion, and should be rejected.

The second of these models (Degorre) avoids this by assigning l to be a point on the unit sphere. This has the correct degrees of freedom, but the model breaks the symmetry between x and y (which should surely exist), and for that reason I would also reject it.

The third model (Hall) is more interesting. l is once again a point on the unit sphere, and it is symmetric between x and y. This might be viable, and I can't think of a good reason why this model couldn't work (although it would still need some theoretical justification, which isn't provided: right now it is just throwing together functions until something is found that gets the right result).

Of course, these three models need not be the only possibilities.

Each of these models has P(a,b|l,x,y,B) taking on a value of 0 or 1 (preserving determinism according to the earlier definition), while P(l|x,y,B) is some function of l, x and y.

We can write P(l|x,y,B) P(x,y|B) = P(l \cap (x,y)|B)

(\cap means a logical "and") In practice, we know what the values of x and y are when the experiment is set up. Thus, since probability is a description of our knowledge, P(x,y|B) = 1. In a deterministic system, every probability only depending on the background information can only be 0 or 1. Thus P(l \cap (x,y)|B) would be 0 or 1. This would imply that P(l|x,y,B) is 0 or 1. None of the proposed models satisfy this condition, and I can't see how one could make the usual quantum mechanical predictions while doing so.

Thus, while these super-deterministic theories maintain determinism for the outcomes of the experiments, they break it for either the underlying hidden variables or the measuring system. This means that a system of this sort would not describe a purely deterministic universe, which invalidates the whole goal of the project.

Also, quantum physics allows us to calculate the probabilities from an initial state at any time to a final state. One does not need to go back to the start of the universe (or, alternatively, one can imagine a universe governed by a quantum physics which is identical to that which governs our own except that it began fully formed at an arbitrary late time, lacking any correlation between the particle and the measuring device). If we choose an initial state at a time after the particle and measuring devices are causally disconnected, the quantum mechanical calculation would remain the same, but the justification for the correlation between the particle and the measuring device would disappear. Thus such a correlation could play no role in the underlying metaphysics of the imaginary universe. We would need a different explanation for the entanglement. In that case, we would expect that the same explanation would hold in our universe, since the physics is the same.

And of course, any such a model of correlation between the particle and the measuring device needs some justification; we shouldn't just choose something arbitrarily.

In summary, a super-deterministic model needs justification; the proposed mechanism for the correlation from causal chains going back to a single event is insufficient, and the universe described by such a system still isn't deterministic. It maintains determinism in the place where most people say it is broken, only to lose it elsewhere.

12. Nigel Cundy
Posted at 23:02:50 Wednesday September 25 2019

Super-determinism (part 3)

A quick clarification of my last comment:

The paper I was critiquing defined determinism as P(a,b|l,x,y,B) is either 0 or 1. This means that the observations (a and b) are fully determined by the hidden variables (l). But this is not in doubt; it's the whole point of a hidden variables system.

P(l|x,y,B) describes the evolution of the hidden variables themselves. If this evolution is deterministic, then this should be 0 or 1.

To have a deterministic system, you need both the hidden variables to evolve deterministically, and the observables to be determined by the hidden variables. The super-deterministic models only address the first of these conditions.

I have no issue with an interpretation of quantum physics which requires some unseen parameters. My own view (which is in part that the wavefunction at least in part represents our uncertainty of the underlying variables of the system) implies that there are hidden variables. The difference is that I don't believe that the evolution of the "hidden variables" is deterministic, nor the link between the observable and the variables.

13. Michael Brazier
Posted at 03:06:42 Monday September 30 2019

Quantum states as knowledge

Thinking of quantum states as representing our knowledge of a particle system gives plausible answers for EPR experiments, where Bell's Theorem or an analog applies. It sounds reasonable that measuring one particle of an entangled pair changes our knowledge of the other particle, not that particle's actual state.

But when I try to use that interpretation for quantum interference, it gets much less plausible. In the basic two-slit experiment, for instance, it implies that the particle definitely goes through one slit or the other, and the interference pattern shows up because we the observers don't know which one it went through. That's quite weird, since the interference pattern is an observable physical effect. How can what actually happens depend on what an experimenter knows, or doesn't know?

14. Nigel Cundy
Posted at 21:10:01 Monday September 30 2019

Quantum states as knowledge

The one thing which I think everyone can agree on about the interpretation of quantum physics is that at some point it is going to become weird. I think that is true for every interpretation. And, of course, the double slit experiment and entanglement are the archetypal places we see the weirdness.

My interpretation is partly based on the following premises:

1) Calculations in quantum mechanics are primarily concerned with predicting the results of experiments in the face of an indeterminate physics. In the double slit experiment, the information we have at the start is the layout of the slits, and that there is an electron emerging from whatever source we are using. The result we are trying to predict is where will the electron end up on the screen.

2) Because physics is fundamentally indeterminate, we cannot be certain which path the electron will take. We therefore need to express the result in terms of some way of parametrising uncertainty.

3) The standard way we parametrise uncertainty in classical physics is probability, which has the same mathematical structure as frequency. However, this is unable to capture the relevant internal degrees of freedom of the particle. Thus in quantum physics, we need an alternative measure, and the correct one to use is the quantum mechanical amplitude. The amplitude, being a complex number (or complex vector quantity when we move beyond electromagnetism) doesn't obey the same rules as probability. Therefore our classical intuitions are going to break down. This is the point where weirdness enters this interpretation (and I think that every other point of weirdness ultimately reduces to this).

4) However, when the quantum particle interacts with a "classical" system (defined as one whose off-diagonal terms in the density matrix are negligible), we need to use a combination of the classical probability and quantum amplitudes in the predictions. For example, if we are to measure that the particle will go through one set of paths or another; interference with the classical system has the effect destroy any interference effects between those two sets of paths when we make our predictions about the ongoing path of the particle. Introducing a classical element affects how we do the calculation.

5) In the double slit experiment, the particle does go along one path or another. We don't know which path it is, and therefore have to express our uncertainty as an amplitude conditional on all our knowledge. The amplitudes for different paths can cancel out, leading to the standard interference pattern.

6) When we look at the slits to see which one the electron passes through, then our knowledge is updated. We re-calculate the interference pattern based on that knowledge (i.e. the particle goes through one slit or the other). This predicts that the final interference pattern will be the sum of the two single slit diffraction patterns.

I think that it is step 6 which causes the biggest difficulty. After all, the electron should surely "choose" which slit it goes through before we decide whether or not to measure it. Our measurement shouldn't affect the electrons going through the other slit, and yet, seemingly, it does. I think that the answer to this is that our predictions are conditional on both the initial state of the electron and our knowledge of the rest of the system. If the rest of the system is just the two slits, then the electron wavefunction and its possible paths is all we need to consider. However, if we have a measuring device on one of the slits, then our predictions are based on the wavefunction of the combined system, both the electron and the measuring device. In particular, if the measuring device is classical (i.e. our uncertainty concerning it negligible interference effects and is thus represented by a probability rather than an amplitude), then combining the quantum amplitude with this classical probability is enough to cause the different possible paths of the electron (though one slit or the other) to decohere, removing the effect of the interference on our predictions.

So in the double slit experiment, the electron goes down some path. We don't know what that path is. If we know both the initial and final state, then there is no uncertainty about where the electron ended up. If we know only the initial state, then we can make predictions for the distribution of possible end states based on our knowledge of the system. Those predictions ought to remain expressed as amplitudes. However, to compare against experiment, we need to convert the amplitude to a probability so we can compare with a frequency distribution.

Our predictions don't determine where the electron will end up. Except for the few dark spots on the interference pattern, a single electron could hit anywhere on the detector screen. Our knowledge doesn't determine the path of any individual electron passing through the two slits. It is only when a large number of hits that we see the interference pattern emerge. All we predict is a statistical distribution of an ensemble of individual electrons (or, more precisely, the distribution you would get after an infinite number of measurements). The nature of that distribution is dependent on only the overall experimental set-up. Our knowledge doesn't affect the path of a single electron, because that is indeterminate. Our knowledge doesn't affect the final frequency distribution, because that is solely determined by the experimental set up.

Anyway, those are my thoughts (perhaps slightly clumsily expressed). Please let me know if you disagree with any of it, or I didn't explain something clearly. This is still something of a work in progress, so I welcome criticism.

17. John Not Real Name
Posted at 11:34:01 Monday October 7 2019

Double-Slit Experiment

Dr Nigel Cundy,

Our class did the double-slit experiment on Thursday (10.10.19) but the slit width was too large so we have to repeat it.

Anyway the link should be to a paper by Nature Physics which determined ,to keep it brief, ( ) that larger structures can be waves. So people can be waves (as their particles are also waves). From what I understand there would be no such thing as points in space (my teacher thinks so)as waves do not take a particular point in space-time.

Does this mean teleportation is possible?

Why is it that the observer do not comprehend itself to be in two places at once (or at least me)?

Finally If points in space are meaningless then how can the experiment conclude that interference occurred as it was not in a particular position?

Asking you this may be pointless as your conception (which to the degree I understand I accept) of Quantum Physics is based on points (I think)but I hope you are able to clarify the conclusions and my misconceptions.

Thank You!

18. Nigel Cundy
Posted at 22:35:31 Tuesday October 8 2019

Double slit experiment

Dear John,

Thanks for your comment.

Firstly, when it said larger objects show interference effects, remember that term is relative. It is discussing objects of around 2000 atoms, which is impressive, but that's still somewhere around 18-20 orders of magnitude smaller than the number of atoms in a strand of human hair -- so nowhere near enough for a person. And, of course, even that is very difficult to obtain.

There are two main reasons why we don't see quantum effects on the large scale. First of all, there is the de Broglie wavelength, which gives (roughly speaking) the size of quantum effects. This is inversely proportional to the momentum, and given that the various parts of us are in constant vibrational locomotion, this will be inversely proportional to the mass of the particle. (One can get a similar result from the uncertainty principle relating the spread of the location and momentum wavefunctions, Delta x Delta p >= hbar/2). For an electron or other sub-atomic particle, this is relatively large; for us it is incredibly small. Thus we are smeared out over a small area -- but it is much too small for us to notice.

Secondly, there is decoherence. This happens when you have a highly interacting system: a quantum particle interacting with a large number of other particles (called the environment). (Usually in the standard QM calculations and effects, we consider particles in isolation). Given a number of assumptions -- most importantly statistical independence of the particles making up the environment, and that the particle is in some way coupled or entangled with aspects of the environment -- after averaging over the environmental effects we find that the quantum mechanical features such as superposition and interference effects are diminished. Once again, for us, all our molecules and atoms are in such a strongly interacting system, so we won't (on the whole) experience quantum effects. (I do wonder if that is wholly correct: in particular, with regards to brain function, but that's controversial and not something I know much about.)

Your teacher suggested that since particles are described by waves, they don't occupy a single point in space. That is a bit more controversial; there are numerous different interpretations of quantum physics. In my own interpretation (very much a minority view) the particle does occupy a definite point, and the wavefunction describes our uncertainty. (this interpretation makes entanglement and measurement easy to explain, but leaves us with a headache when considering superposition; your teacher's interpretation is great for superposition, but makes the measurement problem difficult to explain). Of course, quantum objects are in practice neither waves nor particles but something else (individual excitations of a quantum field), so one cannot just call them waves or say that the particle occupies all space like a wave, as though that tells the whole story.

There are of course claims about Quantum Teleportation, but this is more hype than the sort of teleportation you see on Star Trek or Blake's 7. It basically takes a pair of entangled particles and uses that to copy the state of one particle to another. It is a transmission of information rather than matter, and more importantly we can't control what information is transmitted, which makes it pretty much useless for large scale objects. It works for things like individual photons, but the problems above still apply when you try to apply it to larger objects, plus the need to set up an entangled copy of yourself.

The other interesting phenomena is quantum tunnelling, where there is a small probability that a particle heading towards a potential barrier could pass through that barrier and emerge on the other side (something which would be impossible in classical mechanics given that the energy of the particle is smaller than the size of the barrier). This is analogous to somebody occasionally being able to walk through a wall. Except, of course, again we (and walls) are far too large for the effect to be observed at the macroscopic level.

Is teleportation possible -- at the level of subatomic particles, and if you abandon the traditional meaning of the word "teleportation", then yes. For all practical purposes, no, or at least not by these means.

Why is it that the observer do not comprehend itself to be in two places at once? a) we are too big; b) our De-Broglie wavelength is far too small for us to notice. c) it wouldn't be us as a whole in two places at once, but individual atoms in our brain -- and if it happens, it would just be part of the normal brain mechanism, and the means by which we perceive things rather than something we can perceive; d) this depends on certain interpretations of QM which I don't agree with.

As for points in space being meaningless -- no. We still depend on a geometrical background for space, which describes individual points. The best you might say is that particles don't occupy single points, but are spread out over a small area, but even that is stating too much. One can choose a space time basis where the eigenstates describe single points. If your measuring device is represented by an operator whose eigenstates are individual locations, then you will measure the particle to be at a single point in space. (Of course, in practice there will always be some experimental error, so you will never get this precise, but it is theoretically possible at least in some cases.)

19. John Not Real Name
Posted at 09:44:41 Wednesday October 9 2019

Just a Clarification.

I have to ensure my comments did not mis-represent my teacher's theories (wholly my fault sorry).

His interpretation is that particles are everywhere at the same time (perturbations of fields) and our view that the universe has specific points is merely an illusion which works well to allow our brain to conceive of something that would otherwise be too complicated.

Secondly my teacher questioned whether to think of points in space is meaningful (in reference to the paper and my questions).

I will admit to adding on the statement on the waves: "as waves do not take a particular point in space-time." (though I do suspect he agrees with this).

20. Nigel Cundy
Posted at 16:47:25 Saturday October 12 2019

Orthodox vs Wolfgang Smith's interpretations

To get back to John's questions in comment #2.

The Copenhagen interpretation (as I understand it) is a hyper-realist interpretation of the wavefunction (which is not necessarily the same as realism in philosophy). It treats the wavefunction as reality. So the wavefunction corresponds to the physical state of an electron. It isn't localised at any one point, but spread out over an area; the electron does not have definite properties between measurements. This wavefunction evolves deterministically under the Schroedinger equation. However, the process of measurement introduces a non-deterministic change, forcing the wavefunction to collapse into one or other of the eigenstates of the operator that represents whatever it is that we are measuring. Thus indeterminacy in quantum mechanics only occurs when the quantum world interacts with a classical observer.

Wolfgang Smith, in my view, is on the right track, but because he only considers quantum mechanics rather than field theory, he doesn't go as far as he should.

I'll start by discussing two different families of quantum mechanical interpretations. (Note that this brief discussion is over-simplified, and there are considerable variations in both families, and not everyone would agree with everything I say about their particular family). The first is the wavefunction ontonic family, which identifies the wavefunction with the physical state. The second is the wavefunction epistemic family, which identifies the wavefunction as our knowledge of something (which might be the physical state). So, for example, let us suppose that we pre-select some basis for describing the wavefunction: perhaps eigenstates of the location operator. In practice, the wavefunction will be in a superposition of these eigenstates. The standard interpretation would be to say that the electron must be in some state or another. Advocates for the wavefunction ontonic-family would say that the superposition is reality. Advocates for the wavefunction epistemic family of interpretations would say that the wavefunction is in one particular location eigenstate, but we don't know which one, and the wavefunction is an expression of our uncertainty.

Wolfgang Smith, as I understand him, is saying that both these groups of people are making the same fundamental mistake: they divide the world into actual existence and actual non-existence. Instead, one also has potential existence. The wavefunction represents this third class; it tells us what the electron could be potentially.

He maintains a distinction between the corporeal object, which is what we perceive (the measurement outcome), and the physical object, which is its description under physical law (the wavefunctions). Standard interpretations, such as the Copenhagen, equate the two. Smith maintains the distinction. The measurement process is when there is an ontological transformation from the physical representation to the corporeal.

A macroscopic physical object is more than just the sum of its microscopic parts. Substances are macroscopic objects; they are actual. The parts of the object lack that form of existence; they only exist potentially or virtually within the substance. Wavefunction collapse is thus equivalent to the actualisation of a potential.

So there are two main distinctions between Smith's view and that of the Copenhagen philosophy. Smith believes that there is a distinction between the macroscopic substances and their physical parts. Parts exist only in potential to a larger substance. The Copenhagen picture doesn't make this distinction, and continues to adopt the mechanistic view that the various molecules and sub-molecular objects are the real things, while a macroscopic object is just an aggregate of them. Secondly, Smith describes the wavefunction of quantum objects as describing something which exists potentially, while the Copenhagen interpretation views the wavefunction as describing actual or substantial existence (and denies the possibility of potentiality, and probably wouldn't think of things in terms of classical substances).

21. Michael Brazier
Posted at 00:33:23 Sunday October 13 2019

Wolfgang Smith's interpretation

There's an implication of Smith's view that could be experimentally checked, in principle: a corporeal object could not be kept in a superposed state indefinitely. After some time (presumably inversely related to its mass) the object's interaction with quantum particles would become a measurement and realize one of the potential results.

So the maximum mass of "Schrodinger's cats" that can be achieved in a lab becomes philosophically interesting. I know fullerene molecules have been held in superposition; anyone know what the current record is?

I got the idea from Roger Penrose's book The Road to Reality - he suggested it as a test of the idea that gravity causes wavefunction collapses, but the reasoning is similar.

24. Codex
Posted at 21:58:25 Monday August 17 2020

Angels moving the planets

Hello Dr. Cundy,

I just discovered your blog and have to say I’m very impressed! I’m glad someone like you is knowledgeable about both physics and philosophy and is attempting to build a bridge between the two disciplines, we definitely need more of that.

That said, I was a little disappointed at how quickly you dismissed the idea that angels drive the motion of the heavenly bodies. As you yourself stated in this article, the laws of physics are descriptions of how God relates to the world, they are not actual explanations for why something happens, and so what in modern physics has disproved the idea God has given it to the angels to move the heavenly bodies such that their movement is describable in terms of laws? The Scriptures themselves speak about the heavenly bodies as if they are living creatures to an extent, and there is a close association between angels and the heavenly bodies throughout the Bible, that most certainly extends beyond mere metaphor. And this idea was pretty much believed by all of the Church fathers, including up to Thomas Aquinas, just read his commentary on the 4th day of creation.

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