PART I~ Why I chose to explore neutrinos and the cosmological argument.
When I was sixteen years old, I began watching the show Young Sheldon. I repeatedly heard of the term “neutrino,” and the term sparked my curiosity. I wanted to know what they were and why physicists cared about them. Part of this project aims to bring in those early scattered searches into a clear and refined understanding.
The cosmological argument was made relevant to me while I was preparing for a philosophy competition on the existence of good and evil. In a nutshell, the cosmological argument claims that our universe requires an ultimate explanation, often referred to as God (Aristotle, 1998; Aquinas, 1981). This led me to think more broadly: could neutrino physics perhaps tell us anything useful about the origin of the universe?
Another reason I chose these topics is because it would allow me to appreciate the world around me more. The poet David Whyte claimed that: “Gratitude is not a passive response to something we have been given; gratitude arises from paying attention, from being awake in the presence of everything that lives within and without us…” (Whyte, 2014). I aim to use this EPQ as a means of nurturing my knowledge of the universe and by extension allowing me to be grateful for the world that I live in.
I was drawn to this title because it does not sit comfortably within a single subject. Neutrinos belong to the realm of particle physics, while the cosmological argument belongs to philosophy. Physics can describe the early development of the universe, but philosophy asks whether dependent things can explain themselves at all.
And finally, it will hopefully strengthen my university application, as well as allow me to refine my academic skills for later life. I think this EPQ is a great opportunity to develop self study skills as well as in-depth research. I hope I can produce a high standard of work!
Part II~ What are neutrinos?
The Neutrino was first conceptualised in 1930 by Wolfgang Pauli and was later discovered by Clyde Cowan and Frederick Reines in 1956 (Pauli, 1930; Cowan et al., 1956). In their experiment, an antineutrino interacted with a proton in water, producing a positron and a neutron. The positron annihilated with an electron and produced gamma rays, while the neutron was captured shortly afterwards by cadmium giving a delayed signal. Detecting these linked signals provided strong evidence that neutrinos existed (Cowan et al., 1956).
Neutrinos are elementary particles, meaning they are not made of any constituent parts. They are leptons, so they have a spin one-half and obey Fermi–Dirac statistics (which are essentially the distribution of particles in a quantum system). They are extremely abundant in our universe: vast numbers pass through our bodies every second with almost no effect.
There are three neutrino flavours, the electron, muon and tau. A neutrino produced in one flavour can be detected as another. This is known as neutrino oscillation. The discovery of oscillation was significant because it showed that neutrinos have non-zero mass, which meant the early Standard Model was incomplete. This is important because it shows us that physics is incomplete; the Standard Model is essentially what the periodic table is to chemists. Hence showing that neutrino physics also pushes us to grasp a clearer understanding of the world we live in.
Neutrinos interact only through the weak nuclear force and gravity. They do not participate in the electromagnetic or strong interactions. Because of this, they are famously difficult to detect and are often described as “ghost particles.” Most pass through matter without interacting at all.
When neutrinos do interact, the interaction is usually described as either neutral-current or charged-current. In a neutral-current interaction, the neutrino exchanges a Z boson and remains a neutrino. In a charged-current interaction, it exchanges a W boson and produces its corresponding charged lepton: an electron neutrino can produce an electron, a muon neutrino a muon, and a tau neutrino a tau, provided there is enough energy available.
Their weak interaction explains why neutrino detectors must be so large. Observatories are often built underground, underwater or in ice so that other sources of radiation can be screened out. The DONUT experiment, for example, observed only a tiny number of tau-neutrino interactions out of an enormous number of candidate events, illustrating how elusive these particles are (Kodama et al., 2001).
Neutrinos and antineutrinos are closely related, and physicists are still investigating whether neutrinos may be their own antiparticles, otherwise known as Majorana particles. Neutrinos are among the most abundant particles in the universe, yet they are among the hardest to study.
They are tiny and elusive, but their properties may help answer some of the largest questions in cosmology.
Part III~ The Big Bang
The Big Bang is the most accepted theory on the universe’s early development. It is based on solutions to Einstein’s general relativity equations. According to the standard model of cosmology, our universe began around 13.8 billion years ago in an extremally hot dense point (known as a singularity), and expanded outwards (Aghanim et al., 2020). A brief period of rapid expansion known as cosmic inflation is why we think the universe is homogenous, or appears to be the same everywhere.
As the universe cooled, energy gave rise to particles, and within the first few minutes, protons and neutrons combined. This process is often referred to as Big Bang nucleosynthesis. This produced most of the universe’s hydrogen and lithium. For the first three hundred and eighty thousand years, the universe remained too hot for electrons to bind stably to nuclei, so light could not travel freely. Once neutral atoms formed, photons decoupled from matter and began moving through space, leaving behind the CMB, or the cosmic microwave background (Aghanim et al., 2020; Mather et al., 1990).
The Big Bang is supported by Hubble’s law. In 1929, Edwin Hubble showed that distant galaxies are receding from us, and the further the galaxy from the Milky Way, the quicker it is receding (Hubble, 1929). He used Cepheid variable stars to measure astronomical distances. Their pulsation period is related to their luminosity, making the readings off of them more precise then using other stars. He compared these with redshift data, and found these observations supported the idea that our universe is continually expanding (Hubble, 1929).
Another line of evidence is the cosmic microwave background. When the universe cooled enough for electrons and protons to combine into neutral hydrogen, light was finally able to travel freely. The radiation has since then been stretched by the universe’s expansion into microwaves. Arno Penzias and Robert Wilson detected this background radiation in 1965, and later measurements by COBE showed that it had almost perfect blackbody spectrum, exactly what would be expected if the early universe had once been hot and dense (Penzias and Wilson, 1965; Mather et al., 1990).
Overall, the Big Bang model is strongly supported by several things, particularly the cosmic microwave background, the abundance of light elements, and the continual expansion of the universe. However, it does not explain if anything happened “before” the earliest moments described by current physics. Some alternative models have been proposed, including eternal inflation and cyclic cosmologies, but these remain controversial and face theoretical challenges. The Borde–Guth–Vilenkin theorem is often cited against past-eternal expansion in many inflationary models, although it does not prove that every possible cosmological model must have an absolute beginning (Borde, Guth and Vilenkin, 2003).
Another important product of the early universe is the cosmic neutrino background, often referred to as relic neutrinos. These are the neutrino counterparts of the CMB. In the standard cosmological model, neutrinos decoupled from the rest of matter and radiation when the universe was about one second old, at a temperature of roughly ten billion kelvin. Since then, they have travelled almost freely through space. Today, they are expected to have a temperature of about 1.95 K and a number density of about 336 relic neutrinos per cubic centimetre in total, counting all flavours and antiparticles (Aghanim et al., 2020). Because they decoupled much earlier than photons, relic neutrinos would let us probe a far earlier stage of cosmic history than the CMB, even though they are much harder to detect directly.
For this EPQ, that matters because the Big Bang model gives strong empirical evidence that the universe has a describable early history, while relic neutrinos push our understanding even closer to that beginning. Yet science alone may not answer the deeper metaphysical question of why there is a universe at all. That is why this project needs to combine cosmology with philosophical reasoning when considering whether there is a first source or ultimate ground of existence.
PART IV~ Evidence for the CvB
The cosmic neutrino background has not yet been detected directly, largely because relic neutrinos have extremely low energies and interact more weakly than solar or reactor neutrinos. Even so, their existence is strongly supported.
During Big Bang nucleosynthesis, relic neutrinos affected the neutron-to-proton ratio in the early universe, which influenced the eventual abundance of light elements such as helium and deuterium. The calculations which included the relic neutrino background fit the observed abundances better than without them (Aghanim et al., 2020).
Furthermore, free-streaming neutrinos altered the gravitational potential energy in the early universe and left a measurable imprint on the structure of the CMB. Brent Follin and collaborators identified the expected phase-shift signature in the CMB power spectrum, giving strong indirect support for the cosmic neutrino background (Follin et al., 2015).
Looking at the early expansion rate of the universe, cosmologists often describe the relativistic content of the early universe using the effective number of neutrino species, N_eff. Observations of the CMB are consistent with a value close to the Standard Model expectation of 3.046, which strongly supports the existence of a relic neutrino background rather than no such background at all (Aghanim et al., 2020).
It is important to stress that indirect evidence is still genuine evidence. Many entities in science have been accepted because their effects are measurable long before they were directly observed in a more intuitive way. The CvB occupies a similar position.
The reason why direct detection of relic neutrinos is difficult is that the universe has been expanding for billions of years, which has cooled relic neutrinos to extremely low energies. Their interactions are therefore extremely rare. As a broader idea, it shows us the present limits of technology.
For this dissertation, the CvB matters because it pushes our evidence further back in time than the CMB does. The CMB formed roughly three hundred and eighty thousand years after the Big Bang; relic neutrinos are more reliable for looking at the early cosmos because they were formed just one second after the universe’s expansion. So the CvB is not an absolute proof, but it does heavily support the Big Bang theory (Aghanim et al., 2020; Follin et al., 2015).
PART V~ The Cosmological argument
Before explaining the cosmological argument, it’s important to clearly define two terms.
- Dependent or contingent existences: These are things which rely on something else.
- Necessary existences: Things which depend on nothing and are self sufficient.
The cosmological argument is an umbrella term for arguments which say that contingent things, such as animals or plants rely on a necessary being which depends on nothing itself (Aristotle, 1998; Aquinas, 1981; Avicenna, 2005).
One version of the argument comes from St. Thomas Aquinas. He argues that contingent things cannot explain themselves why they exist. If everything were contingent, then everything would depend on something else, and so there would be no final explanation as to why anything exists in the first place. He concludes that because of this, there must be a contingent thing that cannot explain that everything depends on (Aquinas, 1981).
David Hume criticises this reasoning. He uses the example of a chain, if each link is held up by another, by explaining just one link, we have explained the entire chain. This challenges Aquinas’ idea on finding a necessary being that everything depends on (Hume, 1779).
Another major form is the Kalam cosmological argument. Its basic structure is as follows:
1 Whatever begins to exist has a cause
2 The universe began to exist
3 Therefore the universe has a cause
Avicenna worked on this idea, making his own argument. He splits all things into three categories:
1 Impossible things {i.e. squared circles}
2 Contingent things {like me and you, we need water to survive and so we are dependant}
3 Necessary things {things that rely on nothing at all}
He adds to his argument that anything made of parts must be dependent. Its parts can be separated or arranged differently, so it does not exist through itself. A necessary being in contrast must be simple and unchanging in form (Avicenna, 2005).
The argument is still widely debated. While some philosophers argue that the universe simply is a fact requiring no explanation, others argue that even if a necessary being does exist, it doesn’t make clear which religion is true. Regardless, the cosmological argument remains influential as many thinkers find it unsatisfying to say that our universe requires no explanation.
For this dissertation, I will use Avicenna’s argument, because it appears the clearest and most watertight to me. This is because neutrinos are a contingent part of a contingent universe, and they are unable to prove God by themselves, but can still support the philosophical case for a necessary ground of reality (Avicenna, 2005).
PART VI~ Neutrinos and the cosmological argument
Since neutrinos were present since the beginning of the universe, they can help us understand what happened at the universe’s beginning in more depth. We know that relic neutrinos were present from the first second of the big bang, however they are unable to explain why the universe exists at all (Aghanim et al., 2020). This takes us from cosmology to philosophy.
But before we bridge the gap, we must first explore other theories on the origin of the universe, to understand why the Big Bang fits so well with the cosmological argument.
One proposal is that the universe emerged from a quantum vacuum. This is the lowest energy state in quantum field theory, and while it is a “vacuum,” particles and energy do exist within it. This quantum vacuum is what people refer to when they talk about the universe coming from “nothing.” So the theory is not problematic in and of itself, rather it is often misrepresented by the general public.
An alternative proposal is the cyclical universe model, where cosmic expansion is followed by a compression, and this cycle goes on indefinitely. This model avoids a singular starting point, which is problematic. Entropy should theoretically increase with each cycle, but this would be unsustainable. The Borde–Guth–Vilenkin theorem suggests that any universe with a positive average expansion rate cannot be eternal. This does not necessarily rule out other theories, but provides further evidence for the Big Bang, because of the singular start point it proposes (Borde, Guth and Vilenkin, 2003).
Since we have strong evidence to show that the Big Bang is the most likely start of the early universe, we can now see how that ties into the cosmological argument.
The premises are as follows:
1 Whatever begins to exist has a cause.
2 The universe began to exist.
3 Therefore, the universe has a cause.
We know the first premise to be true based on experience, we can see that cats don’t fall from the sky with no apparent reasoning, which is strengthened by our scientific instinct to describe events. As another example, if a rock goes past our head, we know that it must have been thrown, it did not launch itself into the air. This means that whatever begins to exist must have a cause. The second premise is supported, not philosophically, but rather through the cosmic neutrino background. The CvB suggests that the universe began and so has a finite history, rather than it existing forever (Aghanim et al., 2020; Follin et al., 2015). Hence we can conclude that based on current scientific findings, the universe began to exist, And if both of these premises are true, then the conclusion must be that the universe has a cause.
Avicenna’s metaphysics develops this line of thought in a different way. He argues that things in existence are either necessary or possible. A necessary being exists through itself and depends on nothing else. A possible, or contingent being does not contain the reason for its own existence and must therefore depend on something external (Avicenna, 2005). Neutrinos clearly fall into the second category. They are produced through specific physical processes, possess finite properties such as mass and flavour states, and depend on the laws and initial conditions of the universe.
Neutrinos illustrate the contingent character of our reality. The cosmic neutrino background can tell us about the universe’s earliest physical state, but cannot explain the origins of the universe. This fits in with Avicenna’s metaphysics, contingent beings cannot ultimately explain themselves. Their existence points beyond themselves to a necessary existence, something that is self-sufficient (Avicenna, 2005).
And so, neutrinos do not prove God’s existence on their own, but rather they support wider philosophical debate on whether or not there is a creator of the universe. They strengthen the case that the universe had a finite beginning, while also showing us the contingency of things within our universe.
Part VII~ World religions and their view on God
This chapter is designed to consider how major religions/world-views relate to the cosmological argument. The idea for this was not to decide which religion is true, but only to see where these beliefs stand when we talk about the cosmological argument. The cosmological argument in and of itself does not establish the full truth of any one religion, but is just a proof for God’s existence.
In Christianity, the cosmological argument is often linked to classical theism: which is the belief that God is eternal and the creator of all contingent reality. After the council of Nicaea in AD 325, mainstream Christianity affirmed that God is one being in three persons: Father, Son and Holy Spirit. The council helped define orthodox teaching about the divinity of the Son in response to early disputes. From the standpoint of the cosmological argument, Christian theology deems God as the ultimate uncaused first cause.
The difficulty lies in the concept of the trinity. According to Avicenna, this necessary being must have no changing parts, which is what the trinity suggests, there are three beings that are independent of each other, yet have the same essence. In John 5:19, it says that “the Son can do nothing by himself,” could suggest a form of dependence that sits uneasily with complete equality between Father and Son (John 5:19, NRSV). Christian theologians argue that this reflects the distinction of persons rather than inequality in divine nature. The son is no less divine than the Father. Even so, this means that Christianity does not simply assert a first cause; it adds complexity because of the three persons within the expression of God.
Judaism affirms a creator who is necessary, (made of no constituent parts, and cannot be rearranged) and in the sense it fits naturally with the cosmological argument. Philosophically it appears more clear than Trinitarian Christianity. However, it is not the cosmological argument itself that raises concerns, but rather it is the barrier for entry to become Jewish. For example, in Judaism, for a male to become Jewish he needs to be circumcised. Past the age of seven, this can cause extreme pain, and in some cases, even death.
For that reason, the most relevant point for this dissertation is not whether Judaism is socially inclusive, but whether its theology aligns with the conclusions of natural theology. In that respect, Judaism is important because it preserves a strong doctrine of divine unity and creation, both of which sit comfortably with cosmological reasoning. The argument from contingency does not prove Judaism specifically, but Jewish monotheism is clearly consistent with the idea that all dependent existence ultimately rests on one necessary being.
Turning to Atheism, this belief concludes that the universe does not require a divine first cause. One common atheist response to the cosmological argument is that not everything that begins to exist must have a cause in the ordinary sense. Often quantum events are mentioned as evidence of this, because Quantum mechanics essentially relies on things just “beginning to exist” from nothing. So we could argue that the universe in principle could have arisen without a personal creator. However, quantum physics does not show that something comes from absolutely nothing, rather it describes events within physical laws that can be in two positions at the same time. Because of this, the appeal to quantum mechanics weakens a simplistic version of the first premise, but it does not fully remove the deeper metaphysical question of why there is a reality governed by such laws in the first place.
Overall, world religions are relevant to the cosmological argument because they offer different conceptions of what the necessary ground of existence might be. Christianity connects the first cause to a triune God, though this introduces further debates about coherence and divine simplicity. Judaism connects it to a single creator, God, which many philosophers regard as metaphysically cleaner. Atheism resists the move from cosmic origin to divine cause altogether, but often struggles to explain why contingent reality exists at all. The cosmological argument therefore does not settle religious truth on its own, but it does provide a framework for comparing which worldviews best account for the existence of the universe.
Part VIII~ Evaluating limitations
Bridging the gap between neutrinos and metaphysics was the greatest challenge in this EPQ. I realised that for this to be successful, I had to have this link clear in my mind. The way I did this was by using the cosmological argument as a basis for me to explore both topics: philosophy to explain the first premise and neutrinos to explore the second premise. Because of this, I spent a lot of time revising the fifth and sixth chapter to show that there was a link between them.
Having said this, there will always be a level of discordance between the two, neutrinos can not explain God’s existence by themselves, which is originally what I thought. I found that reading philosophical material was challenging, and would often have to read a source several times to understand it. Most of the scientific sources I used were published academic papers that would have been peer-reviewed. I had to refer to some science blogs to better understand the individual topics I was exploring. I found these help me explain the facts from research papers in more depth, and allowed me to comprehend the physics I was reading.
There is however the limitation of theories changing based on new found evidence. Truthfully, nothing can be done about this, other than mentioning other theories and trying to understand why they are less astute than the most prominent one.
I realised from philosophical sources that the information was far more subjective, and so I would have to be more careful with what I picked. I tried to use reliable sources that were well cited and popular as much as possible. Because of the nature of the project, tying in physics and philosophy, I have had to interact with a variety of sources, some objective, and some subjective.
Another limitation is that all of my sources were secondary. Because of the abstract nature of the project, I was unable to conduct any experiments by myself. A lot of the physics had to be simplified, which means that the EPQ is more descriptive than an actual research paper. This is not necessarily bad because it means it is more accessible to people.
A third limitation is the risk of confirmation bias. Because I believe in God, it is very easy for me to make a case only for God’s existence and ignore the counterarguments. I think that a future version of this EPQ could do with clearer engagement with atheist philosophers, and perhaps looking at a wider scope of religions and how they relate to the cosmological argument.
A final limitation is the breadth of the project. By putting neutrinos as the EPQ title, I avoided talking about gravitational-wave cosmology. I could have also made my work on inflation more detailed, or engaged with things such as quantum gravity.
Overall, the nature of the project has meant I have had to do a lot of independent research, which has opened my horizon to more reading material; I now read more academic papers to explore my interests after completing this EPQ. I have found that this project has greatly improved my planning skills. I began using a calendar for my EPQ, which I now also use for all of my A-Level study. Furthermore, I have also learnt how to do citations, which I have found has helped me in other writing projects, such as my literature NEA.
Part IX~ Conclusion
The purpose of this dissertation was to explore whether or not neutrinos could serve as a foundation for comprehending the origin of the universe, and by extension, if this could be tied to the cosmological argument. I had the opportunity to assess the nature of neutrinos as well as the philosophy behind cosmological argument, and its history and development.
The scientific side of the project showed that the universe began as a hot, dense point, and expanded over time. Part of this evidence included Hubble’s law, which says that galaxies further than us have a higher recessional speed than the one closer to us, the cosmic microwave background and Big Bang nucleosynthesis (Hubble, 1929; Penzias and Wilson, 1965; Mather et al., 1990; Aghanim et al., 2020). Our understanding of the cosmic neutrino background strengthens this understanding (Aghanim et al., 2020; Follin et al., 2015). For the purposes of the EPQ, I concluded that the Big Bang model is the strongest account on the history of the universe.
However, the main conclusion of this project is not that neutrinos directly prove God’s existence. Instead, neutrinos are able to explain the second premise of the cosmological argument, that the universe began to exist. I made this prominent with Avicenna’s metaphysics, neutrinos are possible beings: they arise in conditions they do not control and do not exist through themselves (Avicenna, 2005).
This project showed me the difficulty of integrating physics and philosophy, there were many times I did not understand what I was reading, and I found it challenging to distill these complicated topics down. After conducting this EPQ, I think there is a case to be made that neutrinos do have a place in the cosmological argument, although not directly, they can still be used to understand the universe’s existence.
GLOSSARY.
- Bosons: In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles interact with the weak force.
- CMB: The Cosmic Microwave Background is the cooled remnant of the first light that could ever travel freely throughout the Universe. This ‘fossil’ radiation was released after the Big Bang. Scientists consider it as an echo or ‘shockwave’ of the Big Bang.
- Contingent existences: Occurring or existing only if (certain circumstances) are the case; dependent on.
- CvB: The cosmic neutrino background is a proposed background particle radiation composed of neutrinos. They are sometimes known as relic neutrinos.
- Ferm dirac statistics: the probability of non-interacting, identical particles with half-integer spin (fermions like electrons) occupying specific quantum energy states at a given temperature, adhering to the Pauli exclusion principle.
- Leptons: These are fundamental, elementary particles that do not experience the strong nuclear force.
- Metaphysics: The branch of philosophy that deals with the first principles of things. This includes abstract concepts such as the nature of being, time and space.
- Necessary existences: Things which depend on nothing and are self.
- N_eff: Is the effective number of neutrino species or effective relativistic degrees of freedom. It is a parameter used in cosmology to describe the total energy density of relativistic particles (other than photons) in the early universe.
- Singularity: A point in space-time such as the centre of a black hole or the moment of the Big Bang where gravitational forces are so intense that density and curvature become infinite, causing the known laws of physics to break down.
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