Seeking Ultimates

An Intuitive Guide to Physics, Second Edition

Peter T. Landsberg

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9780429525162
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Seeking Ultimates: An Intuitive Guide to Physics, Second Edition takes us on a journey that explores the limits of our scientific knowledge, emphasizing the gaps that are left. The book starts with everyday concepts such as temperature, and proceeds to energy, the Periodic Table, and then to more advanced ideas. The author examines the nature of ti

Chapter 1

What this book is about

1.1 Introduction

Our wish to understand the cosmos takes us to physics! It is the most fundamental of the sciences: even in biology or studies of the brain, the concepts from physics are essential. The snag is that physics has the reputation of being mathematical and hard to understand. We get around this problem here by the use of intuition. That is my first purpose. There is no mathematics in this book.

A red thread runs through this work to show that things are not as cut and dried as people often think: I emphasize, and that is my second purpose, that the notion of incompleteness is central to the whole of science.

1.2 My story

It may help if I tell you first a little about myself. In the troubled atmosphere of 1939, when I had just arrived in England and I had to think about how to make my way in life, there fell into my hands a copy of Sir Arthur Eddington’s Gifford lectures [1.1]. A single sentence, but an exciting one (in his Chapter 10), lit in me the desire to become a scientist:

‘All authorities seem to agree that at, or nearly at, the root of everything in the physical world lies the mystic formula pq – qp = ih.’

One formula to understand the universe! How exciting! That should not be beyond me! But Eddington had cheated a little, for now that I understand it, the universe is still a bit of a puzzle. But he had inspired me, and he became one of my heroes. Life without heroes is a bore, and I soon acquired others; I have indicated a hero for each chapter. Suffice it to say that I shall be very content if I can do for you, without cheating, what Eddington did for me!

In this exposition it is not all frustration and regret that we are so ignorant! There are lighter moments and historical sidelights to cheer us up. And of course there is satisfaction at what has been achieved. But we should admit that there are limits to what we can assert with confidence, even though these are not always noted. Fortunately, between the scientifically known on the one hand and the scientifically uncertain, inaccessible and doubtful on the other, lies a magical borderland. It is worth knowing for its own sake, for in it flourish practically all real human delights; and they are not easily analysable by science: generosity, romance, beauty and love.

1.3 Intuition

In contemplating the universe and the physics which governs it you may well feel that you have been dropped into the middle of a jungle without a compass—lost in surroundings which are far removed from everyday experience. This is where intuition can help.

Using intuition and no mathematics I aim to take you on a journey to the limits of at least some scientific knowledge; when we finally get close to the borders of the ‘jungle’ we will glimpse views of discoveries yet to come and will be able to throw light on the many gaps in our knowledge. Let this book act as a compass on this journey. The idea of using intuition is that it should enable you to actually ‘feel’ relationships which are absorbed into the bones, as it were, using physical insight instead of mathematics. The students, the teacher, and indeed everybody, finds this to be hard, but greatly rewarding. It moves intellectual connections closer to the plane where you understand things. Here science comes closer to poetry and induces a genuine sense of wonder. Even a mathematically inclined person can profit from this approach. By dropping mathematics he or she may feel that this is like ‘riding without a horse’. I would assure them that it is more than that. I have one warning: intuition is not enough to create new physics (which we do not actually need to do in this book). To achieve this, intuition must be coupled to good experimental and/or mathematical know-how.

1.4 Incompleteness

Now to the red thread. There is hardly any part of the scientific enterprise which can be filed away as fully ‘understood’. There is always another question which stimulates further thought, more discoveries are made or new restrictions are found. Further, the theories underlying what is known from experiment are always provisional and approximate.

We thus have a ‘rule of incompleteness’ which says that when presented with a theory of a part of reality, you will always find failures or incompleteness provided you look hard enough. Focus on these spots, and you may find interesting new results. This new rule of thought must eventually take its place along with already famous rules: that you should treat others as you would have them treat you; and the rule of dialectics that, when there are two opposites, it is rewarding and intellectually stimulating to look for a synthesis. The new rule adds to these and brings out the ‘dynamics of science’.

Is all this really needed? It is, if we recall recent suggestions that the opposite situation holds true in science [1.2, 1.3] or even in other fields [1.4]. These ideas are stimulating. But many scientists would not agree when it is suggested that the great giants of the past, who have given us not only relativity, quantum mechanics and cosmology, but also logic, calculus and the study of chaos, have made such a good job of it, that the things which are left to discover [1.5] in science are either pretty dull or too hard. We shall find little support for these views in this book.

1.4.1 An absence of fit

So there is a graininess in our description of the surrounding world, rather as we find in a television picture or on a photographic film. If you look hard enough, you will often find that something is missing. This phenomenon reveals itself in rather diverse and sometimes surprising ways. However, it is fascinating to find it. It makes you realise that scientific theory and experiment are often incomplete or imperfect. But make no mistake: they usually work well enough.

As an abstract statement it is not surprising that there is a mismatch between the world ‘in itself and our understanding or description of it—philosophers told us long ago that they are not the same: the language we use is not always appropriate. Thus the notion of position and velocity as applied to a particle becomes fuzzy in quantum theory, when applied to one particle at one instant.

The second purpose of this book, the ‘red thread’, is of interest by virtue of the detailed examples which one encounters in seeking ultimates, but often finds incompleteness and imperfection.

1.4.2 Types of imperfection

Of course everybody who is engaged in creative work looks for imperfections with a view to improving his or her creation. However, the imperfections mentioned above are not always of this type. We may be stuck with them and they cannot be removed easily or by the stroke of a pen. At best they will be removed as science takes its course over many decades. But as science marches on, new gaps in developing knowledge appear, while some old gaps may be filled.

The imperfections seem to come in three types:

(i) Intrinsic imperfections. Science itself may give us limits to what we can know. For example, given a starting point, what is the final state of a chaotic system (Chapter 5)? What are the highest and lowest temperatures that can actually be reached (Chapter 2)? It does not look as if we shall ever know. This is intrinsic incompleteness.

(ii) Limit-imperfections of theory. A hard look at scientific concepts may show that certain restrictions are not needed, or that they are unrealistic or artificial. For example, the Periodic Table is not fixed once and for all, but can be greatly expanded (section 3.4). Some theories utilize ‘isolated’ systems, but closer scrutiny shows that these cannot actually exist (section 4.1). These are removable, i.e. temporary, imperfections. The law of thought mentioned in section 1.4 above follows: given a scientific result, theorem or picture, see what you can discover by looking hard at the conditions of its validity.

(iii) Imperfections due to lack of knowledge. These are important since there is always a hope that they will be removed reasonably soon. There may be a problem because of missing data which are, however, likely to be supplied in the future. For example, is there a Higgs boson (Chapter 3)? Does Newton’s gravitational constant change with time (Chapter 8)? Why is there practically no antimatter in the observed universe (section 7.9)

The broader questions: what is the origin of life? what is the nature of consciousness or of the brain? are even more basic. Our difficulties here arise from the innate complexity of the phenomena themselves, and, if real understanding is to arise at all, it can be expected only after decades of investigation.

These types of imperfection will be encountered often in this book, but will not normally be distinguished from one another. Do not worry if you cannot yet understand the following more advanced, and so far unanswered, questions:

• Which cosmological model is most appropriate (section 7.3)?

• The numerical values of many physical constants cannot be explained theoretically (section 8.5).

• Infinities occur in physical theory, e.g. at the big bang, and cannot be readily handled (section 8.4).

• Our understanding of irreversibility and entropy increase is still incomplete (section 4.4).

• First causes have a place in theology, but cannot be handled by science (section 9.4).

There are two more general points worth making.

(i) Scientific results are always approximate. So in some sense they are always wrong! That is why there are clever scientists who improve our understanding and make theories more nearly right. Whatever is wrong in current science acts as a spring that encourages people to advance the subject. But we will never reach an end. ‘The end of science?’ is a question which, in this author’s view, has ‘No’ as the simple answer. We pursue completeness: she is an attractive, though elusive, lady. We are engaged on a quest for elusive completeness!

(ii) To see the work of a scientist in a broader background, consider the difference between scientists and, say, artists. Artists make their individual contributions: their architecture, their paintings, their sculpture remain as witnesses of their work. Scientists, on the other hand, drop their contributions into a river of knowledge which moves on and on, though their names may occasionally survive in history books, street names and possibly in the inventions that arose from their work. So we see that the pleasure in pursuing science derives for many scientists from the work itself, from the good it may cause to be done, and only for some of them from the attributes of influence and power which may result.

1.5 Human aspects

The mathematical sophistication and complication in some of the arguments of physics can lead to exaggerated claims, which have to be withdrawn later. Some ‘theorems’ which were part of the physics literature for decades furnish examples which will surprise even the experts (see section 6.6.1). This is one of the reasons why intuitive understanding is so important: it acts as a check on current ideas, and on complicated mathematics, and it serves as a springboard for new advances.

Research can be a cut-throat activity pursued by intelligent and ambitious people. Some always want to get there first, achieve power and/or publicity from their research and its presentation; figure 1.1 gives a humorous illustration. To attain this aim they may present a distorted picture. This is just human nature and the general public must be made aware of it, and then make allowance for it. But for others, including this author, research can be an outcome of teaching. If you teach carefully, research follows naturally. It does not follow necessarily of course, but the prerequisites are there. Cut-throat competition is best left to those who like it. I shall have more to say on this in Chapter 10.

Figure 1.1 Paul Klee 1903: Two people meet; each judges the other to have a higher position in life. © DACS 1999

1.6 Reaso...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Introduction
• 1 What this book is about
• 2 There is no free lunch. Temperature and energy: science for the environment (Hero: Count Rumford)
• 3 Painting by numbers. Elements and particles: science as prediction (Hero: Dmitri Mendeleev)
• 4 Why you cannot unscramble an egg. Time and entropy: science and the unity of knowledge (Hero: Ludwig Boltzmann)
• 5 How a butterfly caused a tornado. Chaos and life: science as synthesis (Hero: Charles Darwin)
• 6 Now you see it, now you don’t. Quantum theory: science and the invention of concepts (Hero: Max Planck)
• 7 The galactic highway. Cosmology: science as history (Hero: Albert Einstein)
• 8 Weirdness or purity. Mathematics: science as numbers (Hero: Arthur Eddington)
• 9 The last question. Does God exist? (Hero: Blaise Pascal)
• 10 Love of my life. Science as human activity (Hero: readers are invited to choose their own)
• Glossary
• References
• Name Index
• Index