The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford Landmark Science)

by Roger Penrose

Consider the two events R and Q in Fig. 5.21. According to S, the event R takes place before the event Q, because R lies on an earlier simultaneous space than Q; but according to M, it is the other way around, Q lying on an earlier simultaneous space than R. Thus, to one observer, the event R takes place before Q, but for the other, it is Q that takes place before R! (This can only happen because R and Q are what are called spatially separated, which means that each lies outside the other’s light cone, so that no material particle or photon can travel from one event to the other.) Even with quite slow relative velocities, significant differences in time-ordering will occur for events at great distances. Imagine two people walking slowly past each other in the street.

Re read whole section. Time is contingent on light cones, meaning time is not universal and materials inside the light cone of two events would experience time differently. If two objects are movijng towards me I will see the object closest to me 1st, followed by the second object. However, if there was an observer behind said objects facing me he would see the second object (relative to me) first and the first object (relative to me) second. think of two baseballs being thrown at me to visualise this concept.

The above considerations are ‘local’. However, if one is allowed to make (not quite local) measurements of sufficient precision, one may, in principle, ascertain a difference between a ‘true’ gravitational field and a pure acceleration. In Fig. 5.25 I have shown, a little exaggerated, how an initially stationary spherical arrangement of particles, falling freely under the earth’s gravity, would begin to be affected by the non-uniformity of the (Newtonian) gravitational field. The field is non-uniform on two accounts. First, because the centre of the earth lies some finite distance away, particles nearer to the earth’s surface will accelerate downwards faster than those which are higher up (recall Newton’s inverse square law). Second, for the same reason, there will be slight differences in the direction of this acceleration, for different horizontal displacements of the particles. Because of this non-uniformity, the spherical shape begins to distort slightly–into an ‘ellipsoid’. It lengthens in the direction of the earth’s centre (and also in the opposite direction), since the parts nearer to the centre experience a slightly greater acceleration than do the parts more distant; it narrows in the horizontal directions, owing to the fact that the accelerations there act slightly inwards, in the direction of the earth’s centre.

Basically how black holes operate

The geodesics are the curves on that surface which (locally) are ‘shortest routes’.

What is ‘matter’? It is the real substance of which actual physical objects – the ‘things’ of this world – are composed. It is what you, I and our houses are made of. How does one quantify this substance? Our elementary physics text-books provide us with Newton’s clear answer. It is the mass of an object, or of a system of objects, which measures the quantity of matter that it contains. This indeed seems right – there is no other physical quantity that can seriously compete with mass as the true measure of total substance. Moreover it is conserved: the mass, and therefore the total matter content, of any system whatever must always remain the same. Yet Einstein’s famous formula from special relativity E = mc2 tells us that mass (m) and energy (E) are interchangeable into one another.

Mass is the best source of energy to measure since its conservational.

The conserved quantity that takes over the role of mass is an entire object called the energy–momentum four-vector.

This seems to be pure paradox. Yet, it is a definite implication of what our best classical theories – and they are indeed superb theories – are telling us about the nature of the ‘real’ material of our world. Material reality according to classical theory, let alone in the quantum theory that we are about to explore, is a much more nebulous thing than one had thought. Its quantification – and even whether it is there or not – depends upon distinctly subtle issues and cannot be ascertained merely locally! If such non-locality seems puzzling, be prepared for much greater shocks to come.

To many, the term ‘quantum theory’ evokes merely some vague concept of an ‘uncertainty principle’, which, at the level of particles, atoms or molecules, forbids precision in our descriptions and yields merely probabilistic behaviour. Actually, quantum descriptions are very precise, as we shall see, although radically different from the familiar classical ones. Moreover, we shall find, despite a common view to the contrary, that probabilities do not arise at the minute quantum level of particles, atoms, or molecules–those evolve deterministically – but, seemingly, via some mysterious larger-scale action connected with the emergence of a classical world that we can consciously perceive. We must try to understand this, and how quantum theory forces us to change our view of physical reality.

Unfortunately, different theorists tend to have very different (though observationally equivalent) viewpoints about the actuality of this picture. Many physicists, taking their lead from the central figure of Niels Bohr, would say that there is no objective picture at all. Nothing is actually ‘out there’, at the quantum level. Somehow, reality emerges only in relation to the results of ‘measurements’. Quantum theory, according to this view, provides merely a calculational procedure, and does not attempt to describe the world as it actually ‘is’. This attitude to the theory seems to me to be too defeatist, and I shall follow the more positive line which attributes objective physical reality to the quantum description: the quantum state. There is a very precise equation, the Schrödinger equation, which provides a completely deterministic time-evolution for this state. But there is something very odd about the relation between the time-evolved quantum state and the actual behaviour of the physical world that is observed to take place. From time to time–whenever we consider that a ‘measurement’ has occurred–we must discard the quantum state that we have been laboriously evolving, and use it only to compute various probabilities that the state will ‘jump’ to one or another of a set of new possible states. In addition to the strangeness of this ‘quantum jumping’, there is the problem of deciding what it is about a physical arrangement that decrees that a ‘measurement’ has actual...

How are these puzzles to be resolved? The original Newtonian scheme of particles certainly needs to be supplemented by Maxwell’s field. Can one go to the other extreme and assume that everything is a field, particles being little finite-sized ‘knots’ of some kind of field? This has its difficulties also, for then particles could vary their shapes continuously, wriggling and oscillating in infinitely many different kinds of ways. But this is not what is seen. In the physical world, all particles of the same species appear to be identical. Any two electrons, for example, are just the same as each other. Even atoms or molecules can take on only discretely different arrangements.3 If particles are fields, then some new ingredient is needed to enable fields to take on discrete characteristics.

THE TWO-SLIT EXPERIMENT

There is nothing puzzling about an ordinary macroscopic classical wave travelling through two slits at once in this way. A wave, after all, is just a ‘disturbance’, either of some continuous medium (field), or of some substance composed of myriads of tiny point-like particles. A disturbance could pass partly through one slit and partly through the other. But here things are very different: each individual photon behaves like a wave entirely on its own! In some sense, each particle travels through both slits at once and it interferes with itself!

Interesting to note the difference between particle and wave like duality. Waves perturb existing matter, and particles are the substantive mass.

Does the photon actually split in two and travel partly through one slit and partly through the other? Most physicists would object to this way of phrasing things. They would insist that while the two routes open to the particle must both contribute to the final effect, these are just alternative routes, and the particle should not be thought of as splitting into two in order to get through the slits. As support for the view that the particle does not partly go through one slit and partly through the other, the modified situation may be considered in which a particle detector is placed at one of the slits or the other. Since when it is observed, a photon – or any other particle – always appears as a single whole and not as some fraction of a whole, it must be the case that our detector detects either a whole photon or no photon at all. However, when the detector is present at one of the slits, so that an observer can tell which slit the photon went through, the wavy interference pattern at the screen disappears. In order for the interference to take place, there must apparently be a ‘lack of knowledge’ as to which slit the particle ‘actually’ went through.

Here, θ is the angle which the pair of points z and w subtend at the origin in the Argand plane (see Fig. 6.9). (Recall that the cosine of an angle is the ratio ‘adjacent/hypotenuse’ for a right-angled triangle. The keen reader who is unfamiliar with the above formula may care to derive it directly, using the geometry introduced in Chapter 3. In fact, this formula is none other than the familiar ‘cosine rule’, slightly disguised!) It is this correction term 2|w||z| |cos θ that provides the quantum interference between quantum-mechanical alternatives. The value of cos θ can range between –1 and 1. When θ = 0° we have cos θ = 1 and the two alternatives reinforce one another so that the total probability is greater than the sum of the individual probabilities. When θ = 180° we have cos θ = –1 and the two alternatives tend to cancel one another out, giving a total probability less than the sum of the individual ones (destructive interference). When θ = 90° we have cos θ = 0 and we get an intermediate situation where the two probabilities do add. For large or complicated systems, the correction terms generally ‘average out’ – because the ‘average’ value of cos θ is zero – and we are left with the ordinary rules of classical probability! But at the quantum level these terms give important interference effects.

This is fucking nuts. Pythagoras how are you so prominent

it is zero (destructive interference!), again in agreement with observation. At the exactly intermediate points we have w = iz or w = – iz (so that cos θ = 0) whence |w + z |2 = |w ± iw |2 = |w|2 + |w |2 = 2|w|2 giving twice the intensity as for just one slit (which would be the case for classical particles). We shall see at the end of the next section how to calculate where the bright, dark, and intermediate places actually are.

quantum level the individual alternative routes have only amplitudes, not probabilities.

I am taking the view that the physical reality of the particle’s location is, indeed, its quantum state ψ.

planes. This will prove useful in our understanding the two-slit experiment. Fig. 6.10. (a) The graph of a real function of a real variable x. (b) The graph of a complex function ψ of a real variable

Here, quantum mechanics provides us with a remarkable economy. The wavefunction ψ already contains the various amplitudes for the different possible momenta!

The interpretation of ψ is that, for each particular choice of p, the complex number ψ(p) gives the amplitude for the particle to have momentum p.

time-development of a wave packet is Schrödinger’s equation, which tells us how the wave-function actually evolves in time. In effect, what Schrödinger’s equation says is that if we decompose

Regarding ψ as describing the ‘reality’ of the world, we have none of this indeterminism that is supposed to be a feature inherent in quantum theory – so long as ψ is governed by the deterministic Schrödinger evolution. Let us call this the evolution process U. However, whenever we ‘make a measurement’, magnifying quantum effects to the classical level, we change the rules. Now we do not use U, but instead adopt the completely different procedure, which I refer to as R, of forming the squared moduli of quantum amplitudes to obtain classical probabilities!4 It is the procedure R, and only R, that introduces uncertainties and probabilities into quantum theory. The deterministic process U seems to be the part of quantum theory of main concern to working physicists; yet philosophers are more intrigued by the non-deterministic state-vector reduction R (or, as it is sometimes graphically described: collapse of the wavefunction). Whether we regard R as simply a change in the ‘knowledge’ available about a system, or whether we take it (as I do) to be something ‘real’, we are indeed provided with two completely different mathematical ways in which the state-vector of a physical system is described as changing with time. For U is totally deterministic, whereas R is a probabilistic law; U maintains quantum complex superposition, but R grossly violates it; U acts in a continuous way, but R is blatantly discontinuous. According to the standard procedures of quantum mechanics there is n...

Reason for uncertainties qm

Is there any reason to take such a picture seriously? Can we not regard the photon as simply having a 50 per cent probability that it is in one of the places and a 50 per cent probability that it is in the other? No, we cannot! No matter for how long it has travelled, there is always the possibility that the two parts of the photon’s beam may be reflected back so that they encounter one another, to achieve interference effects that could not result from a probability weighting for the two alternatives.

Of course, such an experiment has never been carried out for path-lengths of the order of a light-year, but the stated result is not seriously doubted (by conventional quantum physicists!). Experiments of this very type have actually been carried out with path-lengths of many metres or so, and the results are indeed in complete agreement with the quantum-mechanical predictions (cf. Wheeler 1983). What does this tell us about the reality of the photon’s state of existence between its first and last encounter with a half-reflecting mirror? It seems inescapable that the photon must, in some sense, have actually travelled both routes at once!

(The ‘Pythagorean theorem’, |ψ|2 = |ψY|2 + |ψN|2, asserts that these probabilities sum to unity, as they should!) Note that the probability that |ψ〉 jumps to |ψY〉 is given by the ratio by which its squared length is reduced upon this projection.

The term ‘spin’ indeed suggests something like the spin of a cricket ball or baseball. Recall the concept of angular momentum which, like energy and momentum, is conserved

Spin is conserved by an object which makes it similr to mass which is certainly conservational. This is unlike the classical notion of spin which degrades over time.

A particle whose spin is an odd-number multiple of ℏ/2 (i.e. ℏ/2, 3ℏ/2, or 5ℏ/2 etc.) is called a fermion, and it exhibits a curious quirk of quantum-mechanical description: a complete rotation through 360° sends its state-vector not to itself but to minus itself! Many of the particles of Nature are indeed fermions, and we shall be hearing more about them and their odd ways – so vital to our very existence – later.

What fermions are.

The remaining particles, for which the spin is an even multiple of ℏ/2, i.e. a whole-number multiple of ℏ (namely 0, ℏ, 2ℏ, 3ℏ,. . .), are called bosons. Under a 360° rotation, a boson state-vector goes back to itself, not to its negative.

What bosons are

This correspondence is called stereo-graphic projection, and it has many beautiful geometrical properties (e.g. it preserves angles and maps circles to circles). The projection gives us a labelling of the points of the sphere by complex numbers together with ∞, i.e. by the set of possible complex ratios q. A sphere labelled in this particular way is called a Riemann sphere. The significance of the Riemann sphere, for the spin states of an electron, is that the direction of spin given by | ↗〉 = w |↑〉 + z |↓〉 is provided by the actual direction from the centre to the point q = z/w as marked on the Riemann sphere. We note that the north pole corresponds to the state | ↑〉, which is given by z = 0, i.e. by q = 0, and the south pole to | ↓〉, given by w = 0, i.e. by q = ∞. The rightmost point is labelled by q = 1, which provides the state |→ 〉 = |↑ 〉 + |↓〉, and the leftmost point by q = –1, which provides |←〉 = |↑〉 – |↓〉. The farthest point around the back of the sphere is labelled q = i, corresponding to the state |↑〉 + i|↓〉 where the spin points directly away from us, and the nearest point, q = –i, corresponds to |↑〉 – i|↓〉, where the spin is directly towards us. The general point, labelled by q, corresponds to |↑〉 + q |↓〉.

However, it is possible to copy a quantum state if we are prepared to destroy the state of the original. For example, we could have an electron in an unknown spin-state |α〉 and a neutron, say, in another spin-state |γ〉. It is quite legitimate to exchange these, so that the neutron’s spin-state is now |α〉 and the electron’s is |γ〉. What we cannot do is duplicate |α〉, (unless we already know what |α〉 actually is)! (Cf. also Wootters and Zurek 1982.) Recall the ‘teleportation machine’ discussed in Chapter 1 (p. 35). This depended upon it being possible, in principle, to assemble a complete copy of a person’s body and brain on a distant planet. It is intriguing to speculate that a person’s ‘awareness’ may depend upon some aspect of a quantum state. If so, quantum theory would forbid us making a copy of this ‘awareness’ without destroying the state of the original – and, in this way, the ‘paradox’ of teleportation might be resolved. The possible relevance of quantum effects to brain function will be considered in the final two chapters.

You can't copy quantum states without destroying the original so the idea of teleporting consciousness means your original body is destroyed; sorry bucko.

Photon spin is called polarization, which is the phenomenon on which the behaviour of ‘polaroid’ sunglasses depends.

Interesting fact

There is something rather remarkable and puzzling about this description. One is frequently led to believe that, in some appropriate limiting sense, the quantum descriptions of atoms (or elementary particles or molecules) will necessarily go over to classical Newtonian ones when the system gets large and complicated. However, just as it stands, this is simply not true.

In fact, the rules are such that, in a clear sense, particles of a specific type have to be precisely identical not just, say, extremely closely identical. This applies to all electrons, and it applies to all photons. But, as it turns out, all electrons are identical with one another in a different way from the way in which all photons are identical! The difference lies in the fact that electrons are fermions whereas photons are bosons. These two general kinds of particles have to be treated rather differently from one another.

One implication of this is that no two fermions can be in the same state. For if they were, interchanging them would not affect the total state at all, so we would have to have: –|ψ〉 = |ψ〉, i.e. |ψ〉 = 0, which is not allowed for a quantum state. This property is known as Pauli’s exclusion principle,13 and its implications for the structure of matter are fundamental. All the principal constituents of matter are indeed fermions: electrons, protons and neutrons. Without the exclusion principle, matter would collapse in on itself!

Fig. 6.33. Schrödinger’s cat – with additions.

Reminds me of an egyptian hieroglyphic wall carving.

VARIOUS ATTITUDES IN EXISTING QUANTUM THEORY

Spoot theories qm

Another viewpoint, also logical in its way, but providing a picture no less strange, is that of many worlds, first publicly put forward by Hugh Everett III (1957). According to the many-worlds interpretation, R never takes place at all. The entire evolution of the state-vector – which is regarded realistically – is always governed by the deterministic procedure U. This implies that poor Schrödinger’s cat, together with the protected observer inside the container, must indeed exist in some complex linear combination, with the cat in some superposition of life and death. However the dead state is correlated with one state of the inside observer’s consciousness, and the live one, with another (and presumably, partly, with the consciousness of the cat – and, eventually, with the outside observer’s also, when the contents become revealed to him). The consciousness of each observer is regarded as ‘splitting’, so he now exists twice over, each of his instances having a different experience (i.e. one seeing a dead cat and the other a live one). Indeed, not just an observer, but the entire universe that he inhabits splits in two (or more) at each ‘measurement’ that he makes of the world. Such splitting occurs again and again – not merely because of ‘measurements’ made by observers, but because of the macroscopic magnification of quantum events generally – so that these universe ‘branches’ proliferate wildly. Indeed, every alternative possibility would coexist in some vast superposi...

Many worlds theory rebutt

At the quantum level, we must treat such ‘alternatives’ as things that can coexist, in a kind of complex-number-weighted superposition. The complex numbers that are used as weightings are called probability amplitudes. Each different totality of complex-weighted alternatives defines a different quantum state, and any quantum system must be described by such a quantum state.

These two evolution procedures were described in a classic work by the remarkable Hungarian/American mathematician John von Neumann (1955). His ‘process 1’ is what I have termed R – ‘reduction of the state-vector’ – and his process 2 is U – ‘unitary evolution’ (which means, in effect that probability amplitudes are preserved by the evolution). In fact, there are other – though equivalent – descriptions of quantum-state evolution U, where one might not use the term ‘Schrödinger’s equation’. In the ‘Heisenberg picture’, for example, the state is described so that it appears not to evolve at all, the dynamical evolution being taken up in a continual shifting of the meanings of the position/momentum coordinates. The various distinctions are not important for us here, the different descriptions of the process U being completely equivalent.

U and R

Recall the discussion on pp. 260-1 and Fig. 5.22. Two people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability. In fact neither of the people can yet know of the launching of the space fleet. They can know only later, when telescopic observations from earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter,2 and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past. Was there then any uncertainty about that future? Or was the future of both people already ‘fixed’?

Highly coordinated motion is acceptable and familiar if it is regarded as being an effect of a large-scale change and not the cause of it. However, the words ‘cause’ and ‘effect’ somewhat beg the question of time-asymmetry. In our normal parlance we are used to applying these terms in the sense that the cause must precede the effect. But if we are trying to understand the physical difference between past and future, we have to be very careful not to inject our everyday feelings about past and future into the discussion unwittingly.

Time asymmetry.

However, there is something else involved in our use of the terms ‘cause’ and ‘effect’ which is not really a matter of which of the events referred to happen to lie in the past and which in the future. Let us imagine a hypothetical universe in which the same time-symmetric classical equations apply as those of our own universe, but for which behaviour of the familiar kind (e.g. shattering and spilling of water glasses) coexists with occurrences like the time-reverses of these. Suppose that, along with our more familiar experiences, sometimes water glasses do assemble themselves out of broken pieces, mysteriously fill themselves out of splashes of water, and then leap up on to tables; suppose also that, on occasion, scrambled eggs magically unscramble and de-cook themselves, finally to leap back into broken eggshells which perfectly assemble and seal themselves about their newly-acquired contents; that lumps of sugar can form themselves out of the dissolved sugar in sweetened coffee and then spontaneously jump from the cup into someone’s hand. If we lived in a world where such occurrences were commonplace, surely we would ascribe the ‘causes’ of such events not to fantastically improbable chance coincidences concerning correlated behaviour of the individual atoms, but to some ‘teleological effect’ whereby the self-assembling objects sometimes strive to achieve some desired macroscopic configuration. ‘Look!’, we would say, ‘It’s happening again. That mess is going to assembl...

Why is it that, in the world in which we happen to live, it is the causes which actually do precede the effects; or to put things in another way, why do precisely coordinated particle motions occur only after some large-scale change in the physical state and not before it? In order to get a better physical description of such things, I shall need to introduce the concept of entropy. In rough terms, the entropy of a system is a measure of its manifest disorder.

Clearly this casts doubt on the original argument. We have not deduced the second law. What that argument actually showed was that for a given low-entropy state (say for a gas tucked in a corner of a box), then, in the absence of any other factors constraining the system, the entropy would be expected to increase in both directions in time away from the given state (see Fig. 7.6). The argument has not worked in the past direction in time precisely because there were such factors. There was indeed something constraining the system in the past. Something forced the entropy to be low in the past. The tendency towards high entropy in the future is no surprise. The high-entropy states are, in a sense, the ‘natural’ states, which do not need further explanation. But the low-entropy states in the past are a puzzle. What constrained the entropy of our world to be so low in the past? The common presence of states in which the entropy is absurdly low is an amazing fact of the actual universe that we inhabit – though such states are so commonplace and familiar to us that we do not normally tend to regard them as amazing. We ourselves are configurations of ridiculously tiny entropy! The above argument shows that we should not be surprised if, given a low-entropy state, the entropy turns out to be higher at a later time. What should surprise us is that entropy gets more and more ridiculously tiny the farther and farther that we examine it in the past!

We are the product of a lack of entropy.

We must all be supremely grateful to the green plants – either directly or indirectly – for their cleverness: taking atmospheric carbon dioxide, separating the oxygen from the carbon, and using that carbon to build up their own substance. This procedure, photosynthesis, effects a large reduction in the entropy. We ourselves make use of this low-entropy separation by, in effect, simply recombining the oxygen and carbon within our own bodies. How is it that the green plants are able to achieve this entropy-reducing magic? They do it by making use of sunlight. The light from the sun brings energy to the earth in a comparatively low-entropy form, namely in the photons of visible light. The earth, including its inhabitants, does not retain this energy, but (after some while) re-radiates it all back into space. However, the re-radiated energy is in a high-entropy form, namely what is called ‘radiant heat’ – which means infra-red photons. Contrary to a common impression, the earth (together with inhabitants) does not gain energy from the sun! What the earth does is to take energy in a low-entropy form, and then spew it all back again into space, but in a high-entropy form (Fig. 7.7). What the sun has done for us is to supply us with a huge source of low entropy. We (via the plants’ cleverness) make use of this, ultimately extracting some tiny part of this low entropy and converting it into the remarkable and intricately organized structures that are ourselves.

Fig. 7.7. How we make use of the fact that the sun is a hot-spot within the darkness of space.

Receiving low entropic energy from the sun

What about the low-entropy nuclear energy in the uranium-235 isotope that is used in nuclear power stations? This did not come originally from the sun (though it may well have passed through the sun at some stage) but from some other star, which exploded many thousands of millions of years ago in a supernova explosion! Actually, the material was collected from many such exploding stars. The material from these stars was spewed into space by the explosion, and some of it eventually collected together (through the agency of the sun) to provide the heavy elements in the earth, including all its uranium-235. Each nucleus, with its low-entropy store of energy, came from the violent nuclear processes which took place in some supernova explosion. The explosion occurred as the aftermath of the gravitational collapse5 of a star that had been too massive to be able to hold itself apart by thermal pressure forces. As the result of that collapse and subsequent explosion, a small core remained – probably in the form of what is known as a neutron star (more about this later!). The star would have originally contracted gravitationally from a diffuse cloud of gas, and much of this original material, including our uranium-235, would have been thrown back into space. However, there was a huge gain in entropy due to gravitational contraction, because of the neutron-star core that remained. Again it was gravity that was ultimately responsible – this time causing the (finally violent) condensa...

Where does uranium 235 come from

Now, it follows from the equations of Einstein’s general relativity that this positively closed universe cannot continue to expand forever. After it reaches a stage of maximum expansion, it collapses back in on itself, finally to reach zero size again in a kind of big bang in reverse (Fig. 7.11(b)). This time-reversed big bang is sometimes referred to as the big crunch. The negatively curved and zero-curved (infinite) universe FRW-models do not recollapse in this way. Instead of reaching a big crunch, they continue to expand forever.

Einsteins thought on energy rules in the universe

From that moment, one ten-thousandth of a second after creation, until about three minutes later, the behaviour has been worked out in great detail (cf. Weinberg 1977) – and, remarkably, our well-established physical theories, derived from experimental knowledge of a universe now in a very different state, are quite adequate for this.

The universes first few minutes of expansion.

Any red giant star will have a white dwarf at its core, and this core will be continually gathering material from the main body of the star. Eventually, the red giant will be completely consumed by this parasitic core, and an actual white dwarf – about the size of the earth – is all that remains. Our sun will be expected to exist as a red giant for ‘only’ a few thousand million years. Afterwards, in its last ‘visible’ incarnation – as a slowly cooling dying ember* of a white dwarf – the sun will persist for a few more thousands of millions of years, finally obtaining total obscurity as an invisible black dwarf.

A literal or metaphorical black star- of course the metaphor is analogous to 'nothing'