This is an extremely slow process for black holes about the mass of the Sun (produced by supernovas) or larger ones (like those thought to be at
galactic centers), taking on the order of 1067 years or longer! Smaller black holes would evaporate faster, but they are only speculated to exist as
remnants of the Big Bang. Searches for characteristic γ -ray bursts have produced events attributable to more mundane objects like neutron stars
accreting matter.
Figure 34.14 This Hubble Space Telescope photograph shows the extremely energetic core of the NGC 4261 galaxy. With the superior resolution of the orbiting telescope, it
has been possible to observe the rotation of an accretion disk around the energy-producing object as well as to map jets of material being ejected from the object. A
supermassive black hole is consistent with these observations, but other possibilities are not quite eliminated. (credit: NASA and ESA)
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Figure 34.15 The control room of the LIGO gravitational wave detector. Gravitational waves will cause extremely small vibrations in a mass in this detector, which will be
detected by laser interferometer techniques. Such detection in coincidence with other detectors and with astronomical events, such as supernovas, would provide direct
evidence of gravitational waves. (credit: Tobin Fricke)
Figure 34.16 Stephen Hawking (b. 1942) has made many contributions to the theory of quantum gravity. Hawking is a long-time survivor of ALS and has produced popular
books on general relativity, cosmology, and quantum gravity. (credit: Lwp Kommunikáció)
Figure 34.17 Gravity and quantum mechanics come into play when a black hole creates a particle-antiparticle pair from the energy in its gravitational field. One member of the
pair falls into the hole while the other escapes, removing energy and shrinking the black hole. The search is on for the characteristic energy.
Wormholes and time travel The subject of time travel captures the imagination. Theoretical physicists, such as the American Kip Thorne, have
treated the subject seriously, looking into the possibility that falling into a black hole could result in popping up in another time and place—a trip
through a so-called wormhole. Time travel and wormholes appear in innumerable science fiction dramatizations, but the consensus is that time travel
is not possible in theory. While still debated, it appears that quantum gravity effects inside a black hole prevent time travel due to the creation of
particle pairs. Direct evidence is elusive.
The shortest time Theoretical studies indicate that, at extremely high energies and correspondingly early in the universe, quantum fluctuations may
make time intervals meaningful only down to some finite time limit. Early work indicated that this might be the case for times as long as 10−43 s , the
time at which all forces were unified. If so, then it would be meaningless to consider the universe at times earlier than this. Subsequent studies
indicate that the crucial time may be as short as 10−95 s . But the point remains—quantum gravity seems to imply that there is no such thing as a
vanishingly short time. Time may, in fact, be grainy with no meaning to time intervals shorter than some tiny but finite size.
The future of quantum gravity Not only is quantum gravity in its infancy, no one knows how to get started on a theory of gravitons and unification of
forces. The energies at which TOE should be valid may be so high (at least 1019 GeV ) and the necessary particle separation so small (less than
10−35 m ) that only indirect evidence can provide clues. For some time, the common lament of theoretical physicists was one so familiar to
struggling students—how do you even get started? But Hawking and others have made a start, and the approach many theorists have taken is called
Superstring theory, the topic of the Superstrings.
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34.3 Superstrings
Introduced earlier in GUTS: The Unification of Forces Superstring theory is an attempt to unify gravity with the other three forces and, thus, must contain quantum gravity. The main tenet of Superstring theory is that fundamental particles, including the graviton that carries the gravitational force,
act like one-dimensional vibrating strings. Since gravity affects the time and space in which all else exists, Superstring theory is an attempt at a
Theory of Everything (TOE). Each independent quantum number is thought of as a separate dimension in some super space (analogous to the fact
that the familiar dimensions of space are independent of one another) and is represented by a different type of Superstring. As the universe evolved
after the Big Bang and forces became distinct (spontaneous symmetry breaking), some of the dimensions of superspace are imagined to have curled
up and become unnoticed.
Forces are expected to be unified only at extremely high energies and at particle separations on the order of 10−35 m . This could mean that
Superstrings must have dimensions or wavelengths of this size or smaller. Just as quantum gravity may imply that there are no time intervals shorter
than some finite value, it also implies that there may be no sizes smaller than some tiny but finite value. That may be about 10−35 m . If so, and if
Superstring theory can explain all it strives to, then the structures of Superstrings are at the lower limit of the smallest possible size and can have no
further substructure. This would be the ultimate answer to the question the ancient Greeks considered. There is a finite lower limit to space.
Not only is Superstring theory in its infancy, it deals with dimensions about 17 orders of magnitude smaller than the 10−18 m details that we have
been able to observe directly. It is thus relatively unconstrained by experiment, and there are a host of theoretical possibilities to choose from. This
has led theorists to make choices subjectively (as always) on what is the most elegant theory, with less hope than usual that experiment will guide
them. It has also led to speculation of alternate universes, with their Big Bangs creating each new universe with a random set of rules. These
speculations may not be tested even in principle, since an alternate universe is by definition unattainable. It is something like exploring a self-
consistent field of mathematics, with its axioms and rules of logic that are not consistent with nature. Such endeavors have often given insight to
mathematicians and scientists alike and occasionally have been directly related to the description of new discoveries.
34.4 Dark Matter and Closure
One of the most exciting problems in physics today is the fact that there is far more matter in the universe than we can see. The motion of stars in
galaxies and the motion of galaxies in clusters imply that there is about 10 times as much mass as in the luminous objects we can see. The indirectly
observed non-luminous matter is called dark matter. Why is dark matter a problem? For one thing, we do not know what it is. It may well be 90% of
all matter in the universe, yet there is a possibility that it is of a completely unknown form—a stunning discovery if verified. Dark matter has
implications for particle physics. It may be possible that neutrinos actually have small masses or that there are completely unknown types of particles.
Dark matter also has implications for cosmology, since there may be enough dark matter to stop the expansion of the universe. That is another
problem related to dark matter—we do not know how much there is. We keep finding evidence for more matter in the universe, and we have an idea
of how much it would take to eventually stop the expansion of the universe, but whether there is enough is still unknown.
Evidence
The first clues that there is more matter than meets the eye came from the Swiss-born American astronomer Fritz Zwicky in the 1930s; some initial
work was also done by the American astronomer Vera Rubin. Zwicky measured the velocities of stars orbiting the galaxy, using the relativistic
Doppler shift of their spectra (see Figure 34.18(a)). He found that velocity varied with distance from the center of the galaxy, as graphed in Figure
34.18(b). If the mass of the galaxy was concentrated in its center, as are its luminous stars, the velocities should decrease as the square root of the distance from the center. Instead, the velocity curve is almost flat, implying that there is a tremendous amount of matter in the galactic halo. Although
not immediately recognized for its significance, such measurements have now been made for many galaxies, with similar results. Further, studies of
galactic clusters have also indicated that galaxies have a mass distribution greater than that obtained from their brightness (proportional to the
number of stars), which also extends into large halos surrounding the luminous parts of galaxies. Observations of other EM wavelengths, such as
radio waves and X rays, have similarly confirmed the existence of dark matter. Take, for example, X rays in the relatively dark space between
galaxies, which indicates the presence of previously unobserved hot, ionized gas (see Figure 34.18(c)).
Theoretical Yearnings for Closure
Is the universe open or closed? That is, will the universe expand forever or will it stop, perhaps to contract? This, until recently, was a question of
whether there is enough gravitation to stop the expansion of the universe. In the past few years, it has become a question of the combination of
gravitation and what is called the cosmological constant. The cosmological constant was invented by Einstein to prohibit the expansion or
contraction of the universe. At the time he developed general relativity, Einstein considered that an illogical possibility. The cosmological constant was
discarded after Hubble discovered the expansion, but has been re-invoked in recent years.
Gravitational attraction between galaxies is slowing the expansion of the universe, but the amount of slowing down is not known directly. In fact, the
cosmological constant can counteract gravity’s effect. As recent measurements indicate, the universe is expanding faster now than in the
past—perhaps a “modern inflationary era” in which the dark energy is thought to be causing the expansion of the present-day universe to accelerate.
If the expansion rate were affected by gravity alone, we should be able to see that the expansion rate between distant galaxies was once greater than
it is now. However, measurements show it was less than now. We can, however, calculate the amount of slowing based on the average density of
matter we observe directly. Here we have a definite answer—there is far less visible matter than needed to stop expansion. The critical density ρ c
is defined to be the density needed to just halt universal expansion in a universe with no cosmological constant. It is estimated to be about
(34.3)
ρ c ≈ 10−26 kg/m3.
However, this estimate of ρ c is only good to about a factor of two, due to uncertainties in the expansion rate of the universe. The critical density is
equivalent to an average of only a few nucleons per cubic meter, remarkably small and indicative of how truly empty intergalactic space is. Luminous
matter seems to account for roughly 0.5% to 2% of the critical density, far less than that needed for closure. Taking into account the amount of dark
matter we detect indirectly and all other types of indirectly observed normal matter, there is only 10% to 40% of what is needed for closure. If we
are able to refine the measurements of expansion rates now and in the past, we will have our answer regarding the curvature of space and we will
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determine a value for the cosmological constant to justify this observation. Finally, the most recent measurements of the CMBR have implications for
the cosmological constant, so it is not simply a device concocted for a single purpose.
After the recent experimental discovery of the cosmological constant, most researchers feel that the universe should be just barely open. Since
matter can be thought to curve the space around it, we call an open universe negatively curved. This means that you can in principle travel an
unlimited distance in any direction. A universe that is closed is called positively curved. This means that if you travel far enough in any direction, you
will return to your starting point, analogous to circumnavigating the Earth. In between these two is a flat (zero curvature) universe. The recent
discovery of the cosmological constant has shown the universe is very close to flat, and will expand forever. Why do theorists feel the universe is flat?
Flatness is a part of the inflationary scenario that helps explain the flatness of the microwave background. In fact, since general relativity implies that
matter creates the space in which it exists, there is a special symmetry to a flat universe.
Figure 34.18 Evidence for dark matter: (a) We can measure the velocities of stars relative to their galaxies by observing the Doppler shift in emitted light, usually using the
hydrogen spectrum. These measurements indicate the rotation of a spiral galaxy. (b) A graph of velocity versus distance from the galactic center shows that the velocity does
not decrease as it would if the matter were concentrated in luminous stars. The flatness of the curve implies a massive galactic halo of dark matter extending beyond the
visible stars. (c) This is a computer-generated image of X rays from a galactic cluster. The X rays indicate the presence of otherwise unseen hot clouds of ionized gas in the
regions of space previously considered more empty. (credit: NASA, ESA, CXC, M. Bradac (University of California, Santa Barbara), and S. Allen (Stanford University))
What Is the Dark Matter We See Indirectly?
There is no doubt that dark matter exists, but its form and the amount in existence are two facts that are still being studied vigorously. As always, we
seek to explain new observations in terms of known principles. However, as more discoveries are made, it is becoming more and more difficult to
explain dark matter as a known type of matter.
One of the possibilities for normal matter is being explored using the Hubble Space Telescope and employing the lensing effect of gravity on light
(see Figure 34.19). Stars glow because of nuclear fusion in them, but planets are visible primarily by reflected light. Jupiter, for example, is too small to ignite fusion in its core and become a star, but we can see sunlight reflected from it, since we are relatively close. If Jupiter orbited another star, we
would not be able to see it directly. The question is open as to how many planets or other bodies smaller than about 1/1000 the mass of the Sun are
there. If such bodies pass between us and a star, they will not block the star’s light, being too small, but they will form a gravitational lens, as
discussed in General Relativity and Quantum Gravity.
In a process called microlensing, light from the star is focused and the star appears to brighten in a characteristic manner. Searches for dark matter
in this form are particularly interested in galactic halos because of the huge amount of mass that seems to be there. Such microlensing objects are
thus called massive compact halo objects, or MACHOs. To date, a few MACHOs have been observed, but not predominantly in galactic halos, nor
in the numbers needed to explain dark matter.
MACHOs are among the most conventional of unseen objects proposed to explain dark matter. Others being actively pursued are red dwarfs, which
are small dim stars, but too few have been seen so far, even with the Hubble Telescope, to be of significance. Old remnants of stars called white
dwarfs are also under consideration, since they contain about a solar mass, but are small as the Earth and may dim to the point that we ordinarily do
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not observe them. While white dwarfs are known, old dim ones are not. Yet another possibility is the existence of large numbers of smaller than
stellar mass black holes left from the Big Bang—here evidence is entirely absent.
There is a very real possibility that dark matter is composed of the known neutrinos, which may have small, but finite, masses. As discussed earlier,
neutrinos are thought to be massless, but we only have upper limits on their masses, rather than knowing they are exactly zero. So far, these upper
limits come from difficult measurements of total energy emitted in the decays and reactions in which neutrinos are involved. There is an amusing
possibility of proving that neutrinos have mass in a completely different way.
We have noted in Particles, Patterns, and Conservation Laws that there are three flavors of neutrinos ( νe , vµ , and vτ ) and that the weak interaction could change quark flavor. It should also change neutrino flavor—that is, any type of neutrino could change spontaneously into any other,
a process called neutrino oscillations. However, this can occur only if neutrinos have a mass. Why? Crudely, because if neutrinos are massless,
they must travel at the speed of light and time will not pass for them, so that they cannot change without an interaction. In 1999, results began to be
published containing convincing evidence that neutrino oscillations do occur. Using the Super-Kamiokande detector in Japan, the oscillations have
been observed and are being verified and further explored at present at the same facility and others.
Neutrino oscillations may also explain the low number of observed solar neutrinos. Detectors for observing solar neutrinos are specifically designed
to detect electron neutrinos νe produced in huge numbers by fusion in the Sun. A large fraction of electron neutrinos νe may be changing flavor to
muon neutrinos vµ on their way out of the Sun, possibly enhanced by specific interactions, reducing the flux of electron neutrinos to observed levels.
There is also a discrepancy in observations of neutrinos produced in cosmic ray showers. While these showers of radiation produced by extremely
energetic cosmic rays should contain twice as many vµ s as νe s, their numbers are nearly equal. This may be explained by neutrino oscillations
from muon flavor to electron flavor. Massive neutrinos are a particularly appealing possibility for explaining dark matter, since their existence is
consistent with a large body of known information and explains more than dark matter. The question is not settled at this writing.
The most radical proposal to explain dark matter is that it consists of previously unknown leptons (sometimes obtusely referred to as non-baryonic
matter). These are called weakly interacting massive particles, or WIMPs, and would also be chargeless, thus interacting negligibly with normal
matter, except through gravitation. One proposed group of WIMPs would have masses several orders of magnitude greater than nucleons and are
sometimes called neutralinos. Others are called axions and would have masses about 10−10 that of an electron mass. Both neutralinos and
axions would be gravitationally attached to galaxies, but because they are chargeless and only feel the weak force, they would be in a halo rather
than interact and coalesce into spirals, and so on, like normal matter (see Figure 34.20).
Figure 34.19 The Hubble Space Telescope is producing exciting data with its corrected optics and with the absence of atmospheric distortion. It has observed some MACHOs,
disks of material around stars thought to precede planet formation, black hole candidates, and collisions of comets with Jupiter. (credit: NASA (crew of STS-125))
Figure 34.20 Dark matter may shepherd normal matter gravitationally in space, as this stream moves the leaves. Dark matter may be invisible and even move through the
normal matter, as neutrinos penetrate us without small-scale effect. (credit: Shinichi Sugiyama)
Some particle theorists have built WIMPs into their unified force theories and into the inflationary scenario of the evolution of the universe so popular
today. These particles would have been produced in just the correct numbers to make the universe flat, shortly after the Big Bang. The proposal is
radical in the sense that it invokes entirely new forms of matter, in fact two entirely new forms, in order to explain dark matter and other phenomena.
WIMPs have the extra burden of automatically being very difficult to observe directly. This is somewhat analogous to quark confinement, which
guarantees that quarks are there, but they can never be seen directly. One of the primary goals of the LHC at CERN, however, is to produce and
detect WIMPs. At any rate, before WIMPs are accepted as the best explanation, all other possibilities utilizing known phenomena will have to be
shown inferior. Should that occur, we will be in the unanticipated position of admitting that, to date, all we know is only 10% of what exists. A far cry
from the days when people firmly believed themselves to be not only the center of the universe, but also the reason for its existence.
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34.5 Complexity and Chaos
Much of what impresses us about physics is related to the underlying connections and basic simplicity of the laws we have discovered. The language
of physics is precise and well defined because many basic systems we study are simple enough that we can perform controlled experiments and
discover unambiguous relationships. Our most spectacular successes, such as the prediction of previously unobserved particles, come from the
simple underlying patterns we have been able to recognize. But there are systems of interest to physicists that are inherently complex. The simple
laws of physics apply, of course, but complex systems may reveal patterns that simple systems do not. The emerging field of complexity is devoted
to the study of complex systems, including those outside the traditional bounds of physics. Of particular interest is the ability of complex systems to
adapt and evolve.
What are some examples of complex adaptive systems? One is the primordial ocean. When the oceans first formed, they were a random mix of
elements and compounds that obeyed the laws of physics and chemistry. In a relatively short geological time (about 500 million years), life had
emerged. Laboratory simulations indicate that the emergence of life was far too fast to have come from random combinations of compounds, even if
driven by lightning and heat. There must be an underlying ability of the complex system to organize itself, resulting in the self-replication we recognize
as life. Living entities, even at the unicellular level, are highly organized and systematic. Systems of living organisms are themselves complex
adaptive systems. The grandest of these evolved into the biological system we have today, leaving traces in the geological record of steps taken
along the way.
Complexity as a discipline examines complex systems, how they adapt and evolve, looking for similarities with other complex adaptive systems. Can,
for example, parallels be drawn between biological evolution and the evolution of economic systems? Economic systems do emerge quickly, they
show tendencies for self-organization, they are complex (in the number and types of transactions), and they adapt and evolve. Biological systems do
all the same types of things. There are other examples of complex adaptive systems being studied for fundamental similarities. Cultures show signs
of adaptation and evolution. The comparison of different cultural evolutions may bear fruit as well as comparisons to biological evolution. Science also
is a complex system of human interactions, like culture and economics, that adapts to new information and political pressure, and evolves, usually
becoming more organized rather than less. Those who study creative thinking also see parallels with complex systems. Humans sometimes organize
almost random pieces of information, often subconsciously while doing other things, and come up with brilliant creative insights. The development of
language is another complex adaptive system that may show similar tendencies. Artificial intelligence is an overt attempt to devise an adaptive
system that will self-organize and evolve in the same manner as an intelligent living being learns. These are a few of the broad range of topics being
studied by those who investigate complexity. There are now institutes, journals, and meetings, as well as popularizations of the emerging topic of
complexity.
In traditional physics, the discipline of complexity may yield insights in certain areas. Thermodynamics treats systems on the average, while statistical
mechanics deals in some detail with complex systems of atoms and molecules in random thermal motion. Yet there is organization, adaptation, and
evolution in those complex systems. Non-equilibrium phenomena, such as heat transfer and phase changes, are characteristically complex in detail,
and new approaches to them may evolve from complexity as a discipline. Crystal growth is another example of self-organization spontaneously
emerging in a complex system. Alloys are also inherently complex mixtures that show certain simple characteristics implying some self-organization.