The Fabric of the Cosmos

Chapter 1

Space, Time and Why Things Are as They Are

What is Reality?

"Surely, reality is what we think it is; reality is revealed to us by our experiences."

"To one extent or another, this view of reality is one many of us hold, if only implicitly. I certainly find myself thinking this way in day-to-day life; it's easy to be seduced by the face nature reveals directly to our senses. Yet, in the decades since first encountering Camus' text, I've learned that modern science tells a different story. The overarching lesson that has emerged from scientific inquiry over the last century is that human experience is often a misleading guide to the true nature of reality. Lying just beneath the surface of the everyday is a world we'd hardly recognize."

The Fabric of the Cosmos, p.5, Brian Greene

Classical Physics

  • Classical physics revealed that there is an order to the universe

  • What happens in the universe is explicable and predictable; it is accessible to mathematical analysis

  • Physical phenomena are explained within a single theoretical framework

  • Newton's handful of equations synthesized everything known about motion in space and time

  • What is space and time?

    • For Newton, space and time simply were -- they formed an inert scaffolding in which events unfolded

    • Newton's equations described motion in space and time; some meaning has to be given to what "space" and time" are

    • Newton declares them to be absolute immutable entities

    • Some argued persuasively that it made little sense to ascribe existence to something you can't feel, grasp or effect

    • But the predictive power of Newton's equations quieted the critics

  • For the next two hundred years, Newton's conception of absolute space and time is dogma

Relativistic Physics

  • In the 1860's, James Maxwell extended the framework of classical physics to include electrical and magnetic forces

  • The mathematics required a higher level of training, but the new equations were as successful in explaining electrical and magnetic phenomena as Newton's were in explaining motion

  • In 1894 Albert Michelson remarked "most of the grand underlying principles have been firmly established"

  • In 1900 Lord Kelvin noted "two clouds" on the horizon:

    • Certain properties of light's motion were difficult to explain

    • Some aspects of the radiation objects emit when heated were unexplained

  • Within the decade, these "two clouds" ignited a revolution in physics

    • The first was addressed by Albert Einstein's special theory of relativity and general theory of relativity

    • The second was addressed by quantum mechanics

  • Einstein realized that Newton's conception of space and time were flawed

    • Space and time are not absolute

    • Space and time are part of unified whole; they warp and curve; they are not rigid, unchanging structures

    • We experience a relativistic reality, but it manifests itself only under extreme conditions (high speed or high gravity)

    • Newtonian physics still provides an approximation that is extremely accurate and useful

    • But utility and reality are very different standards

Quantum Physics

  • The end result of investigating the second "cloud" mentioned by Lord Kelvin

  • Core feature of classical physics is that if you know the position and velocity of all objects at a particular moment:

    • Then Newton's and Maxwell's equations can tell you the positions and velocities at any other moment, past or future

    • Classical physics declares that the past and future are etched into the present

    • This feature is also shared by both special and general relativity

  • By the 1930's, physicists were forced to introduce a whole new concept: quantum mechanics

    • Even if you make most perfect measurements possible of how things are today, the best you can ever hope to do is predict the probability that things will be one way or another at some future time, or were one way or another in the past

    • The universe is not etched into the present; the universe participates in probabilities; probability is deeply woven into quantum reality

    • In classical physics, things are one way or the other; quantum mechanics describes a universe in which things hover in a haze of being partly one way and partly another; things become definite only when a suitable observation is made

    • The outcome that is realized cannot be predicted; we can only calculate the probability that things will turn out one way or the other

  • Quantum mechanics, taken at face value, implies that something you do over here can be instantaneously linked to something over there, regardless of distance (EPR Paradox)

    • The emergence of such instantaneous connections from the mathematics was interpreted by Einstein as evidence that quantum mechanics was incomplete

      • In the 1980s, researchers confirmed that there can be instanteneous bond between what happens at widely separated locations

      • This requires a rethinking and updating of the meaning of time and space

      • Quantum mechanics reveals that in certain circumstances, objects that are widely separated in space behave as if they are a single entity

    • Quantum mechanics does not provide an explanation of why time seems to have a direction (always going from past to future)

Cosmological Physics

  • Where does time's symmetry come from?

  • Nothing in the equations of fundamental physics shows any sign of treating one direction in time differently from the other

  • Yet that is completely at odds with what we experience

  • Current thinking is that a highly ordered environment at the time of the big bang may have imprinted a direction in time

    • In the 1960s evidence mounted to support big bang cosmology; observations revealed a nearly uniform haze of microwave radiation permeating space

    • Big bang theory suffered from significant shortcomings

      • It had trouble explaining why space had the overall shape revealed by observation

      • It offered no explanation for why the temperature of the microwave radiation was uniform throughout space

  • This required the introduction of the theory of inflation (1980s)

    • Inflation theory modifies standard big bang theory by introducing a brief burst of extremely rapid expansion of the universe

    • The size of the universe increased by a factor of 1030 in less than 10-30 seconds

      • This conjecture goes a long way toward explaining the shape of space and the uniformity of the microwave radiation

      • Still, inflation theory rests on the equations Einstein discovered in his theory of general relativity

      • The equations accurately describe large and massive objects

      • But accurate theoretical analysis of small objects (such as when the universe was a mere fraction of a second old) requires quantum mechanics

      • The problem is that when the equations of general relativity are co-mingled with the equations of quantum mechanics, chaos results

  • The absence of mathematical tools with which to analyze conditions of huge density, high energy and high temperature present at the universe's birth prevent us from understanding space and time fully

    • Space and time are are entwined with the origin of the universe

    • Theories (equations) must be found that can cope with the energies and densities of the universe at its birth while still giving reasonable answers to cosmological questions that are consistent with general relativity

Unified Theory

  • With special theory of relativity and general theory of relativiy, Einstein united space, time and gravity

  • Central obstacle toward finding a unified theory is the fundamental conflict between general relativity and quantum mechanics

  • General relativity works exceptionally well when applied to cosmology: time, space, stars, galaxies, motion

  • Quantum mechanics works exceptionally well when applied to nano-objects: atoms, electrons, photons

  • When the two theories are used in conjunction, they produce non-sensical answers: infinities result

    • For example, when general relativity and quantum mechanics are used to calculate the probability that some process involving gravity will take place, the answers found show an infinite probability

    • This conflict has been recognized for more than 50 years

      • Researchers use general relativity to analyze large, massive objects

      • They use quantum mechanics to analyze small, light objects

      • Keeping the theories at a safe distance from each other has resulted in stunning technological advances

      • But this does not result in a lasting peace in physics

      • Without a successful union between general relativiy and quantum mechanics, the end of collapsing stars and the origin of the universe would remain forever mysterious

      • Currently, there is a detente, or at least a peaceful co-existence, so that more tractable problems can analyzed

  • On the horizon, the leading contender for a successful union is string theory

String Theory

  • Superstring theory does not deny the existence of fundamental particles (electrons, atoms, quarks, photons)

  • However, it does not treat them as mathematical points; it claims these particles are composed of tiny fibers of energy some 10-20 times smaller than the atomic nucleus, shaped like a string

  • The strings are said to vibrate

  • Different vibration frequencies are said to endow fundamental particles with certain properties

  • Superstring theory attempts to combine general relativity and quantum mechanics into a single, consistent theory

  • Unfortunately, the mathematics is consistent only if we subject our notion of spacetime to yet another revolution

    • Instead of three spatial and one time dimension, superstring theory requires 9 spatial dimensions and one time dimension

    • Different versions of the theory (M-theory) require 10 space dimensions and one time dimension

"Each generation takes over from the previous, pays homage to its predecessors' hard work, insight, and creativity, and pushes up a little further. New theories and more refined measurements are the mark of scientific progress, and such progress builds on what came before, almost never wiping the slate clean. Because this is the case, our task is far from absurd or pointless. In pushing the rock up the mountain, we undertake the most exquisite and noble of tasks: to unveil this place we call home, to revel in the wonders we discover, and to hand off our knowledge to those who follow."

The Fabric of the Cosmos, p.22, Brian Greene

Chapter 2

Is Space a Human Abstraction or a Physical Entity?

What Is Space?

  • Think about a bucket of spinning water:

    • Initially the bucket and the water are both stationary; the surface of the water is flat

    • If the bucket begins to spin, the water remains stationary at first; the surface remains flat

    • After awhile the water is also spinning; the surface of the water is concave

    • If the bucket stops spinning, the water continues to spin for awhile; the surface of the water is concave

  • Why is this?

Relativity Before Einstein

  • Motion has meaning only in a relational sense; an object's velocity can be specified only in relation to another object

  • But there are circumstances under which motion seems intrinsic

    • You are able to declare you are moving (without external comparisions) when you "feel" it

    • This is the case of accelerated motion (your speed or direction changes)

  • But what is it about changes in velocity that allows it to stand alone, to have intrinsic meaning, without reference to external objects?

  • Descartes said an object at rest will remain at rest unless an external force compels otherwise

  • Similarly, an object moving at constant velocity will continue in motion unless an external force compels otherwise

    • Newton asked 'what do these notions mean?': remain motionless with respect to what; move at constant velocity with respect to what?

    • Newton was grappling with the very foundation of what motion means; he did not accept that accelerated motion, such as spinning, was somehow beyond the need of external comparisons

  • Imagine running the bucket experiment in deep space; say an astronaut is in a cylinder and the cylinder begins to spin; the astronaut knows he is spinning because he can feel a force pushing him against the sides of the cylinder

    • Newton's question is: in totally empty space (no sun, no moon, no distant stars), what could possibly serve as the "something" with respect to which the astronaut feels he is spinning? (what accounts for the concave surface of the water when the bucket is spinning, when there is nothing to relate it to?)

    • You cannot relate the concave surface of the water to the bucket (that is, you cannot explain why the surface of the water is concave by relying on the relative motion between the bucket and the water)

      • (1) At first, when the bucket and water are both stationary, the surface of the water is flat (there is no relative motion between the bucket and the water)

      • (2) After the bucket begins to spin (but not the water) the surface of the water remains flat (there is relative motion betwee the bucket and the water)

      • (3) After the water itself is spinning the surface of the water is concave (there is no relative motion between the bucket and the water)

      • (4) As the bucket slows and finally stops, the surface of the water remains concave; the water is still spinning (there is relative motion between the bucket and the water)

    • What explains the difference between the shape of the water's surface when the relative motion between the bucket and the water is the same, as in (2) and (4)?

    • Newton answered by proposing that space is the relevant frame of reference; space itself is "something" with respect to which an object is moving or is at rest; i.e. an object is moving when it is moving with respect to absolute space or an object is at rest when it is at rest with respect to absolute space

  • The relative motion between the water and the bucket cannot account for the observations; but, according to Newton, the relative motion between the water and absolute space can; space itself provides the frame of reference for defining motion

  • But what is "absolute space"? Newton himself said:

    • "I do not define time, space, place and motion, as they are well known to all"

    • "Absolute space, in its own nature, without reference to anything external, remains always similar and unmovable"

"It is indeed a matter of great difficulty to discover and effectually to distinguish the true motions of particular bodies from the apparent, because the parts of that immovable space in which those motions are performed do by no means come under the observations of our senses."

Sir Isaac Newton's Mathematical Principle of Natural Philosophy and His System of the World, trans. A. Motte and Florian Cajori (Berkeley: University of California Press, 1934, vol. 1, p. 12)

"So Newton leaves us in a somewhat awkward position. He puts absolute space front and center in the description of the most basic and essential element of physics - motion - but he leaves its definition vague and acknowledges his own discomfort about placing such an important egg in such an elusive basket. Many others have shared this discomfort."

The Fabric of the Cosmos, p. 29, Brian Greene

Is Space Real?

  • Should we ascribe reality to space, like the chair you are sitting on?

  • Leibniz claimed that space is nothing more than a convenient way of encoding where things are relative to each other

    • Space has no independent meaning or existence

    • If all objects were removed from space (if it were completely empty), then it would be as meaningless to talk of space as to talk about an alphabet without any letters

    • If we are fundamentally unable to detect space, or changes within space, how can we claim that it exists?

  • At this point Newton stepped in and dramatically changed the debate

    • Newton claimed that absolute space does have consequences that are observable: acceleration

    • A spinning bucket of water undergoes acceleration: it's surface becomes concave

    • Newton claims this is motion relative to absolute space

    • According to Newton, we are free to contemplate the world from any perspective, but some perspectives are more equal than others

      • From the point of view of an ant on an ice skater's boot, it is the ice arena that is spinning

      • From the point of view of a spectator in the arena, it is the ice skater that is spinning

      • The two vantage points seem equally valid

      • But Newton claims one is more valid than the other, since if the ice skater is spinning, his arms will splay outward, but if the arena is spinning then his arms will not splay outward

  • For the next two hundred years, Newton's view is paramount

  • In the 1870's Ernst Mach asks if relative motion can account for the concave shape of the water in a spinning bucket

  • Imagine you are floating in space, motionless, weightless

    • If you begin to spin at this point, you will notice it by reference to the distant stars

    • Suppose there are no distant stars? Will you feel it? Will your arms splay out?

    • Our current experience says yes, but this example is unlike anything we have experienced

  • Mach argues that in an otherwise empty universe, there is no way to distinguish spinning from not spinning because there is nothing else to reference

  • If Mach is right and there is no notion of spinning in an empty universe (which would eliminate Newton's justification for absolute space), then how does he explain the concave shape of the water in a spinning bucket?

  • Imagine a universe that is not completely empty (just a distant star in some direction)

    • Such a reference point would still provide a means of detecting motion, so it seems reasonable to assume that you would be able to feel it as well

    • But how can the absence or presence of a single star make such a difference, somehow acting as a switch that allows the sensation of spinning?

    • Perhaps Mach is simply wrong

  • Mach answers that the force you would feel from spinning would be proportional to the amount of matter in the universe

  • Only relative motion and relative acceleration; you feel acceleration only when you accelerate relative to the average distribution of other material in the universe

  • Without any other material or references for comparison, Mach claims there would be no way to experience acceleration

"Generations of physicists have found it deeply unsettling to imagine that the untouchable, ungraspable, unclutchable fabric of space is really a something - a something substantial enough to provide the ultimate, absolute benchmark for motion. To many it has seemed absurd, or at least scientifically irresponsible,, to base an understanding of motion on something so thoroughly imperceptible, so completely beyond our senses, that it borders on the mystical .Yet these same physicists were dogged by the question of how else to explain Newton's bucket. Mach's insights generated excitement because they raised the possibility of a new answer, one in which space is not a something, an answer that points back toward the relationist conception of space advocated by Leibniz. Space, in Mach's view, is very much as Leibniz imagined - it's the language for expressing the relationship between one object's position and another's. But, like an alphabet without letters, space does not enjoy an independent existence."

The Fabric of the Cosmos, p. 37, Brian Green

"During the first few decades after Mach introduced his ideas, these questions couldn't be answered. For the most part, the reason was that Mach's suggestion was not a complete theory or description, since he never specified how the matter content of the universe would exert the proposed influence. If his ideas were right, how do the distant stars and the house next door contribute to your feeling that you are spinning when you spin around? Without specifying a physical mechanism to realize his proposal, it was hard to investigate Mach's ideas with any precision."

The Fabric of the Cosmos, p. 38, Brian Greene

  • Rather than the Newtonian benchmark for motion (invisible, absolute space), Mach proposed a benchmark that is open for all to see: the matter that is distributed throughout the universe

  • Einstein drew inspiration from Mach's proposal to develop his own theory of gravity: the general theory of relativity

Chapter 3

Is Spacetime an Einsteinian Abstraction or a Physical Entity?

Is Empty Space Empty?

  • How is it that a machine that doesn't touch you can determine whether you're carrying metallic objects?

  • How is it that a device that remains outside your body can take a detailed picture of the inside of your body?

  • How is it that a needle swings and points to the north even though nothing is apparently moving it?

  • James Maxwell set the stage for Einstein's insights

    • Faraday is credited with developing the concept of a field

    • In the mid-1800's, Maxwell discovered 4 equations that provided a rigorous framework for understanding electricity and magnetism

  • The invisible something is called a magnetic or electric field and to our intuition, appears to fill a region of space and thereby exert a force

  • Einstein dismantled the rigid, absolute structures that Newton had erected

  • By the time Einstein was done, time became enmeshed with space and one could not be pondered separately from the other

  • Changes in the electric field can produce changes in the magnetic field, which produce changes in the electric field, etc.

  • These fields are now called the electromagnetic field

    • Cell phones and radios work over great distances because of electromagnetic fields

    • Same for wireless Internet connections

  • Later, we will talk about gravitational fields, nuclear fields, Higgs fields - concept of a field is central to physics

The Luminiferous Ether

  • Maxwell found that changes or disturbances to electromagnetic fields travel in a wavelike manner at the speed of 300*10^6m/s

  • That is the same value as for the speed of light

  • Maxwell realized that light is nothing more than an electromagnetic wave

    • He linked the force produced by magnets, the influence exerted by electric charges and light into a single concept

  • But what does it mean for a wave to travel at the speed of 300*10^6m/s? Travel at that speed relative to what?

    • Maxwell's equations gave this number without specifying or relying on any particular reference

    • It was postulated that electromagnetic waves traveled at that speed relative to something called the "luminiferous ether"

    • It was suggested that his equations implicitly took the point of view of someone at rest with respect to the ether

  • Note that the ether has a striking similarity to Newton's absolute space; both originated in attempts to provide a reference for defining motion

    • Defining accelerated motion led to absolute space

    • Defining light's motion (or an electromagnetic wave) led to the ether

  • But what is the ether? what is it made of? where did it come from? does it exist everywhere?

  • The same questions can be asked of space

  • The test for defining absolute space was Mach's idea of spinning in an otherwise empty universe

  • But the test for defining the ether consisted in measuring the speed of light

    • In 1887 Albert Michelson and Edward Morley established that the speed of light is constant regardless of the speed of the light source through the ether

    • In 1905 Albert Einstein wrote On the Electrodynamics of Moving Bodies; this paper marked the end of the luminiferous ether and changed our understanding of space and time

Relative Space and Relative Time

  • What would a light wave look like if you chased after it at the speed of light?

  • You should be able to reach out and grab some motionless light; but it turns out that Maxwell's equations do not allow light to stand still

  • Einstein reasoned that:

    • Since experiments were not able detect the ether

    • And Maxwell's equations did not specify any medium for light to travel through

    • Both experiment and theory should converge to the same result

      • Therefore there is no ether

      • Light does nor require a medium for it to propagate

      • And it's speed (300*10^6m/s) is just that, relative to anything and everything

  • Maxwell's theory does not allow for stationary light; light is never stationary, regardless of your state of motion, it moves at the same speed relative to you

  • According to Newton, there is an absolute, universal conception of time that applies everywhere and everywhen

  • But what actually happens is that the speed of light is fixed for all observers

    • Observer A, standing still, measures the speed of light and gets a result of 300^10^6m/s

    • Observer B, moving at 200*10^6m/s relative to observer A also measures the speed of light and gets 300*10^6m/s

    • Observer A sees that for every hour that passes, light travels 300*10^6m/s and observer B travels 200*10^6m/s, so observer A concludes light is speeding away from observer B at 100*10^6/ms

    • Observer B sees that for every hour that passes, light travels 300*10^6m/s and when he returns he reports to observer A that the light was streaming away from him at 300*10^6m/s

  • How can this be?

    • It must be that observer A's measurement of distances and durations are based on different inputs than observer B's measurements

    • Velocity = Distance / Time; both observer A and B get the same value for the speed of light

    • So Einstein concluded that Newton's ideas about absolute space and absolute time must be wrong

    • When observers are moving relative to each other, they will not find identical values for measurements of distance and duration

    • This can be explained only if their perceptions of space and time are different

  • Newton thought that motion through space was separate from motion through time

  • But Einstein found they are intimately linked

  • Image a car moving North; all of its motion is in that direction

    • If the car turns right 45 degrees, it will move partially North and partially East (but slower in each direction)

    • That is one way to think about the motion of observers who are moving relative to each other

    • A car standing still relative to you is moving through time with you (moving North)

    • A car moving away from you is moving through space (North) relative to you and moving through time (East) relative to you

    • The occupant of the car is experiencing a shortened space and a shortened time relative to the stationary you

  • In Special Relativity (1905), Einstein declares the combined speed of any object's motion through space and its motion through time is always equal to the speed of light

  • Einstein realized that two observers in relative motion to each other have clocks that measure time differently

  • This leads to the conclusion that observers moving relative to each other have different notions of simultaneity

    • Observers in relative motion to each other do not agree on what things happen at the same time

    • If Newton's notion of absolute space and absolute time were correct, each observer would agree about the simultaneity of an event; but this is not how the universe works; different observers slice up a region of spacetime in different ways

      • Absolute space does not exist

      • Absolute time does not exist

      • Having dismantled Newton's absolute space and absolute time, Einstein explained the above by introducing the notion of absolute spacetime

  • In an otherwise empty universe, with respect to what is a bucket spinning?

    • According to Newton, with respect to absolute space

    • According to Mach, there is no sense in which the bucket can be said to spin

    • According to Einstein, with respect to absolute spacetime

General Relativity

  • Einstein realized that in special relativity, his conclusions about the speed of light did not align with Newton's conception of gravity

    • In Newtonian physics, the effect of gravity is instantaneous

    • In special relativity, the speed of light is constant for all observers, regardless of their relative motion to each other (and it is also the maximum propagation speed of a wave)

    • Absolute spacetime provides a something with respect to which objects can be said to accelerate

  • Newton sidestepped the issue of how gravity actually propagates; one might suggest that it is a field, much like what Maxwell described for the electromagnetic force; today, that is the picture we have of gravity, but making that idea consistent with Special Relativity is not easy

  • Einstein's key breakthrough involves realizing the true nature of accelerated motion

    • In special relativity, observers feel no motion and are justified in claiming they are stationary

    • Accelerated motion is different: observers can feel accelerated motion

    • Einstein concluded that gravity and accelerated motion are two sides of the same coin

  • The force one feels from gravity and the force one feels from gravity are the same; they are equivalent: the principle of equivalence

    • Due to equivalence, gravity must be nothing but warps and curves in the fabric of spacetime

    • According to Einstein, "It's as if matter and energy imprint a network of chutes and valleys along which objects are guided by the invisible hand of the spacetime fabric. That [...] is how gravity exerts its influence."

    • Einstein viewed the warping of spacetime as the manifestation of a gravitation field

    • He was able to find equations that do for gravity what Maxwell's equations do for electromagnetism

    • Warps and ripples (gravity) travels from place to place at the speed of light

  • In general relativity, space and time become players in the cosmos

    • Matter here causes space to warp there, which cause matter over there to move, which causes space way over there to warp, etc

    • Space, time, matter and energy all influence one another

    • While still debated, the present conclusion is that spacetime as described in General Relativity, provides the reference for motion; spacetime is a something

"In Newton's view and subsequently that of special relativity, space and then spacetime were invoked as entities that provide the reference for defining accelerated motion. And since, according to these perspectives, space and spacetime are absolutely unchangeable, the notion of acceleration is absolute. In general relativity, though, the character of space is completely different. Space and time are dynamic in general relativity; they are mutable; they respond to the presence of mass and energy; they are not absolute. Spacetime and, in particular, the way it warps and curves, is an embodiment of the gravitational field. Thus, in general relativity, acceleration relative to spacetime is a far cry the the absolute, staunchly unrelational conception invoked by previous theories. Instead [...] acceleration relative to general relativity's spacetime is relational. It is not acceleration relative to material objects like stones or stars, but it is acceleration relative to something just as real, tangible, and changeable: a field - the gravitational field."

The Fabric of the Cosmos, p. 75, Brian Green

  • With the development of quantum mechanics, the plot only thickens

    • Concepts of empty space and of nothingness take on a whole new meaning

    • The concept that space is a medium that separates one object from another (that allows us to declare that one object is distinct from another) is thoroughly challenged by quantum mechanics