Momentum Physics Quotes

I've come to believe that there exists in the universe something I call "The Physics of The Quest" — a force of nature governed by laws as real as the laws of gravity or momentum. And the rule of Quest Physics maybe goes like this: "If you are brave enough to leave behind everything familiar and comforting (which can be anything from your house to your bitter old resentments) and set out on a truth-seeking journey (either externally or internally), and if you are truly willing to regard everything that happens to you on that journey as a clue, and if you accept everyone you meet along the way as a teacher, and if you are prepared – most of all – to face (and forgive) some very difficult realities about yourself... then truth will not be withheld from you." Or so I've come to believe.

Ideas come at any moment -- except when you demand them. Most ideas come while I'm physically active, at the gym, with friends, gardening, so I always carry pen and paper. My first draft is always written in longhand. But once the first dozen chapters, more like short stories, are written, then momentum builds until I can't leave the project until it's done.

The uncertainty principle “protects” quantum mechanics. Heisenberg recognized that if it were possible to measure the momentum and the position simultaneously with a greater accuracy, the quantum mechanics would collapse. So he proposed that it must be impossible.

Why do so many of us profess our belief in God but trust money for our security?

The BIG push means being able to develop and sustain momentum toward your goal; it is the process of actively replacing excuses with winning habits, the ultimate excuses blockers. Moreover, it is being willing to go to the wall for what you want or believe in, to push beyond your previous mental and physical limits, no matter what it takes.

At first it had been a torrent; now it was a tide, with a flow and ebb. During its flood she could almost fool them both. It was as if out of her knowledge that it was just a flow that must presently react was born a wilder fury, a fierce denial that could flag itself and him into physical experimentation that transcended imagining, carried them as though by momentum alone, bearing them without volition or plan. It was as if she knew somehow that time was short, that autumn was almost upon her, without knowing yet the exact significance of autumn. It seemed to be instinct alone: instinct physical and instinctive denial of the wasted years. Then the tide would ebb. Then they would be stranded as behind a dying mistral, upon a spent and satiate beach, looking at one another like strangers, with hopeless and reproachful (on his part with weary: on hers with despairing) eyes.

The principle of vis inertiae (...) seems to be identical in physics and metaphysics. It is not more true in the former, that a large body is with more difficulty set in motion than a smaller one, and that its subsequent momentum is commensurate with this difficulty, than it is, in the latter, that intellects of the vaster capacity, while more forcible, more constant, and more eventful in their movements than those of inferior grade, are yet the less readily moved, and more embarrassed, and full of hesitation in the first few steps of their progress

angular momentum appears in two forms : one of them is angular momentum of motion, and the other is angular momentum in electric and magnetic fields. There is angular momentum in the field around the magnet, although it does not appear as motion, and this has the opposite sign to the spin. If

If you are trying to get momentum in marketing, business, marriage, your physical condition, or your parenting, take your best focused intensity over time and multiply it by God for unstoppable momentum.

I think I repeated the Heisenberg Uncertainty Principle in my head at least one thousand times: the mathematical product of the combined uncertainties of concurrent measurements of position and momentum in a specified direction could never be less than Planck’s constant, h, divided by 4π. This meant, rather encouragingly, that my uncertain position and zero momentum and the Beast Responsible for the Sound’s uncertain position and uncertain momentum had to sort of null each other out, leaving me with what is commonly known in the scientific world as “wide-ranging perplexity.

A great coach once told me that when pain sets in during a workout, it takes less mental energy to push harder than it does to think about slowing down or stopping. I've found that to be true: Momentum matters, physically and mentally.

Women experience the world as mystery. Kept ignorant of technology, economics, most of the practical skills required to function autonomously, kept ignorant of the real social and sexual demands made on women, deprived of physical strength, excluded from forums for the development of intellectual acuity and public self-confidence, women are lost and mystified by the savage momentum of an ordinary life

Harvard professor I. Bernard Cohen has pronounced, “Franklin’s law of conservation of charge must be considered to be of the same fundamental importance to physical science as Newton’s law of conservation of momentum.

The engines slapped against each other like two steel balls on a Newton's cradle, neither soft nor giving ground, just the savage brutal equalising momentum of physics that only the crushing and dissolving of metal could resolve

My earliest memories are of CP4 — that's a Kähler manifold that looks locally like a vector space with four complex directions, though the global topology's quite different. But I didn't really grow up there; I was moved around a lot when I was young, to keep my perceptions flexible. I only used to spend time in anything remotely like this" — he motioned at the surrounding more-or-less-Euclidean space — for certain special kinds of physics problems. And even most Newtonian mechanics is easier to grasp in a symplectic manifold; having a separate visible coordinate for the position and momentum of every degree of freedom makes things much clearer than when you cram everything together in a single three-dimensional space.

That spring when life was very hard and I was at war with my lot and simply couldn’t see where there was to get to, I seemed to cry most on escalators at train stations. Going down them was fine but there was something about standing still and being carried upwards that did it. From apparently nowhere tears poured out of me and by the time I got to the top and felt the wind rushing in, it took all my effort to stop myself from sobbing. It was as if the momentum of the escalator carrying me forwards and upwards was a physical expression of a conversation I was having with myself. Escalators, which in the early days of their invention were known as ‘travelling staircases’ or ‘magic stairways’, had mysteriously become danger zones.

Wherever and whenever a physical law can be invoked in the discussion, the debate is guaranteed to be brief:No, your idea for a perpetual motion machine will never work; it violates well-tested laws of thermodynamics. No, you can't build a time machine that will enable you to go back and kill your mother before you were born - it violates causality laws. And without violating momentum laws, you cannot spontaneously levitate and hover above the ground, whether or not you are seated in the lotus position.

What keeps the electrons from simply falling in? This principle: If they were in the nucleus, we would know their position precisely, and the uncertainty principle would then require that they have a very large (but uncertain) momentum, i.e., a very large kinetic energy.

object in motion wants to keep going in the same direction, and the larger a rolling snowball gets, the more of a fool you have to be to dare to stand in its path. That’s what sportspeople mean by “momentum,” whereas in physics lessons at school teachers talk about the “principle of

You might say that the only reason for the anti-neutrino is to make the conservation of energy right. But it makes a lot of other things right, like the conservation of momentum and other conservation laws, and very recently it has been directly demonstrated that such neutrinos do indeed exist.

The thought of just how inadequate the body's natural defenses --skull, bone, brain-- were in the face of the advanced physics-- lead, gun-powder, momentum -- of invented death. It all seemed so absurd to him: that a life comprising so many accumulated years could be interrupted with such indifferent swiftness.

Heisenberg's uncertainty relation measures the amount by which the complementary descriptions of the electron, or other fundamental entities, overlap. Position is very much a particle property - particles can be located precisely. Waves, on the other hand, have no precise location, but they do have momentum. The more you know about the wave aspect of reality, the less you know about the particle, and vice versa. Experiments designed to detect particles always detect particles; experiments designed to detect waves always detect waves. No experiment shows the electron behaving like a wave and a particle at the same time.

Another class of universal truths is the conservation laws, where the amount of some measured quantity remains unchanged no matter what. The three most important are the conservation of mass and energy, the conservation of linear and angular momentum, and the conservation of electric charge. These laws are in evidence on Earth, and everywhere we have thought to look—from the domain of particle physics to the large-scale structure of the universe. In spite of this boasting, all is not perfect in paradise. It happens that we cannot see, touch, or taste the source of eighty-five percent of the gravity we measure in the universe. This mysterious dark matter, which remains undetected except for its gravitational pull on matter we see, may be composed of exotic particles that we have yet to discover or identify. A small minority of astrophysicists, however, are unconvinced and have suggested that there is no dark matter—you just need to modify Newton’s law of gravity. Simply add a few components to the equations and all will be well. Perhaps

By far the most important consequence of the conceptual revolution brought about in physics by relativity and quantum theory lies not in such details as that meter sticks shorten when they move or that simultaneous position and momentum have no meaning, but in the insight that we had not been using our minds properly and that it is important to find out how to do so.

We’re all “magnets.” And what we focus on is magnetized to us. We think thoughts, and those thoughts vibrate (remember, everything is energy -- and energy vibrates). Through that vibration, since like attracts like, those thoughts then draw in other energy with more and more momentum until the “thing” that was being magnetized finally “pops” into our manifested physical reality.

We have posited that the fundamental theory is background independent, which means there are no symmetries. This in turn means that we cannot regard energy and momentum, and their conservation, as emergent from the properties of space. But we still have to explain why energy and momentum play the ubiquitous role they do in the structure of the equations of physics. Further, we have hypothesized that space is not present at the fundamental level in nature, but is emergent. So if we want energy and momentum to play a role in physics, there seems to be no alternative but to put them in at the beginning. What we want

The power of the deductive network produced in physics has been illustrated in a delightful article by Victor F. Weisskopf. He begins by taking the magnitudes of six physical constants known by measurement: the mass of the proton, the mass and electric charge of the electron, the light velocity, Newton's gravitational constant, and the quantum of action of Planck. He adds three of four fundamental laws (e.g., de Broglie's relations connecting particle momentum and particle energy with the wavelength and frequency, and the Pauli exclusion principle), and shows that one can then derive a host of different, apparently quite unconnected, facts that happen to be known to us by observation separately ....

Many of the important principles in twentieth century physics are expressed as limitations on what we can know. Einstein's principle of relativity (which was an extension of a principle of Galileo's) says that we cannot do any experiment that would distinguish being at rest from moving at a constant velocity. Heisenberg's uncertainty principle tells us that we cannot know both the position and momentum of a particle to arbitrary accuracy. This new limitation tells us there is an absolute bound to the information available to us about what is contained on the other side of a horizon. It is known as Bekenstein's bound, as it was discussed in papers Jacob Bekenstein wrote in the 1970s shortly after he discovered the entropy of black holes.

It was about this same time that Oppenheimer met the great Danish physicist Niels Bohr, whose lectures he had attended at Harvard. Here was a role model finely attuned to Robert’s sensibilities. Nineteen years older than Oppenheimer, Bohr was born—like Oppenheimer—into an upper-class family surrounded by books, music and learning. Bohr’s father was a professor of physiology, and his mother came from a Jewish banking family. Bohr obtained his doctorate in physics at the University of Copenhagen in 1911. Two years later, he achieved the key theoretical breakthrough in early quantum mechanics by postulating “quantum jumps” in the orbital momentum of an electron around the nucleus of an atom. In 1922, he won the Nobel Prize for this theoretical model of atomic structure.

If we had an atom and wished to see the nucleus, we would have to magnify it until the whole atom was the size of a large room, and then the nucleus would be a bare speck which you could just about make out with the eye, but very nearly all the weight of the atom is in that infinitesimal nucleus. What keeps the electrons from simply falling in? This principle: If they were in the nucleus, we would know their position precisely, and the uncertainty principle would then require that they have a very large (but uncertain) momentum, i.e., a very large kinetic energy. With this energy they would break away from the nucleus. They make a compromise: they leave them- selves a little room for this uncertainty and then jiggle with a certain amount of minimum motion in accordance with this rule.

Einstein’s “physical strategy” began with his mission to generalize the principle of relativity so that it applied to observers who were accelerating or moving in an arbitrary manner. Any gravitational field equation he devised would have to meet the following physical requirements: • It must revert to Newtonian theory in the special case of weak and static gravitational fields. In other words, under certain normal conditions, his theory would describe Newton’s familiar laws of gravitation and motion. • It should preserve the laws of classical physics, most notably the conservation of energy and momentum. • It should satisfy the principle of equivalence, which holds that observations made by an observer who is uniformly accelerating would be equivalent to those made by an observer standing in a comparable gravitational field.

The result that Noether obtained was stunning. She showed that to every continuous symmetry of the laws of physics there corresponds a conservation law and vice versa. In particular, the familiar symmetry of the laws under translations corresponds to conservation of momentum, the symmetry with respect to the passing of time (the fact that the laws do not change with time) gives us conservation of energy, and the symmetry under rotations produces conservation of angular momentum. Angular momentum is a quantity characterizing the amount of rotation an object or a system possesses (for a pointlike object it is the product of the distance from the axis of rotation and the momentum). A common manifestation of conservation of angular momentum can be seen in figure skating-when the ice skater pulls her hands inward she spins much faster.

Einstein’s “mathematical strategy,” on the other hand, focused on using generic mathematical knowledge about the metric tensor to find a gravitational field equation that was generally (or at least broadly) covariant. The process worked both ways: Einstein would examine equations that were abstracted from his physical requirements to check their covariance properties, and he would examine equations that sprang from elegant mathematical formulations to see if they met the requirements of his physics. “On page after page of the notebook, he approached the problem from either side, here writing expressions suggested by the physical requirements of the Newtonian limit and energy-momentum conservation, there writing expressions naturally suggested by the generally covariant quantities supplied by the mathematics of Ricci and Levi-Civita,” says John Norton.

Heisenberg’s more famous and disruptive contribution came two years later, in 1927. It is, to the general public, one of the best known and most baffling aspects of quantum physics: the uncertainty principle. It is impossible to know, Heisenberg declared, the precise position of a particle, such as a moving electron, and its precise momentum (its velocity times its mass) at the same instant. The more precisely the position of the particle is measured, the less precisely it is possible to measure its momentum. And the formula that describes the trade-off involves (no surprise) Planck’s constant. The very act of observing something—of allowing photons or electrons or any other particles or waves of energy to strike the object—affects the observation. But Heisenberg’s theory went beyond that. An electron does not have a definite position or path until we observe it. This is a feature of our universe, he said, not merely some defect in our observing or measuring abilities.

The German mathematician Emmy Noether proved in 1915 that each continuous symmetry of our mathematical structure leads to a so-called conservation law of physics, whereby some quantity is guaranteed to stay constant-and thereby has the sort of permanence that might make self-aware observers take note of it and give it a "baggage" name. All the conserved quantities that we discussed in Chapter 7 correspond to such symmetries: for example, energy corresponds to time-translation symmetry (that our laws of physics stay the same for all time), momentum corresponds to space-translation symmetry (that the laws are the same everywhere), angular momentum corresponds to rotation symmetry (that empty space has no special "up" direction) and electric charge corresponds to a certain symmetry of quantum mechanics. The Hungarian physicist Eugene Wigner went on to show that these symmetries also dictated all the quantum properties that particles can have, including mass and spin. In other words, between the two of them, Noether and Wigner showed that, at least in our own mathematical structure, studying the symmetries reveals what sort of "stuff" can exist in it.

Bohr was a colossus in the world of physics. The only scientist to achieve a similar degree of influence during the first half of the twentieth century was Albert Einstein, who was as much his rival as his friend. In 1922, Bohr had already received the Nobel Prize, and he had a gift for discovering young talents and bringing them under his wing. Such was the case with Heisenberg: during their strolls in the mountains, he convinced the young physicist that, when discussing atoms, language could serve as nothing more than a kind of poetry. Walking with Bohr, Heisenberg had his first intuition of the radical otherness of the subatomic world. “If a mere particle of dust contains billions of atoms,” Bohr said to him as they were scaling the massifs of the Harz range, “what possible way is there to talk meaningfully of something so small?” The physicist—like the poet—should not describe the facts of the world, but rather generate metaphors and mental connections. From that summer onwards, Heisenberg understood that to apply concepts of classical physics such as position, velocity and momentum to a subatomic particle was sheer madness. That aspect of nature required a completely new language.” Excerpt From: Benjamín Labatut. “When We Cease to Understand the World”.

Talmy points out how the mindset behind force dynamics is very different from our best understanding of force and momentum from Newtonian physics. The force-dynamic model in language singles out one entity and conceives of another as impinging on it, whereas in physics neither object in an interaction is privileged. Language conceives of the agonist as having an inner impulse toward motion or rest, whereas physics treats an object as simply continuing at its current velocity. Language distinguishes motion and rest as qualitatively distinct tendencies, whereas physics treats rest as a velocity that happens to be zero. Language treats the antagonist as exerting a force that is stronger than the intrinsic tendency of the agonist. In Newtonian physics, an action and its reaction are opposite and equal, so a pair of touching objects that are at rest, or are moving at a constant velocity, must exert equal forces on each other (if one force were stronger, the two would accelerate in that direction). In language, things can just happen, without stated causes-The book toppled off the shelf; The sidewalk cracked-whereas in physics every event has a lawful antecedent. And in physics, the distinction between causing, blocking, permitting, and helping plays no obvious role.

Louis de Broglie, who carried the title of prince by virtue of being related to the deposed French royal family, studied history in hopes of being a civil servant. But after college, he became fascinated by physics. His doctoral dissertation in 1924 helped transform the field. If a wave can behave like a particle, he asked, shouldn’t a particle also behave like a wave? In other words, Einstein had said that light should be regarded not only as a wave but also as a particle. Likewise, according to de Broglie, a particle such as an electron could also be regarded as a wave. “I had a sudden inspiration,” de Broglie later recalled. “Einstein’s wave-particle dualism was an absolutely general phenomenon extending to all of physical nature, and that being the case the motion of all particles—photons, electrons, protons or any other—must be associated with the propagation of a wave.”46 Using Einstein’s law of the photoelectric affect, de Broglie showed that the wavelength associated with an electron (or any particle) would be related to Planck’s constant divided by the particle’s momentum. It turns out to be an incredibly tiny wavelength, which means that it’s usually relevant only to particles in the subatomic realm, not to such things as pebbles or planets or baseballs.

All people have religions. It's like we have religion receptors built into our brain cells, or something, and we'll latch onto anything that'll fill that niche for us. Now, religion used to be essentially viral -- a piece of information that replicated inside the human mind, jumping from one person to the next. That's the way it used to be, and unfortunately, that's the way it's headed right now. But there have been several efforts to deliver us from the hands of primitive, irrational religion. The first was made by someone named Enki about four thousand years ago. The second was made by Hebrew scholars in the eighth century B.C., driven out of their homeland by the invasion of Sargon II, but eventually it just devolved into empty legalism. Another attempt was made by Jesus -- that one was hijacked by viral influences within fifty days of his death. The virus was suppressed by the Catholic Church, but we're in the middle of a big epidemic that started in Kansas in 1900 and has been gathering momentum ever since." "Do you believe in God or not?" Hiro says. First things first. "Definitely." "Do you believe in Jesus?" "Yes. But not in the physical, bodily resurrection of Jesus." "How can you be a Christian without believing in that?" "I would say," Juanita says, "how can you be a Christian with it? Anyone who takes the trouble to study the gospels can see that the bodily resurrection is a myth that was tacked onto the real story several years after the real histories were written. It's so National Enquirer-esque, don't you think?

There can be a sadness when you move from one state to another, as we often find comfort in what we know best and what we have become accustomed to. Transition can bring with it fear, as well as a desire to look to another for aid, just as the child looks to the ferryman. The Six of Swords, being in the suit of the mind, on a higher level represents the journeys of the mind and the transition to new ideas and ways of thinking; on a lower level, it relates to any transition we undergo that involves leaving something behind. We can imagine that the woman and child in the boat are being ferried to a new life, away from something in the past that may have hurt or threatened them. The ferryman may be the father of the child, or he may be a stranger they have hired for help in getting across the river. We can see that, whilst they do not have all of their possessions with them on this journey to a new life, they have retained a few chests that contain some belongings. When we move to a new state of mind or being, or undergo a spiritual transition or a physical move, we never truly leave the past behind; the trick is being able to differentiate between good baggage and bad baggage. Sometimes we can use the past, and all we have learned and gained from it, to propel us forward in momentum across the river to the other side. Sometimes we cling only to the baggage from the past that weighs us down, and in that case the weight may be too heavy for the boat and start to sink it. It is, ultimately, our choice as to what we pack in the chests that we take with us on the journey.

If we ascribe the ejection of the proton to a Compton recoil from a quantum of 52 x 106 electron volts, then the nitrogen recoil atom arising by a similar process should have an energy not greater than about 400,000 volts, should produce not more than about 10,000 ions, and have a range in the air at N.T.P. of about 1-3mm. Actually, some of the recoil atoms in nitrogen produce at least 30,000 ions. In collaboration with Dr. Feather, I have observed the recoil atoms in an expansion chamber, and their range, estimated visually, was sometimes as much as 3mm. at N.T.P. These results, and others I have obtained in the course of the work, are very difficult to explain on the assumption that the radiation from beryllium is a quantum radiation, if energy and momentum are to be conserved in the collisions. The difficulties disappear, however, if it be assumed that the radiation consists of particles of mass 1 and charge 0, or neutrons. The capture of the a-particle by the Be9 nucleus may be supposed to result in the formation of a C12 nucleus and the emission of the neutron. From the energy relations of this process the velocity of the neutron emitted in the forward direction may well be about 3 x 109 cm. per sec. The collisions of this neutron with the atoms through which it passes give rise to the recoil atoms, and the observed energies of the recoil atoms are in fair agreement with this view. Moreover, I have observed that the protons ejected from hydrogen by the radiation emitted in the opposite direction to that of the exciting a-particle appear to have a much smaller range than those ejected by the forward radiation. This again receives a simple explanation on the neutron hypothesis.

Democracy, the apple of the eye of modern western society, flies the flag of equality, tolerance, and the right of its weaker members to defense and protection. The flag bearers for children's rights adhere to these same values. But should democracy bring about the invalidation of parental authority? Does democracy mean total freedom for children? Is it possible that in the name of democracy, parents are no longer allowed to say no to their children or to punish them? The belief that punishment is harmful to children has long been a part of our culture. It affects each and every one of us and penetrates our awareness via the movies we see and the books we read. It is a concept that has become a kingpin of modern society and helps form the media's attitudes toward parenting, as well as influencing legislation and courtroom decisions. In recent years, the children's rights movement has enjoyed enormous momentum and among the current generation, this movement has become pivotal and is stronger than ever before. Educational systems are embracing psychological concepts in which stern approaches and firm discipline during childhood are said to create emotional problems in adulthood, and liberal concepts have become the order of the day. To prevent parents from abusing their children, the public is constantly being bombarded by messages of clemency and boundless consideration; effectively, children should be forgiven, parents should be understanding, and punishment should be avoided. Out of a desire to protect children from all hardship and unpleasantness, parental authority has become enfeebled and boundaries have been blurred. Nonetheless, at the same time society has seen a worrying rise in violence, from domestic violence to violence at school and on the streets. Sweden, a pioneer in enacting legislation that limits parental authority, is now experiencing a dramatic rise in child and youth violence. The country's lawyers and academics, who have established a committee for human rights, are now protesting that while Swedish children are protected against light physical punishment from their parents (e.g., being spanked on the bottom), they are exposed to much more serious violence from their peers. The committee's position is supported by statistics that indicate a dramatic rise in attacks on children and youths by their peers over the years since the law went into effect (9-1). Is it conceivable, therefore, that a connection exists between legislation that forbids across-the-board physical punishment and a rise in youth violence? We believe so! In Israel, where physical punishment has been forbidden since 2000 (9-2), there has also been a steady and sharp rise in youth violence, which bears an obvious connection to reduced parental authority. Children and adults are subjected to vicious beatings and even murder at the hands of violent youths, while parents, who should by nature be responsible for setting boundaries for their children, are denied the right to do so properly, as they are weakened by the authority of the law. Parents are constantly under suspicion, and the fear that they may act in a punitive manner toward their wayward children has paralyzed them and led to the almost complete transfer of their power into the hands of law-enforcement authorities. Is this what we had hoped for? Are the indifferent and hesitant law-enforcement authorities a suitable substitute for concerned and caring parents? We are well aware of the fact that law-enforcement authorities are not always able to effectively do their jobs, which, in turn, leads to the crumbling of society.

In the above equation, p is the momentum of the electron as it moves around the center of the nucleus and is the wavelength. It is amazing that this equation is a physical reality, for it states that an electron's "orbital" wavelength, a wave-like property, is related to how fast it is going around the nucleus, its momentum. The larger the wavelength, the slower and lighter the particle-recall that momentum is the product of the mass and velocity of a particle.

Planck's constant sets the scale for the wave-like nature of particles. It is a tiny number, which means that we don't see the waviness of macroscopic matter because we are moving slowly compared to the fast quantum particles zipping around the atom. If we were very tiny, we would see our inner waviness. De Broglie's connection between the wavelength of a particle and its momentum is at the heart of the famous uncertainty principle. And it was Werner Heisenberg that was able to precisely formulate it.

A good way to understand the uncertainty principle is to consider a wave where we have complete certainty in its frequency, like a pure tone. Now, I ask you, where is the wave? The wave with its many periodic oscillations is distributed across a very large distance, meaning that a wave of definite frequency will have an arbitrary position. Now let's consider a traveling wave pulse, which only exists for a short duration of time, like a beat. I can localize where the pulse is, but its frequency is not well defined because its frequency is not well defined because a frequency requires many repeating cycles, and a pulse does not have enough width to define a definite frequency. This is Heisenberg's uncertainty principle: it says that the more you can know about the position, the less you can know about its frequency, and vice versa. But we just learned that the frequency is proportional to the momentum, so the more one knows about the momentum of a particle, the less one knows about its position, and vice versa. This is incredibly profound. When scientists want to understand nature, they use instruments to probe and measure it. What the uncertainty principle tells us is that no matter how careful we are, no matter how precise our instrumentation, we can never pin down both the particle-like and the wave-like properties of a quantum entity, whether it be a photon or an electron, a quark or a neutrino. The uncertainty principle is a statement that is fundamental to nature, to the universe, whether we are there to measure it or not.

In order to get a cyclic universe, the contracting past universe has to emerge into an expanding universe. Cosmologists call this phenomenon a cosmic bounce. Think of dropping a ball. For the ball to change direction, it has to hit the ground, decelerate, come to a stop, and change its downward velocity. This happens naturally due to momentum conservation and the elasticity of the ball. Similarly the "speed" of the decelerating universe will come to a halt and bounce into an expanding state after reaching a vanishing speed. In order for this to happen, we need a field that makes space-time like an "elastic" ball; called a ghost field, this field is an infinite reservoir of negative energy. Physicists do not like ghost fields because they can quantum mechanically transform to an infinite amount of light energy spontaneously. This happens because, according to an exchange Feynman diagram, the photon, the lightest particle in nature, can steal negative energy from the ghost field to create an explosive amount of photons. We don't see such explosive signatures of ghost fields today, so if cyclic universes are for realand do depend on ghost fields, then the ghost fields have figured out a clever way to not decay into photons. Nina Arkani-Hamed of the Institute for Advanced Studies and his colleagues proposed one way this could happen: the ghost field condenses, which bounds the negative energy to a finite value, preventing further decay into photons.

This loss of momentum is exactly what should happen if light is a particle: when an X-ray photon comes in and hits a more or less stationary electron in a target, it gives up some of its momentum to the electron, which starts moving. After the collision, the photon has less momentum, and thus a longer wavelength, exactly as Compton observed.

Also in 1923, a French Ph.D. student named Louis Victor Pierre Raymond de Broglie* made a radical suggestion: he argued that there ought to be symmetry between light and matter, and so a material particle such as an electron ought to have a wavelength. After all, if light waves behave like particles, shouldn’t particles behave like waves? De Broglie suggested that just as a photon has a momentum determined by its wavelength, a material object like an electron should have a wavelength determined by its momentum: γ = h/p which is just the formula for the momentum of a photon (page 24) turned around to give the wavelength.

So, if all material objects are made up of particles with wave properties, why don’t we see dogs diffracting around trees? If a beam of electrons can diffract off two rows of atoms, why can’t a dog run around both sides of a tree to trap a bunny on the far side? The answer is the wavelength: as with the sound and light waves discussed earlier, the dramatically different behavior of dogs and electrons encountering obstacles is explained by the difference in their wavelengths. The wavelength is determined by the momentum, and a dog has a lot more momentum than an electron.

What does it mean to add together lots of different waves with different wavelengths in this way? Well, each wave corresponds to a particular momentum—a different velocity for the (single) bunny moving through the yard. When we add them all together, what we’re doing is saying that there’s a chance of finding the bunny in each of those different states

Adding these states together is the origin of the uncertainty principle. If we want a narrow and well-defined wave packet, so that we know the position of the bunny very well, we need to add together a great many waves to do that. Each wave corresponds to a possible momentum for the bunny, though, which gives a large uncertainty in the momentum—it could be moving at any one of a large number of different speeds. On the other hand, if we want to know the momentum very well, we can use a small number of different wavelengths, but this gives us a very broad wave packet, with a large uncertainty in the position. The bunny can only have a few possible speeds, but we can no longer say where it is with much confidence.

Looked at in terms of wavefunctions, then, we can see that this relationship is much more than just a practical limit due to our inability to measure a system without disturbing it. Instead, it’s a deep statement about the limits of reality. We saw in chapter 1 that quantum particles behave like particles—photons have momentum and collide with electrons in the Compton effect (page 25). We also saw that quantum particles behave like waves—electrons, atoms, and molecules diffract around obstacles and form interference patterns. The price we pay for having both of these sets of properties at the same time is that position and momentum must always be uncertain. The meaning of the uncertainty principle is not just that it’s impossible to measure the position and momentum, it’s that these quantities do not exist in an absolute sense.

When we account for the wave nature of the electron, we are forced to discard the whole idea of electrons as planets. Instead, the electron hovers around the nucleus in a fuzzy sort of “cloud,” with a position that is uncertain, but confined to a region near the nucleus, and a momentum that is uncertain, but limited to values that keep it near the nucleus. Bohr’s idea of allowed energy states still applies—the electron will always have one of the limited number of energy values predicted by Bohr’s theory—but these states no longer correspond to electrons moving in particular orbits.

Electrons must always have uncertainty in both their position and momentum, and that means that the energy of an electron in an atom can never be zero. To have zero energy while still being part of an atom, an electron would need to be not moving, sitting right on top of the nucleus. This is impossible, as we’ve already seen—the closest we can come is to make a narrow electron wave packet centered on the nucleus, which will include lots of different states with nonzero momentum

uncertainty principle: it is impossible to know both the position and the momentum of an object perfectly at the same time. If you make a better measurement of the position, you necessarily lose information about its momentum, and vice versa.

To measure the position of an electron, you need to do something to make it visible, such as bouncing a photon of light off it and viewing the scattered light through a microscope. But the photon carries momentum (as we saw in chapter 1 [page 24]), and when it bounces off the electron, it changes the momentum of the electron. The electron’s momentum after the collision is uncertain, because the microscope lens collects photons over some range of angles, so you can’t tell exactly which way it went. You can make the momentum change smaller by increasing the wavelength of the light (decreasing the momentum that the photon has available to give to the electron), but when you increase the wavelength, you decrease the resolution of your microscope, and lose information about the position.* If you want to know the position well, you need to use light with a short wavelength, which has a lot of momentum, and changes the electron’s momentum by a large amount. You can’t determine the position precisely without losing information about the momentum, and vice versa.

Uncertainty is not a statement about the limits of measurement, it’s a statement about the limits of reality. Asking for the precise position and momentum of a particle doesn’t even make sense, because those quantities do not exist.

How do we get a wave packet by combining many waves? Well, let’s start with two simple waves, one corresponding to a bunny casually hopping across the yard, and another one with a shorter wavelength (the graph below shows 20 full oscillations of one, in the same space as 18 of the other), corresponding to a bunny moving faster, perhaps because it knows there’s a dog nearby. Now let’s add those two wavefunctions together. “Wait a minute—now we have two bunnies?” “No, each wavefunction describes a bunny with a particular momentum, but it’s the same bunny both times.” “But doesn’t adding them together mean that you have two bunnies?” “No, in this case, it just means that there are two different states* you might find the single bunny in. When you look out into the yard, there’s some probability of finding the bunny moving slowly, and some probability of finding it moving a little faster. The way we account for that mathematically is by adding the two waves together.

For quantum physics, in addition to predicting and explaining phenomena that range over fifteen orders of magnitude in energy, has done something else: it has triggered a radical upheaval in our understanding of the world. In place of the tidy cause-and-effect universe of classical physics, quantum physics describes a world of uncertainties, or indeterminism: of limits to our knowledge. It describes a world that often seems to have parted company with common sense, a world at odds with some of our strongest intuitive notions about how things work. In the quantum world, subatomic particles have no definite position until they are measured: the electron orbiting the nucleus of an atom is not the pointlike particle we usually imagine but instead a cloud swathing the nucleus. In the quantum world, a beam of light can behave as a wave or a barrage of particles, depending on how you observe it. Quantities such as the location, momentum, and other characteristics of particles can be described only by probabilities; nothing is certain. “It is often stated that of all the theories proposed in this century, the silliest is quantum theory,” the physicist Michio Kaku wrote in his 1995 book Hyperspace. “In fact, some say that the only thing that quantum theory has going for it is that it is unquestionably correct.

It’s not just that measurement changes the state of the system, it’s that what we can measure is limited by the fact that position and momentum are undefined until we measure them.

You know, Heisenberg’s uncertainty principle? The uncertainty in the position of an object multiplied by the uncertainty in the momentum is greater than Planck’s constant over four pi? Which means that when one uncertainty is small, the other must be very large.

Physicality’s a cage. And a liberation. The cells I’ll fill in, they’re magnificent, burgeoning with aliveness! I’m dialed into them like a station on a radio transmitting constantly. First faint and distant, but growing, amassing, volumizing the very idea of a person this body aims to harbor. Glowing like the universe, always growing. Each new cell increases my momentum, tightening the tether.

There is a profound truth in this perspective, as it penetrates and dissolves the usual belief or assumption that the ego, our thoughts, and physical reality are more real than more subtle levels of reality. Even when we have tasted a deeper reality, we often return to an ego-centered perspective because of the momentum of our involvement with the physical and mental realms. Even in the face of profound experiences to the contrary, there's a habit of assuming that our physical body and our beliefs and other thoughts are what is most important, so much so that we think that everything that pops into our heads is important. We even use the argument, “That’s what I think” to justify our position, as if thinking something makes it true. Since our most common thought or assumption is the assumption that "I am the body" or "I am my thoughts, feelings, and desires," this pointing to the falseness or incompleteness of those most basic beliefs is

In his first philosophical lecture on modern physics that Pauli gave in November 1934 to the Zurich Philosophical Society he said that only a formulation of quantum theory would be satisfactory which expresses the relation between the value of [the fine structure constant] and charge conservation in the same complementary was as that between the space-time description and energy-momentum conservation.

Blessed are the poor, for theirs is the kingdom of God (Luke 6:20). I'm learning what it means to descend, which is so revolutionary it often leaves me gasping. I have been trying to ascend my entire life. Up, up, next level, a notch higher, the top is better, top of the food chain, all for God's work and glory, of course. The pursuit of ascension is crippling and has stunted my faith more than any other evil I've battled. It has saddled me with so much to defend, and it doesn't deliver. I need more and more of what doesn't work. I'm insatiable, and ironically, the more I accumulate, the less I enjoy any of it. Instead of satisfaction, it produces toxic fear in me; I'm always one slip away from losing it all. Consequently, my love for others is tainted because they unwittingly become articles for consumption. How is this person making me feel better? How is she making me stronger? How is he contributing to my agenda? What can this group do for me? I am an addict, addicted to the ascent and thus positioning myself above people who can propel my upward momentum and below those who are also longing for a higher rank and might pull me up with them. It feels desperate and frantic, and I'm so done being enslaved to the elusive top rung. When Jesus told us to 'take the lowest place' (Luke 14:10), it was more than just a strategy for social justice. It was even more than wooing us to the bottom for communion, since that is where He is always found. The path of descent becomes our own liberation. We are freed from the exhausting stance of defense. We are no longer compelled to be right and are thus relieved from the burden of maintaining some reputation. We are released from the idols of greed, control, and status. The pressure to protect the house of cards is alleviated when we take the lowest place. The ascent is so ingrained in my thought patterns that it has been physically painful to experience reformation at the bottom. The compulsion to defend myself against misrepresentation nearly put me in the grave recently. I was tormented with chaotic inner dialogues, and there were days I was so plagued with protecting my rung that I couldn't get out of bed. With every step lower, the stripping-away process was more excruciating. I had no idea how tightly I clung to reputation and approval or how selfishly I behaved to maintain it. Getting to the top requires someone else to be on the bottom; being right means someone else must be wrong. It is the nature of the beast.

I’ll just change my wavelength by changing my momentum. I can run very fast.” “Nice try, but the wavelength gets shorter as you go faster. To get your wavelength up to the millimeter or so you’d need to diffract around a tree, you’d have to be moving at 10-30 meters per second, and that’s impossibly slow. It would take a billion years to cross the nucleus of an atom at that speed, which is way too slow to catch a bunny.

A particle-like object has a definite position (you know right where it is), a definite velocity (you know how fast it’s moving, and in what direction), and a definite mass (you know how big it is). You can multiply the mass and velocity together, to find the momentum.

Momentum determines what will happen when two particles collide. When a moving object hits a stationary one, the moving object will slow down, losing momentum, while the stationary object will speed up, gaining momentum.

confined it, Heisenberg would argue, is that its momentum became almost completely indeterminate.

Ticker tape fever. During the run-up to the 1929 crash on Wall Street, many people had become addicted to playing the stock market, and this addiction had a physical component—the sound of the ticker tape that electronically registered each change in a stock’s price. Hearing that clicking noise indicated something was happening, somebody was trading and making a fortune. Many felt drawn to the sound itself, which felt like the heartbeat of Wall Street. We no longer have the ticker tape. Instead many of us have become addicted to the minute-by-minute news cycle, to “what’s trending,” to the Twitter feed, which is often accompanied by a ping that has its own narcotic effects. We feel like we are connected to the very flow of life itself, to events as they change in real time, and to other people who are following the same instant reports. This need to know instantly has a built-in momentum. Once we expect to have some bit of news quickly, we can never go back to the slower pace of just a year ago. In fact, we feel the need for more information more quickly. Such impatience tends to spill over into other aspects of life—driving, reading a book, following a film. Our attention span decreases, as well as our tolerance for any obstacles in our path.

To make this idea work alongside Einstein's relativity, De Poi had to introduce the idea of extra dimensions. If a wave carried a particle's energy and momentum through physical space, it would involve movement faster than the speed of light, and relativity forbids this. So De Poi sets things up so that it is a phase wave rather than a matter wave. Here, believe it or not, the wave is an undulating complex number that oscillates in an abstract dimension. That might sound mad to you already. But it gets worse.

Isaac Newton famously noted that an object in motion tends to stay in motion, while an object at rest tends to stay at rest. Sir Isaac focused on physical objects—planets, pendulums, and the like—but the same concepts can be applied to the social world. Just like moons and comets, people and organizations are guided by conservation of momentum. Inertia. They tend to do what they’ve always done.

How can you say that? You’re a religious person yourself.” “Don’t lump all religion together.” “Sorry.” “All people have religions. It’s like we have religion receptors built into our brain cells, or something, and we’ll latch onto anything that’ll fill that niche for us. Now, religion used to be essentially viral—a piece of information that replicated inside the human mind, jumping from one person to the next. That’s the way it used to be, and unfortunately, that’s the way it’s headed right now. But there have been several efforts to deliver us from the hands of primitive, irrational religion. The first was made by someone named Enki about four thousand years ago. The second was made by Hebrew scholars in the eighth century B.C., driven out of their homeland by the invasion of Sargon II, but eventually it just devolved into empty legalism. Another attempt was made by Jesus—that one was hijacked by viral influences within fifty days of his death. The virus was suppressed by the Catholic Church, but we’re in the middle of a big epidemic that started in Kansas in 1900 and has been gathering momentum ever since.” “Do you believe in God or not?” Hiro says. First things first. “Definitely.” “Do you believe in Jesus?” “Yes. But not in the physical, bodily resurrection of Jesus.

Subatomic particles have no meaning as isolated entities. They are understood as interconnections between the observer, their preparation of an experiment, and the subsequent results. The bottom line is that space isn't something that objects are in. Position and momentum are just part of the meta-object's frequencies equation.

Belief systems are ephemeral and have a self-reinforcing component. This self-reinforcing characteristic allows you to experience the sustained reality of that belief system because it is constantly being chosen second to second. It is a type of momentum going in one direction and inspires you to act and select the same way in the next moment.

Boyd got the idea for “O-O-D-A” loops (he used dashes indicate that the steps are not distinct, but flow into each other) from observing the effects of jerky, unexpected, and abrupt maneuvers in air-to-air combat. After deciding that it was his quick OODA loops that allowed him to fight this way, Boyd defined “agility” in these terms: A side in a conflict or competition is more agile than its opponent if it can execute its OODA loops more quickly. This generalizes the term agility from air-to-air combat and from warfare in general. It also turns out to be equivalent to the definition floated in chapter II, the ability to rapidly change one’s orientation, since it is orientation locking up under the stress of competition and conflict that causes OODA loops to slow and makes one predictable, rather than abrupt and unpredictable. Speed, that is physical velocity, may provide an important tactical option, but it is not The Way.77 In fact, speed increases momentum, which can make one more predictable.

impressions barrage, Lee could no longer grasp the meaning of Vivian's voice as it went on and on explaining things like "crystal cells," "selenoid cells," "grey matter pyramidal cells," powered somehow by atomic fission, "nerve loops" and "synthesis gates" which were not to be confused with "analysis gates" while they looked exactly the same…. Apart from this at least one half of his mental and physical energy had to be expanded in suppressing nausea and bracing himself against the gyrations which still jerked his feet from under him and made friction disks of his shoulders as his body swayed from side to side. All of a sudden he felt that he was being derailed. There was an opening in the plastics wall of the cylinder; a curved metal shield like the blade of a bulldozer jumped into his path, caught him, slowed down his momentum and delivered him safely at a door marked "Apperception-Center 24." It opened and within its frame there stood an angel neatly dressed in the uniform of a registered nurse. "There," said the angel, "at last. How did you like your little Odyssey through The Brain, Dr. Lee?" Lee pushed a hand through the mane of his hair; it felt moist and much tangled up. "Thanks," he said. "It was quite an experience. I enjoyed it; Ulysses, too, probably enjoyed his trip between Scylla and Charybdis—after it was over! It's Miss Leahy, I presume." The reception room where he

The uncertainty principle of quantum mechanics, coupled with the relations of special relativity, tell us that, using physical constants, we can relate a particle’s mass, energy, and momentum to the minimum size of the region in which a particle of that energy can experience forces or interactions.

the more precisely a particle’s position is measured, the less precisely the particle’s momentum can be known.

Certain first-year-physics conservation-of-momentum issues dictated that I be showered with former pig bowel contents in order to enhance shareholder value.

Three major points are: You get probabilities, not definite answers. You don't get access to the wave function itself, but only a peek at processed versions of it. Answering different questions may require processing the wave function in different ways. Each of those three points raises big issues. The first raises the issue of determinism. Is calculating probabilities really the best we can do? The second raises the issue of many worlds. What does the full wave-function describe, when we're not peeking? Does it represent a gigantic expansion of reality, or is it just a mind tool, no more real than a dream? The third raises the issue of complementarity. To address different questions, we must process information in different ways. In important examples, those methods of processing prove to be mutually incompatible. Thus no one approach, however clever, can provide answers to all possible questions. To do full justice to reality, we must engage it from different perspectives. That is the philosophical principle of complementarity. It is a lesson in humility that quantum theory forces to our attention. We have, for example, Heisenberg's uncertainty principle: You can't measure both the position and the momentum of particles at the same time. Theoretically, it follows from the mathematics of wave functions. Experimentally, it arises because measurement requires active involvement with the object being measured. To probe is to interact, and to interact is potentially to disturb. Each of these issues is fascinating, and the first two have gotten a lot of attention. To me, however, the third seems especially well-grounded and meaningful. Complementarity is both a feature of physical reality and a lesson in wisdom, to which we shall return.

The orbital motion of the electron causes a magnetic moment μ = -(e/2mc)j antiparallel to the angular momentum.

The uncertainty principle tells us that you need high-momentum particles to probe or influence physical processes at short distances, and special relativity relates that momentum to a mass.

My appreciation for order and regularity, even if it inconvenienced me, meant I never had much trouble with one of the main traditional objections to Christianity (or any religion that posits a loving God): the problem of evil - the question of how any pain and suffering could be countenanced by an all-powerful, all-good God. Consider the simpler problem of natural evils and accidents (falling masonry, flooding, car crashes, virulent flus, etc.). For God to deliver us from all natural pains, the laws of physics would have to be studded with asterisks specifying all the times that flying, twisted metal would need to flout the conservation of linear momentum to stop just short of breaking our bones. I knew what such a world would look like, for it had already been imagined in the sagas of Norse mythology. In one legend, the godling Baldr prophesies his own death, and all the other gods of the Norse pantheon try to save him. The gods and goddesses of Asgard travel the world, extracting a vow from every natural and created thing, be it bird, plant, stone, or sword, never to do Baldr any harm. Once his safety is secured, the Asgardians amuse themselves at feasts by throwing knives and other weapons at Baldr, in order to watch the objects keep their promises, defy their natures, and leave him unhurt. Blades blunt themselves, stones soften, and poison neutralizes itself, all to avoid inflicting any pain on Baldr. To preclude the problem of evil, it seemed, any god would have to give us the same guarantee afforded Baldr. The world around us would have to warp itself to shield us from the weather, from accidents, from gravity, until the laws of physics were unworthy of the name. There couldn't be scientists or empiricism in this kind of world, since the nature of matter would be too protean for us to gain intellectual purchase on. The problem of evil has always seemed to me to be the price we pay for having an intelligible world, one that we can investigate, understand, and love. If miracles were to be possible, they would have to stay below some threshold level of frequency so that they remained clear exceptions to the general course of causality (as in the case of poor, strange Baldr) instead of undoing the rule entirely.

To talk of humans as 'transcendent' is not to ascribe to them spiritual properties. It is, rather, to recognize that as subjects we have the ability to transform our selves, our natures, our world—an ability denied to any other physical being. In the six million years since the human and chimpanzee lines first diverged on either side of Africa's Great Rift Valley, the behaviour and lifestyles of chimpanzees have barely changed. Human behaviour and lifestyles clearly have. Humans have learnt to learn from previous generations, to improve upon their work, and to establish a momentum to human life and culture that has taken us from cave art to quantum physics and the conquest of space. It is this capacity for constant innovation that distinguishes humans from all other animals. All animals have an evolutionary past. Only humans make history.

Over the past few months, we have introduced a number of great benefits and tools to make us more productive, efficient and fun. With the introduction of initiatives like FYI, Goals and PB&J, we want everyone to participate in our culture and contribute to the positive momentum. From Sunnyvale to Santa Monica, Bangalore to Beijing—I think we can all feel the energy and buzz in our offices. To become the absolute best place to work, communication and collaboration will be important, so we need to be working side-by-side. That is why it is critical that we are all present in our offices. Some of the best decisions and insights come from hallway and cafeteria discussions, meeting new people, and impromptu team meetings. Speed and quality are often sacrificed when we work from home. We need to be one Yahoo, and that starts with physically being together. Beginning in June, we’re asking all employees with work-from-home arrangements to work in Yahoo offices. If this impacts you, your management has already been in touch with next steps. And, for the rest of us who occasionally have to stay home for the cable guy, please use your best judgment in the spirit of collaboration. Being a Yahoo isn’t just about your day-to-day job, it is about the interactions and experiences that are only possible in our offices. Thanks to all of you, we’ve already made remarkable progress as a company—and the best is yet to come. Jackie

Yet despite the fact that gravity is different from other physical forces, there is a profound harmony integrating gravity with all of the rest of physics. Einstein's theory is not something foreign to the other laws, but it presents them in a different light. (This is particularly so for the laws of conservation of energy, momentum, and angular momentum.) This integration of Einstein's gravity with the rest of physics goes some way to explaining the irony that Newton's gravity had provided a paradigm for the rest of physics despite the fact, as Einstein later showed, that gravity is actually different from the rest of physics! Above all, Einstein taught us not to get too complacent in believing, at any stage of our understanding, that we have, as yet, necessarily found the appropriate physical viewpoint.

Benefits of Being Nice • You set positive karma into motion. • What you give is what you get back in return. • You are more likable. • People will treat you better. • You will reduce personal stress. • You will make friends more easily. • You can improve someone else’s day. • You will have less drama in your life. • It takes less energy than being otherwise. • It makes you a more valuable team player. • You create a sense of emotional safety for others. • It can keep you physically and psychologically safe. • You set a positive example for others to play nicely. • You will build bridges of cooperation and collaboration. • You will improve personal and professional interactions • Lastly, being nice feels nice!

According to this, the state of a quantum system is some definite but abstract thing in an equally abstract Hilbert space. The one state can, so to speak, be looked at from different points of view. A cubist painting might give you a flavour of the idea. In relativity, different coordinate systems on space-time correspond to different decompositions into space and time. In quantum mechanics, the different coordinate systems, or bases, are equally startling in their physical significance. They determine what will happen if different kinds of measurement, say of position or of momentum, are made on the system by instruments that are external to the system. The state in Hilbert space is an enigmatic gem that presents a different aspect on all the innumerable sides from which it can be examined. As Leibniz would say, it is a city multiplied in perspective. Dirac was entranced, and spoke of the 'darling transformation theory'. He knew he had seen into the structure of things. What he saw was some real but abstract thing not at all amenable to easy visualization. But the multiplication of viewpoints and the mathematical freedom it furnished delighted him.

The act of going up into Full Arm Balance combines elements of physics and biomechanics. Joint rhythm couples with momentum, so that the body floats up into the pose with control. Begin in Downward Facing Dog Pose. Then step one foot forward, keeping the knee bent. This shifts the center of gravity and brings the weight forward into the hands, taking the arms into a more vertical position. Pause here if you are new to the pose. Get used to positioning the arm bones so that the mechanical and anatomical axes align with one another. Start to rock the weight over the hands in a 1-2-3 type of rhythm; then engage the thigh, buttocks, and lower back muscles to lift the back leg straight up onto the wall. Combine the momentum generated by rocking forward and back with the force of the spinal extensor muscles to lift the other leg.

Over the twentieth century, as physics developed, Planck's construction took on ever greater significance. Physicists came to understand that each of the quantities c, G, and h plays the role of a conversion factor, one you need to express a profound physical concept: 1) Special relativity postulates symmetry operations (boosts, a.k.a. Lorentz transformations) that mix space and time. Space and time are measured in different units, however, so for this concept to make sense, there must be a conversion factor between them, and c does the job. Multiplying a time by c, one obtains a length. 2) Quantum theory postulates an inverse relation between wave-length and momentum, and a direct proportionality between frequency and energy, as aspects of wave-particle duality; but these pairs of quantities are measured in different units, and h must be brought in as a conversion factor. 3) General relativity postulates that energy-momentum density induces space-time curvature, but curvature and energy density are measured in different units, and G must be brought in as a conversion factor.

In this chapter we will look at the entire edifice of QFT. We will see that it is based on three simple principles. We will also list some of its achievements, including some new insights and understandings not previously mentioned. THE FOUNDATION QFT is an axiomatic theory that rests on a few basic assumptions. Everything you have learned so far, from the force of gravity to the spectrum of hydrogen, follows almost inevitably from these three basic principles. (To my knowledge, Julian Schwinger is the only person who has presented QFT in this axiomatic way, at least in the amazing courses he taught at Harvard University in the 1950's.) 1. The field principle. The first pillar is the assumption that nature is made of fields. These fields are embedded in what physicists call flat or Euclidean three-dimensional space-the kind of space that you intuitively believe in. Each field consists of a set of physical properties at every point of space, with equations that describe how these particles or field intensities influence each other and change with time. In QFT there are no particles, no round balls, no sharp edges. You should remember, however, that the idea of fields that permeate space is not intuitive. It eluded Newton, who could not accept action-at-a-distance. It wasn't until 1845 that Faraday, inspired by patterns of iron filings, first conceived of fields. The use of colors is my attempt to make the field picture more palatable. 2. The quantum principle (discetization). The quantum principle is the second pillar, following from Planck's 1900 proposal that EM fields are made up of discrete pieces. In QFT, all physical properties are treated as having discrete values. Even field strengths, whose values are continues, are regarded as the limit of increasingly finer discrete values. The principle of discretization was discovered experimentally in 1922 by Otto Stern and Walther Gerlach. Their experiment (Fig. 7-1) showed that the angular momentum (or spin) of the electron in a given direction can have only two values: +1/2 or -1/2 (Fig. 7-1). The principle of discretization leads to another important difference between quantum and classical fields: the principle of superposition. Because the angular momentum along a certain axis can only have discrete values (Fig. 7-1), this means that atoms whose angular momentum has been determined along a different axis are in a superposition of states defined by the axis of the magnet. This same superposition principle applies to quantum fields: the field intensity at a point can be a superposition of values. And just as interaction of the atom with a magnet "selects" one of the values with corresponding probabilities, so "measurement" of field intensity at a point will select one of the possible values with corresponding probability (see "Field Collapse" in Chapter 8). It is discretization and superposition that lead to Hilbert space as the mathematical language of QFT. 3. The relativity principle. There is one more fundamental assumption-that the field equations must be the same for all uniformly-moving observers. This is known as the Principle of Relativity, famously enunciated by Einstein in 1905 (see Appendix A). Relativistic invariance is built into QFT as the third pillar. QFT is the only theory that combines the relativity and quantum principles.

Minimize brick, maximize mission.

Each of the most basic physical laws that we know of corresponds to some invariance, which in turn is equivalent to a collection of changes which form a symmetry group. The symmetry group describes all the variations that can be formed from an initial seed pattern whilst still leaving some underlying theme unchanged. Thus, for example, the conservation of energy is equivalent to the invariance of the laws of motion with respect to translations backwards or forwards in time (that is, the result of an experiment should not depend on the time at which it was carried out, all other factors being identical); the conservation of linear momentum is equivalent to the invariance of the laws of motion with respect to the position of your laboratory in space, and the conservation of angular momentum to an invariance with respect to the directional orientation of your laboratory in space.

We need three daily wins to build momentum and make progress: a physical win, a spiritual win, and a mental win. Get busy winning!

Even in the equations that had been formulated to describe electromagnetism, there is no natural directionality to the interactions of particles; the equations look the same going both directions. If you looked at a video of atoms interacting, you could play it backward and you wouldn’t be able to tell which was correct. It is only in the macroworld of objects, people, planets, and so on, the world governed by entropy, that causation appears to unfold in a single direction. The second law of thermodynamics describes the increasing disorder in the universe at macroscales and is often seen as equivalent to the one-way arrow of time. More and more physicists over the past few decades, sensitive to the nondirectionality that seems to rule at the micro or quantum level, have begun to question the no-teleology rule. Recall that the tiny particles making up the matter and energy of the physical universe are really like worms or strings snaking through the block universe of Minkowski spacetime. Their interactions, which look to us a bit like tiny balls colliding on a billiard table, are from a four-dimensional perspective more like threads intertwining; the twists and turns where they wrap around each other are what we see as collisions, interactions, and “measurements” (in the physicists’ preferred idiom). Each interaction changes information associated with those threads—their trajectory through the block universe (position and momentum) as well as qualities like “spin” that influence that trajectory. According to some recent theories, a portion of the information particles carry with them actually might propagate backward rather than forward across their world lines. For instance, an experiment at the University of Rochester in 2009 found that photons in a laser beam could be amplified in their past when interacted with a certain way during a subsequent measurement—true backward causation, in other words.8 The Israeli-American physicist Yakir Aharonov and some of his students are now arguing that the famous uncertainty principle—the extent to which the outcome of an interaction is random and unpredictable—may actually be a measure of the portion of future influence on a particle’s behavior.9 In other words, the notorious randomness of quantum mechanics—those statistical laws that captured Jung’s imagination—may be where retrocausation was hiding all along. And it would mean Einstein was right: God doesn’t play dice.*23 If the new physics of retrocausation is correct, past and future cocreate the pattern of reality built up from the threads of the material world. The world is really woven like a tapestry on a four-dimensional loom. It makes little sense to think of a tapestry as caused by one side only;

What is conserved, in modern physics, is not any particular substance or material but only much more abstract entities such as energy, momentum, and electric charge. The permanent aspects of reality are not particular materials or structures but rather the possible forms of structures and the rules for their transformation.

There are two questions we might ask about the particle in this wave packet: (1) Where is it, and (2) what is its momentum? Physicists discovered that you can ask one of these questions, but not both. For example, once you ask “Where is it?” and you fix a wave-particle in a location, it becomes a particle. If you ask “What is its momentum?” you have decided that movement is the critical factor; therefore you must be talking about a wave. So is this thing we are talking about, the “wave-particle,” a particle or a wave? It depends on which of the two questions we decide to ask. At any given moment, that wave-particle can be either a particle or a wave because we can’t know both the location and the momentum of the wave-particle. In fact, as it turns out, until we measure either its location or its momentum, it is both particle and wave simultaneously. This concept is known as the Heisenberg Uncertainty Principle, and it is one of the fundamental building blocks of modern physics.

Biological systems are influenced by the laws of physics, and it may be that mycelium exploits the natural momentum of matter, just like salmon take advantage of the tides.

As a mathematician Fantappiè could not accept that half of the solutions of the fundamental equations where rejected and in 1941, while listing the properties of the forward and backward in time energy, Fantappiè discovered that forward in time energy is governed by the law of entropy, whereas backward in time energy is governed by a complementary law that he named syntropy, combining the Greek words syn which means converging and tropos which means tendency. Listing the mathematical properties of syntropy Fantappiè discovered: energy concentration, increase in differentiation, complexity and structures: the mysterious properties of life! In 1944 he published the book “Principi di una Teoria Unitaria del Mondo Fisico e Biologico”[5] (Unitary Theory of the Physical and Biological World) in which he suggests that the physical-material world is governed by the law of entropy and causality, whereas the biological world is governed by the law of syntropy and retrocausality. We cannot see the future and therefore retrocausality is invisible! The dual energy solution suggests the existence of a visible reality (causal and entropic) and an invisible reality (retrocausal and syntropic). The first law of thermodynamics states that energy is a constant, a unity that cannot be created or destroyed but only transformed, and the energy-momentum-mass equation suggests that this unity has two components: entropy and syntropy. We can therefore write: 1=Entropy+Syntropy which shows that syntropy is the complement of entropy. Syntropy is often mistaken with negentropy. However, it is fundamentally different since negentropy does not take into account the direction of time, but considers time only in the classical way: flowing forward. Life lies between these two components: one entropic and the other syntropic, one visible and the other invisible, and this can be portrayed using a seesaw with entropy and syntropy playing at the opposite sides, and life at the center. This suggests that entropy and syntropy are constantly interacting and that all the manifestations of reality are dual: emitters and absorbers, particles and waves, matter and anti-matter, causality and retrocausality