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Newton's Laws and Reality: A Mathematical Perspective

Dive into Isaac Newton's foundational laws of motion and gravity that shape our perception of reality. Explore the deterministic and objective nature of Newtonian reality, where only quantifiable objects exist. Discover the mathematical precision that guides our understanding of matter and existence in this thought-provoking exploration.

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Newton's Laws and Reality: A Mathematical Perspective

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  1. What is Reality? Isaac Newton vs Quantum Physics

  2. Our modern day picture of reality comes from Isaac Newton (1642-1727). • First scientific portrait of existence/reality • One fundamentally different from the myriad versions of reality (one or more per culture) conceived from the dawn of humanity, and still persisting in the world today.

  3. Our reality is based on Newton’s 3 Laws of Motion: • Inertia: if an object is left alone, it will continue undisturbed. • Static objects remain at rest. • Moving objects remain in motion. • True everywhere for all things • Abolishes ghosts, demons, goblins, spirits, gods, etc from our reality • Force: a force applied to an object will cause a change in momentum. • Momentum is quantifiable mathematically = Mass X Speed • This law tells us precisely how a force (e.g. friction or gravity) will change the objects motion. • The mathematical precision of this Law has allowed us to determine the nature of matter (reality) in ever increasing detail. • Mutual Action: to every action there is always an equal and opposite reaction. • Any time two objects collide, each exerts a force on the other.

  4. Newton’s 3 Laws of Motion

  5. To these 3 Laws of Motion, Newton added the Law of Universal Gravitation: every object in the universe exerts a force on every other object. • Newton invented Calculus to explain all of these laws mathematically. • Set the standard for all scientific descriptions of reality: if it cannot be explained mathematically, it is NOT REAL.

  6. Newton’s picture of reality presumes three basic ideas: #1 1) Newton’s laws give us a picture consisting of objects, each of which has a specific, quantifiable state. • Each object has one innate position, one speed, and once constant mass. • The object is not possessed by any spirits nor can its nature change on the whim of some god.

  7. Newton’s picture of reality presumes three basic ideas: #2 2) Newton describes a deterministic universe. • Every effect has a specific cause and each distinct cause produces one distinct effect. • Only when a force acts on an object does the object change its motion, and the response is immediate and absolute.

  8. Newton’s picture of reality presumes three basic ideas: #3 3) Newton’s laws describe reality in entirely objective terms. • Only discrete, mathematically verifiable objects are real. • There is no place for mind consciousness, will, soul, or God. (Newton himself was a devout believer in the Christian God, and would be very upset with the reality his laws have set out for us.)

  9. Our Newtonian Reality Reality consists ONLY of pieces of matter that differ simply in shape, mass, location, and motion. Newton’s reality is composed of nonsentient (not self aware) objects that change according to three exact, mathematical laws of motion.

  10. What does it mean for something to exist, to be real? • Objects exist because we can detect them with our senses. A desk exists because we can see it, touch it, etc. • Based on repeated inspection, we also assume that the desk is something independent of our senses. It is really out there and will go on existing even when we don’t touch it, see it, etc. • While this is a reasonable assumption, it is still an assumption. • It is simpler to make our model of reality on the basis that the desk has an independent existence than to suppose that when we look away it vanishes, and only reappears when we look back.

  11. This all seems straightforward enough. But all things said to exist are not as concrete as a desk. What about…?

  12. Okay, but what about…? Atoms, for example, are too small to see or touch, or to sense directly in anyway. • Our knowledge of them comes indirectly, via tools like high-powered microscopes. • The data from these tools must be processed and interpreted by humans. • At the sub-atomic level there are limits to what we can sense, and particles (really small objects) do not behave according to the Newton’s Laws. Does this mean they do not exist, that they are not real?

  13. Okay, but what about…? Then there are even more abstract entities such as fields, as in a gravitational field. • It is readily apparent that gravity is real; we can observe and even feel its effects, yet we cannot see or touch the field itself.

  14. Okay, but what about…? What about concepts we use in daily life, such as citizenship or information? Certainly they are realeven though we cannot see or touch them. • We may be able to see or touch the medium for storing or displaying information, such as a computer disc or a screen, but we cannot perceive the information itself directly. Still, it is real, right?

  15. Okay, but what about…? There is also a category of things that are broadly described as cultural—for example music or literature. • The definitive rock ‘n’ roll of Led Zeppelin cannot be equated with the CD you hold in your hand; it exists somehow differently, yet is still just as real. • Nor can religion or politics be identified merely with the people who practice them, yet they exist in a less-than-concrete, yet very real way.

  16. Okay, but what about…? Finally, there is the realm of mathematics and logic, the things(?) we use to discover and describe reality itself, at least in science. • Your math teacher will tell you about an existing theorem about, say, prime numbers. • You can see it represented with written symbols, but the theorem itself cannot be seen or touched. It is completely abstract, yet it is still real, right?

  17. Okay, but what about…? How about dreams? A dream is real, at least for the dreamer, yet it is considerably less substantial than a desk. • Similarly thoughts, emotions, memories, etc. cannot be dismissed as nonexistent, although their existence is different from that of the “objective” world.

  18. Do any of these abstract ideas exist anywhere in anyway beyond our own imaginations? Or is it that our imaginations actually create the reality of these abstractions?

  19. In the Words of Dr Quantum Reality is not just the physical world; it’s the relationship of the mind with the physical world that creates the perception of reality. There is no reality without a perception of reality. --Dr. Fred Alan Wolf

  20. Let us return to the desk, the one thing we know for sure is real because we can verify its existence objectively. What is the desk, in reality? Newton tells us that to understand the whole, one must break it down to its constituent parts. Understand all the parts, you understand the whole.

  21. This desk is REAL, right? Look at the parts we see before us. A piece of laminated wood, some stainless steel metal, some paint, some plastic, some nuts and bolts; we could go on and on. We have a bunch of parts—but where is the desk? A Buddhist would tell you that the desk has no existence outside of your mind. It is only a concept—it is not real. Objectively, there are only parts.

  22. Parts of the Parts Of Course, we can break the parts down even further, to see what parts the parts are made of. Eventually we get beyond molecular structure to the atoms. All objects (including desks) are made up of atoms.

  23. Let’s look at the classical model of the atom (since we can’t actually look at an atom itself, though surely it exists, right?) Here we have a generic atom consisting of particles called electrons orbiting around a nucleus consisting of tightly packed neutrons and protons. Newtonian objects?

  24. If this was to scale, the nucleus would be smaller than a marble, and the nearest electron a grain of salt circling in an orbit approximately the circumference of our school gym This means that an atom is almost entirely made up of empty space! This means, in reality, this desk is almost entirely made up of empty space! This means, in reality, YOU are almost entirely made up of empty space!

  25. More Parts !?! But now we have more parts—electrons, protons, and neutrons—so we need to understand these parts so we can understand the whole, the atom, and ultimately, the desk. • This “classical” model of the atom (above) was abandoned by physicists early in the 20th century. • It does not represent the realityof the atom at all, though high school students still are taught this model as a simplification of the reality.

  26. Quantum Reality Now we are in the realm of quantum physics—the subatomic world, the level of the inconceivably small; the foundation of our world, our reality, you and me (literally). Here all of Newton’s Laws, the cornerstones of our reality, DO NOT WORK!!

  27. Albert Einstein:Four Revolutionary Ideas One hundred and three years ago Albert Einstein (1879-1955) wrote four fundamental papers, all in the course of a few months, beginning a whole new way of understanding reality. The first paper claimed that light must sometimes behave like a stream of particles with discrete energies, “quanta.”

  28. Albert Einstein:Four Revolutionary Ideas • The second paper offered an experimental test for the theory of heat and proof of the existence of atoms. • The third paper addressed a central puzzle for physicists of the day – the connection between electromagnetic theory and ordinary motion – and solved it using the "principle of relativity."

  29. Albert Einstein:Four Revolutionary Ideas The fourth showed that mass and energy are two parts of the same thing, mass=energy (E=mc2)—the greatest result of relativistic physics AND a completely new definition of reality. Of course, it was all proved mathematically by Einstein, as well as experimentally by thousands of scientists over the past 100 years.

  30. Einstein’s 4th paper:E=mc2 What does this really mean? Energy equals Mass multiplied by the Constant squared The Constant is the velocity of light, the speed of light (about 186,000 miles per second) This means….MASS IS ENERGY!

  31. Mass = Energy X Speed of Light2 If matter IS energy that means that in reality this desk is really just a bottle of energy. Furthermore, if you increase one side of the equation, the other side increases equally. If you increase the Energy value by, say, speeding the object up, it must lead to a corresponding increase in Mass. So in reality this means that the faster you travel, the heavier you are.

  32. Einstein’s 3rd paper:Relativity theory • Time is the 4th dimension fundamentally connected to our three-dimensional world. • Everything measured in space must be measured in time also. • We have already seen how E=mc2 tells us that as speed (velocity) increases, mass is relatively heavier. • Similarly, because time is tied to the increasingly heavier object, time passes relatively slower! • These effects only become dramatic as one approaches the speed of light, but have been proven experimentally with nuclear clocks and really fast airplanes. • Get it? Mass, Energy & Time are relative—Relativity theory.

  33. Relativity Theory

  34. Reality huh? Say goodbye to Isaac Newton’s objective reality! Measurements of mass, time, even length and width, are NOT constant, but in reality relative to the velocity of the observer.

  35. Einstein’s 1st & 2nd papers Einstein’s second paper proved mathematically that atoms exist in reality. • Enough said. In his first paper Einstein takes us beyond his very real atoms to the sub-atomic level, and gives birth to Quantum Physics.

  36. Our Quantum Reality Remember, Einstein’s first paper proved that light must sometimes behave like a stream of particles with discrete energies, “quanta.” This contradicted the accepted view of reality that light consisted of waves, not particles. Before Einstein, only electron, neutrons, protons, etc. were particles.

  37. Following Einstein, scientists have discovered that… • sometimes light demonstrates the characteristics of a wave • sometimes light demonstrates the characteristics of a particle. • Even stranger, sometimes electrons, neutrons, and protons—particles—demonstrate the characteristics of a wave. • Whether a beam of light or an electron in an atom is, in reality, a particle or a wave depends, literally, upon how you look at it!

  38. Remember the classical model of the atom: • Well, when we actually try to look at it, (remember we have to rely on sophisticated tools to detect this level of reality): • sometimes we see electrons orbiting the nucleus like in the above picture, but when we use different tools… • sometimes we see what looks like an electron field enveloping the nucleus, a probability wave across all possible points of the electron’s orbit.

  39. The Reality of Light… …is just as strange. Light is a particle when we actually look at it, BUT light is a wave when we DO NOT look at it. In reality, light is both a particle AND a wave at the same time! Let us consult Dr. Quantum…

  40. The Reality of Light…

  41. Take a look… Quantum physics tells us that the way we look at something affects what it is—this means that ultimately, there is NO OBJECTIVE REALITY! Without the OBSERVER, there is no reality at all!!

  42. In the Words of Dr Quantum There is no absolute “out there” unless there is mind “in here” that perceives it. The observer effect says that there is no reality until that reality is perceived. This profound insight tells us that we alter every object in the world simply by paying attention to it. What is “out there” depends on what we choose to look for. --Dr Fred Alan Wolf

  43. More crazy aspects of our Quantum Reality The Heisenberg Uncertainty Principle tells us that there are natural limits to how complete our picture of reality can even be. • We cannot simultaneously know the speed AND the position of an object—airplane or electron. • If we measure where it is, its position, it is no longer moving, so how can we measure its speed? • If we measure its speed it is moving, so how can we say where it is? Newton said that if we understood all the parts of a whole, we would know the whole, but now we know there are limits to how much we can know about all the parts.

  44. More crazy aspects of our Quantum Reality Quantum Tunneling: Let's say you are throwing a rubber ball against a wall. You know you don't have enough energy to throw it through the wall, so you always expect it to bounce back. Quantum mechanics, however, says that there is a small probability that the ball could go right through the wall (without damaging the wall) appear on the other side! With something as large as a rubber ball, though, that probability is so small that you could throw the ball for billions of years and never see it go through the wall. Still, it is NOT IMPOSSIBLE! But with something as tiny as an electron, tunneling is an everyday occurrence. You accept and apply this reality almost everyday: without it computer chips would not exist, and a 'personal‘ computer would take up an entire room.

  45. Quantum Tunneling

  46. More crazy aspects of our Quantum Reality Reality is Non-Local Consider two electrons • electron e+ has positive spin • electron e- has negative spin These two electrons encounter each other, and because of their complimentary spin, bond “in orbit” around each other. Scientists isolate these two electrons, bonded in their local relationship, and separate them e+ stays here in Denver e- is sent to a lab in Switzerland We subject our electron (e+) to an electromagnet, reversing its spin. Here in Denver, we now have an e- The lab in Switzerland will simultaneously measure their e- electron as transformed into an e+! The effect one particle can have on another particle does not depend upon their mutual proximity. Again, let us consult Dr. Quantum…

  47. Quantum Entanglement

  48. Reality is non-local Yet another blow to our Newtonian Reality! This means that every particle that has come in contact with another particle can affect that particle no matter where it is. Since ALL particles were in infinite contact during the so-called Big Bang, this means all particles can affect all other particles! If all particles are connected in this way, their disconnectedness must not be real. There are not, in reality, a bunch of little parts called particles. Instead there is just ONE…whatever ya wanna call it… …Quantum Field? Matrix?

  49. The Matrix You think of yourself a separate and distinct object from the desk you are sitting in, but as you sit there right now, you are exchanging electrons with the desk, like two drops of water whose borders come in contact. There is not really two drops of water at all, just water. There is not really you and a desk, just…a quantum field.

  50. In the Words of Dr Quantum Distinctions are not real. They are fleeting whispers of an all-pervading, subtle, non-expressive potential reality. The world is not made of separate things. Mind is not separate from matter. And you are not separate from any other being, animal, vegetable, living, dead, or seemingly inanimate matter. --Dr Fred Alan Wolf

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