Physics Equations Quotes & Sayings

It was basic research in the photoelectric field-in the photoelectric effect that would one day lead to solar panels. It was basic research in physics that would eventually produce the CAT scan. The calculations of today's GPS satellites are based on the equations that Einstein put to paper more than a century ago. — Barack Obama

There is a mathematical underpinning that you must first acquire, mastery of each mathematical subdiscipline leading you to the threshold of the next. In turn you must learn arithmetic, Euclidian geometry, high school algebra, differential and integral calculus, ordinary and partial differential equations, vector calculus, certain special functions of mathematical physics, matrix algebra, and group theory. For most physics students, this might occupy them from, say, third grade to early graduate school - roughly 15 years. Such a course of study does not actually involve learning any quantum mechanics, but merely establishing the mathematical framework required to approach it deeply. — Carl Sagan

All right," Malcolm said. "Let's go back to the beginning." He paused, staring at the ceiling. "Physics has had great success at describing certain kinds of behavior: planets in orbit, spacecraft going to the moon, pendulums and springs and rolling balls, that sort of thing. The regular movement of objects. These are described by what are called linear equations, and mathematicians can solve those equations easily. We've been doing it for hundreds of years." "Okay," Gennaro said. "But there is another kind of behavior, which physics handles badly. For example, anything to do with turbulence. Water coming out of a spout. Air moving over an airplane wing. Weather. Blood flowing through the heart. Turbulent events are described by nonlinear equations. They're hard to solve - in fact, they're usually impossible to solve. So physics has never understood this whole class of events. Until about ten years ago. The new theory that describes them is called chaos theory. — Michael Crichton

Infinity ... is used in physics simply as a shorthand for a very big number. — Victor J. Stenger

Look, if you're going to insist that I've taught you something, I guess I should give you a final exam." "Really?" "One question." "Sure." "Go look at an electron microscope photograph of an atom, okay? Don't just glance at it. It is very important that you examine it very closely. Think about what it means." "Okay." "And then answer this question. Does it make your heart flutter?" "Does it make my heart flutter?" "Yes or no. It's a yes or no question. No equations allowed." "All right, I'll let you know." "Don't be dense. I don't need to know. You need to know. This exam is self-graded. And it's not the answer that counts, it's what you do with the information." We locked eyes. His younger face flashed in my mind. The energetic, smiling bongo drum player I had seen pictured in the front of his book, The Feynman Lectures on Physics. A question popped from my lips. — Anonymous

If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future). — Benoit Mandelbrot

What counts, I found, is not what you cover, but what you uncover. Covering subjects in a class can be a boring exercise, and students feel it. Uncovering the laws of physics and making them see through the equations, on the other hand, demonstrates the process of discovery, with all its newness and excitement, and students love being part of it. — Walter Lewin

Among many, many others, the following things were definitely not interesting: the pupillary sphincter, mitosis, baroque architecture, jokes that have physics equations as punch lines, the British monarchy, Russian grammar, and the significant role that salt has played in human history. — John Green

In the one real, time-drenched universe, everything has a particular history precisely because it is finite, and not part of an infinite array. Moreover, the cosmological use of the infinite serves to mask the failure of a physical theory taken beyond the boundaries of its proper domain of application. The most notable instance is the inference in contemporary cosmology of an infinite initial singularity from the field equations of general relativity. Finally, the admission of the mathematical infinite into natural science effaces the difference, which we emphasize, between nature and mathematics. Nature works in time, with which mathematics has trouble. Mathematics offers, among other things, the infinite, which nature abhors. — Lee Smolin

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation. — Paul Dirac

The lovely paradox of willing compliance with what an ancient prophet called "the great plan of happiness," is that conformity to law breeds both freedom and individualism. We may think a leaping child, in the euphoria of his imagination, enjoys unfettered freedom when he tells us he is going to land on the moon. But the rocket scientist hard at work in the laboratory, enmeshed in formulae and equations she has labored to master, and slaving away in perfect conformity with the laws of physics, is the one with true freedom: for she will land on the moon; the boy will not. — Terryl L. Givens

Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future ... If someone can hit on the right lines along which to make this development, it m may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply the ... My own belief is that this is a more likely line of progress than trying to guess at physical pictures. — Paul Dirac

The aim of Mathematical Physics is not only to facilitate for the physicist the numerical calculation of certain constants or the integration of certain differential equations. It is besides, it is above all, to reveal to him the hidden harmony of things in making him see them in a new way. — Henri Poincare

In Oppenheimer's view, it would be a waste of his precious time, or of mine, to concern ourselves with the details of particular solutions. This was how the philosophy of reductionism led Oppenheimer and Einstein astray. Since the only purpose of physics was to reduce the world of physical phenomena to a finite set of fundamental equations, the study of particular solutions such as black holes was an undesirable distraction from the general goal. Like Hilbert, they were not content to solve particular problems one at a time. They were entranced by the dream of solving all the basic problems at once. And as a result, they failed in their later years to solve any problems at all. — Freeman Dyson

No physicist started out impatient with common-sense notions, eager to replace them with some mathematical abstraction that could be understood only by rarified theoretical physics. Instead, they began, as we all do, with comfortable, standard, common-sense notions. The trouble is that Nature does not comply. If we no longer insist on our notions of how Nature ought to behave, but instead stand before Nature with an open and receptive mind, we find that common sense often doesn't work. Why not? Because our notions, both hereditary and learned, of how Nature works were forged in the millions of years our ancestors were hunters and gatherers. In this case common sense is a faithless guide because no hunter-gatherer's life ever depended on understanding time-variable electric and magnetic fields. There were no evolutionary penalties for ignorance of Maxwell's equations. In our time it's different. — Carl Sagan

Watson continued: Elon is brilliant. He's involved in just about everything. He understands everything. If he asks you a question, you learn very quickly not to go give him a gut reaction. He wants answers that get down to the fundamental laws of physics. One thing he understands really well is the physics of the rockets. He understands that like nobody else. The stuff I have seen him do in his head is crazy. He can get in discussions about flying a satellite and whether we can make the right orbit and deliver Dragon at the same time and solve all these equations in real time. It's amazing to watch the amount of knowledge he has accumulated over the years. I don't want to be the person who ever has to compete with Elon. You might as well leave the business and find something else fun to do. He will outmaneuver you, outthink you, and out-execute you. — Ashlee Vance

Everything, however complicated - breaking waves, migrating birds, and tropical forests - is made of atoms and obeys the equations of quantum physics. But even if those equations could be solved, they wouldn't offer the enlightenment that scientists seek. Each science has its own autonomous concepts and laws. — Martin Rees

Lecter sits in his armchair with a big pad of butcher paper doing calculations. The pages are filled with the symbols both of astrophysics and particle physics. There are repeated efforts with the symbols of string theory. The few mathematicians who could follow him might say his equations begin brilliantly and then decline, doomed by wishful thinking. Dr. Lecter wants time to reverse - no longer should increasing entropy mark the direction of time. He wants increasing order to point the way. — Thomas Harris

Even before string theory, especially as physics developed in the 20th century, it turned out that the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle. — Edward Witten

The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved. — Paul Dirac

If one is working from the point of view of getting beauty into one's equation, ... one is on a sure line of progress. — Paul A.M. Dirac

I now want to tell three stories about advances in twentieth-century physics. A curious fact emerges in these tales: time and again physicists have been guided by their sense of beauty not only in developing new theories but even in judging the validity of physical theories once they are developed. Simplicity is part of what I mean by beauty, but it is a simplicity of ideas, not simplicity of a mechanical sort that can be measured by counting equations or symbols. — Steven Weinberg

A mathematician believes that describing the speed of Mercury with equations amounts to science. — Bill Gaede

I became an atheist because, as a graduate student studying quantum physics, life seemed to be reducible to second-order differential equations. Mathematics, chemistry and physics had it all. And I didn't see any need to go beyond that. — Francis Collins

The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics. — John Von Neumann

One of the various theories proposed to explain the negative result of the famous Michelson-Morley experiment with light waves (conceived to measure the absolute space), was based on the ballistic hypothesis, i.e. on postulating that the speed of light predicted by Maxwell's equations was not given as relative to the medium but as relative to the transmitter (firearm). Had that been the case, the experiment negative results would have not caused such perplexity and frustration (as we shall see in forthcoming sections). — Felix Alba-Juez

I tell my students they can procrastinate as long as they follow three rules: 1. No going onto the computer during their procrastination time. It's just too engrossing. 2. Before procrastinating, identify the easiest homework problem. (No solving is necessary at this point.) 3. Copy the equation or equations that are needed to solve the problem onto a small piece of paper and carry the paper around until they are ready to quit procrastinating and get back to work. "I have found this approach to be helpful because it allows the problem to linger in diffuse mode - students are working on it even while they are procrastinating." - Elizabeth Ploughman, Lecturer of Physics, Camosun College, Victoria, British Columbia — Barbara Oakley

This is often the way it is in physics - our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. Even worse, there often seems to be a general agreement that certain phenomena are just not fit subjects for respectable theoretical and experimental effort. — Steven Weinberg

Anybody who has done high school physics knows Newton's Third Law. For every action there is an equal and opposite reaction. You push against a wall; it pushes back against you. I love the poetry hidden in these truths, in the many laws we've discovered that underpin the universal fabric. We search for meaning ever hungrier, perhaps even with desperation: the symmetry in the equations freaks us out; for all we know, there is just us on this lonely little marble in the inky void. — Sean J Halford

Extra dimensional theories are sometimes considered science fiction with equations. I think that's a wrong attitude. I think extra dimensions are with us, they are with us to stay, and they entered physics a long time ago. They are not going to go away. — Leonard Susskind

If time is treated in modern physics as a dimension on a par with the dimensions of space, why should we a priori exclude the possibility that we are pulled as well as pushed along its axis? The future has, after all, as much or as little reality as the past, and there is nothing logically inconceivable in introducing, as a working hypothesis, an element of finality, supplementary to the element of causality, into our equations. It betrays a great lack of imagination to believe that the concept of "purpose" must necessarily be associated with some anthropomorphic deity. — Arthur Koestler

The reason Dick's physics was so hard for ordinary people to grasp was that he did not use equations. The usual theoretical physics was done since the time of Newton was to begin by writing down some equations and then to work hard calculating solutions of the equations. This was the way Hans and Oppy and Julian Schwinger did physics. Dick just wrote down the solutions out of his head without ever writing down the equations. He had a physical picture of the way things happen, and the picture gave him the solutions directly with a minimum of calculation. It was no wonder that people who had spent their lives solving equations were baffled by him. Their minds were analytical; his was pictorial. — Freeman Dyson

Science is beautiful when it makes simple explanations of phenomena or connections between different observations. Examples include the double helix in biology and the fundamental equations of physics. — Stephen Hawking

What appear to be the most valuable aspects of the theoretical physics we have are the mathematical descriptions which enable us to predict events. These equations are, we would argue, the only realities we can be certain of in physics; any other ways we have of thinking about the situation are visual aids or mnemonics which make it easier for beings with our sort of macroscopic experience to use and remember the equations. — Celia Green

In the history of science it happens not infrequently that a reductionist approach leads to a spectacular success. Frequently the understanding of a complicated system as a whole is impossible without an understanding of its component parts. And sometimes the understanding of a whole field of science is suddenly advanced by the discover of a single basic equation. Thus it happened that the Schrodinger equation in 1926 and the Dirac equation in 1927 brought a miraculous order into the previously mysterious processes of atomic physics. The equations of Erwin Schrodinger and Paul Dirac were triumphs of reductionism. Bewildering complexities of chemistry and physics were reduced to two lines of algebraic symbols. These triumphs were in Oppenheimer's mind when he belittled his own discovery of black holes. Compared with the abstract beauty and simplicity of the Dirac equation, the black hole solution seemed to him ugly, complicated, and lacking in fundamental significance. — Freeman Dyson

Many physicists these days sound like the Delphic oracle - with equations. — John Twelve Hawks

So far as we know, all the fundamental laws of physics, like Newton's equations, are reversible. — Richard P. Feynman

Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell's equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein's field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul Dirac once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that "there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world. — Clifford A. Pickover

A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78. — Paul Dirac

While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. I'm no better than anyone else at understanding what makes people tick, particularly women. — Stephen Hawking

All the standard equations of mathematical physics can be separated and solved in Kerr geometry. — Subrahmanyan Chandrasekhar

In quantum mechanics there is A causing B. The equations do not stand outside that usual paradigm of physics. The real issue is that the kinds of things you predict in quantum mechanics are different from the kinds of things you predict using general relativity. Quantum mechanics, that big, new, spectacular remarkable idea is that you only predict probabilities, the likelihood of one outcome or another. That's the new idea. — Brian Greene

But Miss Ferguson preferred science over penmanship. Philosophy over etiquette. And, dear heavens preserve them all, mathematics over everything. Not simply numbering that could see a wife through her household accounts. Algebra. Geometry. Indecipherable equations made up of unrecognizable symbols that meant nothing to anyone but the chit herself. It was enough to give Miss Chase hives.

The girl wasn't even saved by having any proper feminine skills. She could not tat or sing or draw. Her needlework was execrable, and her Italian worse. In fact, her only skills were completely unacceptable, as no one wanted a wife who could speak German, discuss physics, or bring down more pheasant than her husband. — Eileen Dreyer