Spacetime Quotes

Even today, I am in total awe of the following wondrous chain of ideas and interconnections. Guided throughout by principles of symmetry, Einstein first showed that acceleration and gravity are really two sides of the same coin. He then expanded the concept to demonstrate that gravity merely reflects the geometry of spacetime. The instruments he used to develop the theory were Riemann's non-Euclidean geometries-precisely the same geometries used by Felix Klein to show that geometry is in fact a manifestation of group theory (because every geometry is defined by its symmetries-the objects it leaves unchanged). Isn't this amazing? ~ Mario Livio

Sense of beauty, perception, and the mathematical universe are all part of the same texture. ~ Neeti Sinha

You are telling me that I did something because I was going to do something."
"Well, didn't you? You were there."
"No, I didn't - no ... well, maybe I did, but it didn't feel like it."
"Why should you expect it to? It was something totally new to your experience."
"But ... but - " Wilson took a deep breath and got control of himself. Then he reached back into his academic philosophical concepts and produced the notion he had been struggling to express. "It denies all reasonable theories of causation. You would have me believe that causation can be completely circular. I went through because I came back from going through to persuade myself to go through. That's silly."
"Well, didn't you? ~ Robert A. Heinlein

It is scandalous the way some scientists accept uncritically some of the most ridiculous speculations, such as the plurality of worlds, the opinion that spacetime has more than 4 dimensions, that particles can move faster than light, or that human life can be prolonged indefinitely. ~ Mario Bunge

The Universe is continuously emerging as a fresh creation at every moment. All point to this same, extraordinary insight. The Universe is not static, nor is its continuation assured. Instead, the Universe is like a cosmic hologram that is being continuously upheld and renewed at every instant.14 A universal encouragement found across the world's wisdom traditions is to live in the 'NOW.' This core insight has a clear basis in physics: The present moment is the place of direct connection with the entire Universe as it arises continuously. Each moment is a fresh formation of the Universe, emerging seamlessly and flawlessly. ~ Alexis Karpouzos

There was a long history of speculation that in quantum gravity, unlike Einstein's classical theory, it might be possible for the topology of spacetime to change. ~ Edward Witten

We have one real candidate for changing the rules; this is string theory. In string theory the one-dimensional trajectory of a particle in spacetime is replaced by a two-dimensional orbit of a string. Such strings can be of any size, but under ordinary circumstances they are quite tiny, ... a value determined by comparing the predictions of the theory for Newton's constant and the fine structure constant to experimental values. ~ Edward Witten

Thorne sent his answers to Franklin in the form of heavily researched memos. Pages long, deeply sourced, and covered in equations, they were more like scientific journal articles than anything else. Franklin's team wrote new rendering software based on these equations and spun up a wormhole. The result was extraordinary. It was like a crystal ball reflecting the universe, a spherical hole in spacetime. ~ Anonymous

I first began to worry about this during the summer of 1989, when it began to be clear that string theory would not quickly lead to a unique theory of everything. Henry Tye, a string theorist from Cornell University, had told me of his computer program to produce new string theories. When you run Tye's program, you input a rough description of a universe you would like to describe. You tell it the dimension of spacetime, and something about how the world should look. It outputs all the string theories it can construct that lead to the world you requested, one per page. ~ Lee Smolin

Go on from here, Ada, please. (She). Billions of boys. Take one fairly decent decade. A billion of Bills, good, gifted, tender and passionate, not only spiritually but physically well-meaning Billions, have bared the jillions of their no less tender and brilliant Jills during that decade, at stations and under conditions that have to be controlled and specified by the worker, lest the entire report be choked up by the weeds of statistics and waist-high generalizations. No point would there be, if we left out, for example, the little matter of prodigious individual awareness and young genius, which makes, in some cases, of this or that particular gasp an unprecedented and unrepeatable event in the continuum of life or at least a thematic anthemia of such events in a work of art, or a denouncer's article. The details that shine through or shade through: the local leaf through the hyaline skin, the green sun in the brown humid eye, tout ceci, vsyo eto, in tit and toto, must be taken into account, now prepare to take over (no, Ada, go on, ya zaslushalsya: I'm all enchantment and ears), if we wish to convey the fact, the fact, the fact - that among those billions of brilliant couples in one cross section of what you will allow me to call spacetime (for the convenience of reasoning), one couple is a unique super-imperial couple, sverhimperator-skaya cheta, in consequence of which (to be inquired into, to be painted, to be denounced, to be put to music, or to the question and death, ~ Vladimir Nabokov

In spacetime, all events are baked together: a four-dimensional continuum. Past and future are no more privileged than left and right or up and down. ~ James Gleick

The body is an arrangement in spacetime, a patterning, a process; the mind is a process of the body, an organ, doing what organs do: organize. Order, pattern, connect ... an immensely flexible technology, or life strategy, which if used with skill and resourcefulness presents each of us with that most fascinating of all serials, The Story of My Life. ~ Ursula K. Le Guin

So, in one slightly technical line, here's the mathematical skinny. There's an equation in string theory that has a contribution of the form (D-10) times (Trouble), where D represents the number of spacetime dimensions and Trouble is a mathematical expression resulting in troublesome physical phenomena, such as the violation of energy conservation mentioned above. As to why the equation takes this precise form, I can't offer any intuitive, nontechnical explanation. But if you do the calculation, that's where the math leads. Now, this simple but key observation is that if the number of spacetime dimensions is ten, not the four we expect, the contribution becomes 0 times Trouble. And since 0 times anything is 0, in a universe with ten spacetime dimensions the trouble gets wiped away. That's how the math plays out. Really. And that's why string theorists argue for a universe with more than four spacetime dimensions. ~ Brian Greene

In the popular imagination, the Big Bang is a great explosion; at one time there was nothing, then matter erupted into previously empty space. However, the Big Bang is the beginning of spacetime itself, not an event in time. ~ Taner Edis

A full explanation of this is beyond the scope of this book, suffice to say that Einstein was forced into this bold move primarily because Maxwell's equations for electricity and magnetism were incompatible with Newton's 200-year-old laws of motion. Einstein abandoned the Newtonian ideas of space and time as separate entities and merged them. In Einstein's theory there is a special speed built into the structure of spacetime itself that everyone must agree on, irrespective of how they are moving relative to each other. This special speed is a universal constant of nature that will always be measured as precisely 299,792,458 metres (983,571,503 feet) per second, at all times and all places in the Universe, no matter what they are doing. This ~ Brian Cox

A singularity is a point or region in spacetime at which some physical quantity such as the density of mass or energy, the temperature, or the strength of the gravitational field, becomes infinite. Whenever they happen, they pose serious difficulties for physics because they signal a breakdown in the description of the world in mathematical terms. ~ Lee Smolin

However, in broad brushstrokes, we might say this: You're a pattern in spacetime. A mathematical pattern. Specifically, you're a braid in spacetime-indeed one of the most elaborate braids known. ~ Max Tegmark

What you or I would recognize as an alien invasion by tentacled horrors from beyond spacetime Angleton would see as a teachable moment. ~ Charles Stross

Ain't spacetime a bitch," said Ram. "Noted," said the expendable. "Nineteen times. ~ Orson Scott Card

The claim that the universe *began* with the big bang has no basis in current physical and cosmological knowledge. The observations confirming the big bang do not rule out the possibility of a prior universe. ~ Victor J. Stenger

These electric and magnetic fields can be elegantly unified into what's known as the electromagnetic field, represented by six numbers at each point in spacetime. As we discussed in Chapter 7, light is simply a wave rippling through the electromagnetic field, so if our physical world is a mathematical structure, then all the light in our Universe (which feels quite physical) corresponds to six numbers at each point in spacetime (which feels quite mathematical). These numbers obey the mathematical relations that we know as Maxwell's equations, shown in Figure 10.4. ~ Max Tegmark

Physicists traced the failure to the jitters of quantum uncertainty. Mathematical techniques had been developed for analyzing the jitters of the strong, weak, and electromagnetic fields, but when the same methods were applied to the gravitational field-a field that governs the curvature of spacetime itself-they proved ineffective. This left the mathematics saturated with inconsistencies such as infinite probabilities. ~ Brian Greene

We believe in marbles that disintegrate when we search for them but that are as real as any genuine marble when we're not looking for them. Our very nature is such as to prevent us from fully understanding its very nature. Poised midway between the unvisualizable cosmic vastness of curved spacetime and the dubious, shadowy flickerings of charged quanta, we human beings, more like rainbows and mirages than like raindrops or boulders, are unpredictable self-writing poems - vague, metaphorical, ambiguous, and sometimes exceedingly beautiful. [...] What one gives up on is a childlike sense that things are exactly as they appear, and that our solid-seeming, marble-like "I" is the realest thing in the world; what one acquires is an appreciation of how tenuous we are at our cores, and how wildly different we are from what we seem to be. ~ Douglas R. Hofstadter

So: if you buy the notion that reality consists of the things in your freeze-frame mental image right now, and if you agree that your now is no more valid than the now of someone located far away in space who can move freely, then reality encompasses all of the events in spacetime. ~ Brian Greene

This was a golden age, in which we solved most of the major problems in black hole theory even before there was any observational evidence for black holes. In fact, we were so successful with the classical general theory of relativity that I was at a bit of a loose end in 1973 after the publication with George Ellis of our book The Large Scale Structure of Space–Time. My work with Penrose had shown that general relativity broke down at singularities, so the obvious next step would be to combine general relativity - the theory of the very large - with quantum theory - the theory of the very small. In particular, I wondered, can one have atoms in which the nucleus is a tiny primordial black hole, formed in the early universe? My investigations revealed a deep and previously unsuspected relationship between gravity and thermodynamics, the science of heat, and resolved a paradox that had been argued over for thirty years without much progress: how could the radiation left over from a shrinking black hole carry all of the information about what made the black hole? I discovered that information is not lost, but it is not returned in a useful way - like burning an encyclopedia but retaining the smoke and ashes.
To answer this, I studied how quantum fields or particles would scatter off a black hole. I was expecting that part of an incident wave would be absorbed, and the remainder scattered. But to my great surprise I found there seemed to be emission from the black hole itsel ~ Stephen Hawking

Tegmark argues that "our universe is not just described by mathematics-it is mathematics" [emphasis added]. His argument starts with the rather uncontroversial assumption that an external physical reality exists that is independent of human beings. He then proceeds to examine what might be the nature of the ultimate theory of such a reality (what physicists refer to as the "theory of everything"). Since this physical world is entirely independent of humans, Tegmark maintains, its description must be free of any human "baggage" (e.g., human language, in particular). In other words, the final theory cannot include any concepts such as "subatomic particles," "vibrating strings," "warped spacetime," or other humanly conceived constructs. From this presumed insight, Tegmark concludes that the only possible description of the cosmos is one that involves only abstract concepts and the relations among them, which he takes to be the working definition of mathematics. ~ Mario Livio

Space is a spin network whose nodes represent its elementary grains, and whose links describe their proximity relations. Spacetime ~ Carlo Rovelli

Meanwhile, someplace in the world, somebody is making love and another a poem. Elsewhere in the universe, a star manyfold the mass of our third-rate sun is living out its final moments in a wild spin before collapsing into a black hole, its exhale bending spacetime itself into a well of nothingness that can swallow every atom that ever touched us and every datum we ever produced, every poem and statue and symphony we've ever known - an entropic spectacle insentient to questions of blame and mercy, devoid of why.
"In four billion years, our own star will follow its fate, collapsing into a white dwarf. We exist only by chance, after all. The Voyager will still be sailing into the interstellar shorelessness on the wings of the "heavenly breezes" Kepler had once imagined, carrying Beethoven on a golden disc crafted by a symphonic civilization that long ago made love and war and mathematics on a distant blue dot.
But until that day comes, nothing once created ever fully leaves us. Seeds are planted and come abloom generations, centuries, civilizations later, migrating across coteries and countries and continents. Meanwhile, people live and people die - in peace as war rages on, in poverty and disrepute as latent fame awaits, with much that never meets its more, in shipwrecked love.
I will die.
You will die.
The atoms that huddled for a cosmic blink around the shadow of a self will return to the seas that made us.
What will survive of us are shoreless ~ Maria Popova

Nonetheless, in all cases matter tells spacetime how to curve, and spacetime tells matter how to move. ~ Lisa Randall

What lies north of the North Pole? ~ Stephen Hawking

A brane is a distinct region of spacetime that extends through only a (possibly multidimensional) slice of space. The word "membrane" motivated the choice of the word "brane" because membranes, like branes, are layers that either surround or run through a substance. ~ Lisa Randall

So, Einstein's theory of gravity is a theory of causal structure. It tells us that the essence of spacetime is causal structure and that the motion of matter is a consequence of alterations in the network of causal relations. What is left out from the notion of causal structure is any measure of quantity or scale. ~ Lee Smolin

Every Navy warship assigned to the Sol protection fleet flashed in towards Earth, knitting together in a defensive formation that extended out beyond lunar orbit. Weapons platforms that had spent decades stealthed in high orbit emerged to join the incredible array of firepower lining up on the Swarm. All over the planet, force fields powered up, shielding the remaining cities. Anyone outside an urban area was immediately teleported in to safety. The T-sphere itself was integrated into the defence organization, ready to ward off energy assaults against the planet by rearranging spacetime in a sharp curve. ~ Peter F. Hamilton

Everything dreams. The play of form, of being, is the dreaming of substance. Rocks have their dreams, and the earth changes.... ~ Ursula K. Le Guin

The big question in cosmology in the early 1960s was did the universe have a beginning? Many scientists were instinctively opposed to the idea, because they felt that a point of creation would be a place where science broke down. One would have to appeal to religion and the hand of God to determine how the universe would start off. This was clearly a fundamental question, and it was just what I needed to complete my PhD thesis.
Roger Penrose had shown that once a dying star had contracted to a certain radius, there would inevitably be a singularity, that is a point where space and time came to an end. Surely, I thought, we already knew that nothing could prevent a massive cold star from collapsing under its own gravity until it reached a singularity of infinite density. I realised that similar arguments could be applied to the expansion of the universe. In this case, I could prove there were singularities where space–time had a beginning.
A eureka moment came in 1970, a few days after the birth of my daughter, Lucy. While getting into bed one evening, which my disability made a slow process, I realised that I could apply to black holes the casual structure theory I had developed for singularity theorems. If general relativity is correct and the energy density is positive, the surface area of the event horizon - the boundary of a black hole - has the property that it always increases when additional matter or radiation falls into it. Moreover, if two black holes coll ~ Stephen Hawking

Never make a calculation until you know the answer. Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox and puzzle. Courage: No one else needs to know what the guess is. Therefore make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case life as a spacetime expert, however long, is more fun! ~ John Archibald Wheeler

It is theoretically possible to warp spacetime itself, so you're not actually moving faster than the speed of light, but it's actually space that's moving. ~ Elon Musk

We are focus-points of consciousness, [...] enormously creative. When we enter the self-constructed hologrammetric arena we call spacetime, we begin at once to generate creativity particles, imajons, in violent continuous pyrotechnic deluge. Imajons have no charge of their own but are strongly polarized through our attitudes and by the force of our choice and desire into clouds of conceptons, a family of very-high-energy particles which may be positive, negative or neutral. [...] Some common positive conceptions are exhilarons, excytons, rhapsodons, jovions. Common negative conceptions include gloomons, tormentons, tribulons, agonons, miserons.
"Indefinite numbers of conceptions are created in nonstop eruption, a thundering cascade of creativity pouring from every center of personal consciousness. They mushroom into conception clouds, which can be neutral or strongly charged - buoyant, weightless or leaden, depending on the nature of their dominant particles.
"Every nanosecond an indefinite number of conception clouds build to critical mass, then transform in quantum bursts to high-energy probability waves radiating at tachyon speeds through an eternal reservoir of supersaturated alternate events. Depending on their charge and nature, the probability waves crystallize certain of these potential events to match the mental polarity of their creating consciousness into holographic appearance. [...]
"The materialized events become that mind's experience, freighted ~ Richard Bach

David Park is a physicist and philosopher at Williams College in Massachusetts with a lifelong interest in a time which he too thinks doesn't pass. For Park, the passage of time is not so much an illusion as a myth, "because it involves no deception of the senses.... One cannot perform any experiment to tell unambiguously whether time passes or not." This is certainly a telling argument. After all, what reality can be attached to a phenomenon that can never be demonstrated experimentally? In fact, it is not even clear how to think about demonstrating the flow of time experimentally. As the apparatus, laboratory, experimenter, technicians, humanity generally and the universe as a whole are apparently caught up in the same inescapable flow, how can any bit of the universe be "stopped in time" in order to register the flow going on in the rest of it? It is analogous to claiming that the whole universe is moving through space at the same speed - or, to make the analogy closer, that space is moving through space. How can such a claim ever be tested? ~ Paul Davies

Like any place in Reality, the Street is subject to development. Developers can
build their own small streets feeding off of the main one. They can build
buildings, parks, signs, as well as things that do not exist in Reality, such as
vast hovering overhead light shows, special neighborhoods where the rules of
three-dimensional spacetime are ignored, and free-combat zones where people can
go to hunt and kill each other.
The only difference is that since the Street does not really exist -- it's just
a computer-graphics protocol written down on a piece of paper somewhere -- none
of these things is being physically built. They are, rather, pieces of
software, made available to the public over the worldwide fiber-optics network.
When Hiro goes into the Metaverse and looks down the Street and sees buildings
and electric signs stretching off into the darkness, disappearing over the curve
of the globe, he is actually staring at the graphic representations -- the user
interfaces -- of a myriad different pieces of software that have been engineered
by major corporations. In order to place these things on the Street, they have
had to get approval from the Global Multimedia Protocol Group, have had to buy
frontage on the Street, get zoning approval, obtain permits, bribe inspectors,
the whole bit. The money these corporations pay to build things on the Street
all goes into a trust fund owned and op ~ Neal Stephenson

Quantum particles do not behave like tennis balls, but like the quantum particles they are. To get from one place to another, they take all the possible paths in space and time as long as these paths link their starting point to their end point. The particle [...] literally went everywhere. Simultaneously. To the left and to the right of the post. And through it. And outside the room. And into the future and back - until the moment when it hit a detector on the wall. ~ Christophe Galfard

Conscious realism makes a bold claim: consciousness, not spacetime and its objects, is fundamental reality and is properly described as a network of conscious agents.31 To earn its keep, conscious realism must do serious work ahead. It must ground a theory of quantum gravity, explain the emergence of our spacetime interface and its objects, explain the appearance of Darwinian evolution within that interface, and explain the evolutionary emergence of human psychology. ~ Donald D. Hoffman

All of the patterns we've discussed of course exist in four dimensions rather than three, and the metaphors about braids, cables and trees, shouldn't be taken too literally. The key point is simply that you can be an unchanging pattern in spacetime-the specific details of this pattern are less important for the points we're making. This pattern is part of the mathematical structure that is our Universe, and the relations between different parts of the pattern are encoded in mathematical equations. As we saw in Chapter 8, Everett's quantum mechanics endows you with an even more interesting-but no less mathematical-structure, since a single you (the tree trunk) can split into many branches, each feeling that they're the one and only you
we'll return to this later. ~ Max Tegmark

What sort of work do you do?"
Lifting her skirts with one hand, still holding the owl in the other, she started for the cottage. "Quickening. Citizens of this spacetime call it clockwork magic."
--- ~ Sharon Lynn Fisher

You have to get old because of the geometry of spacetime. ~ Brian Cox

If we don't accept any common beliefs, we can't exist in spacetime. But when we don't believe in age, at least we don't have to die because our numbers change. [ ... ] When you don't believe in birthdays, the idea of aging turns a little foreign to you. You don't fall into trauma over your sixteenth birthday or your thirtieth or the big Five-Oh or the deadly Century. You measure your life by what you learn, not by counting how many calendars you've seen. If you're going to have trauma, better it be the shock of discovering the fundamental principle of the universe that some date predictable as next July. ~ Richard Bach

We begin life as uninhibited explorers with a boundless fascination for the ever growing world to which we have access. And what I find amazing is that if that fascination is fed, and if it's challenged, and if it's nurtured, it can grow to an intellect capable of grappling with such marvels as the quantum nature of reality, the energy locked inside the atom, the curved spacetime of the cosmos, the elementary constituents of matter, the genetic code underlying life, the neural circuitry responsible for consciousness, and perhaps even the very origin of the universe.
- Brian Greene ~ Brian Greene

You must accept that the universe does not owe you anything. It has already given you everything. ~ Don Murphy

This was undoubtedly one of symmetry's greatest success stories. Glashow, Wienberg, and Salam managed to unmask the electromagnetic and weak forces by recognizing that underneath the differences in the strengths of these two forces (the electromagnetic force is about a hundred thousand times stronger within the nucleus) and the different masses of the messenger particles lay a remarkable symmetry. The forces of nature take the same form if electrons are interchanged with neutrinos or with any mixture of the two. The same is true when photons are interchanged with the W and Z force-messengers. The symmetry persists even if the mixtures vary from place to place or from time to time. The invariance of the laws under such transformations performed locally in space and time has become known as gauge symmetry. In the professional jargon, a gauge transformation represents a freedom in formulating the theory that has no directly observable effects-in other words, a transformation to which the physical interpretation is insensitive. Just as the symmetry of the laws of nature under any change of the spacetime coordinates requires the existence of gravity, the gauge symmetry between electrons and neutrinos requires the existence of the photons and the W and Z messenger particles. Once again, when the symmetry is put first, the laws practically write themselves. A similar phenomenon, with symmetry dictating the presence of new particle fields, repeats itself with the strong nuclear force ~ Mario Livio