The Fabric of the Cosmos: Space, Time, and the Texture of Reality

by Brian Greene

Again, although it’s hard to accept at a gut level, there is no paradox here: observers in relative motion do not agree on simultaneity—they do not agree on what things happen at the same time.

Thus, although Newton definitely got it wrong, his intuition that there was something absolute, something that everyone would agree upon, was not fully debunked by special relativity. Absolute space does not exist. Absolute time does not exist. But according to special relativity, absolute spacetime does exist.

In an otherwise empty universe, with respect to what is the bucket spinning? According to Newton, the answer is absolute space. According to Mach, there is no sense in which the bucket can even be said to spin. According to Einstein’s special relativity, the answer is absolute spacetime.

And so, with these developments we learn that geometricalshapes of trajectories in spacetime provide the absolute standard that determines whether something is accelerating.

While you can shield yourself from electromagnetic and nuclear forces, there is no way to shield yourself from gravity.

All this led Einstein to conclude that the force one feels from gravity and the force one feels from acceleration are the same. They are equivalent. Einstein called this the principle of equivalence.

Since gravity and acceleration are equivalent, if you feel gravity’s influence, you must be accelerating.

Einstein would argue that it was Newton’s head that rushed up to meet the apple, not the other way around.

But as an important point of principle, the link Einstein found between gravity and acceleration means, once again, that we are justified only in considering stationary those observers who feel no forces whatsoever.

An accelerated observer carves spatial slices that are warped.

General relativity provides the choreography for an entwined cosmic dance of space, time, matter, and energy.

The conclusion we draw is that even in general relativity, empty spacetime provides a benchmark for accelerated motion.

Although the issue is still debated, as we’ve now seen, the most straightforward reading of Einstein and his general relativity is that spacetime can provide such a benchmark: spacetime is a something.

Entangling Space WHAT DOES IT MEAN TO BE SEPARATE IN A QUANTUM UNIVERSE?

The World According to the Quantum

Quantum mechanics shows that the best we can ever do is predict the probability that an experiment will turn out this way or that. And as quantum mechanics has been verified through decades of fantastically accurate experiments, the Newtonian cosmic clock, even with its Einsteinian updating, is an untenable metaphor; it is demonstrably not how the world works.

Physicists call this feature of the universe locality, emphasizing the point that you can directly affect only things that are next to you, that are local.

The Red and the Blue

Roughly speaking, even though the two particles are widely separated, quantum mechanics shows that whatever one particle does, the other will do too.

Classical physics predicts that electrons fired at a barrier with two slits will produce two bright stripes on a detector. (b) Quantum physics predicts, and experiments confirm, that electrons will produce an interference pattern, showing that they embody wavelike features.

We see that even individual, particulate electrons, moving to the screen independently, separately, one by one, build up the interference pattern characteristic of waves.

Probability and the Laws of Physics

When we locate an electron, we always find all of its mass and all of its charge concentrated in one tiny, pointlike region.

The wave, Born proposed, is a probability wave.

The probability waves envisioned by Born also have regions of high and low intensity, but the meaning he ascribed to these wave shapes was unexpected: the size of a wave at a given point in space is proportional to the probability that the electron is located at that point in space. Places where the probability wave is large are locations where the electron is most likely to be found. Places where the probability wave is small are locations where the electron is unlikely to be found. And places where the probability wave is zero are locations where the electron will not be found.

After calculating the purported probability wave for the electron in a given experimental setup, we carry out identical versions of the experiment over and over again from scratch, each time recording the measured position of the electron. In contrast to what Newton would have expected, identical experiments and starting conditions do not necessarily lead to identical measurements. Instead, our measurements yield a variety of measured locations. Sometimes we find the electron here, sometimes there, and every so often we find it way over there. If quantum mechanics is right, the number of times we find the electron at a given point should be proportional to the size (actually, the square of the size), at that point, of the probability wave that we calculated. Eight decades of experiments have shown that the predictions of quantum mechanics are confirmed to spectacular precision.

Over the last eight decades, the ubiquity and utility of quantum mechanical probability waves to predict and explain experimental results has been established beyond any doubt. Yet there is still no universally agreed-upon way to envision what quantum mechanical probability waves actually are. Whether we should say that an electron’s probability wave is the electron, or that it’s associated with the electron, or that it’s a mathematical device for describing the electron’s motion, or that it’s the embodiment of what we can know about the electron is still debated.

Even though he could not say what it was, Einstein wanted to convince everyone that there was a deeper and less bizarre description of the universe yet to be found.

The probability wave encodes the likelihood that the electron, when examined suitably, will be found here or there, and that truly is all that can be said about its position. Period.

A probability wave with a uniform succession of peaks and troughs represents a particle with a definite velocity. But since the peaks and troughs are uniformly spread in space, the particle’s position is completely undetermined. It has an equal likelihood of being anywhere.

Thus, while quantum mechanics does not give definitive answers regarding particle speeds or positions, it does, in certain situations, give definitive statements regarding the relationships between the particle speeds and positions.

Bell and Spin

First, particles—for example, electrons and photons— can spin only clockwise or counterclockwise at one never-changing rate about any particular axis; a particle’s spin axis can change directions but its rate of spin cannot slow down or speed up.

Second, quantum uncertainty applied to spin shows that just as you can’t simultaneously determine the position and the velocity of a particle, so also you can’t simultaneously determine the spin of a particle about more than one axis.

But if you measure an electron’s spin about any randomly chosen axis, you never find a fractional amount of spin. Ever. It’s as if the measurement itself forces the electron to gather together all its spinning motion and direct it to be either clockwise or counterclockwise about the axis you happened to have focused on. Moreover, because of your measurement’s influence on the electron’s spin, you lose the ability to determine how it was spinning about a horizontal axis, about a back-and-forth axis, or about any other axis, prior to your measurement.

Bell found that there is a bona fide, testable consequence associated with a particle having definite spin values. By using axes at three angles, Bell provided a way to count Pauli’s angels.

A particle, according to quantum theory, cannot have a definite position and a definite velocity; a particle cannot have a definite spin (clockwise or counterclockwise) about more than one axis; a particle cannot simultaneously have definite attributes for things that lie on opposite sides of the uncertainty divide.

Einstein, Podolsky, and Rosen set out to show that quantum mechanics provides an incomplete description of the universe. Half a century later, theoretical insights and experimental results inspired by their work require us to turn their analysis on its head and conclude that the most basic, intuitively reasonable, classically sensible part of their reasoning is wrong: the universe is not local. The outcome of what you do at one place can be linked with what happens at another place, even if nothing travels between the two locations—even if there isn’t enough time for anything to complete the journey between the two locations. Einstein’s, Podolsky’s, and Rosen’s intuitively pleasing suggestion that such long-range correlations arise merely because particles have definite, preexisting, correlated properties is ruled out by the data. That’s what makes this all so shocking.

This sounds totally bizarre. But there is now overwhelming evidence for this so-called quantum entanglement. If two photons are entangled, the successful measurement of either photon’s spin about one axis “forces” the other, distant photon to have the same spin about the same axis; the act of measuring one photon “compels” the other, possibly distant photon to snap out of the haze of probability and take on a definitive spin value—a value that precisely matches the spin of its distant companion. And that boggles the mind.

Particle properties, in this majority view, come into being when measurements force them to—an idea we will examine further in Chapter 7. When they are not being observed or interacting with the environment, particle properties have a nebulous, fuzzy existence characterized solely by a probability that one or another potentiality might be realized.

TIME AND EXPERIENCE

The Frozen River DOES TIME FLOW?

Does time really flow? If it does, what actually is flowing? And how fast does this time-stuff flow? Does time really have an arrow? Space, for example, does not appear to have an inherent arrow—to an astronaut in the dark recesses of the cosmos, left and right, back and forth, and up and down, would all be on equal footing—so where would an arrow of time come from? If there is an arrow of time, is it absolute? Or are there things that can evolve in a direction opposite to the way time’s arrow seems to point?

Does Time Flow?

Yet, as hard as physicists have tried, no one has found any convincing evidence within the laws of physics that supports this intuitive sense that time flows. In fact, a reframing of some of Einstein’s insights from special relativity provides evidence that time does not flow.

A less than widely appreciated implication of Einstein’s work is that special relativistic reality treats all times equally. Although the notion of now plays a central role in our worldview, relativity subverts our intuition once again and declares ours an egalitarian universe in which every moment is as real as any other.

The Persistent Illusion of Past, Present, and Future

Observers moving relative to each other have different conceptions of what exists at a given moment, and hence they have different conceptions of reality.

Every moment is. Under close scrutiny, the flowing river of time more closely resembles a giant block of ice with every moment forever frozen into place.

Human language is far better at capturing human experience than at expressing deep physical laws.