Showing posts with label time. Show all posts
Showing posts with label time. Show all posts

Friday, January 25, 2013

Dark Energy: Too Big To Fail

[1/31/13 update: Many thanks to David Wiltshire for clarifying some points in the comments, and for addressing critics of his ideas. -EC]

According to today’s mainstream science, about 71% of the Cosmos is made of something that scientists have never seen, detected, directly observed, or even indirectly observed. It’s “dark energy,” first described in the late 1990s as a repulsive or anti-gravitational property of empty space. By measuring supernovae in distant galaxies, astronomers inferred that not only is the universe getting larger, the expansion is getting faster with time. Physicists started speculating about what might be responsible for the acceleration, and the newly minted concept of dark energy quickly became the accepted explanation. In fact, today it’s built into the standard cosmological model of a universe that expands with an ever-accelerating rate.

Dark energy has also gone mainstream: As viewers of popular-science TV programs know well, in the very distant future, the repulsive effects of dark energy may become so dominant that they tear apart galaxies, stars, planets — eventually even the atoms that currently make up your body — in a highly dramatic “big rip” that marks the end of the universe.

From the outset, the concept of dark energy seemed to me like a bad idea. We had a set of observations we didn’t fully understand, and in response, we externalized the problem onto some unseen but supposedly real agent “out there” that must be to blame. It didn’t sound like the best approach. It seemed very possible that we misinterpreted the supernova measurements, so why the rush to invent a brand new form of energy (which would need to comprise three-quarters of the universe!) to explain this interpretation? Surely, no one can say that all other alternative explanations had been exhausted. Inventing dark energy was a bit like losing your homework assignment, and then promptly deciding that your family must have an invisible and undetectable dog who ate it.

It turns out that in 2007, David Wiltshire of New Zealand’s University of Canterbury explained how the apparently accelerating expansion of the universe could be an illusion due to our perspective in the Milky Way. According to Einstein’s general theory of relativity, a clock can run at different rates depending on the local strength of gravity; near a massive star, for example, a clock will run more slowly than an identical clock positioned far away. From the perspective of an observer close to the star, everything (including the nearby clock) will appear to be running normally, while the distant clock seems to run fast; to an observer near the clock in deep space, meanwhile, the local time will appear to pass normally as usual, but from that perspective, the gravitationally bound clock seems to run slow. Gravity’s effect on time is universally accepted. If your GPS receiver didn’t account for general relativity, your navigation directions would lose accuracy in minutes.

Wiltshire’s insight was that light from the supernovae traverses huge stretches of space where there is little to no matter, so clocks there would run fast as judged by observers near galaxies, such as ourselves. When astronomers study supernovae on the other side of these voids, the measurements are affected by the fact that the voids are expanding faster than the space closer to us (as judged here on Earth). According to Wiltshire’s calculations, if you lived in one of these voids, you’d judge the universe to be about 18 billion years old — several billion years older than how things appear here, where matter and gravity slow clocks as well as the expansion of space. The end result is that the Milky Way resides in a “Hubble bubble,” a local region beyond which all of the rest of the universe appears to be expanding away, at an accelerating rate. Similarly, if you lived in a galaxy on the other side of a large void, the Milky Way would appear to be accelerating away from you. You would be living in a Hubble bubble there, too.

The first time I read about Wiltshire’s insight, my reaction was disbelief: “Surely they must have thought of that!” But apparently, they hadn’t. The equations that cosmologists use to study the universe’s large-scale structure are extremely difficult to work with, so some simplifying assumptions have been made in order to construct workable models. One of these is to describe space everywhere as a uniformly expanding fluid. This assumption has been a part of the mathematics of cosmology (in the so-called Friedmann equations) since 1922, before we even knew there were other galaxies beyond our own. Given the brutally difficult equations, which could not otherwise be solved, the Friedmann solutions have been a part of cosmology bedrock ever since. However, we now know that the large-scale structure of the universe is not at all uniform; there are walls of galaxy clusters separated by enormous voids, so if Einstein is correct, the universe is not a uniformly expanding fluid. Time flows, and therefore expansion happens, faster in some places than in others.

Wiltshire argues that a necessarily uneven expansion of the universe previously hadn’t been considered because (1) physicists are used to considering relativistic effects on time only in the extreme conditions of black holes and particle-accelerator experiments, and (2) they have assumed that such effects in intergalactic space would be extremely weak. They are indeed weak, but Wiltshire has done the math to show how the cumulative effects become huge over billions of years and across vast distances of space.

According to Google Scholar, Wiltshire’s original paper has been cited 123 times to date; it’s certainly not being ignored. There appear to be few or no papers that refute the concept of non-uniform expansion due to relativistic effects. In fact, most of the papers build upon the idea.

So why, in 2013, is “dark energy” still a thing? Beats me! In his excellent book The Trouble With Physics, Lee Smolin describes how modern physics can unwittingly construct opaque, monstrous theories that become intellectual dead-ends with no practical uses, but which nevertheless persist for sociological and financial reasons. First, a few innocent working assumptions are laid down, and then models are built on those assumptions, and then others build upon those models, and so on — until there’s a mini-industry of researchers working in the field and collecting funding, with the original assumptions rarely re-examined. This is what has happened with dark energy: Even though we now have a viable explanation for the appearance of cosmic acceleration, a bad alternative has become entrenched. Careers have been forged based on the cosmological model that includes dark energy. And in a potential embarrassment for the ages, the 2011 Nobel Prize in Physics was awarded for what the prize committee called “the discovery of the accelerating expansion of the universe.” Dark energy is too big to fail!

Beyond academia, the public never should have been asked to have faith in a mysterious, undetectable force that’s out there but at the same time all around us. Invoking such ideas makes it impossible to maintain the clear distinctions between religion and science, at least in the public eye. But even today, the History Channel tells us “we now know” that most of the universe is made of mysterious dark energy. NASA does the same, on a public-education page called “Universe 101.” Houston, we have a problem.

Perhaps there are physicists who secretly hope the dark-energy concept will gradually die out. But in popular science, which is usually well behind the curve, the myth of dark energy will undoubtedly linger for years on the websites and the TV programs. We deserve better.

Monday, January 14, 2013

Why The Speed Of Light Is Constant

When many people first learn that the speed of light is constant — that it’s the same everywhere in the universe, and is measured the same by all observers — it all seems kind of arbitrary. It’s strange enough that the speed of light is a “cosmic speed limit,” beyond which no object can go. But, how can the speed of anything possibly be a constant value? When I’m in an airplane and I walk forward up the aisle, I am going faster than the plane itself, something that could be verified by an observer on the ground. My total speed, relative to the ground, will be the speed of the plane plus my walking speed. (Subtract the speed if I’m walking in the other direction, toward the tail.) Yet, if I measure the speed of a light beam coming from a laser aboard a plane or a spaceship, I’ll always get the same result of 186,000 miles per second, whether the beam is facing forward, backward, or sideways, or even if it’s beamed from the spaceship in any direction and measured on the ground. Why?

It actually has to be this way. A world in which the speed of light varied might be impossible logically (see below), or at least could be so messed up and incoherent that complex structures such as galaxies and intelligent life might not be possible.

Consider a thought experiment: You set up a rapidly rotating beacon in deep space, with a radio antenna on it. (Radio waves are an invisible form of light.) The antenna is transmitting a radio signal consisting of a sequence of natural numbers: 1, 2, 3, and so on. Far away from the transmitter, you tune in your receiver and wait for the beacon to start spinning and transmitting the sequence. What kind of signal will you receive?

That depends on whether the speed of light is constant or not. Let’s imagine that it isn’t. In that case, the speed of the radio signal in your direction would change according to the velocity of the transmitting antenna, as with the example of walking up the aisle of an airplane: As the beacon spins, sometimes the antenna would be coming toward you — which would “throw” the signal faster in your direction — and sometimes it would be moving away, which would subtract some miles per hour from the signal’s speed. So, parts of the signal would be traveling toward you faster than other parts. Naturally, if the speed of different portions of the signal is different, the faster portions will reach you sooner than the slower portions. This effect would worsen the farther away you are from the beacon, and the faster the beacon is spinning. You might end up receiving a steady sequence of numbers like this:

1 - 2 - 3 - 7 - 8 - 9 - 4 - 5 - 6 - 10 - 11 - 12 - 16 - 17 - 18 - 13 - 14 - 15 ...

Here, the 7 - 8 - 9 segment is arriving sooner than the 4 - 5 - 6 segment, even though it was actually transmitted later. If this were a television signal rather than a sequence of numbers, with the antenna on a large rotating disc, the program would be really messed up. A political candidate might be seen giving a concession speech, followed by a speech where he seems confident he’ll win. I’m not sure that causal impossibilities would result from incoherent information flying around the universe,* but surely the formation of large structures such as galaxies, responding gravitationally to far-away moving bodies, would be affected (if gravity would even exist in such a universe).

Now let’s consider what happens in a world where the speed of light is constant. In this case, all portions of the signal are transmitted at the same speed relative to you, even as the beacon rotates, so no portion reaches you faster than any other. The numbers arrive in the correct sequence, just as they were transmitted. However, the only way this can possibly work (as Einstein showed) is if measurements of time and distance change for various observers. For a transmitting antenna on a rotating beacon, this produces a relativistic Doppler effect — a slowing down and speeding up of the signal, almost like a vinyl record being played back off-center, something like this:

1 ---- 2 --- 3 -- 4 - 5 - 6 -- 7 ---- 8 --- 9 -- 10 - 11 - 12 -- 13 ---- 14 --- 15 ...

If the TV antenna on the disc were transmitting American Idol, you’d see the show from beginning to end without interruption — no unexpected spoiler — but the slowing down and speeding up might make it sound as if the singer and the band can’t stay on key to save their lives (which in reality happens sometimes).

As it turned out, the constant speed of light was confirmed by the Dutch astronomer Willem de Sitter in 1913, through observations of double star systems, where two stars are rotating around each other closely. He realized that if the speed of light varied as the stars advanced toward us or receded away, the orbits would appear erratic. The system might appear blurry or scrambled and incoherent, and from great distances the laws of motion would appear not to work at all. However, such was not the case in any system that de Sitter observed, and this was used as evidence to support Einstein’s special theory of relativity and the constancy of the speed of light. All observations made to date support the same conclusions.

Personally, I think that the constant speed of light is a hint that the universe is fundamentally informational (the “it from bit” hypothesis proposed by the great physicist John Wheeler). This idea says that matter/energy and spacetime emerge from a deeper layer of existence that’s based purely on information. In our universe, information in the form of light always passes from point A to point B in a coherent, sequential fashion, for every observer — it’s space and time (and even mass) that all change accordingly to suit it. There might be a lesson there.


* I haven’t been able to come up with a paradox of cause and effect, resulting just from some information traveling faster than other information. In the days when some news came by rail and some by telegraph, you might have heard that Lincoln’s assassin had been caught before you heard that Abe had been shot — but nobody went back in time to kill John Wilkes Booth. Still, I suspect there is a thought experiment that would show it couldn’t work. If you have any ideas, please comment.

Tuesday, February 7, 2012

Resolving the “Twin Paradox”

Fans of science-fiction space travel know that if someone goes on a rocket at close to the speed of light, he will age more slowly than someone back home. Returning to Earth and reuniting with a twin, he would find that the twin had aged more, perhaps by years. If the trip is long enough and gets really close to the speed of light, the returning traveler could find an Earth that’s millions of years in the future, maybe even devoid of human life. For many people, that’s the “twin paradox” — how could something this strange possibly happen?

Actually, twins aging differently isn’t the issue; no paradox there. The “paradox” lies in the fact that according to relativity (the very effect that causes the twins to age differently), the ideas of motion and rest are relative. Suppose rather than leaving from Earth, the experiment is done in deep space. Twin A takes off and leaves Twin B behind. But, once the twins are separated, who’s to say which twin is moving and which is at rest? After all, if you consider the picture from the perspective of either twin, it’s the other one that’s moving. Twin A sees Twin B receding rapidly in the rear-view mirror, just as if Twin B was the one who had taken off. In relativity, the question of moving vs. stationary depends upon the perspective of the observer. Shouldn’t this mean that the aging will be equal for both twins when they finally reunite? That’s the “twin paradox.”



The twin paradox isn’t really a paradox, because it can be resolved in several ways. For one thing, the situation isn’t symmetrical. One of the twins, Twin A, has to turn around at some point, whereas Twin B can just cool his heels. Physicists say that Twin B remains in an inertial reference frame — a state of constant motion (or rest), without any change in speed. Twin A, though, spends portions of his trip in two different inertial reference frames, one on the way out, and one on the way back, and in between he has to slow down, stop, and accelerate in the other direction. (Or, he could make a circular U-turn, but that still counts as an acceleration.) It’s clear how changing velocity affects the local passage of time, from the formula known as the Lorentz transformation: Higher velocities mean slower clocks, so as Twin A slows down, his onboard clock begins speeding up. Twin B’s velocity never changes, though. Therefore, it’s wrong to say the twins are moving in identical ways relative to the other.

Thinking this through, the situation is a bit peculiar. How does Twin A and his mechanical onboard clock “know” that they had turned around? Suppose Twin B, rather than staying put, secretly takes off in the other direction, goes even faster, turns around, and races back to the starting point, just in time to meet the returning Twin A. In that case, Twin B would age slower than Twin A — who, having just gone on a fast trip that included turning around, expects to meet an older Twin B. Instead he finds a younger Twin B. How does Twin B (and his clock) know that he had gone farther and faster than Twin A?

The solution all comes down to the turning-around part: acceleration. When you’re in an inertial reference frame, you can’t tell whether you’re moving or not. You could be sitting in your living room, or you could be on a rocket ship going 99% the speed of light. Close your eyes and the situations are indistinguishable. However, when you’re slowing down or speeding up, or making a turn, you can definitely tell that something’s going on. You feel a pull toward one direction, just as you do in a car with the brakes applied. This acceleration* is what causes a clock (biological or otherwise) to slow down. For Twin B who secretly went on a really fast trip, his larger accelerations slowed down his biological clock even more than Twin A’s, who now needs a facelift to look as young as his twin again.

When you add gravity into the mix, it gets even stranger. Twin A — rather than turning on the reverse-thrust engine to slow down and turn around — could instead have a close call with a massive star, and like Halley’s comet, take a tight orbit around and be fired back toward his starting point. In such a situation, the ship is in free fall with respect to the star, and counter-intuitively, doesn’t feel the acceleration as it gets slung back toward Twin B. Our traveler could continue his game of three-dimensional billiards in the weightless environment of his ship, even as it hooks sharply around the star. If there were no windows, he might not even know when he was passing behind and starting to head back. Yet incredibly, the curvature of space from the star’s gravity would slow down time aboard the ship. While the traveling twin works on his weightless billiards game, the stay-at-home twin would have the time to master not only billiards but also croquet and miniature golf, much to Twin A’s later envy.

The “twin paradox” is one of those cases where the universe just works out perfectly right, out of sheer mathematical consistency. Relative velocity determines the rate at which clocks tick; Einstein showed that this malleability of time is necessary in a universe where the speed of light is measured the same by all observers. Therefore, changing velocity (accelerating) changes the local rate at which time passes. All of this can be calculated from the Lorentz transformation. But a star’s gravity will also slow down time for Twin A and his ship, by exactly the same amount as if he had used his engines to slow down and turn around. The curvature of space due to gravity — by having the ability to sling a spaceship around and back in the other direction, on momentum alone — simply has to make an adjustment to the ship’s onboard clocks. Otherwise the math wouldn’t work out. And then we’d have a real paradox.

Anything in our universe with mass slows down clocks in its wake. For the Earth, the effect is not only measurable, it needs to be built into your GPS to avoid large, cumulative errors that would render it useless. Thanks to Einstein’s discovery, you can reliably arrive at your destination. Isn’t it nice when things work out?



* The term “acceleration” refers to both slowing down and speeding up. Slowing down is simply accelerating in the opposite direction.

Monday, February 6, 2012

The Zero Universe

The world is like a great theater where we watch history unfold. This colossal story features a cast of billions, who not only witness the arc of its epic plot, but also actively take part in its creation. Look around you; it’s raucous and noisy inside this theater we call “the world.” But, if it were possible for us to step outside the theater and take a look, there would be nothing.

Inside, the theater is a mind-boggling swirl of information, actions, and reactions; from the outside, as seen by a cosmic Google Earth beyond space and time, it’s completely empty. I am not just making a cute metaphor here — this is a real feature of our universe, with profound implications.

It seems that in the final analysis, when all things are considered, the universe adds up to exactly zero. For one example (there are others at the bottom), consider the relationship between space and time. Bear with me as I review an idea from high-school geometry. If we have a triangle that includes a 90° angle, we can use the Pythagorean theorem to determine the length of the diagonal from the length of the right-angle sides:

a2 + b2 = c2

where a and b are the lengths of the right-angle sides, and c is the length of the diagonal. A nifty geometrical diagram proves why this is true. If you make a square box along each of the three sides, then each box has an area of the length of that side, squared. The area of the smaller squares adds up to the area of the largest square: If a = 3 and b = 4, then c = 5.


The Pythagorean theorem works in three dimensions, too. If you see a blimp in the sky, you can calculate the exact straight-line distance to the blimp by knowing its altitude above the ground (the value z), as well as how far east-west (x) and north-south (y) you'd have to go to get right under the blimp:

x2 + y2 + z2 = d2

where d is the distance to the blimp. I don't have a 3D diagram, but you can prove it for yourself with a little effort.

Now it gets interesting. This trick extends to four dimensions. Time is typically cited as the fourth dimension. Does the decidedly non-geometric idea of time work into the Pythagorean theorem? Incredibly, it does — but first, you have to convert the time measurement into a distance-like measurement. Then, the total distance you’re calculating is the spacetime distance in the bizarre four-dimensional world where east-west, north-south, up-down, and earlier-later mean the same thing, only in eight different directions. Represented by the letter s, spacetime distance (also known as a Minkowski interval) is determined by an amazing formula. Let’s break it down:

x2 + y2 + z2 – (ct)2 = s2

As before, x is the distance (for example) to the east, y is north, and z is up, but we’ve added a fourth term for time (t), which gets multiplied by a constant, c. Notice the minus sign before the term for time. When it comes to distance through spacetime, elapsed time counteracts spatial distance, and vice versa: If we travel a distance through space, and do it in a very short interval of time,* the distance traversed is effectively reduced. This is why a space traveler could reach stars across the galaxy within their lifetime if they got close enough to the speed of light. Time goes in the opposite “direction” of space!

That constant, represented by c? It’s the same c that represents the speed of light in equations such as E = mc2. What better number to convert units of time (seconds) into a distance-like measurement — after all, we know that for light, there are 186,000 miles per second. See what Einstein did there? The speed of light is more than just a speed; it’s a universal conversion factor that turns time into a distance-like measurement. By treating time as a negative and multiplying it by c, we can exchange time and space in our formulas as readily as nature exchanges them. That’s what special relativity is all about.

This extra meaning of the speed of light has interesting consequences. If you could look out the window of a rocket going at the speed of light, you wouldn’t “c” a thing — the entire universe would vanish to a point through Lorentz contraction. In order for space and time to enter into what we call “reality,” they must be measured by an observer, something not traveling at the speed c. In the real world, that’s anything with mass. For any observer with mass (make your own couch-potato joke), zero spacetime distance separates into the components familiar to us: a measurable amount of space and a measurable amount of time.

It’s as if the presence of mass causes “zero” to pull apart into the familiar ideas of spatial distance and temporal duration, like taffy. But since the universe is by definition everything there is, you have to be inside the universe to witness this incredible stretching apart of zero, to experience space and time as different things. If you were taking in the all-seeing “God’s-eye view” from a timeless, spaceless, massless perspective outside, you would see the same thing the speed-of-light traveler sees — nothing. To witness the action, you have to be inside the theater, in your seat.

Space and time cancel out to exactly zero for the universe as a whole. But that’s just one example of the zero-sum nature of the physical world. A few others:
• The mass–energy of everything in the universe is exactly balanced by the universe’s gravitational energy. The latter is expressed as a negative number, just as time is in the spacetime formula. A while back Alex Filippenko, who’s a familiar smiling face to science-TV geeks, co-wrote an essay about how this means the universe may have come from “nothing at all.” Like the pulling apart of space and time, mass–energy and gravitational energy were also pulled apart in the Big Bang.
• For similar reasons, the net charge of the universe is generally believed to be zero, with the number of positively charged particles equaling the number of negative. (This is unproven.)
• Certain pairs of phenomena, like electricity and magnetism or mass and the curvature of space, are linked such that they seem to keep each other in check. The great physicist John Wheeler was fascinated by these “automatic” connections, pointing out how they are constrained together by zero sums, the way the ends of a see-saw are always the same total distance from horizontal. “That this principle should pervade physics, as it does,” he asked in 1986, “is that the only way that nature has to signal to us a construction without a plan, a blueprint for physics that is the very epitome of austerity?”

On the one hand, it’s surprising that quantities totaling zero show up again and again in nature. But on the other it makes sense, if the universe is a closed system incorporating everything there is. As a teen I remember being into the Taoist idea of Yin and Yang — I thought that in the final analysis, the universe as a whole couldn’t be anything but perfectly balanced. On a level deeper than I imagined, I may have been right.


* Slow speeds (which mean long elapsed times) cause the time part of the formula to overwhelm the space part, resulting in large spacetime distances. Spacetime distances only get small when you approach the speed of light, for example, covering 186,000 miles in 1.1 seconds — then the (negative) time part almost cancels the space part.