Showing posts with label relativity. Show all posts
Showing posts with label relativity. Show all posts

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.

Friday, March 9, 2012

Gravity Is Not A Rubber Sheet

Every physics demonstration of gravity uses the familiar “rubber sheet” model: We are shown a stretched piece of rubber, or perhaps the surface of a trampoline. A heavy ball is placed in the middle, distorting the sheet. Now a smaller ball, pushed in the general direction of the heavy ball, will follow a curved path, as if “attracted” by the mass. If given a particular kind of shove, it will circle around the heavy ball for a while, “orbiting” like a planet around a star. Thus the model demonstrates how an object with mass warps the fabric of space, causing the paths of other objects to curve in the direction of the larger object. Objects follow straight paths through space, but if that space happens to be curved by a massive object nearby, their paths will curve. Since Einstein, we’ve known that this is what causes gravitational attraction.

When I was first getting interested in physics, the rubber-sheet model of gravity bothered me. For one thing, it only works in gravity! It seemed that the rolling ball was just curving downhill. Tilt the sheet without warping it, and its path will curve the same way. In the weightlessness of the International Space Station, I figured, the model wouldn’t do anything. I didn’t like that gravity was required in order to demonstrate how gravity works. It was like a model that shows where wind comes from, but which only works when it’s windy.

Something else disturbed me. When the rubber-sheet model is presented in diagram form (in books, for example), the diagrams are often inconsistent. Empty space is depicted as a flat grid of straight lines, but when a massive object is added, some of the lines suddenly form circles. The graph-paper grid turns into a pushed-in dartboard or spider-web pattern, with circular elements representing potential orbits around the mass. Thinking that maybe I had discovered something, I wondered: At what point do the open-ended straight lines of empty space start joining together to form closed circles? If we took an empty region of space and gradually started adding mass to it, when would the circles appear? I was perplexed — the diagrams never show that transition, just the before and after!

What’s wrong with this picture?

The problem of course lies not in Einstein’s theory, but in the rubber-sheet model. It isn’t a perfect analogy for gravity.

It’s a coincidence that real gravity on Earth causes a rubber sheet to warp in a manner that suggests the warping of space. You could just as easily turn the model upside down, and push the ball up against the rubber sheet, and the sheet would be warped in the same way (just in the opposite direction). The rubber-sheet model of gravity is intended to demonstrate how a massive object causes space to curve, so it’s the warping of the sheet that’s important, not the direction.

When a two-dimensional surface is curved into a third dimension, its geometry changes. No longer do the laws of Euclid, which most of us learned in 9th grade, apply: The angles of a triangle do not add up to 90°, for example. In ordinary geometry, two parallel lines never meet; in the non-Euclidean geometry of a curved surface, parallel lines can meet. Imagine that you and a friend began walking from the equator to the north pole. Initially, your paths would be exactly parallel, but since the Earth’s surface curves, the paths would intersect at your destination. Similarly, if two objects were moving in parallel from empty space toward a star, their paths would eventually converge — even with no sideways forces acting upon them.

As it happens, the rubber-sheet model would work in zero gravity, if you warped the sheet with some other force (say, by pushing the end of a broomstick against it), and if you got the rolling ball to remain on the surface somehow (perhaps with a bit of static electricity). In that case, the ball’s path would appear to curve as it attempted to follow a straight line on this non-flat surface. And two balls, nudged along parallel paths toward the depression, would approach each other as the surface under them began to curve.

As for the grid that’s often laid over the rubber sheet, it’s only there to help you see the shape of the surface. The straight or circular lines are a human invention; there is no such grid in space. The actual paths that objects trace through warped space are, well, the actual paths that they trace. These can be circles, ellipses, parabolas, or hyperbolas, depending on the trajectory of the object.

Planets and comets go their own way — they have no use for grid lines.

The rubber-sheet model does give a general idea of how gravity deflects the path of an object. But it’s a crude demonstration, as the Earth’s gravity fouls the geometric effect that the model is intended to demonstrate.* When you see the rolling ball get “attracted” to the larger ball, much of that deflection is just the ball rolling downhill, as it would on a tilted, flat surface. A true tabletop demonstration of gravity, where objects follow stable orbits along a surface due to geometry alone — would be interesting to watch. Until then, don’t take the conventional version too seriously.



* Consider what would happen if you rolled a ball inside the surface of a vertical tube in a frictionless vacuum. Under Earth’s gravity, the ball would inevitably spiral down to the floor. But in zero G, it would follow a circular path forever. This circular orbit, not the spiral, is the accurate representation of the “straight-line path” that would be followed on the surface due only to its geometry.

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.

Thursday, April 21, 2011

The Case For Metaphysics

In addition to my work as a comedian and musician, I’ve collaborated on several YouTube videos exploring the theory of the biocentric universe. This is the radical proposition that the activity of our evolving biological superorganism produces the universe that we see — that a pre-existing universe of nonliving matter did not create the first living thing through chance, some ten billion years after a real and actual event we call the Big Bang. Instead, the theory says, the universe is effectively only as old as life itself. Some find this concept so outrageous, they think it must be a part of my satire, but it isn’t. I’m fascinated by this revolutionary, spectacularly godless cosmological view, in which the universe began as nothing in particular, the echoes of the Big Bang are the now-observed physical back-story for that beginning, and quasars undergo retrocausality through decoherence across billions of light years.

The basic idea is that nothing in the universe comes predefined; by default, the entire thing is but a swarm of probability, just like the “electron cloud” of an atom. We know that electrons are not little dots of electron-stuff that whizz around the atomic nucleus like tiny planets. Physics in the 20th century revealed that such electrons can be described only in terms of probability — the probability that a person, machine, etc., will find an actual electron at a specific location, if that location is checked. This is a well-known principle of quantum mechanics.

That principle of probability-by-default may extend to the entire universe; for a half-century, physicists have entertained that the whole thing is a quantum system. But for the purposes of this discussion, it comes down to the following question: Are the physical properties of all particles of matter independently predefined and absolute, possessed intrinsically by each individual particle? Or, are these properties relevant only with regard to the particle’s interaction with other things, such as other particles or living observers? Is there, for example, a specific beta-radiation particle with a specific momentum and charge traveling from the far side of the Alpha Centauri star system, right now?

Most science enthusiasts would answer yes without hesitation, because that’s the view of the universe we live with. In Western scientific tradition, we assume that the workings of the physical world occur on their own in the background, regardless of whether we happen to be there to watch or know anything. Observation and measurement are merely the process of discovering what’s already in predefined existence, we believe. But are we sure this is entirely true? To paraphrase the classic zen question: If a particle is emitted by Alpha Centauri and no one is around to see it, is it really there?

For those averse to anything philosophical-like, this is where the hackles go up. When we speak of the existence or nonexistence of an unobserved object, we’re making a distinction that’s metaphysical — we’re dealing with the fundamental nature of being, something that’s outside the realm of ordinary observation and measurement. Such a conjecture seems to offer no scientific value, because it can’t be directly tested in the laboratory. As a result, there seems to be a pervasive attitude that ideas involving metaphysics have no real value to the modern world at all. On the biocentric videos, many comments can be summarized thus: “This is just philosophy. You can say all you want that things don’t exist if we aren’t around to perceive them, but that’s bullshit. You’re only changing the definition of the word ‘exist.’ Things exist whether we’re there to perceive them or not.”

This is a naive argument. One cannot dismiss a metaphysical position on the grounds that it is “just philosophy,” because whichever side of the issue you come down on, there is no escaping metaphysics. To assert that an object does possess absolute properties — qualities that exist independently of its interactions with other things — is to take a metaphysical position as well. Chew on that idea awhile. The assumption of an absolute defined particle somewhere off in the galaxy is equally “just philosophy,” and equally “bullshit,” as the idea that it’s only potentially there, not actually there. Having been brought up in the tradition of Western thought, we all carry around this assumption of absolute physical characteristics, possessed intrinsically and independently by every last microscopic object in the universe, as if assigned on the day of Creation by an omnipotent God. In physics, this assumed principle is known as realism. But the brute fact remains, there is no evidence whatsoever supporting absolute realism. None! If you’re a thinking person, you should seriously ask yourself: How scientific is it to base an entire physical worldview on a metaphysical position, a possibly flawed fundamental assumption for which there is no supporting empirical evidence?

Now, here’s where it gets really interesting. Quantum mechanics has been baffling physicists and lay people alike for 80-odd years. The findings of decades of experiments, such as delayed choice and quantum eraser, are extremely difficult to square with the traditional metaphysical foundation of absolute, pre-existing properties of matter. This is partly why there are so many quantum-mechanics interpretations; those that try the hardest to accommodate absolute realism, such as Bohmian mechanics and the transactional interpretation, are complex, bizarre, and highly controversial. But, believe it or not, every finding from every quantum mechanics experiment ever performed is consistent with the alternative metaphysical framework, where the physical properties of matter are relevant only in relation to systems capable of measuring them somehow. This concept follows quite simply from a broad generalization of Einstein’s special relativity, which showed that velocity and simultaneity are never absolute and can be described only in relation to an observer’s frame of reference. (See our video titled It’s All Relative.)

The great physicist Richard Feynman once said that philosophy is as useful to physicists as ornithology is to birds. This is the “shut up and calculate” view, in which physics is employed only to predict the behavior of physical systems — the purely empirical approach that shuns any discussion of meaning or the “true” fundamental nature of things. But are numbers and calculations all we want to get out of science? After all, the Ptolemaic model of astronomy was surprisingly accurate at predicting eclipses and other events — but the reason we adopted the later Copernican model wasn’t only to improve the accuracy of astronomical calculations. Turns out, it’s quite useful to know that the planets really do orbit the Sun, and do not orbit the Earth while moving on an intricate system of invisible circles or “epicycles,” as was once believed. The Sun-centered model provides the basis for a more fundamental and elegant explanation of what’s really going on in the relationships between the Sun, planets, and Earth.

A fundamental explanation is exactly what some physicists are seeking from the increasingly legitimate theories of observer-centered realism, which profess that observation is an active and intrinsic element in the unfolding of reality. (The biocentric universe is one such theory. Here’s another.) Experiments may soon unlock numerous mysteries that have come on the heels of both quantum mechanics and cosmology. For example, why did the initial conditions of the Big Bang produce a universe that appears to be fine-tuned for life? To answer this question under the standard metaphysics, we either need to appeal to an intelligent God, or invoke multiple universes combined with the anthropic principle, a conjecture that I find unsatisfactory. Neither proposition is testable, so we’re back to basing our explanations on unsupportable assertions — which, I regret to say, is not a scientific endeavor, no matter how many shows about the multiverse are broadcast on the Science Channel. (Paul Davies has chimed in on this. For an exhaustive look at how contemporary science is becoming increasingly “faith-based,” read Lee Smolin’s The Trouble With Physics.)

I know what you’re thinking: Like the multiverse, a metaphysical position cannot be directly tested in the lab, so how can it ever be a part of science? Some theories do prevail despite not being directly testable. Evolution theory, for example, is accepted primarily because a huge amount of evidence, from multiple disciplines, is fully consistent with the theory, to the point where unforeseen details like the genetic code were predicted to exist, and subsequently confirmed. This is basically why multiverse theories are accepted as well: because the conjecture of multiple universes is consistent with the real observation of a seemingly fine-tuned universe. However, quantum mechanics is far more consistent with the metaphysical position of observer-centered realism, compared to the opposing metaphysical view of absolute realism. So if the entire universe is a quantum system, we need to think about what that means for cosmology and the universe’s initial conditions, which we have long assumed to be absolute. Indeed, Stephen Hawking theorizes that the universe may not have had a unique beginning — that its initial conditions existed in quantum superposition, just like the electrons of an atom’s electron cloud. In other words, the initial conditions were not fixed and singular, assigned either by God or by chance. Instead, they are relevant only in relation to today’s universe, in which physicists calculate them from the “top down,” i.e., working backward from the present conditions that we do observe. No intelligent God, or multiverse, necessary.

Personally, I believe that observer-centered realism will be confirmed, albeit indirectly. Just within the past month it was found that molecules of DNA are able to interact with quantum systems in ways that ordinary, non-biological molecules do not. Perhaps this is the first of many discoveries pointing to the fundamental role that biology plays in physics, which will then lead to a revolution in technology and medicine. But that will never happen unless we entertain alternative metaphysical viewpoints about our place in the world as observers. If we take that leap, someday soon we might see the real benefits of interpreting empirical science through a metaphysical lens — which at last will prove that metaphysics isn’t “just philosophy” after all.