Wednesday, November 18, 2009

Fabric of the Cosmos, chapter 3 part II.

In previous chapters, we have examined the development of cosmology up to the time of Einstein. In the second half of this chapter, Einstein eventually examines some of his own previously held suppositions and realizes some adjustments need to be made. He finds, ironically enough, that perspective means a lot. It's a lesson that a lot of us could use to learn, too. Too often, we are either too complacent or too afraid to be outside the box. But outside the box generally is the only place where you can get a good view.

Fabric of the Cosmos
Brian Greene
Chapter Three, part two
Relativity and the Absolute
Is Spacetime an Einsteinian Abstraction or a Physical Entity?

The Bucket, According to Special Relativity

The relativity of time and space requires a dramatic change in our thinking. Yet there is an important point, mentioned earlier and illustrated now by the loaf of bread, which often gets lost: Not everything in relativity is relative. Even if you and I were to imagine slicing up a loaf of bread in two different ways, there is still something that we would fully agree upon: the totality of the loaf itself. Although our slices would differ, if I were to imagine putting all of my slices together and you were to imagine doing the same for all your slices, we would reconstititute the same loaf of bread. How could it be otherwise? We both imagined cutting up the same loaf.

Similarly, the totality of all the slices of space at successive moments of time, from any single observer's perspective, collectively yield the same region of spacetime. The region itself, like the loaf of bread, has an independent existence. Absolute space does not exist. Absolute time does not exist. But according to special relativity, absolute spacetime does exist.

In the first part of chapter three, the idea that creation begins with light was discussed - here is a good point to expand a bit on the creation of the spacetime continuum. The Sages discussed (as we mentioned in previous posts) how the Ain Sof was at first everywhere, but evacuated an area to make the "void" or "womb" where creation could occur. This process is called Tzimtzum.

From Chabad's webpage Tzimtzum - the Principles of Kabbalah:
"...While some Kabbalistic texts speak of a gradual contraction of Divine Power as it streamed into this finite world, eventually reaching a point of complete concealment in this world, the Kabbalah of the Arizal, however, held a different view. According to the Arizal, there was a quantum leap from infinite to finite, calling this leap of states Tzimtzum (contraction).

In order to visualize how this happens, the Etz Chaim of Rabbi Chaim Vital presents the following structure. The power and ability of the Ein Sof is called the Or Ein Sof (the Light of the Ein Sof). Because physical light is perceived as being ethereal and intangible, and because light gives life and warmth, it is often used in Kabbalah as a metaphor for Divine Power.

...In order for creation to take place it was necessary somehow to conceal this infinite Light, thus creating a vacuum for the Finite Light to be revealed.

...Imagine a circle, and the circle is full of the Or Ein Sof. No finite existence may be created within this circle for the Light of the Infinite totally occludes it. The Tzimtzum concealed the Or Ein Sof so that within the circle is left a void within which something finite can be created."

In Einstein's thought, then, according to special relativity it's not just a "void," it's an actual "thing" which is, basically, the "boundaries" of spacetime - the "loaf" which can be sliced into various views and perspectives. Greene continues:

Even though two observers in relative motion slice up spacetime in different ways, there are things they still agree on. As a prime example, consider a straight line not just through space, but through spacetime.

For an object's trajectory through spacetime to be straight, the object must not only move in a straight line through space, but its motion must also be unifrom through time - that is, both its speed and direction must be unchanging and hence it must be moving with constant velocity. The geometrical shape of trajectories in spacetime are independent of the time slicing one uses.

This is a simple yet critical realization, because with it special relativity provided an absolute criterion - one that all observers, regardless of their constant relative velocities, would agree on - for deciding whether or not something is accelerating. If the trajectory an object follows through spacetime is a straight line, like that of the gently resting astronaut, it is not accelerating. If the trajectory an object follows has any other shape but a straight line through spacetime, it IS accelerating. For example, should the astronaut fire up her jetpack and fly around in a circle over and over again, or should she zip out toward deep space at ever increasing speed, her trajectory through spacetime would be curved - the telltale sign of acceleration.

And so, with these developments we learn that geometrical shapes of trajectories in spacetime provide the absolute standard that determines whether something is accelerating. Spacetime, not space alone, provides the benchmark. In this sense, then, special relativity tells us that spacetime itself is the ultimate arbiter of accelerated motion.

Gravity and the Age Old Question

...Mach never really specified a mechanism whereby distant stars and other matter in the universe might play a role in how strongly your arms splay outward when you spin or how forcefully you feel pressed against the inner wall of a spinning bucket. Einstein began to suspect that if there were such a mechanism it might have something to do with gravity.

...In special relativity, to keep the analysis tractable, he had completely ignored gravity. Maybe, he speculated, a more robust theory which embraced both special relativity and gravity would come to a different conclusion regarding Mach's ideas. Maybe, he surmised, a generalization of special relativity that incorporated gravity would show that matter, both near and far, determines the force we feel when we accelerate.

...Also..special relativity, with its central dictum that the speed of light is the fastest that anything or any disturbance can travel, was in direct conflict with Newton's universal law of gravity - the monumental achievement that had for over 200 years predicted with fantastic precision the motion of the moon, the planets, comets, and all things tossed skyward. The experimental success of Newton's law notwithstanding, Einstein realized that according to Newton, gravity exerts its influence from place to place, from the sun to the earth, from the earth to the moon, from any-where to any-there, instantaneously, in no time at all, much faster than light! And that directly contradicted special relativity.

To illustrate the contradiction...[lets say] hostile aliens zap the moon... Newton's law predicts that the water would start to recede from high tide, because of the loss of the moon's gravitational pull, about a second and a half BEFORE you saw the moon disappear from the sky.

...The reason is that, according to Newton, at the very moment the moon disappears its gravitational pull would instantaneously disappear, and without the moon's gravity, the tides would immediately start to diminish. Yet, since it takes light 1.5 seconds to travel the 1/4 million miles between the earth and the moon, you wouldn't immediately see that the moon had disappeared...

Thus, according to Newton's approach, gravity can affect us before light - gravity can outrun light - and this, Einstein felt certain, was wrong.

Einstein's journey toward general relativity began with a key question that Newton, rather sheephishly, had sidestepped two centuries earlier. How does gravity exert its influence over immense stretches of space? How does the vastly distant sun affect earth's motion?

There is a similarity between this problem and the one Faraday and Maxwell solved in the 1800s, using the idea of a magnetic field, regarding the way a magnet exerts influence on things that it doesn't literally touch. So you might suggest a similar answer: ... the gravitational field. And, broadly speaking, this is the right suggestion. But realizing this answer in a manner that does not conflict with special relativity is easier said than done.

Einstein's key breakthrough was tightly linked to the very issue Newton highlighted with the bucket: What is the true nature of accelerated motion?

The Sages also wrestled with the contrast between God's eternal unchanging nature and the fact that creation, had a definite beginning, is never still and is finite.

The Chabad article continues:
"...This “first” Tzimtzum was the most radical in the sense that it was the quantum leap that allowed finitude to surface. It must be noted that the concealment of the Or Ein Sof did not affect Atzmut itself, for Atzmut is the essence of G-d which transcends everything, including changes.

...This is what Malachi the prophet meant when he spoke, “I, G-d, have not changed.” G-d remains the same after creation as before creation. He remains totally aloof from any change within the creation. All change took place within a manifestation of revealed power–the Or Ein Sof.

Hassidism explains that what was left after the Tzimtzum were the “letters of the residue” (Reshimu). The Zohar states that “He engraved letters in the supernal purity” (i.e. in the Or Ein Sof). This means that when it arose in G-d’s will to create the world, “G-d measured out within Himself in potential what would exist in actuality.” In the Zohar, this act of measuring out is referred to as “engraving letters.” These letters signify the structuring and formation of the Divine will prior to the Tzimtzum. They are the potential for limitation that existed within the Or Ein Sof.

...The revelation of Vessels came about through the Tzimtzum, although they existed in an abstract form before the Tzimtzum. As previously stated, within the Or Ein Sof was also the power of finitude. Prior to the Tzimtzum these “Letters” were filled with Or Ein Sof and they represented only the potential for limitation.

The function of the Tzimtzum was to remove the Or Ein Sof that flooded the letters so that limitation and finitude could be actualized.

In order for there to be diversity within the creation, it was necessary to reveal different qualities or attributes within the Divine. These “attributes” are called Sefirot and they are the building blocks of creation. Every Sefirah (attribute) is composite of Lights and Vessels."

In other words, it's a change in perspective which gives us a point of view that reveals motion. As the old saying goes in the midwest, "if the tornado appears as if it is not moving - run," because it's coming directly toward you. In order to see its motion, you have to change your perspective - viewed head on, it appears to be standing still but rest assured, tornados do not stand still. Neither does creation. Though God's attributes are eternal and unchanging, by moving some more into focus and others farther away from focus, movement, so to speak, is perceived - but the nature of them does not change. In the same way, gravity becomes motion to us because we arrive at a perspective where we can detect it, not because it isn't otherwise happening. Greene continues:

The Equivalence of Gravity and Acceleration

In special relativity, Einstein's main focus was on observers who move with constant velocity - observers who feel no motion and hence are all justified in proclaiming that they are stationary and that the rest of the world moves by them. But accelerated motion is different, because you CAN feel it. There is no way to shield yourself from its influence. If you're standing on planet earth yo mare subject to planet earth's gravitational pull. It's inevitable. There is no way around it. While you can shield yourself from electromagnetic and nuclear forces, there is no way to shield yourself from gravity. In one of those flashes of insight that scientists spend s lifetime longing for, Einstein realized that gravity and accelerated motion are two sides of the same coin.

Just as by changing your planned motion (to avoid accelerating) you can avoid feeling squeezed back in your car seat or feeling pushed sideways on the train, Einstein understood that my suitably changing your motion you can also avoid feeling the usual sensations associated with gravity's pull. As a matter of fact, NASA trains astronauts for the gravity-free environment of outer space by having them ride in a modified 707 airplane, nicknamed the Vomit Comet, that periodically goes into a state of free fall. Similarly, by a suitable change in motion you can create a force that is essentially identical to gravity. The same is true of other kinds of accelerated motion.

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 argued that only those observers who feel no force at all - including the force of gravity - are justified in declaring that they are not accelerating. Such force-free observers provide the true reference points for discussing motion, and it's this recognition that requires a major turnabout in the way we usually think about such things. feel gravity's influence only when you resist it. By contrast, when you fully give into to gravity you don't feel it.

Having forged the link between gravity and acceleration, Einstein was now ready to take up Newton's challenge and seek an explanation of how gravity exerts its influence.

Resisting, or struggling, to reach past the barrier of spacetime and connect with the eternal is the very raison d'etra of Judaism, right down to ...the name "Israel" (Yisrael), meaning "the one who wrestled with G-d" or "the Champion of G-d." By going against the customs and traditions of other nations and keeping Torah instead, we struggle daily against the concealment of God and strive toward enlightenment. We are made in God's image - we have the same attributes, though obviously less powerfully. We can embrace those attributes and strengthen them through Torah observance, or we can weaken them and let they atrophy by doing things the world's way. To put it another way, like gravity, we don't really feel the force that ungodliness exerts on us until we resist against it. It's easy to stay trapped inside creation and never work toward connecting with the Being outside of it. Staying in the box is always less trouble than getting out of it.

Warps, Curves, and Gravity.

Through special relativity, Einstein showed that every observer cuts up spacetime into parallel slices that he or she considers to be all of space at successive instants of time, with the unexpected twist that observers moving relative to one another at constant velocity will cut through spacetime at different angles. If one such observer should start accelerating, your might guess that the moment-to-moment changes in his speed and/or direction of motion would result in moment-to-moment changes in the angle and orientation of his slices. Roughly speaking, this is what happens.

The differently angled cuts through the spacetime loaf smoothly merge into slices that are curved but fit together as perfectly as spoons in a silverware tray. An accelerated observer carves spatial slices that are warped.

With this insight, Einstein was able to invoke the equivalence principle to profound effect. Since gravity and acceleration are equivalent, Einstein understood that gravity itself must be nothing but warps and curves in the fabric of spacetime.

If you roll a marble along a smooth wooden floor, it will travel in a straight line. But if you've recently had a terrible flood and the floor dried with all sorts of bumps and warps, a rolling marble will no longer travel along the same path. Einstein applied this simple idea to the fabric of the universe. He imagined that in the absence of matter or energy - no sun, no earth, no stars - spacetime, like the smooth wooden floor, has no warps or curves. It's flat.

Einstein then imagined that the presence of matter or energy has an effect on space much like the effect the flood had on the floor. Matter and energy, like the sun, cause space (and spacetime) to warp and curve. Anything moving through warped space - such as the earth moving in the vicinity of the sun - will travel along a curved trajectory. It's as if matter and energy imprint a network of chutes and valleys along which objects are guided by the invisible hand of the spacetime fabric. That, according to Einstein, is how gravity exerts its influence.

Footnote: Time is also warped by matter and energy. And just as a warp in space means that space is stretched or compressed, a warp in time means that time is stretched or compressed. In fact, it turns out that the warping of space caused by ordinary bodies like the earth and sun (as opposed to black holes) is far less pronounced than the warping they inflict on time.

The footnote is particularly interesting to read. Think about that for a moment - something with sufficient energy warps space or time. Our own planet warps time to some extent (of course we know it has a gravitational field). And, since we know the equations for time work both ways, forward and backward, then time could be warped either backward or forward. In the Tanakh, there are two instances when time was manipulated. In the first, time was run backward, and in the second, it seemed to stand still.

Isaiah 38:4 Then the word of Adonai came to Yeshaiyahu, saying, Isa 38:5 "Go, and tell Chizkiyahu, 'Thus says Adonai, the God of David your father, "I have heard your prayer. I have seen your tears. Behold, I will add fifteen years to your life. Isa 38:6 I will deliver you and this city out of the hand of the king of Ashur, and I will defend this city. Isa 38:7 This shall be the sign to you from Adonai, that Adonai will do this thing that he has spoken. Isa 38:8 Behold, I will cause the shadow on the sundial, which has gone down on the sundial of Achaz with the sun, to return backward ten steps. So the sun returned ten steps on the sundial on which it had gone down."'"

Jos 10:12 Then spoke Yehoshua to Adonai in the day when Adonai delivered up the Amori before the children of Yisra'el; and he said in the sight of Yisra'el, Sun, stand you still on Giv`on; You, Moon, in the valley of Ayalon. Jos 10:13 The sun stood still, and the moon stayed, Until the nation had avenged themselves of their enemies. Isn't this written in the book of Yashar? The sun stayed in the midst of the sky, and didn't hurry to go down about a whole day. Jos 10:14 There was no day like that before it or after it, that Adonai listened to the voice of a man: for Adonai fought for Yisra'el.

These two examples are largely considered to be "scientifically" impossible, proof that the text is simply mythology. But here Einstein's work shows that they are not impossible after all. Obviously, a great deal of energy would be required - but there are no limits on God's resources. One could argue that even if the first example were "doable," that the second one could not be, because nothing in creation "stands still." But that perception is relative - like the tornado, it depends on your position as to whether or not something appears to be moving. To Joshua and his army, the sun appeared to stand still because their relative motion had been aligned to it - not that the earth stopped rotating, but that time was warped so that the earth's rotation was constant relative to the sun's position.

Greene continues:

The mathematical result Einstein embodied in what are called the Einstein Field Equations. Einstein viewed the warping of spacetime as the manifestation - the geometrical embodiment - of a gravitational field. By framing the problem geometrically, Einstein was able to find equations that do for gravity what Maxwell's equations did for electromagnetism.

Of equal importance, since general relativity specifies the detailed mechanism by which gravity works, it provides a mathematical framework for determining how fast it transmits its influence. The speed of transmission comes down to the question of how fast the shape of space can change in time. That is, how quickly can warps and ripples - ripples like those on the surface of a pond caused by a plunging pebble - race from place to place through space? He found that warps and ripples - gravity, that is - do not travel from place to place instantaneously, as the do in Newtonian calculations of gravity. Instead, they travel at exactly the speed of light. If aliens plucked the moon from its orbit, the tides would recede 1.5 seconds later, at the exact moment we'd see that the moon had vanished.

So light - matter/energy, in this case expressed as gravity - is still solidly found as the basis for activity in our universe. So far, so good. The light has been divided, transformed, manipulated, combined, and moved through what used to be the void. As the sages say, became vessels to hold the attributes of the light. Our perception of a solid, inert, still world bears little resemblance to the reality of the dynamics of our matter, which is interchangeable with light, hurtling through time and space. Indeed, our perception of our own spacetime continuum is so very wrong that is astonishing that anyone would say with a straight face that what is measurable and viewable around us is all there is, and that its true nature can be known from our horribly flawed perception.

General Relativity and the Bucket

In Newton's age, space and time do not respond to happenings in the universe. spacetime - the loaf, as we've been calling it, is taken as a given, once and for all. In general relativity, all this changes. Space and time become players in the evolving cosmos. Matter here causes space to warp there, which causes matter over there to move, which causes space way over there to warp even more, and so on. General relativity provides the choreography for an entwined cosmic dance of space, time, matter, and energy.

This is a stunning development. But we now come back to our central theme: What about the bucket? Does general relativity provide the physical basis for Mach's relationist ideas, as Einstein hoped it would?

General relativity is subtle and it had features that took many years for physicists, including Einstein himself, to appreciate completely. AS these aspects ere better understood, Einstein fount it increasingly difficult to fully incorporate Mach's principle into general relativity. Little by little, he grew disillusioned with Mach's ideas and by the later years of his life came to renounce them.

Mach argued that when the spinning water's surface become concave, or when you feel your arms splay outward, or when the rope tied between the two rocks pulls taut, this has nothing to do with some hypothetical - and, in his view, thoroughly misguided - notion of absolute space (or absolute anything, in our more modern understanding). Instead, he argued that it's evidence of accelerated motion with respect to all the matter that's spread throughout the cosmos. Were there no matter, there'd be no notion of acceleration and none of the enumerated physical effects (concave water, splaying arms, taut rope) would happen.

What does general relativity say?

The benchmarks for all motion and accelerated motion in particular are freely falling observers - observers who have fully given in to gravity and are being acted on by no other forces. Now, a key point is that the gravitational force to which a freely falling observer acquires arises from all the matter (and energy) spread throughout the cosmos. The earth, the moon, the distant planets, stars, gas clouds, quasars, and galaxies all contribute to the gravitational field (in geometrical language, to the curvature of spacetime) right where you're now sitting. Things that are more massive and less distant exert a greater gravitational influence, but the gravitational field you feel represents the combined influence of the matter that's out there.

Thus, in general relativity, when an object is said to be accelerating, it means the object is accelerating with respect to a benchmark determined by matter spread throughout the universe. That's a conclusion which has the feel of what Mach advocated. So, in this sense, general relativity does incorporate some of Mach's thinking.

Without gravity, spacetime is not warped. It takes the simple, uncurved shape - and that means we are back in the simpler setting of special relativity.

In contradiction to what Mach would have predicted, general relativity comes to the same answer as special relativity and proclaims that even in a otherwise empty universe, you will feel pressed against he inner wall of the spinning bucket... The conclusion we draw is that even in general relativity, empty spacetime provides a benchmark for accelerated motion.

Spacetime and the Third Millennium

The verdict? 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."

In Newton's view and also that of special relativity, space and spacetime were invoked as entities that provide the reference for defining accelerated motion. And since, according to these perspectives, space and spacetime are absolutely unchangeable, this notion of acceleration is absolute. In general relativity, though, the character of spacetime is completely different. Space and time are dynamic in general relativity: they are mutable. They respond to the presence of mass and energy - they are not absolute. Spacetime, and in particular the way it warps and curves, is an embodiment of the gravitational field. Thus, in general relativity, acceleration relative to spacetime is a far cry from absolute, staunchly unrelational conception invoked by previous theories.

Instead, acceleration relative to general relativity's spacetime is relational. It is acceleration relative to something just as real, tangible, and changeable - a field, the gravitational field. In this sense, spacetime - by being the incarnation of gravity - is so real in general relativity that the benchmark it provides is one that many relationists can comfortably accept.

Indeed, since 1905 with Einstein did away with the luminiferous aether, the idea that space is filled with invisible substance has waged a vigorous comeback. Key developments in modern physics have reinstituted various forms of an aetherlike entity, none of which set an absolute standard for motion like the original luminiferous aether, but all of which thoroughly challenge the naive conception of what it means for spacetime to be empty. Moreover, the basic role that space plays in a classical universe - as the medium that separates one object from another, as the intervening stuff that allows us to declare definitively that one object is distinct and independent from another - is thoroughly challenged by startling quantum connections.

Space is not, of course, empty as the ancients imagined it - we are literally swimming in a sea of various particles, waves, fields, and energies, not to mention affected by matter that is light-years away from us. The universe is an interconnected place after all - and according to Einstein's theory there is an objective standard - a truth, if you will - out there by which all things are observed and measured. Everything that is relative is relative "to" something.

All of the -isms, philosophies, religions, cultures and traditions that we espouse either measure well against the standard or they do not, and we often cannot tell from our stale perspective how something is measuring. But one thing we do know - if we're floating along without resisting, we are never going to have a perspective that will reveal the concealed to us. If we know we need to struggle against something but don't, we will never reach it. Our struggle is to resist the complacency and strive to reach the infinite. And a God who went to all this trouble to withdraw from an area so that the void and creation could come into being would not leave his creations stuck in this void without a means to reach outside it. By obeying Torah (not the Rabbis) we "align" our circuitry, our electromagnetic field, to the correct wavelength and with prayer we use our "in-tune" frequency to connect to the Divine.

We don't have to understand exactly how it works - it just does.

No comments: