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THE FABRIC of the COSMOS, Brian Greene, 2004
```(annotated and with added bold highlights by Epsilon=One)
```(annotated and with added bold highlights by Epsilon=One)
Chapter 14 – Up in the Heavens and Down in the Earth
Einstein in Drag
In his decade-long struggle to formulate the general theory of relativity, Einstein sought inspiration from a variety of sources. Most influential of all were insights into the mathematics of curved shapes developed in the nineteenth century by mathematical luminaries including Carl Friedrich Gauss, Janos Bolyai, Nikolai Lobachevsky, and Georg Bernhard Riemann. As we discussed in Chapter 3, Einstein was also inspired by the ideas of Ernst Mach. Remember that Mach advocated a relational conception of space: for him, space provided the language for specifying the location of one object relative to another but was not itself an independent entity. Initially, Einstein was an enthusiastic champion of Mach's perspective, because it was the most relative that a theory espousing relativity could be. But as Einstein's understanding of general relativity deepened, he realized that it did not incorporate Mach's ideas fully. According to general relativity, the water in Newton's bucket, spinning in an otherwise empty universe, would take on a concave shape, and this conflicts with Mach's purely relational perspective, since it implies an absolute notion of acceleration. Even so, general relativity does incorporate some aspects of Mach's viewpoint, and within the next few years a more than $500 million experiment that 'has been in development for close to forty years will test one of the most prominent Machian features.
The physics to be studied has been known since 1918, when the Austrian researchers Joseph Lense and Hans Thirring used general relativity to show that just as a massive object warps space and time — like a bowling ball resting on a trampoline — so a rotating object drags space (and time) around it, like a spinning stone immersed in a bucket of syrup. This is known as frame dragging and implies, for example, that an asteroid freely falling toward a rapidly rotating neutron star or black hole will get caught up in a whirlpool of spinning space and be whipped around as it journeys downward. The effect is called frame dragging because from the point of view of the asteroid — from its frame of reference — it isn't being whipped around at all. Instead, it's falling straight down along the spatial grid, but because space is swirling (as in Figure 14.1) the grid gets twisted, so the meaning of "straight down" differs from what you'd expect based on a distant, nonswirling perspective.
To see the connection to Mach, think about a version of frame dragging in which the massive rotating object is a huge, hollow sphere. Calculations initiated in 1912 by Einstein (even before he completed general relativity), which were significantly extended in 1965 by Dieter Brill and Jeffrey Cohen, and finally completed in 1985 by the German physicists and Herbert Pfister and K. Braun, showed that space inside the hollow sphere would be dragged by the rotational motion and set into a whirlpool-like spin. 1 If a stationary bucket filled with water — stationary as viewed from a distant vantage point — were placed inside such a rotating sphere, the calculations show that the spinning space would exert a force on the stationary water, causing it to rise up the bucket walls and take on a concave shape.
Figure 14.1 A massive spinning object drags space — the freely falling frames — around with it.
This result would have pleased Mach no end. Although he might not have liked the description in terms of "spinning space" — since this phrase portrays spacetime as a something — he would have found it extremely gratifying that relative spinning motion between the sphere and the bucket causes the water's shape to change. In fact, for a shell that contains enough mass, an amount on a par with that contained in the entire universe, the calculations show that it doesn't matter one bit whether you think the hollow sphere is spinning around the bucket, or the bucket is spinning within the hollow sphere. Just as Mach advocated, the only thing that matters is the relative spinning motion between the two. And since the calculations I've referred to make use of nothing but general relativity, this is an explicit example of a distinctly Machian feature of Einstein's theory. (Nevertheless, whereas standard Machian reasoning would claim that the water would stay flat if the bucket spun in an infinite, empty universe, general relativity disagrees. What the Pfister and Braun results show is that a sufficiently massive rotating sphere is able to completely block the usual influence of the space that lies beyond the sphere itself.)
In 1960, Leonard Schiff of Stanford University and George Pugh of the U.S. Department of Defense independently suggested that general relativity's prediction of frame dragging might be experimentally tested using the rotational motion of the earth. Schiff and Pugh realized that according to Newtonian physics, a spinning gyroscope — a spinning wheel that's attached to an axis — floating in orbit high above the earth's surface would point in a fixed and unchanging direction. But, according to general relativity, its axis would rotate ever so slightly because of the earth's dragging of space. Since the earth's mass is puny in comparison with the hypothetical hollow sphere used in the Pfister and Braun calculation above, the degree of frame dragging caused by the earth's rotation is tiny. The detailed calculations showed that if the gyroscope's spin axis were initially directed toward a chosen reference star, a year later, slowly swirling space would shift the direction of its axis by about a hundred-thousandth of a degree. That's the angle the second hand on a clock sweeps through in roughly two millionths of a second, so its detection presents a major scientific, technological, and engineering challenge.
Four decades of development and nearly a hundred doctoral dissertations later, a Stanford team led by Francis Everitt and funded by NASA is ready to give the experiment a go. During the next few years, their Gravity Probe B satellite, floating 400 miles out in space and outfitted with four of the most stable gyroscopes ever built, will attempt to measure frame dragging caused by the earth's rotation. If the experiment is successful, it will be one of the most precise confirmations of general relativity ever achieved, and will provide the first direct evidence of a Machian effect. 2 Equally exciting is the possibility that the experiments will detect a deviation from what general relativity predicts. Such a tiny crack in general relativity's foundation might be just what we need to gain an experimental glimpse into hitherto hidden features of spacetime.
The physics to be studied has been known since 1918, when the Austrian researchers Joseph Lense and Hans Thirring used general relativity to show that just as a massive object warps space and time — like a bowling ball resting on a trampoline — so a rotating object drags space (and time) around it, like a spinning stone immersed in a bucket of syrup. This is known as frame dragging and implies, for example, that an asteroid freely falling toward a rapidly rotating neutron star or black hole will get caught up in a whirlpool of spinning space and be whipped around as it journeys downward. The effect is called frame dragging because from the point of view of the asteroid — from its frame of reference — it isn't being whipped around at all. Instead, it's falling straight down along the spatial grid, but because space is swirling (as in Figure 14.1) the grid gets twisted, so the meaning of "straight down" differs from what you'd expect based on a distant, nonswirling perspective.
To see the connection to Mach, think about a version of frame dragging in which the massive rotating object is a huge, hollow sphere. Calculations initiated in 1912 by Einstein (even before he completed general relativity), which were significantly extended in 1965 by Dieter Brill and Jeffrey Cohen, and finally completed in 1985 by the German physicists and Herbert Pfister and K. Braun, showed that space inside the hollow sphere would be dragged by the rotational motion and set into a whirlpool-like spin. 1 If a stationary bucket filled with water — stationary as viewed from a distant vantage point — were placed inside such a rotating sphere, the calculations show that the spinning space would exert a force on the stationary water, causing it to rise up the bucket walls and take on a concave shape.
Figure 14.1 A massive spinning object drags space — the freely falling frames — around with it.
This result would have pleased Mach no end. Although he might not have liked the description in terms of "spinning space" — since this phrase portrays spacetime as a something — he would have found it extremely gratifying that relative spinning motion between the sphere and the bucket causes the water's shape to change. In fact, for a shell that contains enough mass, an amount on a par with that contained in the entire universe, the calculations show that it doesn't matter one bit whether you think the hollow sphere is spinning around the bucket, or the bucket is spinning within the hollow sphere. Just as Mach advocated, the only thing that matters is the relative spinning motion between the two. And since the calculations I've referred to make use of nothing but general relativity, this is an explicit example of a distinctly Machian feature of Einstein's theory. (Nevertheless, whereas standard Machian reasoning would claim that the water would stay flat if the bucket spun in an infinite, empty universe, general relativity disagrees. What the Pfister and Braun results show is that a sufficiently massive rotating sphere is able to completely block the usual influence of the space that lies beyond the sphere itself.)
In 1960, Leonard Schiff of Stanford University and George Pugh of the U.S. Department of Defense independently suggested that general relativity's prediction of frame dragging might be experimentally tested using the rotational motion of the earth. Schiff and Pugh realized that according to Newtonian physics, a spinning gyroscope — a spinning wheel that's attached to an axis — floating in orbit high above the earth's surface would point in a fixed and unchanging direction. But, according to general relativity, its axis would rotate ever so slightly because of the earth's dragging of space. Since the earth's mass is puny in comparison with the hypothetical hollow sphere used in the Pfister and Braun calculation above, the degree of frame dragging caused by the earth's rotation is tiny. The detailed calculations showed that if the gyroscope's spin axis were initially directed toward a chosen reference star, a year later, slowly swirling space would shift the direction of its axis by about a hundred-thousandth of a degree. That's the angle the second hand on a clock sweeps through in roughly two millionths of a second, so its detection presents a major scientific, technological, and engineering challenge.
Four decades of development and nearly a hundred doctoral dissertations later, a Stanford team led by Francis Everitt and funded by NASA is ready to give the experiment a go. During the next few years, their Gravity Probe B satellite, floating 400 miles out in space and outfitted with four of the most stable gyroscopes ever built, will attempt to measure frame dragging caused by the earth's rotation. If the experiment is successful, it will be one of the most precise confirmations of general relativity ever achieved, and will provide the first direct evidence of a Machian effect. 2 Equally exciting is the possibility that the experiments will detect a deviation from what general relativity predicts. Such a tiny crack in general relativity's foundation might be just what we need to gain an experimental glimpse into hitherto hidden features of spacetime.