The Fabric of the Cosmos: Space, Time, and the Texture of Reality by Brian Greene
Authors: Brian Greene
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designs. Their grids differ by a rotation.
Now, following the insight of Einstein's mathematics professor Hermann Minkowski (who once called his young student a lazy dog), consider the region of spacetime as an entity unto itself: consider the complete flip book as an object in its own right. To do so, imagine that, as in Figure 3.3b, we expand the binding of the flip-card book and then imagine that, as in Figure 3.3c, all the pages are completely transparent, so when you look at the book you see one continuous block containing all the events that happened during a given time interval. From this perspective, the pages should be thought of as simply providing a convenient way of organizing the content of the block—that is, of organizing the events of spacetime. Just as a street/avenue grid allows us to specify locations in a city easily, by giving their street and avenue address, the division of the spacetime block into pages allows us to easily specify an event (Itchy shooting his gun, Scratchy being hit, and so on) by giving the time when the event occurred—the page on which it appears—and the location within the region of space depicted on the pages.
Figure 3.3 ( a ) Flip book of duel. ( b ) Flip book with expanded binding.
Here is the key point: Just as Lisa realized that there are different, equally valid ways to slice up a region of space into streets and avenues,
Figure 3.3 ( c ) Block of spacetime containing the duel. Pages, or "time slices," organize the events in the block. The spaces between slices are for visual clarity only; they are not meant to suggest that time is discrete, a question we discuss later.
Einstein realized that there are different, equally valid ways to slice up a region of spacetime—a block like that in Figure 3.3c—into regions of space at moments of time.
The pages in Figures 3.3a, b, and c—
with, again, each page denoting one moment of time
—provide
but one of the
many possible slicings.
This may sound like only a minor extension of what we know intuitively about space, but it's the basis for overturning some of the most basic intuitions that we've held for thousands of years. Until 1905, it was thought that everyone experiences the passage of time identically, that everyone agrees on what events occur at a given moment of time, and hence, that everyone would concur on what belongs on a given page in the flip book of spacetime. But when Einstein realized that two observers in relative motion have clocks that tick off time differently, this all changed. Clocks that are moving relative to each other fall out of synchronization and therefore give different notions of simultaneity. Each page in Figure 3.3b is but one observer's view of the events in space taking place at a given moment of his or her time. Another observer, moving relative to the first, will declare that the events on a single one of these pages
do not
all happen at the same time.
This is known as the
relativity of simultaneity,
and we can see it directly. Imagine that Itchy and Scratchy, pistols in paws, are now facing each other on opposite ends of a long, moving railway car with one referee on the train and another officiating from the platform. To make the duel as fair as possible, all parties have agreed to forgo the three-step rule, and instead, the duelers will draw when a small pile of gunpowder, set midway between them, explodes. The first referee, Apu, lights the fuse, takes a sip of his refreshing Chutney Squishee, and steps back. The gunpowder flares, and both Itchy and Scratchy draw and fire. Since Itchy and Scratchy are the same distance from the gunpowder, Apu is certain that light from the flare reaches them simultaneously, so he raises the green flag and declares it a fair draw. But the second referee, Martin, who was watching from the platform, wildly squeals foul play, claiming that Itchy got the light signal from the explosion before Scratchy did. He explains that because the train was
Now, following the insight of Einstein's mathematics professor Hermann Minkowski (who once called his young student a lazy dog), consider the region of spacetime as an entity unto itself: consider the complete flip book as an object in its own right. To do so, imagine that, as in Figure 3.3b, we expand the binding of the flip-card book and then imagine that, as in Figure 3.3c, all the pages are completely transparent, so when you look at the book you see one continuous block containing all the events that happened during a given time interval. From this perspective, the pages should be thought of as simply providing a convenient way of organizing the content of the block—that is, of organizing the events of spacetime. Just as a street/avenue grid allows us to specify locations in a city easily, by giving their street and avenue address, the division of the spacetime block into pages allows us to easily specify an event (Itchy shooting his gun, Scratchy being hit, and so on) by giving the time when the event occurred—the page on which it appears—and the location within the region of space depicted on the pages.
Figure 3.3 ( a ) Flip book of duel. ( b ) Flip book with expanded binding.
Here is the key point: Just as Lisa realized that there are different, equally valid ways to slice up a region of space into streets and avenues,
Figure 3.3 ( c ) Block of spacetime containing the duel. Pages, or "time slices," organize the events in the block. The spaces between slices are for visual clarity only; they are not meant to suggest that time is discrete, a question we discuss later.
Einstein realized that there are different, equally valid ways to slice up a region of spacetime—a block like that in Figure 3.3c—into regions of space at moments of time.
The pages in Figures 3.3a, b, and c—
with, again, each page denoting one moment of time
—provide
but one of the
many possible slicings.
This may sound like only a minor extension of what we know intuitively about space, but it's the basis for overturning some of the most basic intuitions that we've held for thousands of years. Until 1905, it was thought that everyone experiences the passage of time identically, that everyone agrees on what events occur at a given moment of time, and hence, that everyone would concur on what belongs on a given page in the flip book of spacetime. But when Einstein realized that two observers in relative motion have clocks that tick off time differently, this all changed. Clocks that are moving relative to each other fall out of synchronization and therefore give different notions of simultaneity. Each page in Figure 3.3b is but one observer's view of the events in space taking place at a given moment of his or her time. Another observer, moving relative to the first, will declare that the events on a single one of these pages
do not
all happen at the same time.
This is known as the
relativity of simultaneity,
and we can see it directly. Imagine that Itchy and Scratchy, pistols in paws, are now facing each other on opposite ends of a long, moving railway car with one referee on the train and another officiating from the platform. To make the duel as fair as possible, all parties have agreed to forgo the three-step rule, and instead, the duelers will draw when a small pile of gunpowder, set midway between them, explodes. The first referee, Apu, lights the fuse, takes a sip of his refreshing Chutney Squishee, and steps back. The gunpowder flares, and both Itchy and Scratchy draw and fire. Since Itchy and Scratchy are the same distance from the gunpowder, Apu is certain that light from the flare reaches them simultaneously, so he raises the green flag and declares it a fair draw. But the second referee, Martin, who was watching from the platform, wildly squeals foul play, claiming that Itchy got the light signal from the explosion before Scratchy did. He explains that because the train was
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