**Pondering Einstein **

Bravo! Your special Einstein issue [September] is excellent! By focusing many writers on one topic, you’ve reminded us of two important lessons. First, that physics is like any other human endeavor: It and its practitioners are subject to as many interpretations as there are interpreters. Second, a dose of humility is still good medicine, even for a pantheon of modern physicists, because when a Newton or an Einstein does come along, his or her greatness is always defined by the trampling of majority-accepted “truths.”

**RICHARD THEISS**

**Sammamish, Washington**

I can think of dozens of scientists whose work was more important than Einstein’s. His work was mostly theoretical and has been of little use to humanity. I rate Watson and Crick, Newton, Bernoulli, Faraday, Clausius, and dozens of others as being more important scientists than Einstein.

**CALVIN NEILL **

**Wimberley, Texas**

As I was reading the summaries of Einstein’s theories of relativity [“Einstein in a Nutshell”], a few questions came up about the accepted Einsteinian view of time and space. First, what happened to the commonsense conceptualization of space as nothingness—the nothingness between objects or matter that fills the empty intervals between events that we call time? How can nothingness suddenly become a fabric that can exert force upon objects? The idea that nothingness exerts force or has a shape that is not determined by forces or material limits seems about as substantial as the idea of an ether, and no more logical than the idea that objects pull with gravity. Also, how can light be considered a constant if the terms that light is measured with—space and time—are not constant?

**KAREN E. NESS **

**Vancouver, Washington **

*Part of the reason Einstein’s ideas sound so strange is that we are using linguistic metaphors to describe his theories rather than the mathematical equations that describe them much more accurately. At any rate, common sense is an unreliable guide in evaluating how the universe behaves on scales that lie far outside human experience. Scientists abandoned the notion of an ether because they could find no evidence to support it, even though it appealed to their common sense about how light travels through a vacuum. Scientists now accept Einstein’s relativity because they find an impressive match between theory and observation, even though concepts such as curved space-time run counter to human intuition. One of these observations is that the speed of light in a vacuum always appears the same. Einstein concluded that the constancy of light reveals a deep cosmic truth: The laws of physics appear the same to all observers, regardless of their state of motion. This constancy is possible only if each observer is perceiving the universe relative to his or her local definition of time and space.*

*— The editors*

Theoretical physicist Michio Kaku’s four-dimensional inflating balloon is a wonderful device for describing a cosmic positive curvature of space-time [“Einstein in a Nutshell”]. But the balloon need not be expanding. If, as is stated elsewhere in the article, positive curvature causes light frequencies to stretch, thereby shifting them toward the red end of the spectrum, then space-time need not expand in order for us to observe the redshift. As necessitated by relativity, we would see more positive curvature from the bottom of Earth’s or the solar system’s gravitational trough than we would see in open space. I suggest that space-time could be better described as expansive than expanding.

**JERRY W. DOWNS **

**Laguna Beach, California**

*It is the stretching of space, rather than the curvature of space (which is quite small), that can account for the redshift of the distant galaxies, which is why scientists have concluded that the universe is expanding. An expanding universe can have either positive or negative curvature. Think of a plastic balloon (with positive curvature) or the surface of a trumpet or a saddle (with negative curvature) made of plastic. In either case, it’s possible to stretch the plastic, expanding the distance between any two points on the surface, thereby creating a redshift. Scientists have recently confirmed (using satellites such as the Wilkinson Microwave Anisotropy Probe, along with other experiments) that the curvature of the universe is neither positive nor negative but actually close to zero. (This still leaves open the possibility that our visible universe is a tiny, flat surface in a much bigger universe with positive or negative curvature.) So the universe is both expanding and expansive.*

*— Michio Kaku*

Thanks for a wonderfully informative issue! One comment: In “Plucking the Strings of Relativity,” Michael S. Turner says “the singularity at the center of a black hole . . . could be a wormhole, or shortcut, to another place in our universe or even to another universe entirely.” But the effects of relativity mean that it takes an infinite amount of time for an object to fall into a black hole, so the wormhole is effectively closed from the standpoint of anyone external to the event horizon. From the perspective of the person falling in, the wormhole seems to be a one-way trip to an infinitely distant future. Does a wormhole that cannot be used in a finite amount of time exist in any real sense? It’s certainly not a “shortcut”!

**ARLIN ANDERSON **

**Madison, Alabama **

*Theorists have yet to resolve whether Einstein’s theory even permits wormholes. Current indications are that the required space-time tunnels cannot persist long enough to be traversed, but for the sake of argument we will assume that usable wormholes exist. The journey to the center of a black hole and back out takes infinitely long only as viewed from the outside. From the perspective of the person falling in, the trip happens in a finite period. Depending upon where and when the traveler emerges, the passage through a black hole could be a fabulous shortcut, allowing him to travel across the universe in a short time. The trip through a black hole could even take the traveler back to a place and time in his own past. Of course, traveling back in time to the same place raises questions about the relationship between cause and effect (for example, intervening in an event crucial to your own existence). In the language of relativity theory, doing so would involve the existence of “closed timelike curves,” loops in time that curve in on themselves. Some exotic solutions to Einstein’s equations allow such curves; however, Stephen Hawking’s chronology protection conjecture states that in mathematically sensible solutions of Einstein’s theory, closed timelike curves cannot exist. But who knows? Hawking recently lost a bet about black holes and information—maybe he is wrong here too!*

*— Michael S. Turner*