buy viagra lowest price
cheap generic viagra
order cialis in us
order cheap viagra online
cheap cialis in canada
buy discount cialis
viagra price
find cheap viagra online
generic viagra
low cost viagra
buy sildenafil in canada
erectile dysfunction
buying generic viagra
cheap cialis from canada
cialis 10mg
buy viagra online
buy sildenafil cheap
buy cheapest cialis
cialis rx
order viagra no prescription
buying viagra
buying cialis online
buy viagra from india
cialis cheapest price
order cialis cheap online
order no rx cialis
cialis 10 mg
overnight viagra
tablet viagra
buy generic cialis online
cialis bangkok
buy generic viagra
viagra canada
find viagra online
buy and purchase sildenafil online
cheap generic cialis
viagra rx
no prescription cialis
find cialis
50 mg viagra
viagra vs cialis
buy sildenafil online
order cialis without prescription
cheap viagra online
cialis information
viagra cost
100 mg viagra
purchase viagra
viagra
viagra from canada
buy viagra internet
drug viagra online purchase
order cialis no rx
discount cialis
discount viagra
discount viagra without prescription
viagra without rx
certified viagra
find discount viagra
cialis no online prescription
cost of viagra
find cialis without prescription
buy discount viagra online
buy cheap cialis
lowest price cialis
viagra pharmacy online
viagra cheap
sale viagra
order viagra online
cheap cialis tablet
order cialis overnight delivery
buy cialis low price
cheap viagra without prescription
cheapest cialis price
viagra online without prescription
buy sildenafil low cost
compare viagra prices online
buy cialis on line
buy cialis generic
impotence
viagra tablets
buy viagra generic
cialis
buy viagra low price
viagra purchase
best price for viagra
25mg viagra
buy cialis from india
cialis drug
order viagra on internet
low cost cialis
buy discount viagra
impotence treatment
viagra pill
order viagra from us
buy sildenafil in uk
overnight cialis
cialis soft tab
viagra medication
cialis cheap
impotence pills
discount cialis online
cheapest cialis online
order cialis from canada
cialis no prescription
viagra cheap drug
cheap viagra tablets
buy viagra without prescription
viagra online pharmacy
viagra approved
find cheap cialis
cost cialis
buy viagra on line
cialis 20 mg
buy cialis cheap
cheapest viagra
free cialis
buy cheap cialis online
pharmacy cialis
cialis without rx
cialis overnight shipping
compare cialis prices online
cheap cialis overnight delivery
cialis tablets
20 mg cialis
order viagra from canada
cheap viagra from usa
buy cheap viagra internet
cheapest cialis
10 mg cialis
purchase cialis
buy sildenafil citrate
cheap cialis no prescription
order generic viagra
cialis online cheap
cheap cialis on internet
drug cialis
buy sildenafil internet
cialis from india
no rx cialis
viagra cheapest price
where to buy cialis
order cialis in canada
cialis medication
cialis pharmacy
discount cialis no rx
cialis no rx required
viagra overnight shipping
cialis sales
buy cialis from canada
cialis prescription
cheap viagra in uk
purchase cialis overnight delivery
cialis price
where to buy viagra
viagra no rx required
cheap viagra overnight delivery
viagra india
buying generic cialis
cialis malaysia
cialis pill
cialis for order
cialis soft
order viagra in canada
generic viagra online
cialis for sale
impotence medication
online viagra
viagra soft
viagra pharmacy
purchase viagra overnight delivery
buy cialis on internet
cialis canada
order discount cialis online
buy viagra overnight delivery
cheapest viagra price
buy cialis from us
cheap cialis from usa
generic cialis cheap
viagra no rx
lowest price for cialis
buy sildenafil online without a prescription
viagra vendors
cost of cialis
generic viagra cheap
cialis free delivery
viagra in malaysia
viagra uk
find cialis online
order viagra without prescription
find discount viagra online
cheap cialis from uk
drug viagra
cialis in uk
cialis without a prescription
viagra in australia
find no rx cialis
drug cialis online purchase
cialis free sample
buy cialis internet
viagra generic
find cheap viagra
cheapest generic cialis online
find cheap cialis online
compare cialis prices
order viagra no prescription required
viagra us
cheap viagra in usa
find discount cialis
purchase cialis no rx
no prescription viagra
cialis online
viagra no online prescription
fda approved cialis
cheap cialis pharmacy
buy viagra no prescription required
cialis side effects
viagra in uk
viagra no prescription
viagra in us
cialis pharmacy online
find viagra
cheapest generic cialis
cost viagra
buy viagra cheap
buy cialis in canada
buy cialis no prescription required
buy cialis us
order cialis from us
100mg viagra
free viagra
find discount cialis online
cheap viagra
cialis buy online
cialis overnight
buy sildenafil canada
cialis 20mg
cheapest cialis prices
viagra without prescription
order cheap viagra
cheap price viagra
buy no rx viagra
purchase viagra no rx
pharmacy viagra
find viagra no prescription required
cheapest generic viagra
cialis in malaysia
cialis purchase
buy cialis lowest price
order no rx viagra
cheapest generic viagra online
order viagra
cheap cialis
where to order viagra
fda approved viagra
buy no rx cialis
purchase viagra without prescription
cheap cialis no rx
cialis online stores
cheap cialis in uk
find cialis on internet
certified cialis
price of viagra
purchase cialis online
cheapest viagra prices
find viagra on internet
buy cheapest cialis online
buy discount cialis online
buy viagra from us
buy cheapest cialis on line
cialis cheap drug
buy cialis online cheap
find cialis no prescription required
cialis us
cheap viagra pill
viagra free sample
cheap viagra tablet
viagra online cheap
cheap cialis in usa
cheap cialis without prescription
order viagra no rx
order viagra cheap online
viagra prescription
discount cialis overnight delivery
cialis australia
buy viagra on internet
cialis buy drug
order viagra in us
cialis vendors
cialis tablet
viagra drug
viagra tablet
cialis cost
cheap cialis tablets
cialis discount
buy cialis in us
online pharmacy cialis
sale cialis
cheap viagra on internet
buy viagra in us
discount viagra overnight delivery
25 mg viagra
cheap price cialis
buy cheapest viagra
cheap viagra no rx
viagra online stores
order generic cialis
viagra online review
best price viagra
cialis overnight delivery
cialis pills
cialis online review
buy cialis overnight delivery
order viagra overnight delivery
buy viagra no rx
cheapest sildenafil citrate
viagra free delivery
viagra sale
50mg viagra
buy cialis without prescription
cialis prices
tablet cialis
find viagra without prescription
viagra order
buy cheap viagra online
viagra pills
cialis in bangkok
cialis without prescription
order discount viagra
buy viagra in canada
viagra bangkok
lowest price for viagra
pharmacy online
cheap cialis online
viagra for sale
cialis cheap price
discount viagra online
impotence cure
cheap cialis internet
approved viagra pharmacy
cialis approved
cheap viagra from canada
10mg cialis
viagra prices
cialis in us
compare viagra prices
cialis vs viagra
viagra internet
cheapest viagra online
buy cheapest viagra online
online cialis
viagra side effects
generic cialis online
buy cheap viagra
order cheap cialis online
viagra online
viagra malaysia
buy cheapest viagra on line
order cialis no prescription required
cialis buy
approved cialis pharmacy
viagra in bangkok
cheap viagra pharmacy
order cialis no prescription
lowest price viagra
cialis sale
order cialis online
order cialis on internet
order discount viagra online
best price cialis
cialis no rx
viagra buy online
online pharmacy viagra
cheap cialis pill
cheap viagra in canada
cialis online without prescription
cheap viagra from uk
cheap viagra internet
find no rx viagra
buy sildenafil in spain
order cheap cialis
order discount cialis
impotence drugs
buy cialis no rx
purchase cialis without prescription
viagra overnight delivery
viagra discount
no rx viagra
buy generic cialis
viagra without a prescription
buy viagra us
discount viagra no rx
viagra soft tab
viagra cheap price
cialis order
purchase viagra online
cialis generic
viagra information
discount cialis without prescription
viagra buy drug
buy cheap cialis internet
cialis internet
20mg cialis
buy viagra
cialis in australia
viagra australia
viagra buy
generic drugs
viagra from india
buy viagra online cheap
buy cialis
cialis from canada
pfizer viagra
price of cialis
cialis uk
viagra overnight
buy generic viagra online
buying viagra online
buy cialis online
viagra for order
cheap viagra no prescription
viagra sales
generic cialis
buy viagra from canada
best price for cialis
order cialis
cialis online pharmacy
buying cialis
where to order cialis
cialis indiaWhen I reviewed Peter Woit’s book “Not Even Wrong,” Several readers of this blog were puzzled by my claim that string theory does not attempt to reconcile Einstein’s theory of gravity and quantum theory. After all, isn’t string theory supposed to be realizing Einstein’s dream of unifying gravity with the other forces, into a final theory of everything, as Brian Greene, the Columbia University string theorist, reminds us in a New York Times op-ed article today? And if not, have the string theorists — and all those who popularize their work — been fooling the public all along? Here I will try to help correct the misconception, and also guess how it may have arisen.
String theory — if it turns out to be a well-defined, experimentally verified theory — would achieve an astonishing feat among others: it would “quantize” gravity. This means that the force of gravity would become for the first time a bona fide part of quantum physics. But that is not the same as saying that string theory would include a “quantized” general relativity. The versions of string theory that physicists consider promising would only include a radically simplified version of general relativity, Einstein’s theory of gravity.
Einstein posited that the geometry of space is not fixed and immutable, but that it changes responding to the presence of matter and energy. The presence of a heavy object — say, a star like the Sun — creates a “depression” in the fabric of space (often pictured as a heavy ball resting on a rubber sheet — the analogy by the way is not entirely accurate, but hopefully it gives the idea).
In turn, how matter and energy move in space is affected by the changing structure of space itself. The “force” of gravity is in a sense apparent, just like the centrifugal forces you feel riding a rollercoaster are the result of the rollercoaster being curved. (Again, the analogy is not exact, but please bear with me.)
In string theory, on the other hand, space is static. The theory is not yet capable of predicting that heavy objects curve space. In particular, the theory cannot explain mesmerizing phenomena like the formation of black holes (when the depression becomes infinitely deep), or the gravitational lensing astronomers see around galaxies. This problem is known as “background dependence,” meaning that string theory has to assume the shape of the universe as a “background” known and assigned once and for all(1).
Strings also seem to be very fastidious about what universe you put them into. Initially, string theory only seemed compatible with a “flat” universe. When physicists showed in the late 1990s that there were a few other possibilities for string-compatible universes, that was seen as a huge breakthrough. Still, it was like saying, string theory takes not only vanilla ice cream, but also chocolate and strawberry — but forget about Wavy Gravy or Cherry Garcia. The other string-compatible universes would be curved and evolving (as opposed to flat and static), but still as a background. Their evolution would be unaffected by what the strings do.
All of this is true of the approaches to string theory that people have been working on for the last 20 years. A different, “background independent” approach to string theory, called string field theory, was proposed in the mid-1980s, but most physicists soon abandoned it after discovering that it seemed to be unworkable.
At the same time, it is true as Greene says that a successful string theory would be able for the first time to model gravity in the language and mathematics of quantum theory — a problem that’s been nagging physicists ever since quantum theory became seen as expressing the fundamental nature of physics laws. Hopefully, a “single equation” would be found that explains all forces of nature — gravity, the weak and strong nuclear forces, the electromagnetic force, and even the mysterious dark energy.
Gravity according to string theory would still keep some of the great achievements of Einstein’s theory. It would be a force that propagates at the speed of light, rather than instantaneously as in Newton’s spooky “action at a distance.” And it would fully be consistent with Einstein’s earlier, “special” relativity, with its slowing clocks, shrinking measuring sticks, paradoxes of the twins, and so on.
Such a theory could in principle be accurate within a wide range of applicability, namely as long as you do experiments far from massive objects, and if you forget about trying to predict anything about the universe as a whole.
Would this achieve Einstein’s dream? Yes and no. Einstein certainly wanted to unify physics, but his version of the dream involved wrestling the other forces off the grip of quantum theory — which he helped father and then despised — rather than letting quantum theory get its grip on gravity. In today’s article, Greene does warn the reader on this point. But he seems to gloss over the fact that the problem of fully recovering general relativity would remain open.
Why and how have a lot of people come to believe such a misconception about string theory, namely, that string theorists are working on fully integrating general relativity into a unified theory? I believe it’s due in large part due to the perils of popularizing science. While physicists who also act as science communicators could be more open on this point, part of the fault could also be ours — the science journalists’.
If you have to express what string theory is to someone who knows nothing about physics, and if you must do that in one or two sentences, it is imperative that you give your reader (or the listener or T.V. spectator) a lifesaver to grasp onto. At least some of the words you are going to say must be familiar to the reader, or else you’ve lost them. The only word that is guaranteed to sound familiar to most people is Einstein. The reader will ask, what is physics? Oh, it’s what Einstein did. At least I have a mental pigeonhole where to put this guy.
At the same time, the need to avoid overwhelming the reader almost always forces you to make stark choices on what to leave out, as all of us who write about science will attest. So Greene was right to somehow mention Einstein’s name in there, and probably also not to go too much into the details.
Still, all of us who communicate science could probably try harder to avoid misleading the reader. “Whenever you are translating mathematical work into natural language, there’s inevitably going to be some imprecisions,” New York Times science writer George Johnson once said to me in a telephone interview. However, he said, “I like to subtly work in a disclaimer, sometimes, just to remind people that — especially when you write about physics, and quantum mechanics particularly — a really precise description that would do complete justice to the phenomena is going to require differential equations.” That’s what Johnson often does in his books, and that’s some advice we science communicators could all try to follow. (Read the complete Q&A with George Johnson)
(1) Here’s how Stephon Alexander, a theoretical physicist at the University of Pennsylvania, explained this to me in more technical terms:
When one quantizes string theory, it is done on a fixed space-time background. This background is usually Minkowski space time. Therefore the metric is fixed. Most string theories have another symmetry which is called conformal invariance (observables are invariant under dilations (magnification)) In order for the quantum theory to respect this symmetry and be consistent, something called the Beta function must vanish -the Beta function is a quantum measure of the deviation from conformal invariance. It turns out that the condition for a vanishing beta function is exactly the Einstein Equations. However, even though the Einstein field equations are present, their solutions are only consistent with string theory for the background which gave the beta functions, Minkowski space. Other space-times are difficult to obtain in string theory because most usually break supersymmetry and the gravity theories are supergravity theories which only satisfy supersymmetric gravitational configurations.
You can leave a response, or trackback from your own site.
Nice post, Davide. You certainly cleared up some of my misconceptions about what String Theory is doing.
I’m going to read it over again, and maybe we can talk about it next week. (I took off today to go skateboarding).
-Buzz Skyline
Comment by James R — October 20, 2006 @ 5:22 pm
I’m sorry, but this is wrong. String perturbation theory makes sense (although can be difficult to quantize) on any background that satisfies the Einstein field equations, not just Minkowski space. Even in this context, string theory does explain “that heavy objects curve space”, at least perturbatively.
Within more nonperturbative approaches (the main example being AdS/CFT), one can go much further. In AdS/CFT, there is no background dependence except at the boundary of spacetime.
You also say that “Initially, string theory only seemed compatible with a “flat” universe. When physicists showed in the late 1990s that there were a few other possibilities for string-compatible universes, that was seen as a huge breakthrough”. The existence of multiple solutions was well-known back to the dawn of string theory; as mentioned above, string perturbation theory is compatible with any solution to the appropriate Einstein field equations. What was accomplished in the late 1990s was the issue of moduli fixing. The previous geometries all could deform continuously in such a way that led to massless fields that we do not observe. The accomplishment was to get rid of those fields and to make plausible that one could obtain solutions with a positive cosmological constant.
Comment by Aaron Bergman — October 23, 2006 @ 5:41 pm