Search FQXi


David Vognar: "Completeness theorem: If a system’s components can transduce, that system..." in The Entropic Price of...

Georgina Woodward: "On obtaining the singular, relative, measurement product it replaces the..." in The Present State of...

Steve Dufourny: "The paper of Wilczek of course is very relevant considering the idea about..." in The Noise of Gravitons

Georgina Woodward: "Material neuronal structure in which memory is encoded, physical records..." in Quantum Physics and the...

Steve Dufourny: "It is really how we consider the structure of the spacetime, and also how..." in The Noise of Gravitons

Aleksandr Maltsev: "Hi Georgina, Write a letter to" in Quantum Physics and the...

Georgina Woodward: "In quantum experiments using particles, there won't be swapping with a..." in The Present State of...

Aleksandr Maltsev: "I shortened the phrase Zeeya Merali  «Why does time flow….?    How..." in Time's Arrow, Black Holes...

click titles to read articles

The Entropic Price of Building the Perfect Clock: Q&A with Natalia Ares
Experiments investigating the thermodynamics of clocks can teach us about the origin of time's arrow.

Schrödinger’s A.I. Could Test the Foundations of Reality
Physicists lay out blueprints for running a 'Wigner's Friend' experiment using an artificial intelligence, built on a quantum computer, as an 'observer.'

Expanding the Mind (Literally): Q&A with Karim Jerbi and Jordan O'Byrne
Using a brain-computer interface to create a consciousness 'add-on' to help test Integrated Information Theory.

Quanthoven's Fifth
A quantum computer composes chart-topping music, programmed by physicists striving to understand consciousness.

The Math of Consciousness: Q&A with Kobi Kremnitzer
A meditating mathematician is developing a theory of conscious experience to help understand the boundary between the quantum and classical world.

February 6, 2023

Taming Infinity
General relativity and quantum mechanics could be perfectly compatible—as long as you know how to handle infinity, that is.
by Anil Ananthaswamy
FQXi Awardees: Richard Woodard
January 10, 2010
Bookmark and Share

Richard Woodard (and camel)
Everybody knows that quantum mechanics and general relativity are incompatible—leading to the decades-long search for a theory of quantum gravity that could combine the two. But everybody could well be wrong, according to particle physicist Richard Woodard. He thinks that the mismatch between the two could be nothing more than an illusion, created by the complicated math techniques used in attempts to unite them.

Woodard clearly remembers the time he fell in love with particle physics. It was fall, 1977. A self-confessed "hot-shot" who had tackled graduate-level quantum mechanics with ease as an undergraduate at Case Western Reserve University, Ohio, Woodard arrived at Harvard University for graduate studies with thoughts that quantum mechanics was going to get tougher and more complex. And he was ready for it.

But then he took his first course in quantum field theory, being taught by Nobel Laureate Steven Weinberg. "It was one of the seminal experiences of my life," says Woodard. "The idea that you could write down the DNA of the universe in just a few statements—a brush stroke on a piece of paper—was just awesome. I recall lying in my bed in my dormitory room, just staring up at the ceiling to look at something blank, because I was overwhelmed by the power of the ideas that were being put into my mind by those lectures."

There’s a saying at Harvard that you don’t really understand quantum field theory until you have taken it three times. So, Woodard found himself studying it once more, under Sidney Coleman. Woodard was learning from men who had been instrumental in creating the standard model of particle physics, which seemed to be perfect, explaining everything that was observed in the lab.

Well, almost perfect.

Quantum Mountains

"That left one big unsolved problem, and that was gravity," says Woodard, now at the University of Florida, Gainsville. Every young theorist wanted to tackle quantum gravity—meshing quantum mechanics with general relativity—but the professors at Harvard heavily discouraged their students from going down that perilous route. But Woodard was sold on it. "We theorists are like mountain climbers. We see a tall mountain, and we just got to climb it."

I was overwhelmed by
the power of ideas
that were being put
into my mind.
- Richard Woodard
So Coleman, his PhD advisor, agreed to let Woodard climb that quantum-gravity mountain with Stanley Deser, who was at nearby Brandeis University. Since then, Woodard has devoted his professional life to quantum gravity.

While quantum field theory does a fantastic job of describing electromagnetism, and the strong and weak nuclear forces, it doesn’t work for Einstein’s theory of gravity. No matter how hard you work at applying quantum field theory to gravity, you get the same, dramatically wrong, answer: infinity.

"If you take the theory seriously, it says that when I wave my arm, every being in the solar system gets fried by hard gravitational radiation. That’s obviously not true," says Woodard. "So, right now we just have nonsense."

Something is clearly going wrong—but where? Almost everyone agrees that quantum mechanics is not the culprit. Most particle theorists think that the problem lies with general relativity. But Woodard thinks they are in danger of throwing the baby out with the bathwater. He argues that just because the calculations don’t work, that doesn’t mean general relativity is wrong, or incompatible with quantum mechanics. And it doesn’t mean that we need to introduce string theory, loop quantum gravity, or any other exotic new physical theory. Instead, the blame could lie with the approximate techniques used to carry out quantum field theory calculations.

In an ideal world, physicists wouldn’t have to make approximations. But we don’t live in an ideal world. Anyone who has taken high-school physics will remember having to simplify complicated problems in order to have any chance of applying textbook equations—pretending that cars are perfect cuboids sliding along frictionless roads, say.

Sweeping Away Infinity

Similarly, physicists are often forced to make approximations as they try to solve equations that describe things that can be measured, such as the total energy of a quantum system. Except for the simplest systems, these equations are impossible to solve exactly. That’s when physicists start approximating—using a technique known as perturbation theory—and the trouble begins.

Physicists make their best
guess when simulating
quantum systems on
computers. But is the guess
good enough for gravity?
The trick with perturbation theory is to start with one of the few ideal quantum systems that you can solve completely and then perturb them, so they look approximately like the situation that you actually want to study. For gravity, this is where things get nasty. Specifically, you end up with an answer in the form of a power series expansion or a never-ending string of numbers, each multiplied by higher powers of Newton’s constant for the strength of gravity, G, times even powers of the energy or mass, E, of the thing being computed (1 + aGE2 + bG2E4+ cG3 E6 +…, where a,b,c…are pure numbers). Because G times any energy or mass that can be accessed in particle physics is such a small number, just a few terms of the expansion would be wonderfully accurate—if only the pure numbers a, b, c, and so on were finite. But they aren’t, leading to an infinite answer.

This infinity issue isn’t confined to gravity. But for the other forces, physicists have clever ways to sweep these infinities under the carpet and recover meaningful answers. "We get a finite result that is in beautiful agreement with nature," says Woodard.

Unfortunately, these don’t work for gravity, so the calculations blow up in your face. "It is quite likely that perturbation theory is giving us misleading results," says Woodard.

It’s like figuring out
what is in a room
behind a locked
door. And we don’t
even know if there’s
a room there.
- Roberto Casadio
Woodard is scrutinizing perturbation theory’s power series expansion. Could the series expansion for gravity be wrong? Could the terms of the series involve, for example, the logarithm of G? He thinks so. "What I am speculating is that general relativity is the right theory of quantum gravity and that there is a very good series expansion for it," says Woodard. "It just isn’t conventional perturbation theory."

The first step for Woodard is to try and calculate the masses of fundamental particles, like electrons, using his alternative series expansion. In the 1960s,Richard Arnowitt, Stanley Deser and Charles Misner showed how to calculate the mass of a particle using classical general relativity. "I’m trying to extend that to quantum physics," says Woodard, who will be using his FQXi grant of over $37,000 towards this work.

Woodard is also helped by clues that any corrections to general relativity must either be tiny or else disguised as something that we don’t recognize as a quantum correction. That’s because we do not recognize any large quantum gravitational effects around us.

Light Reflections

One way to see such effects would be to examine the propagation of light. Imagine bouncing a beam of light off the surface of Alpha Centauri, the nearest star. We can calculate just how long the beam should take to come back to Earth. Assuming we had detectors good enough to measure the reflection, we could test our calculations. And all would be well if spacetime is classical. But in quantum gravity, spacetime is subject to fluctuations. "That signal would traverse the quantum geometry, which is itself fluctuating. Sometimes the fluctuation would be such as to cause that signal to go a little bit faster than in our average geometry," says Woodard. In that case, the reflected beam would arrive earlier than expected.

Of course, we’re a long way from testing anything like that right now. But whatever quantum gravitational effects there are, they are virtually undetectable in our current experiments, and that will influence the development of any alternative to conventional perturbation theory, says Woodard.

Another physicist who works on quantum gravity, Roberto Casadio of the University of Bologna, Italy, calls Woodard "a brilliant and extremely dedicated scientist." He admires the fact that Woodard doesn’t take the failure to apply quantum field theory to gravity using perturbation theory as a sign that we need any new theories of physics, "a common lore which has led to a (totally uncontrollable) amount of visionary ideas about quantum gravity."

Still, quantum gravity remains an enigma, thanks in part to the lack of experimental evidence for it. "It’s like figuring out what is in a room behind a locked door, and we do not even know if there is a room there," says Casadio. "Just because of this, any approach to quantum gravity remains an act of faith."

Comment on this Article

Please read the important Introduction that governs your participation in this community. Inappropriate language will not be tolerated and posts containing such language will be deleted. Otherwise, this is a free speech Forum and all are welcome!
  • Please enter the text of your post, then click the "Submit New Post" button below. You may also optionally add file attachments below before submitting your edits.

  • HTML tags are not permitted in posts, and will automatically be stripped out. Links to other web sites are permitted. For instructions on how to add links, please read the link help page.

  • You may use superscript (10100) and subscript (A2) using [sup]...[/sup] and [sub]...[/sub] tags.

  • You may use bold (important) and italics (emphasize) using [b]...[/b] and [i]...[/i] tags.

  • You may also include LateX equations into your post.

Insert LaTeX Equation [hide]

LaTeX equations may be displayed in FQXi Forum posts by including them within [equation]...[/equation] tags. You may type your equation directly into your post, or use the LaTeX Equation Preview feature below to see how your equation will render (this is recommended).

For more help on LaTeX, please see the LaTeX Project Home Page.

LaTeX Equation Preview

preview equation
clear equation
insert equation into post at cursor

Your name: (optional)

Recent Comments

3D and a constant of evolution where the mass increases......the number of spheres is specific in the 2 senses, the same.

The gravity polarises the light a finite system where the volume evolves.The rotations around the universal center take all its sense.

The gravity is like a modulator of evolution.

I d like insist on one thing, the "space time" is only understood near the walls, cosmologicals or quant.,like just a locality under parameters or a moment.In the...

Alleluia .

and EUREKA from BELGIUM .hihihihi


The reason the two theories don't unite is time and space are two in quantum mechanics and one in Einsteins theory.

2/3 SPACE+ 2/3 SPACE+ 2/3 SPACE= 2 SPACE.+

2/3 TIME+ 2/3 TIME+ 2/3 TIME= 2 TIME.


If we divide four equations by four we get four equations in one. Which is Einsteins one space/time.

So we can put quantum mechanics and Einsteins theory togther 12 12...

read all article comments

Please enter your e-mail address:
Note: Joining the FQXi mailing list does not give you a login account or constitute membership in the organization.