What is singularity and why do all laws of physics break down at singularity?

Asked by: Aditya Pattani


When a physicist refers to a singularity he or she is generally referring to a quantity which is infinite. Specifically, a quantity which approaches infinity as another parameter goes to zero, such as

It isn't true to say that all laws of physics break down at a singularity. You can imagine the problems though -- how do we interpret an infinite mass or infinite energy or infinite force? Usually we assume that there is some new set of laws or some new way of looking at the problem that makes the apparent singularity go away.

Here's an example. You may be familiar with Hooke's law for the force exerted by a spring: F=kx where k is the tension of the spring and x is the distance it is stretched. Now write the equation as k=F/x. Written this way it would seem that if you compare the tension between any two points on the spring, it grows and grows the closer together the two points are. In fact, two points spaced infinitesimally apart seem to have an infinite tension! It's just a manifestation of the 1/x limit above.

But of course that's not true. If you really want to know what's happening at small distance scales you can't use the classical physics behind Hooke's law. At some point x drops below the spacing between molecules in the spring's metal. Now Hooke's law no longer applies and you have to use atomic physics to explain the spring's properties. So in the large-scale theory (Hooke's law) there was no fundamental distance scale: x could be as small as you want. But at some point this law breaks down. In the small-scale theory (quantum mechanics and atomic physics) there is a fundamental distance scale: the atomic spacing. We would say that the singularity has been 'resolved.'

Most people worry about singularities involving general relativity: two examples being a black hole and the singularity that classical general relativity predicts was our universe at the moment it began. If you try to apply the laws of general relativity in these situations you will inevitably find the same 1/x singularities I've been talking about. How are we going to resolve these singularities? We expect quantum mechanics to do the job, since it is the theory that correctly describes physics at small distance scales. Unfortunately, while we have good theories of atomic physics, we don't real have a good theory of quantum gravity. Many of us think string theory will ultimately provide the resolution to these problems.

In short then, a singularity represents an infinity and we generally don't think nature is infinite. The problem arises from not having some kind of 'floor' built into a theory that keeps you from taking the limit of 1/x as x goes to zero. The way out is to apply a new theory that has such a floor, such as quantum mechanics or string theory (quantum gravity).

Answered by: Brent Nelson, M.A. Physics, Ph.D. Student, UC Berkeley



Science Quote

'Strange is our situation here upon the earth. Each of us comes for a short visit, not knowing why, yet sometimes seeming to divine a purpose.'

Albert Einstein
Science Sidebar | Science Education Articles
Cool Summer Science Projects

Why not make science a part of your family’s summer? Perhaps you can set aside one day a week for outdoor projects—maybe Mad Scientist Monday or Scientific Saturday? Here are a few ideas to help get you started. Continue reading ...

10 Ways to Keep Your Kids Interested In Science

Young children are natural scientists: they ask questions, pick up sticks and bugs outside, and are curious about the world around them. But as they get a bit older, many kids gradually lose their interest in science. They might see it as just another task at school, something that doesn't apply to their lives. Of course nothing could be further from the truth, so here are ten ways you can remind your kids that science is everywhere. Most of these are fun for adults, too! Continue reading ...

Top Selling

Here are our physics & astronomy bestsellers:
Magnetic Levitator - Classic
3D Magnetic Field Tube
KonusScience 5 Way Microscope Kit
Revolving Multi-Color Fiberoptic Light
Tin Can Robot 4M Kit
Potato Clock 4M Kit
Mini Plasma Ball
Clean Water Science 4M Kit
Top Secret - Spinning Top


USC University of Southern California Dornsife College Physics and Astronomy Department McMaster University Physics and Astronomy Department