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Dr. Christopher S. Baird

Can you go fast enough to get enough mass to become a black hole?

Category: Physics      Published: June 18, 2013

black hole
Artistic rendering of a black hole. Public Domain Image, source: Christopher S. Baird.

Traveling at high speed does not affect your mass, even in Einstein's theory of Special Relativity. For some reason, pre-college teachers, popular science books, and older physics textbooks claim that objects gain mass when they are traveling at higher speeds. This claim is wrong. If you define something called "relativistic mass" that is completely different from regular mass, then this claim could be made to look true. But doing so is very confusing and misleading. Today's physicists no longer treat the motion energy of an object as "relativistic mass" because doing so is misleading. When an object gains speeds, the entity that it gains is called "kinetic energy", even in Special Relativity. The total energy of a moving object is therefore its rest energy plus its kinetic energy. The rest energy of an object is contained in its mass. The relativistic total energy of a moving object is:

E = mc2/(1-v2/c2)1/2

In this equation, m is the mass of the object (which does not change no matter how hast the object is moving), c is the speed of light, and v is the speed of the object. If the object is not moving, v = 0, then there is no kinetic energy and the total energy just equals the rest energy. Plugging v = 0 into the equation above, we end up with the famous equation E = mc2. The rest energy of an object is therefore mc2, telling us that the rest energy is contained completely in the form of mass. The kinetic energy EK is therefore the total energy minus the rest energy:

EK = Emc2

EKmc2(1/(1-v2/c2)1/2 – 1)

This equation shows us that as the speed increases, the kinetic energy increases, but the mass never changes. In the limit that the speed of the object v approaches the speed of light in vacuum c, the kinetic energy becomes infinite. The law of conservation of energy tells us that to get an object traveling with infinite kinetic energy, we have to give it infinite energy. This act is clearly impossible as there is only a finite amount of energy in the observable universe. This facts means that objects with mass can never travel exactly at the speed of light in vacuum, as that state would require infinite energy. But objects can get very close to the speed of light.

Mass is the property of an object that describes two things:

  1. The object's resistance to acceleration. Larger masses accelerate less when a given force is applied.
  2. The object's ability to experience gravity. Larger masses feel larger forces in a given gravitational field.

When an object is traveling at a high speed, its resistance to acceleration does not change and its ability to experience gravity does not change. The mass of an object therefore does not change when it travels at high speed. This fact is predicted by Einstein's theories and verified by experiment. An object can never be turned into a black hole, or even be made slightly overweight by speeding it up.

Topics: black hole, energy, gravitational mass, gravity, inertia, inertial mass, mass, relativistic mass, relativity, speed of light