Wednesday, October 31, 2012

Boy of Age 16 Asks Me about Relativity, etc. 13. Mass and Weight

Illustration of the first experiment performed by Eötvös to determine whether the inertial mass equals the gravitational mass. If the ratio F1 to F2 of centrifugal forces depending on inertial masses would differ
from the ratio G1 to G2 of gravitational forces depending on graviattional masses, the rod
would rotate. The mirror is used to monitor the rotation. Subsequent experiments used
a different setup for improved accuracy. For details, see the "Eötvös experiment"
page of Wikipedia. Image by Petteri Aimonen (Own work)
[Public domain], via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: When a body travels at the speed of light, it's mass will be much bigger than at rest. But what about its gravity or weight? It will also be much bigger than at rest. Is this correct?

Ted: It is an excellent question, but I have to correct the expression of your question a little bit before answering it. The body of non-zero mass cannot travel with just the speed of light but can only approach that speed. So, you should say, "When a body travels near the speed of light, …" You're right to expect that when a body's mass becomes larger with increasing speed, the body's weight or the gravitational force acting on the body also becomes larger compared with its weight when it was at rest in the same gravitational field. This is the result of "the equivalence principle" of general relativity, i.e., the law of the equality of the inertial and gravitational mass. Since the 17th century, repeated experiments demonstrated that inertial and gravitational mass are equivalent. One of the methods of such experiments is shown above. In 1915, Einstein included this observation a priori in the equivalence principle of general relativity.

Aaron: Thank you so much for your answer. By the way, Have you heard about Dr. Who?

Ted: No, I have not. I am not so much interested in science fiction stories except for old ones. However, I have learned from Wikipedia the followings about it: Doctor Who is a science fiction television program produced by the BBC and originally broadcast from 1963 to 1989. The program depicts the adventures of a mysterious, time-traveling humanoid alien who is known only as the Doctor and explores time and space in the "TARDIS," a sentient machine for four-dimensional traveling. (There is further information about its history, episodes, characters, etc. in the Wikipedia page) Thanks for your mentioning of Dr. Who.

Further reading
  1. "Mass versus weight," in Wikipedia, the free encyclopedia.
  2. "Mass," ibid.
  3. "Gravitation," ibid.
  4. "Equivalence principle," ibid.

(Originally written on June 9 and 20, 2011.)