- #1
James MC
- 174
- 0
Hi there,
In Newtonian mechanics, forces "compose". In other words:
##F_{net}=\sum_iF_i##
This states that the net force on a system of particles is the sum of each of the forces on each indiviudal particle. Similarly, the force on particle i due to a system of particles indexed by j is:
##F_i=\sum_jF_{ij}##
The former is sometimes called "the composition of forces", the latter "the superpositon of forces". Similar additivity principles hold for Newtonian gravitational forces.
My question is, do forces add like this in relativity theory? I've found practically no discussion of this online! The only discussions I've found is where one person says that the superposition of forces, in certain cases, is "not allowed in general relativity". And also where one person says that "due to relativity of simultaneity of events we cannot simply sum up the forces applied to the system, for different inertial observers. There are special conditions, when such a summation can be carried out: either the forces are static, or they are applied to the same spatial point."
I'm particularly interested in special relativity, and am not sure I follow what the above author is saying. Does the composition/superposition of forces hold in all cases, in special relativity?
Let me know your thoughts! :)
In Newtonian mechanics, forces "compose". In other words:
##F_{net}=\sum_iF_i##
This states that the net force on a system of particles is the sum of each of the forces on each indiviudal particle. Similarly, the force on particle i due to a system of particles indexed by j is:
##F_i=\sum_jF_{ij}##
The former is sometimes called "the composition of forces", the latter "the superpositon of forces". Similar additivity principles hold for Newtonian gravitational forces.
My question is, do forces add like this in relativity theory? I've found practically no discussion of this online! The only discussions I've found is where one person says that the superposition of forces, in certain cases, is "not allowed in general relativity". And also where one person says that "due to relativity of simultaneity of events we cannot simply sum up the forces applied to the system, for different inertial observers. There are special conditions, when such a summation can be carried out: either the forces are static, or they are applied to the same spatial point."
I'm particularly interested in special relativity, and am not sure I follow what the above author is saying. Does the composition/superposition of forces hold in all cases, in special relativity?
Let me know your thoughts! :)