# Why do we invent non-physical concepts (like e.g. point particles) to study physical phenomenons?

There is nothing exist like point particles in reality then why did we invented the notion of point particles and how does it relate to real world?

• There is nothing exist like point particles in reality That is still an open question, as far as I know. They could be very small, "all " we notice is the charge of the object, not the object, if there is one, itself. – user146020 Mar 2 '17 at 12:55
• – user146020 Mar 2 '17 at 12:57

Why do we invent non physical concept to study physical phenomenons?

People invented arithmetic ( a non physical concept) to distribute the produce of their cultivations, geometry ( a non physical concept) to study how to distribute the land they cultivated.

Then it was found that geometrical concepts fitted physical observations, stars, planets and even could give the circumference of the earth.

Arabs continued with the invention of algebra, which helped in solving problems with arithmetic faster. The the dark ages came, and the study pf physics was stuck in descriptions by Aristotle and Demokritos, words words words.

Physics took off with the mathematical tools invented for the needs of studying observations, like falling apples, after the enlightenment calculus was nurtured by many people and for physics used extensively by Newton , and modeling observations by complicated mathematics took off.

Modeling is assuming simple behaviors for representations of physical observables , testing whether calculations fit the data, and whether predictions are accurately validated.

If the nonphysical concept of mathematics ( and the use of point particles) had not been invented, at best we would still be living in the technology of the middle ages, at worst, the stone age.

• What i understood after reading the answers is that we can assume any thing and can build a model on those assumption as far as that model behaves exactly like real phenomenon whether those assumptions exist in real world or not. Am i right or wrong ? – Remy Mar 3 '17 at 4:55
• Correct, because the assumptions are in the choice of the correspondence of mathematics for that particular physics problem . extra axioms that pick up a subset of mathematical solutions that fit observations and are predictive. For example taking the center of mass of a rocket as a point particle can predict its trajectory given boundary conditions even though the rocket is not a point particle. – anna v Mar 3 '17 at 4:59
• Is axis of rotation in rotating bodies also an assumption ? – Remy Mar 3 '17 at 5:06
• yes, the mathematical solutions of assuming an axis fits the data given the boundary conditions – anna v Mar 3 '17 at 5:10
• I disagree. The axis of rotation is not an assumption, you can show that a rigid body rotates instantaneously around one axis. You are confusing modeling with approximating things with easily modeled mathematics - thus something very small with a point. Once you are able to see to those small sizes, what you investigate at those scales now needs to be modeled as something not a point. You can't assume anything and get anything useful from it. The genius of scientific exploration is understanding and making the right approximations and ignoring inconsequential issues at that scale, for a while – Bob Bee Mar 3 '17 at 5:37

To be able to understand very physical properties and ideas, simpler theories and concepts have to be developed.

Physics on the whole is not perfect, it is a way to model what is seen around the world. With something like a planet, understanding what happens to the mass if it is considered as a point source simplifies a lot of the mathematics and gives a very good approximation. In fact, a lot of very complicated problems cannot be solved if objects are not considered as point particles.

Applying a force for example if the object is not considered a point source would be very difficult. The force would have to be summed over for all the particles in a system which is not feasible. Instead if the object is simplified it is much easier to understand what is going to happen to he object when it is for instance interacting with something else.

Also, especially in fields such as Quantum Mechanics, non-physical concepts are very important (especially at an undergraduate level) to gain very good intuition into the subject area and understand reasons for why things happen.

• you are saying that these point particles are assumption to approximate calculations of motion of a body. – Remy Mar 2 '17 at 13:09
• You could add that for many applications the point mass model is actually exact (gives the same result as considering an extended mass). For instance the gravitational field of a homogeneous density sphere is identical to that of a point mass at the center of the sphere. The point mass model is not sufficient if you are concerned about rotations or in-homogeneous bodies. – user1583209 Mar 2 '17 at 13:12
• Yes but not always, take a very small object such as an electron. Due to its very minute size and volume, they are just considered to be a point as observed from a distance. This same comparison is extended to larger macroscopic bodies, and used to make very complicated systems with trillions of electrons into a point that is very small. – Sumant Mar 2 '17 at 13:14

then why did we invented the notion of point particles

Because that makes it simpler to work with.

• Sometimes we say "it costs 24 \$" even though it is actually 23.99 \$.
• We also usually say that there are 365 days on a year, even though there actually are $\sim$365.24.

We are accepting a tiny error margin, when that really doesn't matter at the scale we are working at. If you are working with everyday size-scales, then you really don't have to consider the actual size of stuff like charges, atoms, electrons etc. - the modelling of them as point-like is fine, fine, fine.

• wow it is three times fine a bit overwhelming . – Remy Mar 2 '17 at 15:14
• @Remy I know how to make a point (pun!). – Steeven Mar 2 '17 at 15:47