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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?

Qmechanic
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Remy
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    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. –  Mar 02 '17 at 12:55
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    Related: http://physics.stackexchange.com/q/234979/ –  Mar 02 '17 at 12:57

3 Answers3

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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.

anna v
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  • 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 03 '17 at 04:55
  • 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 03 '17 at 04:59
  • Is axis of rotation in rotating bodies also an assumption ? – Remy Mar 03 '17 at 05:06
  • yes, the mathematical solutions of assuming an axis fits the data given the boundary conditions – anna v Mar 03 '17 at 05:10
  • 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 03 '17 at 05:37
  • And I think that making those right approximations and ignoring what one surmises can be ignored, and getting then to the right models that they lead you to, is the essence of a real scientific theory, it is the real theoretical physics. The rest is pure observation and description - which however also requires to decide what is important to see and what should being ores and reduced to observe the relevant fact - and that construction is then the heart of experimental physics. Both are the human mind trying to approximate and understand physics, in the process we come closer to the physics – Bob Bee Mar 03 '17 at 05:44
  • @BobBee I am answering in my comment in the framework of the OP question, why a "point". In the same way, an axis is "points in a row" and does not exist in the same way that points do not exist except within our models. – anna v Mar 03 '17 at 07:09
  • @BobBee one can force any physical axis through any body, and make it rotate around it , the mathematical axis will be points in a row, not a rod which is the physical axis, through the body, when trying to calculatete the torques and forces. – anna v Mar 03 '17 at 09:04
  • Not what it usually meant. Physical rotation can always be defined to be around an axis. Didn't say a rod, said an axis. It s how we describe the rotation. Can't go around carrying rods for everything, but if one wanted to place (a very thin) rod in that axis the rod would actually not move – Bob Bee Mar 03 '17 at 17:52
  • If point particles have 0 dimension then how can you fit a rod with a spatial extension. – Remy Mar 03 '17 at 19:26
  • @Remy . It is an idealized mathematically locus, the same as taking the center of mass point, you have a mathematical line at the center of the rod and then you can fit the behavior of rotations and torques to the observations – anna v Mar 03 '17 at 20:20
  • @annav I have almost understood the whole concept and thank you for your detailed explanation. But i felt that you did not differentiate a lot between mathematical point and physical point particle (or point-like particle ).Is it fine to consider them both exactly the same ? A point particle has all the properties mathematical point of but it also has mass or charge. I understand you used term mathematical point for the purpose of explanation. but when we talk about physics in every day life we shall have to say a point particle not a mathematical or geometrical point .What is your take on it? – Remy Mar 04 '17 at 06:20
  • Mathematically we treat extended objects by using points representing them. If the object represented by a point, an electron for example, has an extent it is something that measurements will have to decide. At the moment the modeling of the standard model which has a number of point particles, https://en.wikipedia.org/wiki/File:Standard_Model_of_Elementary_Particles.svg , is validated . Experiments continue to set limits to what the possible radius of an electron may be. – anna v Mar 04 '17 at 06:53
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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.

Sumant
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  • you are saying that these point particles are assumption to approximate calculations of motion of a body. – Remy Mar 02 '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 02 '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 02 '17 at 13:14
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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.

Steeven
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