# Can a force that has magnitude of an irrational number be exerted? [duplicate]

Can a force, which has magnitude of an irrational number or does not end (ex : 1/3), act upon any particle?

If photon of particular wavelength lambda has some energy say E, then can the photon/group of photons exert a force which is irrational in its magnitude. If yes, then how?

If the desired force is pi(3.1415...), how can this force be attained by sum of force in a finite amount of time.

pi = 3 + 0.1 + 0.04 + 0.001 + 0.0005 + 0.00009 + ....... The above sequence does not end; And if a photon can exert a finite amount at a time, we would either require infinite amount of time or infinite amount of photons to create an infinitesimally small force.

My teacher says that the forces which are of magnitude of any irrational number are exerted on bodies. And it is just the incapability of humans that we cannot image that particular magnitude.

## marked as duplicate by David Z♦Oct 15 '16 at 8:56

• Saying that a number "doesn't end" because it's irrational doesn't make sense. A force of pi Newtons is just as reasonable as a force of 2 Newtons, for example. And photons can have any wavelength, including irrational. – Wood Oct 15 '16 at 8:09
• Possible duplicates: physics.stackexchange.com/q/52273/2451 and links therein. – Qmechanic Oct 15 '16 at 8:24

The irrationallity of numbers is just a mathematical concept. It makes it hard to display, but nothing more.

Remember that the world works in continuous ways. Not discreet ways. If you have a force at 100 N and you decrease it gradually to 0 N, you will pass over each and every value in between. And both $1/3$ as well as $\pi$ and $e$ and $\sqrt 2$ etc. are in between.

If we must go to the deepest core of things, everything is split into quantas and does position itself in discrete values of energy etc. This should be so negligibly tiny at our size scale, though, that the effect will be so far out on a far, far decimal that I can't even guess how far.

• I cannot understand that if I decrease the force from 100 to 0 how can I get to 1/3. How can I understand this? – Parth Maske Oct 15 '16 at 8:14
• @ParthMaske If you remove 1/3 from this continuous set of numbers in this interval, then you have a hole in the interval. But the world doesn't make "jumps". Quantum leaps do, though, but are simply too small to be considered. Rather the world is continuous, so the force passes through each and every value in its ways to another value. – Steeven Oct 15 '16 at 8:31
• @ParthMaske In Newtonian mechanics, values like force can be expressed as real valued functions of real parameters. Look up the statement of the Intermediate value theorem. – Praneet Srivastava Oct 15 '16 at 8:42
• @Steeven If we agree that the world behaves in a discrete way at smaller scales, even if it is negligible we cannot consider it as continuous as it can either be continuous or discrete - we cannot have a hole and no hole. – Parth Maske Oct 15 '16 at 8:48