# Are Newton's three laws of motion correct? [closed]

New technology brings new ideas with these new ideas we have to look at the old ones. Where else is a better place to start then Newton's three laws of motion! With our common age of technology do we apply these "old laws of physics" into our new age?

• For range of validity of Newton's laws, see e.g. Wikipedia. Nov 2, 2012 at 1:26
• @Qmechanic Yes, but that article unfortunately mixes in an un-encyclopedic discussion about how outdated all of 17th century physics is, while the OP only asked about the 3 laws of motion.
– user10851
Nov 2, 2012 at 4:33
• – user4552
Jul 18, 2013 at 14:51

"Newton's Laws" are - like most physics - a mathematical model that describes how the world - or the universe - works.

All models are wrong, in that they don't describe the complete complexity of the physical world, but some models are useful, in that they let us make predictions.

Newton's Laws, as a model, work well, unless you are dealing with things that have very large mass, move at a significant fraction of the speed of light, or are very small in size. At that point, things like relativity, and the uncertainty principal become significant.

Newtons' Laws also don't work very well in isolation when you consider things like air resistance or friction, for example.

• Not all models are wrong for sure. They are only wrong until we find the right one, and then it is right. Nov 2, 2012 at 16:50

Of course Newton's three laws of motion are correct, because they were verified several hundred of years ago and they continue working today, for such systems. Science is accumulative.

What modern physics has done is to constraint the range of validity of those laws. Although some 18th century physicists believed that the laws were valid elsewhere, we know today that Newton laws are only valid for problems involving low velocities (when compared with the speed of light) and not too large or too small masses.

This accumulative character of the scientific knowledge is the reason which you find Newton laws in any modern textbook on physics and the reason for which his laws continue being applied to everyday problems (e.g. by mechanical engineers).

Wikipedia has the following text:

Newton's laws were verified by experiment and observation for over 200 years, and they are excellent approximations at the scales and speeds of everyday life. Newton's laws of motion, together with his law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena.

These three laws hold to a good approximation for macroscopic objects under everyday conditions. However, Newton's laws (combined with universal gravitation and classical electrodynamics) are inappropriate for use in certain circumstances, most notably at very small scales, very high speeds (in special relativity, the Lorentz factor must be included in the expression for momentum along with rest mass and velocity) or very strong gravitational fields. Therefore, the laws cannot be used to explain phenomena such as conduction of electricity in a semiconductor, optical properties of substances, errors in non-relativistically corrected GPS systems and superconductivity. Explanation of these phenomena requires more sophisticated physical theories, including general relativity and quantum field theory.

In quantum mechanics concepts such as force, momentum, and position are defined by linear operators that operate on the quantum state; at speeds that are much lower than the speed of light, Newton's laws are just as exact for these operators as they are for classical objects. At speeds comparable to the speed of light, the second law holds in the original form $$\mathbf{F} = \mathrm{d}\mathbf{p}/\mathrm{d}t$$, where $$\mathbf{F}$$ and $$\mathbf{p}$$ are four-vectors.

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– user4552
Jul 18, 2013 at 14:45
• @Ben No, that's not true (the part about copying from WP). Content on SE is CC-licensed under the same license Wikipedia uses, as indicated at the bottom of the page and in the ToS, so it complies with the share-alike clause. (Of course posts here also cannot constitute plagiarism, which is technically a separate issue.) Jul 18, 2013 at 17:19

If you mean the specific "three laws of motion" (as opposed to Newtonian mechanics in general) --

• the first law is generalised to the geodesic principle in general relativity,
• second law is replaced by $F=(\gamma^3, \gamma)ma$,
• third law is replaced in general relativity, since momentum isn't conserved (instead of $\partial_\mu T^{\mu\nu}=0$, you have "conservation along spacetime" $\nabla_\mu T^{\mu\nu}=0$).