# Are Newton's three laws of motion essentially correct

1. Sep 21, 2004

### InvariantBrian

Newton's three laws are;

1. Inertia
2. f=ma
3. for every action there is an equal an opposite reaction.

It seems to me that the first and third law are still valid with the theory of relativity. And the second law f=ma is generally true in so far as it is correct to say that there exists an invariant universal relation between force mass and acceleration. Newton did not know that time, space and mass vary with respect to velocity. But I am inclined to say that newton's ideas were incomplete rather than simply wrong. I am interested in what others may have to say about this.

Thanks

Brian.

2. Sep 21, 2004

### pervect

Staff Emeritus
To go from Newton's laws to the relativistic version, let P be the momentum

Newton

p=mv, F=dp/dt

Relativistic

p=mv/sqrt(1-(v/c)^2), F=dp/dt

3. Sep 22, 2004

### InvariantBrian

oh that's interesting. So you can update Newton's second Law? and do you agree about the first law and the third?

4. Sep 22, 2004

### omin

I see the general principle in the second law covering the basis of every theory possible. Its seems to tie any type of velocity with any type of acceleration. For example, "time, space and mass vary with respect to velocity", proves a constant is needed to test for acceleration rate. Otherwise, we would have no idea how much anything varies and would call it unquantifiable. But unquantibiable is limited only by the precision of what we can sense through our basic senses direct or through indirect instrumentation aided sensing. I'd say, Newton hit it on the head and no theory will every out do the second law, in terms of comparision, the basic principle of physics.

5. Sep 22, 2004

### HallsofIvy

The only thing I find peculiar about this is that it implies that someone MIGHT say that Newton was wrong! Newton was amazing correct for the situation he was talking about. Relativity just extends it to extreme speeds and extreme masses comparitively. In any case there is no such thing as a "perfect" theory. Even relativity is not 'complete' because we don't know everything. It will, eventually, be superceded by a more accurate theory- this is the nature of the scientific process. (Actually, so much has been added to or 'adjusted' on relativity, one could argue that it has already been superceded.

6. Sep 22, 2004

### Ba

This actually is Newton's second law of motion and is phrased in a way that it actually fits in with relativity. At least it seems so to me.

7. Sep 22, 2004

### pervect

Staff Emeritus
Personally I think it's simpler to think of Newton's laws as saying that momentum is a conserved quantity, and that force is the rate of change of momentum. Relativistic dynamics is basically the same as Newtonian dynamics with a slightly different definition of momentum.

Therre are several ways besides Newton's laws to get classical mechanics, among the most interesting is the principle of least action, often known as Hamilton's principle.

an online java applet which illustrates this approach is at:

http://www.eftaylor.com/software/ActionApplets/LeastAction.html

a good encylopedia article (but it gets technical fast) is:

http://en.wikipedia.org/wiki/Euler-Lagrange

8. Sep 22, 2004

### mijoon

I don't know why anyone would call them incorrect.They are a specific case of the more general principals of GR. It is likely, that we will one day view GR also as a specific case of some even more general theory.
That doesn't make Newton incorrect, nor would it make Einstein wrong.

9. Sep 22, 2004

### InvariantBrian

But isn't there some type of electromagnetic phenomena that violates the third law?

10. Sep 26, 2004

### Antonio Lao

The 3rd law is based on central forces. The magnetic force is not a central force.

11. Sep 26, 2004

### robphy

These problems with the Third Law for electromagnetic phenomena arise when the interaction takes place over a distance ("action at a distance").

Note that the Third Law is an instantaneous statement
$\vec F_\text{on A due to B} = -\vec F_\text{on B due to A}\quad \text{"now"}$.
Since electromagnetism is really a relativistic theory (where distant simultaneity [what "now" is] is observer-dependent), the introduction of the electromagnetic field saves the third law [in the sense that the field carries momentum] since the interaction is now local (as they are for contact forces).

12. Sep 26, 2004

### Antonio Lao

The 3rd law in the form

$$F_{12}+F_{21}=0$$

is really time independent. It is true in the past, at present, and in the future. But in the form

$$m_1 a_{12}+m_2a_{21}=0$$

the accelerations come into being the instant the masses come into existence. But if the masses are equal then the accelerations are equal in magnitudes but opposite in directions. The result is no accelerations, the masses are either at rest or move at constant speed as a group of 2-body system. Zero accelerations imply constant velocity. And this constant velocity can be the speed of light in vacuum.

Last edited: Sep 26, 2004
13. Sep 27, 2004

### Antonio Lao

for attractive force, the accelerations exist up to half the distance between the two point-particles. But the mass ratio equalling to the negative ratio of two vectors of acceleration does not make any sense.

$$\frac{m_1}{m_2}= - \frac{\vec{a}_{21}}{\vec{a}_{12}}$$

I could be mistaken, but in order to define mass ratio, another conservation law must be invoked. This is the conservation of angular momentum.

Last edited: Sep 27, 2004
14. Sep 27, 2004

### pmb_phy

In going to special relativity;

First Law - Newton's first law remains valid.

Second Law - The second law remains valid as well. However you wrote it down incorrectly. Newton's second law is not F = ma. Its F = dp/dt. Only when m = constant does F = ma. Even Newton didn't hold that F = ma. Newton held that force is proportional to changes in momentum. In SR Inertia is properly though of as a bodies resistance to changes in momentum.

The definition of momentum remains valid as well. I.e. momentum is still given by p = mv. For tardyons (particles for which v < c) m = m(v) = m0/(1 - v2/c2)1/2 where m0 = m(0) (m0 is what pervect labels "m"). m0 is called proper mass or sometimes rest mass (I dislike the term "rest mass" myself). For a derivation please see

http://www.geocities.com/physics_world/sr/inertial_mass.htm

Third Law - Newton's Third Law is not always valid even in non-relativistic physics. It sometimes fails when there are charges involved. But in SR it always holds for contact forces.

Note - Everything above applies to particles. If the object in question is not a particle then p = m0v/(1 - v2/c2)1/2 is not always valid. For example, a rod which is moving in the direction parallel to its length. If the rod is loosing mass uniformly in its rest frame (e.g. by emitting radiation uniformly along its length) then p = m0v/(1 - v2/c2)1/2 does not hold. The relationship is more complicated. See the bottom of this page

http://www.geocities.com/physics_world/sr/invariant_mass.htm

If the mass of the rod is constant but is under stress then the momentum not given by p = m0v/(1 - v2/c2)1/2 either. Stress adds to inertial mass but it only does so when the body is moving. For an example which will shed light on this see

I'm working on another example but I've put it aside for the time being. I'll get back to it next year.

Pete

15. Sep 27, 2004

### InvariantBrian

But can Newton's third law be interpreted in such a way as to make it correct?

I found the following statement on the web...

'It is often contended that Newton's third law is
incorrect when electromagnetic forces are included: if
a body A exerts a force on body B, then body B will in
general exert a different force on body A (the force
considered is the Lorentz force, generated by electric
and magnetic fields). Modern theory predicts that the
electromagnetic field generated by such interactions
itself transports momentum via electromagnetic
radiation. Newton's third law becomes correct if the
momentum of the field is included in the calculations'

could you please comment on this statement?

thank you.

16. Sep 27, 2004

### InvariantBrian

I am not a science major. Is the above equation an interpretation of Newton's third law that is valid today?

thank you.

17. Sep 27, 2004

### trendy

first law

I am sorry to interupt this nice discussion but I need an answer to a question that I couldn't find on the web.

Why does Newton's first law hold? I mean is there an explanation why does an object in motion tend to stay in motion? Is this still a principle derived from observation or we can explain it?

Thanks.

18. Sep 28, 2004

### Antonio Lao

Newton's laws of motion is based on the concept of mass. The forces are all central forces. When masses are in motion, these define a concept of momentum. In my own opinion, the conservation of momentum, which is implied in the 3rd law, should be the 1st law, and the 1st law move to being the 3rd law. The 1st did mention a force but the 3rd law of action and reaction directly or explicitly defined the force. This force exists only if there are at least two bodies involve in the interaction. So, we can say all interactions are 2-body but by the superposition principle, all these 2-body interactions can be added together. Newton's laws as summarized in the law of conservation of linear momentum is as valid today as it was yesterday.

The theory of electromagnetism as formulated by Maxwell is based on the concept of electric charge. The Lorentz force, though still conservative (conservation of electric charge), has a non-central magnetic force. It can also be noted that mass does not appear in the Lorentz force equation.

But in order to determine the constants of these theories, both the force of gravity and force of electromagnetism must be used in the experimental laboratories. What we ended up is the charge to mass ratio and then independently find the unit of charge (quantum of charge). But as of now, we still do not have a value for the quantum of mass. From my own research, I am hypothesizing that the Planck mass is the quantum of mass and it has a positive and a negtive value. Yet we have to explain why the mass of the electron is only 1/2 MeV.

19. Sep 28, 2004

### InvariantBrian

But if Newton's third law is stated in these two equations, does it adequately account for the force interactions in electric charges?

$$m_1 a_{12}+m_2a_{21}=0$$

$$F_{12}+F_{21}=0$$

20. Sep 28, 2004

### Antonio Lao

InvariantBrian,

It does not. Newton's laws of force are for the inertial force (2nd law) and the law of universal gravitation. Both of these forces depended on the concept of mass only.

The concept of electric charge as formulated by Maxwell was invented about 200 years after the death of Newton. The force that depended on the concept of electric charge is called the Lorentz force, the sum of electric force and magnetic force.

The force that depended on the weak charge is called weak nuclear force.

The force that depended on the color charge is called strong nuclear force.

Although all charged particles also have mass, the effect of these force-from-mass are negligible by comparison to the other forces. The strength of each force is the coupling constant determined by experiments for each force.