# Newton's laws cannot be proven

1. Jan 14, 2010

Newton's laws cannot be proven!!

As far as i know, Newtons laws are.....

1st Law-- A body at remains at rest and a body at uniform motion remains at uniform motion unless an external for acts on it.

2nd Law-- F=ma

3rd Law-- Every action has an equal and opposite reaction.

No method has been designed to prove these three laws. However, these laws are vital in almost the whole of physics.

I heard that we believe in these laws because all the measurements and experiments are in agreement with these laws.. What does this exactly mean? Can somebody give an example.

Also, as far as i know, 1st and 2nd law hold only in inertial frame of reference and Newtonian mechanics does not work when the speed of any object approaches the speed of light. Does the 3rd law still work in an accelerating frame of reference and when the speed of the object approaches the speed of light? If yes then why so?

It would be great if someone could give me an answer.

2. Jan 14, 2010

### CFDFEAGURU

Re: Newton's laws cannot be proven!!

Newtonian mechanics cannot be used when traveling near or at the speed of light. Newtonian mechanics uses the notion of absolute time. In the 4-dimensional curved spacetime the notion of absolute time is not used. Proper time is used instead. (I will not go into detail on what proper time and worldlines are.)

That is all I will comfortably say on this subject.

Thanks
Matt

3. Jan 14, 2010

### R Power

Re: Newton's laws cannot be proven!!

yes these can't be proved but there is no point of thinking about proving them.

Because these are fundamental, e.g 1+2 = 3, can you prove this? This is fundamental man has made maths like this.
Yes, ofcourse newton's laws are not designed artificially like numbers, but these are considered fundamental.
The physics required to prove newton's laws would be totally different. There need to be more fundamental phenomenon in nature or more fundamental approach in order to prove them then. Because in order to prove that 10x3 > 5x4 u can say that divide both sides by 10 and we all know that 3>2 but can you prove that 3>2 ??? In order to prove this you need more fundamental approach than this which according to me doesn't exist because it is defined that 3 is > 2.
Similarly, newtons laws can't be explained by today's experiments because they all are application of these laws. So, we need more fundamental approach in macromechanics since these laws were basically for macroscopic bodies when newton defined them.
and yes, newtons laws are perfectly valid only in inertial frames. Now, this is what you ca call some more fundamental thing, relativity. Since newtons laws were not satisfying relativity these were enclosed under a boundary called inertal frame.

I don't know i'm 100% or even 50% correct. I apolozise if i wrote anything incorrect because im not a master of mechanics.

4. Jan 14, 2010

### Andy Resnick

Re: Newton's laws cannot be proven!!

Laws #1 and #3 are consequences of Law #2 for cases when F = 0, so there's really only one "Newton's Law" (and it's F = dp/dt, not F = ma).

Even so, Newton's law is most accurately understood to be a *definition* of force (or alternatively, mass). The utility of Newton's law occurs when there is an analytical form for the force: F = -kx, or Gmm'/r^2, or e(E+v x B), or some other formula. Newton's law connects kinematics (things we can measure, like velocity and position) with dynamics (causes). It's important to remember that 'force' is not directly measurable.

F = dp/dt has been found to agree with any experiment for which v/c <<1, or when relativistic effects are much less than experimental error. F = dp/dt is in agreement with (nonrelativistic) quantum mechanics. Newton's law can also be generalized to include continuum mechanics, statistical mechanics, and much more.

5. Jan 14, 2010

### Staff: Mentor

Re: Newton's laws cannot be proven!!

Definition or not, every time you use Newton's laws and your results match the prediction, you are adding to the substantial body of proof that these laws have.

6. Jan 14, 2010

### MaxwellsDemon

Re: Newton's laws cannot be proven!!

One doesn't go out to prove laws in science. Laws are just statements concerning what is observed to be true. The first of Newton's laws basically just defines a force as something which changes the motion of an object. The second law makes that statement precise by putting it in the language of mathematics. So the first two laws of motion just say, "Here is what a force is and here is how you calculate it." The physics of Newton is all really bound up in that third law. Newton's third law of motion isn't valid for objects moving at relativistic speeds.

7. Jan 14, 2010

### D H

Staff Emeritus
Re: Newton's laws cannot be proven!!

*No* scientific theory can be proven true. Newton's laws are no exception. Compare this to mathematical theorems, which can be proven true. In fact, mathematical conjectures are not called theorems until they have been proven to be true.

Scientific theories are at best provisionally true. They can be proven false -- all it takes is one lousy experiment. Newton's laws have in fact been proven to be false. Special and general relativity are better (read: more accurate) models for things that go very fast or near things that are very massive. Quantum mechanics is a better model at the atomic scale. Newton's laws are still used today because they are approximately true in the realm of the not too fast, not too massive, and not too small.

==========================================

I disagree (except with the parenthetical remark). Laws #1 and #2 are essentially definitive, the first law defining momentum and the second, force. Law #3 is a beast of a different color. It is a scientific law. The third law is equivalent to the conservation of linear and angular momentum.

8. Jan 14, 2010

### wofsy

Re: Newton's laws cannot be proven!!

Here is an example for the first Law which was really discovered by gallileo.

Inclined plane experiments show that a ball rolling down one plane from an initial height will rise to the same height on another plane no matter what its inclination. The length of the inclined plane does not matter - only the height. Thus a longer plane rising to the same height would be flatter - i.s. it would rise at a smaller angle. In the limit of an infinitely long plane the particle would move forever. This is Newton's first law.

9. Jan 15, 2010

Re: Newton's laws cannot be proven!!

Thanx alot!!
I feel i am understanding what you all mean..
Still..
Can somebody explain me why 3rd law doesnot work in accelerating frame of reference or when the object approaches the speed of light...

10. Jan 15, 2010

### MaxwellsDemon

Re: Newton's laws cannot be proven!!

The third law doesn't work in relativity mainly because in relativity there is a finite speed of cause and effect. Forces in relativity take time to propagate. Also velocities in relativity don't add in the usual everyday vtotal = v1 + v2 sort of way. Those two facts conflict with the whole "equal and opposite" part of the third law.

11. Jan 15, 2010

### D H

Staff Emeritus
Re: Newton's laws cannot be proven!!

MaxwellsDemon just addressed the latter question. I'll discuss the failure of Newton's 3rd law in non-inertial frames.

Strictly speaking, Newton's laws are only valid in an inertial frame. (Yet another interpretation of Newton's first law is that it defines the concept of an inertial frame of reference.) Various fictitious forces need to be invented to make Newton's first two laws appear to apply in a non-inertial frame. For an accelerating frame, one must introduce an inertial force to the equations of motion. Rotating frames require the addition of the fictitious centrifugal and coriolis forces. These fictitious forces have two things in common: (1) The fictitious force acting on some object is always proportional to the mass of the object, and (2) There is no third-law counterpart to these fictitious forces. In other words, fictitious forces do not obey Newton's third law.

12. Jan 15, 2010

### DaveC426913

Re: Newton's laws cannot be proven!!

Subtle distinction:
Newton's Laws are not theories. Thoeries and laws are distinct.

Theories try to explain, using a model, how something happens.
Laws are simply a description of what we observe, without any attempt to explain why or how.

One might say theories are us telling nature how she behaves; whereas laws are nature telling us how she behaves.

13. Jan 15, 2010

### Andy Resnick

Re: Newton's laws cannot be proven!!

Law #1 is obtained from law #2 by setting F = 0. Law #3 is also obtained from Law #2- two particles in a box, total F = 0, let the particles collide.

14. Jan 15, 2010

### D H

Staff Emeritus
Re: Newton's laws cannot be proven!!

What is momentum? An inertial reference frame? Newton was not a dummy. He would not have written the first law if it was merely a special case of the second.

This does not follow.

15. Jan 15, 2010

### ZapperZ

Staff Emeritus
Re: Newton's laws cannot be proven!!

Actually, if one thinks about it, Newtonian mechanics (and laws) can be derived from the principle of least action. See, for example, J. Hanc et al., Am. J. Phys. v.71, p.386 (2003). So essentially, what isn't "proven" (if there is such a thing in science) is the principle of least action, since that is the starting point.

But as has been mentioned already in this thread, one verifies ideas in science. One doesn't prove them in the strict sense of logical or mathematical proof.

Zz.

16. Jan 15, 2010

Staff Emeritus
Re: Newton's laws cannot be proven!!

And to show that there are differences of opinion depending on what you start, I would look at it differently than Zz, in that you can rigorously mathematically prove that you can go from a least action principle to equations of motion. What you need as a starting point is how you calculate the action - that's where the connection with reality comes in,

No matter how you slice it, you will always need two pieces - a piece that is a generalization based on observation of the real world, and a piece that lets you extend this mathematically.

17. Jan 15, 2010

### wofsy

Re: Newton's laws cannot be proven!!

I wonder to what extent Newton's Laws were merely laws and to what extent they underpinned a theory.

Here are some questions that make me wonder.

- Newton's Laws require a notion of absolute space. Is this not a theoretical construct?

Leibniz rejected Newton's Laws precisely because he felt that the idea of absolute space violated the Principle of Sufficient Reason.

Newton hypothesized absolute space so that his laws could be true. Is this not a theory much like the theory of Relativity? Is is not an anti-theory of Relativity?

- Newton in his day was accused of reviving the Physics of Aristotle. His first Law is a reformulation of Aristotle's law that says that a body in motion comes to rest unless acted upon by an external force - a fact that is clear from observation. I wonder why the revival of Aristotelian style thinking was controversial and perhaps for its time this revival was making a theoretical statement about what can and can not be known of the world. When he wrote that he needed no hypotheses I think he may have been affirming Aristotelian empiricism.

- I also wonder what the ideas of force were in his time. F = Ma seems almost to be a definition but it must have meant something in the context of earlier ideas of force. If so,this equation would have theoretical content.

18. Jan 15, 2010

### DocZaius

Re: Newton's laws cannot be proven!!

I think this discussion might be slightly tangential (since this concerns something other than whether Newton's Laws can or cannot be proven), but I don't think Newton's Laws require absolute space. Newton's Laws seem to work perfectly well within the framework of Galilean Relativity which concerns relative locations and relative speeds. An absolute time, however is a necessity for Newton's Laws as they were originally written.

19. Jan 15, 2010

### D H

Staff Emeritus
Re: Newton's laws cannot be proven!!

Wherever did you get this idea? Newton's first law is a rejection of Aristotelian physics.

Newton's mechanics was controversial precisely because it rejected Aristotelian thinking. Aristotelian physics was still the rule rather than the exception in the education system in Newton's time. That said, other giants had previously laid the groundwork for Newton's works. Newton's first law is essentially a reiteration of statements by Galileo and others.

Newton's second law is now viewed as defining the concept of force. A quibble: Newton's second law says F=dp/dt, not F=ma.

20. Jan 20, 2010

### Cider123

Re: Newton's laws cannot be proven!!

I would like to give my own stab at this.

Starting with F=ma, I have taken the time to type in boldface the vector quantities. This is important to how I view the equation.

Writing it this way, it becomes surprisingly easy to separate Mathematics and Physics in this particular case. Here is what I mean:

Acceleration, a, is simply the second and first derivative of position and velocity respectively. No 'physics' is involved in this definition, just Calculus. Remember those simple physics problems where you find the trajectory of a ball? This Trajectory or path is just a simple function in space. Remember how to solve for it?

If you are given the three vectors initial position, initial velocity, and acceleration (they are functions of time), then it is a simple integral to find the position of the ball at all times.

Of these 3 vectors, 1 is decidedly harder to measure than the rest (can you guess which one?). It's acceleration(as a function of time).

Think about throwing a ball in real life. We can take a ruler and find its starting position, and with some cunning we can even determine the initial velocity (for example we can place the ball on a train traveling at a known velocity and bring the train to an abrupt stop, causing the ball to continue to travel at its original velocity-some imagination with friction required).

But we can easily imagine a situation where the acceleration of the ball at all times is hard to determine. For example, we can attach some rockets to the ball, ionize it and place it in a randomly varying electric field, and throw pies at it.

So some guy named Newton comes along and says:
'Well we have this time-dependent vector called acceleration; I am a genius so I will define this other time-dependent vector called force; it will be equal to a scalar value called mass multiplied by acceleration. Now all we have to do is determine the 'force' acting on an object at all times and we can naturally derive acceleration.'

So how do you determine the 'force' acting on an object at all times? The previous posters have mentioned this already; we use various Theories (Theory of Gravitation, etc.). These theories perform the important task of defining a force with respect some variables. In the case of gravity, force is inversely proportional to distance squared, etc.

So in the end, where do we get our confidence in F=ma? Well we subject our Theories to some pretty rigorous tests. The original poster asked for an example, so I'll try to provide one.

Let's say I work at NASA and my boss wants me to send a space shuttle from Earth to Jupiter to take some pictures, then over to Mars for some more pictures, and finally to Pluto for tea and biscuits. Well I get out my Solar System chart and plot a Trajectory. I give myself a reasonable Initial Position and Initial Velocity and find the Acceleration needed to trace out my path; only Calculus is required here.

Then I say, what can provide my space shuttle with this acceleration? Well I know rocket boosters and planetary gravitation provide a force... (theories)

Is there some nifty law I can use to get from a force to an acceleration?

21. Jan 20, 2010

### wofsy

Re: Newton's laws cannot be proven!!

The crux was that Aristotle's laws as Newton's were hypothesis free, purely empirical without any reference to purpose, design, or the Principle of Sufficient reason. People knew that Newton was reaffirming Aristotle's approach to Science, an approach that had been somewhat repudiated with the overthrow of the Ptolemaic system - which people criticized because it violated the principle of sufficient reason.

Ancient notions of force were probably quite complicated and Newton's law reduces these notions to a purely empirical formula.

The Aristotelian/Newtonian view lived on and may still have some residual life today. opposition to it has also lived on. Einstein for instance. affirmed the Principle of Sufficient reason. A good book on this controversy is Poincare's Science and Hypothesis.

Last edited: Jan 20, 2010
22. Jan 20, 2010

### dE_logics

Re: Newton's laws cannot be proven!!

Well, IMO, we are living in a world of assertion assuming everything that we see around is actually happening. Many people know this is not the case, and so we have other forums in physicsform apart from classical physics where we discuss conditions when s != d/t. But we can't confirm those theories also to 100%...stuff like LHC just increase their accuracy while some fail...like string theory.