My question is which law of Newton is the most fundamental? I am talking of the laws of motion...
Uhhhh. I'd have to say that they are all equally fundamental. The definition of fundamental means that something is not derived from something else. How can you have one fundamental thing being more fundamental than another fundamental thing. If that were the case, the second fundamental thing, wouldn't really be fundamental would it?
I fear I might not agree with you...When you do not have the option to derive something from another,you have to look for something else...
What do you mean by "fundamental"? This word has multiple meanings, and the answer depends on which meaning you choose. Most basic? Newton intentionally ordered the laws the way he did, starting with the most basic concept. Most universal? There is no such thing as a force-free object, and magnetism violates the third law. The second law is the most universally true. Most profound? We would be lost without the third law. The concept of equal but opposite reactions is used everyday by scientists and engineers.
Newton's Laws are not derived from anything let alone each other. They are all equally fundamental in that sense. They are statements made about our observations of nature through experiment.
Now, the theory of Newtonian mechanics assumes these laws to be true and builds a theory around them. In this sense, the theory of Newtonian Mechanics is derived from Newton's Laws using inductive logic, in other words, a logical argument style based around assuming certain principles to be true. These principles must be shown to be true by something outside of the argument, in our case, Newton's laws are tested using experiments, not proven in the argument (the theory). In this way, all science is based on observation and inductive logic.
I disagree. The first law can be derived from the second. The first law is simply the special case of the second where a = 0.
The second and third laws are "equally fundamental".
The modern view is that the first law defines the concept of an inertial frame, the second law defines the concept of force, and the third further qualifies that forces come in equal but opposite pairs.
OK, I can see that too, even though it seems like somewhat circular reasoning to me. I am sure there are some subtelties that I am missing.
I agree with DH to some extent...
The Oxford dictionary says fundamental means "of central or primary importance".It is neither the "basic" nor the measure of "universality".
I agree that Newton wrote his laws according to the order of simplicity.However there was yet another reason.Again,2nd law is universal...however,it does not include the concept of "jerk",the third time derivative of displacement...
Firstly,they are all intertwind and different parts of the same underlying symmetry of nature.But I think I can regard the third law as more profound than the first two laws.
Newton’s 3rd law is valid in any frame, inertial and non inertial, it is independent of the concept of inertia.
Let me justify that truly, 3rd law is independent of 1st and 2nd laws.
My plan to check whether 3rd law is independent of 1st law and 2nd law is to see
i) When 3rd law is valid, in which frame we are.
ii) When it is not valid, in which frame we are.
i) When 3rd law is valid we are in an inertial frame; but we may also be in a non-inertial frame!! Since 3rd law deals with only interaction forces (as per its statement) ['interaction force' only means one can find who applies the force on whom and how is himself affected] even in an accelerating frame, these forces satisfy 3rd law. After we know about frames and forces, we can identify them to be real forces.
ii) When it is not valid, we cannot conclusively say that we are in a non-inertial frame. There are cases in electrodynamics where in an inertial frame non-relativistic charge particles do not satisfy 3rd law in spite of their real interaction. You may choose to read Griffiths, 8.2: Momentum.
Note, we need not use 2nd law for calculating force magnitudes, 3rd law gives them ready- made to us.
Another essential concept I wish to show is that force is the result of an interaction between two systems is made explicit by the 3rd law.This affects both the bodies involved.And one cannot simply apply F=ma on an isolated body even in an inertial frame.So,it is an essential concept in making sense to the other two laws...
As DH said, "isolated" bodies cannot be conceived in reality" ,"3rd law fails in some cases", 2nd law also does not describe the reality in its full.Since,in general,force is a function of time,there are other higher order derivatives that are needed to describe the motion appropriately.
Generally,we are interested to see if the law applies to desired degree of accuracy.
The 2nd law is valid only in an inertial frame of reference and the definition of inertial frame is provided by the first law.
The hard part is deciding whether the first law (conservation of velocity in a closed system) is more or less fundamental than the third law (total force=0 in a closed system).
Conservation of momentum being the more fundamental,we should give preference to third law (total force=0 in a closed system)---that is what momentum principle is...And conservation of velocity follows from this as a special case...
What about magnetism? It violates the third law.
What is "force"? The third law most certainly is not independent of the second, because it is the second law that defines "force", and it defines it in terms of the behavior of a body in an "inertial frame".
What is an "inertial frame"? Now the first law comes into play.
*Let me mention that in magnetostatics, Newton's 3rd law holds.Now,regarding the magnetism in matter:
(i)magnetism,at the root level,is either non-linear or quantum phenomena.In fact, the magnetic force is a peculiar thing...You cannot apply even F=ma here,this force does not do any work.And the reason why Newton's laws (do not blame only 3rd law) do not hold good is because of the fact that magnetism is essentially different from classical physics.
However,in electrodynamics,3rd law truly does not hold.I have mentioned this.Griffiths shows a nice example.There conservation of momentum rescues us.But I suspect again that is because of the fact that these cases simply goes beyond the scope the classical physics.Momentum cannot be simply defined as mass times velocity in those cases.
*Force is more than a matter of definition.It is a feature of Physics.None of newton's laws is able to describe the correct sense associated with it.They only deal with the real and inertial aspect of the force.
So,the physical concept of force is already there.We call the magnetic force also to be a "force" and fictitious force also to be a "force".Newton uses the inertial aspect of the concept.
3rd law does not depend on 2nd law as it does not require to calculate m=...kg,
a=...m/s^2 etc.It deals only with the force of interaction...
*Yes,I agree that inertial frame is defined by the first law...We often omit to note that first law also gives an intuitive idea of acceleration and higher order derivatives.It says "the change of state of motion..."
Hmm.... The first law doesn't say anything about "change of state of motion" in my copy of Newton's Principia.
Actually Principia starts with 8 definitions, and ten pages of discussion about them, which are more "fundamental" than the three laws. For example, Newton says that time is absolute, and he also says that there it may be no possible way to do an experiment which can verify that assertion.
Actually he DEFINES "force" as "anything which changes the uniform motion of an object" (my paraphrase of definition 4), so the first law is true by definition. The second law defines a way to assign a magnitude to a force. The third law gives says that this definiton of the magnitude of a force is useful because it is consistent, in the sense that "equal" forces have equal effects.
He then justifies laws 2 and 3 by deriving some corollaries (for example the "parallelogram of forces") that can be demonstrated by experiment.
Then the REAL mathematical fun and games begins at the start of Book I, "On the motion of bodies"...
I do not have the copy of principia n my hand,though I have seen it in library desk.However,I am to some extent familiar with the notions of absolute space and time due to newton.
A statement of the first law may be:A body continues to be in its state of rest or of uniform motion unless it is compelled to change its state by an external force impressed upon it.
I heard that he starts the book writing that he would not define space and time as everyone knows them...
I did not see your point in this post...
Can you be a littlee specific?
Thus far,I have mainly written what I have thought and tried to make my logic convincing.But there may be flaws...Can anyone find out some other way to look at this?
(1) You have more-or-less brushed off everyone's input. If you don't want to listen, why ask? (2) Philosophy is little more than mental masturbation.
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