# Talk:Force/Archive 6

## Wave-wave interactions

The article makes no mention of waves, yet a wave has a property analogous to momentum in h/lambda. Do wave-wave interactions result in changes in wavelength, and therefore momentum, and if so is force a necessary, or a meaningful, concept in considering wave-wave interactions? Should this be covered also in the article? Skeptical-H (talk) 00:27, 12 April 2008 (UTC)

Waves allow for the transference of momentum and carry momentum, but the only way to change the momentum of a wave is if the force couples to the energy of the wave. For example, electromagnetic forces affect an electromagnetic wave, but the strong nuclear force does not. ScienceApologist (talk) 12:10, 13 April 2008 (UTC)
Yes, but my question was really about whether the language of the article would apply if the subject of the force were a wave, rather than a particle or other massy object. We can understand pushing and pulling an object because we can envisage where an object begins and ends (it has boundaries), but a wave doesn't have the same tangibility. Take a tsunami, for example. Mid-ocean it has a wavelength of several hundred kilometres and relatively low momentum but on the coast its wavelength is compressed to a few metres with enormous momentum. Now presumably this acceleration is brought about by forces propagated through the water from the sea bed, but on which part of the wave do they operate? The wave is just the surface of the sea. In this case, I suppose, the forces are really acting upon the water molecules, and the wave is just an emergent property of the molecules in aggregate motion, but is this the case for all waves? Are all waves (including electromagnetic waves, for example) merely appearances, their apparent momentum being simply a statistic summarising that of the particles through which they propagate. In other words, is it in fact the case that, in every case, forces act only on particles? Or are there circumstances when forces act directly upon waves as entities in their own right? In which case, and I suppose I'm answering my own question here, does the gauge boson carrying the force effect the acceleration by merging as a wave with the subject wave, frequency modulating the wave as a consequence, and, reciprocally, is such a wave capable of splitting into a gauge boson wave and frequency-modulated daughter wave? If these are correct, would it be useful to include a section to this effect in the article? Skeptical-H (talk) 11:55, 16 April 2008 (UTC)
Waves carry energy. E=mc2. Therefore waves carry something like "mass" (at least, the energy of the wave behaves the same way through general/special relativity). That's the easiest way to think about it. In your tsunami example, the wavelength of the tsunami stays the same: only its amplitude changes. There is no acceleration and energy of the tsunami is conserved. Since there is no acceleration, there are no forces. The apparent momentum of an electromagnetic wave is, in the limit where forces are considered, tied up in its individual photons. These photons can exchange momentum with charged objects and, when they do, the forces measured obey Newton's laws even though photons are technically waveparticles. Forces do not act on waves in the same sense because forces are ultimately defined for point-particles which a wave is sort of the opposite of. In order to explain how forces act on "waves" you essentially look at the "particle nature" of your wave and then back-calculate the result. Frequency modulation/ interference/ superposition of two waves is effectively the transfer of momentum, but in order to determine the "force" we must localize the wave into something that approximates a particle. I hope this explanation helps. ScienceApologist (talk) 12:46, 16 April 2008 (UTC)

## Force as a concept

One thing that bothers me in the lead is that it may not immediately put in perspective to the lay reader that in physics force is a scientific construct used to help model our universe. The phrase "In physics" succinctly indicates that to those that understand scientific method, but for the wider audience I wonder if needs more explanation. Even on a more advanced level as this article shows, there is ambiguity. I suppose it depends on the level and breadth of audience the article is designed for. Ward20 (talk) 19:16, 13 April 2008 (UTC)

I think if a reader just hung out with the lead, the reader would probably not catch the nuance of what Wilczek is saying. However, without some of the background provided by the rest of the article, it would be inappropriate for us to mention this kind of critique too early. The article as it currently stands strikes a balance in this regard. My opinion, of course. YMMV. ScienceApologist (talk) 14:21, 16 April 2008 (UTC)

## potential energy paragraph

In the 'potential energy' paragraph you write that :
"Instead of a force, the mathematically equivalent concept of a potential energy field can be used for convenience."
Then, you write : "Forces can be classified as conservative or nonconservative. Conservative forces are equivalent to the gradient of a potential while non-conservative forces are not."

In the first sentence, it seems all forces are conservative since they are 'equivalent' (why?) to the 'concept of a potential energy field', and 'conservative forces are equivalent to the gradient of a potential'. In the last sentence, you say not all forces are conservative.Randomblue (talk) 02:06, 14 April 2008 (UTC)

Great point. The first sentence is actually wrong. I'll try to reword it. ScienceApologist (talk) 19:10, 14 April 2008 (UTC)

## Some ideas for a simplified lead

I have had a go a rewriting the lead following comments on the FAC. I have dropped a few phrases and delinked some terms I thought distracting. It's nothing more than suggestions; see what people think:

A force is a push or pull that can cause an object to accelerate.[1] Force has both magnitude and direction, making it a vector quantity. An object will accelerate in proportion to the net force acting upon it and in inverse proportion to the object's mass. An equivalent definition is that the net force on an object is equal to the rate of change of momentum it experiences.[2] Forces acting on three-dimensional objects may also cause them to rotate, deform, or result in a change in pressure. Torque determines rotational effects: the rotational equivalent of forces. Stress forces created within the object determine deformation and pressure.[3][4]
Since antiquity, scientists have used the concept of force in the study of stationary and moving objects. These studies culminated with the descriptions made by the third century BC philosopher Archimedes of how simple machines functioned. The rules Archimedes determined for how forces interact in simple machines are still a part of modern physics.[5] Earlier descriptions of forces by Aristotle incorporated fundamental misunderstandings, which would not be resolved until the seventeenth century when Isaac Newton correctly described how forces behaved.[4] Newtonian descriptions of forces remained unchanged for nearly three hundred years.
Current understanding of quantum mechanics and the standard model of particle physics associate forces with the fundamental interactions accompanying the emission or absorption of gauge bosons. Only four fundamental interactions are known: in order of decreasing strength, they are: strong, electromagnetic, weak, and gravitational.[3] High-energy particle physics observations, in the 1970s and 1980s, confirmed that the weak and electromagnetic forces are expressions of a unified electroweak interaction.[6] Einstein in his Theory of General Relativity explained that curvature of space-time is an attribute of gravity, though perceived as a force.

BillC talk 21:07, 15 April 2008 (UTC)

• I support it. Let's see how our lay-readers feel. ScienceApologist (talk) 21:49, 15 April 2008 (UTC)
I'll replace the current lead with it to see if it flys. Cheers! Wassupwestcoast (talk) 21:58, 15 April 2008 (UTC)

## First line

The article begins by stating that force is "A force is a push or pull that can cause an object to accelerate." But the reference given (reference 1) already gives a different definition. I do maths and I am used to the way math people talk, that is, they give the precise definition, no beating around the bush. i guess this article starts by given an approximated definition of force and little by little tries to find a better, more encompassing, defintion. I can see that both approaches have its benefits. To fix the situation, i suggest that instead of starting with "A force is a push or pull that can cause an object to accelerate." it should start like: "As a first approximation, one can thing of force as a push or pull that can cause an object to accelerate or deform."

Though, I would much much perfer to start reading something like: "As a first approximation, force is the way matter can interact with matter. For example, the Earth interacts with the moon causing it to accelerate. This interaction is mediated by the gravitational force. A person throwing or squeazing a ball is an interaction between two pieces of matter that is mediated by a electromagnetic force. Notice, however, that the effects of the interaction between two pieces of matter can be not only an acceleration or a deformation. Indeed, most chemical reactions are the interation of matter having consequences different from a change in velocity or shape. Usualy, chemical reactions are carried out by electromagnetic forces."

... or something similar...

or something like this. Also, the references look quite basic. There is a book called "On the concepts of Force" or something like this that I believe would be a nice reference to quote (this is not the same thing as the article in the reference list that has a similar name). —Preceding unsigned comment added by 155.198.157.118 (talk) 14:01, 16 April 2008 (UTC)

I think you are taking a phenomenological approach to forces rather than a strictly theoretical one. Problem is, forces are much maligned as a concept in the physics community. They are useful conceptually but they have some theoretical problems (we're currently wrestling with them elsewhere). I'm not sure that your proposal for a lead is appropriate because it offers imprecise explanations to very complicated phenomena under the guise of "it's all force!". This is very similar to Feynman's critique in Surely You're Joking, Mr. Feynman of a basic textbook for physical science that explained without so much as a discussion that "energy" was what made plants grow, cars move, the sun shine, etc. Feynman pointed out that by using the idea that "energy does it", the book was missing the full explanations for each of these physical processes that were interconnected and subtle. ScienceApologist (talk) 14:25, 16 April 2008 (UTC)

(1) I agree I'm taking a phenomenological approach. But you have to start somewhere. I believe that is better to start with something more conceptual. Regardless of your criticism, my main objection is still up. The first phrase is misleading. It is too subtle just to say that that force is what can cause acceleration if you want to include in it the fact that forces are used to exmplain the deformation of objects. Also, the weak force is used to explain the decay of some particles. So, saying that force is a push or pull, like the undergrad books do, is at best misleading.

• Response: Deformations and weak decays are pushes and pulls. We actually discuss this in the article! ScienceApologist (talk) 23:22, 21 April 2008 (UTC)

(2) I agree that my tone may lead to the assumption that "all is force". I guess we are two pieces of matter interacting over the internet and to explain this phenomena by evoking forces would be crazy. However, your usage of Feynman's critique is unjust. And, in reality that paragraph I wrote is much based on Feynman's writing. Just read Feynman's QED and you see that what I wrote about chemical reactions is there. Anyway, what Feynman is saying is that the guy wrote a whole book of generic statements. I had only one paragrah! As for detailed description of how forces work, one should check the wiki description of specific forces or take courses in physics...

• Response: While I'm thrilled you're reading QED, you shouldn't take away anything about "forces" from that discussion. He is dealing with interactions. The forces emerge when you finish integrating over all possible photon paths. What Feynman was actually referring to was two pages with nothing more than a sentence or two on each page. ScienceApologist (talk) 23:22, 21 April 2008 (UTC)

(3) About the second phrase. Now, that one is really wrong. A vector is NOT something that has magnitude and direction. I read this definition in countless undergrad books - it is annoying to see it repeated here. Best to say that "the properties of forces make them behave like vectors" or something in this vein. and link the word vector the its wiki description.

• Response: A vector is something with magnitude and direction as far as we're concerned for physical models. True, mathematicians have a much more rigorous definition of a vector that becomes useful in general relativity, but it's not relevant here. ScienceApologist (talk) 23:22, 21 April 2008 (UTC)

(4) summing up: I believe the first phrase is a bad one - i guess people are not complaining about it bc it's what everyone read in undergrad years; so, it's wrong but in a familiar way, hence we accept it. If all of you don't like my attempt to fix it, fine. But what should be there instead? Also, second phrase is really bad. 18:05, 16 April 2008 (UTC)

• Response: I don't think you've really made your case for it being a "bad phrase". In fact, it's one of the best phrases we've got. I'm all open for alternative suggestions, but until you actually propose a wording for discussion, this objection is essentially not actionable. ScienceApologist (talk) 23:22, 21 April 2008 (UTC)
• No. This NASA definition IS the exact one. This is not a bad one: this is the best we have. There is no other. (Well you can rephrase it with synonims or more or less words but the content will always be the same). I am very sorry but Newton's second law is a law of physics and not a definition! The force is the cause and the acceleration is the effect. The way both quatities are related is a law of physics (which can be denied or supported by experimental facts) and not a definition (which cannot). If this would be false, Newton's second law would be an identity and not an equation! Vb (talk) 07:00, 17 April 2008 (UTC)
• Response: You are taking a Platonic line about what a definition is that is not accepted by the majority of our sources. ScienceApologist (talk) 23:22, 21 April 2008 (UTC)
• I guess you missed the point. First, we are looking for a proper definition of the concept of force and NOT of the equation F=ma. None would find it strange to give a definition of acceleration or mass. So, what's the problem with given a definition of F? Second, there are situations where there is a force but no acceleration. So, your claim that the whole idea of the concept of force is subsummed in F=ma is wrong. For example, the gravitational field is a force field. It does more than just causing things to accelerate - it can bend space time. To me, at least in a naive version, force is what intermediate the interaction between things. Things can interact in many different ways, having consequences that are different from acceleration...
• Notice that, as I first pointed out, NASA's definition is DIFFERENT from the one provided. They at least mention that forces can deform things... and, anyway if what i tried to provide is phenomenological, then what nasa is saying is quite classical mechanical... —Preceding unsigned comment added by 83.67.85.107 (talk) 10:25, 17 April 2008 (UTC)
• Response: The key word in the first sentence of the article is "can". As in "able to". It doesn't always result in an acceleration, but it "can". That's what makes a "force" a force. ScienceApologist (talk) 23:22, 21 April 2008 (UTC)
• Dear 83.67.85.107, I utterly agree with you. The definition of F has nothing to do with F=ma. I also prefer NASA's definition to the definition provided in this article. Some authors of this article think "the concept of force is subsummed in F=ma". This is my problem. Thus I agree with you when you say they are wrong! Vb (talk) 11:13, 17 April 2008 (UTC)
• Response. That's like saying the definition of redshift has nothing to do with z=delta lambda/lambda. It's just a POV opposed to mathematical definitions. ScienceApologist (talk) 23:22, 21 April 2008 (UTC)
• No! z=delta lambda/lambda is a definition just like p=mv or L=rxp, etc... However U=RI and F=ma are no definitions but laws of physics! Of course F has something to do with ma but only if Newton's second law is valid. In the context of classical physics, of course, F=ma as a consequence of Newton's second law but NOT as a consequence of the definition of force. If this were the case F=ma would be a truism, wouldn't have any empirical content. Vb 08:49, 22 April 2008 (UTC)
• Look, Vb, I understand your argument, but it's simply not the only way to look at it. The problem you are having is that you are giving undue weight to ideas and formulations that deviate away from inertial mass being proportional to force so that non-ohmic matter is posited to exist. This is precisely the same thing as z=delta lambda/lambda. There could, in principle, be non-ohmic wavelengths that were not so proportional across the entire spectrum, for example. The issue is that mathematical definitions of physical quantities are always truisms until someone comes up with a better mathematical definition. One can rewrite Ohm's law to take into account non-ohmic resistivity. One can rewrite Newton's law to take into account inertial mass deviations as well. However, since there are no verified empirical uses of such a reformulation, by scientific induction we conclude that F=ma is an empirical definition. That's the sources. That's what we must report at Wikipedia. If you don't like it, publish and get the sources to conform to your perspective. See WP:V and WP:TRUTH. ScienceApologist (talk) 13:44, 22 April 2008 (UTC)
• Well let me cite this article itself: "The use of Newton's second law as a definition of force has been disparaged in some of the more rigorous textbooks,[3][13] because it is essentially a mathematical truism. " I am not working at the University anymore so that I don't have access to correct physics/mechanics books. The problem with many physics books is that their public is young students or pupils which are not interested in (too young to understand) the philosophical difference between definition and principle. Vb09:27, 23 April 2008 (UTC)
• Sure, that's a problem. But the issue is that it is not Wikipedia's problem. ScienceApologist (talk) 12:59, 23 April 2008 (UTC)

Feynman's take: (copied from here):

Let us ask, "What is the meaning of the physical laws of Newton, which we write as _F = ma_? What is the meaning of force, mass, and acceleration?" Well, we can intuitively sense the meaning of mass, and we can _define_ acceleration if we know the meaning of position and time. We shall not discuss those meanings, but shall concentrate on the new concept of _force_. The answer is equally simple: "If a body is accelerating, then there is a force on it." That is what Newton's laws say, so the most precise and beautiful definition of force imaginable might simply be to say that force is the mass of an object times the acceleration. Suppose we have a law that says that the conservation of momentum is valid if the sum of all external forces is zero; then the question arises, "What does it _mean_, that the sum of all external forces is zero?" A pleasant way to define that statement would be: "When the total momentum is constant, then the sum of the external forces is zero." There must be something wrong with that, because it is just not saying anything new. If we have discovered a fundamental law, which asserts that the force is equal to the mass times the acceleration, and then _define_ the force to be the mass times the acceleration, we have found out nothing. We could also define force to mean that a moving object with no force acting on it continues to move with constant velocity in a straight line. If we then observe an object _not_ moving in a straight line with a constant velocity, we might say that there is a force on it. Now such things certainly cannot be the content of physics, because they are definitions going in a circle. The Newtonian statement above, however, seems to be the most precise definition of force, and one that appeals to the mathematician; nevertheless, it is completely useless, because no prediction whatsoever can be made from a definition. One might sit in an armchair all day long and define words at will, but to find out what happens when two balls push against each other, or when a weight is hung on a spring, is another matter altogether, because the way bodies _behave_ is something completely outside any choice of definitions. For example, if we were to choose to say that an object left to itself keeps its position and does not move, then when we see something drifting, we could say that must be due to a "gorce"--a gorce is the rate of change of position. Now we have a wonderful new law, everything stands still except when a gorce is acting. You see, that would be analogous to the above definition of force, and it would contain no information. The real content of Newton's laws is this: that the force is supposed to have some _independent properties_, in addition to the law _F = ma_; but the _specific_ independent properties that the force has were not completely described by Newton or by anybody else, and therefore the physical law _F = ma_ is an incomplete law. It implies that if we study the mass times the acceleration and call the product the force, i.e., if we study the characteristics of force as a program of interest, then we shall find that forces have some simplicity; the law is good program for analyzing nature, it is a suggestion that the forces will be simple. Now the first example of such forces was the complete law of gravitation, which was given by Newton, and in stating the law he answered the question, "What is the force?" If there were nothing but gravitation, then the combination of this law and the force law (second law of motion) would be a complete theory, but there is much more than gravitation, and we want to use Newton's laws in many different situations. Therefore in order to proceed we have to tell something about the properties of force.

Rracecarr (talk) 16:08, 23 April 2008 (UTC)

Thanks for the quote, Rracecarr. However, I don't know that there is much we can do with this fact. I think there are two parts to the definition of a force: one) that it is a push or a pull; two) that it can cause mass to accelerate. Perhaps by focusing on the second point so much, we lost sight of the first. I am of the opinion that the current definition does justice to the definition of force simply because it establishes as important this "quantity" known as "force". I view it similar to every other physical quantity we have articles about. Momentum, Luminosity, Voltage: they're all described with respect to their fundamental quantities. Force is related to mass, distance, and time in a particular way. Whenever you see those arrangements of mass, distance, and time, you have a force. It is circular, true, but that's they way it is. We are not here to right great wrongs. ScienceApologist (talk) 19:07, 23 April 2008 (UTC)
So I utterly agree with both Feynman and NASA's definition. Force is defined as anything causing acceleration or deformation of bodies. This implies that force has vector properties. I also agree with this article's lead as it stands now. However this does not imply that F=ma. F=ma is the second basic postulate of classical physics. It is by no way a definition. This is not because many books intended for high school or low level university students claim so that it is true. Wikipedia has to do better than this. Wikipedia has to pick up the most reliable sources and not to count how many text books claim something. Vb 07:03, 24 April 2008 (UTC) —Preceding unsigned comment added by 79.233.217.28 (talk)

\\ \\Regarding: Response: A vector is something with magnitude and direction as far as we're concerned for physical models. No, it's not. For example, the state VECTOR of a particle in quantum mechanics is, well, a vector. Tell me then, what is its direction?? I hope now you see the nonsense(s) you are saying. Best them to use the words "spatial vector" and give the link to this one. Let's be clear here. Mathematicians spent a lot of time to come up with this very precise definition of vectors. If you want to rebel and use some half cooked notion, well, use the name of "spatial vector". \\

Oh, come now. The state vector in quantum mechanics has a direction. You just have to know what the basis you are in. Then the direction is a direction in the space spanned by that set of basis vectors. ScienceApologist (talk) 15:49, 13 May 2008 (UTC)

• Oh, you come now. what you just wrote is not even wrong - is not even a sentence. it is completely irelevant to the problem at hand to say what is the "direction" of a quantum state. You really want to force your way into making people believe that the "definition" of a vector as something that has magnitude and direction makes perfect sense? Look, let me reapt to you, mathematicians took a looong time to give a precise definition to what is a vector. if you want to use a half cooked notion, go ahead, but then use the proper name (spatial vector) and give a link to the wikipedia entry.
—Preceding unsigned comment added by 155.198.157.118 (talk) 19:41, 29 May 2008 (UTC)

\\ Anyway, ScienceApologist, keep up with the good job in reading and quoting "You're surely joking mr Feynman". But I sugest that at one point you should move to more advanced stuff. I mean, even the references of this entry are all based on undergrad level books, if not less. Max Jammer book on the topic is not even mentioned... \\

Max Jammer's book is great, but it is treating the subject from a philosophical rather than a pragmatic set-up. The issue is, of course, that Jammer is orienting his ideas in historical contexts which is fine for most thoughtful analyses and certainly should be included in our article, but it shouldn't be the focus of the article. ScienceApologist (talk) 15:49, 13 May 2008 (UTC)

\\ So, let us keep with the definition of a force as something that causes a push or pull, or something that "could have caused" a push or a pull. I moment of thought will show how insane is the definition. Only people that were already indoctrinated in this mumble jumbo way of thinking will agree with it. 17:48, 2 May 2008 (UTC)

Not sure how to interpret this comment... ScienceApologist (talk) 15:49, 13 May 2008 (UTC)

I see that now you changed your first phrase to include the assumption that the object being acted upon has mass... that is not good, for say, gravity can make light bend, light has no mass. 18:02, 2 May 2008 (UTC)

But is gravity a "force" when it does this? I say no. Geodesics are not forces in the sense that we generally use the term. That's why force is disparaged as a concept. ScienceApologist (talk) 15:49, 13 May 2008 (UTC)

Regarding ScienceApologist comment on neutron decay. Notice that the statement that the force is a push/pull in that case was written in quotation marks - as it should. Notice that when you say the momentum of the particle changed, you mean that its quadri-momenta changed (so, not only a change in space direction, but also a change in p_0, the energy. To state that at this level a force is simply a push or pull as you are trying too is insane. 18:10, 2 May 2008 (UTC)

Not really insane, it's conceptually important for some. What is your goal here? ScienceApologist (talk) 15:49, 13 May 2008 (UTC)
What I don't understand is why so many people insist that you have to use acceleration to define a force, when in fact it's usually measured statically (think: weighing scales). I'm with Lord Kelvin (or whoever it was): if I can measure some quantity, in some meaningful sense I know what it is, even if I have some wrong ideas about how it behaves.
Given the long arguments we've had about the definition of force on this page, I shouldn't complain about the current first sentence. As SA says, it does cover static cases. But it could be better: too many people will read it as confirming that Newton II is a definition, because they will see the crucial word as 'acceleration'. For us more empirical types, the crucial phrase is 'push or pull': which everyone understands intuitively. The trouble is, school physics brainwashes us into accepting that this understanding has something to do with acceleration. Ain't true, in my case at least: 'push or pull' brings to mind what it feels like to hold a heavy suitcase, pull in a tug-of-war, arm-wrestle, and so on: in other words, to provide one component force in a quasi-static equilibrium. To the extent that 'force' actually means anything, that's what it means. That's why Aristotle and Archimedes could write quite a lot of sense about force without at all understanding the link with acceleration. Just as we use thermometers to parlay our direct sense of "hot" and "cold" into a quantitative temperature scale, we use scales and spring balances to parlay our direct sense of "push" and "pull" (and "weight") into a quantitative force scale, defined at every step using static equilibrium. Then, when we finally set them in motion, every pendulum really does confirm the empirical validity of Newton's second law.
Of course, it turns out that force is not a very useful concept in quantum mechanics or GR. A philosopher could argue that we have trouble defining force because ultimately there is no such thing, it's an illusion of the everyday, mesoscopic world. And therefore it's not 'wrong' to define it by some equation. But IMHO it fails to give clue. PaddyLeahy (talk) 20:46, 13 May 2008 (UTC)

What we have as the definition of a force is: force is what coulda-shoulda-oughta cause a push or a pull, not that it does. But, if you are light passing by Earth, that pull you feel, that brings you closer to Earth, even though it has magnitude (after all if you replace Earth by the sun the pulling is stronger) and direction (it moves towards the Earth), that my friends is not a force... you see, you need mass to feel what we want to call a force! Also, if you do a super fine job as Jammer does in pin-pointing what a force means to us, well, that is not relevant as well, for to us, a force is something "pragmatical". So, if you came here to learn what a force is, go away, because the prejudices of the person writing this article produced an explanation which doesn't hold water... —Preceding unsigned comment added by 155.198.157.118 (talk) 20:00, 29 May 2008 (UTC)

I mean, Jammer wrote a book and we're writing one sentence. I'm currently re-reading his book and I don't think he would be obstinately opposed to our definition.
ScienceApologist (talk) 20:21, 29 May 2008 (UTC)

## Incorrect formula of Newton's Second Law in the section of Special Relativity of this article

If a particle with non zero-rest mass is moving along the x-axis, instead of

${\displaystyle F_{x}=\gamma ma_{x}}$,

the equation should be

${\displaystyle F_{x}=\gamma ^{3}ma_{x}}$

Where ${\displaystyle m}$ represents rest mass, ${\displaystyle \gamma }$ represents Lorentz Factor

The equation of the force that is orthogonal to the direction of the moving particle is correct. That is the main reason why in the early development of Special Relativity, Einstein and the others use the term "Longtitunal mass" and "Transverse mass". It was until Richard C. Tolman introduced the concept of relativistic mass, which is equivalent of energy and is the proportional constant between momentum and velocity. For more information, see Mass in special relativity. Thljcl (talk) 09:03, 22 April 2008 (UTC)

Yeah, people keep changing it. I'm not sure why. ScienceApologist (talk) 13:45, 22 April 2008 (UTC)

## Newton's Second Law does not mean F=ma

In the opening of this article, it is stated that "According to Newton's Second Law, an object will accelerate in proportion to the net force acting upon it and in inverse proportion to the object's mass". This statement can be represented by the equation of ${\displaystyle {\vec {F}}=m{\vec {a}}}$. The definition of Newton's Second Law, according to Newton's Second Law is The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction.

Following the definition of Newton's Second Law, we will get the following equation

${\displaystyle {\vec {F}}_{net}={\frac {d(m{\vec {v}})}{dt}}}$

where:

${\displaystyle {\vec {F}}\!}$ is the force vector
${\displaystyle m\!}$ is Relativistic mass
${\displaystyle {\vec {v}}\!}$ is the velocity vector
${\displaystyle t\!}$ is time.

Only if we assume relativistic mass is constant, which is approximately equal to rest mass when the speed of the particle is much lower than the the speed of light. ${\displaystyle {\vec {F}}=m{\vec {a}}}$ is a good approximation in low-speed limit. However, it does not represent Newton's Second Law. Newton's Second Law remains valid in Special Relativity. ${\displaystyle {\vec {F}}=m{\vec {a}}}$ however is not valid when the speed of the moving object is comparable to the speed of light in vaccum.[User:Thljcl|Thljcl]] (talk) 09:38, 22 April 2008 (UTC)

You are correct in this, but it is needlessly nitpicky. The statement is true for the proper formulations of "mass" and "acceleration". In the case of special relativity, it is irresponsible for us to make any claims since spacetime invariance is not the same thing as spatial invariance and temporal invariance put together. That's the issue. The definition works with the "proper" definitions of mass/acceleration. There are a lot of ways to criticize F=ma. I'm not sure that we need to beat the reader over the head with them. ScienceApologist (talk) 19:10, 23 April 2008 (UTC)
I agree with ScienceApologist. This is "needlessly nitpicky". However NASA's definition of force is not changed by special relativity. Only the wrong definition F=ma is changed. This is one argument more against understanding F=ma as a definition. Vb 07:10, 24 April 2008 (UTC) —Preceding unsigned comment added by 79.233.217.28 (talk)
[User talk:Thljcl|talk] is not only correct as to the real content of the law, but also is historically more accurate. It is not nit picking to be accurate both as to historical matters and as to scientific content. It also is less complicated (as well as less misleading) to state the law in terms of momentum, an everyday term with intuitive appeal. Brews ohare (talk) 17:25, 4 May 2008 (UTC)

## Revision of Newton's second law

I've rearranged the material in this article. By interchanging two paragraphs, momentum is placed first, as is historically and scientifically accurate. The incorrect historical statements have been removed and a link given to better information in the Newton's laws article. The completely contradictory statements about mass determination have been weeded out to present a non-contradictory perspective. Nonsense about "counting atoms" to find mass was deleted ( 105 neon atoms it is not the same as 105 lead atoms). Discussion about the first law (largely a restatement of discussion in the first law section ) was edited and transferred to first law. Brews ohare (talk) 17:36, 4 May 2008 (UTC)

## Feynman Diagram does not show "Force"

The Feynman Diagram shown in this article describes a beta decay, not a force interaction. This leaves the reader wondering what this diagram has to do with the article's subject "force"? Perhaps the existing Feynman diagram in this article could be replaced with one showing the repulsion of 2 electrons (via a virtual photon). --I'm hoping that the contributor who posted these excellent Feynman diagram images can find others from the same free source--. Once Force is explained in terms of Feynman diagrams, we can then point out that these diagrams are useful for many other purposes and refer the reader to the article on Feynman Diagrams. Substar (talk) 20:08, 27 May 2008 (UTC)

1. ^ "glossary". Earth Observatory. NASA. Retrieved 2008-04-09. Force: Any external agent that causes a change in the motion of a free body, or that causes stress in a fixed body.
2. ^ See for example pages 9-1 and 9-2 of Feynman, Leighton and Sands (1963).
3. ^ a b e.g. Feynman, R. P., Leighton, R. B., Sands, M. (1963). Lectures on Physics, Vol 1. Addison-Wesley.; Kleppner, D., Kolenkow, R. J. (1973). An introduction to mechanics. McGraw-Hill..
4. ^ a b University Physics, Sears, Young & Zemansky, pp18–38
5. ^ Heath,T.L. "The Works of Archimedes (1897). The unabridged work in PDF form (19 MB)". Archive.org. Retrieved 2007-10-14.
6. ^ Cite error: The named reference final_theory was invoked but never defined (see the help page).