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What if Newton had thought differently?

  1. Jan 3, 2010 #1
    I am a very mathematical person. I excel in my mathematics courses. In physics, on the other hand, I have always felt less than an expert. I am by no definition a bad physics student. Being mathematically minded I see relationships easily. So physics is not difficult for me to do. What has always bothered me is an apparent lack of causality in the derivation of physics formula. Allow me to elaborate as that last statement is not concise. I understand the relationships between concepts; I do not understand how those relationships can be assured. For example, why does F=ma or for ohmic circuits V=IR. I believe I have come to an understanding of what is the source of this distress, and I believe it is purely theoretical.

    My observation, I came upon it while thinking about mechanics, but I believe is to be general and true for all branches of physics, is that if Newton had thought slightly differently we would be using different laws of physics. These laws would have the same meaning, but our calculated values and derived units would be completely different as would the calibration on our instrumentation. A self consistent system could be formed form the saying , for example, that F=m/a. One could then begin to derive all of mechanics from this and the definitions of mass and acceleration. These laws would appear differently, they would yield different derived units, and different calculated values for "forces". The base units (mass, displacement, time, etc) would remain the same. One could construct a fully self consistent experimental framework from this assumption as well as many others.

    Agree, disagree. Refutations? I'm interested to hear counterarguments.
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  3. Jan 3, 2010 #2


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    There is only one good reason for any physics formula: experimental results. If one were to write "F= m/a", what force would give an acceleration of 0? That should have occured to you immediately. It might make more sense to ask about "F= m+ a" but now what would "F" mean? In order to get an acceleration of 0 you would have to apply a force of "m". But "force" already had a physical meaning from observation and experimentation that makes that non-sense.
  4. Jan 3, 2010 #3
    As I stated before, I if you used this formulation then Force would be measured by a device consistent with F=m/a. We measure our physical quatities in abstract terms, force only has a quantitative measure relative to man's definition of a unit of force. Though your point regarding what force is developed when a=0 is valid; disproving one formulation does not disprove all others.
  5. Jan 3, 2010 #4
    Well, it's just a matter of definition... your force is directly connected with Newton's...
    Now can you imagine a formulation of mechanics that is not equivalent to Newton's but consistent with experiment? For example, where laws of physics are described by 1st order differential equations?
  6. Jan 3, 2010 #5


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    You are forgetting that for many new theories, they started off with the PHENOMENOLOGICAL model first. That means that these are done based on a description of the experimental observations without deriving something out of First Order principles. I could give you a mass-spring system and ask you to determine the relationship between the the restoring force and the extension of the spring. Do you think it matters HOW I think it should behave regardless of how it REALLY behaves? In fact, without knowing ANY physics, one can do such investigation, and assuming that it is done properly, a person could come up with the SAME relationship between the restoring force and the extension. This is the phenomenological model, and the description is UNIQUE.

  7. Jan 3, 2010 #6
    I understand what you are saying, but if we had defined the concepts such as force differently from its inception, would we not come up with laws that mean the same thing in our new framework, but are expressed differently from the form proposed by Newton. I am not saying physics as it is today is wrong. I am not so naive to think that probable. I am simply proposing that by modifying the mathematical definition of a force one can derive consistent relationships that are just as accurate in the new framework as it is in the real one. Perhaps I have a fundamental misunderstanding. Why must F=ma rather than, for example, F=a/m. Velocity is clearly defined as a distance traveled in a particular time interval. Net force is defined as the change in an objects momentum; what is momentum? Momentum is the product of mass times velocity. I read this and think: "How mathematical. But where is the physical basis?" This leads me to think that the framework is arbitrary, but perhaps convenient. Please illuminate me, politely.
  8. Jan 3, 2010 #7


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    This is getting to be a bit silly, because you're just playing algebra.

    Nature doesn't really CARE how we define things. In the spring-mass system, I could easily ask for the relationship between the restoring force versus the inverse extension! Would that make you feel any better? And how has it change the way we describe the system?

    In solid state physics, rather than describing things in real space, it is often useful to describe the system in "reciprocal space". Has this changed the way we then see and described the system? No! I can always transform back to whatever space I want to be in.

    You will note that I can easily describe the dynamics of a system not using Newton's force laws, but also Lagrangian/Hamiltonian formalism in which "forces" do not exist! In fact, using that approach, the principles of Least Action governs the dynamics of the system, rather "forces". Yet, do you think this somehow changed the way we view our universe? They both give us the SAME, UNIQUE dynamical description of the system, i.e. if I want to know where it is at a given time t, they both give the SAME, identical answer.

    You will need to show how, simply by redefining things, you come up with an entirely new conclusion. Till then, I don't see the point of this exercise.

  9. Jan 3, 2010 #8
    I am not proposing a change to the current systems and methods. I was simply exploring the idea for the joy of it. It was an interesting idea to me and one that afforded me an opportunity to learn. Relax physics is independent of any person's interpretation. Which is my point in all this.
  10. Jan 3, 2010 #9
    I think the previous responders missed your point, tell me if this is what you mean: Using the spring-mass example, let's say you have developed a mechanics where Z=m/a (note that 'Z' stands for 'Zorce' which is 'Zach's Force'). Now run through the calculations in your Z-mechanics and determine say, the position of the mass vs. time. Do you get the same result as seen in experiment (and as found using Newtons mechanics)? If so, maybe you have found a new set of definitions and corresponding laws of motion. If not, you made a mistake somewhere in formulating your mechanics.

    Now, go ahead and do it - show us this Z-mechanics. I don't think it's impossible that you could do this, but I think it's harder than you might imagine.:wink:
  11. Jan 3, 2010 #10
    Funny. Everyone is so serious here its nice to see some levity. I don't suggest that I am capable of creating, as you call it a "z-mechanics" (very funny by the way), nor do I endorse it as a realistic method. There is nothing wrong with our current view of classical mechanics. I was simply making a point for the purpose of discussion. You seemed to understand what I was attempting to say more more clearly than the other posters.
    The point was that you could create fully consistient system with a different definition of "force". In the above F=m/a the units woudl be in kg*s^2/m^2. This is not a Newton. Therefore the answer would not be the same as what you would obtain in newtonian mech., but it would be equivalent, in this case, by some factor.
    Call the force and antinewton for kicks :).
    (antinewton value)=k(newtonvalue) where k is a constant of units m^4/s^4. That would convert from our antinewton system to the newton system. It would be the equivalent of shifting the scalings on a coordiante plane and inverting the axis.

    *Note to posters, stop freaking out. This isn't rewriting physics.*
  12. Jan 3, 2010 #11

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    It doesn't seem that way. It seems that you have come up with the idea that the formulation of mechanics is not unique (subject to trivial changes like unit changes), but react to any counter argument with "yes, but maybe there's a formulation where that counter-argument doesn't apply."

    It's a little like standing on a rooftop arguing whether reindeer can fly - and every time you push one off and it plummets, the person you are arguing with says, "OK, but all you really proved is that that reindeer can't fly." That may be logically true, but it's also a pointless waste of time. And reindeer.

    I suggest you read FLOP, section 12-1, on "gorces".
  13. Jan 3, 2010 #12


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    You know, something similar to what you describe has actually happened in physics. It has to do with the transition from newtonian dynamics to special relativity. Historically, that transition was levered in by use of what is referred to as 'the light postulate'. That was the light postulate that Einstein introduced in 1905.

    Now, in any logical system there is great freedom to interchange axiom and theorem without altering the content of the system. The following has been noticed independently many times: If you take the Principle of relativity of inertial motion, and you push the ramifications of that principle to the utmost, you find that there are in fact two systems of spacetime transformations that satisfy the principle of relativity of inertial motion: the Galilean transformations and the Lorentz transformations. At that stage experiment can decide which transformations are appropriate.

    The first time I encountered that way of arriving at special relativity was in an essay by Palash B. Pal: http://arxiv.org/PS_cache/physics/pdf/0302/0302045v1.pdf" [Broken]
    The very first person to point it out, I think, was Minkowski, who showed it in 1908.

    What I'm getting at is that while arriving at Galilean relativity was a major achievement, we see in retrospect that the observations didn't necessarily imply Galilean relativity. Of course, for Newton and his contemporaries it would have been totally counterproductive to question the adoption of Galilean relativity. But I find it fascinating that in retrospect we can see that logically they did have the option of considering the Lorentz transformations.

    Last edited by a moderator: May 4, 2017
  14. Jan 3, 2010 #13


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    But this isn't even anywhere close to what the OP is suggesting. The transition from Newtonian to relativistic dynamics involves not simply redefining (and changing units) of already established physical quantities. It involves an expansion of the definition of those quantities. The "momentum" didn't not get an overhaul of its definition, for example, or that we did not simply switch to a different quantity entirely simply to work with SR.

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  15. Jan 3, 2010 #14


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    That's fine, but you are exploring in a wrong direction. ZZ is partly right when he says you are just playing algebra, but it isn't just algebra: you're also just playing with the definitions of words and that's the bigger component of this. Ie:
    If you play ring around the rosie with the definitions, you could say:

    force = a
    mass = f
    acceleration = m

    ...then your f=m/a is describing the same thing in reality as our a=f/m does now.

    But then as ZZ suggested in post #5, the words "force", "mass", and "acceleration" already had definitions when Newton started exploring how the concepts relate, so while it is sort of true that he could have screwed with the definitions as you suggest, it wouldn't have been a useful thing to do and people would have been left scratching their heads at his word usage. So he kinda didn't have the option to "define the concepts such as force differently from its inception": he wasn't around when the concept of force was defined!

    So you aren't really doing anything useful here. It's just a wrongheaded word game that you are playing and not a meaningful critique of how physics is developed.
    Last edited: Jan 3, 2010
  16. Jan 4, 2010 #15
    Russ - that's why I suggested above that he call his new parameter 'zorce' instead of 'force' (because they are not the same as each other). My take on this is the OP noticed that 'force' is a defined parameter and there is maybe some arbitrarity in it. So, the OP is wondering if we start with mass and position vs. time, can we come up with an alternative set of equations of motion?

    I think the answer is, any alternative mechanics will be reducible to Newton's mechanics (because Newton gives the right answer). Also, Newton's has the advantage that we really do have an intuitive notion of 'force' - a notion we learned as children lifting objects and pushing things around.
  17. Jan 4, 2010 #16
    sorry to get very simple here but surely if newton had thought differently he would have been wrong lol. therefore we wouldn't have newtonian physics we would have Johnsonian physics (Dr Johnson is the physit i am saying then came up with wot newton thought up wrong)
    abstract i know
  18. Jan 7, 2010 #17
    I don't get the OP's point. It sounds like your argument is only about units. And yes you can always formulate them using a different measuring stick(dynes instead of newtons, etc.), but when independent analyses of the situation are done and someone asks "where is the ball gonna go?" everybody is going to agree.
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