What Does F=ma Really Mean? A Closer Look at Newton's Law

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Discussion Overview

The discussion revolves around the interpretation and implications of Newton's second law, F=ma, particularly focusing on the definitions of force, mass, and acceleration. Participants explore the philosophical and empirical foundations of these concepts, questioning their definitions and the circularity that may arise in their explanations.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that defining force and mass without circular reasoning is challenging, as definitions often rely on intuitive concepts that are not rigorously defined.
  • One participant proposes a method of defining mass based on empirical observations of balance and uniform composition, suggesting that mass is time-invariant and transitive.
  • Another participant points out that the definition of force as the rate of change of momentum (F = dp/dt) raises further questions about the nature of momentum itself.
  • Some participants express skepticism about the possibility of defining mass without invoking forces, suggesting that such definitions may inherently lead to circular reasoning.
  • There is a discussion about the historical context of Newton's definitions, with references to terms like "quantity of motion" and how they have evolved in different languages.
  • Concerns are raised about the implications of defining mass as the "amount of stuff" in a system, particularly when considering subatomic particles and relativistic effects.
  • One participant emphasizes the need for clear definitions of mass that are free from force-related concepts, while acknowledging that this may not resolve all questions surrounding the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions of force, mass, and acceleration. Multiple competing views and uncertainties remain regarding how to define these fundamental concepts without circularity.

Contextual Notes

Participants note that definitions of mass and force may depend on empirical observations and philosophical interpretations, which could lead to unresolved questions about their foundational nature.

  • #31
ZapperZ said:
Can someone else translate this for me?

It is crucial for you to understand how I have defined what a force is for your to understand anything else. I'll just write it one more time, but otherwise I'm too tired to argue anymore. anyways, it was a fun argument.

The force acting on a system A by a system B is the mass of system A multiplied by the acceleration system A would have if no other systems were present.
 
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  • #32
suffian said:
It is crucial for you to understand how I have defined what a force is for your to understand anything else. I'll just write it one more time, but otherwise I'm too tired to argue anymore. anyways, it was a fun argument.

The force acting on a system A by a system B is the mass of system A multiplied by the acceleration system A would have if no other systems were present.

1. You are not "someone else".

2. What you just told me is Newton's 2nd Law. Since when did this become YOUR definition of what a "force" is?

3. If #2 is correct, what is the reason you think that *I*, of all people, am not aware of this?

Zz.
 
  • #33
i'm not trying to take credit for Newton. but if Newton very clearly spelled out what he meant by a force then i don't think we would be having this conversation. i just said "my" to prevent confusion over how anyone else might have defined it in their minds.
 
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  • #34
Acceleration also a 'circular' concept.

suffian said:
hmm, my point wasn't to come up any sort of precise standard for mass. Just to make a definition without the use of forces so that none of the definitions are circular.

Actually, it is not just mass and force that must be defined in terms of the other. The concept of acceleration cannot be defined without reference to mass and force. Measuring acceleration requires a frame of reference, which can only be attached to a particle having mass (see A. below). It requires that the frame of reference be unaffected by forces (ie an inertial or rest frame).

Mass is a quality that gives meaning to concepts of space and time. A universe without mass has no frame of reference by which dimensions of distance and time can be measured.

Just how mass comes into existence is one of the great unanswered questions of physics. It is created in nuclear interactions and it is equivalent to stored energy (E=mc^2), but just how it is created is not known.

Footnote A. The principle of relativity states that EM waves/particles (e.g photon) must travel at the speed of light with respect to ALL inertial frames of reference. This implies that all particles moving at the speed of light do not possesses inertial mass. If a particle has mass, it would define an inertial reference frame. If an inertial frame of reference could be associated with a photon, the origin of that frame of reference would have to be moving at the speed of light away from itself (ie. away from the origin of the frame of reference of, say, another photon). This implies that time stands still and distance has no meaning for the photon.

Andrew Mason
 
  • #35
metacristi said:
The problem you [raise] here it's very interesting going well beyond mere science,[belonging rather to the] epistemology of science

I completely agree. Suffian has come upon the fact that F=dp/dt is a definition, and that definitions are unfalsifiable even in principle. I'd like to see this discussion continue in the Philosophy section, so I'm moving it there.
 
  • #36
Tom Mattson said:
I completely agree. Suffian has come upon the fact that F=dp/dt is a definition, and that definitions are unfalsifiable even in principle. I'd like to see this discussion continue in the Philosophy section, so I'm moving it there.

Oh no! It's bad enough that I've had threads I responded to being moved to the TD section. Now I also have one in the Philosophy section? That hurts! :) :)

In case anyone hasn't noticed this, Frank Wilczek, who this week was one of the co-winner of the Nobel Prize in physics, has an essay related to "F=ma" in this month's issue of Physics Today.

http://www.physicstoday.org/vol-57/iss-10/p11.html

Zz.
 
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  • #37
ZapperZ said:
Can someone else translate this for me?

Zz.
It looks like a spring-scale turned on its side to act as a catapault to me (either way, it does the same thing - it measures force via f=ma). So I guess suffian agrees with Tom:
Suffian has come upon the fact that F=dp/dt is a definition.
 
  • #38
Tom Mattson said:
I completely agree. Suffian has come upon the fact that F=dp/dt is a definition, and that definitions are unfalsifiable even in principle. I'd like to see this discussion continue in the Philosophy section, so I'm moving it there.

Are you sure it doesn't belong in the religion and mysticism section? :-p
 
  • #39
Wilczek article

ZapperZ said:
In case anyone hasn't noticed this, Frank Wilczek, who this week was one of the co-winner of the Nobel Prize in physics, has an essay related to "F=ma" in this month's issue of Physics Today.

http://www.physicstoday.org/vol-57/iss-10/p11.html
Interesting article. I tend to agree that the concept of 'force' is not the most useful way to think about certain phenomena. Force is a useful concept when building bridges. It is less useful when trying to understand nuclear interactions. But, fundamentally, it is just a device to help us understand masses and their motions.

I got a lot of flack for suggesting that the concept of the strong nuclear force should be reconsidered ("Gravity in the Nucleus" thread under the Nuclear Particles head). I suggested that we should not necessarily equate high nuclear binding energy with this very complicated force. I wonder what Wilczek thinks of the strong nuclear force...

AM
 
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  • #40
Andrew Mason said:
Interesting article. I tend to agree that the concept of 'force' is not the most useful way to think about certain phenomena. Force is a useful concept when building bridges. It is less useful when trying to understand nuclear interactions. But, fundamentally, it is just a device to help us understand masses and their motions.

I got a lot of flack for suggesting that the concept of the strong nuclear force should be reconsidered ("Gravity in the Nucleus" thread under the Nuclear Particles head). I suggested that we should not necessarily equate high nuclear binding energy with this very complicated force. I wonder what Wilczek thinks of the strong nuclear force...

AM

Considering that he won the Nobel Prize for QCD, or specifically for the formulation of the asymptotic freedom of the strong force in QCD (of which several people have tried to explain to you in that earlier thread), it is VERY clear exactly what he thinks of the strong nuclear force.

But just to be sure, I will ask him tomorrow (Friday) when he gives his lecture here at Argonne.

Zz.
 

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