Re: Can energy conservation be derived from Newton's motion laws

From: Strong_Field (strong_field_at_hotmail.com)
Date: 01/04/05 

Date: Tue, 4 Jan 2005 20:06:36 +0000 (UTC)

"Dan Platt" <DanP57@ispwest.com> wrote in message
news:cqpqkq0hvj@enews3.newsguy.com...

> Grad is usually definable this way (x, dx vectors; s, V scalars):
>
> V(x + s dx) = V(x) + s grad V . dx + O(s^2).

This seems to corroborate what I wrote initially. Ignoring your functions s
and O, I don't know what they are, your expression simplifies essentially to
dy/dx = grad V. Does this definition say more than the definition given in
the other post as a vector pointing in the greatest increase and having the
magnitude of change in velocity?

> ... the idea of conservation of energy is a fundamental (distinct from
> basic) physical idea. Perhaps it is more meaningful to ask what kind of
> force satisfies conservation of energy given Newton's laws. If
> conservation of energy is a dominant physical mode of behavior that
> penetrates into thermodynamics, etc, then all of the important forces
> that will show up in the application of Newton's laws will have a
> gradient-like behavior.

I think you are trying to say that conservation of energy is the fundamental
axiom of physics. If so I agree. The equation itself is a statement of the
conservation of energy. Everything else is derived from the assumption that
perpetual motion is impossible. Let's think about it topologically. In
topology equivalent objects can be transformed into each other. It is only
convention that the shape A is the master shape. Someone will say no the
shape B is the master shape. Similarly in physics there is no master
equation that can be identified as such. In physics any equation can be
derived from the other. Whatever shape you give to it your topology stays
invariant. That’s the energy conservation. The topological invariant. Which
is the equation itself. Because whatever its “shape” is, the equation is the
invariant. Therefore in physics the equation itself is the definition of
energy conservation. As such you cannot derive it from any other equation.
You can only use energy conservation to prove whatever you want. This also
shows that deriving energy conservation from Newton amounts to making
algebraic transformations.

And, conservation of energy is not a “physical mode of behavior.” It is an
axiom. There is nothing physical about it.

> Humans are trying to describe the behavior of things that would be doing
> what they do regardless of whether humans were there to describe them.
> To some extent, the notion of physical law is a human construct, which
> is subject to change as our understanding improves.

You are talking about a philosophical and epistemological concept of
“physical law.” I agree that’s a human construct. But that
discussion is not relevant to “Newton’s laws.” Because
Newton’s Laws are not “physical laws.” They may be laws of
Newtonian physics, but they are not laws of nature in the sense you are
thinking. Newton was a serial definer. He had the authority to establish
his countless definitions as laws of nature in physics. If you look at
the Principia, they are called axioms. In other words, they are
definitions Newton chose to make. By tradition we call them
“laws” out of respect for Newton. As long as we know that they
are laws with an asterisk, I guess there is no harm done to science.

Relevant Pages

  • Re: Science/Physics Forums that SUCK
    ... normal laws of physics that suck, ... strong energy signature within the UV spectrum, ... Onward to the other somewhat important topic of 'Life on Venus' ...
    (sci.physics)
  • Re: MAILGATE sucks, or at least NSA/MI6 sucks
    ... Apparently it's not MAILGATE that sucks, as it's the normal laws of ... physics need be applied whenever questioning whatever's lord NASA ... strong energy signature within the UV spectrum, ... Onward to the other somewhat important topic of 'Life on Venus' ...
    (sci.astro)
  • Re: Science/Physics Forums that SUCK
    ... normal laws of physics that suck, ... strong energy signature within the UV spectrum, ... Onward to the other somewhat important topic of 'Life on Venus' ...
    (sci.astro)
  • Re: Q. about Noether Theorem
    ... > energy in the same way". ... > among our observations and with the known laws of physics. ... > call this a symmetry and say that it implies conservation of the ...
    (sci.physics)
  • Re: Can energy conservation be derived from Newtons motion laws only?
    ... In any derivation, there is the first statement X, and ... > nothing more than a definiton of conservation rules. ... > express the laws of thermodynamics with physics equations. ...
    (sci.physics.research)