# Goldstein classical mechanics discrepancy?

• Syrus
In summary, the conversation discusses a statement in Goldstein's text regarding conservative fields and friction or dissipative forces. The original statement says that these forces are never conservative because F dot ds is always positive. However, the speaker questions whether this is accurate, as most frictional interactions result in negative values of the dot product. After checking other classical mechanics texts, they conclude that Goldstein may have meant to use the word "negative" instead of "positive" in this statement.

## Homework Statement

In Goldstein's text, he discusses conservative fields and then states that "friction or dissipative forces are never conservative since F dot ds is always positive."

From what I recall, most frictional interactions occur in directions opposite the displacement, and would, hence, result in negative values of the dot product. Shouldn't, then, the text read isntead: friction or dissipative forces are never conservative since F dot ds is always non-zero?

I have checked a few other classical mechanics texts and they all seem to have statements along the same lines- so I feel there is a detail I am missing here.

## The Attempt at a Solution

I still have my 1st edition of Goldstein that I used in a course 42 years ago. I found the quote on page 3 and lo and behold I see that I had circled the word "positive" and added a question mark in the margin! I think Goldstein meant to use the word "negative" here (even though you can construct scenarios where a force of friction does positive work).

That's remarkable TSny, thanks for checking!

## 1. What is the Goldstein classical mechanics discrepancy?

The Goldstein classical mechanics discrepancy refers to a discrepancy or disagreement between classical mechanics, which is a theory that explains the motion of macroscopic objects, and quantum mechanics, which is a theory that explains the behavior of particles at the microscopic level.

## 2. How does this discrepancy arise?

The discrepancy arises because classical mechanics and quantum mechanics have different principles and rules that govern their respective systems. Classical mechanics is based on Newton's laws of motion and assumes that particles have definite positions and velocities, while quantum mechanics is based on the principles of uncertainty and superposition, which allow for particles to exist in multiple states at once.

## 3. Why is this discrepancy significant?

This discrepancy is significant because it highlights the limitations of classical mechanics in explaining the behavior of particles at the quantum level. It also raises questions about the nature of reality and the role of observation in determining the behavior of particles.

## 4. How have scientists attempted to resolve this discrepancy?

Scientists have attempted to resolve this discrepancy by developing new theories and models that combine classical and quantum principles. Some examples include the Schrödinger equation, which describes the wave-like behavior of particles, and the path integral formulation, which combines classical and quantum mechanics in a unified framework.

## 5. Is there a definitive solution to this discrepancy?

No, there is currently no definitive solution to this discrepancy. The debate between classical mechanics and quantum mechanics continues, and scientists are still working to develop a theory that can fully explain the behavior of particles at all scales.