Maxwell's Equations: Exact or Approximate?

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    Maxwell's equations
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Discussion Overview

The discussion centers around the nature of Maxwell's equations, specifically whether they are considered exact or approximate. Participants explore the implications of fundamental constants and the physical interpretations of these equations, touching on both theoretical and practical aspects.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that Maxwell's equations are exact mathematically, while others argue that they are only approximations in a physical context.
  • One participant notes that the constants involved in Maxwell's equations, such as epsilon and mu, are measured quantities, which introduces a level of inexactness.
  • There is a suggestion that Quantum Electrodynamics (QED) provides different predictions compared to classical electromagnetism, indicating a potential limitation of Maxwell's equations.
  • Participants discuss the implications of physical definitions and constants, questioning whether anything can be considered exact in a physical sense.
  • Humorous analogies involving apples and cows are used to illustrate points about measurement and physical relevance, though they do not directly address the main topic.

Areas of Agreement / Disagreement

Participants express differing views on the exactness of Maxwell's equations, with no consensus reached. Some maintain they are exact, while others emphasize their approximate nature in physical applications.

Contextual Notes

Participants reference specific constants and their definitions, but there is uncertainty regarding the exact nature of these constants and their implications for the equations. The discussion also touches on the philosophical aspects of measurement and physical reality.

ehrenfest
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Are Maxwell's equations thought to be exact? I realize this question is very open-ended and loosely-phrased.
 
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Yes they are. But keep in mind that each one of maxwell's equations inevitably contains some sort of fundamental constant (mu or epsilon usually; not to mention electric charge etc etc) which are measured quantities and therein not exact.
Does that answer your question?
 
Yes.
 
They're not exactly exact. QED makes slightly different predictions from classical electromagnetism.
 
Mathematically, correct hence exact. Physically, it's a good approximation and only an approximation to model phenomena. Hence not exact physically. Is anything exact physically? No.
 
lzkelley said:
Yes they are. But keep in mind that each one of maxwell's equations inevitably contains some sort of fundamental constant (mu or epsilon usually; not to mention electric charge etc etc) which are measured quantities and therein not exact.

lz, be careful.

which constant in Maxwell's equation is measured and not defined (to an exact value)?
 
Epsilon-not.

Mu-not is defined. At least, that's what my professor said.
 
Poop-Loops said:
Epsilon-not.

Mu-not is defined. At least, that's what my professor said.

you mean this epsilon-not ?
 
  • #10
tgt said:
Mathematically, correct hence exact. Physically, it's a good approximation and only an approximation to model phenomena. Hence not exact physically. Is anything exact physically? No.

I have one apple, I add another one, I have exactly two apples.
 
  • #11
dst said:
I have one apple, I add another one, I have exactly two apples.
Well, if you take into account the masses of the apples, which is what is physically relevant when you buy apples, then you have less mass when the two apples are together, right ? :biggrin:
 
  • #12
humanino said:
Well, if you take into account the masses of the apples, which is what is physically relevant when you buy apples, then you have less mass when the two apples are together, right ? :biggrin:
Pfft, technicalities. If truth be told, the error is in disguise - it's either present in the definition(s) or as a constant in whatever expression you're using.

On the other hand, there is no match for the physics of two cows™.

You have two communist cows.
 
  • #13
Poop-Loops said:
Epsilon-not.

Mu-not is defined. At least, that's what my professor said.

by the way, that's
epsilon-http://www.answers.com/naught&r=67" (epsilon-zero) and similarly for mu-naught.
 
Last edited by a moderator:
  • #14
humanino said:
Well, if you take into account the masses of the apples, which is what is physically relevant when you buy apples, then you have less mass when the two apples are together, right ? :biggrin:

so, that applies, too, when two physicists get together?:wink:
 
  • #15
humanino said:
Well, if you take into account the masses of the apples, which is what is physically relevant when you buy apples, then you have less mass when the two apples are together, right ? :biggrin:

Umm--what? Are you using special relativity?
 
  • #16
rewebster said:
so, that applies, too, when two physicists get together?:wink:
I guess so :smile:
edit
Actually, it depends. If they disagree on the status of "is string a theory ?", their interaction can be very exothermic.
ehrenfest said:
Umm--what? Are you using special relativity?
They have gravitational biding energy, don't they ?
 

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