Maxwell's Equations: Exact or Approximate?

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    Maxwell's equations
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SUMMARY

Maxwell's equations are mathematically exact but physically approximate due to the inherent measurement uncertainties of fundamental constants such as epsilon-not (ε₀) and mu-not (μ₀). While these equations provide a robust framework for classical electromagnetism, they do not yield exact physical predictions because the constants involved are not defined to an exact value. Quantum Electrodynamics (QED) introduces variations in predictions compared to classical interpretations, reinforcing the notion that physical models are approximations rather than absolute truths.

PREREQUISITES
  • Understanding of classical electromagnetism principles
  • Familiarity with fundamental constants such as epsilon-not (ε₀) and mu-not (μ₀)
  • Basic knowledge of Quantum Electrodynamics (QED)
  • Mathematical proficiency in handling equations and approximations
NEXT STEPS
  • Research the implications of Quantum Electrodynamics (QED) on classical electromagnetism
  • Study the definitions and measurements of fundamental constants like epsilon-not (ε₀) and mu-not (μ₀)
  • Explore the concept of physical approximations in scientific modeling
  • Investigate the philosophical implications of "exactness" in physics
USEFUL FOR

Physicists, electrical engineers, and students of electromagnetism seeking to deepen their understanding of the nature of physical laws and the role of measurement in scientific equations.

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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