Maxwell's Equations & GR: How Scientists Got Away With It

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In summary, the Maxwell equations are Lorentz invariant and valid in inertial reference frames, but the experiments that led to them were done on the surface of the Earth which is not an inertial reference frame. However, the Earth's gravity is too weak for this to significantly affect the results.
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Maxwell’s Equations are Lorentz invariant, so they are valid in inertial reference frames, right? However, the surface of Earth is not truly an inertial reference frame, yet the experiments that led to Maxwell’s equations were all done on the surface of Earth.

Does that not pose a small problem?

(a) How were scientists able to get away with this and still have an accurate theory? Is it because the Earth is big enough compared to the experimental set ups that spacetime was close enough to being flat that the divergence in results was too small to notice?

(b) I take it there are general relativistic modifications to Maxwell’s Equations? Could anyone point me to a source that explains the differences between the flat spacetime Maxwell Equations and the GR versions?Thanks!
 
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Maxwell equations survive replacing usual derivatives by covariant derivatives.
 
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sweet springs said:
Maxwell equations survive replacing usual derivatives by covariant derivatives.
Oh my, new operations to look up. Thanks!
 
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I don't think you need to go to curved spacetime to understand the basics of (a). An accelerated observer in Minkowski should do fine locally to deal with the OP's question regarding the effect of acceleration. You should get something like ##\nabla \to \nabla + \vec \alpha/c^2## in the sourced Maxwell's equations. If the correction term ##\sim \vec \alpha/c^2## is small compared to the field derivatives you can forget about the effects of acceleration and ##c^2/\alpha## gives you the typical length scale over which the effects would be relevant. For ##\alpha \sim 10\ \mbox{m/s}^2##, you would find a relevant length scale of about a lightyear (coincidentally, since a year is roughly ##3\cdot 10^7## seconds and therefore ##c/\alpha \sim 1## year).

So:
Sorcerer said:
(a) How were scientists able to get away with this and still have an accurate theory? Is it because the Earth is big enough compared to the experimental set ups that spacetime was close enough to being flat that the divergence in results was too small to notice?
No. It is because the Earth gravity is way too weak for the effect to be noticeable at relevant length scales.
 
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1. What are Maxwell's Equations?

Maxwell's Equations are a set of four partial differential equations that describe the behavior of electric and magnetic fields. They were first published by James Clerk Maxwell in 1865 and are fundamental to the understanding of electromagnetism.

2. What is the significance of Maxwell's Equations?

Maxwell's Equations are considered one of the greatest achievements in the history of physics. They unified the concepts of electricity and magnetism and provided a framework for understanding and predicting the behavior of electromagnetic waves, including light.

3. What is General Relativity (GR)?

General Relativity (GR) is a theory of gravitation developed by Albert Einstein in 1915. It describes the force of gravity as a curvature in the fabric of space-time caused by the presence of mass and energy.

4. How do Maxwell's Equations and GR relate to each other?

Maxwell's Equations and GR are both fundamental theories in physics that describe different aspects of the universe. Maxwell's Equations explain the behavior of electromagnetic fields, while GR explains the behavior of gravity. Together, they provide a comprehensive understanding of the fundamental forces in the universe.

5. How did scientists "get away" with Maxwell's Equations and GR?

The term "get away" suggests that scientists were able to deceive or manipulate others with these theories. However, Maxwell's Equations and GR have been extensively tested and verified through experiments and observations, and have stood the test of time. They are widely accepted by the scientific community and have greatly contributed to our understanding of the universe.

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