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joyz2008
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How do Maxwell's equations predict that the speed of light is constant? I found different answers and some people even said that they don't.
I'm still confused...
I'm still confused...
joyz2008 said:How do Maxwell's equations predict that the speed of light is constant? I found different answers and some people even said that they don't.
I'm still confused...
harrylin said:Different people mean different things with that sound bite...
Heaviside did investigate moving media, if I understand what you're saying here. In 1902, he went as far as assigning a physical meaning to the momentum in an electromagnetic wave in Electromagnetic Theory, Vol. III. It's his "Moving Compressible Ether". I've attached a PDF I created that contains his lead-in description and the derivation using more modern notation/units (obviously it's a completely classical derivation). I've always wanted a mathematician to look at the theory and see where it would lead experimentally. The particularly interesting prediction is that two em waves will interact if strong enough.PhilDSP said:... (Heavyside did not re-transcribe Maxwell's equations for moving media into today's vector form as he did for non-moving media) ...
PhilDSP said:[..] However the attempt to develop equations for moving media was abandoned upon the deaths of Oliver Heavyside and Heinrich Hertz. (Heavyside did not re-transcribe Maxwell's equations for moving media into today's vector form as he did for non-moving media) [..]
fizzle said:Heaviside did investigate moving media, if I understand what you're saying here. In 1902, he went as far as assigning a physical meaning to the momentum in an electromagnetic wave in Electromagnetic Theory, Vol. III.
harrylin said:I'm not sure what you refer to; in any case, Heaviside did predict the effect of moving charges. He did not write it in vector notation but nevertheless with directionality (cos alpha etc.). His 1889 paper in which he expands on Maxwell's theory predicts the same electromagnetic field strengths of moving charges that later also followed from relativity. And that's as it should be: Maxwell's equations are fully compatible with special relativity.
Remember, when you're reading Heaviside (and his contemporaries), you're essentially reading history in the making. It's like watching a live news report from a major event - initial information is fragmented, sometimes wrong, changes over time, names change, etc.PhilDSP said:Thanks for providing the file. It's difficult to put that small snippet into the larger context though. One difficulty with Heavyside is that he defines and uses a lot of unique variables that no one else seems to use and you need to wade through hundreds of pages in his 3 volume series to go back and find their definitions.
fizzle said:Remember, when you're reading Heaviside (and his contemporaries), you're essentially reading history in the making. It's like watching a live news report from a major event - initial information is fragmented, sometimes wrong, changes over time, names change, etc.
fizzle said:The snippet I put in my PDF is just the beginning of his theory. See the referenced pages in EMT Vol. III for the rest of it. What it says, and what I like about it, is that em waves are not linear. For example, if I send extremely strong waves down a transmission line from both ends, when they overlap I'm left with a region of increased "density of space" (this is his "m").
Wow, I'm beginning to wonder if I have a split personality and also post here under the handle "PhilDSP"! For a perfect example of your "simplifications", look at Compton Scattering. Compton noted in his original paper that you can get the correct answers from a semiclassical analysis of the experiment. However, it's much easier to solve the problem as a high-level simple particle interaction; which is what I would call an "engineering solution", i.e. one where you're looking for workable assumptions that you can use to accomplish a task. To me, physics is more about examining the fundamentals to produce and/or validate those "engineering assumptions".PhilDSP said:Nice way of putting it. It could be said that a lot of the issues Maxwell, Heaviside, FitzGerald and Hertz (among others) struggled with were simply discarded or ignored by later theorists in a quest for simpler and more immediate answers. So the mystery remains about certain aspects of their work and whether some of the later simplifications have haunted us for the past 110 years.
Maxwell's equations are a set of four fundamental equations that describe the behavior of electromagnetic fields. These equations show that the speed of light is directly related to the electric and magnetic fields, and that it is a constant value in a vacuum.
The constant speed of light in Maxwell's equations is significant because it means that light travels at the same speed regardless of the observer's frame of reference. This was a groundbreaking discovery in physics and led to the development of Einstein's theory of relativity.
Maxwell's equations show that the speed of light is a fundamental constant in the universe. This can be seen in the form of the equations, which do not change based on the observer's speed or frame of reference. Additionally, experiments have consistently shown that the speed of light is constant.
The constant speed of light has many implications in physics and has led to important discoveries such as the theory of relativity, which has revolutionized our understanding of space and time. It also plays a crucial role in technologies such as telecommunications and GPS systems.
No, Maxwell's equations do not have any exceptions to the constant speed of light. These equations have been extensively tested and have been found to accurately describe the behavior of electromagnetic fields, including the speed of light. Any exceptions or variations would require a modification of the equations.