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Boltzman Oscillation
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So I just learned that in general relativity Magnatic and Electric fields are dependent on the observer. What are some consequences as a result?
Electromagnetism is incompatible with Galilei transformations? I just got into the subject so I dint know that. I won't learn anymore relativity until a year or two, unfortunately. What do you mean there is no theory where it does not happen?Orodruin said:This is true in special relativity as well. Also since electromagnetism is incompatible with Galilei transformations, that really means that there is no theory where this does not happen.
Orodruin said:Maxwell's theory of electromagnetism is inherently relativistic. It is not Galilei invariant as it would single out a particular frame, the frame where the speed of light is c. However, it is Lorentz invariant. This inconsistency is what led to the development of special relativity in the first place. Einstein's 1905 paper was titled "On the electrodynamics of moving bodies" (but in German).
Yes, it is insightful. Thank you very much.Ibix said:If I'm on a train, I don't actually need to factor that into my calculations if I want to do calculations about what would happen if I throw a ball. I can just treat the carriage as stationary and do standard ballistics. Or, if I like making life complicated, I can treat the carriage as moving at 60mph - and do standard ballistics again. I just add 60 to all the initial velocities and add 60t to the positions at time t, and the maths just works.
This is because the laws of (Newtonian) physics are Galilean invariant. Mathematically, in any of the equations, you can replace ##x## with ##x'=x-vt##, where ##v## is a velocity in the x direction, and it all just works.
Electromagnetism doesn't work like that. You can describe a charge moving past a magnet or a magnet moving past a charge. But you cannot transform one solution into the other using Galilean invariance. Ether theories of increasing complexity were an attempt to fix that, but experiments eventually led Einstein to the realisation that electromagnetism didn't work if you replaced ##x## by ##x-vt##, but did if you replaced ##x## with ##x'=\gamma(x-vt)## and ##t'=\gamma(t-vx/c^2)##, where ##\gamma=1/\sqrt{1-v^2/c^2}## - the Lorentz transforms.
Crucially, he also realized that Newton's laws of physics were very slightly inaccurate. He wrote down laws of physics - conservation of momentum and energy and the like - that were the same under the Lorentz transforms, not the Galilean one. So you can still treat the train as moving or stationary as you like - but just adding 60 to the velocities turns out to get you an ever so slightly wrong answer. You'll never notice at everyday speeds, but the point about electromagnetism - and light in particular - is that changes propagate at around the speed of light. So "accurate enough for everyday speeds" doesn't cut it.
Hope that's helpful...
Boltzman Oscillation said:Lorentz invariant means x^2 + y^2 + z^2 - (ct)^2 = s = s' right? What exactly does this tell us? That a position of a particle is also determined by c as opposed to just the xyz positions? This makes me excited for special relativity. I am trying to self learn quantum mechanics but the math is kicking my arse. I don't know if I could take the time to learn special relativity alongside my courses at the moment.
The electric and magnetic effects refer to the phenomena that occur when electric and magnetic fields interact with matter. These effects can include the movement of charged particles, the creation of electric currents, and the generation of electromagnetic waves.
Electric and magnetic fields are closely related and are part of the same fundamental force known as the electromagnetic force. Changes in one field can create changes in the other, and both fields can interact with matter to produce various effects.
Some common examples of electric and magnetic effects include the flow of electricity through wires, the movement of compass needles in the presence of a magnet, and the creation of light and radio waves. These effects have numerous applications in technology, such as in motors, generators, and communication devices.
Electric and magnetic effects play a crucial role in our daily lives, from powering our homes and devices to enabling communication and transportation. Without these effects, many modern technologies would not be possible, and our world would be vastly different.
While electric and magnetic effects have many beneficial applications, they can also have negative consequences. For example, exposure to strong electric or magnetic fields can be harmful to living organisms, and fluctuations in these fields can disrupt electronic devices. Understanding and managing these effects is essential for safe and efficient use of technology.