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There are two classes of methods one could practicably use. 1. Method grounded on Ampère's law If your flux is time-varying, then, in air or dielectric (no conductivity), Ampère's law will give you the time derivative of the electric displacement flux through your loop (call it $\Gamma$): \oint_\Gamma ...

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To get the best possible estimate, obviously you would sample with an infinitely fine grid. In reality this is not possible or practical in most situations, as you want to finish you measurements in a sensible time frame and other considerations like fluctuations over time and damage to the sample/equipment will become an issue. Therefore you need to ...

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This is a really good and important question; I am not a mathematician, and my answer will just point to a few things to consider. The general answer depends on the form of $m(\beta,x)$. Specifically, if you want to determine $\beta$ with the greatest accuracy, you need to choose points which contain "the most information" about $\beta$. You don't always ...

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All the essential elements are already mentioned in this answer and the linked post in comments. So I'll try to give you more intuition with examples. In principle all measurements performed on a system, will disturb it in some way, be it a classical or quantum system. In the former case, the disturbance for the most part is negligible. Telescope ...

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In quantum phyiscs we have a state. In classical physics we have a state. The former is function from configuration space at each time and the later is a point in configuration space for each time. What we call a measurement in classical physics reveals as much information as we want about the state without changing the state. What we call measurement in ...

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The traditional least-squares fitting or chi-squared minimisation route of fitting a straight line makes the implicit assumption that the errors on the x-axis quantity are negligible. If that is so, then there is no reason why you can't use the uncertainty in the gradient as the uncertainty in $R$. I guess from your question though, that this is not the ...

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When you talk about the speed of gravity, you are talking about the speed of gravity waves. If something jerks to one side or changes shape in a way that the change in gravity could be detected at a distance, the progress of that change through space is nothing other than a gravity wave. People have been trying unsuccessfully to directly detect gravity ...

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I shall first appeal to one of the key points of relativity: If you are 22 years old, like me, I can only have affected things up to 22 light years away from me. Things beyond that are untouched by my existence in every sense. If gravity were faster than light (by say a factor of 2) I could then have affected things up to 44 light years away! This is ...

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I think you ask some good questions here, though many have been asked before. I tend to deny any claim that X is infinite, where X is anything from our observable universe. For instance: This is correct. Nothing in our observable universe is infinite. The observable universe is very large, but not infinite. The number of grains of sand on ...

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Is the universe infinite? We don't know, we can't know. And we never will know. But there are some solid reason to think it is, and some solid counter arguments. One argument is based on the fact that we look out at things far away and notice they are all moving away from us. We argue that it is unlikely we happen to be at a unique place in the universe ...

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Archimedes: Get a bucket big enough to contain your whole body at the most shrinking position (like a baby in the womb). Take a note for these following weight scale: Strip off all your clothes - fully naked. Weigh your naked body - Record it as $W_n$ Weigh the bucket - Record it as $W_b$ Put the bucket on the weigh scale Fill that bucket with water ...

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Every few year the Committee on Data for Science and Technology (CODATA) publishes recommended values of the fundamental constants, see http://www.codata.org/. They use the most accurate experimental results available, so yes, the values of the fundamental constants can -- in principle -- change. But what is more likely, is that the number of significant ...

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