But is it a breakthrough compared with the normal way to speed up a convolution, that is to compute it in Fourier space using a Fast Fourier Transform (FFT) or variants (DFT, DCT), etc.? I don't know the answer to this and would like a comparison as it is very relevant to my research work...
Read his paper and his rebuttal. He is basically saying that if the Lorentz law of force is replaced with a more elegant equation (Einstein-Laub), then you naturally obtain the "hidden momentum" terms that are inserted under a covariant transformation. Furthermore, there is another candidate equation, Helmholtz force, which is different but takes care of the "hidden momentum" in a similar way. Predictions in differences in experiments can be made and Mansuripur is attempting to realize these experiments. These experiments will determine if Einstein-Laub is correct or if Helmholtz force is correct. Interestingly, the covariant transformation of the hidden momentum gives a term like the Helmholtz force I believe, so these experiments really should determine who is right.
I really don't see why he is being attacked, his analysis doens't disagree with relativity, it just moves the mathematical terms for the hidden momentum to a different place. What I really find interesting is his claim about the experiments...
I am an OSGS (Optical Sciences Graduate Student) and you don't need Quantum Mechanics to explain the experiment above, all you need is classical wave optics.
Linear polarization is electric field in a specified direction, lets say you have the electric field oscillating in the x direction and in the y direction for the first slit and the second slit respectively. Those directions are orthogonal to one another, so cannot interfere (the inner product is zero). But, if you have some component from both slits in some direction (for your example you will be getting out sqrt/2 of the x component in the 45 degree direction and sqrt/2 of the y component in the 45 degree direction when you insert the 45 degree polarizer, which is basically equivalent to the no polarizer case except you have reduced the amplitude). Then you have slit interference in the classical sense as illustrated here : http://astro1.panet.utoledo.edu/~lsa/_color/14_interference.htm, you will have to scroll down to see the two slit interference. Note that we see a sinusoidal pattern because our eyes view the time averaged irradiance (intensity) of the wave pattern, the the wave pattern itself.
What is different about the quantum case is that you can send, say electrons, through the slits *indivdually*, one at a time and they somehow interfere, that is what is intuitively strange.
The percentages in their study are also higher for engineering and mathematics students.
Another particularly irritating caveat of this study is that they assign any "copying from the internet" to "cybercheating."
1) It is unclear whether in whatever questionnaire that they used whether the adequately distinguished between "copying a few lines with attribution" vs "copying a few lines without attribution."
2) In engineering and mathematics Wikipedia, Planetmath, Physics forums, etc. are usually useful and correct for undergraduate topics. In these disciplines, for an equation, like Newton's method, there really is only one way (or maybe a few ways) of concisely writing down the equation. If a math or engineering student copied an equation from Wikipedia to use on their homework, this study would label that "cybercheating," which is absolutely ridiculous!