Recent content by Quantum River

For near a year, I am so focusing on writing several papers. So I forgot to take the GRE Subject test. On the Internet, I find nearly 20 physics departments, such as the Calfornia universities and Michigan State University, they all require the Subject test score. Could you tell me which...

I am preparing to apply to a graduate school of physics. I have taken the GRE general test and TOEFL. But I have not taken the GRE Subject test. I find nearly all the universities in US require the GRE Subject test. Is there any university that do not require the GRE Subject test? Or I will have...

Anonym, sorry for my rudeness. Your posts provide many resources to think. Although I don't agree with some of your argument, I do think they pose the right and important questions. I think physics is at the verge of another revolution of thoughts. The concepts of time, space, QM could be...

Mathematics is mainly from mind, while physics is mainly from experiments. There is a vast gap here. In the real life, these philosophical things are actually of least importance for lots of people including me. I may use them as a guide of treasure finding, but will not take any of these things...

I am not quite familiar with strong interaction physics. So my judgment may be wrong. Besides his contribution to asymptotic freedom, Gross first derived the heterotic string theory. So Gross may be quite open-minded. Gross’s Nobel lecture is quite surprising about the QFT was nearly discarded...

Gross Nobel lecture on QFT and QCD. http://nobelprize.org/nobel_prizes/physics/laureates/2004/gross-lecture.pdf

Anonym, thanks! Now I am reading some papers on string theory and loop quantum gravity. It is more interesting and there is a lot of creative work to do. I think duality is at the heart of physics. Besides the most important particle-wave duality, there are electromagnetic duality, T-duality...

String theory The basic idea behind all string theories is that the fundamental constituents of reality are strings of extremely small scale (possibly Planck length, about 10−35 m) which vibrate at specific resonant frequencies. Thus, any particle should be thought of as a tiny vibrating...

I was fascinated by the quaternion ring in my senior middle school, but I dropped it when I find it is even impossible to define simple analysis concepts such as limit, derivative, integral in the quaternion ring. In my opinion, our/mathematicians' understanding of such noncommutative things...

I am confused about the relation between condensed matter physics and Quantum field theory (QFT). Here are my "naive" questions. 1. The condensed matter physics deals with the macroscopic physical properties of matter. The number of atoms of the system is as large as Avogadro's number. But in...

Recently I read Michael Atiyah's article "Mathematics in the 20th Century". Atiyah said "21st century might be the era of quantum mathematics or, if you like, of infinite-dimensional mathematics". So mathematicians should ask how many physics mathematicians need?

What is the meaning of temperature in a quantum system? Surely temperature concerns lots of particles. (More is different. -Philip W. Anderson) So the wave function of the system is very very big. Could temperature only exist in a mixed state system. But how do we define temperature? How does...

When we use the Heisenberg representation in QFT, there is no need to discuss wave function anymore. In Heisenberg's matrix mechanics of QM in the early 1920s, Heisenberg didn't need the wave function to calculate the atomic spectrum. And now we do not need to know the wave function in QFT to...

Anonym, I have read quant-ph/0606121 and found several problems. What is the "Real Hilbert Space"? You gave some description about it. But there is no clear definition. What does "tr" mean? "tr" can operate on a complex number (such as the complex number i=sqrt(-1)) and also a matrix. So what...

Einstein's peculiar reasoning of spontaneous emission? Einstein's peculiar reasoning of spontaneous emission Spontaneous emission is the result of quantum mechanics. So we need not use some theorems of thermodynamics to duduce spontaneous emission. But in Einstein's reasoning of spontaneous...