I do not agree. This new "sparser" set could be the same as the original set, except for a finite set of points (for example, if the points in the original set are even).
The natural numbers are the smallest infinite set, aleph_0.
By taking out an infinite subset to the natural numbers (the odd naturals), we get an infinite subset, the even numbers, which has the same size, aleph_0 (e.g. the map n->2n).
We can take an even "sparser" subset of the natural...
Since QM is not deterministic, the future state B is not determined by the previous state A (at time A, B was only a possibility, not a certainty).
Then, when we are at time B, and assuming we could move back in time (of course, we cannot do that, but let us make a Gedankenexperiment), it just...
This seems like choosing a profession. Nothing bad about this, but in my case, I am not speaking about being successful professionally, but about the pleasure to learn, and the pleasure to be able to answer the why why why questions.
I do not disagree with your comment.
Having said that, I repeat the issue of motivation. Maybe some (lucky) students do not need motivation to learn analysis, and they blindly believe the axioms of the real numbers, and everything goes well starting from there.
But some others may be...
Of course, I do not disagree with you.
But what I have said might be useful to at least two kind of people:
1. Students that find difficult to get motivation to start studying analysis from the axioms of the real numbers. This is extremely unmotivated. One could say that mathematical maturity...
What I am going to outline should not be seen as a recommendation for most. Probably only a minority would benefit from it.
One possibility to learn the necessary maths to study physics, from a "mathematical physics" point of view is to first study a degree in maths (and maybe also a Master...
Sure, but how do you prove that these small quantum fluctuations never become macroscopically large? (as it happens in reality).
Also, there is another issue (maybe this one is well understood, and only my knowledge is faulty): CM observes the positions of objects. By observing how the Moon...
There are many arguments for this limit (Ehrenfest theorem, WKB approximation, hbar to 0 in the path integral ...) but I think the lack of spread of the wave packet is not easy to explain, in this limit. I have read (I do not know how certain this claim is) that it is not obvious that CM can be...
Usually it is stated that physics is divided among classical mechanics, classical field theory, quantum mechanics, quantum field theory and statistical mechanics, with hbar, the speed of light and the number of particles being the parameters differentiating all these theories.
However, despite...
I am a person working in the private sector. I studied physics, up to MSc level (QFT, string theory). But then I moved towards the private sector, raising a family, etc.
My wish is to try and understand QFT at the non-perturbative level. I do not need to write any paper on that subject, just to...
Thank you for the explanation, Neumaier.
Do you have any way to reconcile the idea that lattice QCD seems to be a good definition for "non-perturbative QCD", but instead, lattice QED seems not to be a good definition for "non-perturbative QED"?
Intuitively, I would expect the lattice method to...