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...
This thread is old. But I am surprised to read that lattice QED does not need to be the "correct" non-perturbative quantum version of QED (apparently, lattice QED is trivial, but perturbative QED gives correct results, and Neumaier argues that it could be QED is a perfectly fine quantum theory...
I want to ask for opinions about the suggested path to be able to study the book "Quantum Fields and Strings" successfully, from a mathematical physics point of view. Maybe with a first entry with the books of Costello, Hall and Folland.
My interest is as an amateur (financial professional)...
I think I have a solution:
In the Appendix of Leary's "A friendly introduction to mathematical logic", it is stated:
"Think of a set as a collection of objects. If X is a set, we write a 2 X
to say that the object a is in the collection X. For our purposes, it will be
necessary that any given...
1. Item (2) above is key, and we need to see how we understand each other. For me, it is clear that both first order logic and set theory are composed of primitive notions called "proposition". In fact, propositions are all there is, in both first order logic and set theory! For example, the rhs...
But this is really problematic for me. For example, as said before, the statement "this statement is false" is neither true nor false.
Of course, you could claim that traditional versions of sets exclude this kind of statements. But then, how do you know that the statement "x belongs to A" is...
Forget about the undecidability. The key of what I am saying is that with Schuller's "new axiom", it is perfectly clear that "x belongs to A" is a proposition. Without this new axiom, it is not clear at all.
So, by being "x belongs to A" a proposition, the axiom of extensionality is valid...
You repeat, but you do not prove. You claim, basically, that all statements are either true or false. The only "bad" thing that it can happen is that this truth/falsehood cannot be proven through the considered axioms. But with other axioms, it could be different.
This is what you say. But you...
I have an issue with this statement (with the rest of your post, I am OK, it is nothing controversial, I think):
The axiom of extensionality is an iif. And an iif means that both sides have the same truth/false value. I have never seen that an iif can be considered to be valid (as it is, since...
If there is no way to check if two sets are the same, then the ZFC axioms are not always well defined (for example, if there is no way to check if two sets are the same, how is on Earth the axiom of extensionality going to be satisfied?). Instead, with Schuller's new axiom, then yes, everything...
But if you say "only statements that are propositions are considered", and then undecidable statements are not considered, you are using a "dirty trick", since one cannot know, in general, if one is considering a proposition or not.
For example, the statement "this statement is false" is not a...
In Frederic Schuller lectures:
https://www.physicsforums.com/threads/an-additional-constraint-to-the-zfc-axioms.986356/#post-6318922
it can be seen from page 8, in the axiom of the epsilon-relation, that Schuller is doing what I have said before (better, I am saying what he wrote before). He...
The ZFC axioms are statements combining "atomic formulas" such as "p ∈ A" and "A = B", using AND, OR, imply, NOT, for all and exists.
But (it seems to me, at least) there is the implicit assumption that the "atomic formulas", "p ∈ A" and "A = B", are considered to be propositions, i.e. they are...
Now I am going to say something opposite to what I have said initially: the definition of the natural numbers, as per https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers for example, whereby the zero is the empty set, the one is the set formed by the empty set, and so on...
I think that most books consider the membership relationship as formal. There is no "constructive definition" of the membership relationship.
For example, the empty set is called that way because the "intuitive membership relationship" suggests so. But if you take the axioms and see the...
In the past, I have asked in this forum about the concept of set membership, in the context of ZFC.
I guess it is a normal reaction to be a bit surprised by the usual statement in books that the set membership relationship is "undefined".
But I have had this idea: a typical definition of the...