Genady

Here are two slides from Alan Guth's lecture 1 in the MIT class on Early Universe. He has explained there how something can come from nothing while obeying the energy conservation. Don't worry about his use of word "miracle". He uses its meaning as "a very amazing or unusual event, thing, or achievement" (Merriam-Webster)

When I Heard the Learn’d Astronomer BY WALT WHITMAN When I heard the learn’d astronomer, When the proofs, the figures, were ranged in columns before me, When I was shown the charts and diagrams, to add, divide, and measure them, When I sitting heard the astronomer where he lectured with much applause in the lecture-room, How soon unaccountable I became tired and sick, Till rising and gliding out I wander’d off by myself, In the mystical moist night-air, and from time to time, Look’d up in perfect silence at the stars. Perhaps Walt Whitman came to the lecture unprepared. He didn't know how much depth, beauty, perspective he missed. I wonder, who the "learn'd atronomer" was?

(I retracted an erroneous edit only.) It is correct that all these masses have to be put in by hand. Finding the Higgs boson supports the mechanism, nevertheless. (I don't think the OP had any of this in mind. It asked about a mass of the field.)

It would work for me. But, how it reconciles with the SM where particles get their mass from interaction with the Higgs field? Edit: Retracted.

Yes, I wondered where the subject has changed from 'field' to 'electron'. And with no input from the OPer.

Right. Back of a very tiny envelope calculation shows that to have a drop in acceleration 1% over 10 m the radius needs to be 1 km. Here comes the real question: How do I type Greek letters here? I wanted to put 'omega' for the angular velocity...

What my question (see above) relates to, can be found in a variety of sources. A "simple", Feynman-style explanation on how the principle of least action emerges in the path integral picture, is in his book "QED: The Strange Theory of Light and Matter". On pp.42-45 he applies this picture in an example of reflection of light and "derives" the principle of least action, in this case. He concludes, "And that’s why, in approximation, we can get away with the crude picture of the world that says that light only goes where the time is least" (p.45). More generally, on p.123, "This brings us all the way back to classical physics, which supposes that there are fields and that electrons move through them in such a way as to make a certain quantity least. (Physicists call this quantity “action” and formulate this rule as the “principle of least action.”) This is one example of how the rules of quantum electrodynamics produce phenomena on a large scale." More formal derivation is in Zee, A.. Quantum Field Theory in a Nutshell. On p.12, "Applying the stationary phase or steepest descent method ... [to a path integral] we obtain ... the “classical path” determined by solving the Euler-Lagrange equation ... with appropriate boundary conditions." (I've removed the math expressions.) Edit: After re-reading these sections in the books I got the answer to my question. Thus I don't have any more open questions in this thread.

Thank you very much for a very good explanation of what the principle of least action is. Unfortunately, it doesn't relate to my question. But it's OK. You don't necessarily know what my question relates to.

I remember that stationary action "emerges" from the Feynman path integral. Doesn't QM "explain" it?

Do you mean a station is spinning to create 1G at the circumference? Then, acceleration of a circular motion is v2/R. Equate it to 1G and find R for a given v.

I think it does. Why do you think it's weird?

You never need to quote. You just say something like, "Since the process is irreversible [4], ...", where [4] is in the References at the end of your manuscript, directing a reader to the source of this clause.

Scientific journals, at least in this field, also discourage authors from submitting manuscripts with unnecessary quotes.

I've noticed this alien looking "thing" slowly drifting along the reef at the depth of about 10 m. It was about 4-5 m long, 30 cm in diameter. A flexible, hollow tube, so one could put an arm into it. Which I did. Here are more pictures, with a dive buddy of mine for a scale, and some closeups: It took me a while to find out, what it was. Egg mass of a diamondback squid, Thysanoteuthis rhombus.

It sure is. Good luck!

Plants evolved from organisms which were not plants. The not-plants also evolved from organisms which were not plants. The bottom line is, not-plants did not evolve from plants.

No, it has not. Plants split off early from the rest of life. Schematically, so:

Expanding on and paraphrasing the @MigL's statement above: As a mathematician, "I'm not overly concerned with the 'why' of a paradigm, or set of rules, only its 'function'." "Math is simply a tool for describing/investigating the world" of absolute truths, which are independent of the world around us and thus hold and can be trusted when investigating new, unfamiliar worlds.

If I remember correctly, we have an area in the brain which is activated for basic counting - small quantities, comparing sizes, amounts, etc. This area is separate and removed from the language areas, and the two get activated independently in different situations / tasks. This does not support the view that math is at the basis of language. In addition to this, the quantifying systems and languages come in a variety of sophistications in different cultures. In some, language is very rich and complex, while counting is very limited. In others, vice versa. Again, not a refutation, but doesn't support the hypothesis.

I wonder how it is in fishes? E.g. in this Flying Gurnard I saw (in spite of being "Flying" it is a fish, not a bird )

Gerard ’t Hooft has created this website for you: How to become a GOOD Theoretical Physicist (uu.nl)

Don't 'we' understand the difference between a phenomenon and an equation?

@joigus is correct. However, would you elaborate on your question and on how it relates to that quote?