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Hello Pan. My comment'll be very short. Correctly. This is well known so called geometrical interpretation.

More precisely, they are most close to the real model of gravity, but of course they are not right theories (just a sets of rules, which whether well or bad work). However, today we have nothing better than they are.

In fact if you even somebody else try to measure a mass, then you even somebody else can obtain only a (rest) mass. In this sense a mass doesn't increase with velocity, nobody can to measure it because a (rest) mass is an invariant.

Very good impulse

Don't mention it, Pete. Thank's for discussion.

I like it. After Pauli's book everyone should termed the mass... kinda "Oh! yes, of course, I quite forgot (in Pauli's terms, not Einstein) the rest mass..." Just say me, you really use those terms when you read or use the QFT??? There are no the relativistic or rest mass and total and rest...

Energy yes, mass no. What is a relativistic and rest mass or total and rest energy? What for? Moreover with c=1. Energy and mass. In general, I think, that we already have understood each other.

Of course, not. You’ve made mistake again p=mug, where `````____ g=1/Ö1–b2, b=u/c. In Einstein's first paper he really does speak of transverse and longitudinal mass, but he obtain the following equation, ``````````______ W=mV2(1/Ö1–u2/V2–1) where m – mass, V – speed of light. And...

Once again, mass is an invariant concerning Lorentz and Poincare transformation groups. You can't defining mass by gravitation, because measure of attraction within dependence to both an energy and direction of moving. E.g. two photons with the same energy, but the perpendicular momentums will...

Then what is a photon's wave length?

That's mass, you can call it the rest energy, but not rest mass. You've made mistake. In general, E0=mc2, but total energy of particle E is equal to mc2 if and only if the particle's momentum p is equal to zero, because E=p2c2+E02=p2c2+m2c4 Let c=1, then E=p2+E02=p2+m2. The serious...

Of course, but, eventually, that was post in reference to Michael F. Dmitriyev, as the answer to his one.

Because photon has both linear part of four-momentum, and helicity, therefore it needs the four-dimensional space. You can't describe a photon in space having smaller dimensionality. You can't conserve both momentum, and helicity, and spin, without four-dimensional space.

Photon doesn't have mass, it just does have a non-zero linear part of four-momentum, therefore it call a massless linear particle.

Íó çäðàâñòâóéòå, Ìèõàèë, êîëè íå øóòèòå. Ïèøó Âàì ïî-ðóññêè, ïîòîìó, ÷òî Âû çàâåëè çäåñü îôôòîïèê. Íàïðèìåð, ãäå åù¸? Èëè ýòî óòâåðæäåíèå, òàê, "îò áàëäû"? Íå ëó÷øèé ñïîñîá ïîçíàêîìèòüñÿ çíàåòå ëè... Íà âñÿêèé ñëó÷àé Âàì ïîÿñíþ (ó äðóãèõ ïîêà âîïðîñîâ íå âîçíèêàëî), ÷òî ÿ íå õîòåë íàçûâàòü...

Bingo! If we agree with the concept of secondary quantization within the framework of QFT, then of course yes - the (local) time is only difference between two nearest states of the same physical system.

Actually you take one quantization of continuous time for descrete nature of time. Within the framework of QFT the time is discrete. The secondary quantization concept allow to sustitude the time with indexes, because the main difference A1-state from A2-state is the index. We need the time only...

Well... one and the last time. The set theory operates sets by using operations such as x - direct product of sets, Å - direct addition of sets, U - join of sets, Ï - intersection of sets. The main requirement is that the results of all the above operations with sets are sets as well. Only this...

Once more, which of my definitions (formulas) exactly redundant and complicated? The emty set is only a formula, not an axiom (prove me that my definition of FORMULA of empty set is an axiom; the formulas !x=Æ and z=Æ (in Z7 and Z8) can be substituted with full definition of the empty set... am...

Of course! Bingo! And I think so, too! Maybe I was not clear enough. My point is that ZF exclude an axiom of the empty set because the empty set concept is a theorem within the framework of ZF, not an axiom. But I asked Organic to give the empty set definition of his own, because the ZF empty...

Not exactly that way. The system of axioms (of a specific physical theory) may content time as axiom, and may not... time can be only a theorem (e.g. there are axioms of three-dimensional linear space and four-dimensional invariant, such as four-dimensional interval in the Minkowski space-time)...

Within the framework of quantum field theory secondary quantization implies that motion doesn't exist, i.e. time is defined as transition of a physical system with one set of observable values (say, A1-state) to another set of observable values (say, A2-state). If A1-state differs from A2-state...

Why do you need another axiom? Don't you think that we could do with existing ones? In the case of the idea of the set, x is only an uncertain set, nothing else.

Hello there. What do exactly we consider? Whether time does exist or it doesn’t? What is time? Whether is time a dimension of space, enclosing us, or is it part of metrics? Generally, time is not illusion, but motion is. Maybe, the problem is to define time. However, this problem can also be...

No, I don't. My post is there only because of a technical problem.

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For Zermelo-Frenkel system axioms (AUTHOR's DENOTATIONS, not Ito and somebody else) see link below http://physics.nad.ru/img/Sets.gif If you want to understand what exactly author thought, then always use of the author's books or reference

Which of them (axioms)??? Is the section of General physics>Theory Development math section? I thought, that it is a Physics theory development section... If I've misunderstood, then forgive me

You've misunderstood again... "AST" (the axiomatic theory of set), in other word, ZF or NBG (von Neumann/Bernays/Godel). Neither ZF, nor NBG hasn't an "axiom of empty set". Can you demonstrate this axiom within the framework of ZF or NBG??? Just tell where it is?

More specific in what? Why your ideas aren't new extension of mathematics? Or why your ideas may have application in the computer science? If first, then I've demonstrate the inconsistency of your definitions and suggestions with AST. There is no new mathematics. If second, then I think that...