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Started 7 April 2024
"How do we understand special relativity?"
"How do we understand special relativity?"
The Quantum FFF Model differences: What are the main differences of Q-FFFTheory with the standard model? 1, A Fermion repelling- and producing electric dark matter black hole. 2, An electric dark matter black hole splitting Big Bang with a 12x distant symmetric instant entangled raspberry multiverse result, each with copy Lyman Alpha forests. 3, Fermions are real propeller shaped rigid convertible strings with dual spin and also instant multiverse entanglement ( Charge Parity symmetric) . 4, The vacuum is a dense tetrahedral shaped lattice with dual oscillating massless Higgs particles ( dark energy). 5, All particles have consciousness by their instant entanglement relation between 12 copy universes, however, humans have about 500 m.sec retardation to veto an act. ( Benjamin Libet) It was Abdus Salam who proposed that quarks and leptons should have a sub-quantum level structure, and that they are compound hardrock particles with a specific non-zero sized form. Jean Paul Vigier postulated that quarks and leptons are "pushed around" by an energetic sea of vacuum particles. 6 David Bohm suggested in contrast with The "Copenhagen interpretation", that reality is not created by the eye of the human observer, and second: elementary particles should be "guided by a pilot wave". John Bell argued that the motion of mass related to the surrounding vacuum reference frame, should originate real "Lorentz-transformations", and also real relativistic measurable contraction. Richard Feynman postulated the idea of an all pervading energetic quantum vacuum. He rejected it, because it should originate resistance for every mass in motion, relative to the reference frame of the quantum vacuum. However, I postulate the strange and counter intuitive possibility, that this resistance for mass in motion, can be compensated, if we combine the ideas of Vigier, Bell, Bohm and Salam, and a new dual universal Bohmian "pilot wave", which is interpreted as the EPR correlation (or Big Bang entanglement) between individual elementary anti-mirror particles, living in dual universes.
Fred-Rick Schermer added a reply
Abbas Kashani
A lot to work with, Abbas.
However, I am standing in a completely different position, and want to share my work with you. I hope you are interested about this completely distinct perspective.
My claim is that Einstein established a jump that is not allowed, yet everyone followed along.
Einstein and Newton's starting point is the behavior of matter through space. As such, one should find as answer something about the behavior of matter moving through space, and yet Einstein did not do that.
To make the point understandable quickly, Einstein had not yet heard about the Big Bang yet. So, while he devised his special relativity, he actually had not incorporated the most important behavior of matter through space.
Instead, he ended up hanging all behaviors of matter on spacetime. It does not matter that his calculations are correct.
--
Let me find a simple example to show what is going on.
We are doing research on mice in a cage, and after two years we formulated a correct framework that fully captures all possible behaviors of these mice in the cage. That's the setup.
Now comes the mistake:
The conclusion is that the cage controls the mice in their behaviors.
Correctly, we would have said that the mice are in control of themselves, yet the cage restricts them in their behavior. We would not say that the cage controls the mice.
Totally incorrect of course, and yet that is what Einstein did. He established a reality in which matter no longer explains the behavior of matter through space, but made it space (spacetime) that explains the behavior of matter. It is a black&white position that has to be replaced by the correct framework (which is a surprise because it is not based on one aspect, but on both aspects).
--
I know I am writing you from a perspective not often mentioned, and it may not interest you. I'll find out if you are interested in delving deeper into this or not.
Here is an article in which I delve into this matter more deeply:
Article On a Fully Mechanical Explanation of All Behaviors of Matter...
Wolfgang Konle added a reply
"Richard Feynman postulated the idea of an all pervading energetic quantum vacuum. He rejected it, because it should originate resistance for every mass in motion, relative to the reference frame of the quantum vacuum."
Richard Feynman's idea is perfect, and there is no reason to reject it. The existence of vacuum energy, or better dark energy is consistent with Einstein's field equations with a positive cosmological constant.
The energy gain from mass or energy in motion leads to an increasing dark energy density.
The only idea which is missing, is the answer to the question: What happens with the additionally gained energy density?
As an answer to that question I propose the following working hypothese:
This energy is used to recycle star fuel from black holes.
On a first glance, this answer looks as being pure madness, because black holes with their unconvincible gravity seem to be a deposit of matter for eternity.
But in fact there is a plausible possibility. This has to do with the negative energy density of gravitational fields and the non-existence of a negatively definite energy density.
But we need open minded thinking in order to delve deeper into details.
Sergey Shevchenko added a reply
"How do we understand special relativity?"
- the answer to this question, which is really fundamental one, since is about what is some physical theory as a whole; what really means – why and how the postulates of a theory, in this case of the SR, really are formulated, and why and how the postulates
- which in any theory fundamentally – as that happens in mathematics, where axioms fundamentally cannot be proven – aren’t proven; while are formulated only basing on some experimental data, which fundamentally prove nothing, though one experiment that is outside a theory prediction proves that this theory is either wrong, or at least its application is limited.
Returning to the SR, which is based on really first of all four postulates – the SR-1905/1908 versions relativity principle, SR-1905 also on the postulate that light propagates in 3D XYZ space with constant speed of light independently on light source/ an observer’s speeds; and, additionally,
- in both theories it is postulated (i) that fundamentally there exist no absolute Matter’s spacetime, and (ii) - [so] that all/every inertial reference frames are absolutely completely equivalent and legitimate.
In the standard now in mainstream physics SR-1908 additionally to the SR-1905 it is postulated also that observed contraction of moving bodies’ lengths, and slowing down of moving clocks tick rates, comparing with the length and tick rates when bodies and clocks are at rest in “stationary” frames, is caused by the “fundamental relativistic properties and effects”, i.e. “space contraction”, “time dilation”, etc..
Really from yet the (i) and (ii) postulates any number of really senseless consequences completely directly, rigorously, and unambiguously follow, the simplest one is the Dingle objection to the SR;
- from this, by completely rigorous proof by contradiction completely directly, rigorously, and unambiguously it follows , first of all, that
- Matter’s spacetime is absolute, that so some “absolute” frames that are at rest in the absolute 3DXYZ space can exist, while applications, i.e. measurements of distances and time intervals, of moving in the space inertial frames aren’t completely adequate to the objective reality; and
- there exist no the “relativistic properties and effects”.
Etc. However really the SR first of all is based on the indeed extremely mighty Galileo- Poincaré relativity principle.
That is another thing that
- according to SR-1905 relativity principle there is some extremely potent entity “light”, the constancy of which for/by some mystic reasons/ways forces moving bodies to contract and moving clocks to slow down tick rates; and
- the SR 1908 relativity principle is practically omnipotent, so the moving frames, bodies, clocks for/by some mystic reasons/ways really contract/dilate even evidently fundamental space and time.
All that above in the SR really is/are only postulated illusions of the authors, nonetheless, again, the Galileo- Poincaré relativity principle is really . extremely mighty, and the SR indeed in most cases at everyday physical practice is applied in completely accordance with the objective reality. The fundamental flaws of the SR reveal themselves only on fundamental level.
The post is rather long now, so here
Cheers
Sergey Shevchenko added a reply
So let’s continue about what is “special relativity”
In the SS post above it is pointed that Matter’s spacetime is fundamentally absolute, however to say more it is necessary to clarify - what are “space” and “time”, just because of the authors of the SR – and whole mainstream physics till now - fundamentally didn’t/don/t understand what these fundamental phenomena/notions are, the really mystic and simply fundamentally wrong things in the SR were/are introduced in this theory.
What are these phenomena/notions, and what are all other really fundamental phenomena/notions, first of all in this case “Space”, “Time”, “Energy”, “Information”,
- and “Matter”– and so everything in Matter, i.e. “particles”, “fundamental Nature forces” – and so “fields”, etc., which is/are fundamentally completely transcendent/uncertain/irrational in the mainstream philosophy and sciences, including physics,
- can be, and is, clarified only in framework of the Shevchenko-Tokarevsky’s philosophical 2007 “The Information as Absolute” conception, and more concretely in physics in the SS&VT Planck scale informational physical model, in this case it is enough to read
More see the link above, here now only note, that, as that is rigorously scientifically rationally shown in the model, Matter absolutely for sure is some informational system of informational patterns/systems – particles, fields, stars, etc., which, as that is shown in the model, is based on a simple binary reversible logics.
So everything that exists and happens in Matter is/are some disturbances in the Matter’s ultimate base – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which [lattice] is placed in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct); FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP.
The disturbances are created in the lattice after some the lattice FLE is impacted, with transmission to it, by some non-zero at least 4D space, momentum P[boldmeans 4D vector] in utmost universal Matter’s space with metrics (cτ,X,Y,Z). The impact causes in the lattice sequential FLE-by-FLE flipping, which, since the flipping cannot propagate in the lattice with 4D speed more than the flipping speed c=lP/tP [really at particles creation and motion c√2, more see the link, but that isn’t essential here].
Some FLE flipping above along a direct 4D line can be caused by a practically infinitesimal P impact; but if P isn’t infinitesimal, that causes flipping FLE precession and corresponding propagation of the “FLE-flipping point” in the 4D space above along some 4D helix,
- i.e. causes creation of some close-loop algorithm that cyclically runs on FLE “hardware ” with the helix’s frequency ω, having momentum P=mc above, mis inertial mass, the helix radius is λ=λ/P;
- and the helix’s 4D “ axis” is always directed along P – particles are some “4D gyroscopes”.
The post is rather long already, so now
Cheers
All replies (3)
formerly conicet and universidad nacional del litoral
You first have to understand
Problems like water of steam moving at 4 mt per second and you crossing at 3 mt per sec
Whats your real speed?
Then contrast to sr answer at speeds near c
Similar questions and discussions
"How do we understand special relativity?"
"How do we understand special relativity?"
The Quantum FFF Model differences: What are the main differences of Q-FFFTheory with the standard model? 1, A Fermion repelling- and producing electric dark matter black hole. 2, An electric dark matter black hole splitting Big Bang with a 12x distant symmetric instant entangled raspberry multiverse result, each with copy Lyman Alpha forests. 3, Fermions are real propeller shaped rigid convertible strings with dual spin and also instant multiverse entanglement ( Charge Parity symmetric) . 4, The vacuum is a dense tetrahedral shaped lattice with dual oscillating massless Higgs particles ( dark energy). 5, All particles have consciousness by their instant entanglement relation between 12 copy universes, however, humans have about 500 m.sec retardation to veto an act. ( Benjamin Libet) It was Abdus Salam who proposed that quarks and leptons should have a sub-quantum level structure, and that they are compound hardrock particles with a specific non-zero sized form. Jean Paul Vigier postulated that quarks and leptons are "pushed around" by an energetic sea of vacuum particles. 6 David Bohm suggested in contrast with The "Copenhagen interpretation", that reality is not created by the eye of the human observer, and second: elementary particles should be "guided by a pilot wave". John Bell argued that the motion of mass related to the surrounding vacuum reference frame, should originate real "Lorentz-transformations", and also real relativistic measurable contraction. Richard Feynman postulated the idea of an all pervading energetic quantum vacuum. He rejected it, because it should originate resistance for every mass in motion, relative to the reference frame of the quantum vacuum. However, I postulate the strange and counter intuitive possibility, that this resistance for mass in motion, can be compensated, if we combine the ideas of Vigier, Bell, Bohm and Salam, and a new dual universal Bohmian "pilot wave", which is interpreted as the EPR correlation (or Big Bang entanglement) between individual elementary anti-mirror particles, living in dual universes.
Reply to this discussion
Fred-Rick Schermer added a reply
Abbas Kashani
A lot to work with, Abbas.
However, I am standing in a completely different position, and want to share my work with you. I hope you are interested about this completely distinct perspective.
My claim is that Einstein established a jump that is not allowed, yet everyone followed along.
Einstein and Newton's starting point is the behavior of matter through space. As such, one should find as answer something about the behavior of matter moving through space, and yet Einstein did not do that.
To make the point understandable quickly, Einstein had not yet heard about the Big Bang yet. So, while he devised his special relativity, he actually had not incorporated the most important behavior of matter through space.
Instead, he ended up hanging all behaviors of matter on spacetime. It does not matter that his calculations are correct.
--
Let me find a simple example to show what is going on.
We are doing research on mice in a cage, and after two years we formulated a correct framework that fully captures all possible behaviors of these mice in the cage. That's the setup.
Now comes the mistake:
The conclusion is that the cage controls the mice in their behaviors.
Correctly, we would have said that the mice are in control of themselves, yet the cage restricts them in their behavior. We would not say that the cage controls the mice.
Totally incorrect of course, and yet that is what Einstein did. He established a reality in which matter no longer explains the behavior of matter through space, but made it space (spacetime) that explains the behavior of matter. It is a black&white position that has to be replaced by the correct framework (which is a surprise because it is not based on one aspect, but on both aspects).
--
I know I am writing you from a perspective not often mentioned, and it may not interest you. I'll find out if you are interested in delving deeper into this or not.
Here is an article in which I delve into this matter more deeply:
Article On a Fully Mechanical Explanation of All Behaviors of Matter...
Wolfgang Konle added a reply
"Richard Feynman postulated the idea of an all pervading energetic quantum vacuum. He rejected it, because it should originate resistance for every mass in motion, relative to the reference frame of the quantum vacuum."
Richard Feynman's idea is perfect, and there is no reason to reject it. The existence of vacuum energy, or better dark energy is consistent with Einstein's field equations with a positive cosmological constant.
The energy gain from mass or energy in motion leads to an increasing dark energy density.
The only idea which is missing, is the answer to the question: What happens with the additionally gained energy density?
As an answer to that question I propose the following working hypothese:
This energy is used to recycle star fuel from black holes.
On a first glance, this answer looks as being pure madness, because black holes with their unconvincible gravity seem to be a deposit of matter for eternity.
But in fact there is a plausible possibility. This has to do with the negative energy density of gravitational fields and the non-existence of a negatively definite energy density.
But we need open minded thinking in order to delve deeper into details.
Sergey Shevchenko added a reply
"How do we understand special relativity?"
- the answer to this question, which is really fundamental one, since is about what is some physical theory as a whole; what really means – why and how the postulates of a theory, in this case of the SR, really are formulated, and why and how the postulates
- which in any theory fundamentally – as that happens in mathematics, where axioms fundamentally cannot be proven – aren’t proven; while are formulated only basing on some experimental data, which fundamentally prove nothing, though one experiment that is outside a theory prediction proves that this theory is either wrong, or at least its application is limited.
Returning to the SR, which is based on really first of all four postulates – the SR-1905/1908 versions relativity principle, SR-1905 also on the postulate that light propagates in 3D XYZ space with constant speed of light independently on light source/ an observer’s speeds; and, additionally,
- in both theories it is postulated (i) that fundamentally there exist no absolute Matter’s spacetime, and (ii) - [so] that all/every inertial reference frames are absolutely completely equivalent and legitimate.
In the standard now in mainstream physics SR-1908 additionally to the SR-1905 it is postulated also that observed contraction of moving bodies’ lengths, and slowing down of moving clocks tick rates, comparing with the length and tick rates when bodies and clocks are at rest in “stationary” frames, is caused by the “fundamental relativistic properties and effects”, i.e. “space contraction”, “time dilation”, etc..
Really from yet the (i) and (ii) postulates any number of really senseless consequences completely directly, rigorously, and unambiguously follow, the simplest one is the Dingle objection to the SR;
- from this, by completely rigorous proof by contradiction completely directly, rigorously, and unambiguously it follows , first of all, that
- Matter’s spacetime is absolute, that so some “absolute” frames that are at rest in the absolute 3DXYZ space can exist, while applications, i.e. measurements of distances and time intervals, of moving in the space inertial frames aren’t completely adequate to the objective reality; and
- there exist no the “relativistic properties and effects”.
Etc. However really the SR first of all is based on the indeed extremely mighty Galileo- Poincaré relativity principle.
That is another thing that
- according to SR-1905 relativity principle there is some extremely potent entity “light”, the constancy of which for/by some mystic reasons/ways forces moving bodies to contract and moving clocks to slow down tick rates; and
- the SR 1908 relativity principle is practically omnipotent, so the moving frames, bodies, clocks for/by some mystic reasons/ways really contract/dilate even evidently fundamental space and time.
All that above in the SR really is/are only postulated illusions of the authors, nonetheless, again, the Galileo- Poincaré relativity principle is really . extremely mighty, and the SR indeed in most cases at everyday physical practice is applied in completely accordance with the objective reality. The fundamental flaws of the SR reveal themselves only on fundamental level.
The post is rather long now, so here
Cheers
Sergey Shevchenko added a reply
So let’s continue about what is “special relativity”
In the SS post above it is pointed that Matter’s spacetime is fundamentally absolute, however to say more it is necessary to clarify - what are “space” and “time”, just because of the authors of the SR – and whole mainstream physics till now - fundamentally didn’t/don/t understand what these fundamental phenomena/notions are, the really mystic and simply fundamentally wrong things in the SR were/are introduced in this theory.
What are these phenomena/notions, and what are all other really fundamental phenomena/notions, first of all in this case “Space”, “Time”, “Energy”, “Information”,
- and “Matter”– and so everything in Matter, i.e. “particles”, “fundamental Nature forces” – and so “fields”, etc., which is/are fundamentally completely transcendent/uncertain/irrational in the mainstream philosophy and sciences, including physics,
- can be, and is, clarified only in framework of the Shevchenko-Tokarevsky’s philosophical 2007 “The Information as Absolute” conception, and more concretely in physics in the SS&VT Planck scale informational physical model, in this case it is enough to read
More see the link above, here now only note, that, as that is rigorously scientifically rationally shown in the model, Matter absolutely for sure is some informational system of informational patterns/systems – particles, fields, stars, etc., which, as that is shown in the model, is based on a simple binary reversible logics.
So everything that exists and happens in Matter is/are some disturbances in the Matter’s ultimate base – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which [lattice] is placed in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct); FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP.
The disturbances are created in the lattice after some the lattice FLE is impacted, with transmission to it, by some non-zero at least 4D space, momentum P[boldmeans 4D vector] in utmost universal Matter’s space with metrics (cτ,X,Y,Z). The impact causes in the lattice sequential FLE-by-FLE flipping, which, since the flipping cannot propagate in the lattice with 4D speed more than the flipping speed c=lP/tP [really at particles creation and motion c√2, more see the link, but that isn’t essential here].
Some FLE flipping above along a direct 4D line can be caused by a practically infinitesimal P impact; but if P isn’t infinitesimal, that causes flipping FLE precession and corresponding propagation of the “FLE-flipping point” in the 4D space above along some 4D helix,
- i.e. causes creation of some close-loop algorithm that cyclically runs on FLE “hardware ” with the helix’s frequency ω, having momentum P=mc above, mis inertial mass, the helix radius is λ=λ/P;
- and the helix’s 4D “ axis” is always directed along P – particles are some “4D gyroscopes”.
The post is rather long already, so now
Sergey Shevchenko added a reply
So let’s continue about what is “special relativity”.
In the SS posts above it is pointed that everything that exists and happens in Matter is/are some disturbances in the Matter’s ultimate base – the (at least) [4+4+1]4D dense lattice of FLEs, which [lattice] is placed in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, spacetime,
- and that happens always in utmost universal “kinematical” Matter’s space with metrics (cτ,X,Y,Z), and corresponding spacetime with metrics (cτ,X,Y,Z ct), where ct is the real time dimension.
At that particles, most of which compose real bodies, at every time moment exist as “FLE –flipping point” that move along some4D helixes that have frequencies ω, having 4D momentums P=mc, m are inertial masses, a helix radius is λ=λ/P;
- and the helix’s 4D “ axis” is always directed along P – particles are some “4D gyroscopes”.
So in Matter there exist two main types of particles – “T-particles”, which are created by momentums that are directed along the cτ-axis [more generally – by 4D momentums cτ-components, but here that isn’t too essential], and so, if are at rest in the 3DXYZ space, move only along cτ-axis with the speed of light, and at that a T- particle’s algorithm ticks with maximal “own frequency”, the particle’s momentum is P0=m0c, where, correspondingly, m0 is the “rest mass”.
If a such T-particle, after some 3D space impact with a 3D space momentum p, moves also in 3D space with a velocity V, having 4D momentum P=P0+p, its speed along the cτ-axis decreases by the Pythagoras theorem in (1-V2/c2)1/2 , i.e. in reverse Lorentz factor,
- and, at that, despite that the helix’s frequency increases, the algorithm is “diluted by “blank” 3D space FLEs flips. So the “own frequency above” decreases in Lorentz factor, so the algorithm ticks slower; and so, say, moving clocks that are some algorithms as well, tick slower in Lorentz factor as well; if a particle algorithm has some defect, and so at every its tick it can break with some probability, so the particle is unstable and decay, such moving in 3D space particles live longer.
Nothing, of course, happens with time, there is no any the SR’s “time dilation”.
The post is rather long already, so now
Roggers Waibi added a reply
As proposed by Albert Einstein, Special relativity fundamentally transforms our understanding of space, time, and the nature of reality. At its core, special relativity postulates two key principles: the constancy of the speed of light and the relativity of simultaneity. The former states that the speed of light in a vacuum is the same for all observers, regardless of their relative motion. This principle defies common intuition but has been rigorously confirmed by experiments. The latter principle, the relativity of simultaneity, suggests that events that appear simultaneous to one observer may not be simultaneous to another observer in relative motion. Special relativity introduces the concept of spacetime, wherein space and time are intertwined, and observers in relative motion will experience time dilation and length contraction effects. These phenomena have been validated through numerous experiments, such as the famous Michelson-Morley experiment and subsequent tests involving particle accelerators and high-speed particles. Special relativity forms the basis for modern physics, influencing fields ranging from particle physics to cosmology, and challenging our intuitive notions of space and time.
Christian Baumgarten added a reply
Article The Simplest Form of the Lorentz Transformations
Waibi's answer is correct. However, the postulates of SR do not generate understanding. The referenced paper provides evidence that the math underlying SR can mostly be obtained from Hamiltonian notions. Since Hamiltonian concepts are universal in dynamical systems, the mathematical relations of SR are universal as well.
Sergey Shevchenko added a reply
Rather detailed consideration of what the SR is see in series of SS posts in this thread sister https://www.researchgate.net/post/How_do_we_understand_special_relativity/2, pages 1,2;
So here only a few notes to
“…Special relativity introduces the concept of spacetime, wherein space and time are intertwined, and observers in relative motion will experience time dilation and length contraction effects. ..”
- really the concept of spacetime, wherein space and time are intertwined is fundamentally wrong.
Matter’s spacetime is fundamentally unique, fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, ( [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct), where all dimensions fundamentally are independent on each other; utmost universal – “kinematic” spacetime has metrics (cτ,X,Y,Z,ct),
- and, of course, fundamentally there cannot be any intertwining of any dimensions, any “time dilations”, “space contraction”, etc.
So that
“….These phenomena have been validated through numerous experiments, such as the famous Michelson-Morley experiment and subsequent tests involving particle accelerators and high-speed particles… “
- really is quite incorrect. No any “intertwining” , “time dilations”, “space contraction” weren’t experimentally observed – that is fundamentally impossible. All what indeed is observed is/are real contraction of moving bodies lengths, slowing tick rates of moving clocks and intrinsic processes rates in unstable particles,
- but bodies aren’t “space” – though, of course are in space; clocks aren’t “time” though, of course tick in time, which [space and time] compose fundamentally only an empty container where everything in Matter exists and changes.
Though that
“….Special relativity forms the basis for modern physics, influencing fields ranging from particle physics to cosmology, and challenging our intuitive notions of space and time…”
- is essentially correct, since the SR is based on the indeed extremely mighty Galileo-Poincaré relativity principle; and so in everyday physical practice the fact that in the SR the relativity principle is absolutized up to absurd/illusory real interactions of particles, bodies, reference frames, etc., with space/time/spacetime is inessential. Again more see the pointed above SS posts in the linked sister thread.
【NO.18】How the View of Space-Time is Unified (4) - Is Space-Time Expansion a Space-Time Creation?
If it is true that space-time is expanding, how does the measure of space-time change?
The shape of space-time is the shape of the universe; how can expansion without a boundary be called expansion? If the boundary of spacetime is the boundary of the universe, can spacetime expansion with a boundary have no background? How is the boundary maintained? If the boundary of spacetime is infinite, how does it expand?
We will use these paired terms to describe spacetime: infinite/finite, absolute/relative*, flat/curved, continuous/discrete, four-dimensional†/higher-dimensional, and so on. Normally we think of these properties as opposites ‡ and only one or the other can be chosen. But the full range of properties of spacetime will be combinations between these different properties. For example, spacetime has infinite, absolute, continuous, flat, four-dimensional properties, or spacetime has finite, discrete properties, etc. In any case, none of us thinks that there is a concept of "multiple spacetimes", or that spacetime should have its own background, or that spacetime can overlap, although physics suggests that there may be local "warps" in spacetime.
Astronomical observations show that the universe is in a process of accelerated expansion [1][2][3], with all stars moving away at an accelerated rate and possibly never returning. Physics attributes the expansion of space-time to the presence of dark energy with negative pressure [4]. Dark energy has been hypothesized in various ways (including non-existence), one of which is the cosmological constant Λ in Einstein's field equations (the zero-point radiation of space [5], the energy of the vacuum, the zero-point energy [6]).
Physics has not exactly explained the exact relationship between spacetime and the various fields assumed by the Standard Model [7], but only assumes the existence of vacuum energy [8][6], and is not sure which field's vacuum energy it is, whether it is the electromagnetic field, the electron field, the muon field, or the up-quark field, the charm-quark field, the Higgs field [9], or just the sum of their respective vacuum energies. So when it is assumed that space-time is expanding, and vacuum energy is expanding, are they created in it, or are they diffused across the boundary? Are they the driving force or the result? How do they manifest within microscopic particles when expanding at high speeds on the macroscopic scale?
Physics does not explain the origin of the dynamics of the Big Bang, nor does it explain when and how all the various fields in the Standard Model were formed, how they were formed, how they were maintained in existence, and how they evolved along with, or determined, the evolution of the Universe throughout the entire evolution of the Universe from the Big Bang onward. It is not clear how the various particles were excited initially from their own fields, but the explanation of nucleosynthesis [10] to the current period is relatively clear.
Usually we think of the universe as a set of space-time and matter-energy. There are many different models of the universe, and in addition to the Standard Model, there are many cyclic universes and multiverse views [11][15]. Then, when we haven't confirmed the model of the universe, there is no confirmed goal of the evolution of the universe, and there is no confirmed shape and boundary of the universe.
Both Einstein and Hawking say that the universe is "finite and unbounded" [12]. They believe that the universe is a finite three-dimensional sphere with a finite volume but no boundary. Topological theory says, "The boundary of a region has no boundary itself. "** [13]. Wheeler's statement is, "The boundary of a boundary is zero" [14]. What is the result of the infinite extension of the three orthogonal coordinate axes for a finite three-dimensional spherical universe?
Mathematically, there are four combinations between measures and boundaries: finite bounded, infinite unbounded, finite unbounded, and infinite bounded. The first two concepts are clear, but the latter two need to be recognized carefully when translated to physics. The "singularity" is a typical example of an "infinite bounded". Usually in physics, when time or space shrinks to zero, the corresponding physical quantity tends to infinity. For example, E=hν, when ν→0; F=q1*q2/r^2, when r→0. However, we believe that this is only a trend and that there can be no state that reaches a singularity. Therefore, "infinitely bounded" is not real. The Koch Curve, often thought of as a fractal geometry expressing "finite unbounded", is one of the nth iterations of the Koch snowflake that can be implemented in the Wolfram Language as KochCurve[n]¶. The difference between physical reality and mathematics can be shown here, as n cannot be chosen to be infinite, so the Koch Curve will always be in a definite state in reality, and although it can evolve, "finite and unbounded" is a tendency, not a state. The formulation of the Mobius strip††, the irrational numbers, is another way of saying "finite unbounded". In physics, a typical example of "finite unbounded" is the electron. The electron has a fixed charge e, but the boundary of the electric field E of the charge extends infinitely (the field strength is convergent). Of course, the concept of zero-dimensional "point particles" is also a kind of abstract "finite unbounded". In short, in physical terms, finite must have boundaries.
General relativity is the basis for modeling the universe, but is there any good reason why we should be able to determine the evolutionary goals of the universe, its shape, and its boundaries through general relativity alone? Shouldn't such boundaries be "boundary conditions" of GR?
There should not be any boundary conditions, which are the conditions necessary for the model of the universe to hold correctly.
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Notes
‡ As long as we do not have a precise definition of spacetime, viewing these properties as opposites can only be taken for granted. As with the wave-particle duality of particles, which property is presented depends on the observer's perspective; the structure of the particle itself does not change. Further characterizations of spacetime include whether it is inherently existent or generative, whether the vacuum contains energy, and so on.
¶ https:// mathworld.wolfram.com/KochSnowflake.html; Stephen Wolfram, Founder of Wolfram Language, is very interested in the question of the evolution of the universe, and is the author of the book "a new kind of science", which has been trying to find out how the universe evolves using metacellular automata.
** e.g. the two-dimensional region has as its boundary a one-dimensional loop; the loop has no end, that is, it has no boundary itself.
†† The Möbius strip is bounded as long as one does not confuse metrics with boundaries.
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References
[1] Linder, E.V., Exploring the expansion history of the universe. Physical Review Letters, 2003. 90(9): p. 091301.
[2] Riess, A.G., The expansion of the Universe is faster than expected. Nature Reviews Physics, 2020. 2(1): p. 10-12.
[3] Freedman, W.L., The Hubble constant and the expansion age of the Universe. Physics Reports, 2000. 333: p. 13-31.
[4] "Dark Energy Survey, Collaboration." from https://www.darkenergysurvey.org/the-des-project/overview/.
[5] Oks, E. (2021). "Brief review of recent advances in understanding dark matter and dark energy." New Astronomy Reviews 93: 101632.
[6] Carroll, S. M., W. H. Press and E. L. Turner (1992). "The cosmological constant." Annual review of astronomy and astrophysics 30: 499-542.
[7] Group, P. D., P. Zyla, R. Barnett, J. Beringer, O. Dahl, D. Dwyer, D. Groom, C.-J. Lin, K. Lugovsky and E. Pianori (2020). "Review of particle physics." Progress of Theoretical and Experimental Physics 2020(8): 083C001.
[8] Jaffe, R. L. (2005). "Casimir effect and the quantum vacuum." Physical Review D 72(2): 021301.
[9] Springer (2020). 100 Years of Fundamental Theoretical Physics in the Palm of Your Hand: Integrated Technical Treatment.
[10] Cyburt, R. H., B. D. Fields, K. A. Olive and T.-H. Yeh (2016). "Big bang nucleosynthesis: Present status." Reviews of Modern Physics 88(1): 015004.
[11] Carr, B. and G. Ellis (2008). "Universe or multiverse?" Astronomy & Geophysics 49(2): 2.29-22.33.
[12] Hawking, S. W. and M. Jackson (2001). A brief history of time, Bantam Books New York.
[13] Yang, C. N. (1980). "Einstein's impact on theoretical physics." Physics Today 33(6): 42-49.
[14] Misner, C. W., K. S. Thorne and J. A. Wheeler (2017). GRAVITATION, Princoten University Press.
【NO.43】Doubts about General Relativity (8) - How is Energy-Momentum of Gravitational Field Expressed? How is It Transferred? How is It Exchanged?
Free spacetime contains no energy-momentum*, so when objects m are travelling at constant velocity in it, they do not exchange energy-momentum. Non-free spacetime contains energy-momentum. The Einstein field equation of general relativity,
Rµν - (1/2)gµνR = G*Tµν,
expresses the relationship between the energy-momentum (mass) and the structure of spacetime ( metric) at a point (region) in spacetime**. Usually we think that "Gravity couples universally to all forms of energy" [1]. Then, we need to ask three basic questions:
1) What is the best way to express the energy-momentum of the gravitational field? or how are the "long-standing problems about energy-momentum localisation in GR" [2][3][4] addressed? The energy-momentum of the gravitational field is the energy-momentum of the spacetime field, which must be localizable. The energy-momentum of the spacetime field must involve only the spacetime parameter xi(i=0,1,2,3), because the independent spacetime field has no other parameter (or it has some other hidden parameter that does not play an explicit role). But it cannot be expressed directly in terms of spatio-temporal coordinates (t,x,y,z) because they must be background independent, nor can it be expressed in terms of time lengths T and space lengths L because we have no way of determining the measurement boundaries. So what are the remaining covariates? The rates of measure change, curvature, and deflection, etc.. which are the most appropriate? Even if we consider space-time as a "medium", what are the properties of the medium? Density, elasticity? What density? What elasticity?
2) By what means are gravitational fields and other forms of energy-momentum exchanged with each other? Obviously it must be through a common covariate, and then the only option available is the spacetime covariate. Does this qualify that all other forms of energy-momentum must contain spacetime covariates? Includes energy-momentum of dark matter (no dark energy involved). And more critically, the form of these spacetime Attributes and the form in which the spacetime energy-momentum is expressed should be the same, i.e., if the energy-momentum of spacetime is expressed in terms of a change of metric, the other forms of energy-momentum must be related to a change in the spacetime metric; and if it is expressed in terms of a curvature, the other forms must be related to a change in the curvature.
3) Is the energy-momentum of the gravitational field conserved[5]? If the energy-momentum of the gravitational field is not conserved, what will become of the gravitation dominated evolution of galaxies?
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Notes
* We need to distinguish between the concepts of space-time and vacuum.“Are Vacuum and Space Two Separate Things?”，https://www.researchgate.net/post/NO34How_the_View_of_Space-Time_is_Unified_6-Are_Vacuum_and_Space_Two_Separate_Things；
** The concept of a strict "point" interaction does not really exist in physics.
-------------------------------------------
References
[1] Kiefer, C. (2006). Quantum gravity: general introduction and recent developments. Annalen der Physik, 518(1-2), 129-148.
[2] Einstein Ann. d. Phys. 49, 769 (1916).
[3] Hestenes, D. (2021). Energy-Momentum Complex in General Relativity and Gauge Theory. Advances in Applied Clifford Algebras, 31(3), 51.
[4] Møller, C. (1958). On the localization of the energy of a physical system in the general theory of relativity. Annals of Physics, 4(4), 347-371.
[5] Szabados, L. B. (2009). Quasi-local energy-momentum and angular momentum in general relativity. Living Reviews in Relativity, 12(1), 1-163.
【NO.39】Doubts about General Relativity (4) - Who should determine the spacetime metrics of matter itself?
General Relativity field equations [1]:
Gµν = G*Tµν...... (EQ.1).
It is a relation between the matter field (energy-momentum field) Tµν and the spacetime field Gµν, where the gravitational constant G is the conversion factor between the dimensions [2].Einstein constructed this relation without explaining why the spacetime field and the matter field are in such a way, but rather assumed that nine times out of ten, they would be in such a way. He also did not explain why the spacetime field Gµν is described by curvature and not by some other parameter. Obviously, we must find the exact physical relationship between them, i.e., why Tµν must correspond to Gµν, in order to ensure that the field equations are ultimately correct.
We know that matter cannot be a point particle, it must have a scale, and matter cannot be a solid particle, it must be some kind of field. The fact that matter has a scale means that it has to occupy space-time; the fact that matter is a field means that it is mixed with space-time, i.e., matter contains space-time. So, when applying Einstein's field equations, how is matter's own spacetime defined? Does it change its own spacetime? If its own energy-momentum and structure have already determined its own spacetime, should the way it determines its own spacetime be the same as the way it determines the external spacetime? If it is the same, does it mean that the spacetime field is actually a concomitant of the matter field?
If one were to consider a gravitational wave, one could think of it as a fluctuating spacetime field that propagates independently of the material source after it has been disconnected from it. They have decoupled from each other and no longer continue to conform to the field equations (EQ.1). Although gravitational waves are the product of a source, the loss of that source prevents us from finding another specific source for it to match it through the equation (EQ.1). Just as after an electron accelerates, the relationship between the radiated electromagnetic wave and the electron is no longer maintained. Does this indicate the independence of spacetime field energies?
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Related questions
♛ “Does the Energy Tensor Tµν in the Field Equations Contain the Energy-momentum of the Spacetime Field?”：https://www.researchgate.net/post/NO37Doubts_about_General_Relativity_2-Does_the_Energy_Tensor_Tmn_in_the_Field_Equations_Contain_the_Energy-momentum_of_the_Spacetime_Field
♛ “Is the Geometry Interpretation of Gravity a Paradox?”：https://www.researchgate.net/post/NO36_Doubts_about_General_Relativity_1-Is_the_Geometry_Interpretation_of_Gravity_a_Paradox
-----------------------------
References
[1] Grøn, Ø., & Hervik, S. (2007). Einstein's Field Equations. In Einstein's General Theory of Relativity: With Modern Applications in Cosmology (pp. 179-194). Springer New York. https://doi.org/10.1007/978-0-387-69200-5_8
[2] “The Relationship Between the Theory of Everything and the Constants of Nature”：https://www.researchgate.net/publication/377566579_The_Relationship_Between_the_Theory_of_Everything_and_the_Constants_of_Nature_English_Version
【NO.45】 What is Mass? Must the Hierarchy of Mass be Determined Simultaneously by the Origin of Mass?
The concept of mass explained by the Higgs mechanism is able to include all concepts of mass, inertial mass, gravitational mass, mechanical mass, electromagnetic mass [1], kinematic mass, static mass, longitudinal mass, transverse mass [2], bare mass ...... ? Is it the Higgs field that leads to the mass-energy equation? How are coupling relationships established? Do the Couplings Transfer Energy-Momentum?
Although there are many different sub-concepts of mass, a distinguishing feature is that the mass of an object is not reflected, recognisable, or measurable when it is not interacting. We can think of all mass as a property of resistance that only presents itself when an object's state of motion changes§. The so-called "rest mass" can only be regarded as a representation of the amount of static energy, and not vice versa.
Thus, it is clear that masses are essentially the same, differing only in size and form*. This also implies that no matter how many differences there are in the occasions of interaction, as long as the required dimension is the same, they are the same mass. In this way, the Equivalence Principle in GR need not be regarded as a specific condition.
However, mass is not constant, and the magnitude of an object's mass in SR changes according to the Lorentz transformation. This predicts that the mass of an object is related to the increase or decrease in the energy of the object and is bounded by the speed of light.
Higgs physics suggests [3] that the mass of bosons is given by the Higgs mechanism [4]; that the mass of fermions is also given by the Higgs field [10], although this is still an open question [5]; and that Higgs particles themselves give their own mass [3], although this is not a clear-cut conclusion either [6].The Higgs field is a scalar field that pervades space, and is the same as the other elementary particle fields, electron fields, quark fields, etc., co-existing in the vacuum**. They all appear to have the same status, except for the Higgs mechanism.
However, the current Higgs mechanism has some obvious explanation missing.
1) Why does the Higgs field selectively couple to bosons? I.e., how does the Higgs field recognise the bosons W±, Z and γ, g, all of which have energy and perform the same function, and to which the Higgs field selectively assigns mass, or not.
2) The magnitude of the coupling coefficient of the Higgs field determines the mass size of the fermions [10]. Then, the mass hierarchy of the three generations of fermions is determined by the Higgs field¶.Why should the particles all have different couplings coefficients gj to the Higgs field? and where do these values come from[7][8]? Before there is mass, fermions have exactly the same quantum number and they are indistinguishable [9]†. How does the Higgs field recognise these particles? The obvious requirement is that they must have additional parameters, or other physical quantities that do not present . At the same time, The action of the Higgs field on the positive and negative particles (e+,e-; q+,q-; ) is identical. And how does it ignore this difference?
3) If the Higgs field is not coupled to fermions, can fermions really travel at the speed of light like photons without stopping? According to the mass-energy equation E=mc2, are all particles energy before there is mass（or none）? So the coupling of the Higgs field is to energy, do they have to exchange energy between them? What is the energy transfer relation here, E=mc2? If m=0 now, is E fully converted to the raw energy of the particle?
4) If the significance of the existence of inertial mass for fermions, W± can be explained, what is the significance of the Higgs Boson possessing inertial mass itself?Does it really implies the existence of a 'fifth force', mediated by the exchange of Higgs bosons [8]?
5) The shape of the Higgs potential V(Ø) expresses the relationship between the potential and the field strength , V(Ø) ~ Ø [10] ‡ . Ø is hidden in the vacuum ††. How do different Ø present themselves at a given spatial location? Do they interact with other particles in one way?
6) How does the mathematical explanation of the Higgs mechanism map reasonably to physical reality? Must the Higgs potential be an external field? ‡‡ Wouldn't it be better if it were the field of the particle itself? [12] Is the Higgs mechanism for mass completely excludes the relation between mass and spin ?[15]
7) Not all mass is caused by Higgs [10], and potential energy (binding energy) gives mass as well. In this case, is mass still consistent? Doesn't mass become a variable?
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Supplement: Can mass have multiple origins? （2024.9.26）
“The Higgs does seem to be the source of the mass of elementary particles, e.g., the electron; but it is responsible for < 2% of the mass of more complex things, like the proton. The mass of the vast bulk of visible material in the Universe has a different source.”[1] “the Higgs boson is almost irrelevant to the origin of the proton mass. ”[2]
Mass is an important particle property. If mass has surprisingly multiple origins, how do we explain their relationship? Do they produce the same results by similar mechanisms, or completely different ones? Do they all rely on external fields? Is the mass-energy equation, m=E/c^2, a clue to determining the uniform origin of mass? Can a mechanism that does not provide energy provide mass?
Does mass obey the superposition principle? Is it a scalar superposition or a vector superposition? Is it a linear or nonlinear superposition? Let us consider a process in which u, d quarks combine to form a proton p. In the early stages of the evolution of the universe, nothing else in particular existed. u and d automatically combine to form p in such a scenario, like a pair of lovers meeting to form a family. The family is a more stable structure, and the ‘quality’ of life of the family (In Chinese, quality and mass are one word, 质量) has increased. The increased ‘quality’ does not come from outside, but from the union itself.
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Notes
§ Mass is usually thought of as resisting a change in the "state" of matter, but what is the "state"? Why does it resist change? Why can it resist change? My personal reference answer is here [12]: Mass originates from damping the superluminal intent of a spinning light ring and as a result is the fundamental property that distinguishes fermions from bosons.
* Mass is somewhat similar to energy in that it exists in various forms, but the two are fundamentally different.
** Physics doesn't know what parameters to use to describe these fields and doesn't seem to be interested.
‡ “One of the most important open questions in Higgs physics is whether the potential written in that equation is the one chosen by nature. ”[8]
‡‡ "Central to all of Higgs physics is the Higgs potential."[8] C. N. Yang[13]: "Symmetry breaking with the introduction of a field will not be the last theory, although for the time being it is a good theory, like Fermi's theory of beta decay." Expresses his scepticism about the Higgs mechanism.
† With no Higgs field, the electron and electron neutrino would be identical particles, and the W and Z particles, and in fact all standard model fermions, would be massless. [9]
†† The vacuum seems to be the all-powerful vacuum, and physics assigns many functions to the vacuum [14].
¶ The hierarchies among fermion masses and mixing angles, however, remain unexplained.[11]
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References
[1] Thomson, J. J. (1881). XXXIII. On the electric and magnetic effects produced by the motion of electrified bodies. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 11(68), 229-249.
[2] Abraham, M. (1902). Principles of the Dynamics of the Electron (Translated by D. H. Delphenich). Physikalische Zeitschrift 4(1b), 57-62.
[3] Ellis, J. (2013). Higgs physics. arXiv preprint arXiv:1312.5672.
[4] Higgs, P. W. (1964). Broken Symmetries and the Masses of Gauge Bosons. Physical Review Letters, 13(16), 508-509. https://doi.org/10.1103/PhysRevLett.13.508
[5] Ghosh, D., Gupta, R. S., & Perez, G. (2016). Is the Higgs mechanism of fermion mass generation a fact? A Yukawa-less first-two-generation model. Physics Letters B, 755, 504-508.
[6] Consoli, M., & Cosmai, L. (2020). The mass scales of the Higgs field. International Journal of Modern Physics A, 35(20), 2050103.
[7] Melia, F. (2021). The origin of rest-mass energy. The European Physical Journal C, 81(8), 707. https://doi.org/10.1140/epjc/s10052-021-09506-w
[8] Salam, G. P., Wang, L.-T., & Zanderighi, G. (2022). The Higgs boson turns ten. Nature, 607(7917), 41-47. https://doi.org/10.1038/s41586-022-04899-4
[9] Lancaster, T., & Blundell, S. J. (2014). Quantum field theory for the gifted amateur. OUP Oxford.
[10] Schmitz, W. (2019). Particles, Fields and Forces. Springer.
[11] Bauer, M., Carena, M., & Gemmler, K. (2016). Creating the fermion mass hierarchies with multiple Higgs bosons. Physical Review D, 94(11), 115030.
[12]
Preprint Supersymmetric Standard Model (SSM)
[13] C.N.Yang. (2014). 六十八年心路（1945-2012）. 三联书店.
[15] C. N. Yang emphasised: in the context of gauge theory, the conjecture of why we need a theory of gravity with spin electrons. Today I remain believing that this is a key to the future conquest of quantum general relativity.
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【NO.21】 Symmetry, Invariance and Conservation (2)-Can Noether's theorem be extended naturally if spacetime is not curved but inhomogeneous?
Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries[1].
In SR, force-free motion in an inertial frame of reference takes place along a straight-line path with constant velocity. Viewed from a non-inertial frame, on the other hand, this path of motion will be a geodesic curve in a flat spacetime. Einstein made the plausible assumption that this geodesic motion also holds in the non-flat case, i.e. in a spacetime region for which it is impossible to find a coordinate system that leads to the Minkowski metric in SR[2].
All spacetime models can be expressed in terms of the gμν = {4x4} matrix, differing only in the distribution of matrix elements. The gμν of Minkowski spacetime is the unit diagonal matrix {1 -1 -1 -1}; the gμν of Riemann spacetime is { X }. If a new spacetime model is introduced gμν={a0,-a1,-a2,-a3}, which is a non-unit diagonal matrix. (ds)^2=(a0)^2+(a1)^2+(a2)^2+(a3)^2, always holds, interpreting it as a non-uniformly flat spacetime, generalised Minkowski spacetime, and no longer a curved spacetime. Should Noether's theorem maintain its validity in this case.
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References
[1] Marvian, I., & Spekkens, R. W. (2014). Extending Noether's theorem by quantifying the asymmetry of quantum states. Nature Communications, 5(1), 3821. https://doi.org/10.1038/ncomms4821 ;
[2] Rowe, D. E. (2019). Emmy Noether on energy conservation in general relativity. arXiv preprint arXiv:1912.03269.
【NO.52】Unification Issues (1) - Should discreteness and conservation in physics have a common origin?
Physics states that ‘symmetry dictates interaction’ [1][2]; Invariance, symmetry, and conservation are usually approximately the same concepts [3], and the objects of conservation are usually discrete. The basic conservation of energy corresponds to the energy quantum e = hν, the basic conservation of momentum to the momentum quantum P =h/λ, the conservation of charge to the integer charge e, the conservation of the spin number to ℏ/2, the conservation of the particle number to the lepton number, the baryon number [4], and so on.
1) Does Noether's theorem impose a limit on the continuity of energy and momentum [5]?
2) If we regard these discretisations as representing different energy forms, do the symmetries likewise convert when the energy forms convert?
3) Assuming that an abstract energy remains constant in all cases, should there likewise be any symmetries that remain constant all the time to support symmetry evolution?
4) Should these different discretisations have a common origin? If so, how are the relationships between them constructed? Or through what channels are they related?
5) Particle number conservation are all additive and empirical postulates [4], should there be theoretical support behind them?
6) Symmetries are classified into external and internal symmetries [6]; external symmetries are concerned with spacetime coordinate transformations and internal symmetries are concerned with gauge invariance. If they are united, how are inner space symmetries related to external space symmetries?
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References：
[1] Yang, C. N. (1996). Symmetry and physics. Proceedings of the American Philosophical Society, 140(3), 267-288.
[2] Gross, D. J. (1992). Gauge theory-past, present, and future? Chinese Journal of Physics, 30(7), 955-972.
[3] “Symmetry, Invariance and Conservation (1) - Who is the Primary?”；https://www.researchgate.net/post/NO20Symmetry_Invariance_and_Conservation_1-Who_is_the_Primary
[4] Krieger, P. (2006). Conservation Laws - PHY357_Lecture6. https://www.physics.utoronto.ca/~krieger/PHY357_Lecture6.pdf
[5] Kosmann-Schwarzbach, Y. (2011). The Noether Theorems. In Y. Kosmann-Schwarzbach & B. E. Schwarzbach (Eds.), The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century (pp. 55-64). Springer New York. https://doi.org/10.1007/978-0-387-87868-3_3
[6] Wess, J. (2000). From symmetry to supersymmetry. In The supersymmetric world: the beginnings of the theory (pp. 67-86). World Scientific. https://www.changhai.org/articles/translation/physics/sym_and_supersym3.php （中文版）
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