Such a question arises because of three problems
(1) We cannot present geometry in the coordinate free form, although Euclid presented geometry in the coordinate free form, because coordinate system was not known in that time.
(2) Such important physical principle as the relativity principle is formulated as an invariance with respect of a coordinate transformation. Invariance with respect to transformation of the way of description cannot be a physical principle.
(3) One cannot express dimension of Euclidean geometry via Euclidean metric, although all relations of Euclidean geometry can be expressed via metric and only via metric (or via Euclidean world function).
Dear Yuri. You are right. "It cannot be a physical principle". It isn't.
The very serious question about Einstein relativity is that yes, physics uses mathematics and geometry, but physics can't exclusively be geometry. His spacetime is pure mathematics, a geometrical entity. How can we say that space is curved without knowing what space actually is (physically speaking) ? We can't. What is curved? Something which is only a bunch of coordinates?!
The problem is that General Relativity is not a quantum theory, it doesn't describe space from an actual physical point of view... the metric tensor (the father of all tensors in GR) is only a geometrical tool.
On the other hand we know that a real vacuum doesn't exist. We speak of quantum vacuum, vacuum energy, quantum foam and so on... this is the right way: changing our concept of space (let the spacetime be... time is only a consequence of motion. Not a physical entity).
Only in that moment we will rebuild a better theory of relativity which will be less geometrical and more physical. I am sure that the right approach is the fluid dynamic one, starting from a superfluid quantum space, since it is able to reproduce all relativistic effects, also without a curved space (flows of space's quanta are enough). Have a look at my work if you want, I'm going to upgrade it soon with important refinements.
Dear Christian,
Your statement about principle of relativity is the same as I have write in my question. Let me formulate the relativity principle in the “right” physical geometry. Physical geometry G is obtained as a deformation of Euclidean geometry GE. All statements of GE are expressed via world function \sigmaE of GE. Thereafter in all these statements \sigmaE is substituted by world function \sigma of G. As a result one obtains all statements of physical geometry G. Thus, Euclidean geometry GE is described by only space-time structure \sigmaE. Physical geometry G is described also by the only space-time structure \sigma. One can introduce in GE and in G a second structure S. As a result one obtained a fortified geometry. Space-time geometry in nonrelativistic physics is a fortified geometry, because it connects additional structure, describing absolute space distance. The relativity principle states, that the space-time geometry contains only one space-time structure (it is not described by a fortified geometry). This statement does not contain any reference to coordinate system. It may be reated as a physical pinciple.
Your remark about connection between invariance with respect to rotation and the angular momentum conservation is a mathematical relation, which is not a physical principle.
Article Relativity principle in coordinateless presentation
Dear Charles,
You are not right. Invariance with respect to coordinate transformations does not mean coordinate free form of description. If so, then present geometry without reference to coordinates. You cannot. It means, that coordinates bear some part of information on geometry.
As to vector space Ln. Vectors u, which are elements of the vector space Ln are not equivalent to geometrical vectors AB, which are defined as an ordered set of two points {A,B}. Linear vectors u , which are lements of the vector space Ln, may be identified with geometrical vectors AB only if geometrical vectors AB form classes of equivalence. It means that geometry is a logical construction, and equivalence relation is transitive. But from physical point of view the space-time geometries with intransitive equivalence relation have the most interest. Only in such space-time geometries motion of free particle may be stochastic.
Most of contemporary mathematicians accept only those geometries which are logical constructions. These geometries form only small part of possible space-time geometries. Such an approach is inadequate from viewpoint of physics.
Article Geometries with intransitive equivalence relation
Article Metrical Conception of the Space-Time Geometry
Dear Yuri,
Really, we don’t know space-time geometry. We don’t know any experiment that could unambiguously say about geometry of the space-time, because the space-time physically not exists; it is only our vision, it is an attempt to include physical interactions into 4-dimensional geometric model. And we may give the properties (that we see fit) into any of our submission..
1. Euclid spoke about three-dimensional space in which there is motion of objects. Time (as a parameter of motion) was not added to the space by Euclid.
2. The principle of relativity is wrong because there are experiments, the results of which are inconsistent with this principle. So it is not physical one.
3. The dimension of the Euclidean metric equals to 3. It is unambiguously set in Euclidean metric and so this dimension is followed from it.
Sincerely,
Alexander Chepick
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Уважаемый Юрий !
Действительно, мы не знаем о пространственно-временной геометрии. Мы не знаем ни одного эксперимента, который однозначно мог бы сказать о пространственно-временной геометрии, потому что пространство-время физически не существует, это только наше представление, это попытка вложить физические взаимодействия в 4-мерную геометрическую модель. А любому нашему представлению мы вправе придать те свойства, которые мы посчитаем нужными.
1. Евклид говорил о трехмерном пространстве, в котором существует движение объектов. Время (как параметр движения), Евклидом не связывалось с пространством.
2. Принцип относительности неверен, так как существуют эксперименты, результаты которых противоречат этому принципу. Поэтому он не физический.
3. Размерность Евклидовой метрики равна 3. Это однозначно задано в ней, и поэтому следует из нее.
С уважением,
Александр Чепик
Noether's theorem states that invariance to any transformation can be associated with a low of conservation. It is therefore difficult to understand why for momentum (as already mentioned) or energy conservation, for example, it works but not for space-time. Which parts of the theorem would not apply?
Relativity is a landmark in the enterprise to eliminate absolute concepts from science. The relativity principle imply there is no absolute space and/or time. Is coordinate free form thought in absolute terms? Then no relationship with relativity will be possible and it appears to me this is the position Yuri stands for. If not seen absolutely, like the majority of the commentators, then a connection can be formed.
Dear Charles Francis,
I shall not discuss your answer, where you refer to half-ready article from Wikipedia. I shall consider discrete space-time geometry Gd, which is very close to geometry of Minkowski GM, but it used another mathematical formalism. In particular, Gd does not use linear vector space. You believe that linear vector space Ln can be used in any space-time geometry. Furthermore you are consider Ln as a geometry.
The discrete geometry Gd is defined by the condition
|\rhod(P,Q)| does not belong to (0,\lambda0) for any P,Q which belong to \Omega. (*)
where \rhod is the distance and \Omega is the set of points, where Gd is given. \lambda0 is the minimal length. Usually one consider (*) as a constraint on \Omega. As a result one obtains a geometry on a lattice. It is not a geometry. It is a caricature on a geometry. The condition (*) should be considered as a constraint on the distance \rhod or on the world function \sigmad =0.5\rhod2.
The simplest version of \sigma_d looks as follows
\sigmad=sigmaM+0.5\lambda02sgn(\sigmaM) (**)
where \sigmaM is world function of GM
Of course, , the discrete space-time geometry G_d is uniform and isotrothere is a lot of discrete geometries. As far as \sigmad is a function of \sigmaM Gd is uniform and isotropic as well as GM. Besides, Gd has no definite dimension, and one cannot introduce linear vector space in Gd.
Note that dimension is defined in the Euclidean (and Minkowski) geometry as maximal number of linear independent vectors. n vectors P0P1, P0P2,…P0Pn are linear dependent, iff Gram’s determinant Fn(Pn) = ||(P0Pi.P0Pk)|| vanishes. Here scalar product (AB.PQ) is defined via world function
(AB.PQ) = \sigma(A,Q)+ \sigma(B,P) - \sigma(A,P) - \sigma(B,Q) (***)
In order that in a geometry maximal number of linear independent vectors exist, world function of the geometry must satisfy a set of constraints. These conditions a satisfied for geometry of Minkowski, but they are not satisfied for Gd. As a result in Gd there is no definite dimension. Nevertheless Gd can be constructed, because world function \sigmad is known.
In Gd there is no continuous world lines, and world lines of particles are defined as broken lines consisting of rectilinear links. For free particle vectors PsPs+1 Ps+1Ps+2 of the adjacent links are equal. It means
(PsPs+1. Ps+1Ps+2) = | PsPs+1| | Ps+1Ps+2| ,
| PsPs+1| = | Ps+1Ps+2| (****)
Dynamic equations (****) contain two equations, which have nonunique solution. It means that in Gd world line of a free particle wobbles. Although in the limit \lambda0 tends to 0 these wobbling vanish. After averaging one obtains dynamic equations of the gasdynamical type.
(http://gasdyn-ipm.ipmnet.ru/~rylov/mfpdg1e.pdf ) Quantum equations are of the same type. There is a hope, that changing
\sigmad one successes to obtain dynamic equations in the form of quantum equations.
Article Gas Dynamics as a Tool for Description of Nondeterministic Particles
Dear Valentin Curtef,
The Noether theorem is wrong, because the wrong principle of relativity was used in the the proof of it. Unless some conservation law is fulfilled in one coordinate system, it must be fulfilled in another one. Therefore, the conservation laws do not relate with the coordinate transformation!
Sincerely,
Alexander Chepick
---
Уважаемый Valentin Curtef!
Теорема Нетер неверна, так как в ее доказательстве использован неверный принцип относительности. Если некоторый закон сохранения выполнен в одной системе координат, то он должен быть выполнен и в другой. Поэтому законы сохранения совершенно не связаны с преобразованием координат!
С уважением,
Александр Чепик
Dear Charles,
The difference between our positions lies in the following fact. I consider approach of contemporary mathematicians to the space-time geometry as invalid. They consider, that any geometry is a logical construction. When I present physical geometry Gp which is obtained as a deformation of Euclidean geometry GE, they say that such geometries as Gp do not exist, because they are not a logical construction. The mathematicians do not discuss, why a geometry must be a logical construction. They have learn this in the middle school. Your position is the same. You consider that I do not know differential geometry and that all is OK in the contemporary geometry. At such an approach we really do not have a subject for discussion
Dear Alexander Chepik,
You sated that there are results, which are inconsistent with the relativity principle. What do you mean?
Besides, you stated that the dimension of the Euclidean metric equals to 3. What do you say about dimension on Euclidean plane, for instance on a piece of tin-plate?
Finally, you stated that space-time does not exist physically, because it is only our vision. But any physical theory is only our vision. It is a result of our mentality. Is it a reason for denial of science and physics?
Dear Charles,
First of all, you refuse to see my papers, where my pretensions to contemporary space-time geometry are presented. Instead you accuse me in ignorance. Such an approach is nonconstructive. We shall not understand essence of the problem.
You state that non-Euclidean geometry is obtained as a result of deformation of Euclidean geometry. It is not so. Not any change of Euclidean geometry is its deformation. The term deformation means a change of distances between the points. In order one can deform the Euclidean geometry, it must be presented in terms of function of distance (metric). Then changing the function of distance, one deforms the Euclidean geometry.
As far as I know the Euclidean geometry GE is described usually in terms of linear vectors u, which are elements of linear vector space Ln. Linear vector space Ln can be introduced in GE, but it cannot be introduced in geometries Gp, which obtained from GE be means of a deformation. Mathematicians do not consider this problem. They believe that Ln can be introduced in geometry always. If Ln cannot be introduced in geometry G, it means, G is not a geometry. Lncannot introduced in geometry G, if geometrical vectors AB (defined as a set of ordered set of two points {A,B}) do not forms equivalence classes, that is equivalent to the equivalence relation intransitivity. Please, explain me, why geometry G with intransitive equivalence relation is not a geometry, although it contains all geometric relations, which there are in the Euclidean geometry GE.
Dear Charles,
You may write such things whithout knowing, what I have written. Your post contains no information. It is a waste of time.
Dear Yuri,
“… there are results, which are inconsistent with the relativity principle.”
I mean:
- change of shifts of the bands (with the sidereal period), obtained in the interferometers of Michelson-Morley experiment in medium.
- changing (with the sidereal period) of the propagation time of the signal in the cable in the experiments of DeWitt and Cahill;
a strict proportionality to the distance of the sinusoidal change in time of the phase difference between immobile source and receiver of light in the experiments of Glushko ( http://sciteclibrary.ru/rus/catalog/pages/14819.html ) and etc.
“What do you say about dimension on Euclidean plane, for instance on a piece of tin-plate?”
Are all the physical processes occurring only in the plane, do they? For example, electromagnetic processes are impossible to describe on the plane. And we are not flat! Therefore the theory claiming the description of all physical processes cannot have a space with dimension below 3. On the question of whether the minimum dimension of a metric space to be more 3, the laws of Newton and Coulomb negatively answered.
“Finally, you stated that space-time does not exist physically, because it is only our vision. But any physical theory is only our vision. It is a result of our mentality. Is it a reason for denial of science and physics?”
But I have not talked about this denial! And in rest You're completely right! The lack of physical space-time does not deny and science and physics, because it is impossible to deny of the Physics (the reality), and the description of the processes we can put into different ideas about the spaces, even into a Banach space (with the postulate restricting the use of other dimensions).
Sincerely,
Alexander Chepick
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Уважаемый Юрий!
«…результаты, которые не согласуются с принципом относительности.»
Я имею в виду:
- изменение сдвигов полос (с сидерическим периодом), полученное на интерферометрах Майкельсона-Морли в среде;
- изменение (с сидерическим периодом) времени распространения сигнала в кабеле в экспериментах ДеВитта и Кэйхилла;
- строгую пропорциональность расстоянию синусоидального изменения по времени разности фаз света между неподвижными источником и приемником света в экспериментах Глушко, ( http://sciteclibrary.ru/rus/catalog/pages/14819.html ) и т.п.
« Что скажете о размерности на Евклидовой плоскости, например на листе жести?»
А разве все физические процессы происходят только в плоскости? Например, электромагнетизм вообще нельзя описать в плоскости. Да и мы с вами не плоские! Поэтому теория, претендующая на описание всех физических процессов, не может иметь пространство с размерностью ниже 3. На вопрос, может ли минимальная размерность метрического пространства быть больше 3, отрицательно ответили законы Ньютона и Кулона.
«Наконец, Вы заявили, что пространство-время не существует физически, потому что это только наше видение. Но любая физическая теория-это лишь наше видение. Это результат нашего менталитета. Это повод для отрицания науки и физики?»
Но ведь я не говорил о таком отрицании! А так Вы полностью правы! Физическое отсутствие пространства-времени не отрицает ни науку, ни физику, потому что Физику (реальность) вообще невозможно отрицать, а описание процессов мы можем вложить в различные представления о пространствах, даже в Банахово пространство (с постулатом ограничения использования других размерностей).
С уважением,
Александр Чепик
Dear Alexander,
I have run through the paper by Glushko. I must say as follows. The Maxwell equations, describing process of the signal propagation do not contain the velocity of the Earth with respect to ether. But they contain the summary gravitational field of the Sun and of the Earth. This summarized field is different in different positions of the Earth. It is quite reasonable, that results of measurements are different in different cases.
As for me. I use physical space-time geometry Gp, which is obtained as a result of deformation of the Euclidean geometry GE. The geometry Gp is described completely by only space-time structure – world function \sigmap. In the nonrelativistic physics one uses an additional structure absolute space distance S (or absolute time difference T). Thus, the relativity principle states. Space-time geometry is described by the only space-time structure. This principle is valid in curved space-time, but for use this principle one should use the physical space-time geometry.
I must add, that there are space-time geometries Gp with indefinite dimension. Fo instance, discrete space-time geometry. (http://gasdyn-ipm.ipmnet.ru/~rylov/mfpdg1e.pdf or Russian version http://gasdyn-ipm.ipmnet.ru/~rylov/mfpdg1r.pdf
Dear Yuri,
Of course, it is possible to calculate the influence of gravitational potential of the Sun on the average change of the phase of the signal for 10 seconds depending on the time of day, time of year and the distance between the receiver and the source. From these data, it is also possible to calculate the amplitude of the curve for number of crossings through 0, of the phase received by Glushko. This curve should be symmetric only during the equinoxes. But the gravitational influence of the Sun cannot be sidereal. Unfortunately, Glushko did measurement of only three days, this time is not enough to determine sidereal period.
But in experiments Demyanov, DeWitt and Cahill this period can be seen.
Sincerely,
Alexander Chepick
---
Уважаемый Юрий!
Конечно, можно рассчитать влияние гравитационного потенциала Солнца на среднее изменение фазы сигнала за 10 секунд в зависимости от времени суток, времени года и расстояния между приемником и источником. По этим данным можно также посчитать амплитуду полученной Глушко кривой числа переходов фазы через 0. Симметричной эта кривая должна быть только в дни равноденствий. Но гравитационное влияние Солнца не может быть сидерическим. К сожалению, Глушко делал измерение всего три дня, этого срока недостаточно для определения сидеричности. Но в экспериментах Демьянова, ДеВитта и Кэйхилла этот период виден однозначно.
С уважением,
Александр Чепик
Уважаемый Александр,
Я не понял, причем тут сидеричность, если речь идет об определении скорости Земли относительно эфира. Что Вы имеет в виду под термином "сидеричность"?
Dear Yuri. You are right. "It cannot be a physical principle". It isn't.
The very serious question about Einstein relativity is that yes, physics uses mathematics and geometry, but physics can't exclusively be geometry. His spacetime is pure mathematics, a geometrical entity. How can we say that space is curved without knowing what space actually is (physically speaking) ? We can't. What is curved? Something which is only a bunch of coordinates?!
The problem is that General Relativity is not a quantum theory, it doesn't describe space from an actual physical point of view... the metric tensor (the father of all tensors in GR) is only a geometrical tool.
On the other hand we know that a real vacuum doesn't exist. We speak of quantum vacuum, vacuum energy, quantum foam and so on... this is the right way: changing our concept of space (let the spacetime be... time is only a consequence of motion. Not a physical entity).
Only in that moment we will rebuild a better theory of relativity which will be less geometrical and more physical. I am sure that the right approach is the fluid dynamic one, starting from a superfluid quantum space, since it is able to reproduce all relativistic effects, also without a curved space (flows of space's quanta are enough). Have a look at my work if you want, I'm going to upgrade it soon with important refinements.
Dear Yuri,
Conditions of the location on the Earth motionless of the experimental equipment relative to the vector of the Earth's motion in the ether are repeated every sidereal period, i.e., the turnover time of the Earth in the star coordinate system. Therefore, the results of the respective thin experiments are repeated with a sidereal period.
Sincerely,
Alexander Chepick
---
Уважаемый Юрий!
Условия расположения неподвижного на Земле экспериментального оборудования относительно вектора движения Земли в эфире повторяются через сидерический период, то есть, время оборота Земли в звездной системе координат. Поэтому результаты соответствующих тонких экспериментов повторяются с сидерическим периодом.
С уважением,
Александр Чепик
Dear Marco,
I've been wanting to say about your ideas. Subject of mathematics is important too. You do not think about the phenomenon of math. For you math exists in Plato's ideal world. In fact the reason for math existence in the topology (geometry). It is related to the entropy of the system. This is a fundamental point in the understanding of physical reality and existence of our intelligence.
By the way, your phenomenological ideas also have a mathematical description on qualitatively harder level. Pay attention to the invariant manifolds and evolution of the lagrangian coherent structures.
Apparently, the geometry of the theory of relativity fairly closely approximates the topology of spacetime on some range of scales. Non-locality of gravity and other energy problems are in good agreement with invariant structure of multiverse, not universe. They should be in present form of GR. GR geometry substantially limited by principle of short range and lack of knowledge of the topology of surroundings of objects that are included in it in the degraded form of singularities.
If you look closely at the organic structures then you will better understand the nature of time (based on your papers). The causal relationships, on the contrary, are physical objects. But you measure evolution of parts of the system (causal relationships) by comparsion with periodic processes - this is your perception of time. With your hydrodynamic point of view this is a manifestation of the evolution of coherent structures. Dissipative system (Universe) is not autonomous. We can say that the Universe exists in its extended phase space literally.
If you immerse yourself in a scale-invariant processes of self-organized criticality then you get a clue why gravity bad friends with quantum physics, and why it is impossible to apply the canonical approach for quantum model for gravity being inside the non-autonomous (dissipative) system.
May be the only rational way to put together all is self-organization in the evolving dissipative systems. The objective possibility of physical constants stabilization is available on the edge of catastrophic process in scale-invariance. This is what is missing in your model. Besides, your model also has no possibility for adequately explanation of strictly ordered structure of the standard model. There are a number of cosmological questions related to global evolution of the Universe as holistic system at different scales and paradoxes that your model in its pure form can not explain.
I advise you to pay attention to these questions and you will significantly rethink phenomenological attitude to issues of interest.
Best regards, Vasiliy.
Dear Marco,
I also think that the mass does not affect the space, and not gravitating with it. Curvature of the trajectory of the beam a mass of around is due to the different density of the space environment gravitating to this mass.
Sincerely,
Alexander Chepick
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Уважаемый Марко!
Я тоже считаю, что масса не влияет на пространство, и никак не притягивает его. Искривление траектории луча около массы происходит из-за разной плотности космической среды, притягиваемой этой массой.
С уважением,
Александр Чепик
Dear Alexander,
I do not understand, why it is important velocity of the Earth with respect to ether. In the end of nineteenth century the light was considered as a wave process in some medium (ether). But now electromagnetic wave propagates in the space-time. Maxwell equations do not contain a reference to a medium, where the electromagnetic wave propagates. How can one determine velocity of the Earth with respect to ether, if the ether is not mentioned in dynamic equations, which describe propagation of the electromagnetic wave? Do you mean that relativistic mechanics is not valid? Do you mean that ultrarelativistic motion of particles in accelerators should be calculated be nonrelativistic mechanics?
Dear Yuri,
The existence of the velocity of the Earth relative to the ether is proven by many experiments, so the theory of relativity is wrong in the general. Therefore, the velocity of the Earth relative to the ether is not determined by the Maxwell equations, but by other equations.
But in some cases the relativistic mechanics may be approximately or even accurately describe the effects due to the renormalization of units of measurement. In relativistic mechanics the description of the electromagnetic wave is distributed in the mathematical space-time, which does not exist physically.
---
Уважаемый Юрий,
Существование скорости Земли относительно эфира доказано многими экспериментами, следовательно, теория относительности в общем случае неверна. Поэтому скорость Земли относительно эфира определяется не по уравнениям Максвелла, а по другим уравнениям.
Но в частных случаях релятивистская механика может приближенно или даже точно описывать эффекты за счет перенормировки единиц измерения. В релятивистской механике описание электромагнитной волны распространяется в математическом пространстве-времени, которого не существует физически.
Уважаемый Александр,
Я не могу согласиться с тем, что электромагнитные волны описываются не Уравнениями Максвелла, а какими-то другими непонятными уравнениями. Я не могу согласиться с тем, что из того факта, что поперечное электромагнитное поле удовлетворяет волновому уравнению, следует, что электромагнитное поле описывает смещение точек некой сплошной среды (эфира).
Dear Yuri, I am glad to read your strict view for geometry and as consequence how you have immediately understood why mass does not affect space, thus general relativity seems to be a hypothesis rather than a description theory.
If possible, I'd like to argue a little bit more on this, because it is on screen now, after the announcement of 'gravitational ways' 'detection' from LIGO, see my recent works.
Thank you.
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