Let's try to provide a simple determination, which can be understood by majority of people.
Space for me as an engineering student is the three dimensional continuum of Euclidean geometry. However a good exposition of the views of Immanuel Kant on space and time can be seen here:
http://plato.stanford.edu/entries/kant-spacetime/
Starting from our perception I would rather say that Space is the smallest set of independent spatial variables that we need in order to describe unambiguously the concept of a fixed point: For example if you are inside a room you can define a Cartesian coordinate system at one edge of it and then you can scan all the room by the usual 3 variables (x,y,z). So, Space is something that at least ought to be scannable, able to be scanned.
Good starting point, Demetris. But I expect from you the outstanding answer, like you provided for TIME.
Starting from the absolute space and time (Newton) then this absolute conception is transformed into a stratified space with many levels of reality, and each level has its own coordinate systems. Thenn the algebra comes into the picture and thus we have instead of space a lot of algebraic system. The basic example is Algebraic Geometry. Although it is geometry it seems that "space" have disappear and instead we have varieties etc.
To answer what is "space" we should start with absolute space -time and describe the transformation of "space" to algebraic systems.
Space for me as an engineering student is the three dimensional continuum of Euclidean geometry. However a good exposition of the views of Immanuel Kant on space and time can be seen here:
http://plato.stanford.edu/entries/kant-spacetime/
I find this is fine answer, and not so long! :)
Dear @Nageswara, I do share our engineering views!
http://www.youtube.com/watch?v=lFyKxoeemc4
Space is inherent and an axiomatically understood concept. Space does not become a problem of understanding by standardizing the concept to units and axes. Normal perception and activity is easily described within the standard. Extending the standard to perception and metaphysics becomes a problem if the standard and normal experience are abandoned. Mathematics and physics develop paradoxes because of definitions, conventions, and improper application. Most sources of paradoxes involve infinity and infinitesimals as the result of the improper order of operations. Invoking infinity or an infinitesimal improperly or in the wrong order of operations creates a paradox. A paradox invites the abandoning of axiomatic perception.
Paradoxes and loss of axiomatic perception is avoided by recognizing a smallest unit of space (the Planck distance?), using zero only as a place holder, and dropping infinitesimals and infinity.
Time becomes the dimension that measures rate change in space.
Subatomic theory may require other dimensions for understanding forces, but must not be imposed on axiomatic space.
The shortest answer to your question is this:
"space is a mode in which we think and not a condition in which we exist"
Or,
"Space is a form abstracted from matter and exists only in consciousness".
May I bring to your attention that a similar question was asked much earlier: what is space made of?
https://www.researchgate.net/post/What_is_space_made_of
and this was my reply:
"What is 'space' made of? " I believe that in order to answer this question we need first to answer the question" What is space?" This is my 2 cent's worth.
First of all let us be clear about what space- time is not. Many people think of space-time as fabric but that is not correct. Space-time is not fabric. Space and time are not tangible 'things' in the same way that water and air are. Further, It is not correct to think of them as a "medium". I believe it is wrong to consider space-time as a truly physical medium.
Admittedly, this has been the way in which our minds prefer to conceptualize this concept, and has done so since the 19th century. Back then physicists talked of an ether. Today we know that ethers of the kind that behave like a physical medium are simply not present.
Two clues of what space-time is can be afforded by general relativity (GR) and quantum mechanics. GR as developed by Albert Einstein, says, and this is a direct quote from Einstein, that
"Space-time does not claim existence in its own right, but only as a structural quality of the [gravitational] field".
Nobel laureate Steven Weinberg, had this to say about space and time coordinates:
"Space and time coordinates are just four out of many degrees of freedom we need, to specify a self-consistent theory. What we are going to have [in any future Theory of Everything] is not so much a new view of space and time, but a de-emphasis of space and time".
Michael Greene, the co-inventor of super-string theory, hold a similar view
"In the theory of gravity, you can't really separate the structure of space and time from the particles which are associated with the force of gravity [ such as gravitons]. The notion of a string is inseparable from the space and time in which it moves.".
According to General Relativity, as specifically stated by its author Albert Einstein, 'without matter there can be no space-time'. That is because space-time is relational (not a physical "thing"), and without matter there are no relations between physical things.
General Relativity is our most elegant and by far the best-tested theory of how matter, gravitation and space-time work. There are actually two different parts of general relativity. They're often stated as:
Space-time tells matter how to move
Matter tells space-time how to curve.
As mentioned earlier, Einstein described "space and time as 'modes' in which we think and not as conditions in which we exist". Believe it or not this is also the view held in 900 AD by the Arabic physicists Ikhwan al-Safa,
"Space is a form abstracted from matter and exists only in consciousness".
Having answered the question "what is space," I hope you can see that I have also answered your question "what is space made of".
Conceptual question. It is amazing to note that professionals of various disciplines are describing Space differently. I think it can help to synthesize and develop a good research document later. My finding from above discussion (so far) is :
People perceive things in the context of their background knowledge.
Dear Alexander, of course my post was not a definition of space. I just posted it in order for your question not to be 'disappear' again from RG, because I liked it and I wanted to keep it alive!
I will continue in time...
Space in our globe is 3D of time and displacement. However, it is more than this and it is beyond our imagination.
Before I attempt to give a formal definition of Space, I'd like to share some thoughts about the exact meaning of what is going to be defined and how this should be done.
A first thought is that we want to define something with physical sense and not one more abstract mathematical space.
A second thought is that we want to give a definition that will not promote any existing school of thought, but it will try just to define Space. (Promotion is the easy task, formal definition is the hard task)
A third thought is that we have to give, again, a simple definition or, to repeat Alexander's nice motto, "to give an answer for the folks".
[Start of parenthesis]
Dear Issam, I cannot prevent my self from making a parenthesis about your next post:
***According to General Relativity, as specifically stated by its author Albert Einstein, 'without matter there can be no space-time'. That is because space-time is relational (not a physical "thing"), and without matter there are no relations between physical things.***
Here in RG discussions 'has spilled blood' about what is the cause and what is the result in the frame of GR: Gmn=k*Tmn, so when Tmn=0 (absence of 'generalised matter' - mass-energy etc-) there should be Gmn=0 (absense of space-time). But, unfortunately for GR, when Tmn=0 there exist many solutions for Gmn, so...
[End of parenthesis]
Basically speaking, space in 2D is the measurable distance between objects or points, the surface or perimeter of a geometry... in 3D it is the volumetric amount of a shape, object, geometry, body, land, geography.....
Dear Alexander,
I find the that the discussion is very inspiring, so please don´t take it wrong, but what happened to your similar question, which I started to follow, but suddenly disappeared from the "live feed". If you have deleted it for some reason, for me it´s OK :-), but if it was a Research gate staff action, I don´t understand why...
Best Greetings!
Svetlozar
Dear Svetlozar, it just dissapeared as it happened in large computer network. So, I started a new. A person like me, who claims JOSEPH STALIN as his Past Advisor in Philosophy, takes this neusence easy. Kind Regards, Alex.
Dear Alex,
I really liked your "Stalinistic" type of action regarding this issue...:-). I am from a bit younger generation, influenced by the Gorbatchov´s time - I started my PhD studies (at MSU) in 1988. So, during the USSR´s "Perestroika" time... Anyway, when I finished in 1993, I left Russia, not USSR...:-) But, yes, I do agree with you that ,sometimes, it´s indeed better to not complicate too much and act...!!
Best regards,
Svetlozar
SVETLOZAR, the USSR was a Mighty State under Stalin, provided alternative Social System to Western liberal democracy. That was the obligation of State to provide the job to every one, commencing with personal qualifications.
Stalin was succeeded by idiots, trying to grow corn in North Pole, cut grapes at the root, enforcing prohibition. Gorbachev and Yeltsin committed HIGH TREASON, betraying their state they killed.
So, I don't associate myself with Traitors, I became, at my advanced age, an Ideological Communist/Stalinist, I side myself with Victors. My Father was a Red Army Soldier during WW2, I am proud for my Father.
Space, for me, is a room of hopes and probabilities which can be used one's accordance.
A formal definition of Space:
"Space is the minimum required set of variables that you need in order to unambiguously describe the concept of immovability in the system under consideration."
Remarks:
1)Time cannot be included in Space, since they are ontologically different because Time describes the evolution (so the motion), while Space defines the state of no motion.
2)Space is different than Dimension:
http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension
In all cases above we can define immovability or immobility or non motion by using at most three variables.
For those that can read Greek, I suggest to read Section 8.3.2 O Χώρος (The Space) in my book https://www.researchgate.net/publication/243962466_________?ev=prf_pub
There the thesis is: After leaving the concepts of "absolute space" and "absolute time" we have to accept that the "reality" is made up by many levels of reality: microscopic, macroscopic megascopic etc. Each level have its own "space" and units of distacne measure/ We cannot have one stick to measure everything, from megasopic to microscopic. Thus there is no a universal space, but a multitude of local ones. There is also an interesting paper by J. L. Bell, From absolute to local mathematics, which describes the same phenomenon.
Book ΘΕΜΑΤΑ ΣΤΙΣ ΘΕΜΕΛΙΩΔΕΙΣ ΕΝΝΟΙΕΣ ΚΑΙ ΤΑ ΘΕΜΕΛΙΑ ΤΩΝ ΜΑΘΗΜΑΤΙΚΩΝ
Fellows ! I think that VOLUME is more understandable for simple folks identity than SPACE. They buy a Liter of milk, or a Gallon of gasoline, so, the Volume is within their intrinsic instinkts.
Then, I would propose to determine the SPACE as a VOLUME, which contains all Mass and Energy, including dark energy, on the Scale of Universe. Three-D coordinate system located within this volume determines any point in Universe.
Fairous has already mentioned volume in Association with Space.
Dear Alexander
You have asked earlier a question 'what is time' and now your question is 'what is space'. I have answered your questions using Einstein's theory of Special and General Relativity. Now I want to lighten the atmosphere a little, I would like to take an unconventional look at your two questions. Being very fond of museums, I like to connect space and time in this way:
Real museums are places where Time is transformed into Space.”
― Orhan Pamuk, The Museum of Innocence.
Hope you like it.
An interesting book about our theme from a neuro-cognitive view is the following:
[Stanislas_Dehaene,_Elizabeth_Brannon]
SPACE, TIME AND NUMBER IN THE BRAIN
SEARCHING FOR THE FOUNDATIONS OF
MATHEMATICAL THOUGHT
ISSAM, your idea about museums, transforming space into time and vise verse, is really sharp-shooting. I like it very much, thanks for sharing with every one.
Dear Alexander, Dear All,
Please see my work about time definition here:
https://www.researchgate.net/publication/263104630_A_simple_definition_of_Time?ev=prf_pub
It is open to anykind of polite review.
Thank you.
PS Now I will find resources to answer the question about Space...
Article A simple definition of Time
Dear Demetris, I am really impressed with your paper on time. But I am a Physical Chemist, not a professional Theoretical Physicist. So, I would advise you to submit your paper for formal RG review, this option is now available. When you collect different opinions you come with the final version for a Journal in Physics.
I believe you are capable to write similar paper on the subject of SPACE as well.
I am happy with your success.
Dear Alex,
When you write: "Then, I would propose to determine the SPACE as a VOLUME, which contains all Mass and Energy, including dark energy".
If you would allow me, I would like to challenge even more this interesting discussion you have initiated :-) by:
1. "All Mass and Energy" - So this means these are two different things...? In what respect? What about the Einstein´s relation between energy and mass...
2. What is "dark" energy"??
As you, I am also not a theoretical physicist, even worse... - not even a Physical Chemist, but a (bio)chemical engineer, which means more loose ends and inclination for over-simplification of the phenomena in order to be able to have practical "engineering" benefits... Therefore, I would really appreciate if someone could provide meaningful explanations on these two topics...
Dear Svetlosar, its time for bed now, but tomorrow I will answer your questions best to my ability.
As long as I am thinking about Space I wonder if we really can give an answer without using any kind of an already known mathematical space. The first answer is this: OK, Space is simply R^3, so let's not analyse it more. But, why R^3? Is it true or is it just our 3d perception of what is around us? Why shouldn't exist an intelligent creature that could feel a 4d manifold? Is this a true barrier or we are just 3d ants? (Do you remember the cosmological example of a 2d world of ants?) I dare to say that we cannot find an answer to this question with our 3d senses... Anyway, that's the reason why we love Mathematics, because they can pull us out of our limited perception. So, it is reasonable to assume that, since for Maths the concept of n-fold manifold is very often used, then it is possible to exist a universe with a 4d reality. Or, probably the reality is already n-folded, but we can understand only the 3 of those 'dimensions' (oops, bad word, sorry...).
If we accept that our local universe is a 3d one then the answer has been answered Space=R^3 and we finished. But, who can guarantee it to us? Should we ask a 4d being or an immaterial one? Am I entering in Metaphysics now?
OK, let's all return to the ground of our lovely and plenty of water Earth.
We have to answer next preliminary questions:
1)what should be the connection between generalised dimension and Space?
2)should we define Space as a local universe property or should we attempt to enter a sea of local universes approach?
3)should we require a known mathematical structure for Space (Examples: linear vector spaces, topological spaces and so on...), or should we try to define it independently of our known mathematical tools?
Let the next participant to continue now...
Space for me as a human being is where I live, as a scientist is my lab, as an astronomer is where I gaze, as a father is my family, as a theorist is my computer, as an intellectual is my library and as a poet is my source of inspiration. The definition of space varies with respect with who you are and what you do with it.
I believe that “space” is what we perceive as such i..e 3D space + that this 3D space is stratified. If you try to incorporate into your space some internal objects like particles (i.e. functions) then the dimensions will increase rapidly. Even if we are talking about a human, we may have a picture of him in 3D. But we may have other coordinates, i.e health co-ordinates (temperature, pressure, weight, ect. When you look “inside” the number of co-ordinates increase. Using this conception, one can reasonable introduce manifolds and other exotic objects.
SVETLOZAR ! E = mC^2, but not all energy can me transformed to mass and vice verse.
You need nuclear reaction in order to get energy out of mass. In the case of H-Bomb two nucleas of Heavy Hydrogen D colliding produce a Nuclea of Helium, smaller in mass than 2D, so, this defect of mass is transformed into Heat and Radiation, but not all of the initial mass, initially in D. In the case of Chemical reactions mass of products coming out of reaction is equal to the mass of initial components coming into reaction.
Then take an Electromagnetic Wave, having Energy but zero mass. For example, using strong radar you sent Electromagnetic Wave to Lunar surface. The energy of the wave will be absorbed by Lunar rock, dissipating as heat. This heat will be radiated back into the space as infra-red, so, no new mass is obtained from the energy.
Dark energy is the invention of Astronomers and Astro-Physicists. They claim that over 50 % of the energy of Universe is stored in dark energy. Dark energy exerts negative gravity on bodies carrying mass, pushing Universe to expand and accelirating this expansion.
In the case we treat Universe as a VOLUME, this Volume is getting increased with time.
There are more professional folks on this site so, they can correct me, add additional information.
Alexander
I think you are right. More than one century after the publication of the theory of relativity, astronomers and astrophysicists continue to believe they can use Newton's law of gravitation, and classical mechanics, to determine the total mass of a galaxy, by studying the motion of stars in it. They seem to ignore that galaxies are not spherical distributions of mass and that the virial theorem applies where f = m a applies also.
The estimated size of our galaxy is about 100,000 light years. It might be advisable to include, at least, some retardation in the equations of motion when applying Newton's laws. The moment retardation is included, the equations stop being second order differential equations an the first integral called mechanical energy does not exist.
In my project bench here on Research Gate I have uploaded the review paper I have recently written on Modified Gravity as an alternative to Dark Matter. However,
the viral theorem certainly applies to galaxies as they are several dynamical timescales old, independent of their geometry, in both the Dark Matter and modified galaxy scenarios. The virial theorem (2T + W =0) doesn't care about the form of Newton's second law.
Black energy is more appropriately called dark energy; operationally it acts as a negative pressure long range "force" - its misleading to characterize this as "negative gravity".
Questions about Nature and mathematical structures continued...
Have you ever ask yourself why in all useful branches of Mathematics (for example Algebra & Topology) the concept of closure is a key feature? Why all algebraic or topological structures are defined by means of, roughly speaking, object1*object2 is inside the same 'space'? (As * is something formally defined, for example an arithmetic operation). What is the deeper meaning of closure?
As dark energy experience pressure, the body carrying mass and immersed into dark energy experience kind of Arhedemian force, acting on the body with mass, pushing the body out of the center of universe, expanding the universe in volume. This effect is equivalent to negative gravity. Arhimedian force can also be treated as negative gravity.
Dear Demetris,
The deepest meaning of closure is of course "Topological Space". It is well known the Kuratowski's axioms on closure operators, defining the topological space itself! I congratulate you since you ask important questions!
@G. Bothun
Can you please provide a proof of the virial theorem that doesn't care of Newton's laws? I mean something different from this: http://www7b.biglobe.ne.jp/~kcy05t/viriproof.html . Your remarks about the last part of this article http://en.wikipedia.org/wiki/Virial_theorem will be appreciated; as well as a clarification of the meaning of your assertion that "Galaxies are several dynamical timescales old."
@Costas and all, you will like this question:
https://www.researchgate.net/post/What_is_the_essential_difference_between_Algebra_and_Topology
It is complementary to the effort for a Space definition.
We have to clarify so many different in name, but identical in meaning, mathematical terms, in order to find answers about physical questions.
Let's continue the survey for Space.
According to the (well hidden I think) deeper property of Algebra, Topology and other math branches, what really matters is closure or closeness property: If you take two or more objects from your 'entity' (call it Space if you like) then by applying a binary or n-ary operation on them the result should lie inside the same 'entity'. So:
"Space is whatever mathematical entity is suitable for describing a universe with the smallest number of freedom degrees plus the additional property of closure under all defined math operations inside it."
I would like to point out, ghat space is strongly related to the concept of "point". However this concept is very problematic and thus the concept of space is problematic. For this reason some mathematicians prefer to formulate "space" point free. Also algebraic topology avoids "points" and instead talks about triangulations etc.
There is a very nice point-free topologies called "locales-frames". This point free formulation is more friendly to algebraic treatments. For frames and locales see
P; Johnston, Stone Spaces.
Fellows, I try my best to share the Electronic version of book on Cosmos by my Friend, Prof. Eugene Levich, Emeritus crom CCNY. He is a Theoretical Astrophysicist and a Philosopher. Within this work he Theoretically calculated the Hubble Constant for expanding Universe.
Intriguing reference dear Alexander, which is able to departure our discussion to other routes...
I just remind that Cosmos & Genesis & Chaos are Greek words...
Dear Alexander, I read sections of your presented book Cosmos, written from Prof. Eugene Levich. Unfortunately for me, it is very difficult to judge the Religion of a person, even if it is being discussed in a scientific presentation. I always accept the right to freedom of religion and I fully respect the religious beliefs of all. So, even if the motivation is great, I cannot make comments on it. Probably in a private discussion or in another, not scientific, forum we could discuss all. Thank you for providing us with an electronic copy of the book.
Demetris, the book is Theological in the way it is written. The reversed Second Law of Thermodynamis was formulated by Prigogine, who got the Nobel Prise in Chemistry for this work. But Eugene treats it as a common knowlege, which highly irritates readers. Nevertheless, he theoretically calculated number of world constants, his results coinside with experiments within experimental error. Just look at his calculations, skipping religious deviations, which are not used for calculations.
Thanks a lot Alex for giving us the opportunity to read, in my opinion, this great philosophic book! It opens so many questions as well... and also it´s kind of sad (if it is true) that "there are no alternative histories" and all is programmed... We clearly come to the basic "theological" question - when, how and for what purpose...?
"The determinism is indeed rather shocking. Everything happening on Earth is commandeered by the necessity to accommodate and comfortably settle the growing order coming from space. There are of course fluctuations and aberrations. However over a period of time there are no mistakes and nothing is random in the implementation of RSL imperatives. There are no alternative histories..."
Dear Oscar. General Relativity completely substituted Newtonial Mecanics on the Galaxy scale. As mass of photons is zero, light does not interrect with massive bodies in Newtonian Mechanics, but it does interect within General Relativity. Astronomical observation of Mercury in early 1920th confirmed Einstein predictions.
Newtonian Mechanics remains the major tool for Engineering on our Planet Earth.
Alexander. I agree with you. If we are going to study the motion of matter around an object the size of a galaxy we must give up using Newton's and Kepler's laws. We must, at least make relativistic corrections in the sense of the special theory of relativity. Now, the four-momentum of a particle p^u = m c v^u remains constant in magnitude, in Minkowsky's sense, if the mass is constant. That means that, locally, where space-time can be considered Lorentzian, we must adopt a dynamical law where \frac{d p^u}{d s} = F^{uv} p_v, where F^{uv} is a second order antisymmetric tensor, in this approximation we have forces that depend on the actual velocity, similar to the magnetic field, though gravitational in origin, perhaps in the sense described by Oleg D. Jefimenko in his book: Causality, Electromagnetic Induction and Gravitation (Chapter 6, p. 101) The situation becomes more complicated because, if we can see "it", then it is loosing mass, not only in the form of light but in the form of nuclei and electrons, like in the solar wind. So we must have:
\frac{d p^u}{d s} = m c \frac{d v^u}{d s} + v^u c \frac{dm}{ds}
The term \frac{d v^u}{d s} can be written in the for f^{uv}v_v, again, because the magnitude of the four-velocity is one.
There is a tendency to believe that we have to resort to relativistic corrections in the limit of high velocities. That's not so when we are talking about huge distances, because the retardation has to be considered. It was actually that retardation that allowed Roemer to conclude that the speed of light was finite a couple of centuries ago!
A more 'intelligent being oriented' definition:
"For every class of intelligent beings, Space is what its senses and brain abilities allow to feel as a minimum dimensional manifold, needed in order to describe unambiguously the concept of a fundamental 'brick'".
A fundamental brick for the class of human beings is (till now) either a point (then Space=R^3) or a chord (then Space=R^{9+}) or a topological space.
Let's forget our limited abilities and generalize the definition, why not?
Demeteris, please, work out the defenition for simple folks, not just for scientists.
Dear @Alexander, this is ResearchGate discussion among researcher, not a popular science discussion! :)
Sure, Ljubomir, but Demetris succeeded with simple determination of time, understendable for laymen. Let him do the same with Space.
@Demetris
It seems to me that a mathematical description of space is to space as a musical score is to the actual music.
Dear friends, since it was a very difficult year for me (due to PhD program conflicts), I think that, in order to answer such a difficult question, I need Time to explore the liquid phase of Space, the so called 'sea'! I will share my new thoughts after a while.
Thanks all for the discussions and for supporting me at my last 'adventure'.
Demetris,
I think this is the starting of a lot of adventures to come not the last! So be prepared.
There is a Chapter in:
“Chapter 4 - Space, Time, and Modernity”
In: Rifkin, Jeremy. “The European Dream.”
This might be interesting. I have not read it.
Finally the decisive answer to the question of "space" is the given in the lecture of Atiyah!
Dear Costas, just to intrigue you, in order to have a unified approach, you can think about Einstein like Marx: they have done the same amount of "damages" to their specific scientific fields...
More details after vacations...
Only that their specific scientific fields, are introduced by them. So they cannot make damages into their fields! In order to say this you should have a broader view, where you can assed Marx and Einstein!
As long as I remember, neither Einstein nor Marx introduced Physics & Philosophy, respectively.
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