Point in Space: Classical Math & Recent Physics

[LotusPond_14]

hi there...

what is a point in a space?

classical math tells us that a point is:

- an exact location on a plane surface
- it has zero dimension

but it can be viewed of as

- an origin of fundamental forces operating within a dimension. all forces in a dimension must have an origin, thus, it is logical that a point within that dimension must be responsible to create the force.

- it has no dimension but movement or activity can be observed. this follows that a point though it has no dimension, the only way that activity is evident is for the point to have rotation. it also follows that it can rotate either left handed, or right handed.

- the point's spin also, is not confined to a certain plane in a dimension only. for example, in a three dimensional "space", the left handed or right handedness of the point's spin only denotes orientation since the point can spin in all directions.

can you please help me on this if my observations are correct or not beacuse recent physics experiments clearly are going to the direction of this observation.

 

[bhobba]

what is a point in a space?

An object in a mathematical model, usually in basic QM, but not always otherwise, Euclidean geometry.

an origin of fundamental forces operating within a dimension.

And your source of such a claim is?

Before answering that be aware of our forum rules:
https://www.physicsforums.com/showthread.php?t=733933

Thanks
Bill

 

[LotusPond_14]

my origin of the claim is from the central force problem of classical mechanics which aims is to determine the motion of a particle under the influence of a single central force. A central force is a force that points from the particle directly towards (or directly away from) a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center. (from wiki pedia).

the problem applies for bodies having mass (thus having their own dimension in the case within three dimensional space as having length, width and height) but can it be extended to the smallest unit of space available within a dimension (ie the distance between two zero dimensional points in a one dimension subset or dissection in a 3d space) and the interaction of the forces transferred from one point to the next.

 

[Drakkith]

Per wiki: http://en.wikipedia.org/wiki/Point_(geometry )

In modern mathematics, a point refers usually to an element of some set, called space.

More specifically, in Euclidean geometry, a point is a primitive notion upon which the geometry is built. Being a primitive notion means that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms that it must satisfy. In particular, the geometric points do not have any length, area, volume, or any other dimensional attribute. A common interpretation is that the concept of a point is meant to capture the notion of a unique location in Euclidean space.

Note the last sentence. A point is not a physical object. It is a mathematical concept. We can consider objects and events to be located at a point, but we cannot say that the point itself creates anything or is responsible for anything, nor can it have a spin. It's just a way to keep track of the location of things in space.

 

[LotusPond_14]

so how does a force act upon a point in space? does it only transiently convey ; transmit the force into space since it is implied in classical math that it is only a notion to keep track of location of things in space?

 

[Drakkith]

so how does a force act upon a point in space? does it only transiently convey ; transmit the force into space since it is implied in classical math that it is only a notion to keep track of location of things in space?

A force does not act on a point in space, it acts on an object located at that point in space. These interactions are governed by well understood laws.

 

[LotusPond_14]

but those laws as i researched does not have conformity when describing forces within very small objects and forces that govern massive objects why is that so?? i believe in the notion that all forces operating in a dimension must be the same whether the force is acting on a small object or it acts on a massive object and everything in between.

thus it follows that in order for forces acting on objects are the same, the medium in which the objects exist must be of the same "viscosity", (i am describing viscosity because it is observed that space acts like it and is documented in various scientific journals.) but as objects tend to be more massive than others it is logical that the space encompassing massive objects tend to be more stretched than less massive objects.

now, what does space comprises of? is it just a region of nothingness or does space have a very intricate structure? then if it is, it follows that every point in space, which it is a subset of must comprise of a structure so that the space will behave accordingly so as to what the point in space behaves.

 

[bhobba]

i believe in the notion that all forces operating in a dimension must be the same whether the force is acting on a small object or it acts on a massive object and everything in between.

Forces operating in a dimension? I have zero idea what you mean.

The modern view of forces comes from Quantum Field theory:
https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Quantum_field_theory.html
'In perturbative quantum field theory, the forces between particles are mediated by other particles. The electromagnetic force between two electrons is caused by an exchange of photons. Intermediate vector bosons mediate the weak force and gluons mediate the strong force. There is currently no complete quantum theory of the remaining fundamental force, gravity, but many of the proposed theories postulate the existence of a graviton particle that mediates it. These force-carrying particles are virtual particles and, by definition, cannot be detected while carrying the force, because such detection will imply that the force is not being carried. In addition, the notion of "force mediating particle" comes from perturbation theory, and thus does not make sense in a context of bound states.'

now, what does space comprises of? is it just a region of nothingness or does space have a very intricate structure? then if it is, it follows that every point in space, which it is a subset of must comprise of a structure so that the space will behave accordingly so as to what the point in space behaves.

It has a very intricate structure - the vacuum is a very interesting, weird and wonderful thing in Quantum Field Theory.

And general relativity says its dynamical as well - in fact that's the very essence of General Relativity - no prior geometry - meaning geometry itself is dynamical.

And meshing these insights together is one of the greatest challenges of modern physics.

Thanks
Bill

 

[LotusPond_14]

yes general relativity says that space has no geometry but it has structure. so, if space has structure, then the points which comprises space also has structure. although in mathematics the point is only used as a notion to depict a location, it does not mean that a point is non existent.

 

[Drakkith]

i believe in the notion that all forces operating in a dimension must be the same whether the force is acting on a small object or it acts on a massive object and everything in between.

I'm with Bhobba. I don't know what this means. Honestly I can't really make heads or tails of most of your post.

 

[Drakkith]

yes general relativity says that space has no geometry but it has structure. so, if space has structure, then the points which comprises space also has structure.

Each point itself cannot have a structure, but the way they are arranged can be the result of the structure of space.

 

[bhobba]

yes general relativity says that space has no geometry

That's not what it says - it says it has no PRIOR geometry - meaning the space-time geometry (not space - but space-time) is determined by the Einstein Field Equations (EFE's).

Its a very interesting fact of GR that that assumption alone, and a few reasonable physical assumptions, leads to the EFE's.

But this thread is not the place to discuss that - the relativity section is where it belongs.

And Drakkith is correct - points have no structure - they are one of the concepts used in defining what a geometry is. Specifically in GR the geometry is known as a Pseudo Riemannian geometry - but that is just by the by.

Thanks
Bill

 

[LotusPond_14]

in a way that is correct. because points have zero dimension to begin with. but how is it that matter be created from a point in space and in that point only and not elsewhere?

 

[Drakkith]

You seem to be thinking that a point is some sort of physical object. It is not. It is a mathematical construct used in various branches of math, including being one of the building blocks of basic geometry. However, it is possible to have geometry without points: http://en.wikipedia.org/wiki/Noncommutative_geometry

It is important to remember that mathematical concepts do not always apply to the real world, and even when they do, it is only because they happen to be useful in describing reality, not because they are fundamentally true.

 

[bhobba]

but how is it that matter be created from a point in space and in that point only and not elsewhere?

Conceptually matter occupies a point in space - it isn't created from a point.

It is important to remember that mathematical concepts do not always apply to the real world, and even when they do, it is only because they happen to be useful in describing reality, not because they are fundamentally true.

That is both VERY important and VERY true.

Our theories are basically mathematical models.

A point is simply an object in the model.

Thanks
Bill

 

[Drakkith]

in a way that is correct. because points have zero dimension to begin with. but how is it that matter be created from a point in space and in that point only and not elsewhere?

Matter is not created from a point in space, but at a point in space. I don't mean to be nitpicky, but I want to make sure we don't get confused. Matter is only created at that point because that's where the creation event is happening.

 

[LotusPond_14]

its alright sir drakkith. i only observed that when matter is created at a point in space and not from it, then matter will be created at all points in space resulting in non variability. but in reality, this never happened. it is clearly observed that some regions in space have more matter than in some areas. this also is observed here on Earth thus resulting in the variability in the forms of matter existing in our planet. even in outer space there are some regions which are more dense than other areas. if we make the the second statement into account then variability can exist since matter will be created more massive from one point and less massive on the other in relation to the space that governs both points.

so it leads us to wonder if those points in space are static or not.

 

[LotusPond_14]

i am not describing the interaction of the points but the interaction of the space surrounding both points, assuming that the distance of the points are far enough to be observed.

 

[bhobba]

so it leads us to wonder if those points in space are static or not.

By definition a point is static.

And the variability of the density of matter has a lot to do with gravitational clumping - meaning tiny variations in density get magnified over time by gravitational attraction.

It is believed the universe started out fairly homogeneous.

Thanks
Bill

 

[bhobba]

but the interaction of the space surrounding both points

I have zero idea what you mean by that.

Thanks
Bill

 

[Drakkith]

its alright sir drakkith. i only observed that when matter is created at a point in space and not from it, then matter will be created at all points in space resulting in non variability. but in reality, this never happened. it is clearly observed that some regions in space have more matter than in some areas. this also is observed here on Earth thus resulting in the variability in the forms of matter existing in our planet. even in outer space there are some regions which are more dense than other areas. if we make the the second statement into account then variability can exist since matter will be created more massive from one point and less massive on the other in relation to the space that governs both points.

so it leads us to wonder if those points in space are static or not.

The reason that matter is clumped together has two major causes:

1. Gravity pulls matter together, resulting in large clumps that lead to the formation of galaxies, stars, planets, etc.

2. In the very early universe, quantum fluctuations led to certain regions of space being more or less dense than others. The matter in areas of space that were more dense tended to coalesce under gravity to form the first galaxies, while the areas that were less dense tended to have matter pulled from them, forming large voids. Without these fluctuations, the early universe would have been totally homogenous and gravity would not have been able to pull matter together since the force would have been equal in all directions.

 

[LotusPond_14]

sir bhobba i mean that the very space itself surrounding the two points must have influence and not just on the points themselves ... this in aggreement on julian barboun's work that tells us space is dynamic. for example, if we put two planets with the same distance to each other in a static space (since a point by definition is static and space is a region of points), then no orbiting or spinning on its own axis (i.e. movement or activity) will not take place no matter how massive the object is. But if the two planets are put into a dynamic space (thus comprising of dynamic points) the space reacts to the objects by conforming in respect to their masses.

 

[LotusPond_14]

assuming that we don't know about gravity, only the objects and the space between it, it can only be deduced that in order for the objects to have activity, the space between the objects must be capable of transmitting the activity produced by the object.

and if that space is filled with points, then those points must be also capable to transmit the activity. so a dynamic space is not comprised of a static point.

 

[bhobba]

and if that space is filled with points, then those points must be also capable to transmit the activity. so a dynamic space is not comprised of a static point.

Points transmit activity - you lost me.

Thanks
Bill

 

[LotusPond_14]

i am only saying that in order to have a dynamic space, a space that responds to objects, the points that comprises space must also be dynamic. there would be a antithesis if in a dynamic space, it comprises of static points. if it does, space surrounding massive objects would have not been curved.

so how do points in a dynamic space behave?

 

[Drakkith]

What do you mean by "dynamic points"? What do they do that makes them dynamic?

 

[LotusPond_14]

it is said that space curves on massive objects (relating to relativity) thus it is implied that space changes with respect to mass. so if points are by definition are what comprises space and space changes with respect to mass, then points must be changing to order to define that space changes.

if we are to declare that points within a space is static then space itself is static, hence there should be no interaction between objects within that space as it would forbade it to do so.

but objects in the universe interact with one another, and it is the result of the space that allows the objects within it to do so would you aggree?

 

[Drakkith]

I think it's more accurate to say that the relative position of any two points changes, not that the points themselves change.

but objects in the universe interact with one another, and it is the result of the space that allows the objects within it to do so would you aggree?

I think that's a very vague statement that doesn't say much, and I wouldn't try to infer too much from it.

 

[Matterwave]

it is said that space curves on massive objects (relating to relativity) thus it is implied that space changes with respect to mass. so if points are by definition are what comprises space and space changes with respect to mass, then points must be changing to order to define that space changes.

if we are to declare that points within a space is static then space itself is static, hence there should be no interaction between objects within that space as it would forbade it to do so.

but objects in the universe interact with one another, and it is the result of the space that allows the objects within it to do so would you aggree?

General relativity is a 4-dimensional theory. Each point of the base manifold is a space time event, and not merely a point in space. Points in space time do not move around, they correspond to one particular event (e.g. a light flashes). All you can do is relabel the points if you so choose (make a coordinate transformation). Massive objects curve space time, not just space (and indeed the notion of "just space" is more subtle in general relativity than you have so far conceptualized in your posts). The curvature is already there and there's no "space is changing with respect to mass", there's just "space time is curvED with respect to mass".

Of course, this disconnect can happen when we learn about general relativity. We are used to a 3 dimensional world evolving in time, we are not used to thinking 4 dimensionally. As such, our language is specifically adapted in terms of past present and future, and it becomes semantically hard to talk in a 4-dimensinal manner.

 

[LotusPond_14]

now we are including time but how does time behave in a point in space sir matterwave. if we are then to measure spacetime where x=0, y=0, z=0 is it true that time(t) is also zero?

 

[Drakkith]

now we are including time but how does time behave in a point in space sir matterwave. if we are then to measure spacetime where x=0, y=0, z=0 is it true that time(t) is also zero?

No, the choice of what you label your coordinates as is completely arbitrary.

 

[Natsirt]

I don't know about a point but the only scenario where time can be thought of as zero to my mind is if time is not moving and if time's not moving your not moving.

 

[bhobba]

I don't know about a point but the only scenario where time can be thought of as zero to my mind is if time is not moving and if time's not moving your not moving.

I don't know what you mean by time as zero - or even what you mean by time moving - moving has a particular meaning in physics - and it doesn't apply to time. Expressions like time moves on etc are just what we use in everyday conversations and is not what it means in physics.

You might be talking about the direction of time - that's a deep issue and is thought to be associated with entopy:
http://www.itp.phys.ethz.ch/education/fs09/ism/Gloor.pdf

A point's relation to time is in physics time is considered to be what a clock measures, which is expressed as a number. For mathematical convenience, and so we can apply the methods of the calculus, its considered a real number which can be considered as points on a line.

Thanks
Bill

 

[Drakkith]

I don't know about a point but the only scenario where time can be thought of as zero to my mind is if time is not moving and if time's not moving your not moving.

Saying T=0 is merely labeling a point in time as zero to compare it with another point in time. I could say right now is t=0 and 5 seconds ago is T= -5.

 

[Natsirt]

I meant measuring a point in time as zero on whatever scale you would measure time on. And when I said time moving I meant moving within Space-Time.
I guess our descriptions aren't very compatible but I agree with you... Bhobba

 

[Matterwave]

now we are including time but how does time behave in a point in space sir matterwave. if we are then to measure spacetime where x=0, y=0, z=0 is it true that time(t) is also zero?

Nothing behaves "at a point". A point is a point. It has dimension 0, it has no evolution, it is one single event, it is one instant in time at one specific place in space.

 

[bhobba]

I meant measuring a point in time as zero on whatever scale you would measure time on

If that's what you mean then of course I agree - and as Drakkith said it is entirely arbitrary.

And when I said time moving I meant moving within Space-Time. I guess our descriptions aren't very compatible but I agree with you... Bhobba

Now you lost me again. I don't know what you mean by time moving within space-time. I think you can say a particle moves in space-time by the fact it traces out a path in a space-time diagram - but time moving - can't quite grasp that.

Thanks
Bill

 

[LotusPond_14]

sir matterwave but you are referring to is a frame in spacetime. if we are to say that time is dependent on the motion of an object in space time then if all motion comes to a stop then are you implying that time will also stop?? for example if i am to stop moving am i freezing time as well?? if time is dependent on motion then how come the atoms experiencing decay?

time never stops even when an object has no motion sir matterwave.

 

[Drakkith]

That is NOT what Matterwave was saying, and I don't know how you came to that conclusion. He's talking about a single point. Any event in spacetime is described by 4 coordinates (points). Three for the spatial dimensions and one for time. If we label one event as being at T=0, then another event at the same location 1 second later is at T=1.

Remember that this is all about labeling coordinates, where each point is a coordinate in one dimension.

 

[LotusPond_14]

that is correct drakkith. i am only trying to reconcile if the smallest unit of space time (ie. points in any given space plane or space dissect) has importance in the behavior of the objects within space time.

i think that the very points in space within space time not only pertains the location of the object but also the origin of the objects influence to other objects if we are to observe the smallest area possible occupied by that object.

consider a smallest sphere possible to attain in a segment of 4d space and that sphere contains the smallest points possible, then if that sphere are to influence another sphere of the same dimension (length, width, height,and breadth) is the sphere in question is only responsible for that influence or the the very points within that sphere has relative influence to the points on another sphere and the points within the space in which they occupy?

 

[Natsirt]

Now you lost me again. I don't know what you mean by time moving within space-time. I think you can say a particle moves in space-time by the fact it traces out a path in a space-time diagram-bhobba

I agree i was referring to particles moving in space time. time itself moving would be unheard of. Maybe however there could be an undiscovered Space-Time flow caused by cosmic inflation.

 

[Matterwave]

sir matterwave but you are referring to is a frame in spacetime. if we are to say that time is dependent on the motion of an object in space time then if all motion comes to a stop then are you implying that time will also stop?? for example if i am to stop moving am i freezing time as well?? if time is dependent on motion then how come the atoms experiencing decay?

time never stops even when an object has no motion sir matterwave.

I am so confused how you drew this conclusion from my previous post.

 

[Drakkith]

that is correct drakkith. i am only trying to reconcile if the smallest unit of space time (ie. points in any given space plane or space dissect) has importance in the behavior of the objects within space time.

They don't. A point isn't a real object. I don't know how many times I have to say this.

consider a smallest sphere possible to attain in a segment of 4d space and that sphere contains the smallest points possible

There is no limit to how small a section of spacetime can be, nor do points have any size, so your question is already mostly meaningless.

 

[bhobba]

A point isn't a real object. I don't know how many times I have to say this.

Simply think back to good old Euclidean geometry you hopefully learned about at school. A point was defined as having position and no size. Nothing out there has position and no size. Its a conceptualisation useful in modelling things.

In modern times points have been generalised somewhat to mean element of a set - but the principle is exactly the same.

There is no limit to how small a section of spacetime can be, nor do points have any size, so your question is already mostly meaningless.

That's absolutely fundamental.

You can't apply the calculus if it wasn't true.

Thanks
Bill

 

[LotusPond_14]

so how can we reconcile the relationship of an object and the points that comprises the object if the points, since they are only treated of as only a concept thus non existent in the physical world?

the premise that points are static and translating that space is static led Newton to conclude that space and time are absolute.. that very paradigm that Newton laid has been challenged by Mach and Mach's principles led Einstein to develop his theories on relativity.

so, what then are points in space?

 

[Natsirt]

Points in time.

 

[Drakkith]

so how can we reconcile the relationship of an object and the points that comprises the object if the points, since they are only treated of as only a concept thus non existent in the physical world?

There's nothing to reconcile. Points are used to label locations in space and time. They do not comprise objects.

the premise that points are static and translating that space is static led Newton to conclude that space and time are absolute.. that very paradigm that Newton laid has been challenged by Mach and Mach's principles led Einstein to develop his theories on relativity.

Any single point is static in the sense that it is a zero dimensional, mathematical object with no degrees of freedom and no way to change. However, the mathematical space it comprises can change. This is typically represented by showing the position of two points changing relative to one another over time. So the dynamic space is comprised of static points. One could even argue that they aren't even the same points, they're just labeled the same and used to show how real objects would behave in dynamic space.

 

[bhobba]

so how can we reconcile the relationship of an object and the points that comprises the object if the points, since they are only treated of as only a concept thus non existent in the physical world?

The same way surveyors use the points of Euclidean geometry - as mentioned previously they do not exist either in the physical world.

Mathematical models often contain things that do not directly map to objects eg probabilities assigned to sides of a coin.

the premise that points are static and translating that space is static led Newton to conclude that space and time are absolute.. that very paradigm that Newton laid has been challenged by Mach and Mach's principles led Einstein to develop his theories on relativity

Newton was wrong about that and many things - which in no way diminishes his genius.

There were many things, not just philosophical issues you cite, that lead Einstein to create his theories.

But regarding GR he was not able to make progress until he became aware of the tensor calculus which was the right tool for the job. That would seem to be the real key - finding the right way to model the situation.

Thanks
Bill

 

[LotusPond_14]

so if we change the thinking of what really points in space would behave let alone what it really is we will have progress to understand space and time itself? maybe that is the key.

because all current mathematics are focused on the dynamics of the objects themselves and we have only have a vague idea of what space really is correct me if i am wrong sir. if the very medium in which we exist we cannot understand entirely how can we accurately describe the dynamic of the objects that exist in the medium (e.g. space and its higher counterpart, spacetime.)

 

[Dale]

Closed pending moderation.