Point in Space: Classical Math & Recent Physics

[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.

 

[Drakkith]

Since the original question has been answered and the thread has fallen into speculation, it shall remain closed.