Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: flr on 18/09/2013 01:08:03
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Is space a mathematical relation or something real?
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Is space a mathematical relation or something real?
A friend of mine, who is now retired, is an expert in general relativity (GR). Since GR is the science of geometry he wrote up a web page about geometry which is located at
at http://users.wfu.edu/brehme/space.htm
Is there anything more about space that you want to learn beyond this?
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It is possible to describe real things by mathematical relations... They are not mutually exclusive.
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It is possible to describe real things by mathematical relations... They are not mutually exclusive.
How did you conclude that I meant anything different?
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Space as seen via photons is the present moment we all share. ::)
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Space as seen via photons is the present moment we all share. ::)
If you wish to continue to post here then you might want to consider being clearer in your responses. The meaning of this one is too unclear to respond to.
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These questions of what is "real" are always difficult to respond to. In one sense, anything measurable is "real." In the sense of finding the most fundamental description of the universe, we have no idea since we're not there yet. Space as we know and measure it might be due to some more fundamental "stuff"--but that would raise the question of what that stuff was made of...
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Hi petm1,
Space as seen via photons is the present moment we all share.
Would I be right in thinking that what your post says is that photons do not experience time, therefore their existence is just the present moment. You then liken this to our experience of the present?
“No man liveth more than that infinitesimal point of time that is the present”. Marcus Aurelius.
There certainly seems to be a strong feeling in the scientific community that we cannot say that photons don't experience time, don't let that put you off posting!
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The original question from flr: "Is space a mathematical relation or something real?" implied that these two things might be mutually exclusive.
That's not to say that it's easy to write a mathematical relation for the real, messy world - or that, having written an equation, that it will be easy to solve it. The Navier-Stokes equations can in theory be used to predict future weather, but chaotic systems like the weather require huge amounts of processing power, even when you simplify the equations significantly.
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Is space a mathematical relation or something real?
If you tell us what is your definition of "real" we could answer you according to that definition. Or are you asking which is the meaning of the word "real"?
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Einstein felt it didn't make sense to think of space in terms of anything except the fields within it. I think that, if space and time were 'things', they'd be conserved (like charge or momentum).
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Is space a mathematical relation or something real?
If you tell us what is your definition of "real" we could answer you according to that definition. Or are you asking which is the meaning of the word "real"?
For example: is space made of something of real existence or it is simply a mathematical relation between objects?
Is a real background scene in which things are located or it is just math relating things and nothing real .
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If it is a background stage that has real existence, why it is relative? What makes it such a morphing thing (due to relativity of lengths)?
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I don't think space is 'real', as there is nothing stopping you from adding more space to a space, filling it up, more than the geometry defining it, that is :) Take a bucket of nothing and then pour another bucket of nothing in it :) Will its geometry expand?
=
You could also imagine the opposite, use a really large hermetically closed container, open it in a vacuum, to take a bite of that vacuum. Then transport your bite elsewhere. Will the vacuum decrease? If it is 'real', as we define/expect stuff to exist macroscopically, then I just subtracted a portion of it, did I not? the argument aginst it would be that it already must contain a exact same portion of nothing, so I just exchanged a nothing, for a new nothing.. Ah well :)
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It depends on what you would mean by 'being real' of course. Pete's link is very interesting in the way it discuss, and use, light rays for defining a curvature to a space. A vacuum makes no sense, unless you have something to measure it by, and that should here be light (energy) and mass. We exist in this vacuum and it is related to mass and energy (and 'motion'). Geometry is very real, and defines that vacuum, or space, we find. But Lorentz contractions are also real, measurably so, in any experiment made in Cern.
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Take a bucket of nothing and then pour another bucket of nothing in it :) Will its geometry expand?
First of all, it is not possible to take a bucket of nothing. Nothing cannot be quantified in quantities such as '1 bucket', because as soon as we do that is became something.
Ignoring this, then 1 bucket of nothing + 1 bucket of nothing = 2 buckets of nothing is wrong. Correct would be:
1 bucket of nothing = 0 bucket of nothing (because is nothing there)
1 bucket of nothing + 1 bucket of nothing = 0 bucket of nothing + 0 bucket of nothing = 0 bucket of nothing
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Again, this only show that it is absurd to quantify in any way the "nothing" because as soon as we do that the "nothing" became "something".
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The distance from Earth to Moon is almost 1 light-second.
As well I can consider that the distance from Earth to Moon is 1 light-second plus one millions light-years of nothing. Ignoring that "millions light-years of nothing" may be logically incorrect then those "millions light-years of nothing" amounts to "nothing" (i.e. no thing et all) hence the distance from Earth to Moon remains 1 light-second.
If space would be "nothing" what keep things apart? There has to be "a thing" in been objects to keep them apart from each other otherwise they will all be on top of each other.
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Is potential energy a mathematical relation or something real? It's all relative too.
Even though there is not necessarily an absolute scale with a well-defined zero, I would argue that potential energy is pretty real. And even though, analogous to relativistic spacial warping, potential energies can be measured differently by observers in different frames of reference.
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The source of that potential must be something real. The potential is a mathematical representation of the effect of the source. The [generating] source must be real.
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Is potential energy a mathematical relation or something real? It's all relative too.
As JP indicated it's very difficult to say what should be called real and what shouldn't. Many physicists thing of energy as being "real" and that includes all its forms. That's because there is a physical phenomena which directly corresponds to the thing that we're describing using mathematics. In that sense potential energy is very real.
Even though there is not necessarily an absolute scale with a well-defined zero, I would argue that potential energy is pretty real. And even though, analogous to relativistic spacial warping, potential energies can be measured differently by observers in different frames of reference.
The thing that is of physical significance with potential energy is that only differences in it have any physical significance. It is in this sense as well that potential energy is real. You can't forget its meaning when you're asking if its real.
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If you tell us what is your definition of "real" we could answer you according to that definition. Or are you asking which is the meaning of the word "real"?
For example: is space made of something of real existence or it is simply a mathematical relation between objects?
Is a real background scene in which things are located or it is just math relating things and nothing real .
But you actually didn't answer my question, you only refrased it.
When you say "relation between objects" you mean that "objects" are real? And what is an "object" for you? A mathematic entity or something more? Does it have lenght, width, height?
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lightarrow
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And what is an "object" for you? A mathematic entity or something more? Does it have lenght, width, height?
This is a good question for him since the answer is not trivial. In geometry a "geometric object" is not something you'd imagine it to be. I've seen people in another forum, who thought they knew what they were talking about, rant about their disbelief regarding the definition because it didn't fit in with their pre-established idea about what a geometric object is. I sure got insulted that day, merely because someone was ignorant of a definition (it appeared in MTW the same way I explained it but they basically told me that MTW wasn't to be believed! LOL!!!!)
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For example: is space made of something of real existence or it is simply a mathematical relation between objects?
Is a real background scene in which things are located or it is just math relating things and nothing real .
But you actually didn't answer my question, you only refrased it.
When you say "relation between objects" you mean that "objects" are real? And what is an "object" for you? A mathematic entity or something more? Does it have lenght, width, height?
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lightarrow
By "objects" I meant real objects such as a cat or the Moon.
What is between me and the Moon to keep us apart by a well quantified quantity?
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For example: is space made of something of real existence or it is simply a mathematical relation between objects?
Is a real background scene in which things are located or it is just math relating things and nothing real .
But you actually didn't answer my question, you only refrased it.
When you say "relation between objects" you mean that "objects" are real? And what is an "object" for you? A mathematic entity or something more? Does it have lenght, width, height?
--
lightarrow
By "objects" I meant real objects such as a cat or the Moon.
What is between me and the Moon to keep us apart by a well quantified quantity?
What is between you and the moon? Space.
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What is between you and the moon? Space.
And what is that? What is space?
Has the debate on relational vs. container 'theory' of space been solved?
Does relativity of lengths imply relational 'theory' wins?
If so, how could it be that just a mathematical relation and not something of real existence in its own right keep me apart from the Moon?
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But you actually didn't answer my question, you only refrased it.
When you say "relation between objects" you mean that "objects" are real? And what is an "object" for you? A mathematic entity or something more? Does it have lenght, width, height?
By "objects" I meant real objects such as a cat or the Moon.
What is between me and the Moon to keep us apart by a well quantified quantity?
The same thing there is between two different points taken inside an object. If space weren't real, objects couldn't have lenght, width, height at all.
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And what is an "object" for you? A mathematic entity or something more? Does it have lenght, width, height?
This is a good question for him since the answer is not trivial. In geometry a "geometric object" is not something you'd imagine it to be. I've seen people in another forum, who thought they knew what they were talking about, rant about their disbelief regarding the definition because it didn't fit in with their pre-established idea about what a geometric object is. I sure got insulted that day, merely because someone was ignorant of a definition (it appeared in MTW the same way I explained it but they basically told me that MTW wasn't to be believed! LOL!!!!)
Can you talk a bit about it? What did they write?
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If space is not real, in what ever sense one chooses to define real, how is it possible to bend that which does not exist?
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Can you talk a bit about it? What did they write?
Absolutely, my friend. I'm not at home now so I'll have to do this off the cuff. I'll finish when I get hime.
In geometry a geometrical object is something with a set of components and defined according to how those components transform when transforming from one coordinate system to another. The people at the other forum thought that sounded more like a linear transformation than a geometric object. They seemed to have a predetermined idea of what such a thing would be and when it didn't meet their image they started to be jerks about it and started in with the derogatory remarks.
I talked about it here - http://www.thescienceforum.com/physics/36665-definitions.html