What is "spacetime" really?

[lawcat]

no practical purposes?

am i to believe that the employment of higher dimensions in our equations are just a whim? and were not solutions that reflect to the physical behaviors on our scientific experiments?

 

Yes. Higher dimensions have a redundant meaning, other than their parametric value in describing the object of interest. For example, you can chose to say that 5th dimension is density. But density can be described as mass per unit volume, and volume is eucledian. In addition, mass can be described as concentration of particles per unit volume. Then, again, you end up with x,y,z --- which is eucleadian; and some parametric number n representing concentration in x,y,z.

[watcher]

Yes. Higher dimensions have a redundant meaning, other than their parametric value in describing the object of interest. For example, you can chose to say that 5th dimension is density. But density can be described as mass per unit volume, and volume is eucledian.

 

iow, a curved eulidiean space or the presence of varying densities in points of space is equivalent or have the same meaning that space is actually hyperspace. you see. they are interchangeable.

 

so when you say choose, it is a matter of preference but they are saying the same thing. curved space is hyperspace.

[lawcat]

Yeah, but that is nothing more than saying: Because I observe mass, therefore I must assign value to that mass.

 

Look, if angle between x,y,z is not orthogonal, and approaches zero; then, you will have infinately many axis. The only practically usefull set of combination of axis will be the set which includes only 3 orthogonal axis, the number of which will also approach infinity; in the range of infinately many axis related by angles approaching 0. (if you rotate x along y, or z, or some combination of yz; you can draw infinately many x along the pie in z, or y, or yz directions.)

 

If there is infinately many combination of 3-axis orthogonal spaces that can be decribed, then, there are infinately many frames.

 

Notice that, if you move x in the -y, then vector r can be decribe as +r, and the angle of shift as -theta; Conversely, if you move along +y, then r is negative and theta is positive. This is what is meant by symmetry on which everything rests.

 

If we introduce time, then everything moves; then all 3-axis orthogonal frames move. Object can move linearly, or angularly. If object moves only angularly we say it is at rest compared to the only-linearly moving object.

 

If the object moves a little less angularly and picks up linear movement, then we do not say that the object is at rest; the differenc between linear movement of the object compared to only-linearly moving object is smaller.

 

It is all in the changes in vector r, and angles theta, compared to the frame of reference. Time is just a measure in change between linear and angular position, and position can sufficiently be decribed in terms of r and theta; which are functions of eucledian orthogonal space.

[Michael Mooney]

The article lists three possibilities. Throughout this thread you have consistently rejected the possibility of the third. The article doesn't do that. You clearly need to reassess your assumption that the universe must be Euclidean.

 

I don't know what else there is to say.

 

~modest

The third possibility is not only obvious in the list of three but generally accepted as so well established by the mainstream that you once claimed that everyone knows that Euclidean was left behind over a hundred years ago... an obsolete basis for cosmology. And much of the article is in praise of Einstein's application of non-Euclidean, as you have already pointed out. Yet it graciously points out that, ontologically, Euclidean is not dead yet.

 

Then you asked my how I could possibly cite this essay in support of a possibility for the re- legitimization of Euclidean space/cosmology.

 

The above is how. The article does not deal a death blow to Euclid. Almost all the champions of relativity in this forum accept non-Euclidean space, and "spacetime" as a given... including Tormod in his original page one reply. So I think option three has had more than a fair hearing. It totllaly dominates the field... Which makes your accusation above completely ridiculous.

 

Yes, mine is a minority voice. I have been "assessing my position" ever since non-Euclidean space was introduced in my early education. You continue to assume otherwise.

You have no tolerance whatsoever for a minority view of space/cosmology or any disagreement with the mainstream dogma of spacetime as concieved from non-Euclidean perspective.

 

I don't know what else there is to say either.

 

Michael

[watcher]

Look, if angle between x,y,z is not orthogonal, and approaches zero; then, you will have infinately many axis. The only practically usefull set of combination of axis will be the set which includes only 3 orthogonal axis, the number of which will also approach infinity; in the range of infinately many axis related by angles approaching 0. (if you rotate x along y, or z, or some combination of yz; you can draw infinately many x along the pie in z, or y, or yz directions.)

 

If there is infinately many combination of 3-axis orthogonal spaces that can be decribed, then, there are infinately many frames.

 

Notice that, if you move x in the -y, then vector r can be decribe as +r, and the angle of shift as -theta; Conversely, if you move along +y, then r is negative and theta is positive. This is what is meant by symmetry on which everything rests.

 

If we introduce time, then everything moves; then all 3-axis orthogonal frames move. Object can move linearly, or angularly. If object moves only angularly we say it is at rest compared to the only-linearly moving object.

 

If the object moves a little less angularly and picks up linear movement, then we do not say that the object is at rest; the differenc between linear movement of the object compared to only-linearly moving object is smaller.

 

It is all in the changes in vector r, and angles theta, compared to the frame of reference. Time is just a measure in change between linear and angular position, and position can sufficiently be decribed in terms of r and theta; which are functions of eucledian orthogonal space.

 

well, it so whimsical to me that you make it sound like magnitudes and directions only exists in our heads. :shrug:

 

magnitudes, directions, time and infinities in euclidean coordinates are properties that correspond to the real world.

 

Yeah, but that is nothing more than saying: Because I observe mass, therefore I must assign value to that mass.

 

no, our observation does not arbitrarily assign/give value to objects.

the value is intrinsic to the object that we see. our perception does not define objects, we simply see its definition.

[lawcat]

The "just because we can't see it does not mean it is not there" is a religious argument, that has been condemned on these boards so much. Yet, people keep on bringing 5+ dimensions. Where the heck is it, and what physical phenomena supports 7 dimensions?

[modest]

Folks, please keep discussion on topic. Minkowski spacetime and spacetime in GR have 3 spatial dimensions and 1 time dimension.

 

~modest

[maddog]

The third possibility is not only obvious in the list of three but generally accepted as so well established by the mainstream that you once claimed that everyone knows that Euclidean was left behind over a hundred years ago... an obsolete basis for cosmology. And much of the article is in praise of Einstein's application of non-Euclidean, as you have already pointed out. Yet it graciously points out that, ontologically, Euclidean is not dead yet.

Non-Euclidean Geometry does NOT replace Euclidean Geometry !!! #$% Non-Euclidean

Extends Euclidean Geometry, add-to, expands. This is an inclusive concept not exclusive. :confused:

Then you asked my how I could possibly cite this essay in support of a possibility for the re- legitimization of Euclidean space/cosmology.

 

The above is how. The article does not deal a death blow to Euclid. Almost all the champions of relativity in this forum accept non-Euclidean space, and "spacetime" as a given... including Tormod in his original page one reply. So I think option three has had more than a fair hearing. It totllaly dominates the field... Which makes your accusation above completely ridiculous.

Accept what proves useful When it proves useful and only so far as its utility. The paper/website you cite makes no attempt to "deal a death blow" to either Euclidean nor

Non-Euclidean. From what I read, it makes a good presentation of the thinking process.

 

maddog

[arkain101]

The "just because we can't see it does not mean it is not there" is a religious argument, that has been condemned on these boards so much. Yet, people keep on bringing 5+ dimensions. Where the heck is it, and what physical phenomena supports 7 dimensions?

 

I hear what you are saying. Especially by adding more spacial dimensions. I get bothered when I hear people speak of dimensions like other types of universes. Dimensions are not locations, they are measurements of a location. If we use that word for something different than a measurment of a location, we should not use that word!

 

Recently, I was watching a tv show on hawking that sparked some imaginations for me. When we take our 3 dimensions down into the quantum world, they start failing to measure.

 

I thought, the quantum world like an atom with this 'core' and its 'electron' can be thought of like a very thin circular curtain miles away from a small cruched up tissue. And the reason for thinking of it like this is to help abandon the idea of typical stuff.

 

Imagine the curtain rippling in the wind, and the tissue actually being a liquid tissue, that flows into many different forms of crunched up states.

 

This stuff, at this subatomic level is not stuff, we have to abandon what we know and think as material stuff. It is more like a musical morphing of infinity repeatedly becoming the most efficient "shape" possible in a 3 dimensional space, but it can not be measured, not entirely like a big cube on a table that is a form of stuff (mental stuff, words, color, feelings), we can't even measure these tissues entirely with 4 dimensions, or even 5... I really don't know much about these extra dimensional methods of measurement, but I assume they only extend our attempt to measure the currently immeasurable Gremlins of efficiency (the quantum liquid tissues)

 

So when we start asking Where oh Where are these extra dimensions. We should begin first by wondering A) what is the universe made of? And when we have an answer that suffices(?) Then, b)What is a dimension relative to the quantum world?

 

I think what we will find is that everything that exists is both "something that is not there even though we can see it", and at the same time:"just because we can't see it does not mean it is not there"

[arkain101]

I should add that I dont suggest this as any form of an explanation, but rather as a starting point in the right direction related directly to this question,

Where the heck is it?

as based upon my insight of which actually greatly lacks in formal/literal mathematics, so take from that what you will... :hyper:

 

I really know very little detail at the level of insight you have lawcat on these matters so I can't gauge a response to meet as close as possible to your boundaries.

[watcher]

the other dimensions is where the particle disappeared into during it's jump prior to its appearance in its next location..

the place where it tunnels to avoid the emf barrier

 

the question is not where it is, but what lies beneath?

[Michael Mooney]

=

maddog;264715]Non-Euclidean Geometry does NOT replace Euclidean Geometry !!! #$% Non-Euclidean

Extends Euclidean Geometry, add-to, expands. This is an inclusive concept not exclusive. ;)

 

Here is a blast from the past... an exchange between Modest and myself from post 130, p. 13:

Me:

Space: You deny the "objective" measure of distance from earth to sun... well known to be around 93 million miles or 8+ light minutes.

Modest:

I don't mean this as a criticism, but you appear not to understand the most basic concepts of relativity. If you don't understand why there is no absolute distance between the earth and sun then how can you object to the distance being relative?

 

Me:

You seem obsessed with local perspectives, including the "thought experiment" as though a photon "experiences" no time or space in its journey between the two bodies. You refuse to even consider that space might indeed be emptiness, the the actual distance between things, in linear mode, i.e., not subject to curvature. You seem brainwashed by relativity theory, to the extent that you can not or will not even consider for a moment the possibility that what I have said above is true.

Modest:

Your claim has been considered by everyone. It was the default scientific position until 100 years ago. It has been argued on this forum by scores of people. It is called Galilean invariance or absolute Newtonian space, and it has been proven wrong experimentally. No one is failing to grasp what you're saying, we simply know it is wrong.

 

The Euclidean vs non-Euclidean debate has been on here for a very long time. So non-Euclidean "adds" curved space and dilated time and the miracle fabric "spacetime" and renders objective (Euclidean based) distance "all relative"... etc.

 

It is useless to keep re-hashing all of the above.

The take-off point for the whole non-Euclidean paradigm is mentally forcing two parallel lines to converge in "curved space"... which, from the git-go *reifies space* into being "something" rather than the empty volume in which 'things" exist (and have shape, movement, etc.

You don't seem to grasp this most basic issue but rather make the ubiquitous assumption (which now dominates cosmology) that non-Euclidean space/cosmology is too well established to even question... for over 100 years now... as Modest claims above.

 

I beg to difffer... and I ain't much good at beggin'!;)

 

Michael

[Boerseun]

It is useless to keep re-hashing all of the above.

Seems like it! It obviously has absolutely no effect.

 

Oh well, we tried. :shrug:

[maddog]

The Euclidean vs non-Euclidean debate has been on here for a very long time. So non-Euclidean "adds" curved space and dilated time and the miracle fabric "spacetime" and renders objective (Euclidean based) distance "all relative"... etc.

Debate. Where's the debate. For any field of study be it math or otherwise: that which

is and that which is not are two sides of the same coin!! :naughty: :eek_big: Be it Euclidean Geometry

or anything else. So the only argument here is you pointlessly ranting about something

which is Not even a problem.... #$%& These are two branches of Mathematics both valid

for what they do. Your attempts at bashing one is like claiming Flat Earth is obviously

the better description of the Earth because it make sense to you. :lol: :eek: :naughty:

It is useless to keep re-hashing all of the above.

I agree. So stop it!

The take-off point for the whole non-Euclidean paradigm is mentally forcing two parallel lines to converge in "curved space"... which, from the git-go *reifies space* into being "something" rather than the empty volume in which 'things" exist (and have shape, movement, etc.

This is silly. One paradigm often cannot grasp the fundamental concepts of another

paradigm until a "shift" occurs. In you this paradigm shift process must be broken!

You don't seem to grasp this most basic issue but rather make the ubiquitous assumption (which now dominates cosmology) that non-Euclidean space/cosmology is too well established to even question... for over 100 years now... as Modest claims above.

This post is irrelevant to Cosmology and is based solely upon Differential Geometry.

In the "general" sense the "curvature" of a space can be calculated. In the case of

Euclidean Geometry the curvature value [imath]k = 0[/imath] (often called Kappa).

Yes, the essence of Differential Geometry has been around over 100 years.

I beg to difffer... and I ain't much good at beggin'!;)

"Sad but true". - [Metallica]

 

maddog

[Michael Mooney]

Non-Euclidean space makes something out of nothing.

What "curves" besides the trajectories of masses and light as effected by the pull of gravity?

The curved trajectory of light as distorted from straight by gravity does not mean that the light is really going in a straight line and "space itself" is curved by gravity. A fundamental but false assumption of non-Euclidean space and the basis for reified "spacetime."

The assumption under which "curved space" was *invented* is that gravity requires a medium of some sort through which to propagate. When "aether" was discarded, the equally creative fabric "spacetime" was invented.

Objects have shape. Space is empty volume, except where it is occupied by objects. Space does not "have shape."

 

And, yup, it "takes time" for everything to happen... a vital part of velocity too as distance traveled per whatever units of time. Yet the present tense is perpetually ongoing... everywhere.

 

But every time we say that a car is speeding up from 50 to 60 miles an hour the time factor itself is not a thing that speeds up or slows down. The car does that. ("Time dilation" is a reification of "time" based on clocks running faster or slower under different conditions. )

 

Oh... btw... the distance between sun and planets varies with the irregularities of their orbits, but any website on the solar system will give the same "objective" distances... They do not vary with various relative observer perspectives, velocities, etc. The claim that these distance vary with observer relativity is just plain nonsense.

 

This is a wrap.

Michael

[freeztar]

Non-Euclidean space makes something out of nothing.

What "curves" besides the trajectories of masses and light as effected by the pull of gravity?

The curved trajectory of light as distorted from straight by gravity does not mean that the light is really going in a straight line and "space itself" is curved by gravity. A fundamental but false assumption of non-Euclidean space and the basis for reified "spacetime."

The assumption under which "curved space" was *invented* is that gravity requires a medium of some sort through which to propagate. When "aether" was discarded, the equally creative fabric "spacetime" was invented.

Objects have shape. Space is empty volume, except where it is occupied by objects. Space does not "have shape."

 

And, yup, it "takes time" for everything to happen... a vital part of velocity too as distance traveled per whatever units of time. Yet the present tense is perpetually ongoing... everywhere.

 

But every time we say that a car is speeding up from 50 to 60 miles an hour the time factor itself is not a thing that speeds up or slows down. The car does that. ("Time dilation" is a reification of "time" based on clocks running faster or slower under different conditions. )

I'm with you up to this point...

Oh... btw... the distance between sun and planets varies with the irregularities of their orbits, but any website on the solar system will give the same "objective" distances... They do not vary with various relative observer perspectives, velocities, etc. The claim that these distance vary with observer relativity is just plain nonsense.

:smilingsun:

How can you go from a position that claims to understand relativity and does not denounce it...to this?

 

Your claim only makes sense for someone stationed on Earth. The star traveler flying at near light speed towards our solar system sees it quite differently. If you claim that they do not have the distances "correct", then you must be honest with yourself and admit that you (nor the textbooks) have it "correct".

 

I like your absolute now idea, but coupling this with absolute space and claiming that there is no variance is...ummm...completely and ridiculously wrong. This has been proven!

 

As others have stated, it's a bit antiquated and does not account for accurately observed effects.

 

If your position was something like:

 

"Something, or some property of light, creates the bending we see and attribute to "spacetime", but I do not think space can bend"

 

...then you might fare better than you are now. It seems you wish to do away with the "bending" as well as "spacetime". Why throw out the baby with the bathwater?

[Boerseun]

Right.

 

Michael, up to this point, you're basically saying that "space" is merely a reference frame in which stuff exist. Right?

 

As far as I can gather, you're saying that "space" is the xyz reference frame in which everything exist, and is not affected by mass distribution, velocity of individual observers, etc. Right?

 

As far as I can gather, there is no "border" or "limit" or "edge" of any kind to your "space", which is merely a coordination framework imposed on an infinite and eternal empty vacuum - right?

 

You're saying that space itself is nothing, space can't be bent or warped or be affected in any way by the happenings of anything contained within it? Right?

 

A few simple yes/no answer will suffice - I just want to make sure we're on the same page, here.