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From: Ste on 17 Feb 2010 12:39
On 17 Feb, 16:00, Paul Stowe <theaether...(a)gmail.com> wrote:
> On Feb 17, 7:04 am, Ste <ste_ro...(a)hotmail.com> wrote:
>
> > > As we discussed earlier, it may be that we are only AWARE of four
> > > dimensions. It may well be that there are more. Then the way to
> > > entertain this notion is to ask the question, how would something that
> > > is only AWARE of two dimensions become convinced that there is a third
> > > dimension? This turns out to be very answerable.
>
> > I'm afraid that was not my conclusion. As I've said, these
> > possibilities only seem credible to those who already hold them to be
> > credible.
>
> What I've seen here, and even in some books, is a vague improper use
> of the term dimension.  From what I can tell, the term is strictly as
> used, a mathematical concept.  See:
>
> http://mathworld.wolfram.com/Dimension.html
>
> It is often confused with the concept of physical properties such as
> mass, length, time, charge.  Since two of these (length and time) are
> modeled using geometrical dimensionality this leads to the confusion.
> Adding further to this is the unitary systems we assign to the
> physical properties (kilogram, meter, second, Coulomb, ... etc.).  A
> dimension has no physical existence and a physical property has no
> inherent unitary values, we must combine these concepts to make,
> quantify, and describe physical systems and processes.
>
> As time goes on we get more creative on assigning the term.  In
> relativity where we have,
>
>                         dx^2 + dy^2 + dz^2 - ds^2 = 0
>
> The s (ct) term isn't itself a simply point, it's a computed
> projection of a destination (point) dependent upon a physical
> property, the speed c.  To have strict orthogonal axes c must remain
> constant over infinite space.  In turn, if this were true, there would
> be no need for the hydrodynamical equation of General relativity.  In
> fact, all observational evidence to date supports the fact that, by
> strict definition of the term dimension only three primal or actual
> dimensions exist and time is 'mapped' into pseudo forth using the
> physical property of c to do so.

Indeed. Some people look at you funny when you talk of something like
a "five-dimensional database".

I'm convinced that the essential need for the 4th dimension in
relativity, and the significance of 'c', is simply because
electromagnetic propagation delays have become practically
significant. Before the end of the 19th century and the development of
electromagnetic communications over long distances, electromagnetic
effects for all practical purposes moved instantaneously.
From: PD on 17 Feb 2010 12:41
On Feb 17, 9:03 am, kenseto <kens...(a)erinet.com> wrote:
> On Feb 16, 6:42 pm, "Inertial" <relativ...(a)rest.com> wrote:
>
>
>
> > "PD" <thedraperfam...(a)gmail.com> wrote in message
>
> >news:da09c070-e346-42f6-a55f-cabf519d20dc(a)k36g2000prb.googlegroups.com....
>
> > > On Feb 16, 5:17 pm, "Inertial" <relativ...(a)rest.com> wrote:
> > >> "PD" <thedraperfam...(a)gmail.com> wrote in message
>
> > >>news:995b34f4-be02-48bb-b9db-463e3437283a(a)j27g2000yqn.googlegroups.com...
>
> > >> > On Feb 16, 12:57 pm, kenseto <kens...(a)erinet.com> wrote:
> > >> >> On Feb 16, 1:46 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
> > >> >> > Picking and choosing your definitions, Ken?
> > >> >> > Look at the definitions I highlighted for you.
> > >> >> > Look at your freshman physics textbook. Does it tell you that the
> > >> >> > electric field is not physical?
>
> > >> >> In the past you insisted that length contraction in SR is physical and
> > >> >> at that time you think that physical means material.
>
> > >> > No, sir, I *never* said length contraction was material. I said it was
> > >> > PHYSICAL.
>
> > >> >> You even
> > >> >> suggested that length contraction can be measured directly by shooting
> > >> >> lasers from the ends of a moving ruler to the rest frame of the
> > >> >> observer.
>
> > >> > Yes, it is MEASURABLE. Physical things are measurable.
> > >> > Energy is MEASURABLE, it is not material.
> > >> > Magnetic fields are MEASURABLE, they are not material.
> > >> > Radio waves are MEASURABLE, they are not material.
>
> > >> >> So you see you think that length contraction in SR is
> > >> >> material.
>
> > >> > No, it is MEASURABLE. It is not material.
>
> > >> >> Also your SR brother Inertial said in this thread that contraction in
> > >> >> SR means that the atoms get closer....this means material contraction.
>
> > >> > Ken, rather than desperately trying to gather excuses to support your
> > >> > mistaken impression, why don't you just take another look at the
> > >> > correct definitions for physical that I've already shown you? Why
> > >> > don't you reread your freshman physics text again, and check whether
> > >> > it says the electric field is not physical? If you've made a small
> > >> > mistake, then CORRECT IT and move on. If you cannot ever correct a
> > >> > small mistake, you'll never get out of square one. You'll spend all
> > >> > your time searching newsgroups for support for your mistake.
>
> > >> Note that the atoms in a length-contracted rod are physically closer
> > >> together, as measured in the relatively moving inertial frame.  In that
> > >> frame the material that makes up the rod is fitting within a shorter
> > >> distance (ie compressed).
>
> > > Well, I know what you're saying, but I'd be very careful about
> > > terminology here to avoid confusion. Seto thinks of compression as
> > > being solely the effect of a material interaction, such as a
> > > compressive *force* or perhaps a low temperature bath. That's not
> > > what's going on here. So yes, the pole is shorter and since no atoms
> > > have been lost, then the atoms have a different length, but this does
> > > not imply anything squeezing on them (even if Seto can't imagine it
> > > happening any other way).
>
> > I didn't say they were squeezed .. I said they were closer together.
>
> You didn't say that they were squeezed and I didn't interpret that
> they were squeezed.

Well, Ken, you DID say that the ONLY way for something to be
materially shorter is if it is compressed with a force or cooled.

> But when you said that the atoms are closer
> together I interpreted that the pole is materially really gotten
> shorter...iow it is not just a geometic projection effect.
>
> Ken Seto
>
>
>
> > But yes .. it depends on whether one assumes something being compressed
> > implies that there is some external agent compressing it or not.  In this
> > case there isn't an agent .. its just a result of the rotation.  Just like a
> > tilted ladder has a shorter height even though nothing has squeezed it.
>
> > >> However, the intrinsic/proper/rest length of the rod is unchanged, and
> > >> the
> > >> intrinsic/proper/rest distance between the atoms of its material are
> > >> unchanged.
>
> > > The rest length of the rod is unchanged. Since this rest length is the
> > > length measured in only one frame (the rest frame), I'm reticent to
> > > call it an intrinsic property.
>
> > Perhaps more to the point, the frame-dependent length (spatial distance
> > betwen end points at a given time) and the invariant length both correspond
> > in the frame when the object is at rest.  So the invariant length and rest
> > length are always the same value.
>
> > >> So whether of not it's 'materially' compressed (meaning the atoms of the
> > >> material of which it is made are closer together) depends on whether you
> > >> are
> > >> talking about the frame dependent view of the material or the invariant
> > >> view.  Which, when you say it, is bleedingly obvious.
>
> > >> Also note that just because the contraction is MODELLED by a geometrical
> > >> rotation does not mean it there is nothing 'physical' going on wrt
> > >> frame-dependent measurement (which is the sort of measurement we work
> > >> with
> > >> every day, and that makes sense).
>
> > >> It all comes down to whether you are referring to frame dependent or
> > >> invariant measures.  In the pole and barn scenario, when one says "in the
> > >> frame of the barn", that implies we are talking about frame-dependant
> > >> values
> > >> .. and 'length contraction' means the frame-dependent length of the pole
> > >> is
> > >> shorter, and in a frame-dependent view of the pole, the atoms that make
> > >> up
> > >> its material are closer together.-
>
> > > Yes,
>
> > > Seto suffers from a false dichotomy.
>
> > Indeed .. among other things.
>
> > > If there is a change in length,
> > > he believes this can be the result of only two possibilities: a
> > > material interaction that causes a stress in the body; or an optical
> > > illusion.
>
> > > It is neither. He doesn't understand the third possibility.
>
> > Indeed again :):)- Hide quoted text -
>
> > - Show quoted text -- Hide quoted text -
>
> > - Show quoted text -

From: Paul Stowe on 17 Feb 2010 12:42
On Feb 17, 9:16 am, mpalenik <markpale...(a)gmail.com> wrote:
> On Feb 17, 11:00 am, Paul Stowe <theaether...(a)gmail.com> wrote:
>
>
>
>
>
> > On Feb 17, 7:04 am, Ste <ste_ro...(a)hotmail.com> wrote:
>
> > > On 16 Feb, 15:53, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > On Feb 16, 6:59 am, Ste <ste_ro...(a)hotmail.com> wrote:
>
> > > > > No we don't perceive a 3D world. We perceive a 4D world, and have done
> > > > > since the beginning of time (as it were). That's what I'm saying to
> > > > > you: the real world existed long before geometry. And geometry is just
> > > > > a mathematical formalisation of basic concepts that were already
> > > > > physically obvious to anyone who ever considered the issue.
>
> > > > You are quite right! But it turns out we've made some erroneous
> > > > presuppositions about that 4D world. In fact, the presupposition we
> > > > had has a fairly tight specification. We had the notion that the
> > > > universe was structured as what's called a "fiber bundle" (it's a
> > > > mathematical term), with 3 spatial dimensions and an *independent*
> > > > time dimension. This expresses itself in certain ways. For example,
> > > > two observers in relative motion can label coordinates in 3 spatial
> > > > and 1 time dimensions in several possible ways, and it's possible to
> > > > make diagrams that show those relationships. One possible way is the
> > > > "fiber bundle" way that says that the distance between two events in
> > > > space and time (x^2 + y^2 + z^2) will be the same for both observers,
> > > > and this can be traced to the *independence* of the time dimension.
>
> > > Has time ever really been considered "independent"? It seems to me
> > > that much of this "relativity of simultaneity" can be constructed with
> > > reference only to acoustic phenomena.
>
> > > > > > Let's try it this way: what about the picture I drew for you do you
> > > > > > not think could represent physical reality?
>
> > > > > I never said it didn't *represent* physical reality, at least in some
> > > > > way. But my ability to understand requires me to translate that
> > > > > representation into something physical and concrete.
>
> > > > You'll find that this chaining of representations to objects that you
> > > > are already familiar with prevents you from discovering much that is
> > > > wholly new and unfamiliar.
>
> > > As I've said before, I disagree that we ever see anything that is
> > > totally "new and unfamiliar".
>
> > > > > But there is no such thing as a two-dimensional "flatland" in reality.
> > > > > This is much like saying "imagine a place that is not real with people
> > > > > who are not real, and imagine what reality would look like to those
> > > > > people" (which I can only say is unimaginable), and then using this as
> > > > > some sort of proof of a "hidden reality" that is not apparent to
> > > > > people who *are* real. As I say, the four dimensions have been with us
> > > > > since the beginning of time, and people have in one way or another
> > > > > recognised their physical existence since the beginning of time.
>
> > > > As we discussed earlier, it may be that we are only AWARE of four
> > > > dimensions. It may well be that there are more. Then the way to
> > > > entertain this notion is to ask the question, how would something that
> > > > is only AWARE of two dimensions become convinced that there is a third
> > > > dimension? This turns out to be very answerable.
>
> > > I'm afraid that was not my conclusion. As I've said, these
> > > possibilities only seem credible to those who already hold them to be
> > > credible.
>
> > What I've seen here, and even in some books, is a vague improper use
> > of the term dimension.  From what I can tell, the term is strictly as
> > used, a mathematical concept. See:
>
> >http://mathworld.wolfram.com/Dimension.html
>
> > It is often confused with the concept of physical properties such as
> > mass, length, time, charge.  Since two of these (length and time) are
> > modeled using geometrical dimensionality this leads to the confusion.
> > Adding further to this is the unitary systems we assign to the
> > physical properties (kilogram, meter, second, Coulomb, ... etc.).  A
> > dimension has no physical existence and a physical property has no
> > inherent unitary values, we must combine these concepts to make,
> > quantify, and describe physical systems and processes.
>
> > As time goes on we get more creative on assigning the term.  In
> > relativity where we have,
>
> >                         dx^2 + dy^2 + dz^2 - ds^2 = 0
>
> I'm not even going to get into what's wrong with the preceeding
> paragraphs.  Someone else can correct you on that.
>
> I do want to point out, though,  dx^2 + dy^2 + dz^2 - ds^2 = 0 is what
> you have in regular geometry.  ds^2 is a length element squared.  This
> is nothing more than restating:
> dx^2 + dy^2 + dz^2 = ds^2 in a different way.
>
> The path that light travels along can be shown to be:
> dx^2 + dy^2 + dz^2 - dt^2 = 0
>
> but in general, we have
>
> dx^2 + dy^2 + dz^2 - dt^2 = ds^2

Yes, indeed... s is the 'vector length' and x,y,z the orthogonal
displacements in some arbitrarily selected coordinate system.
However, it is specifically the modeling in relativity that adds this
to the LHS as another pseudo orthogonal displacement. You are right,
if written as you prescribe above where s is simply the an actual
displacement vector length in 3-space assigning no special
significance to ct (it just the upper bound due to a physical) you get
back three physical primal 'dimensions'. Then time isn't a dimension,
it is simply another physical property like mass or charge.
From: mpalenik on 17 Feb 2010 12:42
On Feb 17, 12:39 pm, Ste <ste_ro...(a)hotmail.com> wrote:
> On 17 Feb, 16:00, Paul Stowe <theaether...(a)gmail.com> wrote:
>
>
>
> > On Feb 17, 7:04 am, Ste <ste_ro...(a)hotmail.com> wrote:
>
> > > > As we discussed earlier, it may be that we are only AWARE of four
> > > > dimensions. It may well be that there are more. Then the way to
> > > > entertain this notion is to ask the question, how would something that
> > > > is only AWARE of two dimensions become convinced that there is a third
> > > > dimension? This turns out to be very answerable.
>
> > > I'm afraid that was not my conclusion. As I've said, these
> > > possibilities only seem credible to those who already hold them to be
> > > credible.
>
> > What I've seen here, and even in some books, is a vague improper use
> > of the term dimension.  From what I can tell, the term is strictly as
> > used, a mathematical concept.  See:
>
> >http://mathworld.wolfram.com/Dimension.html
>
> > It is often confused with the concept of physical properties such as
> > mass, length, time, charge.  Since two of these (length and time) are
> > modeled using geometrical dimensionality this leads to the confusion.
> > Adding further to this is the unitary systems we assign to the
> > physical properties (kilogram, meter, second, Coulomb, ... etc.).  A
> > dimension has no physical existence and a physical property has no
> > inherent unitary values, we must combine these concepts to make,
> > quantify, and describe physical systems and processes.
>
> > As time goes on we get more creative on assigning the term.  In
> > relativity where we have,
>
> >                         dx^2 + dy^2 + dz^2 - ds^2 = 0
>
> > The s (ct) term isn't itself a simply point, it's a computed
> > projection of a destination (point) dependent upon a physical
> > property, the speed c.  To have strict orthogonal axes c must remain
> > constant over infinite space.  In turn, if this were true, there would
> > be no need for the hydrodynamical equation of General relativity.  In
> > fact, all observational evidence to date supports the fact that, by
> > strict definition of the term dimension only three primal or actual
> > dimensions exist and time is 'mapped' into pseudo forth using the
> > physical property of c to do so.
>
> Indeed. Some people look at you funny when you talk of something like
> a "five-dimensional database".
>
> I'm convinced that the essential need for the 4th dimension in
> relativity, and the significance of 'c', is simply because
> electromagnetic propagation delays have become practically
> significant. Before the end of the 19th century and the development of
> electromagnetic communications over long distances, electromagnetic
> effects for all practical purposes moved instantaneously.

Everybody knew that light traveled at a finite speed long before
relativity. Relativity is not merely a theory that says "light
travels at a finite speed. You need to account for that." Everybody
already knew that and already knew how to do that. From observing the
moons of Jupiter hundreds of years earlier, people could tell that
light traveled with a finite speed. I thought we had gotten past this.
From: mpalenik on 17 Feb 2010 12:43
On Feb 17, 12:42 pm, Paul Stowe <theaether...(a)gmail.com> wrote:
> On Feb 17, 9:16 am, mpalenik <markpale...(a)gmail.com> wrote:
>
>
>
> > On Feb 17, 11:00 am, Paul Stowe <theaether...(a)gmail.com> wrote:
>
> > > On Feb 17, 7:04 am, Ste <ste_ro...(a)hotmail.com> wrote:
>
> > > > On 16 Feb, 15:53, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > > On Feb 16, 6:59 am, Ste <ste_ro...(a)hotmail.com> wrote:
>
> > > > > > No we don't perceive a 3D world. We perceive a 4D world, and have done
> > > > > > since the beginning of time (as it were). That's what I'm saying to
> > > > > > you: the real world existed long before geometry. And geometry is just
> > > > > > a mathematical formalisation of basic concepts that were already
> > > > > > physically obvious to anyone who ever considered the issue.
>
> > > > > You are quite right! But it turns out we've made some erroneous
> > > > > presuppositions about that 4D world. In fact, the presupposition we
> > > > > had has a fairly tight specification. We had the notion that the
> > > > > universe was structured as what's called a "fiber bundle" (it's a
> > > > > mathematical term), with 3 spatial dimensions and an *independent*
> > > > > time dimension. This expresses itself in certain ways. For example,
> > > > > two observers in relative motion can label coordinates in 3 spatial
> > > > > and 1 time dimensions in several possible ways, and it's possible to
> > > > > make diagrams that show those relationships. One possible way is the
> > > > > "fiber bundle" way that says that the distance between two events in
> > > > > space and time (x^2 + y^2 + z^2) will be the same for both observers,
> > > > > and this can be traced to the *independence* of the time dimension.
>
> > > > Has time ever really been considered "independent"? It seems to me
> > > > that much of this "relativity of simultaneity" can be constructed with
> > > > reference only to acoustic phenomena.
>
> > > > > > > Let's try it this way: what about the picture I drew for you do you
> > > > > > > not think could represent physical reality?
>
> > > > > > I never said it didn't *represent* physical reality, at least in some
> > > > > > way. But my ability to understand requires me to translate that
> > > > > > representation into something physical and concrete.
>
> > > > > You'll find that this chaining of representations to objects that you
> > > > > are already familiar with prevents you from discovering much that is
> > > > > wholly new and unfamiliar.
>
> > > > As I've said before, I disagree that we ever see anything that is
> > > > totally "new and unfamiliar".
>
> > > > > > But there is no such thing as a two-dimensional "flatland" in reality.
> > > > > > This is much like saying "imagine a place that is not real with people
> > > > > > who are not real, and imagine what reality would look like to those
> > > > > > people" (which I can only say is unimaginable), and then using this as
> > > > > > some sort of proof of a "hidden reality" that is not apparent to
> > > > > > people who *are* real. As I say, the four dimensions have been with us
> > > > > > since the beginning of time, and people have in one way or another
> > > > > > recognised their physical existence since the beginning of time..
>
> > > > > As we discussed earlier, it may be that we are only AWARE of four
> > > > > dimensions. It may well be that there are more. Then the way to
> > > > > entertain this notion is to ask the question, how would something that
> > > > > is only AWARE of two dimensions become convinced that there is a third
> > > > > dimension? This turns out to be very answerable.
>
> > > > I'm afraid that was not my conclusion. As I've said, these
> > > > possibilities only seem credible to those who already hold them to be
> > > > credible.
>
> > > What I've seen here, and even in some books, is a vague improper use
> > > of the term dimension.  From what I can tell, the term is strictly as
> > > used, a mathematical concept. See:
>
> > >http://mathworld.wolfram.com/Dimension.html
>
> > > It is often confused with the concept of physical properties such as
> > > mass, length, time, charge.  Since two of these (length and time) are
> > > modeled using geometrical dimensionality this leads to the confusion.
> > > Adding further to this is the unitary systems we assign to the
> > > physical properties (kilogram, meter, second, Coulomb, ... etc.).  A
> > > dimension has no physical existence and a physical property has no
> > > inherent unitary values, we must combine these concepts to make,
> > > quantify, and describe physical systems and processes.
>
> > > As time goes on we get more creative on assigning the term.  In
> > > relativity where we have,
>
> > >                         dx^2 + dy^2 + dz^2 - ds^2 = 0
>
> > I'm not even going to get into what's wrong with the preceeding
> > paragraphs.  Someone else can correct you on that.
>
> > I do want to point out, though,  dx^2 + dy^2 + dz^2 - ds^2 = 0 is what
> > you have in regular geometry.  ds^2 is a length element squared.  This
> > is nothing more than restating:
> > dx^2 + dy^2 + dz^2 = ds^2 in a different way.
>
> > The path that light travels along can be shown to be:
> > dx^2 + dy^2 + dz^2 - dt^2 = 0
>
> > but in general, we have
>
> > dx^2 + dy^2 + dz^2 - dt^2 = ds^2
>
> Yes, indeed...  s is the 'vector length' and x,y,z the orthogonal
> displacements in some arbitrarily selected coordinate system.
> However, it is specifically the modeling in relativity that adds this
> to the LHS as another pseudo orthogonal displacement.  You are right,
> if written as you prescribe above where s is simply the an actual
> displacement vector length in 3-space assigning no special
> significance to ct (it just the upper bound due to a physical) you get
> back three physical primal 'dimensions'.  Then time isn't a dimension,
> it is simply another physical property like mass or charge.

My point is you wrote the equation for the length of a 3 dimensional
vector. You did not write the expression for the invariant 4-length.
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