infinite pill-shaped universe?

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Date: 09 Oct 2006 12:50:45
From: Liam
Subject: infinite pill-shaped universe?

Just found this CNN article where measured cosmic radioactivity seems
to indicate the universe is pill-shaped:
http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html

Now, I've just come to grips with the concept of the universe being
infinite and expanding out of a Big...Expanding like "raisin bread" or
an infinitely thick skin of a balloon.

Now this pill-shaped thing? I can't reconcile this in my mind.

Could someone help me understand how both of these can be true, or
whether one theory undermines the other?

Thanks!
Liam

Date: 09 Oct 2006 21:24:40
From: Double-A
Subject: Re: infinite pill-shaped universe?

honestjohn wrote:
> "Double-A" <double-aa@hush.ai> wrote in message
> news:1160437806.971802.241500@i42g2000cwa.googlegroups.com...
> >
> > Brian Tung wrote:
> > > Double-A wrote:
> > > > The universe cannot have both come out of the Big Bang and be
> infinite.
> > > > It has to be one or the other.
> > >
> > > It can be both with little trouble at all. Let's drop down a couple of
> > > dimensions, to make it easier to visualize.
> > >
> > > Suppose that there's a Big Bang that produces a circular universe. I
> > > don't mean a disc, with a circular edge; I mean a circle, so that all of
> > > the galaxies that make up this universe lie along the "edge," so to
> > > speak. If you run back time, you can easily see that the circle can
> > > shrink indefinitely, until it becomes a point right at the Big Bang.
> > >
> > > OK so far? Now, of course, such a universe isn't infinite; a circle has
> > > a well-defined and finite length. So what I'm going to do is to replace
> > > that circle by an infinite slinky. It's now that infinite slinky that
> > > we run backward into time, so that it becomes a point right at the Big
> > > Bang.
> > >
> > > Impossible, you say? The only things that stop us are that there are no
> > > infinite slinkies, and that slinkies have depth; they're not perfectly
> > > flat. But neither of these things are problems in *principle*. We can
> > > imagine an infinitely long slinky, even if we can't produce one in
> > > actuality. And in principle, if a slinky is truly one-dimensional, it
> > > has no thickness at all. That means that you can coil one up as long as
> > > you like--infinitely long, even--and it will never gain any depth. It
> > > will look just like a circle, except that it's not actually closed; if
> > > you move along the slinky universe, you never get back to your starting
> > > point unless you turn back and go the other way.
> > >
> > > Pump things up a couple of dimensions, and you have a universe that can
> > > expand out of a Big Bang and be infinite the whole time. (Actually,
> > > "flatten out" is probably a more accurate term than "expand out.")
> > >
> > > --
> > > Brian Tung <brian@isi.edu>
> > > The Astronomy Corner at http://astro.isi.edu/
> > > Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
> > > The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
> > > My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html
> >
> >
> > If you want to invoke extra dimensions, I would agree with you.
> >
> > But as a three-dimensional construct, a universe that expanded out of a
> > finite size, must still be finite. Fact is, in spite of years of
> > endless speculation about extra dimensions none has yet been observed
> > or detected.
> >
> > Double-A
> >
> Mathematics of Physics only works out correctly when 11 dimensions are used.
> Go figure.
>
> C.H.J.

That's String Theory, another flight of fanciful speculation still
looking for any supporting evidence in the real world.

Double-A

Date: 09 Oct 2006 16:50:07
From: Double-A
Subject: Re: infinite pill-shaped universe?

Brian Tung wrote:
> Double-A wrote:
> > The universe cannot have both come out of the Big Bang and be infinite.
> > It has to be one or the other.
>
> It can be both with little trouble at all. Let's drop down a couple of
> dimensions, to make it easier to visualize.
>
> Suppose that there's a Big Bang that produces a circular universe. I
> don't mean a disc, with a circular edge; I mean a circle, so that all of
> the galaxies that make up this universe lie along the "edge," so to
> speak. If you run back time, you can easily see that the circle can
> shrink indefinitely, until it becomes a point right at the Big Bang.
>
> OK so far? Now, of course, such a universe isn't infinite; a circle has
> a well-defined and finite length. So what I'm going to do is to replace
> that circle by an infinite slinky. It's now that infinite slinky that
> we run backward into time, so that it becomes a point right at the Big
> Bang.
>
> Impossible, you say? The only things that stop us are that there are no
> infinite slinkies, and that slinkies have depth; they're not perfectly
> flat. But neither of these things are problems in *principle*. We can
> imagine an infinitely long slinky, even if we can't produce one in
> actuality. And in principle, if a slinky is truly one-dimensional, it
> has no thickness at all. That means that you can coil one up as long as
> you like--infinitely long, even--and it will never gain any depth. It
> will look just like a circle, except that it's not actually closed; if
> you move along the slinky universe, you never get back to your starting
> point unless you turn back and go the other way.
>
> Pump things up a couple of dimensions, and you have a universe that can
> expand out of a Big Bang and be infinite the whole time. (Actually,
> "flatten out" is probably a more accurate term than "expand out.")
>
> --
> Brian Tung <brian@isi.edu>
> The Astronomy Corner at http://astro.isi.edu/
> Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
> The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
> My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

If you want to invoke extra dimensions, I would agree with you.

But as a three-dimensional construct, a universe that expanded out of a
finite size, must still be finite. Fact is, in spite of years of
endless speculation about extra dimensions none has yet been observed
or detected.

Double-A

Date: 10 Oct 2006 04:41:52
From: Chris L Peterson
Subject: Re: infinite pill-shaped universe?

On 9 2006 16:50:07 -0700, "Double-A" <double-aa@hush.ai > wrote:

>If you want to invoke extra dimensions, I would agree with you.
>
>But as a three-dimensional construct, a universe that expanded out of a
>finite size, must still be finite. Fact is, in spite of years of
>endless speculation about extra dimensions none has yet been observed
>or detected.

Not so. There are many different sorts of independent observation that
support the idea that we live in at least a four dimensional universe.
If the Universe as we see it were a simple three dimensional structure
it would be at odds with what we observe.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

Date: 09 Oct 2006 22:24:13
From: honestjohn
Subject: Re: infinite pill-shaped universe?

"Double-A" <double-aa@hush.ai > wrote in message
news:1160437806.971802.241500@i42g2000cwa.googlegroups.com...
>
> Brian Tung wrote:
> > Double-A wrote:
> > > The universe cannot have both come out of the Big Bang and be
infinite.
> > > It has to be one or the other.
> >
> > It can be both with little trouble at all. Let's drop down a couple of
> > dimensions, to make it easier to visualize.
> >
> > Suppose that there's a Big Bang that produces a circular universe. I
> > don't mean a disc, with a circular edge; I mean a circle, so that all of
> > the galaxies that make up this universe lie along the "edge," so to
> > speak. If you run back time, you can easily see that the circle can
> > shrink indefinitely, until it becomes a point right at the Big Bang.
> >
> > OK so far? Now, of course, such a universe isn't infinite; a circle has
> > a well-defined and finite length. So what I'm going to do is to replace
> > that circle by an infinite slinky. It's now that infinite slinky that
> > we run backward into time, so that it becomes a point right at the Big
> > Bang.
> >
> > Impossible, you say? The only things that stop us are that there are no
> > infinite slinkies, and that slinkies have depth; they're not perfectly
> > flat. But neither of these things are problems in *principle*. We can
> > imagine an infinitely long slinky, even if we can't produce one in
> > actuality. And in principle, if a slinky is truly one-dimensional, it
> > has no thickness at all. That means that you can coil one up as long as
> > you like--infinitely long, even--and it will never gain any depth. It
> > will look just like a circle, except that it's not actually closed; if
> > you move along the slinky universe, you never get back to your starting
> > point unless you turn back and go the other way.
> >
> > Pump things up a couple of dimensions, and you have a universe that can
> > expand out of a Big Bang and be infinite the whole time. (Actually,
> > "flatten out" is probably a more accurate term than "expand out.")
> >
> > --
> > Brian Tung <brian@isi.edu>
> > The Astronomy Corner at http://astro.isi.edu/
> > Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
> > The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
> > My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html
>
>
> If you want to invoke extra dimensions, I would agree with you.
>
> But as a three-dimensional construct, a universe that expanded out of a
> finite size, must still be finite. Fact is, in spite of years of
> endless speculation about extra dimensions none has yet been observed
> or detected.
>
> Double-A
>
Mathematics of Physics only works out correctly when 11 dimensions are used.
Go figure.

C.H.J.

Date: 09 Oct 2006 15:18:50
From: Double-A
Subject: Re: infinite pill-shaped universe?

Dana wrote:
> "Double-A" <double-aa@hush.ai> wrote in message
> news:1160425623.105160.196070@m7g2000cwm.googlegroups.com...
> >
> > Liam wrote:
> > > Just found this CNN article where measured cosmic radioactivity seems
> > > to indicate the universe is pill-shaped:
> > > http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
> > >
> > > Now, I've just come to grips with the concept of the universe being
> > > infinite and expanding out of a Big...Expanding like "raisin bread" or
> > > an infinitely thick skin of a balloon.
> >
> >
> > The universe cannot have both come out of the Big Bang and be infinite.
> > It has to be one or the other.
>
> Why do you say this.

Was the universe infinite at one second after the Big Bang?

Double-A

Date: 09 Oct 2006 14:40:37
From: Dana
Subject: Re: infinite pill-shaped universe?

"Double-A" <double-aa@hush.ai > wrote in message
news:1160432330.054745.200620@i3g2000cwc.googlegroups.com...
>
> Dana wrote:
> > "Double-A" <double-aa@hush.ai> wrote in message
> > news:1160425623.105160.196070@m7g2000cwm.googlegroups.com...
> > >
> > > Liam wrote:
> > > > Just found this CNN article where measured cosmic radioactivity
seems
> > > > to indicate the universe is pill-shaped:
> > > > http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
> > > >
> > > > Now, I've just come to grips with the concept of the universe being
> > > > infinite and expanding out of a Big...Expanding like "raisin bread"
or
> > > > an infinitely thick skin of a balloon.
> > >
> > >
> > > The universe cannot have both come out of the Big Bang and be
infinite.
> > > It has to be one or the other.
> >
> > Why do you say this.
>
> Was the universe infinite at one second after the Big Bang?

OK, good point.

>
> Double-A
>

Date: 13 Oct 2006 14:20:02
From: George Dishman
Subject: Re: infinite pill-shaped universe?

"Dana" <raff242@yahoo.com > wrote in message
news:12iljt4nbg3cd@corp.supernews.com...
>
> "Double-A" <double-aa@hush.ai> wrote in message
> news:1160432330.054745.200620@i3g2000cwc.googlegroups.com...
>>
>> Dana wrote:
>> > "Double-A" <double-aa@hush.ai> wrote in message
>> > news:1160425623.105160.196070@m7g2000cwm.googlegroups.com...
...
>> > > The universe cannot have both come out of the Big Bang and be
>> > > infinite.
>> > > It has to be one or the other.
>> >
>> > Why do you say this.
>>
>> Was the universe infinite at one second after the Big Bang?
>
> OK, good point.

I don't know why you say that, the equations say it
was infinite at _all_ times if it is infinite now.
That is, it was never anything other than infinite.

"Double-A" seems to be making the common mistake of
thinking of the initial event as an explosion in
pre-existing space.

George

Date: 13 Oct 2006 08:47:04
From: richard schumacher
Subject: Re: infinite pill-shaped universe?

The universe is shaped like Brad Guth?

Date: 13 Oct 2006 22:32:23
From: Peter Webb
Subject: Re: infinite pill-shaped universe?

"Dana" <raff242@yahoo.com > wrote in message
news:12iljt4nbg3cd@corp.supernews.com...
>
> "Double-A" <double-aa@hush.ai> wrote in message
> news:1160432330.054745.200620@i3g2000cwc.googlegroups.com...
>>
>> Dana wrote:
>> > "Double-A" <double-aa@hush.ai> wrote in message
>> > news:1160425623.105160.196070@m7g2000cwm.googlegroups.com...
>> > >
>> > > Liam wrote:
>> > > > Just found this CNN article where measured cosmic radioactivity
> seems
>> > > > to indicate the universe is pill-shaped:
>> > > > http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>> > > >
>> > > > Now, I've just come to grips with the concept of the universe being
>> > > > infinite and expanding out of a Big...Expanding like "raisin bread"
> or
>> > > > an infinitely thick skin of a balloon.
>> > >
>> > >
>> > > The universe cannot have both come out of the Big Bang and be
> infinite.
>> > > It has to be one or the other.
>> >
>> > Why do you say this.
>>
>> Was the universe infinite at one second after the Big Bang?
>
> OK, good point.
>
>>
>> Double-A
>>
>
>

No, crap point.

It may take any positive age, and hence be potentially infinite in the
forward direction.

Date: 09 Oct 2006 22:04:04
From: Sorcerer
Subject: Re: infinite pill-shaped universe?

"Liam" <news@celticbear.com > wrote in message
news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...

Date: 09 Oct 2006 20:46:18
From: stapleton
Subject: Re: infinite pill-shaped universe?

I think you can not say the universe is shaped like a pill.
A bit like thinking that peeled orange map of the world
is a true representation of the earth.

No doubt the "pill" shape is a compromised 3-D representation.

"Liam" <news@celticbear.com > wrote in message
news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...
> Just found this CNN article where measured cosmic radioactivity seems
> to indicate the universe is pill-shaped:
> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>
> Now, I've just come to grips with the concept of the universe being
> infinite and expanding out of a Big...Expanding like "raisin bread" or
> an infinitely thick skin of a balloon.
>
> Now this pill-shaped thing? I can't reconcile this in my mind.
>
> Could someone help me understand how both of these can be true, or
> whether one theory undermines the other?
>
> Thanks!
> Liam
>

Date: 09 Oct 2006 20:40:06
From: Sam Wormley
Subject: Re: infinite pill-shaped universe?

Liam wrote:
> Just found this CNN article where measured cosmic radioactivity seems
> to indicate the universe is pill-shaped:
> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>

Egg-shaped Universe? Probably Not
http://www.astro.ucla.edu/~wright/cosmolog.htm#News

"30 Sep 2006 - The Los Angeles Times has a story today about the
paper* that suggests the Universe might be egg-shaped, and that
this might explain the low quadrupole seen in the WMAP (and COBE
DMR) CMB anisotropy maps. This was a silly paper and I said as
much to the reporter John Johnson. Adding an additional
quadrupole from the ellipsoidal Universe will make the
probability of the low observed quadrupole even smaller, unless
there is a reason that the quadrupole from the ellipticity will
be equal and nearly opposite to the quadrupole from inflation.
No such reason is given in this paper. Unfortunately the
referees for the Physical Review Letters missed this, and the
American Institute of Physics issued a press release
(subscription) about the paper".

*http://arxiv.org/abs/astro-ph/0606266

Date: 09 Oct 2006 13:36:06
From: Double-A
Subject: Re: infinite pill-shaped universe?

CptDondo wrote:
> Double-A wrote:
> >
> > The universe cannot have both come out of the Big Bang and be infinite.
> > It has to be one or the other.
>
> Sure it can. You can have a shape with an infinite volume but a finite
> boundary, and vice-versa.

Sounds like a black hole.

Double-A

Date: 09 Oct 2006 20:36:09
From: Algomeysa2
Subject: Re: infinite pill-shaped universe?

Date: 10 Oct 2006 18:28:50
From: jacob navia
Subject: Re: infinite pill-shaped universe?

Algomeysa2 wrote:
> "Liam" <news@celticbear.com> wrote in message
> news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...
>
>>Just found this CNN article where measured cosmic radioactivity seems
>>to indicate the universe is pill-shaped:
>>http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>
>
> Well, back in 2003 the universe was shaped like a soccer ball:
>
> http://news.nationalgeographic.com/news/2003/10/1008_031008_finiteuniverse.html
>
> Now it's shaped like a pill.
>
> I would suggest that the universe will continue to change shape as long as
> scientists need to publish papers....
>
>

!!!!!!!

VERY WELL WRITTEN.

Exactly. All this talk about the "shape of the universe" is just NONSENSE!

Date: 12 Oct 2006 02:48:43
From: Ben Rudiak-Gould
Subject: Re: infinite pill-shaped universe?

Algomeysa2 wrote:
> Well, back in 2003 the universe was shaped like a soccer ball:
>
> http://news.nationalgeographic.com/news/2003/10/1008_031008_finiteuniverse.html
>
> Now it's shaped like a pill.

No astronomer ever claimed it had either of those shapes. Only clueless
reporters did. Furthermore, neither of these claims (the real claims, not
the misreported ones) ever had wide support. Scientists publish conjectures
all the time. Most of them don't pan out. That's not a bad thing. What is a
bad thing is newspapers randomly reporting on speculative papers as though
they were accepted wisdom. It gives people a terribly distorted view of the
scientific process, even if the reporting is accurate, which it never is.

-- Ben

Date: 09 Oct 2006 13:35:10
From: Liam
Subject: Re: infinite pill-shaped universe?

Double-A wrote:
> Liam wrote:
> > Just found this CNN article where measured cosmic radioactivity seems
> > to indicate the universe is pill-shaped:
> > http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
> >
> > Now, I've just come to grips with the concept of the universe being
> > infinite and expanding out of a Big...Expanding like "raisin bread" or
> > an infinitely thick skin of a balloon.
>
>
> The universe cannot have both come out of the Big Bang and be infinite.
> It has to be one or the other.
>

Well, as I understand it, "The Big Bang" is a huge misnomer (and is a
term not even created by scientists.)
http://www.astro.ucla.edu/~wright/nocenter.html
http://www.astro.ucla.edu/~wright/cosmology_faq.html
Evidently the commonly accepted theory is the infinite universe
basically expanded out as every point is the center, and every point
was the origin of a Big Expansion. Like an infinitely thick expanding
balloon skin and or rising raisin bread.

>
> > Now this pill-shaped thing? I can't reconcile this in my mind.
> >
> > Could someone help me understand how both of these can be true, or
> > whether one theory undermines the other?
> >
> > Thanks!
> > Liam
>
>
> "An ellipsoid universe could be caused by a magnetic field pervading
> the cosmos that stretches space-time, he said, or by space-time defects
> such as cosmic strings, immensely dense structures just a proton or so
> wide stretched to intergalactic scales, whose gravity could distort
> space and time."
>
>
> Did anyone consider spin?
>
> Double-A

Date: 11 Oct 2006 18:55:36
From: George Dishman
Subject: Re: infinite pill-shaped universe?

"Liam" <news@celticbear.com > wrote in message
news:1160426110.719469.232780@m7g2000cwm.googlegroups.com...
>
> Double-A wrote:
>> Liam wrote:
>> > Just found this CNN article where measured cosmic radioactivity seems
>> > to indicate the universe is pill-shaped:
>> > http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>> >
>> > Now, I've just come to grips with the concept of the universe being
>> > infinite and expanding out of a Big...Expanding like "raisin bread" or
>> > an infinitely thick skin of a balloon.
>>
>>
>> The universe cannot have both come out of the Big Bang and be infinite.
>> It has to be one or the other.
>>
>
> Well, as I understand it, "The Big Bang" is a huge misnomer (and is a
> term not even created by scientists.)
> http://www.astro.ucla.edu/~wright/nocenter.html
> http://www.astro.ucla.edu/~wright/cosmology_faq.html
> Evidently the commonly accepted theory is the infinite universe
> basically expanded out as every point is the center, and every point
> was the origin of a Big Expansion. Like an infinitely thick expanding
> balloon skin and or rising raisin bread.

That is a good description of the current view.

>> > Now this pill-shaped thing? I can't reconcile this in my mind.
>> >
>> > Could someone help me understand how both of these can be true, or
>> > whether one theory undermines the other?

The whole universe may well be infinite. Think of
yourself on a plane in the middle of an infinite
cloud. Suppose the visibility is 100 yards. The
surface you can see should be a sphere centred on
you with that radius. They are suggesting we can
see a little farther in the horizontal directions
than in the vertical so the shape would be a
rotated ellipse.

Does that help?

George

Date: 09 Oct 2006 13:27:03
From: Double-A
Subject: Re: infinite pill-shaped universe?

Liam wrote:
> Just found this CNN article where measured cosmic radioactivity seems
> to indicate the universe is pill-shaped:
> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>
> Now, I've just come to grips with the concept of the universe being
> infinite and expanding out of a Big...Expanding like "raisin bread" or
> an infinitely thick skin of a balloon.

The universe cannot have both come out of the Big Bang and be infinite.
It has to be one or the other.

> Now this pill-shaped thing? I can't reconcile this in my mind.
>
> Could someone help me understand how both of these can be true, or
> whether one theory undermines the other?
>
> Thanks!
> Liam

"An ellipsoid universe could be caused by a magnetic field pervading
the cosmos that stretches space-time, he said, or by space-time defects
such as cosmic strings, immensely dense structures just a proton or so
wide stretched to intergalactic scales, whose gravity could distort
space and time."

Did anyone consider spin?

Double-A

Date: 09 Oct 2006 15:49:09
From: Brian Tung
Subject: Re: infinite pill-shaped universe?

Double-A wrote:
> The universe cannot have both come out of the Big Bang and be infinite.
> It has to be one or the other.

It can be both with little trouble at all. Let's drop down a couple of
dimensions, to make it easier to visualize.

Suppose that there's a Big Bang that produces a circular universe. I
don't mean a disc, with a circular edge; I mean a circle, so that all of
the galaxies that make up this universe lie along the "edge," so to
speak. If you run back time, you can easily see that the circle can
shrink indefinitely, until it becomes a point right at the Big Bang.

OK so far? Now, of course, such a universe isn't infinite; a circle has
a well-defined and finite length. So what I'm going to do is to replace
that circle by an infinite slinky. It's now that infinite slinky that
we run backward into time, so that it becomes a point right at the Big
Bang.

Impossible, you say? The only things that stop us are that there are no
infinite slinkies, and that slinkies have depth; they're not perfectly
flat. But neither of these things are problems in *principle*. We can
imagine an infinitely long slinky, even if we can't produce one in
actuality. And in principle, if a slinky is truly one-dimensional, it
has no thickness at all. That means that you can coil one up as long as
you like--infinitely long, even--and it will never gain any depth. It
will look just like a circle, except that it's not actually closed; if
you move along the slinky universe, you never get back to your starting
point unless you turn back and go the other way.

Pump things up a couple of dimensions, and you have a universe that can
expand out of a Big Bang and be infinite the whole time. (Actually,
"flatten out" is probably a more accurate term than "expand out.")

--
Brian Tung <brian@isi.edu >
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

Date: 09 Oct 2006 13:33:28
From: Dana
Subject: Re: infinite pill-shaped universe?

"Double-A" <double-aa@hush.ai > wrote in message
news:1160425623.105160.196070@m7g2000cwm.googlegroups.com...
>
> Liam wrote:
> > Just found this CNN article where measured cosmic radioactivity seems
> > to indicate the universe is pill-shaped:
> > http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
> >
> > Now, I've just come to grips with the concept of the universe being
> > infinite and expanding out of a Big...Expanding like "raisin bread" or
> > an infinitely thick skin of a balloon.
>
>
> The universe cannot have both come out of the Big Bang and be infinite.
> It has to be one or the other.

Why do you say this.

Date: 09 Oct 2006 20:49:09
From: stapleton
Subject: Re: infinite pill-shaped universe?

"Double-A" <double-aa@hush.ai > wrote in message
news:1160425623.105160.196070@m7g2000cwm.googlegroups.com...
>
> Liam wrote:
>> Just found this CNN article where measured cosmic radioactivity seems
>> to indicate the universe is pill-shaped:
>> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>>
>> Now, I've just come to grips with the concept of the universe being
>> infinite and expanding out of a Big...Expanding like "raisin bread" or
>> an infinitely thick skin of a balloon.
>
>
> The universe cannot have both come out of the Big Bang and be infinite.
> It has to be one or the other.

I think its beyond our ability to understand in human terms.
Time and space do not exist outside of the "expanding universe".

Date: 10 Oct 2006 18:27:19
From: jacob navia
Subject: Re: infinite pill-shaped universe?

stapleton wrote:
>
> I think its beyond our ability to understand in human terms.
> Time and space do not exist outside of the "expanding universe".
>
>

Excuse me but if "its beyond our ability to understand in human terms"
then it is NOT SCIENCE but religion.

Date: 11 Oct 2006 01:19:47
From: stapleton
Subject: Re: infinite pill-shaped universe?

"jacob navia" <jacob@jacob.remcomp.fr > wrote in message
news:452bc9e5$0$5097$ba4acef3@news.orange.fr...
> stapleton wrote:
>>
>> I think its beyond our ability to understand in human terms.
>> Time and space do not exist outside of the "expanding universe".
>
> Excuse me but if "its beyond our ability to understand in human terms"
> then it is NOT SCIENCE but religion.

There are ALOT of things in science that are not understandable in human
terms.
Take a class in quantum mechanics. You see crazy formulas like:
time * space = mass * energy * Si (Si is a constant)

There are even more thinks in science that are hard to comprehend.

Such as general relativity theory.
As an object approaches the speed of light, its mass becomes infinite and
time slows.

Just trying to imagine the mass of a teaspoon of matter form a black hole
is impossible to imagine. It would be so heavy it would sink to the center
of the earth, keep going, and rebounce multiple times before coming to rest
at the center.

Or Nuetrinos. They pass through the earth as if the earth were thin air.

etc ....

Date: 10 Oct 2006 20:59:50
From: N:dlzc D:aol T:com $dlzc$
Subject: Re: infinite pill-shaped universe?

Dear stapleton:

"stapleton" <alier342@silverman.com > wrote in message
news:TEXWg.10650$vJ2.7810@newssvr12.news.prodigy.com...
>
> "jacob navia" <jacob@jacob.remcomp.fr> wrote in message
> news:452bc9e5$0$5097$ba4acef3@news.orange.fr...
>> stapleton wrote:
>>>
>>> I think its beyond our ability to understand in human
>>> terms. Time and space do not exist outside of the
>>> "expanding universe".
>>
>> Excuse me but if "its beyond our ability to understand
>> in human terms" then it is NOT SCIENCE but religion.
>
> There are ALOT of things in science that are not
> understandable in human terms.
> Take a class in quantum mechanics. You see crazy
> formulas like: time * space = mass * energy * Si
> (Si is a constant)
>
> There are even more thinks in science that are hard to
> comprehend.
>
> Such as general relativity theory.
> As an object approaches the speed of light, its mass

... *energy*, not mass ...

> becomes infinite and time slows.
>
> Just trying to imagine the mass of a teaspoon of matter
> form a black hole is impossible to imagine. It would be
> so heavy it would sink to the center of the earth, keep
> going, and rebounce multiple times before coming to rest
> at the center.

... or even explode out into a whole new Universe.

> Or Nuetrinos. They pass through the earth as if the
> earth were thin air.
>
> etc ....

Good points all.

David A. Smith

Date: 11 Oct 2006 13:36:32
From: stapleton
Subject: Re: infinite pill-shaped universe?

"N:dlzc D:aol T:com (dlzc)" <N: dlzc1 D:cox T:net@nospam.com > wrote in
message news:O_ZWg.3210$v43.2775@fed1read02...
> Dear stapleton:
>
> "stapleton" <alier342@silverman.com> wrote in message
> news:TEXWg.10650$vJ2.7810@newssvr12.news.prodigy.com...
>>
>> "jacob navia" <jacob@jacob.remcomp.fr> wrote in message
>> news:452bc9e5$0$5097$ba4acef3@news.orange.fr...
>>> stapleton wrote:
>>>>
>>>> I think its beyond our ability to understand in human
>>>> terms. Time and space do not exist outside of the
>>>> "expanding universe".
>>>
>>> Excuse me but if "its beyond our ability to understand
>>> in human terms" then it is NOT SCIENCE but religion.
>>
>> There are ALOT of things in science that are not
>> understandable in human terms.
>> Take a class in quantum mechanics. You see crazy
>> formulas like: time * space = mass * energy * Si
>> (Si is a constant)
>>
>> There are even more thinks in science that are hard to
>> comprehend.
>>
>> Such as general relativity theory.
>> As an object approaches the speed of light, its mass
>
> ... *energy*, not mass ...

http://einstein.stanford.edu/content/relativity/q389.html
Experimentally, the increase of mass with velocity has been confirmed to
great precision...

Date: 11 Oct 2006 18:47:55
From: George Dishman
Subject: Re: infinite pill-shaped universe?

"stapleton" <alier342@silverman.com > wrote in message
news:Ar6Xg.21729$Ij.5438@newssvr14.news.prodigy.com...
>
> "N:dlzc D:aol T:com (dlzc)" <N: dlzc1 D:cox T:net@nospam.com> wrote in
> message news:O_ZWg.3210$v43.2775@fed1read02...
>> Dear stapleton:
>>
>> "stapleton" <alier342@silverman.com> wrote in message
>> news:TEXWg.10650$vJ2.7810@newssvr12.news.prodigy.com...
>>>
>>> "jacob navia" <jacob@jacob.remcomp.fr> wrote in message
>>> news:452bc9e5$0$5097$ba4acef3@news.orange.fr...
>>>> stapleton wrote:
>>>>>
>>>>> I think its beyond our ability to understand in human
>>>>> terms. Time and space do not exist outside of the
>>>>> "expanding universe".
>>>>
>>>> Excuse me but if "its beyond our ability to understand
>>>> in human terms" then it is NOT SCIENCE but religion.
>>>
>>> There are ALOT of things in science that are not
>>> understandable in human terms.
>>> Take a class in quantum mechanics. You see crazy
>>> formulas like: time * space = mass * energy * Si
>>> (Si is a constant)
>>>
>>> There are even more thinks in science that are hard to
>>> comprehend.
>>>
>>> Such as general relativity theory.
>>> As an object approaches the speed of light, its mass
>>
>> ... *energy*, not mass ...
>
> http://einstein.stanford.edu/content/relativity/q389.html
> Experimentally, the increase of mass with velocity has been confirmed to
> great precision...

The FAQ:

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Scientifically speaking, mass is invariant.

George

Date: 25 Oct 2006 04:54:39
From: George Dishman
Subject: Re: infinite pill-shaped universe?

William.Mook@gmail.com wrote:
> George Dishman wrote:
> > William.Mook@gmail.com wrote:
> > > Momentum, mass, the galilean notion of relativity, the newtonian notion
> > > of absolute time, - all those aspects of every-day science and
> > > engineering, are hard-wired into our brains.
> >
> > I completely agree, but nature is not so limited
>
> I agree with this.
>
> > and
> > our mathematical description of it should not be so
> > constrained.
>
> Our mathematical description is NOT constrained, and I never said
> anything about our mathematical description, so your point is moot.

I didn't suggest you did, the point remains valid.

> > > You folks make absolute statements that are highly suspect, or plain
> > > wrong, (as when I was told to try again by one poster at one point when
> > > I merely said momentum was mass times velocity! haha.. )
> >
> > That was me, I assumed you knew the answer since
> > you seemed familiar with SR.
>
> I am intimately familiar with special relativity among other things, so
> your presumption that I am wrong is itself wrong! And your statement
> was wrong in the context of my discussion anway.

The context of the discussion is the use of invariant
mass versus "relativistic mass" in SR.

> > The correct equation is:
>
> What is correct and what is not correct depends on the context of our
> discussion. You presume our disagreement stems from my lack of
> knowledge,

I presume no such thing, I believe our disagreement
reflects a change in teaching practice over the last
few decades to get away from the old pseudo-
Newtonian approach to a more fully relativistic
treatment.

> when in reality it stems from your lack of appreciation of
> certain important details in your thought process about knowledge we
> both share..
>
> > p = m [ v c / sqrt(c^2 - v^2) ]
>
> In the context of special relativity this equation has certain
> important meaning. It might be said to be correct in certain contexts.

Indeed, it is obviously only valid for massive objects
and inappropriate for photons, but in the context of
discussing "relativistic mass" it is correct.

> In the low speed context with v << c the statement mass times velocity
> is close enough to be said to be true.

It is close enough to be a useable approximation of
course, but our context was the use of "relativistic
mass" which is specifically used where the
approximation p ~ m v is not adequate.

> For example, if you set c=1 and v=1/1000000 then p = mv is true to one
> part in 5 x 10^-15 If you had a gram of copper and wished to calculate
> the momentum of a gram of the stuff moving at 300 m/sec the difference
> between p=mv and the 'correct' SR formula the error would amount to 5 x
> 10^-15 grams of material. Since the atomic weight of copper is 63.546
> amu, this amounts to 47,367,261 atoms difference, which is
> substantially correct in any realistic since. So, the Newtonian
> equation is obviously an important equation since this is what our
> brains are hardwired to know intuitively -

Our brains are hardwired to know intuitively that
momentum is a linear function of speed as v
approaches c? I don't think so.

> and by referencing this
> equation in our discussion of relativity, our intuitive knowledge is
> tapped to deepen and enrich our understanding of relativity.
>
>
> > or mass multiplied by a slightly more complex function
> > of speed.
>
> Yes, but its a moot point in the context of my earlier discussion as
> I've already pointed out.
>
> > Of course you can group it like this
> >
> > p = [ m c / sqrt(c^2 - v^2) ] v
> >
> > and call the term in square brackets "relativistic mass"
>
> Yes, which allows you to make important connections to your intuitive
> understanding of reality. This explains why it was done this way at the
> outset in our history of learning about the universe.
>
> > but it is just a cludge to allow the old Newtonian equation
> > to be used in a relativistic situation.
>
> If your goal is isolate your intellect from your intuition this is a
> way to proceed. I prefer a more integrative approach since it provides
> the basis of a richer understanding by tapping the into the depths of
> what humans are. As I've already explained about 10x

My goal was to ensure that the lurkers who may
follow these conversations and aren't as familiar
with SR as you are not misled into thinking that
mass varies with speed and are instead aware
that the anachronistic "relativistic mass" is a
composite term which includes the actual invariant
mass and a speed-dependent term which is
frequently associated with the mass in the real
equations. You are welcome to use whatever
approach you like of course.

George

Date: 11 Oct 2006 13:45:30
From: stapleton
Subject: Re: infinite pill-shaped universe?

"stapleton" <alier342@silverman.com > wrote in message
news:TEXWg.10650$vJ2.7810@newssvr12.news.prodigy.com...
>
> "jacob navia" <jacob@jacob.remcomp.fr> wrote in message
> news:452bc9e5$0$5097$ba4acef3@news.orange.fr...
>> stapleton wrote:
>>>
>>> I think its beyond our ability to understand in human terms.
>>> Time and space do not exist outside of the "expanding universe".
>>
>> Excuse me but if "its beyond our ability to understand in human terms"
>> then it is NOT SCIENCE but religion.
>
> There are ALOT of things in science that are not understandable in human
> terms.
> Take a class in quantum mechanics. You see crazy formulas like:
> time * space = mass * energy * Si (Si is a constant)
>
> There are even more thinks in science that are hard to comprehend.
>
> Such as general relativity theory.
> As an object approaches the speed of light, its mass becomes infinite and
> time slows.
>
> Just trying to imagine the mass of a teaspoon of matter form a black hole
> is impossible to imagine. It would be so heavy it would sink to the center
> of the earth, keep going, and rebounce multiple times before coming to
> rest
> at the center.
>
> Or Nuetrinos. They pass through the earth as if the earth were thin air.
>
> etc ....

http://einstein.stanford.edu/content/relativity/q25.html
Perhaps no other concept in all of physics is as impossible to comprehend as
curvature of space,
let alone the curvature of space-time. The equivalency between curvature and
gravitational forces
also appears profoundly counter-intuitive...

Date: 24 Oct 2006 06:54:53
From: George Dishman
Subject: Re: infinite pill-shaped universe?

William.Mook@gmail.com wrote:
> Momentum, mass, the galilean notion of relativity, the newtonian notion
> of absolute time, - all those aspects of every-day science and
> engineering, are hard-wired into our brains.

I completely agree, but nature is not so limited and
our mathematical description of it should not be so
constrained.

> You folks make absolute statements that are highly suspect, or plain
> wrong, (as when I was told to try again by one poster at one point when
> I merely said momentum was mass times velocity! haha.. )

That was me, I assumed you knew the answer since
you seemed familiar with SR. The correct equation is:

p = m [ v c / sqrt(c^2 - v^2) ]

or mass multiplied by a slightly more complex function
of speed.

Of course you can group it like this

p = [ m c / sqrt(c^2 - v^2) ] v

and call the term in square brackets "relativistic mass"
but it is just a cludge to allow the old Newtonian equation
to be used in a relativistic situation.

George

Date: 24 Oct 2006 20:02:56
From:
Subject: Re: infinite pill-shaped universe?

George Dishman wrote:
> William.Mook@gmail.com wrote:
> > Momentum, mass, the galilean notion of relativity, the newtonian notion
> > of absolute time, - all those aspects of every-day science and
> > engineering, are hard-wired into our brains.
>
> I completely agree, but nature is not so limited

I agree with this.

> and
> our mathematical description of it should not be so
> constrained.

Our mathematical description is NOT constrained, and I never said
anything about our mathematical description, so your point is moot.

> > You folks make absolute statements that are highly suspect, or plain
> > wrong, (as when I was told to try again by one poster at one point when
> > I merely said momentum was mass times velocity! haha.. )
>
> That was me, I assumed you knew the answer since
> you seemed familiar with SR.

I am intimately familiar with special relativity among other things, so
your presumption that I am wrong is itself wrong! And your statement
was wrong in the context of my discussion anway.

> The correct equation is:

What is correct and what is not correct depends on the context of our
discussion. You presume our disagreement stems from my lack of
knowledge, when in reality it stems from your lack of appreciation of
certain important details in your thought process about knowledge we
both share..

> p = m [ v c / sqrt(c^2 - v^2) ]

In the context of special relativity this equation has certain
important meaning. It might be said to be correct in certain contexts.

In the low speed context with v << c the statement mass times velocity
is close enough to be said to be true.

For example, if you set c=1 and v=1/1000000 then p = mv is true to one
part in 5 x 10^-15 If you had a gram of copper and wished to calculate
the momentum of a gram of the stuff moving at 300 m/sec the difference
between p=mv and the 'correct' SR formula the error would amount to 5 x
10^-15 grams of material. Since the atomic weight of copper is 63.546
amu, this amounts to 47,367,261 atoms difference, which is
substantially correct in any realistic since. So, the Newtonian
equation is obviously an important equation since this is what our
brains are hardwired to know intuitively - and by referencing this
equation in our discussion of relativity, our intuitive knowledge is
tapped to deepen and enrich our understanding of relativity.

> or mass multiplied by a slightly more complex function
> of speed.

Yes, but its a moot point in the context of my earlier discussion as
I've already pointed out.

> Of course you can group it like this
>
> p = [ m c / sqrt(c^2 - v^2) ] v
>
> and call the term in square brackets "relativistic mass"

Yes, which allows you to make important connections to your intuitive
understanding of reality. This explains why it was done this way at the
outset in our history of learning about the universe.

> but it is just a cludge to allow the old Newtonian equation
> to be used in a relativistic situation.

If your goal is isolate your intellect from your intuition this is a
way to proceed. I prefer a more integrative approach since it provides
the basis of a richer understanding by tapping the into the depths of
what humans are. As I've already explained about 10x

> George

Date: 24 Oct 2006 06:05:43
From:
Subject: Re: infinite pill-shaped universe?

Momentum, mass, the galilean notion of relativity, the newtonian notion
of absolute time, - all those aspects of every-day science and
engineering, are hard-wired into our brains.

Here's the proof. I'll do a simple experiment.

Someone at a job site asked me for an apple. I threw an apple in their
direction. They watched me throw is and grabbed it from the air.

They did this naturally and easily because of the hardwiring in their
brain.

Want to do your own experiment? Learn to juggle three balls easily.
Try it. Its fun, and entertaining! And a practical demonstration of
your innate ability to solve complex problems in Newtonian motion in
real-time.

The ability to predict the precise location of an object flying
ballistically through a gravity field short distances at low speed,-
directly without calculation, as in placing your hand in a position to
catch the object - is a practical demonstration of our hard-wired
understanding of Newtonian/Galilean physics.

Appealing to this innate ability gives knowledge derived from it a
solid grounding in real world experience.

You folks make absolute statements that are highly suspect, or plain
wrong, (as when I was told to try again by one poster at one point when
I merely said momentum was mass times velocity! haha.. ) or are
tangential to the point and obscure clear discussion.

Date: 09 Oct 2006 13:30:42
From: CptDondo
Subject: Re: infinite pill-shaped universe?

Double-A wrote:
>
> The universe cannot have both come out of the Big Bang and be infinite.
> It has to be one or the other.

Sure it can. You can have a shape with an infinite volume but a finite
boundary, and vice-versa.

Date: 09 Oct 2006 13:23:02
From: Liam
Subject: Re: infinite pill-shaped universe?

Hagar wrote:
> "Liam" <news@celticbear.com> wrote in message
> news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...
> > Just found this CNN article where measured cosmic radioactivity seems
> > to indicate the universe is pill-shaped:
> > http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
> >
> > Now, I've just come to grips with the concept of the universe being
> > infinite and expanding out of a Big...Expanding like "raisin bread" or
> > an infinitely thick skin of a balloon.
> >
> > Now this pill-shaped thing? I can't reconcile this in my mind.
> >
> > Could someone help me understand how both of these can be true, or
> > whether one theory undermines the other?
> >
> > Thanks!
> > Liam
> >
>
> What if the early Universe had an axial spin to it and with that spin, it
> had developed a slight equatorial bulge, pretty much like Earth has. Now if
> that spin were to slow down over time, could it create the opposite of a,
> equatorial bulge, something like an equatorial waist, which would give it a
> pill-shaped, somewhat oblong appearance, or would it still remain a sphere
> ??

But the question remains, how can an infinite universe have a finite
and discernable shape?

Date: 09 Oct 2006 13:21:04
From: Dana
Subject: Re: infinite pill-shaped universe?

"Liam" <news@celticbear.com > wrote in message
news:1160425382.126804.139250@k70g2000cwa.googlegroups.com...
>
> Hagar wrote:
> > "Liam" <news@celticbear.com> wrote in message
> > news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...
> > > Just found this CNN article where measured cosmic radioactivity seems
> > > to indicate the universe is pill-shaped:
> > > http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
> > >
> > > Now, I've just come to grips with the concept of the universe being
> > > infinite and expanding out of a Big...Expanding like "raisin bread" or
> > > an infinitely thick skin of a balloon.
> > >
> > > Now this pill-shaped thing? I can't reconcile this in my mind.
> > >
> > > Could someone help me understand how both of these can be true, or
> > > whether one theory undermines the other?
> > >
> > > Thanks!
> > > Liam
> > >
> >
> > What if the early Universe had an axial spin to it and with that spin,
it
> > had developed a slight equatorial bulge, pretty much like Earth has.
Now if
> > that spin were to slow down over time, could it create the opposite of
a,
> > equatorial bulge, something like an equatorial waist, which would give
it a
> > pill-shaped, somewhat oblong appearance, or would it still remain a
sphere
> > ??
>
> But the question remains, how can an infinite universe have a finite
> and discernable shape?
>

I was also going to ask about the claim that the universe is boundless.
By saying the universe has some kind of definite shape, that implies
boundaries.
Or is the boundless part of the thought that the universe will be expanding
without any end that we can see or determine.
What I am trying to say is that the Universe was considered boundless, even
when the scientists thought the universe would eventualy implode, no we know
that the universe will probably always expand. So that is why I ask about
the boundless remark. What exactly are they saying by using boundless.

Date: 09 Oct 2006 15:39:01
From: Brian Tung
Subject: Re: infinite pill-shaped universe?

Dana wrote:
> I was also going to ask about the claim that the universe is boundless.
> By saying the universe has some kind of definite shape, that implies
> boundaries.

Not in the way they mean "boundaries." For instance, the Earth has a
certain shape--almost an oblate spheroid, though ever so slightly fatter
in the southern hemisphere than in the northern. However, the *surface*
of the Earth has no boundaries--there's no "edge" to the Earth. As we
move throughout the universe, our motion is analogous to moving along
the surface of the Earth, so there's no edge to the universe, either.

You should probably take notions of the shape of the universe with a
grain of salt. All cosmological topology is done by measuring certain
properties from within the universe itself; for obvious reasons, no one
has so far been able to exit the universe and look at it from the
outside. So when people say the universe has such-and-such a shape, it
means *as inferred from internal observations*.

For instance, how would you determine that the Earth was spherical if
you could only look down at the ground? One thing you could do, in
principle, is to draw a large triangle, with sides as straight as you
could make them. Nonetheless, you would find, after making precise
measurements, that your angles added up to something more than 180
degrees (the excess being more the bigger the triangle was). This
idea of measuring the local geometry without seeing it embedded in any
larger space (the three-dimensional space of the solar system, in this
case) is something relatively new; it evolved around the turn of the
20th century.

Now, the surface of the Earth is basically a two-dimensional surface--
what mathematicians call a manifold--embedded in three-dimensional
space. The sphere we call it is something we see in three dimensions.
So, in order to properly apprehend the universe in that way, we have to
jump up one dimension (at least): it's a three-dimensional "surface" or
manifold. If it's embedded in any higher space--and this business about
measuring it locally from the inside means there doesn't *have* to be--
then that higher space must have at least four dimensions. So it's not
a pill the way you're used to thinking about pills; this pill has at
least four dimensions.

You might think about it like this. If you were to freeze the universe
(stop it from expanding) and shoot off a beam of light, then eventually,
in principle, that beam of light would hit you in the back some time
later. How much later? That time is sort of a measure of the girth,
the circumference, of the universe. When it is said that the universe
is pill-shaped, it might be better to think of that girth as depending
on the direction in which you shoot that beam of light. If you shoot
it in *this* direction, it's shorter; if you shoot it in that direction,
it's longer. Possibly, if you shoot it in other directions, it doesn't
get back to you at all, because the universe isn't curved the right way.
(If you have a big pill-shaped object, you might only be able to wrap it
in three ways--along its length, its width, and its height.)

--
Brian Tung <brian@isi.edu >
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

Date: 09 Oct 2006 14:53:32
From: Dana
Subject: Re: infinite pill-shaped universe?

"Brian Tung" <brian@isi.edu > wrote in message
news:egej25$ui9$1@praesepe.isi.edu...
> Dana wrote:
> > I was also going to ask about the claim that the universe is boundless.
> > By saying the universe has some kind of definite shape, that implies
> > boundaries.
>
> Not in the way they mean "boundaries." For instance, the Earth has a
> certain shape--almost an oblate spheroid, though ever so slightly fatter
> in the southern hemisphere than in the northern. However, the *surface*
> of the Earth has no boundaries--there's no "edge" to the Earth. As we
> move throughout the universe, our motion is analogous to moving along
> the surface of the Earth, so there's no edge to the universe, either.
>
> You should probably take notions of the shape of the universe with a
> grain of salt. All cosmological topology is done by measuring certain
> properties from within the universe itself; for obvious reasons, no one
> has so far been able to exit the universe and look at it from the
> outside. So when people say the universe has such-and-such a shape, it
> means *as inferred from internal observations*.
>
> For instance, how would you determine that the Earth was spherical if
> you could only look down at the ground? One thing you could do, in
> principle, is to draw a large triangle, with sides as straight as you
> could make them. Nonetheless, you would find, after making precise
> measurements, that your angles added up to something more than 180
> degrees (the excess being more the bigger the triangle was). This
> idea of measuring the local geometry without seeing it embedded in any
> larger space (the three-dimensional space of the solar system, in this
> case) is something relatively new; it evolved around the turn of the
> 20th century.
>
> Now, the surface of the Earth is basically a two-dimensional surface--
> what mathematicians call a manifold--embedded in three-dimensional
> space. The sphere we call it is something we see in three dimensions.
> So, in order to properly apprehend the universe in that way, we have to
> jump up one dimension (at least): it's a three-dimensional "surface" or
> manifold. If it's embedded in any higher space--and this business about
> measuring it locally from the inside means there doesn't *have* to be--
> then that higher space must have at least four dimensions. So it's not
> a pill the way you're used to thinking about pills; this pill has at
> least four dimensions.
>
> You might think about it like this. If you were to freeze the universe
> (stop it from expanding) and shoot off a beam of light, then eventually,
> in principle, that beam of light would hit you in the back some time
> later. How much later? That time is sort of a measure of the girth,
> the circumference, of the universe. When it is said that the universe
> is pill-shaped, it might be better to think of that girth as depending
> on the direction in which you shoot that beam of light. If you shoot
> it in *this* direction, it's shorter; if you shoot it in that direction,
> it's longer. Possibly, if you shoot it in other directions, it doesn't
> get back to you at all, because the universe isn't curved the right way.
> (If you have a big pill-shaped object, you might only be able to wrap it
> in three ways--along its length, its width, and its height.)

Excellent explanation.
You answered a few of my questions with the above.

>
> --
> Brian Tung <brian@isi.edu>
> The Astronomy Corner at http://astro.isi.edu/
> Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
> The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
> My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

Date: 13 Oct 2006 22:27:05
From: Peter Webb
Subject: Re: infinite pill-shaped universe?

I agree - a very well worded explanation.

Date: 13 Oct 2006 16:14:39
From: Sorcerer
Subject: Re: infinite pill-shaped universe?

"Peter Webb" <webbfamily-diespamdie@optusnet.com.au > wrote in message
news:452f861b$0$22937$afc38c87@news.optusnet.com.au...

Date: 09 Oct 2006 17:13:22
From: Michael McCulloch
Subject: Re: infinite pill-shaped universe?

On 9 2006 13:23:02 -0700, "Liam" <news@celticbear.com > wrote:

>But the question remains, how can an infinite universe have a finite
>and discernable shape?

I think the idea of "shape" has more to do with how radiation moves in
the space of the Universe rather than any boundary shape of the whole.

For example, if the Universe is flat, then light travels in straight
lines through the Universe unless locally influenced by gravity.

---
Michael McCulloch

Date: 10 Oct 2006 18:21:58
From: jacob navia
Subject: Re: infinite pill-shaped universe?

Liam wrote:
> Hagar wrote:
>
>>"Liam" <news@celticbear.com> wrote in message
>>news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...
>>
>>>Just found this CNN article where measured cosmic radioactivity seems
>>>to indicate the universe is pill-shaped:
>>>http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>>>
>>>Now, I've just come to grips with the concept of the universe being
>>>infinite and expanding out of a Big...Expanding like "raisin bread" or
>>>an infinitely thick skin of a balloon.
>>>
>>>Now this pill-shaped thing? I can't reconcile this in my mind.
>>>
>>>Could someone help me understand how both of these can be true, or
>>>whether one theory undermines the other?
>>>
>>>Thanks!
>>>Liam
>>>
>>
>>What if the early Universe had an axial spin to it and with that spin, it
>>had developed a slight equatorial bulge, pretty much like Earth has. Now if
>>that spin were to slow down over time, could it create the opposite of a,
>>equatorial bulge, something like an equatorial waist, which would give it a
>>pill-shaped, somewhat oblong appearance, or would it still remain a sphere
>>??
>
>
> But the question remains, how can an infinite universe have a finite
> and discernable shape?
>

RIGHT!!!

IT IS IMPOSSIBLE!!!

Date: 09 Oct 2006 13:19:21
From: Hagar
Subject: Re: infinite pill-shaped universe?

"Liam" <news@celticbear.com > wrote in message
news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...
> Just found this CNN article where measured cosmic radioactivity seems
> to indicate the universe is pill-shaped:
> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>
> Now, I've just come to grips with the concept of the universe being
> infinite and expanding out of a Big...Expanding like "raisin bread" or
> an infinitely thick skin of a balloon.
>
> Now this pill-shaped thing? I can't reconcile this in my mind.
>
> Could someone help me understand how both of these can be true, or
> whether one theory undermines the other?
>
> Thanks!
> Liam
>

What if the early Universe had an axial spin to it and with that spin, it
had developed a slight equatorial bulge, pretty much like Earth has. Now if
that spin were to slow down over time, could it create the opposite of a,
equatorial bulge, something like an equatorial waist, which would give it a
pill-shaped, somewhat oblong appearance, or would it still remain a sphere
??

Date: 09 Oct 2006 13:25:13
From: CptDondo
Subject: Re: infinite pill-shaped universe?

Hagar wrote:
> "Liam" <news@celticbear.com> wrote in message
> news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...
>> Just found this CNN article where measured cosmic radioactivity seems
>> to indicate the universe is pill-shaped:
>> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>>
>> Now, I've just come to grips with the concept of the universe being
>> infinite and expanding out of a Big...Expanding like "raisin bread" or
>> an infinitely thick skin of a balloon.
>>
>> Now this pill-shaped thing? I can't reconcile this in my mind.
>>
>> Could someone help me understand how both of these can be true, or
>> whether one theory undermines the other?
>>
>> Thanks!
>> Liam
>>
>
> What if the early Universe had an axial spin to it and with that spin, it
> had developed a slight equatorial bulge, pretty much like Earth has. Now if
> that spin were to slow down over time, could it create the opposite of a,
> equatorial bulge, something like an equatorial waist, which would give it a
> pill-shaped, somewhat oblong appearance, or would it still remain a sphere
> ??
>
>

Long ago, I wrote a 4-D cad system. I could pretty much show you a
large number of shapes; diamond-like, box-like, square like, tube-like -
and they all were the same thing, a projection of a 4D object onto 3
dimensions, and then onto a 2D screen.

It's meaningless to talk about a 'shape' when there is no frame of
reference to judge that shape by. I personally hope we're in a Marilyn
Monroe universe, complete with red velvet backdrop. Makes about as much
sense as a pill.....

Date: 10 Oct 2006 18:24:29
From: jacob navia
Subject: Re: infinite pill-shaped universe?

CptDondo wrote:
> Hagar wrote:
>
>> "Liam" <news@celticbear.com> wrote in message
>> news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...
>>
>>> Just found this CNN article where measured cosmic radioactivity seems
>>> to indicate the universe is pill-shaped:
>>> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>>>
>>> Now, I've just come to grips with the concept of the universe being
>>> infinite and expanding out of a Big...Expanding like "raisin bread" or
>>> an infinitely thick skin of a balloon.
>>>
>>> Now this pill-shaped thing? I can't reconcile this in my mind.
>>>
>>> Could someone help me understand how both of these can be true, or
>>> whether one theory undermines the other?
>>>
>>> Thanks!
>>> Liam
>>>
>>
>> What if the early Universe had an axial spin to it and with that spin,
>> it had developed a slight equatorial bulge, pretty much like Earth
>> has. Now if that spin were to slow down over time, could it create
>> the opposite of a, equatorial bulge, something like an equatorial
>> waist, which would give it a pill-shaped, somewhat oblong appearance,
>> or would it still remain a sphere ??
>>
>
> Long ago, I wrote a 4-D cad system. I could pretty much show you a
> large number of shapes; diamond-like, box-like, square like, tube-like -
> and they all were the same thing, a projection of a 4D object onto 3
> dimensions, and then onto a 2D screen.
>
> It's meaningless to talk about a 'shape' when there is no frame of
> reference to judge that shape by. I personally hope we're in a Marilyn
> Monroe universe, complete with red velvet backdrop. Makes about as much
> sense as a pill.....

EXACTLY!!!

All this talk about the univers's shape is just NONSENSE!!!
A shape implies a boundary, and the universe has no boundaries.

Date: 10 Oct 2006 16:19:22
From: CptDondo
Subject: Re: infinite pill-shaped universe?

jacob navia wrote:

>> It's meaningless to talk about a 'shape' when there is no frame of
>> reference to judge that shape by. I personally hope we're in a
>> Marilyn Monroe universe, complete with red velvet backdrop. Makes
>> about as much sense as a pill.....
>
> EXACTLY!!!
>
> All this talk about the univers's shape is just NONSENSE!!!
> A shape implies a boundary, and the universe has no boundaries.
>

It's appropriate to talk about a curvature of space, but not a 'shape'
of the universe.

--Yan

Date: 11 Oct 2006 00:40:54
From: George Dishman
Subject: Re: infinite pill-shaped universe?

"CptDondo" <yan@NsOeSiPnAeMr.com > wrote in message
news:12ioajic4garf0c@corp.supernews.com...
> jacob navia wrote:
>
>>> It's meaningless to talk about a 'shape' when there is no frame of
>>> reference to judge that shape by. I personally hope we're in a Marilyn
>>> Monroe universe, complete with red velvet backdrop. Makes about as much
>>> sense as a pill.....
>>
>> EXACTLY!!!
>>
>> All this talk about the univers's shape is just NONSENSE!!!
>> A shape implies a boundary, and the universe has no boundaries.
>>
>
> It's appropriate to talk about a curvature of space, but not a 'shape' of
> the universe.

A brief read of the article suggests they are describing
the shape of the surface of last scattering, i.e. the
limits of the observable part of the universe only.

George

Date: 10 Oct 2006 17:40:20
From: N:dlzc D:aol T:com $dlzc$
Subject: Re: infinite pill-shaped universe?

Dear George Dishman:

"George Dishman" <george@briar.demon.co.uk > wrote in message
news:egha6h$bl7$1@news.freedom2surf.net...
...
> A brief read of the article suggests they are describing
> the shape of the surface of last scattering, i.e. the
> limits of the observable part of the universe only.

Any discussion of which way the "pill" is oriented... say with
respect to the CMBR anisotropy? Wondering if length contraction
has any contribution one way or the other. 300 km/sec is not
enough to yield a 1% contraction, but you never know...

David A. Smith

Date: 10 Oct 2006 18:21:07
From: jacob navia
Subject: Re: infinite pill-shaped universe?

Liam wrote:
> Just found this CNN article where measured cosmic radioactivity seems
> to indicate the universe is pill-shaped:
> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>
> Now, I've just come to grips with the concept of the universe being
> infinite and expanding out of a Big...Expanding like "raisin bread" or
> an infinitely thick skin of a balloon.
>
> Now this pill-shaped thing? I can't reconcile this in my mind.
>
> Could someone help me understand how both of these can be true, or
> whether one theory undermines the other?
>
> Thanks!
> Liam
>

Excuse me but if this "pill universe" has a FORM, WHERE is this
"pill"?

There is NO SENSE to the assertion:

"The universe has the form of a ..." (fill the blanks).

Since:

A "FORM", (the concept of FORM) implies a BOUNDARY, and
that is NONSENSE when we speak about the Universe. If the
universe has the form of a pill, then it must be contained
into something and that "something" that contains that "pill"
IS ALSO PART OF THE UNIVERSE so it can't be that the universe has a form.

Q.E.D.

Date: 10 Oct 2006 09:04:21
From: Hagar
Subject: Re: infinite pill-shaped universe?

"Liam" <news@celticbear.com > wrote in message
news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...
> Just found this CNN article where measured cosmic radioactivity seems
> to indicate the universe is pill-shaped:
> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>
> Now, I've just come to grips with the concept of the universe being
> infinite and expanding out of a Big...Expanding like "raisin bread" or
> an infinitely thick skin of a balloon.
>
> Now this pill-shaped thing? I can't reconcile this in my mind.
>
> Could someone help me understand how both of these can be true, or
> whether one theory undermines the other?
>
> Thanks!
> Liam

Perhaps the early Universe (omni-directionally infinite and very empty)
developed a case of ADD (Attention Deficit Disorder) because there was
nothing to do. So that Intelligent Design Dude blew up some stuff and made
it look like a bid, appetizing Ritalin pill, hoping to entice the Universe
to swallow it. Unfortunately, the Cosmos, like a playful kitten, just
started batting it around, creating the chaos we observe today.

Date: 10 Oct 2006 18:25:18
From: jacob navia
Subject: Re: infinite pill-shaped universe?

Hagar wrote:
> "Liam" <news@celticbear.com> wrote in message
> news:1160423445.892101.40190@m7g2000cwm.googlegroups.com...
>
>>Just found this CNN article where measured cosmic radioactivity seems
>>to indicate the universe is pill-shaped:
>>http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>>
>>Now, I've just come to grips with the concept of the universe being
>>infinite and expanding out of a Big...Expanding like "raisin bread" or
>>an infinitely thick skin of a balloon.
>>
>>Now this pill-shaped thing? I can't reconcile this in my mind.
>>
>>Could someone help me understand how both of these can be true, or
>>whether one theory undermines the other?
>>
>>Thanks!
>>Liam
>
>
> Perhaps the early Universe (omni-directionally infinite and very empty)
> developed a case of ADD (Attention Deficit Disorder) because there was
> nothing to do. So that Intelligent Design Dude blew up some stuff and made
> it look like a bid, appetizing Ritalin pill, hoping to entice the Universe
> to swallow it. Unfortunately, the Cosmos, like a playful kitten, just
> started batting it around, creating the chaos we observe today.
>
>
You should receive the Nobel Prize ASAP!

Date: 11 Oct 2006 00:24:29
From: Mary Poppins
Subject: Re: infinite pill-shaped universe?

Liam wrote:

> Just found this CNN article where measured cosmic radioactivity seems
> to indicate the universe is pill-shaped:
> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>
> Now, I've just come to grips with the concept of the universe being
> infinite and expanding out of a Big...Expanding like "raisin bread" or
> an infinitely thick skin of a balloon.
>
> Now this pill-shaped thing? I can't reconcile this in my mind.
>
> Could someone help me understand how both of these can be true, or
> whether one theory undermines the other?
>
> Thanks!
> Liam

In what size prescription for how much? Will it bankrupt me?

Date: 11 Oct 2006 05:55:47
From: N:dlzc D:aol T:com $dlzc$
Subject: Re: infinite pill-shaped universe?

Dear Mary Poppins:

"Mary Poppins" <gandol@hgnet.org > wrote in message
news:452C800D.3BDC9B69@hgnet.org...
>
> Liam wrote:
>
>> Just found this CNN article where measured cosmic
>> radioactivity seems to indicate the universe is pill-shaped:
>> http://www.cnn.com/2006/TECH/space/10/09/universe.pill/index.html
>>
>> Now, I've just come to grips with the concept of the
>> universe being infinite and expanding out of a Big...
>> Expanding like "raisin bread" or an infinitely thick
>> skin of a balloon.
>>
>> Now this pill-shaped thing? I can't reconcile this in
>> my mind.
>>
>> Could someone help me understand how both of
>> these can be true, or whether one theory
>> undermines the other?
>
> In what size prescription for how much?

Your prescription is all that you can see. You'll take it for
the rest of your life, just like thyroid or insulin.

> Will it bankrupt me?

You won't take anything with you when you go.

Better question... is it covered by insurance/government benefit?
; >)

David A. Smith

Date: 11 Oct 2006 20:30:19
From:
Subject: Re: infinite pill-shaped universe?

rest mass is an invariant. mass is not since it varies with speed.

Date: 11 Oct 2006 21:25:47
From: N:dlzc D:aol T:com $dlzc$
Subject: Re: infinite pill-shaped universe?

Dear William.Mook:

<William.Mook@gmail.com > wrote in message
news:1160623819.805199.226900@c28g2000cwb.googlegroups.com...
> rest mass is an invariant. mass is not since it varies
> with speed.

Mass does not vary with speed. Mass is not a vector, yet
relativistic mass does not correctly describe how a charge
accelerates in a magnetic field.

No *current* physics textbook uses mass for anything except rest
mass.

Baez says mass is rest mass:
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html
Hillman says mass is rest mass:
http://groups.google.com/group/sci.physics/msg/6f1f1b991a0e6c26
Taylor and Wheeler say mass is rest mass:
"Spacetime Physics"
Gary Oas says mass is rest mass:
http://adsabs.harvard.edu/abs/2005physics...4110O
... and here
http://arxiv.org/abs/physics/0504110

... a mixed bag on this site...
http://hyperphysics.phy-astr.gsu.edu/hbase/mass.html#mas
... with lots of disclaimers.

Your usage is non standard, you will get in trouble if you try
and use formulae based on mass = rest mass. And exclamations of
"bullshit" are unconvincing. And hints that everyone else
doesn't understand special relativity should give you a clue...

Believe what you will. I just wish you didn't spread antiquated
usage around like it was gospel.

David A. Smith

Date: 12 Oct 2006 06:49:39
From: Sorcerer
Subject: Re: infinite pill-shaped universe?

"N:dlzc D:aol T:com (dlzc)" <N: dlzc1 D:cox T:net@nospam.com > wrote in
message news:7tjXg.3282$v43.3259@fed1read02...

Date: 11 Oct 2006 20:28:07
From:
Subject: Re: infinite pill-shaped universe?

Double-A wrote:
>
> Yup! Modern physics has consigned "relativistic mass" to the scrap
> heap along with "aether".
>

Bullshit

Date: 11 Oct 2006 20:27:14
From:
Subject: Re: infinite pill-shaped universe?

George Dishman wrote:
> <William.Mook@gmail.com> wrote in message
> news:1160590946.125364.61000@b28g2000cwb.googlegroups.com...
> > Mass is not an invariant quantity, it changes with relative speed.
> > That's what the special and general theory of relativity is all about.
> >
> > The mass of a particle at rest can be invariant. But the mass of a
> > particle in motion changes with its speed. You can see this with
> > electrons in a vacuum tube flying through a magnetic field. This is a
> > typical experiment (or was) that is done in college level physics
> > classes.
> >
> > You have a vacuum tube with an electron gun at one end and a phosphor
> > screen at another. You can change the voltage of the electron gun, and
> > thus, change the velocity of the electrons flying out of the end of the
> > gun. A spot of light glows at the point on the phosphor screen where
> > the electrons strike the phosphor. You can then apply a magnetic field
> > to the electron beam and cause the electrons to be accelerated through
> > an angle, shifting the location of the glowing spot.
> >
> > This is a cool apparatus because you can learn so much about things
> > with it. Knowing a few principles of geometry and electrostatics and
> > electrodynamics, you can weigh electrons, measure their speed and so
> > forth.
> >
> > You can vary the speed of the electrons from about 1% the speed of
> > light to about 90% the speed of light by changing the voltage of the
> > gun from 1,000V to about 100,000V.
> >
> > Once you do a few of these introductory experiments, you can then crank
> > up the voltage and deflect the beam of very high speed electrons and
> > measure their mass at speed. When you do this you see experimental
> > proof that Lorentz effects are real. That is, the mass of a moving
> > electron is far greater than a stationary electron.
> >
> > Now at this point in the course you see an old NSF film that shows that
> > mu-mesons produced by cosmic rays high in the Earth's atmosphere
> > wouldn't make it to the ground unless time to were distorted as
> > described in the Lorentz equations. The coup'd grace is an experiment
> > done in lecture that actually measures mu-mesons coursing through the
> > lecture hall from cosmic space! oooooo...
> >
> > It makes all this bs that people argue endlessly about here stand out
> > for what it is! lol.
>
> Everything you say about the experiments is true and yes
> the effects are real, but in the modern approach mass is
> treated as invariant and the gamma function is treated as
> part of the relation between mass,

REST MASS can be treated as an invariant. MASS cannot. Sorry, you
really don't understand the special theory of relativity if you do not
get this.

http://www.physics.nyu.edu/hogg/sr/sr.pdf

> speed and energy. The
> concept of "relativistic mass" which you describe is
> nowadays seen as being anachronistic even if still useful
> in practical terms.

Relativistic mass is important in any discussion of relativity. Sorry.

Date: 12 Oct 2006 07:43:56
From: George Dishman
Subject: Re: infinite pill-shaped universe?

<William.Mook@gmail.com > wrote in message
news:1160623634.485937.131340@m7g2000cwm.googlegroups.com...
>
> George Dishman wrote:

<snip >

>> Everything you say about the experiments is true and yes
>> the effects are real, but in the modern approach mass is
>> treated as invariant and the gamma function is treated as
>> part of the relation between mass,
>
> REST MASS can be treated as an invariant. MASS cannot. Sorry, you
> really don't understand the special theory of relativity if you do not
> get this.
>
> http://www.physics.nyu.edu/hogg/sr/sr.pdf

Excellent document. It only mentions "relativistic mass" once,
see the first paragraph of section 6.4:

"Just as in non-relativistic 3-space, where 3-momentum
was defined as mass times 3-velocity, in spacetime
4-momentum ~p is mass m times 4-velocity ~u. Under this
definition, the mass must be a scalar if the 4-momentum
is going to be a 4-vector. If you are old enough, you may
have heard of a quantity called "relativistic mass" which
increases with velocity, approaching infinity as an object
approaches the speed of light. Forget whatever you heard;
that formulation of special relativity is archaic and ugly.
The mass m of an object as far as we are concerned is its
rest mass, or the mass we would measure if we were at
rest with respect to the object."

>> speed and energy. The
>> concept of "relativistic mass" which you describe is
>> nowadays seen as being anachronistic even if still useful
>> in practical terms.
>
> Relativistic mass is important in any discussion of relativity. Sorry.

"Forget whatever you heard; that formulation of special
relativity is archaic and ugly."

George

Date: 27 Oct 2006 05:46:00
From:
Subject: Re: infinite pill-shaped universe?

George Dishman wrote:
> William.Mook@gmail.com wrote:
> > Wow, George, you are an argumentative old cuss... hmm...
>
> 'Fraid so ;-)

Welcome to the club!

>
> However, let me remind you of your comment that
> started all this. You wrote in message:
> http://groups.google.co.uk/group/sci.astro/msg/5ab9a4a05fdf1593
>
> > Mass is not an invariant quantity, it changes with relative speed.
> > That's what the special and general theory of relativity is all about.
> >
> > The mass of a particle at rest can be invariant. But the mass of a
> > particle in motion changes with its speed. You can see this with
> > electrons in a vacuum tube ...
>
> Mass varying with speed is most definitely not "what
> the special and general theory of relativity is all about."

Yes it is. We think of mass as a constant unvarying with speed. The
apparent change of mass at high speeds demands an explanation! Which
gives us the 4-form of unvarying mass rotating in 4-space, projected
onto 3-space as a 3-form with apparently varying mass.

> nor IMO is it a good way to start learning what SR or
> GR are really about.

We disagree here.

> > George Dishman wrote:
> > > William.Mook@gmail.com wrote:
> > > > George Dishman wrote:
> > > > > William.Mook@gmail.com wrote:
> > > > > > Momentum, mass, the galilean notion of relativity, the newtonian notion
> > > > > > of absolute time, - all those aspects of every-day science and
> > > > > > engineering, are hard-wired into our brains.
> > > > >
> > > > > I completely agree, but nature is not so limited
> > > >
> > > > I agree with this.
> > > >
> > > > > and
> > > > > our mathematical description of it should not be so
> > > > > constrained.
> > > >
> > > > Our mathematical description is NOT constrained, and I never said
> > > > anything about our mathematical description, so your point is moot.
> > >
> > > I didn't suggest you did, the point remains valid.
> >
> > You are confused here. I never suggested we should constrain our
> > mathematical descriptions.
>
> I know, and I didn't say you did, so now who's being
> argumentative?

I don't know since your reply is very confusing since all context is
lost.

> If you want to push the point, what I
> was saying is that, for example, we shouldn't cast
> our equation for momentum is this form:
>
> p = m_r * v
>
> from which we must have
>
> m_r = m c / sqrt(c^2 - v^2)
>
> only to be compliant with everday experience.

You don't value the depth of everyday experience because you don't see
the deeper connections to non-intellectual experience and the value
they have.

> Much of
> modern science (and all of QM!) is counter-intuitive

Yes.

> and
> students will at some point need to break that connection.

I would say students need to MAKE the connection! lol.

> It is my feeling that writing the equation in this form:
>
> p = m [ v c / sqrt(c^2 - v^2) ]
>
> makes it much clearer that mass is an invariant scalar.
>

Yes.

> > I merely suggested that appealing to
> > intuitive notions of space and time add real depth to our understanding
> > of the mathematics.
>
> I, on the other hand, think it unnecessarily creates a
> misunderstanding, the idea that mass varies with speed.
>

Mass apparently changes with speed in the 3-form projection, this is an
important observation in making a connection to deeper experience.

> > > > > > You folks make absolute statements that are highly suspect, or plain
> > > > > > wrong, (as when I was told to try again by one poster at one point when
> > > > > > I merely said momentum was mass times velocity! haha.. )
> > > > >
> > > > > That was me, I assumed you knew the answer since
> > > > > you seemed familiar with SR.
> > > >
> > > > I am intimately familiar with special relativity among other things, so
> > > > your presumption that I am wrong is itself wrong! And your statement
> > > > was wrong in the context of my discussion anway.
> > >
> > > The context of the discussion is the use of invariant
> > > mass versus "relativistic mass" in SR.
> >
> > As a means to tap into our intuitive understanding of things, yes. I
> > didn't suggest we stop there.
>
> No, you simply said that I was wrong when I said
> the following in message
> http://groups.google.co.uk/group/sci.astro/msg/8307e0dedb0e2f49
>
> >> The FAQ:
> >>
> >> http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html
> >>
> >> Scientifically speaking, mass is invariant.
>
> Again, consider what you said of that:
>

I have considered what I said. You have not! lol.

> > Mass is not an invariant quantity, it changes with relative speed.
> > That's what the special and general theory of relativity is all about.
> >
> > The mass of a particle at rest can be invariant. But the mass of a
> > particle in motion changes with its speed. ...
>
>
> > > > > The correct equation is:
> > > >
> > > > What is correct and what is not correct depends on the context of our
> > > > discussion. You presume our disagreement stems from my lack of
> > > > knowledge,
> > >
> > > I presume no such thing,
> >
> > Whenever you say something like 'the correct equation is...' presumes
> > all other modes of understanding are somehow incorrect.
>
> No, it meant that one equation:
>
> p = m [ v c / sqrt(c^2 - v^2) ]
>
> is accurate to the best of current scientific knowledge while the
>
> p = m v
>
> is only an approximation. It may be a very useful approximation
> but we shouldn't give lurkers the idea that it can be used on all
> occasions.
>
> > You should
> > really avoid brow-beating students in this way. It silences their own
> > rich understanding by assuming they have nothing to contribute merely
> > because it doesn't follow the lesson plan.
>
> I am against giving students incorrect information. Starting
> by showing
>
> p = m [ v c / sqrt(c^2 - v^2) ]
>
> and then go on to discuss the situations where p = mv
> is a valid approximation is IMO much more informative
> and aids the understaing of when use of approximations
> in general is appropriate.
>
> > > I believe our disagreement
> > > reflects a change in teaching practice over the last
> > > few decades
> >
> > A agree. Some things have changed for the worse! lol.
>
> YMMV ;-)
>
> > > to get away from the old pseudo-
> > > Newtonian approach to a more fully relativistic
> > > treatment.
> >
> > Hogwash. The new approaches merely seek to avoid the same tired old
> > questions because they're boring for teachers to handle year in and
> > year out. They're quite efficient to this end. But they have a cost,
> > and that cost is making relativity seem like a different field of
> > experience than the one they know intuitively - which isolates
> > understanding from experience - and which I judge to be a bad thing.
>
> I on the other hand think it gets them into thinking in
> a 4D way which is essential as they move into GR.
>
> > > > when in reality it stems from your lack of appreciation of
> > > > certain important details in your thought process about knowledge we
> > > > both share..
> > > >
> > > > > p = m [ v c / sqrt(c^2 - v^2) ]
> > > >
> > > > In the context of special relativity this equation has certain
> > > > important meaning. It might be said to be correct in certain contexts.
> > >
> > > Indeed, it is obviously only valid for massive objects
> > > and inappropriate for photons, but in the context of
> > > discussing "relativistic mass" it is correct.
> >
> > Except that it avoids any connection with our intuitive understanding
> > of these things evidenced by for example, juggling.
>
> If you want to be a juggler use Newton. If you want to
> work in high-energy physics or cosmology or any other
> field where SR and GR matter then you need to start
> think in 4D.
>
> > > > In the low speed context with v << c the statement mass times velocity
> > > > is close enough to be said to be true.
> > >
> > > It is close enough to be a useable approximation of
> > > course,
> >
> > Which is a starting point of richer understanding, not the end point.
>
> I disagree, IMO, it avoids understanding the true behaviour
> of nature by coating it in a veneer of Newtonian thinking.
>
> > > but our context was the use of "relativistic
> > > mass" which is specifically used where the
> > > approximation p ~ m v is not adequate.
> >
> > Except as a starting point of making connections to the intuitive
> > knowledge that exists in all learners.
>
> No, you simply said my statement
>
> >> Scientifically speaking, mass is invariant.
>
> was wrong. In fact at the ed of your post you
> implied it was "bs".
>
> > > > For example, if you set c=1 and v=1/1000000 then p = mv is true to one
> > > > part in 5 x 10^-15 If you had a gram of copper and wished to calculate
> > > > the momentum of a gram of the stuff moving at 300 m/sec the difference
> > > > between p=mv and the 'correct' SR formula the error would amount to 5 x
> > > > 10^-15 grams of material. Since the atomic weight of copper is 63.546
> > > > amu, this amounts to 47,367,261 atoms difference, which is
> > > > substantially correct in an