Why is space-time 4D? I earnestly hope the first reply will be a
succint, obvious answer.

I'm a fourth-year undergrad at the University of Toronto. I have a
technical knowledge of quantum field theory and general relativity, and
of loop quantum gravity to some small extent (largely from reading John
Baez and Carlo Rovelli). It will be a while yet before my understanding
of string theory (or whatever) has progressed much beyond jargon, though
I am trying my best to think deeply on the matter. Maybe there is some
hope people will have nice answers that I will be able to understand.

Classically, maybe we don't have to ask this question - we can say that
space- time is 4D and that's that. But then again, maybe there is some
deep answer that has occurred to someone. (I know that GR is
qualitatively different with dim 4.)

Similarly with LQG, it seems that people are happy to enforce something
like 4- dimensionality by speaking only of space-time made up of
4-simplexes, so maybe they don't have to answer that question. But
maybe they would like to. Also, my uneducated brain worries, as I
gather others' do, that LQG space-time crumples down to some effective
dimensionality between 0 and 4 at large scales. (Or, for that matter,
that it crumples down from, say, 42 to 4 dimensions.)

Other people tell me that, on some scale between M theory and real life,
space- time is definitely 11-dimensional. 7 of those dimensions are
small and compact, whereas the other 4 are large (and possibly also
compact). On the other hand, I know some people suggested that some or
all of the extra 7 dimensions are only traversed by gravity, but maybe
that is unpopular now?

So my question really is, what's so special about the number four? Is
there nothing in particular? Is 4D a distressingly random fact? If 4
is just an effective dimensionality, this doesn't seem to be an
acceptable answer.

For a while now I've been disturbed by the possibility that MATH selects
4 as the natural dimensionality, once we finally get our heads screwed
on straight about what space-time is.

Thanks,

Michael

wrote:

Why is space-time 4D? I earnestly hope the first reply will be a
succint, obvious answer.

Since space is 3-dimesnional and time is 1-dimensional.

So my question really is, what's so special about the number four?
Is there nothing in particular?

4=1+3.

We know from everyday observation that we are dragged
along a 1-dimensional time and that we can move in three
linearly independent directions, but not more. Since we are
quite local to the universe, this means that the universe must
be locally 1+3-dimensional, at least down to the smallest
currently resolvable distances.

The 6 other dimensions discussed string theorists (10=1+3+6)
are not really space-time dimensions but (loosely speaking) one
charge dimension, two isospin dimensions, and three color
dimensions. We cannot move in these directions, nor are we
moved along these; so thy are not space-time.

Should string theory turn out to match reality
(which, despite claims to the contrary, no one knows),
these extra dimensions would become sort of mixed up with
space-time at imperceptible small distances, which would give
the universe, which in the standard model has only 4
parametrized dimensions, 10 parameterized dimensions
and hence some sort of unity which they call 10D space-time.
But since it is quantized, it resembles very little our
notions of space and time.


Arnold Neumaier

In message , Arnold Neumaier
writes

We know from everyday observation that we are dragged
along a 1-dimensional time and that we can move in three
linearly independent directions, but not more. Since we are
quite local to the universe, this means that the universe must
be locally 1+3-dimensional, at least down to the smallest
currently resolvable distances.

The 6 other dimensions discussed string theorists (10=1+3+6)
are not really space-time dimensions but (loosely speaking) one
charge dimension, two isospin dimensions, and three color
dimensions. We cannot move in these directions, nor are we
moved along these; so thy are not space-time.

Should string theory turn out to match reality
(which, despite claims to the contrary, no one knows),
these extra dimensions would become sort of mixed up with
space-time at imperceptible small distances, which would give
the universe, which in the standard model has only 4
parametrized dimensions, 10 parameterized dimensions
and hence some sort of unity which they call 10D space-time.
But since it is quantized, it resembles very little our
notions of space and time.

Is there anything special mathematically about 3 dimensions?

Presumably an interesting universe (one that we can talk about) requires
complexity and relative stability. That is, not so complicated that
chaos ensues but complicated enough for a wide range of interactions?
I'm wondering whether 3 spatial dimensions is special in any way in that
it's a minimum for complexity and whether 3 could be too chaotic for
stability?

And finally, does the standard model predict/explain the origin of the 3
spatial dimensions?

--
Stephen Riley

On Thu, 30 Oct 2003 06:46:28 +0000 (UTC), in sci.physics.research
wrote:

Why is space-time 4D? I earnestly hope the first reply will be a
succint, obvious answer.

Because there is no experimental evidence that it is anything else.

George D. Freeman IV
the softrat
Curmudgeon-at-Large

--
If the world was a logical place, *men* would ride horses
side-saddle.

wrote in message ...
Why is space-time 4D? I earnestly hope the first reply will be a
succint, obvious answer.

I'm a fourth-year undergrad at the University of Toronto. I have a
technical knowledge of quantum field theory and general relativity, and
of loop quantum gravity to some small extent (largely from reading John
Baez and Carlo Rovelli). It will be a while yet before my understanding
of string theory (or whatever) has progressed much beyond jargon, though
I am trying my best to think deeply on the matter. Maybe there is some
hope people will have nice answers that I will be able to understand.

Classically, maybe we don't have to ask this question - we can say that
space- time is 4D and that's that. But then again, maybe there is some
deep answer that has occurred to someone. (I know that GR is
qualitatively different with dim 4.)

Similarly with LQG, it seems that people are happy to enforce something
like 4- dimensionality by speaking only of space-time made up of
4-simplexes, so maybe they don't have to answer that question. But
maybe they would like to. Also, my uneducated brain worries, as I
gather others' do, that LQG space-time crumples down to some effective
dimensionality between 0 and 4 at large scales. (Or, for that matter,
that it crumples down from, say, 42 to 4 dimensions.)

Other people tell me that, on some scale between M theory and real life,
space- time is definitely 11-dimensional. 7 of those dimensions are
small and compact, whereas the other 4 are large (and possibly also
compact). On the other hand, I know some people suggested that some or
all of the extra 7 dimensions are only traversed by gravity, but maybe
that is unpopular now?

So my question really is, what's so special about the number four? Is
there nothing in particular? Is 4D a distressingly random fact? If 4
is just an effective dimensionality, this doesn't seem to be an
acceptable answer.

For a while now I've been disturbed by the possibility that MATH selects
4 as the natural dimensionality, once we finally get our heads screwed
on straight about what space-time is.

Thanks,

Michael

There are explanations from string theory that explain why we have
three uncompactified spatial dimensions, and the other spatial
dimensions are compacified. According to the Berkenstein-Vafa
mechanism, all the dimensions started out as compact, and shortly
after the Big Bang, the interaction of strings caused three to
uncompactify. This mechanism specifically predicts that exactly three
spatial dimensions will uncompactify. It has to do with how much room
there is for the strings to move around in. Once you have three
infinitely extended spatial dimensions, the strings have so much room
to move around in, they interact rarely enough, that it's not
energetically favorable to decompactify more dimensions.

You can also explain it with the anthropic principle on the grounds
that life will be most likely in a universe with three extended
spatial dimensions. If you had less than three spatial dimensions, the
strings would have such little room to move around in, they would
crowd each other out, and you couldn't have complicated interactions
necessary for life. If you had more than three spatial dimensions, the
strings would have so much extra room to move around in, they would
normally sail right past each other, and its unlikely you would have
really complicated interactions necessary for life.

Jeffery Winkler

http://www.geocities.com/jefferywinkler

Stephen Riley wrote:

Is there anything special mathematically about 3 dimensions?

One thing that is special about three dimensions is the existence
of the cross product, and the corrsponding exceptional isomorphism
so(3)=su(2).


And finally, does the standard model predict/explain the origin of the 3
spatial dimensions?

no, it *assumes* it!

Arnold Neumaier

Arnold Neumaier wrote in message
...

Stephen Riley wrote:

Is there anything special mathematically about 3 dimensions?

One thing that is special about three dimensions is the existence
of the cross product, and the corrsponding exceptional isomorphism
so(3)=su(2).

There's also a version of the cross product in 7 dimensions.

Jeffery Winkler

http://www.geocities.com/jefferywinkler

Dear Michael,

"why is spacetime four-dimensional" or more precisely "why is there one
time and three large and visible spatial directions" is a very deep and
good question - a question that we're so far not able answer fully.

There are some anthropic explanations. Life remotely similar to ours would
be impossible in higher dimensions. The potential energy 1/r would be
replaced by 1/r^2, 1/r^3 etc. in 4+1, 5+1 etc. dimensions, and this would
make the hydrogen atom (or something that replaces it) collapse, for
example. There are other geometric limitations of the life in
dimensionalities different from 3+1. Theoretical physicists today study
physics in various different dimensionalities; many things are universal,
many features depend on the dimension.

Loop quantum gravity takes four dimensions of spacetime as input - which
is not quite right as string theorists say - and therefore it can't ever
answer the question "why 3+1". Some physicists in 8-dimensional or even
11-dimensional spacetime might construct another version of loop quantum
gravity - in fact, these proposals have been suggested even by some
three-dimensional physicists, and most of them know the 2+1-dimensional
version of loop quantum gravity. These versions of LQG depend on the
dimensionality and differ in technical details, but many of them exist.

Although the formalism of spin networks and spinfoams looks discrete - and
does not necessarily carry the microscopic information about the spacetime
dimensionality - it is generally believed that the 3+1-dimensional
spacetime is the only possible spacetime that can emerge from the spin
networks, and there are serious doubts whether a quasi-smooth spacetime at
least of this dimensionality can arise from loop quantum gravity. There
exist classical arguments why this could be possible - the quantized
3+1-dimensional spacetime is a starting point to derive the laws that
govern the spin networks. But there also exist quantum arguments that *no*
smooth spacetime arises from loop quantum gravity at long distances i.e.
there are no long distances at all. There is no indication that the spin
networks might conspire to produce a higher-dimensional spacetime; more
likely they crumple into a chaotic collection of vertices and edges.

String theory is the only known theory - and as most of its practitioners
are convinced, it is the only theory ever - that has the capacity to
answer such deep questions: why is the number of dimensions what it is?
Why do we see exactly this spectrum of elementary particles and forces?
The simplest calculation of the total spacetime dimensionality says that
there must be 9 spatial and 1 time direction in string theory. A modern
update of string theory - M-theory - shows that string theory (in a more
general sense) contains 10+1-dimensional spacetimes, too.

There are many geometrical shapes that these dimensions can have, and most
of these possibilities include the idea that the manifold spanned by
several dimensions can be compact. (When a manifold is too small, its
geometry - and even the notion of its dimensionality - becomes slightly
ill-defined, because of wrapped strings and other effects.) While 3+1
dimensions can remain large, the 6 "additional" dimensions may be
compactified. The spacetime is then - in the simplest model - a Cartesian
product of the 3+1-dimensional Minkowski space and a 6-dimensional compact
manifold (a Calabi-Yau manifold). Generalizations with warped geometry or
7-dimensional manifolds (in M-theory) exist.

None has been able to find a convincing argument why exactly 3+1
dimensions should remain large, although people have tried. For example,
Brandenberger and Vafa proposed an interesting mechanism that seems to
imply that after the Big Bang, only 3 spatial dimensions were allowed to
grow because the strings that are wound around these dimensions tend to
stop their expansion, but if only 3 dimensions are becoming large, the
wound strings are not efficient enough and eventually a thermal
fluctuation will allow 3 dimensions to grow.

Well, this was an interesting argument, but because of the 2nd superstring
revolution this argument became even less convincing than it used to be:
today, strings are known not to be the only players in string theory.

In fact, today it seems likely that some sort of anthropic explanation
will eventually have to be accepted for the dimensionality of spacetime -
and the fact that supersymmetry is broken. It's because we know almost
certainly that many Universes with a different number of large dimensions
(between 5 and 11, for example) are possible and consistent.

On the other hand, I know some people suggested that some or
all of the extra 7 dimensions are only traversed by gravity, but maybe
that is unpopular now?

This is the braneworld scenario - in which all particles of the standard
model are stuck on a "brane" which is an object who dimensionality is
smaller than the dimensionality of spacetime. Gravity is dynamics of
geometry of the whole spacetime - and therefore it always acts everywhere
(it is always made of closed strings in perturbative string theory) while
photons, electrons and other particles may be stuck on the brane. If the
extra dimensions (perpendicular to the brane) are large enough, the
gravity will be diluted, which would also explain why it is so weak.

The braneworlds are still popular because none has been able to show that
there is something fundamentally wrong about them, and they provide us
with a chance that the LHC will be able to see string theory, extra
dimensions, or quantum gravity of small black holes - very exciting
prospects. This still makes *phenomenologists* - and not only them - very
excited because we could see something truly fascinating in 5 years.

On the other hand, most string *theorists* are sceptical and they still
prefer (=find more likely) the conventional models in which the extra
dimensions are much smaller than what we're gonna be able to see in the
next centuries.

Best wishes
Lubos
__________________________________________________ ____________________________
E-mail: fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
phone: work: +1-617/496-8199 home: +1-617/868-4487
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Superstring/M-theory is the language in which God wrote the world.

In article ,
Jeffery wrote:

There are explanations from string theory that explain why we have
three uncompactified spatial dimensions, and the other spatial
dimensions are compacified. According to the Berkenstein-Vafa
mechanism, all the dimensions started out as compact, and shortly
after the Big Bang, the interaction of strings caused three to
uncompactify.

Can you provide a citation for this? I couldn't find any papers on
arxiv by both Bekenstein and Vafa, and I didn't see any likely titles
for either of them individually either, nor any abstracts containing
"bekenstein vafa". Googling various permutations didn't yield
anything either.


--
================================================== ====================
Kevin Scaldeferri Calif. Institute of Technology
The INTJ's Prayer:
Lord keep me open to others' ideas, WRONG though they may be.

a écrit dans le message news:
...

Why is space-time 4D? I earnestly hope the first reply will be a
succint, obvious answer.

Because the set of the octonions isn't a group for the multiplication.

--
~~~~ clmasse at free dot fr
Liberty, Equality, Profitability.