Well, I dont want to speculate too much regarding applying transfinite
set theory to physics, but it certainly warrants contemplation.

I think that it is certainly true that there is at least one point in
the universe. I dont know how to prove it.

Most people would also agree that there are countably infinitely many
such points. I dont know how to prove it.

And, it seems very likely that there are uncountably infinitely many
points in the universe, and again, I have no proof.

It seems reasonable that there are lines, planes, and manifolds. But I
have no proof.

If all of this stuff regarding time and existence is valid, then you
also have a different kind of point which Cantor did not have. You have
trivial points. Or, what "appear" to be trivial points. I have no idea
if this could give insight into a new angle at looking at transfinite
cardinals, but stranger things have happened. It might be the case that
the "illusion" of trivial points gives rise to the "illusion" of a new
transfinite cardinal - and would'nt that be a treat !! However, I have
no reason to say that such a thing exists or not, I'm just sitting here
wondering about things.


Many people assume that Minkowski(3+1) is continuous, or to be more
specific, that the actual physical manifold in which we exist is
continuous. Most people make that assumption, but there is no proof.

But if you allow triviality, then you can probably make a very
reasonable argument that points in the universe must be separated by
points which either exist or do not exist. In either case, the result
is continuity. Paradoxically, between any two existing points you can
have nonexisting points, hence, discontinuity. So, continuity and
discreteness "appear" to coexist - all because time becomes
unobservable. You could almost create something which looks like a
proof, but would almost certainly be laughed at by most people. The
fundamental thing, however, is that time and length become
unobservable, and this makes the argument much more convincing. The
mechanism for this process is very easy to understand and believe.

So, while the results are incredible, the mechanism which facilitates
the results is highly credible.

LEFTY wrote:
Well, I dont want to speculate too much regarding applying transfinite
set theory to physics, but it certainly warrants contemplation.

I think that it is certainly true that there is at least one point in
the universe. I dont know how to prove it.

Most people would also agree that there are countably infinitely many
such points. I dont know how to prove it.

And, it seems very likely that there are uncountably infinitely many
points in the universe, and again, I have no proof.

It seems reasonable that there are lines, planes, and manifolds. But I
have no proof.

If all of this stuff regarding time and existence is valid, then you
also have a different kind of point which Cantor did not have. You have
trivial points. Or, what "appear" to be trivial points. I have no idea
if this could give insight into a new angle at looking at transfinite
cardinals, but stranger things have happened. It might be the case that
the "illusion" of trivial points gives rise to the "illusion" of a new
transfinite cardinal - and would'nt that be a treat !! However, I have
no reason to say that such a thing exists or not, I'm just sitting here
wondering about things.


Many people assume that Minkowski(3+1) is continuous, or to be more
specific, that the actual physical manifold in which we exist is
continuous. Most people make that assumption, but there is no proof.

But if you allow triviality, then you can probably make a very
reasonable argument that points in the universe must be separated by
points which either exist or do not exist. In either case, the result
is continuity. Paradoxically, between any two existing points you can
have nonexisting points, hence, discontinuity. So, continuity and
discreteness "appear" to coexist - all because time becomes
unobservable. You could almost create something which looks like a
proof, but would almost certainly be laughed at by most people.

The fundamental thing, however, is that time
and length become unobservable,

No... this is not true and it is a trap many fall into.

1. You may take a trajectory where the forces between
you and another moving particle do not change.
Time will elapse. (It only waits for women)

2.You may take a trajectory where the forces between
you and another particle do change.
Time will elapse. Time will have some relation
to the change in forces.

Using the second statement, you can construct a
valid co-ordinate system with time as axis. But
to be continuous, it will violate the quite
sensible first statement for many trajectories.

Theoretical physicists don't use the term 'force'
much anymore. This may be why. ;-)

Sue...

and this makes the argument much more convincing. The
mechanism for this process is very easy to understand and believe.

So, while the results are incredible,

What is incredible... radio or magnetism ?

Sue...

the mechanism which facilitates
the results is highly credible.

The fundamental thing, however, is that time
and length become unobservable,

No... this is not true and it is a trap many fall into.


On large scales, you cant build a clock out of the whole universe. It
does not tick. You can never observe it's operation. Time becomes
unobservable.

On small scales, Planck says that there is a smallest interval of time
- but gives no explanation how that could happen. Planck's view leads
to many absurd paradoxes.

Bottom line, our ability to observe dimensionality is limited. Very
simple.


1. You may take a trajectory where the forces between
you and another moving particle do not change.
Time will elapse. (It only waits for women)


Of course. Time always elapses. Planck says that you and the particle
cannot be separated by less than Planck length. That is silly. If the
distance were less than Planck length it would simply be unobservable.
Individual items might "appear" to occupy the same location at the same
time, but this is impossible. That would violate uniqueness of objects.

To refresh - I have a dollar bill in my hand. I claim that it is really
1,000,000 dollars, all the bills are identical - even occupying the
same exact position in space. 999,999 of those bills are trivial.

2.You may take a trajectory where the forces between
you and another particle do change.
Time will elapse. Time will have some relation
to the change in forces.


This is true, of course, and time is certainly treated as if it is
continuous in ordinary usage. Planck says it's not. Somehow it is
discrete. This discreteness must be due to a constraint on
observability.



Using the second statement, you can construct a
valid co-ordinate system with time as axis. But
to be continuous, it will violate the quite
sensible first statement for many trajectories.

Theoretical physicists don't use the term 'force'
much anymore. This may be why. ;-)

Sue...

and this makes the argument much more convincing. The
mechanism for this process is very easy to understand and believe.

So, while the results are incredible,

What is incredible... radio or magnetism ?


Nonlocality.

:]

better answer - I think.....

1. You may take a trajectory where the forces between
you and another moving particle do not change.
Time will elapse. (It only waits for women)


This is true. But you cannot observe this system for less than Planck
time.

2.You may take a trajectory where the forces between
you and another particle do change.
Time will elapse. Time will have some relation
to the change in forces.


Also true, but same arguemnt applies as in first case.


Suppose that the universe is infinitely large in size. Would it ever be
possible to measure it's diameter ? No. You cannot observe an infinite
length in it's entirety. There _must_ be a cosmic equivalent of Planck
length, whether the universe is infinite or not.

Same thing for infinitesimally small lengths. Infinitessimally small is
by definition always greater than zero. But you'll never be able to
observe something like that, because it's liek trying to measure
infinity. Even if you had instruments with infinite precision, you
would be zooming in forever and never find bottom. It cannot be
observed. Something _must_ give between here and infinity.

Hence, scale.

LEFTY wrote:

Consider any physical object which really does exist. The Earth, your
car, Los Angeles, whatever. I ask you to make an observation of that
object using whatever method you wish - but you MUST make your
observation very quickly, you must complete the observation in LESS
than PlanckTime. You will not be able to observe anything, and must
report back to me that these things are "unobservable". You cannot
confirm whether they exist, or not.

It's all a matter of relative scales.


Is that so cranky ?

An "observer" needn't be a sentient being. A rock, or a single
atom, can act as an "observer", and it is required to observe
for less than the Planck time then how can _it_ be said to
exist?

Hmmmm - a good question. Really, you've illustrated a paradox created
by Planck, who never explains how time could possibly have an "absolute
bottom".

Palnck's thinking seems to follow the trend of those who searched for
that "fundamental widgit" from which all things were composed. People
have been looking for the fundamental Leggo. Thats why Planck thinks
that time has an "absolute bottom".

Planck had it backwards. There is no fundamental chunk of time, rather,
there is a fundamental chunk of existence based on our ability to
observe time, and this ability to observe has nothing to do with
instrumentation, and everything to do with what the universe wants us
to observe.


If Planck is right, then :
"When the universe was created, it was already 1*10^(-44) seconds old."


The only reason to say such things is to use physics as a surrogate for
confucianism.

Prove it.

LEFTY wrote:
[snip]

There is no fundamental chunk of time,

One of us is confused; if time is continuous, then one observes
everything, always, for "less than planck time", because "less than
planck time" is contained/included in *any* amount of time, including
one exact bit of planck time. I vote for this. But you're telling me I
can't observe for "less than planck time".
Maybe observing any part of an infinite length *is* observing that
length in it's entirety.

rather,
there is a fundamental chunk of existence based on our ability to
observe time,

I don't observe time when I'm sleeping...(sorry)

I don't observe you when you walk behind a wall. If I could "see"
smaller than an electron, maybe I'd see you through the wall...either
way your existence, even though it may affect me, doesn't depend on my
ability to observe you, or any knowledge of your existence on my part.


and this ability to observe has nothing to do with
instrumentation, and everything to do with what the universe wants us
to observe.

Existence is observed. It's the only thing the universe has decided
to show us.
Nonexistence is not observed. (Hundred-foot tall flame-throwing
babies exist conceptually as a comeback to the above statement).This
doesn't mean that whatever isn't observed doesn't exist.
Doesn't existence preclude nonexistence? Nonexistence can't have
relationships to anything, so how does one define it sensibly?
The concept of "nothing" serves only to reinforce the reality of
"something", since without the reality the concept has no meaning.


If Planck is right, then :
"When the universe was created, it was already 1*10^(-44) seconds old."

Only certain humans need the universe to have had a beginning. One
thing's for sure - if it was "created" from "nothing", at some point in
time, then "nothing" is actually something containing time, and the
potential for the creation of the universe. Nice nothing ya got
there...


Remember I said "one of us..." (might be both)

p

LEFTY wrote:
The fundamental thing, however, is that time
and length become unobservable,

No... this is not true and it is a trap many fall into.


On large scales, you cant build a clock out of the whole universe. It
does not tick. You can never observe it's operation. Time becomes
unobservable.

Universalclock:
the energy is conserved if and only if the physical laws are
invariant under time translations (if their form does not depend on
time)
http://en.wikipedia.org/wiki/Noether's_theorem


On small scales, Planck says
Planck had an ultraviolet catastrophe...
You don't.

Planck sez:
the continuity between the static and
the dynamic fields and, with it, the complete
understanding we have enjoyed, until now, of
the fully investigated interference
phenomena - would have to be sacrificed,
both being very unhappy consequences for
today's theoreticians.
http://nobelprize.org/physics/laurea...k-lecture.html



that there is a smallest interval of time
- but gives no explanation how that could happen. Planck's view leads
to many absurd paradoxes.

You are confusing Planck's PoV with the formalism
of OM.

I quantise a wall drawing squares on it. I do not
expect to by a tiny can of paint perfectly sized to
the squares.


Bottom line, our ability to observe dimensionality is limited. Very
simple.

Speak for yourself.



1. You may take a trajectory where the forces between
you and another moving particle do not change.
Time will elapse. (It only waits for women)


Of course. Time always elapses.
Planck says that you and the particle
cannot be separated by less than Planck length. That is silly. If the
distance were less than Planck length it would simply be unobservable.
Individual items might "appear" to occupy the same location at the same
time, but this is impossible. That would violate uniqueness of objects.

To refresh - I have a dollar bill in my hand. I claim that it is really
1,000,000 dollars, all the bills are identical - even occupying the
same exact position in space. 999,999 of those bills are trivial.

2.You may take a trajectory where the forces between
you and another particle do change.
Time will elapse. Time will have some relation
to the change in forces.


This is true, of course, and time is certainly treated as if it is
continuous in ordinary usage. Planck says it's not. Somehow it is
discrete. This discreteness must be due to a constraint on
observability.


Can you offer a URL where Planck "says" all these
silly things ?





Using the second statement, you can construct a
valid co-ordinate system with time as axis. But
to be continuous, it will violate the quite
sensible first statement for many trajectories.

Theoretical physicists don't use the term 'force'
much anymore. This may be why. ;-)

Sue...

and this makes the argument much more convincing. The
mechanism for this process is very easy to understand and believe.

So, while the results are incredible,

What is incredible... radio or magnetism ?


Nonlocality.

You need all that math to see the attraction between
a charged comb and pith ball is real cool ?

Sue...



:]

"LEFTY" wrote in message
ups.com...
|
| The fundamental thing, however, is that time
| and length become unobservable,
|
| No... this is not true and it is a trap many fall into.
|
|
| On large scales, you cant build a clock out of the whole universe. It
| does not tick.

Of course it ticks, and you CAN build a clock out of the entire unverse.
See the tick (fixed font):
| Merc | Venus |Earth |Solar | Mars | Watch |
|_______|_______|_______|_______|_______|________|
| |88/ |88/ | 88 / | 88/ |88/ |
Mercury | 1 | 225 | 365 | 1 | 687 | 68400 |
|_______|_______|_______|_______|_______|________|
| 225/ | | 225/ | 225/ | 225/ | 225/ |
Venus | 88 | 1 | 365 | 1 | 687 | 68400 |
|_______|_______|_______|_______|_______|________|
| 365/ | 365/ | | 365/ | 365/ | 365/ |
Earth year| 88 | 225 | 1 | 1 | 687 | 68400 |
|_______|_______|_______|_______|_______|________|
| 1/ | 1/ | 1/ | | 1/ | 1/ |
Solar day| 88 | 225 | 365| 1 | 687 | 68400 |
|_______|_______|_______|_______|_______|________|
| 687/ | 687/ | 687/ | 687/ | | 687/ |
Mars | 88 | 225 | 365| 1 | 1 | 68400 |
|_______|_______|_______|_______|_______|________|
| 68400/| 68400/| 68400/| 68400/| 68400/| |
Watch(sec)| 88 | 225 | 365| 1 | 687 | 1 |
|_______|_______|_______|_______|_______|________|

Each entry in the table is a ratio between a pair of oscillators.
Change one oscillator and you change every ratio in its row and column
without affecting the others.


| You can never observe it's operation. Time becomes
| unobservable.

Time is very observable. I'm part owner of this clock,
which hasn't lost or gained a picosecond in 3,500 years.
http://witcombe.sbc.edu/earthmysteries/EMStonehenge.jpg

Androcles.