Re: How many things can happen in a single instant?
From: Igor Khavkine (igor.kh_at_gmail.com)
Date: 12/25/04
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Date: Sat, 25 Dec 2004 21:26:37 +0000 (UTC)
Mike Helland wrote:
> All words are completely meaningless and useless until some human
being
> decides otherwise.
That is quite true. In theoretical physics words are given meaning in
two different ways. One way is to assign a name to an experimental
fact,
an observation that everyone can reasonably agree on. The other way is
to assign a name to a mathematical object. Pre-existing notions of what
each name means in non-scientific language is only a guide to choosing
this nomenclature.
> Are you trying to tell me that you're refusing to engage in direct
> conversation with me because you don't have any idea what "change" is
> supposed to mean?
Pretty much, or rather I have no idea what *you* mean by "change". You
have yet to assign a meaning to it that is either independent of the
meaning given to "time", or is well defined mathematically. Philosophy
is easy, but in physics, the devil, as you know, is in the details.
> Here's a mathematical model in the form of a computer program (Visual
> FoxPro):
[...]
Unfortunately the pseudocode you present does not come close to meeting
the expected standard. Let me give you an example. Consider classical
mechanics. State of a given system is defined by a bunch of numbers, we
say that these numbers correspond to degrees of freedom (coordinates)
and their momenta. All these numbers are also functions of one real
variable, which I'll denote by the letter t. We call the variable t
time and the change of the values of the degrees of freedom and their
momenta with respect to time is called evolution. Evolution is
specified by a given differential equation. We say that this
differential equation defines the dynamics of our system and certain
terms in it define forces or potentials.
Using this type of mathematical model, I can already describe a large
number of experimentally realizable situations. For example any system
that can be modeled as a bunch of point particles already fits. Also,
all the terms that are used to describe this model, such as "time",
"degree of freedom", "dynamics", ..., are well defined independent of
their meaning in non-scientific discourse. I expect any framework that
touts itself as an alternative to be at least as easy to interpret.
In fact, changing this model slightly, I can realize in part the idea
you are proposing. So far all degrees of freed of the theory are on
equal footing. Let me pick one of them, say T(t), such that the
equation T(t)=T_0 is invertible for t=T^{-1}(T_0). I will call T(t) a
clock. I can then replace any other degree of freedom x(t) by an
equivalent function of the clock X(T). Hence the notion of time t can
be eliminated and be replaced by an equivalent notion of a clock T. The
deficiency of this model is that T is treated differently than all the
other degrees of freedom. The challenge is now to come up with
something better. And by better I mean that it should be able to
reproduce all that is predicted by the old theory which is observed.
This is the challenge you must meet before you can attract any
significant attention. Crude toy models are helpful for you to figure
out what you need to do to meet this challenge. But they are not
sufficient to convince anyone else.
> Igor Khavkine wrote:
> > Your conclusion about the surface area of a black hole horizone are
> > most likely wrong. This area is tied to many properties of a black
> > hole, including mass, life time, temperature. All of these
parameters
> > are in principle measurable and are not expected to give zero.
>
> Your gut feelings on the likelyness of whether it is likely wrong or
> not is not the point. What is observed is the point.
You are right. I did not want to make any definite statement here,
because my knowledge of the relevant observations is not great. But
I'll say that observations of what we believe to be black holes do
yield non-zero estimates for the horizon surface area. If I am
mistaken, perhaps someone mor knowledgeable can correct me.
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