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MikeHelland


Registered: Dec 2003
Posts: 181

Computer Simulations and Spacetime

An update on an earlier post about special relativity, looking for crituqes:

Looking for a critique of the following write-up:


The Problem:


Create a computer simulation of the universe


This is a software engineering problem that requires some physics
knowledge.


It is tempting to think that something like a pong game, a three
dimensional space with some objects boucing around and a few more
interesting features like mass and thermodynamics, would be adequate
enough to solve the problem of simulating the universe.


But it isn't that simple, according to the scientific knowledge we have
of the universe today. Specifically, that kind of model fails to
account for the insights provided by relativity and quantum mechanics.


Newton's model was based on absolute space and absolute time, but
Einstein abandonded those concepts and made a model from relative space
and relative time that combine to make a four dimensional structure
called spacetime. In doing so, he was able to eliminate an absolute
reference frame, which allowed him to make the speed of light constant
in all relative frames, providing an explanation of the
Michelson-Morley experiment among other things.


If our solution to the problem is a good solution, the simulation
should reproduce accurate predictions of the results of actual
experiments, such as the Michelson-Morely experiment. Which brings up
The Relativity Problem:


Create a computer simulation of the universe using spacetime


The wikipedia states:


"The basic elements of spacetime are events, these being represented by
points in the spacetime. Examples of events include the explosion of a
star, or the single beat of a drum.


A spacetime is independent of any observer. However, in describing
physical phenomena (which occur at certain moments of time in a given
region of space), each observer chooses a convenient coordinate system.
Events are specified by four real numbers in any coordinate system."


Spacetime may be independent of an observer, but in order for it to
actually describe the universe, we must supply it measurements that are
depedent on an observer. This is important to know.


If a computer algorithm were made for spacetime, that would not be a
computer simulation. To create a computer simulation we would need
initial conditions to which our algorithm can be applied successively.
Since the initial conditions for the simulation must be relative to
some observer, the simulation itself would be a simulation of the
observable universe according to one observer. While that simulation
may provide enough data to use as initial conditions to simulate the
universe according to a second observer, there are several issues with
going that route:


1. there will be observers outside of the original observer's light
cone, meaning the scope of the simulation will always be severely
limited
2. even if another set of initial conditions can be derived from the
original simulation, that requires the initialization of another
simulation


Those are severe problems that boil down to one critical problem: in
order to simulate the universe for all observers using spacetime, more
than one simulation is required.

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Old Post 12-22-2005 05:09 PM
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Stedman


Registered: Dec 2005
Posts: 5

Mike,

I too am a big fan of the "Problem" you purpose. In fact, I too am interested in the solving the same problem: To write a computer simulation of th universe.

(In fact, on a more philosophical note, I think that deep down everyone is at least a little interested in making this happen. :)) It's one of the main reasons that I majored in physics in college.

Let me offer you a suggestion, hopefully it will help. I'm not a complete expert, so some things might not be exactly accurate. But here's what I can offer:

So it maybe that in this discussion of special relativity you are not thinking quite generally enough. Often the simply mathematical structure of special relativity gets disguised in all sorts of "flowery language".

Here's all that's really going on:
In Newtonian mechanics we are concerned with a continuous 3-dimensional set called R^3. We define a metric, or a "measure of distance" on the set R^3 called the Euclidean metric, defined as Sqrt[x^2 + y^2 +z^2], that we must have before we can even start talking about distances, etc. The metric is not a mathematical axiom. It is in fact an empirically determined postulate. Now, any particle's position in R^3 can be expressed as a parameterized curve from R -> R^3. This curve is x(t), called the world line of the particle. The parameter t is called "time".

Now in Special Relativity, here's all we do:
1. Change from R^3 to R^4.
2. Define a new metric: Sqrt[x^2 + y^2 + z^2 - (c^2)t^2]. c is the "speed of light".
3. Now every particle (ie pong ball) has a position function which is a map R -> R^4, still a parameterized curve, but this time in R^4 rather than R^3. The parameter to this curve is now called L (lambda, actually), giving us a function u(L) = (x(L), y(L), z(L), t(L)), a point in R^4 instead of R^3.

All we have done, really, is just add another dimension, to make time just like another component of space. However, we change the metric a little so that time is still different. All the stuff about light cones, simultaneity, and observers observing different things all comes from this simple model of world lines in R^4 with the "Lorentz metric" instead of the "Euclidean metric". An "observer" treats the fourth coordinate t as if in the Newtonian world. This is what makes observations different for each observer. But overall the universe is simply treating t as another space coordinate (with different metric component). So we can still in fact talk of "one universe".

The statement that a particle cannot travel out of it's light cone is simply the statement that the "magnitude" of du/dL must be negative.

Hope this helps. Best,
--Stedman

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Old Post 12-26-2005 07:23 PM
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MikeHelland


Registered: Dec 2003
Posts: 181

Stedman,

You're comparing spacetime to be exactly equal to the universe.

And if it were, there would be one universe, and thus one simulation could simulate a universe based on spacetime.

But if you want a real simulation, spacetime is only going to be an algorithm. There is more to the simulation than that. You'll need initial conditions for your rules.

Those initial conditions, when calculating things like length contraction, are going to require relative velocity being expressed in the inputs.

Thus the simulation, as the rules and initial conditions together, are only going to represent the universe according to one observer. You'll need more simulations with different initial conditions to get the rest.

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Old Post 12-30-2005 08:26 PM
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MikeHelland


Registered: Dec 2003
Posts: 181

I posted the original message to sci.physics.research on usenet, and it was rejected.

If anyone can show how length contraction of a rod is calculated without having a relative velocity for the rod, I'd be interested in seeing it.

I think the moderator of that group is rejecting the post about computer programs because it is critical of relativity.

Thoughts?

MobyDikc wrote:
> On 12/25/05, Igor Khavkine <ikha...@uwo.ca> wrote:

> > vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
> > > Since the initial conditions for the simulation must be relative to
> > > some observer, the simulation itself would be a simulation of the
> > > observable universe according to one observer.
> > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> > The above is false.

> There are two statements in there, please help me identify the
> incorrect one.

> If the computer is to simulate relativistic effects in spacetime, then
> the inputs must include relative velocity.

> The computer program based on those initial inputs would be simulating
> the universe from the perspective of an observer.

> Which of those statements is false and why?

Igor has replied and informed me that both statements are false.

If the following statement is false:

> If the computer is to simulate relativistic effects in spacetime, then
> the inputs must include relative velocity.

then it must be true that the length contraction of rod measured by an
observer can be calculated without knowing the relative velocity of
the rod.

Can someone show that calculation?

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Old Post 12-30-2005 08:30 PM
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MikeHelland


Registered: Dec 2003
Posts: 181

If anyone can show a problem with the following logic I'd love to see it.




Universe Postulate

There is one universe with one set of laws and one set of initial conditions

Mind Postulate

The mind is a self-referential axiomatic sub-system of the universe

Measurement Postulate

Measurements such as distance, duration, and mass are statements of the mind

Relative Measurement Postulate

Measurements at high speeds vary between minds, a phenomenon known as length contraction and time dilation


A theory consistent with these postulates does not exist in mainstream physics, because special relativity fails the first postulate. Here's why:

If the universe's laws include space-time, then the initial conditions, the inputs that special relativity requires to calculate length contraction, must contain relative velocity, the measurements of an observer. If the initial conditions are the measurements of an observer, then the measurements cannot include information about other observer's outside the original observer's lightcone. Therefore, in order for the laws of special relativity to predict relativistic measurements for every observer in the universe, a unique set of initial conditions is required for every observer.

Which contradicts the universe postulate: there is supposed to be one universe with one set of laws and one set of initial conditions.

There might be some new and interesting way to modify space-time so that a single set of inputs predicts relativistic effects for every observer, but that has yet to be created and there is a perfectly good reason to think that it will never be created: special relativity describes a static universe in 4 dimensions where the past, present, and future are defined together, not a universe whose state is constantly progressing from the initial state according to the laws.

Special relativity and the universe postulate are fundamentally incompatible.

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Old Post 01-10-2006 05:33 PM
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