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Four-dimensionalism claims that the universe is basically one huge space-time worm and that everything exists at once (however you want to say that since "internal time" is then just another coordinate in this worm and I'm talking about the look from the outside).

OTOH, all processes in the universe seem to follow an energy economic principle (second law of thermodynamics), that is, everything tries to reach a state of lowest energy.

Now I'm wondering if that isn't enough to refute the idea of 4D-ism: For it to be the correct theory about space-time, you'd need a lot more matter (at least) because every point in time must be materialized as a "solid" state. That means for everything can happen within what we perceive as "one second", one state must be encoded.

Quantum processes happen at attoseconds (10^-18s), so you need at least 10^18 states just to encode one second of the 4D worm.

So my argument is that, just to prove the theory, you're "wasting" insane amounts of whatever the universe is made of.

Is that correct or am I missing something?

NOTE: English is not my mother language, so I may have use the wrong terms but I hope you get the idea.

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Not sure this is even a physics question. Remember however there is a holographic principle stating that all information in a N-dimensional space can be encoded on a (N-1)-dimensional boundary. If that principle holds true, I don't see any problem. –  Raskolnikov Nov 28 '10 at 13:03
    
Isn't 4D-ism a physical theory? –  Aaron Digulla Nov 28 '10 at 13:37
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Never heard of it. Unless it means: the universe can be described as a 4-dimensional manifold, then it is a part of for instance GR or quantum field theory, but in and of itself, it is not rich enough to constitute a physical theory. –  Raskolnikov Nov 28 '10 at 13:47
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The second law of thermodynamics doesn't state that "everything tries to reach a state of lowest energy". Think about a hot cup of tea, the tea cools down to room temperature, but the room heats up by a corresponding amount of heat (not by the same amount of temperature). The energy remains the same - it merely becomes less usable. Hence, the entropy increases. –  Ebenezer Sklivvze Nov 28 '10 at 14:10
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Nothing in the Wikipedia entry for four-dimensionalism suggests that it is a physical theory. What is at stake in deciding whether we believe 4D-ism seems to be how "real" the past and future are compared to the present. From a physicist's perspective this is completely irrelevant. Physical theories make no reference to the "present" since they should be able to describe events in the past and future as well. Not to mention the fact that the "present" is only defined with respect to an observer's reference frame (special relativity). –  Greg P Nov 28 '10 at 17:00

1 Answer 1

In both cases you need a very large infinity of states to describe the universe. Whether you treat time as a special coordinate, and thus use standard mechanics with trajectories, velocities etc., or if you treat time as just one of the four coordinates in a special four dimensional manifold, these coordinates are assumed to vary continuously.

The difference between the two representations are the following:

  • In 3d you have the concept of a place, and of a time-evolution; in 4d you have the concept of an event, or series of events.
  • In 3d time and space are absolute, in 4d are bound to an observer and freely mix, in general relativity they are curved, even absolutely (e.g. the whole universe might not be flat).
  • In 3d you have one "copy" of matter that evolves through time; in 4d you have one "copy" of matter as well, which "lives" along a 4d curve, describing its position at each time (depending on the observer).

So, both theories are just as economical.

Now, you may be interested by the many-world hypothesis. That theory is much more expensive as a (at least partial) copy of the universe is created each time a measurement is made. However, though, nothing changes - energy only tends to settle to local minima and not necessarily absolute ones: each copy of the universe has then its minima to tend to, and nothing is out of place.

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+1 for the explanation. There is a point which I still don't understand: Can you please elaborate what you mean by "which 'lives' along a 4d curve"? As I understood, the whole system is static in 4d and what we understand as "present" is just a specific slice in which my brain happens to thinks "present". This also leads to full determinism because the future is already a solid, never-changing fact even though I haven't experienced it, yet. –  Aaron Digulla Nov 28 '10 at 18:08
    
Note: I'm aware of the many-world hypothesis and I don't like it for similar reasons but my guts don't reject it as much as 4D-ism. :-) –  Aaron Digulla Nov 28 '10 at 18:13
    
I mean that in 4d a point is an event, and a curve is a "lifetime", of e.g. a particle. The curve is not "walked on" as it were... The representation is static. Your brain sees as "present" a slice of this 4d universe defined as your past light cone. A slice is a 3-manifold to be exact. There is no particular determinism implied, as all the laws of physics are deterministic except for QM, which is compatible with space-time (not the curved one though). –  Ebenezer Sklivvze Nov 28 '10 at 18:36

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