(Ehm... is this more of a lounge topic?.. I don''t know) I''d like to hear your reasoning on the following statements. The first statement is a fact (as far as it is known at the moment). Each of the other statements is a deduction from the previous one(s), according to my logic: 1. Time is the 4th dimention of the universe. => 2. Time is part of the universe. => 3. The universe as a whole (including time) is not moving through time. => 4. The n-dimentonal shape of the universe is static (from #3) and well defined (by "well defined" I mean that it is either one shape or another, but not two or more simultaneously). => 5. The n-dimentional wave functions of all the particles in the universe are also well-defined (ok, maybe not, but then how can the shape of the universe be well defined??). => 6. All events are predetermined. ( This alone is a major conclusion, but I go further: ) => 7. Let''s assume for the sake of argument, that time travel is possible, and someone travels back in time at some point. His actions in the past then lead to exactly the same events as are suggested by his history knowledge, or they lead to an alternative event sequence. Since all events are predetermined, the alternative event sequence must also be predetermined. => 8. Whatever the traveler does in the past results in a predetermined event sequence which does not conflict with any other event sequences, since all wave functions are well defined. => 9. Time travel cannot produce paradoxes. Michael K., Co-designer and Graphics Programmer of "The Keepers" We come in peace... surrender or die!

quote:Original post by Trap
The step 3 to 4 is not correct. The universe being well defined is not a deduction but a premise.

Yes, I suposse this isn''t really a deduction (although the statement that the shape of the universe is static is indeed a deduction), but it does seem like a rather logical assumption...

Actually, consider this:

If the shape of the universe is not well defined, that means the universe can be in any one of a set of shapes. This may be a discreete or continueous set, that does not matter. Each such shape is then well defined on its own, and according to #5, the corresponding wave functions are also well defined. If the state of the universe is the sum of its shape and all wave functions within it, then this means that the universe can occupy any one of a discreet or continuous set of states.

But if the universe isn''t moving through time, it cannot transition from one state to another - it must occupy all possible states simultaneously (if the universe doesn''t occupy a certain state, then that state is not possible within the universe). This is the same as saying that there are several (perhaps an infinite number of) paralel universes, each of which occupies a well defined state. These may or may not be connected to each other (i.e. some of the event sequences starting in one paralel universe may or may not end up in another), it doesn''t matter either.

In that case, define "multiverse" as the collection of all coexisting states of the universe (in other words, the collection of all paralel universes). Since each such state is well defined, the overall state of the multiverse is also well defined, and the above reasoning now applies to this multiverse.

You could also treat the coordinate that identifies the individual states of the universe as simply another dimention, and you would arrive at the same result.

quote:
There is a funny paradoxon in your reasoning: Discovering that all events are predetermined doesn''t change anything.

Hehe.. yes. But then, it makes perfect sense: if all events are predetermined, then the discovery of that fact and the resulting event sequence are also predetermined. So naturally, the discovery does not change anything, since the following events have been predetermined to be that way all along.


MagicScript: Until I do, could you summarize some of the relevant points discussed in it?

Michael K.,
Co-designer and Graphics Programmer of "The Keepers"


We come in peace... surrender or die!

quote:Original post by technobot
=> 4. The n-dimentonal shape of the universe is static (from #3) and well defined (by "well defined" I mean that it is either one shape or another, but not two or more simultaneously).
=> 5. The n-dimentional wave functions of all the particles in the universe are also well-defined (ok, maybe not, but then how can the shape of the universe be well defined??).
=> 6. All events are predetermined.

You have much to learn of quantum mechanics. It is most definitely possible to exist in what is known as a super-position of two states, where you could be one and the other at the same time. Stuff is not predetermined. When you take a measurement of anything there are certain levels of probability that that thing will change to particular states randomly from its super-position. (It *must* become one state or another.)

quote:Original post by Doc
It is most definitely possible to exist in what is known as a super-position of two states, where you could be one and the other at the same time. Stuff is not predetermined. When you take a measurement of anything there are certain levels of probability that that thing will change to particular states randomly from its super-position. (It *must* become one state or another.)

It is true that a particle can exist in a superposition of two or more simpler states, but superposition is itself a state. If you take two or more well defined wave functions and superposition them, you simply get a new well defined wave function, which is the sum of the simpler ones.

If you consider the wave function of a particle before, during, and after a measurement, it may very well be well defined throughout the process, whether it is a superposition of simpler functions or not at any given point in time. You may not be able to determine the wave function at any given moment, but that does not mean it is necessarily not well defined (again, by "well defined" I mean that it is a single function, superpositioned from simpler ones or not, whether you can or cannot determine what it actually is). And if you look at the n-dimentional version of the function (with time bing one of those n dimentions), then assuming it is well defined for each time coordinate t, then it is well defined all over. I remind you that QM prohibits the location and momentum of a particle (as well as other property pairs) from being both well defined at the same time, but there is no prohibition that the wave function itself would be well defined.

Yes, over a large number of measurments we get a probabilistic ditribution of results, but each individual measurment gives a discreete, well defined result. If all events are predetermined, then all measurement results are also predetermined, and more so - they are predetermined to give the exact distribution that we get, which to us seems random.

The question is then - are the wave functions indeed well defined or not. According to the reasoning in my 2nd post, if time is part of each version of the universe, meaning that the overall state of that each such version - time included - is static, then the overall state of the multiverse has to be well defined, and that includes the n-dimentional wave functions of the particles it contains.

Michael K.,
Co-designer and Graphics Programmer of "The Keepers"


We come in peace... surrender or die!

A little hint for you: Physics is not like mathematics in that you cannot take one statement, and from it derive countless other properties (in general, of course).

Physics is instead a science, and, as such, we must "derive" properties via experimentation. Yes, some properties of reality can be deduced through theoretical calculations, but a whole lot of what we know, we know because we observed it. Things that cannot be directly observed become imensely difficult to prove, and in fact can often only be proven by indirect observation, not by a logical chain of conclusions as many mathematical proofs go.

http://chaos.webhop.org

quote:Original post by technobot
If you consider the wave function of a particle before, during, and after a measurement, it may very well be well defined throughout the process {snip}

If you measure something that''s in a state of superposition it changes. It becomes one of the functions it was a superposition of, the chances of which state it changes to depend on what parameters the superposition has.

quote:
Yes, over a large number of measurments we get a probabilistic ditribution of results, but each individual measurment gives a discreete, well defined result. If all events are predetermined, then all measurement results are also predetermined, and more so - they are predetermined to give the exact distribution that we get, which to us seems random.

The fact that the wavefunction changes due to measurement means that subsequent measurements on the same thing will not produce different results - you will always get the same result back. However, if you had a large number of identical things in identical superpositions then the results of measuring each of those things would build a predictable (if you knew the superposition parameters) distribution.

The maths are like this, we have a particle in a superposition wavefunction p = a*p1 + b*p2 (a and b are complex, but that doesn''t really matter). If you try to take a measurement of that particle p will become p1 or p2 depending on a and b (well, their squares, actually). This random state selection means that you cannot talk about predeterminism since a measurement may change the state of the particle in a way that cannot be predetermined, but only talked about in terms of probabilities.

quote:Original post by Doc
If you measure something that''s in a state of superposition it changes. It becomes one of the functions it was a superposition of, the chances of which state it changes to depend on what parameters the superposition has.

I never said it didn''t change across the time coordinate. I only said that if all events are predetermined, then that change is also predermined.

quote:
The fact that the wavefunction changes due to measurement means that subsequent measurements on the same thing will not produce different results - you will always get the same result back. However, if you had a large number of identical things in identical superpositions then the results of measuring each of those things would build a predictable (if you knew the superposition parameters) distribution.

Yes, ok. But the fact is, each measurment gives a single well defined result. And if all events are indeed predetermined, then the measurements are predetermined to give the exact results that we are getting, and thus are bound to appear to behave exactly like they do in fact appear to behave. My logic suggests that they are indeed predetermined, but as have been said above, this cannot be physically proven yet. So at the moment, I suppose this is a bit more of a phylosophical question than a physical one...

quote:
The maths are like this, we have a particle in a superposition wavefunction p = a*p1 + b*p2 (a and b are complex, but that doesn''t really matter). If you try to take a measurement of that particle p will become p1 or p2 depending on a and b (well, their squares, actually). This random state selection means that you cannot talk about predeterminism since a measurement may change the state of the particle in a way that cannot be predetermined, but only talked about in terms of probabilities.

You are mixing two different meaning of "predetermine" here. Yes, we cannot determine in advance what the exact result of a measurment will be, and must rely on statistical methods, but that does not mean that the result is not "bound to be" exacty what we would get.

To us, the results of previous measurments are known with 100% certainty. We do not know and cannot predict exactly what future measurements will give (we can only give statistical estimates). But if all events are predetmined, those future measurments have essentially already been done. To someone in the distant future, their results are also known with 100% certainty. From our point of view, we cannot predict those results with that amount of certainty, but they are already known in the full scope of the universe/multiverse. That is, if all events are really predetermined.

Michael K.,
Co-designer and Graphics Programmer of "The Keepers"


We come in peace... surrender or die!