Large Hardon Collider

[Boyiee]

Honestly I'd be happier if the LHC did make dragons instead of these stupid higgs particles.

[Kryssan]

Also, is it just me, or has a certain person been quite busy as of late? If I'm not logged in I no longer see avatars or signatures, at all.

[Evensong]

If I'm not logged in I no longer see avatars or signatures, at all.

You are right; I've just checked and the only one with an image on this page is Mizango! Oh, the privileges of those in power!

[Eliseos]

You are right; I've just checked and the only one with an image on this page is Mizango! Oh, the privileges of those in power!

We must end special privileges. I will not allow my tax dollars to go to unmindful spending.

[Max™]

So I was thinking the other day... I'm pretty sure I've lost my goddamn mind at this point.

Quantum Mechanics implies we're in a coarse grained history, where small variations are summed into a single 4 Dimensional structure.

If you have large enough variations from the boundary conditions to produce a different history, you should produce a bundle of related histories, spaced across a 5th Dimension.

If you include the possible ways the Universe could have unfolded from the original conditions with the same initial physics, but different symmetry breakings, and the bundles of histories related by those physics, you'd get a 5 D sphere which emerged from the same seed "singularity".

If you consider all possible singularity variations from all possible sets of structures complex to contain their observers, you populate a 6th Dimension with 5 D sphere Universes.

If you consider the set of all possible spaces, including those which are not complex enough to contain observers, you populate a 7th Dimension.

If you consider the set of all possible self consistent structures, you populate an 8th Dimension, which is arguably Mathematics itself.

http://i341.photobucket.com/albums/o...aluniverse.jpg

[Eliseos]

I always have a problem with > 4 dimension theories. If we can't physically measure it, it isn't physically apart of our universe, and doesn't apply to us. Therefore it enters the realm of philosophy, and that isn't anywhere close to science (though it can be argued that philosophy leads us to scientific answers). Plus, I don't really see how you can just make the connection of history, physics, space, and math to extra dimensions.

[Max™]

A dimension is an expressed degree of freedom.

In order to express variations in possible histories, and variations between symmetry bundles, you need another degree of freedom.

In order to express the variations in possible physics, you need another degree of freedom.

In order to express the variations of all possible spaces, yep, another degree of freedom.

It is arguable that the ordering applied there would only seem apparent from our perspective, and that perhaps mathematics would be the nth dimension, all self consistent structures.

The leap is my own, yes, but it is shared by Tegmark and others, and well founded in logical principles which make it more than merely philosophical postulation.


This isn't the same sort of extra dimensions as string theory, which is silly, as those are more like extra directions within a space of physics itself.

[Cadsuane]

So I was thinking the other day... I'm pretty sure I've lost my goddamn mind at this point.

Quantum Mechanics implies we're in a coarse grained history, where small variations are summed into a single 4 Dimensional structure.

If you have large enough variations from the boundary conditions to produce a different history, you should produce a bundle of related histories, spaced across a 5th Dimension.

If you include the possible ways the Universe could have unfolded from the original conditions with the same initial physics, but different symmetry breakings, and the bundles of histories related by those physics, you'd get a 5 D sphere which emerged from the same seed "singularity".

If you consider all possible singularity variations from all possible sets of structures complex to contain their observers, you populate a 6th Dimension with 5 D sphere Universes.

If you consider the set of all possible spaces, including those which are not complex enough to contain observers, you populate a 7th Dimension.

If you consider the set of all possible self consistent structures, you populate an 8th Dimension, which is arguably Mathematics itself.

Here's a youtube for you:

http://www.youtube.com/watch?v=0ca4miMMaCE

[Eliseos]

I don't really agree with those being "degrees of freedom". That implies that we have some say in how they are handled, or their outcome. We (as of this writing) can't change a history, our laws of space and time, the laws of mathematics, or the fundamental constants of our universe. Unless I am completely misunderstanding you, and degree of freedom means something completely different that what I am interpreting.

[Max™]

Exploring the 10th dimension thing, yeah, but here's the problem with their logic.

The 5th Dimension alone is enough to express the variations between all possible histories emerging from the same symmetry breaking, and all possible symmetry breaking variations.

The variation of the 4th Dimension into histories only requires 1 extra degree of freedom.

The possible variations of histories includes all possible versions of our Universe from the singularity to the end of time, so the 7th Dimension they posit wouldn't be necessary.

They previously stated requiring a 6th Dimension to bend a 4th Dimensional history through the 5th Dimension of possible histories, but they are neglecting the coarse graining of small variations, and the actual nature of that 5th Dimension of possible histories. If you somehow managed to move into another history in your bundle, or a vastly different bundle, you'd be traveling across the 5-D sphere Universe.

Just as we can move around in 3 D by traveling across the 4 D history Universe.

The 6 D set of possible observable Universes with different singularities, and thus completely different initial physics, is given in that youtube as the 8th Dimension.

The 9th is then posited as a way to move between them, and the 10th is again posited as all possible Universes... though the 8th was already.

Above the possible Universes would be Spaces, as Universes are spaces with complex enough self interaction to contain observers, the set of spaces contains more than just Universes.

Then everything possible, beyond just universes, well... mathematics is a catalog of everything which does not contradict itself.


I am not implying we can change them, I mean they are expressed, we are part of it, not creating it.

[Eliseos]

I'm not saying you're wrong, I'm just saying you aren't really giving any reasons as to why they are what you're saying they are. You're just giving the what without the why. Why is the fifth dimension history, or is it just arbitrary which one is which? Is history related to time somehow (in a non-obvious way)?

[Max™]

From our perspective.

It is histories because it contains the same expression of physical constants from the primal symmetry breaking, but with variations in the way events happen on a large scale.

The difference between heads and tails on a coin flip can fit in a single 4 D history.

The difference between Hitler getting struck by lightning on his 13th birthday and the history we saw requires another history.

Similar in most ways, but different enough to be unique.

The most similar histories would be related by closeness across the 5th dimension, with the edge of the bundle of histories sharing our physical constants being related by similarity to the other bundles in that the primal symmetry was broken in only a slightly different way. The electron is just a little heavier, the amount of hydrogen vs helium in the early Universe was 0.01% off, etc.

Just applying the numerical labels starting from our expressed 3 Dimensional space which is embedded in an expressed 4 Dimensional spacetime. I prefer the term history because it is viewed as a consistent path from the inside.

[Woozie]

I always have a problem with > 4 dimension theories. If we can't physically measure it, it isn't physically apart of our universe, and doesn't apply to us. Therefore it enters the realm of philosophy, and that isn't anywhere close to science (though it can be argued that philosophy leads us to scientific answers). Plus, I don't really see how you can just make the connection of history, physics, space, and math to extra dimensions.

We can't physically measure wave functions either, so by that logic, the entire field of quantum theory (and quantum field theory, and the standard model of particle physics, and literally every other theory that isn't Newtonian or relativity) is philosophy. In fact, wave functions have no real physical interpretation. They're mathematical entities that we can extract information out of (and they're generally complex, whereas measurements and observations have to yield real values).

As a matter of fact, higher dimensions are more physical than the wave functions of quantum mechanics. Even though we can't measure higher dimensions now, it is possible to measure or observe higher dimensions in theory. Whether or not it will ever be practical is another matter, but theoretically, higher dimensions can be physically observed and measured directly with the appropriate equipment and on the appropriate energy scales.

Wave functions, on the other hand, are immeasurable, even in theory. In fact, it's literally one of the postulates of quantum mechanics. By the postulates of quantum theory, the result of any measurement must be an eigenvalue of operator corresponding to the quantity being measured. So if we want to measure momentum, our result is an eigenvalue of the momentum operator (well, technically it just has to be in the spectrum. For continuous quantities [like momentum of a free particle], the eigenstates aren't even in the physical Hilbert space that wave functions are required to be in, so making a physical interpretation makes even less sense), not the eigenstate. States can only be inferred indirectly based on the eigenvalue given. If I measure the momentum of a particle to be x amount of kilograms*meters/second or whatever units I'm using, the most I can really say about the wave function is that x was one of it's eigenvalues. Of course, there could be as many as an infinite amount of states that had x as an eigenvalue, so we're still not sure about the state. You probably talk about wave functions and their properties all the time in modern physics or other physics courses, but when it comes to experiments, you're always measuring spin/momentum/magnetic fields/etc, not wave functions.

One could argue that eigenvalues give operators a meaningful physical interpretation, but it certainly doesn't give a meaningful interpretation of the wave function itself. And like I said, the postulates of quantum theory clearly state that the result of a measurement has to be an eigenvalue. States are immeasurable. They are (generally) complex vectors that live in hilbert space (a purely mathematical universe), and have no physical interpretation, no units, no dimensions, no anything. So if you believe quantum theory is science (and not philosophy), then dimensions higher than four certainly are too.

Edit: Actually, I take back what I said about operators having a meaningful interpretation. Technically they're only defined in the hilbert space too.

Plus, I don't really see how you can just make the connection of history, physics, space, and math to extra dimensions.

I'm not sure what you meant by that.

Edit: I just realized that Max's definition of extra universes is way different than the usual. Maybe his are measurable, or maybe they are just philosophy, I don't know.

[Eliseos]

We can't physically measure wave functions either, so by that logic, the entire field of quantum theory (and quantum field theory, and the standard model of particle physics, and literally every other theory that isn't Newtonian or relativity) is philosophy. In fact, wave functions have no real physical interpretation. They're mathematical entities that we can extract information out of (and they're generally complex, whereas measurements and observations have to yield real values).

As a matter of fact, higher dimensions are more physical than the wave functions of quantum mechanics. Even though we can't measure higher dimensions now, it is possible to measure or observe higher dimensions in theory. Whether or not it will ever be practical is another matter, but theoretically, higher dimensions can be physically observed and measured directly with the appropriate equipment and on the appropriate energy scales.

Wave functions, on the other hand, are immeasurable, even in theory. In fact, it's literally one of the postulates of quantum mechanics. By the postulates of quantum theory, the result of any measurement must be an eigenvalue of operator corresponding to the quantity being measured. So if we want to measure momentum, our result is an eigenvalue of the momentum operator (well, technically it just has to be in the spectrum. For continuous quantities [like momentum of a free particle], the eigenstates aren't even in the physical Hilbert space that wave functions are required to be in, so making a physical interpretation makes even less sense), not the eigenstate. States can only be inferred indirectly based on the eigenvalue given. If I measure the momentum of a particle to be x amount of kilograms*meters/second or whatever units I'm using, the most I can really say about the wave function is that x was one of it's eigenvalues. Of course, there could be as many as an infinite amount of states that had x as an eigenvalue, so we're still not sure about the state. You probably talk about wave functions and their properties all the time in modern physics or other physics courses, but when it comes to experiments, you're always measuring spin/momentum/magnetic fields/etc. You're never actually measuring the wave function itself.

One could argue that eigenvalues give operators a meaningful physical interpretation, but it certainly doesn't give a meaningful interpretation of the wave function itself. And like I said, the postulates of quantum theory clearly state that the result of a measurement has to be an eigenvalue. States are immeasurable. They are (generally) complex vectors that live in hilbert space (a purely mathematical universe), and have no physical interpretation, no units, no dimensions, no anything. So if you believe quantum theory is science, then dimensions higher than four certainly are too.

See, this is exactly the type of response I want from Max when he posts his theories. I'm not taking a jab at you Max, I just have a hard time following your trains of thought and I am usually left with a "why?" in my mind whenever I read your posts.

Anyway, Woozie, you're absolutely right. I should have clarified what I said to something like "I always have a problem thinking about theories with > 4 dimensions." Some of these theories, like the wave properties of matter, are so abstract that it at times doesn't seem like science. I'm still trying to wrap my head around Schrodinger's equation and its applications. Like we were discussing earlier, that's why I'm better at the more computational side of physics, than on the theoretical side. I can generally explain my way through various theories to my friends, but it's so much easier for me if I can go "Hey, just look at this equation, this yields this in that variable and this means that".

We can still measure something about the particle, whether it is an expectation value for some property of it, its energy, the state its in, and all that. I guess what I meant to say in my original statement is that we can't really describe anything about higher dimensions beyond just a "this could be how it is", which is why I keep asking Max to explain how he came to those conclusions, rather than just say how it is.

[Eliseos]

I'm not sure what you meant by that.

Edit: I just realized that Max's definition of extra universes is way different than the usual. Maybe his are measurable, or maybe they are just philosophy, I don't know.

I meant more how he places each in a separate dimension. I was asking how he came to the conclusion that history, physics, space, and math all get their separate dimension.

[Woozie]

See, this is exactly the type of response I want from Max when he posts his theories. I'm not taking a jab at you Max, I just have a hard time following your trains of thought and I am usually left with a "why?" in my mind whenever I read your posts.

Anyway, Woozie, you're absolutely right. I should have clarified what I said to something like "I always have a problem thinking about theories with > 4 dimensions." Some of these theories, like the wave properties of matter, are so abstract that it at times doesn't seem like science. I'm still trying to wrap my head around Schrodinger's equation and its applications. Like we were discussing earlier, that's why I'm better at the more computational side of physics, than on the theoretical side. I can generally explain my way through various theories to my friends, but it's so much easier for me if I can go "Hey, just look at this equation, this yields this in that variable and this means that".

We can still measure something about the particle, whether it is an expectation value for some property of it, its energy, the state its in, and all that. I guess what I meant to say in my original statement is that we can't really describe anything about higher dimensions beyond just a "this could be how it is", which is why I keep asking Max to explain how he came to those conclusions, rather than just say how it is.

You're not the only one who has trouble following Max. I'm not dissing Max or anything, he's definitely a smart guy, but the way he types is arguments make them seem like gibberish. I can never extract a decent point or a coherent argument from what he says, and most of the time it seems like he's not even answering the question or the issue at hand. I'm sure you know you're stuff pretty well, Max, but the way you argue will always make it hard for you to get anything across, regardless of whether you're right or wrong.

But anyways, in terms of actual geometric dimensions higher than four, some of the theories propose that if we create a high enough energy event, we could measure things that could tell us whether or not extra dimensions exist. We could see their direct effects on our experiment even if we can't see the actual dimensions themselves. Some theorist even proposed that we could send effects or messages or other types of influences through these dimensions (for example, some theories propose that gravity travels through these extra dimensions) Whether or not these theories are correct is another matter, but if they are correct, extra spacial dimensions are definitely less abstract than quantum physics. I don't know if that answers your question or addresses your concerns or not. I could be misinterpreting what you said.

[Woozie]

I meant more how he places each in a separate dimension. I was asking how he came to the conclusion that history, physics, space, and math all get their separate dimension.

Oh okay, well he's definitely talking about something completely different than I am lol.

@Max: I don't see how math could possibly be it's own dimension. Wouldn't this mean we'd have to define dimensions outside the context of math? Math and physics certainly aren't "degrees of freedom" unless you have a completely different definition of degree of freedom. And this debate is certainly entering the realm of philosophy (unless we can empirically show that math and physics are 'dimensions').

[Eliseos]

Nah, that's pretty much what I'm looking for. Is that one of the theories about the graviton, that we could potentially observe it and then disappear (presumably to some other dimension/membrane)? I think I read something about that in one of Greene's books, but that may have been the string theory interpretation to it, and I'm not very familiar with other ToEs besides string/m-theory.

[Kuya]

We're not going to have that "the universe is made of numbers" philosophy debate again, are we? That was frustrating.

[Eliseos]

Oh okay, well he's definitely talking about something completely different than I am lol.

@Max: I don't see how math could possibly be it's own dimension. Wouldn't this mean we'd have to define math outside the context of dimensions? Math and physics certainly aren't "degrees of freedom" unless you have a completely different definition of degree of freedom. And this debate is certainly entering the realm of philosophy (unless we can empirically show that math and physics are 'dimensions').

That's where my confusion came in too. I don't see how one dimension (math) can describe the other (physics).