Nothing more can be told without you telling us in what way the boot fails;) Do you get some error message? And if so at what stage of the boot process?
"but it is my understanding that at least in the case of relativity you can always normalize all calculations with respect to time..."
I don't know what you mean precisely by the tem "normalize" here.
"But! Isn't all "modern" physics essentially Newtonian physics with added corrections for curvature? And so the "space" is still essentially 3 dimensional. Meaning that it is impossible to traverse the other "dimensions" in both directions"
The space in relativity theories is indeed 4 dimensional. But the 4th dimension (time) is seriously intermingled with the other three dimensions. A massive body moving through space must move through time. And the coordinates get "mixed" when transforming into a different initial frame. Think of a normal rotation in euclidian 3-space. The coordinates get mixed. In the case of relativity a coordinate system change is a parametrized linear transformation on minkowski 4-space (one that leaves the norm of vector differences invariant, so basically it's a "rotation" in minkowski space). So the fourth coordinate cannot be "normalized" away. Except for maybe in the classical limit of relative velocities that are small compared to the speed of light. But then again, in the case of light they cannot be done away at all.
I'm starting to tell fairy tales now:) But i think the most clear way to see why this could be indeed fundamentally new physics is by way of the noether theorem. The notion of a symmetries in the physical space gives raise to "conserved values" like energy, momentum, etc.. There are some aspects of particle physics where spatial symmetries "break" (i.e. some particle descriptions are not invariant to symmetry operations). Maybe the same aspect can be formulated in a higher dimensional space without this break of symmetry. In this way the higher dimensional space could maybe lead to new insights..
Maybe someone with more of a clue might want to comment on this
I actually glanced over the paper. Transporting a message across this text medium is hard. If i came across high nosed or teacher like, i am sorry. Anyways, the point made is that there is a significant difference between i.e. simply stacking up more numbers (making the array larger) per point of the space and changing the dimensionality of the underlying space. Of course you are right in that we now simply need six coordinates to single out a point of the space instead of the previous four. But we aren't done with that. If we had i.e. a theory somewhat close to general relativity on such a space, then the tangent space at each point would become six dimensional, too. Thus vectors and 1-forms gain two more components, too. And higher rank tensors need more components.. I.e. a rank 2 tensor (co- and contravariance left aside) needs 6*6 = 36 components already as opposed to a rank 2 tensor on a 4 dimensional spacetime, where we only need 4*4 = 16 components.
In this sense the change of the dimensionality of the underlying space is very different from just using 2 more numbers in our theories..
Maybe this was clear to you from the start though and i have misread your post. My apologies if that's the case. I might have interpreted the words "independent variables describing the conditions of the system" wrongly. This, to me, sounds more like the number of values needed i.e. to describe the state of a field at each point (i.e. the number of independent tensor components needed for i.e. the different quantities used in the maxwell equations in tensorial notation).
No, this is a little bit different from simply 6 dimensional arrays. The physical theories of these days already use entities with more components than 3 [or 4 in minkowski space and general relativity]. Ever heard of tensors, etc?
All these quantities are "fields" on the basic 3 [or 4] dimensional spacetime. One example would be the energy-momentum-tensor which has 20 independent components IIRC.
But in this theory the dimensionality of the basic space is changed. Thus there really are six orthogonal directions in space. And the physically relevant quantities are then fields on this 6-dimensional spacetime.
I am not in the position to understand the paper. But i suppose these extra two dimensions need not really stand on an equal footing with the traditional 3 [or 4] dimensions of everyday experience.. They might be i.e. "looped" or in some other way very "smallish". Or it might be an artefact of resulting physical theories base on this six-dimensional spacetime, that we never travel in these two orthogonal directions. Who knows.
Slashdot Mirror
Ok yeah, then it's some sort of incompatibility between the burnt cd and the cd drive in that computer.. It has nothing to do with linux i'd say :)
Nothing more can be told without you telling us in what way the boot fails ;) Do you get some error message? And if so at what stage of the boot process?
"but it is my understanding that at least in the case of relativity you can always normalize all calculations with respect to time..." I don't know what you mean precisely by the tem "normalize" here. "But! Isn't all "modern" physics essentially Newtonian physics with added corrections for curvature? And so the "space" is still essentially 3 dimensional. Meaning that it is impossible to traverse the other "dimensions" in both directions"
:) But i think the most clear way to see why this could be indeed fundamentally new physics is by way of the noether theorem. The notion of a symmetries in the physical space gives raise to "conserved values" like energy, momentum, etc.. There are some aspects of particle physics where spatial symmetries "break" (i.e. some particle descriptions are not invariant to symmetry operations). Maybe the same aspect can be formulated in a higher dimensional space without this break of symmetry. In this way the higher dimensional space could maybe lead to new insights..
The space in relativity theories is indeed 4 dimensional. But the 4th dimension (time) is seriously intermingled with the other three dimensions. A massive body moving through space must move through time. And the coordinates get "mixed" when transforming into a different initial frame. Think of a normal rotation in euclidian 3-space. The coordinates get mixed. In the case of relativity a coordinate system change is a parametrized linear transformation on minkowski 4-space (one that leaves the norm of vector differences invariant, so basically it's a "rotation" in minkowski space). So the fourth coordinate cannot be "normalized" away. Except for maybe in the classical limit of relative velocities that are small compared to the speed of light. But then again, in the case of light they cannot be done away at all.
I'm starting to tell fairy tales now
Maybe someone with more of a clue might want to comment on this
I actually glanced over the paper. Transporting a message across this text medium is hard. If i came across high nosed or teacher like, i am sorry. Anyways, the point made is that there is a significant difference between i.e. simply stacking up more numbers (making the array larger) per point of the space and changing the dimensionality of the underlying space. Of course you are right in that we now simply need six coordinates to single out a point of the space instead of the previous four. But we aren't done with that. If we had i.e. a theory somewhat close to general relativity on such a space, then the tangent space at each point would become six dimensional, too. Thus vectors and 1-forms gain two more components, too. And higher rank tensors need more components.. I.e. a rank 2 tensor (co- and contravariance left aside) needs 6*6 = 36 components already as opposed to a rank 2 tensor on a 4 dimensional spacetime, where we only need 4*4 = 16 components.
In this sense the change of the dimensionality of the underlying space is very different from just using 2 more numbers in our theories..
Maybe this was clear to you from the start though and i have misread your post. My apologies if that's the case. I might have interpreted the words "independent variables describing the conditions of the system" wrongly. This, to me, sounds more like the number of values needed i.e. to describe the state of a field at each point (i.e. the number of independent tensor components needed for i.e. the different quantities used in the maxwell equations in tensorial notation).
No, this is a little bit different from simply 6 dimensional arrays. The physical theories of these days already use entities with more components than 3 [or 4 in minkowski space and general relativity]. Ever heard of tensors, etc? All these quantities are "fields" on the basic 3 [or 4] dimensional spacetime. One example would be the energy-momentum-tensor which has 20 independent components IIRC. But in this theory the dimensionality of the basic space is changed. Thus there really are six orthogonal directions in space. And the physically relevant quantities are then fields on this 6-dimensional spacetime. I am not in the position to understand the paper. But i suppose these extra two dimensions need not really stand on an equal footing with the traditional 3 [or 4] dimensions of everyday experience.. They might be i.e. "looped" or in some other way very "smallish". Or it might be an artefact of resulting physical theories base on this six-dimensional spacetime, that we never travel in these two orthogonal directions. Who knows.