I guess it first depends if time is a dimension or a mental perception.
It seems that time is a mathematically proven dimension. I read a book called "The History of the Square Root of -1" in which it is postulated that the three spacial dimensions are described on the Cartesian grid system by the quadrants that have at least one positive co-ordinate; (+,_), (-,+), (+,+). It would appear from the information in this book at least that what is described by the one quadrant that has no + (positive co-ordinate), that being the quadrant (-,-), that the equations seem to be describing time.
As far as I'm aware time is still most often taken to be continuous, even in most leading quantum gravity theories. It's the space component of spacetime that is quantized, and of course the problem (of quantum gravity) is that we don't understand how to quantize the force of gravity.
Take that with a grain of salt as I'm not a physicist. I'm trying to get through a rather technical book that explains approaches to Quantum Gravity, but I haven't gotten very far yet and I only understand about half of it. (it's also been a while since I've had a chance to take it up)
Quantization of any dimensions is a fascinating topic. Some thoughts :
- many theories get into trouble as infinities appear when one tries to extract testable numbers for comparison with experiment. The mathematical basis is frequently an integration or summation over continuous sets - meaning that the distance between members of the set can be as small as you like.
- Planck is good study of this. Take a cavity with energy in it. Add up all the energies from all the possible modes within it. If you say energy has a continuous spectrum then you get infinity, if you say it has discrete levels then you don't. While Planck never liked this method - and he associated discreteness with the oscillators, not the energy itself - he accepted that it gave the right answer.
- Einstein generalised and said that it was the ( photon ) energies that came in lumps ie. not of arbitrary size. Problem apparently solved. DeBroglie came along and generalised further ....... leading to a whole host of rulings about discrete/quantum numbers that we have today.
- but still it was the 'things', the particles, that were discrete but not the background itself. I'd reckon that at least Special Relativity, which allows the abstraction of swapping spatial and time dimensions depending on the observer, would require that both space and time must be quantised or neither. All or nothing.
- now the problem with discrete sets or tuples thereof ( ordered pairs say ) is that discretising produces anisotropy ( preferred directions ) that you don't get with continuous ones. So spacetime would become an array of points, so any given arbitrary direction won't necessarily intersect with such a lattice. Since we don't see preferred directions ( to date ) then any grid must be a fine one indeed.
Cheers, Mike.
( edit ) One other interesting theme is that of confinement. If you have a free electron - an abstract concept really in that one can't actually escape the universe - then it will/can exhibit continuous energy values. But bung it in some force/potential well so that it has to hang about then it will take on one of several discrete levels with finite non-zero jumps between. Hence electron 'shells' and the whole of chemistry. Ultimately the discrete levels are a product of requiring a single valued function over a cyclic range. So if I go around the nucleus 360 degrees I come back to the start, and some functional value has to match at 0 degrees which is of course also 360 degrees. This then restricts what would otherwise be continuous to discrete behaviour.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
In quantum chromodynamics you start computing at the nodes of a space-time lattice, then you shorten the interval between two points in space-time, By making the interval going to zero you should end up with a continuous space-time. But at a given length you end up to a kind of phase transition. This is all I can remember of an article in Scientific American by my Trieste fellow citizen Claudio Rebbi, who was (is?) at Brookhaven. It reminded me of the finite elements method of engineering.
Tullio
I guess it first depends if time is a dimension or a mental perception.
If time is simply the by-product of matter interfering with the "flow" of time, then that might begin to explain the elusiveness of the "Theory of Everything" which seeks the point at which gravity is unified with the other grand forces in nature.
Quantization of any dimensions is a fascinating topic. Some thoughts :
- many theories get into trouble as infinities appear when one tries to extract testable numbers for comparison with experiment. The mathematical basis is frequently an integration or summation over continuous sets - meaning that the distance between members of the set can be as small as you like.
- Planck is good study of this. Take a cavity with energy in it. Add up all the energies from all the possible modes within it. If you say energy has a continuous spectrum then you get infinity, if you say it has discrete levels then you don't. While Planck never liked this method - and he associated discreteness with the oscillators, not the energy itself - he accepted that it gave the right answer.
- Einstein generalised and said that it was the ( photon ) energies that came in lumps ie. not of arbitrary size. Problem apparently solved. DeBroglie came along and generalised further ....... leading to a whole host of rulings about discrete/quantum numbers that we have today.
- but still it was the 'things', the particles, that were discrete but not the background itself. I'd reckon that at least Special Relativity, which allows the abstraction of swapping spatial and time dimensions depending on the observer, would require that both space and time must be quantised or neither. All or nothing.
- now the problem with discrete sets or tuples thereof ( ordered pairs say ) is that discretising produces anisotropy ( preferred directions ) that you don't get with continuous ones. So spacetime would become an array of points, so any given arbitrary direction won't necessarily intersect with such a lattice. Since we don't see preferred directions ( to date ) then any grid must be a fine one indeed.
Cheers, Mike.
( edit ) One other interesting theme is that of confinement. If you have a free electron - an abstract concept really in that one can't actually escape the universe - then it will/can exhibit continuous energy values. But bung it in some force/potential well so that it has to hang about then it will take on one of several discrete levels with finite non-zero jumps between. Hence electron 'shells' and the whole of chemistry. Ultimately the discrete levels are a product of requiring a single valued function over a cyclic range. So if I go around the nucleus 360 degrees I come back to the start, and some functional value has to match at 0 degrees which is of course also 360 degrees. This then restricts what would otherwise be continuous to discrete behaviour.
I have read much about the angst that having the equations blow up to infinity has caused investigators over the years, but what if the infinities are the correct answers and only misunderstood because we are looking for answers to one thing and getting answers that pertain to something else because we are in fact asking the wrong questions?
I have read much about the angst that having the equations blow up to infinity has caused investigators over the years, but what if the infinities are the correct answers and only misunderstood because we are looking for answers to one thing and getting answers that pertain to something else because we are in fact asking the wrong questions?
Traditionally infinity means 'naughty', translating to 'impossible' thus unrealistic. My sense is that a new type of maths is required to cope with quantisation. Currently we do continuous variables and then quantise on top of that. We didn't need continuity until we went from the rationals to the irrationals. Irrationals are defined by a limit process and not axiomatic derivation from finite algebra. That's when the inexactness crept in .....
A: Think of a number
B: Yup, got one
A: Now mine is twice whatever you thought
B: OK, I thought of a bigger one now
A: Same again, I've got twice whatever you thought
....
So when we say that the longest side of the right triangle with other side lengths being one is SQRT(2), we mean that we define a new type of number to be the solution to that. If you're going to quantise then you'll have to chuck out Pythagorus' Theorem as an exact construct.
Indeed I think the apparently screwy logic of quantum mechanics is a reflection of the language we use and the assumptions represented. We need a different hammer. It'd probably be something that a being from another dimension would state as obvious, but would be hard to reverse engineer using ingrained assumptions from the set we're in.
Maybe an ant's life is a succession of planes, with the occasional boundary, to walk across. If you don't know about gravity, and thus the idea of 'vertical', then you'd categorise regions as : the easy planes ( 3D floor ), more slippery ones ( 3D wall ) and some where your fellow ants just suddenly disappear from ( 3D roof ) **...... :-)
Cheers, Mike.
( edit ) **Whence they would magically reappear on an 'easy' plane, but somewhat worse for wear, having exceeded the 'speed of ant'. Action at a distance ....
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
RE: RE: I guess it first
)
It seems that time is a mathematically proven dimension. I read a book called "The History of the Square Root of -1" in which it is postulated that the three spacial dimensions are described on the Cartesian grid system by the quadrants that have at least one positive co-ordinate; (+,_), (-,+), (+,+). It would appear from the information in this book at least that what is described by the one quadrant that has no + (positive co-ordinate), that being the quadrant (-,-), that the equations seem to be describing time.
As far as I'm aware time is
)
As far as I'm aware time is still most often taken to be continuous, even in most leading quantum gravity theories. It's the space component of spacetime that is quantized, and of course the problem (of quantum gravity) is that we don't understand how to quantize the force of gravity.
Take that with a grain of salt as I'm not a physicist. I'm trying to get through a rather technical book that explains approaches to Quantum Gravity, but I haven't gotten very far yet and I only understand about half of it. (it's also been a while since I've had a chance to take it up)
Quantization of any
)
Quantization of any dimensions is a fascinating topic. Some thoughts :
- many theories get into trouble as infinities appear when one tries to extract testable numbers for comparison with experiment. The mathematical basis is frequently an integration or summation over continuous sets - meaning that the distance between members of the set can be as small as you like.
- Planck is good study of this. Take a cavity with energy in it. Add up all the energies from all the possible modes within it. If you say energy has a continuous spectrum then you get infinity, if you say it has discrete levels then you don't. While Planck never liked this method - and he associated discreteness with the oscillators, not the energy itself - he accepted that it gave the right answer.
- Einstein generalised and said that it was the ( photon ) energies that came in lumps ie. not of arbitrary size. Problem apparently solved. DeBroglie came along and generalised further ....... leading to a whole host of rulings about discrete/quantum numbers that we have today.
- but still it was the 'things', the particles, that were discrete but not the background itself. I'd reckon that at least Special Relativity, which allows the abstraction of swapping spatial and time dimensions depending on the observer, would require that both space and time must be quantised or neither. All or nothing.
- now the problem with discrete sets or tuples thereof ( ordered pairs say ) is that discretising produces anisotropy ( preferred directions ) that you don't get with continuous ones. So spacetime would become an array of points, so any given arbitrary direction won't necessarily intersect with such a lattice. Since we don't see preferred directions ( to date ) then any grid must be a fine one indeed.
Cheers, Mike.
( edit ) One other interesting theme is that of confinement. If you have a free electron - an abstract concept really in that one can't actually escape the universe - then it will/can exhibit continuous energy values. But bung it in some force/potential well so that it has to hang about then it will take on one of several discrete levels with finite non-zero jumps between. Hence electron 'shells' and the whole of chemistry. Ultimately the discrete levels are a product of requiring a single valued function over a cyclic range. So if I go around the nucleus 360 degrees I come back to the start, and some functional value has to match at 0 degrees which is of course also 360 degrees. This then restricts what would otherwise be continuous to discrete behaviour.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
In quantum chromodynamics you
)
In quantum chromodynamics you start computing at the nodes of a space-time lattice, then you shorten the interval between two points in space-time, By making the interval going to zero you should end up with a continuous space-time. But at a given length you end up to a kind of phase transition. This is all I can remember of an article in Scientific American by my Trieste fellow citizen Claudio Rebbi, who was (is?) at Brookhaven. It reminded me of the finite elements method of engineering.
Tullio
RE: I guess it first
)
If time is simply the by-product of matter interfering with the "flow" of time, then that might begin to explain the elusiveness of the "Theory of Everything" which seeks the point at which gravity is unified with the other grand forces in nature.
Sorry people I have no
)
Sorry people I have no proof... :-)
I just have a feeling we are traveling through the fourth dimension and its quantized at the Planck length..
There are some who can live without wild things and some who cannot. - Aldo Leopold
RE: Quantization of any
)
I have read much about the angst that having the equations blow up to infinity has caused investigators over the years, but what if the infinities are the correct answers and only misunderstood because we are looking for answers to one thing and getting answers that pertain to something else because we are in fact asking the wrong questions?
RE: I have read much about
)
Traditionally infinity means 'naughty', translating to 'impossible' thus unrealistic. My sense is that a new type of maths is required to cope with quantisation. Currently we do continuous variables and then quantise on top of that. We didn't need continuity until we went from the rationals to the irrationals. Irrationals are defined by a limit process and not axiomatic derivation from finite algebra. That's when the inexactness crept in .....
A: Think of a number
B: Yup, got one
A: Now mine is twice whatever you thought
B: OK, I thought of a bigger one now
A: Same again, I've got twice whatever you thought
....
So when we say that the longest side of the right triangle with other side lengths being one is SQRT(2), we mean that we define a new type of number to be the solution to that. If you're going to quantise then you'll have to chuck out Pythagorus' Theorem as an exact construct.
Indeed I think the apparently screwy logic of quantum mechanics is a reflection of the language we use and the assumptions represented. We need a different hammer. It'd probably be something that a being from another dimension would state as obvious, but would be hard to reverse engineer using ingrained assumptions from the set we're in.
Maybe an ant's life is a succession of planes, with the occasional boundary, to walk across. If you don't know about gravity, and thus the idea of 'vertical', then you'd categorise regions as : the easy planes ( 3D floor ), more slippery ones ( 3D wall ) and some where your fellow ants just suddenly disappear from ( 3D roof ) **...... :-)
Cheers, Mike.
( edit ) **Whence they would magically reappear on an 'easy' plane, but somewhat worse for wear, having exceeded the 'speed of ant'. Action at a distance ....
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal