Yes indeed. The gold standard being sought here is the simultaneous multi-mode detections & study of evolving structures from supernovae and likewise events. What an exciting time to be an astronomer.
Cheers, Mike
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
There are significant health risks at that altitude, not just inconvenience but real danger to the unwary.
The mid infrared range is normally where water vapor - that strongest greenhouse gas keeping us all warm - masks signals of interest. The observations will be interesting.
Cheers, Mike.
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
At the moment too little specifications. The spectrograph is just 2 channels at once. But probably that's a question of money, and a better spectrograph can become installed later. That's the advantage of telescopes on earth, even at high attitude.
Go and do physics and maths for 10+ years at university level ? :-)
Seriously, what is proposed is that the definition of 'distance' in spacetime perhaps includes non-quadratic terms.
Take the good old Euclidean metric for 3D space then ds2 = dx2 + dy2 + dz2 being positive definite (because squares of real numbers are always non-negative, and summing non-negative numbers only gives a non-negative answer) you can take the square root of ds2 to get a distance being a real number. Suppose, to be perverse, you throw in a linear term for one of the directions (say along the y-axis) then : ds2 = dx2 + dy + dz2 and now nothing is positive definitely (dy could be large and negative) and you might have ds2 < 0 and ds becomes ? what, an imaginary number maybe? Clearly you lose a traditional/classical idea of distance. That's not terrible per se. After all Riemann et al taught us to relax about non-classical geometries. The Lorentzian metric in spacetime (ds2 = dx2 + dy2 + dz2 - dt2, where I have set c = 1) can give you that also; separating spacetime into 'light cones' centred per point, yielding time-like (ds2 < 0) or space-like (ds2>0) regions and the surface of the 'cone' is null or ds2 = 0.
Thus a linear term for the co-ordinate differences yields other geometries of which Finsler geometry is one example. Importantly one can rephrase Einstein's GR equations in terms of the new geometries, with all the implications like gravitational waves and cosmology stuff that we already have. The remainder of the paper referred to is opaque in detail to me, I don't know the relevant mathematics.
Cheers, Mike
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
Reading things on this subject just makes me want to spin around even more in both or all directions Tom
Mike Hewson wrote:
Go and do physics and maths for 10+ years at university level ? :-)
You must have also learned how to type close to the speed of light Mike since you typed all of that faster than me reading both of those articles the Tom posted and then typing out my one-liner
Go and do physics and maths for 10+ years at university level ? :-)
You must have also learned how to type close to the speed of light Mike since you typed all of that faster than me reading both of those articles the Tom posted and then typing out my one-liner
Hi Magic! ;-)
I think the funny/weird metrics are exciting because one of them, or a group of them, may get around or even explain the 'paradox', for want of a better word, of the central singularity of black holes. That's where GR ought meet QM. I wonder what the Finsler et al geometries have to say about that. Watch this space I guess.
Cheers, Mike.
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
Go and do physics and maths for 10+ years at university level ? :-)
Seriously, what is proposed is that the definition of 'distance' in spacetime perhaps includes non-quadratic terms.
Excuse me??? Where on earth did you get this from? It is very clear in Definition 1.2.2 of Dr Heefer's thesis (which I presume is the paper you refer to later on) that, even in Finsler geometry, a metric is a symmetric bi-linear (ie quadratic) form,
g =gijdxidxj
This is even more clear in Definition 1.2.1. If you have any reference which suggests anything different, please provide a full citation, including page or section number.
In the next bit, it seems to me as if your definition of a "classical" geometry is just Euclidean geometry. I suppose most people would think the same, for no other reason than we all learn Euclidean geometry from Day One, and then learn about the other stuff if we go on to study mathematics in university.
Riemannian geometry is, in fact, nothing more than geometry in which Euclid's fifth postulate (the one about parallel lines) is no longer assumed; thus, Riemannian geometry is also "classical". The same holds true with Lorentzian geometries, wherein the metric ("distance function") is no longer presumed to be positive definite.
Note that Lorentz metric and Lorentzian metric are not the same thing: a Lorentz metric (of which the Minkowski metric is one example) is a Lorentzian metric on a 4-dimensional space with signature (3,1). OTOH, a Lorentzian metric is, as I said, simply a metric/distance function which is no longer required to be positive definite.
Finsler spaces differ from Riemannian spaces in that they introduce an asymmetry (anisotropy) into the geometry. In Riemannian space, the length of a vector is equal to that of its negative. In Finsler space, this is relaxed, so the direction a vector is pointing becomes as important as its position. Please don't ask me to try to explain this further: I didn't understand it in 1982, and I really still don't understand it today.
Yes indeed. The gold standard
)
Yes indeed. The gold standard being sought here is the simultaneous multi-mode detections & study of evolving structures from supernovae and likewise events. What an exciting time to be an astronomer.
Cheers, Mike
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
https://phys.org/news/2024-04
)
https://phys.org/news/2024-04-observatory-chile-highest-world-aims.html
A Proud member of the O.F.A. (Old Farts Association). Be well, do good work, and keep in touch.® (Garrison Keillor)
There are significant health
)
There are significant health risks at that altitude, not just inconvenience but real danger to the unwary.
The mid infrared range is normally where water vapor - that strongest greenhouse gas keeping us all warm - masks signals of interest. The observations will be interesting.
Cheers, Mike.
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
Hello! At the moment too
)
Hello!
At the moment too little specifications. The spectrograph is just 2 channels at once. But probably that's a question of money, and a better spectrograph can become installed later. That's the advantage of telescopes on earth, even at high attitude.
Kind regards and happy crunching
Martin
https://phys.org/news/2024-06
)
https://phys.org/news/2024-06-gravitational-geometry-spacetime.html
So how do we get our head around this new geometry?
A Proud member of the O.F.A. (Old Farts Association). Be well, do good work, and keep in touch.® (Garrison Keillor)
https://interestingengineerin
)
https://interestingengineering.com/space/slowest-spinning-neutron-star-emits-radio-signals
Hmmm... tired of spinning around? Take break...
A Proud member of the O.F.A. (Old Farts Association). Be well, do good work, and keep in touch.® (Garrison Keillor)
Go and do physics and maths
)
Go and do physics and maths for 10+ years at university level ? :-)
Seriously, what is proposed is that the definition of 'distance' in spacetime perhaps includes non-quadratic terms.
Take the good old Euclidean metric for 3D space then ds2 = dx2 + dy2 + dz2 being positive definite (because squares of real numbers are always non-negative, and summing non-negative numbers only gives a non-negative answer) you can take the square root of ds2 to get a distance being a real number. Suppose, to be perverse, you throw in a linear term for one of the directions (say along the y-axis) then : ds2 = dx2 + dy + dz2 and now nothing is positive definitely (dy could be large and negative) and you might have ds2 < 0 and ds becomes ? what, an imaginary number maybe? Clearly you lose a traditional/classical idea of distance. That's not terrible per se. After all Riemann et al taught us to relax about non-classical geometries. The Lorentzian metric in spacetime (ds2 = dx2 + dy2 + dz2 - dt2, where I have set c = 1) can give you that also; separating spacetime into 'light cones' centred per point, yielding time-like (ds2 < 0) or space-like (ds2>0) regions and the surface of the 'cone' is null or ds2 = 0.
Thus a linear term for the co-ordinate differences yields other geometries of which Finsler geometry is one example. Importantly one can rephrase Einstein's GR equations in terms of the new geometries, with all the implications like gravitational waves and cosmology stuff that we already have. The remainder of the paper referred to is opaque in detail to me, I don't know the relevant mathematics.
Cheers, Mike
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
Tom M
)
Reading things on this subject just makes me want to spin around even more in both or all directions Tom
You must have also learned how to type close to the speed of light Mike since you typed all of that faster than me reading both of those articles the Tom posted and then typing out my one-liner
MAGIC Quantum Mechanic
)
Hi Magic! ;-)
I think the funny/weird metrics are exciting because one of them, or a group of them, may get around or even explain the 'paradox', for want of a better word, of the central singularity of black holes. That's where GR ought meet QM. I wonder what the Finsler et al geometries have to say about that. Watch this space I guess.
Cheers, Mike.
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
Mike Hewson wrote: Go and do
)
Excuse me??? Where on earth did you get this from? It is very clear in Definition 1.2.2 of Dr Heefer's thesis (which I presume is the paper you refer to later on) that, even in Finsler geometry, a metric is a symmetric bi-linear (ie quadratic) form,
g =gijdxidxj
This is even more clear in Definition 1.2.1. If you have any reference which suggests anything different, please provide a full citation, including page or section number.
In the next bit, it seems to me as if your definition of a "classical" geometry is just Euclidean geometry. I suppose most people would think the same, for no other reason than we all learn Euclidean geometry from Day One, and then learn about the other stuff if we go on to study mathematics in university.
Riemannian geometry is, in fact, nothing more than geometry in which Euclid's fifth postulate (the one about parallel lines) is no longer assumed; thus, Riemannian geometry is also "classical". The same holds true with Lorentzian geometries, wherein the metric ("distance function") is no longer presumed to be positive definite.
Note that Lorentz metric and Lorentzian metric are not the same thing: a Lorentz metric (of which the Minkowski metric is one example) is a Lorentzian metric on a 4-dimensional space with signature (3,1). OTOH, a Lorentzian metric is, as I said, simply a metric/distance function which is no longer required to be positive definite.
Finsler spaces differ from Riemannian spaces in that they introduce an asymmetry (anisotropy) into the geometry. In Riemannian space, the length of a vector is equal to that of its negative. In Finsler space, this is relaxed, so the direction a vector is pointing becomes as important as its position. Please don't ask me to try to explain this further: I didn't understand it in 1982, and I really still don't understand it today.