Is that always true? Is that all bundled in with what is 'seen' for entropy?
Well you're certainly hitting the mark on the tricky deep questions! Dunno .... :-)
Quote:
Are we observing first hand effects or are we actually conjuring up abstractions that describe what we observe for what actually are second-level effects of underlying mechanisms?...
The actual 'secret' is that we only really have 'effective theories' not 'truths'. Each type or mode of description has it's assumptions, which are usually related to some physical scale like a size ( 'bigger than an atom' ) or a speed ( 'much slower than lightspeed' ) or a mass/energy ( 'heavier than a quark' ) etc ....
These are domains of description and there is a 'correspondence' principle that says theories ought agree in the regions where they overlap. Like General Relativity 'becoming' Special Relativity when the acceleration/gravity goes to zero, and Special Relativity 'becomes' Newtonian when speeds are low, or Quantum Mechanics 'approaches' Classical Dynamics with increasing size.
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
Red = high velocity light;
Green = low velocity light;
Black = real-world observed wavefronts (after refraction).
(Try to ignore the visual illusion, the red -> green lines are straight lines.)
Huygens idea was 'wavelets', that is wherever light hit some point that point then became a source of radiation. These wavelet-fronts thus combine ( with phase adjustments ) to get the next 'full' wavefront. So it is a way of modelling the jump from one phase surface to the next :
A feature is that you could run this diagram backwards too. So the description doesn't specify a time direction, but that's OK. I've found a terrific page with a neat applet that is a great demo you ought fiddle with.
But refraction is still explicable with the idea of the slower medium causing that wavefront section that has already entered lagging the line of the bit that hasn't. What isn't often stated is that ( generally, classically at least ) the frequency doesn't change with movement across the boundary. Looking at the earlier discussion of phase ( k*x - w*t ) then if w is constant, but the speed has lessened, then the wavelength must be shorter ( speed = frequency * wavelength ). That means a given phase value is returned to ( 'cos it is cyclic ) in a shorter distance, so the wavefronts ( surface of a given phase ) or wavelets are closer.
Quote:
Aside: Should there be a small force of radiation pressure associate with the refractive deflection?...
Yes, light has momentum thus if you deflect it you must supply a force. Newton's law of action/reaction is really conservation of momentum in disguise.
Quote:
Where multiple paths of insights all converge on the same representation, that has just got to be 'interesting'!
Heck! With the ground we're covering, it's nearly a semester's worth of optics! That's my fault though, as I did encourage questions! :-) :-)
Quote:
But then also... Do we see repeated structures for the many equations in physics because our world naturally follows those structures? Or are we merely seeing an artefact of the mathematical tools that we are using?... Is there some underlying assumption that then forces all our tools to be "hammers" that then can only see "nails" regardless of the job?
What we've discussed is more or less a 'linear' approach, in that we are assuming yet another principle - that of 'linear superposition'. This means roughly that if I have two waves in some area you just add them together to get the total ( the phase takes care of interference ). That is often honoured by reality. Certainly for light if the energies aren't too high ( else we start creating particle/anti-particle pairs ... ). For gravitational waves, no. Einstein's GR equations are non-linear. Though they are often modelled as linear ( especially well away from the source ). Linear maths is much easier so is a preferred hammer. Or at least the first approximation used, before one refines ....
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
Here's yet another way to view the velocity of the wave. Take any two arbitrary points in ( one dimensional ) spacetime. Call them A and B.
For A the phase of the wave is :
k * x_A - w * t_A
and for B :
k * x_B - w * t_B
now the difference in phase for these points is :
( k * x_B - w * t_B ) - ( k * x_A - w * t_A )
= k * ( x_B - x_A ) - w * ( t_B - t_A )
Now suppose I want to say that these two points represent the same phase value, or if you like they are samples of the same wave front. Then I set that phase difference is zero, so
k * ( x_B - x_A ) = w * ( t_B - t_A )
which re-arranges to
( x_B - x_A ) / ( t_B - t_A ) = w / k
You'll recognise the left hand side as a velocity ( a distance divided by a time interval ) and w / k = wavelength * frequency as before. If you consider a left going wave, you'd have a plus for the w * t term within the phase, and end up with (-1) * w / k. So this derivation makes the direction/sense of the wave's travel explicit.
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
Ahh, this I did not know. Counter-intuitive, isn't it? One of the benefits of mass=0 I suppose. There must be more to it than this. It seems like we are only working with some of the pieces of the puzzle.
If you travel at light speed, you must have zero ( rest ) mass. And vice versa. This is required to be consistent with relativity, but probably could well reflect something deeper too. Time doesn't pass for a photon, meaning that at light speed clocks stop ( or time and clocks don't have meaning ). If you have a rest mass and increase your speed then you'd get faster and faster but never actually reach c. You're kinetic energy just grows and grows without limit. As KE = m * v^2 / 2, then m = 0 means KE = 0. If m > 0 then KE will grow if v increases, but by then you have to use another formula for KE. Or you can say mass increases with speed .... I think SLAC had to double it's beam energy for a particular upgrade just to get a further 60 mph closer to c. So it used just as much energy to gain that extra 60 mph, as it did to get the first 179,000 or so mph !! So 'counter-intuitive' is right on!!! :-)
Quote:
Was that an add??? LOL. Looks like a crappy product to me. The things people come up with...
Yup, it's utter BS ..... it just levers the force of your own muscles to squeeze the tube. Golly gee .... :-)
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
In brief... (Still puzzling about hammers, cause, effect, theories, and... Then there's logolopolis*;-) )
Quote:
If you travel at light speed, you must have zero ( rest ) mass. And vice versa. This is required to be consistent with relativity, but probably could well reflect something deeper too. Time doesn't pass for a photon, ...
Do you need time to pass for something to be able to exhibit mass?
That is, as delta t -> 0, mass -> 0, or below some limit of delta t, mass becomes in effect 0 ?
Regards,
Martin
* A Dr Who story in which mathematicians have religiously dedicated themselves to reshape the universe by working through their mental calculations. A sort of exercising the equivalence principle in that if the mathematics faithfully describe the universe, then manipulating the mathematics should also manipulate that universe itself... (Which might be true within a simulation :-) )
Ahh, this I did not know. Counter-intuitive, isn't it? One of the benefits of mass=0 I suppose. There must be more to it than this. It seems like we are only working with some of the pieces of the puzzle.
If you travel at light speed, you must have zero ( rest ) mass. And vice versa. This is required to be consistent with relativity, but probably could well reflect something deeper too. Time doesn't pass for a photon, meaning that at light speed clocks stop ( or time and clocks don't have meaning ). If you have a rest mass and increase your speed then you'd get faster and faster but never actually reach c. You're kinetic energy just grows and grows without limit. As KE = m * v^2 / 2, then m = 0 means KE = 0. If m > 0 then KE will grow if v increases, but by then you have to use another formula for KE. Or you can say mass increases with speed .... I think SLAC had to double it's beam energy for a particular upgrade just to get a further 60 mph closer to c. So it used just as much energy to gain that extra 60 mph, as it did to get the first 179,000 or so mph !! So 'counter-intuitive' is right on!!! :-)
I thought that as you approach the speed of light... your mass approaches infinity..
There are velocities that can be greater than the speed of light.. Microwave phase velocities in a wave guide can be greater than the speed of light..
Quote:
Was that an add??? LOL. Looks like a crappy product to me. The things people come up with...
Yup, it's utter BS ..... it just levers the force of your own muscles to squeeze the tube. Golly gee .... :-)
Cheers, Mike.
There might be a savings ... Were you ever hungover in the morning and squeeze to much toothpaste on your brush..:-)
As a matter of fact everybody uses to much toothpaste..
There are some who can live without wild things and some who cannot. - Aldo Leopold
... Or you can say mass increases with speed .... I think SLAC had to double it's beam energy for a particular upgrade just to get a further 60 mph closer to c. So it used just as much energy to gain that extra 60 mph, as it did to get the first 179,000 or so mph !! So 'counter-intuitive' is right on!!! :-)
I thought that as you approach the speed of light... your mass approaches infinity..
Indeed so. As shown in the SLAC example above.
Quote:
There are velocities that can be greater than the speed of light.. Microwave phase velocities in a wave guide can be greater than the speed of light..
Also such as the speed of gossip and the speed of anticipation... Similarly so for the 'end' of a quickly sweeping radar beam...
Except ofcourse there is no 'physical' entity or form of communication that is actually superluminal in those examples.
For your phase velocity example, is it just not a case that there is a 'blob' travelling at a finite (sub-luminal) speed that itself changes shape and so gives the illusion of a superluminal shift of the feature that you are looking for?...
... Or you can say mass increases with speed .... I think SLAC had to double it's beam energy for a particular upgrade just to get a further 60 mph closer to c. So it used just as much energy to gain that extra 60 mph, as it did to get the first 179,000 or so mph !! So 'counter-intuitive' is right on!!! :-)
I thought that as you approach the speed of light... your mass approaches infinity..
Indeed so. As shown in the SLAC example above.
Quote:
There are velocities that can be greater than the speed of light.. Microwave phase velocities in a wave guide can be greater than the speed of light..
Also such as the speed of gossip and the speed of anticipation... Similarly so for the 'end' of a quickly sweeping radar beam...
Except ofcourse there is no 'physical' entity or form of communication that is actually superluminal in those examples.
For your phase velocity example, is it just not a case that there is a 'blob' travelling at a finite (sub-luminal) speed that itself changes shape and so gives the illusion of a superluminal shift of the feature that you are looking for?...
In brief... (Still puzzling about hammers, cause, effect, theories, and... Then there's logolopolis*;-) )
Don't forget the guy who hit himself on the head repeatedly with a hammer. He said he did it because it felt so good when he stopped! Thinking about physics can be rather like that! :-)
Quote:
Do you need time to pass for something to be able to exhibit mass?
Yes, actually. In the sense that mass is an inertial quantity. In F = ma it's the amount that tells how much ooomph produces such and such a change in motion. To measure an actual mass amount I have to interact over some time interval and compare before and after. Force is the time rate of change of momentum. Thus before I kick a particular soccer ball lying on the ground I don't yet know if it is a cleverly painted balloon, or a concrete sphere. My toes will no doubt tell me ... :-)
Ditto for measuring mass via gravity. Scales and the like. You'll always find the need for before & after comparisons.
Quote:
* A Dr Who story in which mathematicians have religiously dedicated themselves to reshape the universe by working through their mental calculations. A sort of exercising the equivalence principle in that if the mathematics faithfully describe the universe, then manipulating the mathematics should also manipulate that universe itself... (Which might be true within a simulation :-) )
Ah, they'd fit right in with Roger Penrose - he goes for that Platonic correspondence b/w math & reality. Was that the episode where they became trapped in an Escher like recursion? Leaving by the right door brought them back in on the left, or by going upstairs you came out of the cellar? And it got worse so that with time the effective distance around a 'loop' reduced. I really enjoyed that story. I recall Peter Davison was the doc then.
Quote:
I thought that as you approach the speed of light... your mass approaches infinity..
In middle age you can do that without moving.
Quote:
There are velocities that can be greater than the speed of light.. Microwave phase velocities in a wave guide can be greater than the speed of light..
I got a tachyonic message last week, sent this week, saying someone would bring that up. :-)
So I wrote :
Quote:
A subtle point, but in some discussions you need to be careful of the distinction between phase velocity ( = c ) of a single photon/frequency and the group velocity ( roughly an average ) of a gaggle of them.
You have to find out which c they are talking about. The one they can actually measure or the value they put into the wave equation. The group velocity is dw/dk, but the phase velocity is w/k. These are identical for a single photon. But in a mix of photons not necessarily so. What these superluminal phase velocities effectively refer to is that if the packet/group changes 'shape' - by becoming a narrower pulse, say - then we can deduce that some of the photons 'must have caught up to the pack' to achieve that. But only the transit time of a pulse, and it's width, was really measured over some span. The distance traveled divided by the time to do it does not come out as superluminal.
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
... so good when he stopped! Thinking about physics can be rather like that! :-)
Ouch?
Quote:
Quote:
Do you need time to pass for something to be able to exhibit mass?
Yes, actually. In the sense that mass is an inertial quantity. In F = ma ... have to interact over some time interval and compare before and after. ...
... And light behaves masslessly and yet is a packet of energy (and so should have an associated mass). Particles gain infinite mass as they approach the speed of light... And light is timeless with photons surviving the entire life of our present universe...
There's something rather tantalising there methinks...
* A Dr Who story in which mathematicians have religiously dedicated themselves to reshape the universe by working through their mental calculations. A sort of exercising the equivalence principle in that if the mathematics faithfully describe the universe, then manipulating the mathematics should also manipulate that universe itself... (Which might be true within a simulation :-) )
Ah, they'd fit right in with Roger Penrose - he goes for that Platonic correspondence b/w math & reality. Was that the episode where they became trapped in an Escher like recursion? ... it got worse so that with time the effective distance around a 'loop' reduced. I really enjoyed that story. ...
So did I.
That one is "Castrovalva" although I remember it as "Recursive Occlusions" and it was very cleverly done. A key plot feature was that the diarist for the inhabitants scrupulously recorded the day's events day by day in a large diary. There was also a second diary that had been filled with the history prior to the present diary. Both diaries, old history and new, both looked by the condition of their covers and the pages to be very new...
RE: Is that always true? Is
)
Well you're certainly hitting the mark on the tricky deep questions! Dunno .... :-)
The actual 'secret' is that we only really have 'effective theories' not 'truths'. Each type or mode of description has it's assumptions, which are usually related to some physical scale like a size ( 'bigger than an atom' ) or a speed ( 'much slower than lightspeed' ) or a mass/energy ( 'heavier than a quark' ) etc ....
These are domains of description and there is a 'correspondence' principle that says theories ought agree in the regions where they overlap. Like General Relativity 'becoming' Special Relativity when the acceleration/gravity goes to zero, and Special Relativity 'becomes' Newtonian when speeds are low, or Quantum Mechanics 'approaches' Classical Dynamics with increasing size.
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
RE: Why do we not actually
)
Huygens idea was 'wavelets', that is wherever light hit some point that point then became a source of radiation. These wavelet-fronts thus combine ( with phase adjustments ) to get the next 'full' wavefront. So it is a way of modelling the jump from one phase surface to the next :
A feature is that you could run this diagram backwards too. So the description doesn't specify a time direction, but that's OK. I've found a terrific page with a neat applet that is a great demo you ought fiddle with.
But refraction is still explicable with the idea of the slower medium causing that wavefront section that has already entered lagging the line of the bit that hasn't. What isn't often stated is that ( generally, classically at least ) the frequency doesn't change with movement across the boundary. Looking at the earlier discussion of phase ( k*x - w*t ) then if w is constant, but the speed has lessened, then the wavelength must be shorter ( speed = frequency * wavelength ). That means a given phase value is returned to ( 'cos it is cyclic ) in a shorter distance, so the wavefronts ( surface of a given phase ) or wavelets are closer.
Yes, light has momentum thus if you deflect it you must supply a force. Newton's law of action/reaction is really conservation of momentum in disguise.
Heck! With the ground we're covering, it's nearly a semester's worth of optics! That's my fault though, as I did encourage questions! :-) :-)
What we've discussed is more or less a 'linear' approach, in that we are assuming yet another principle - that of 'linear superposition'. This means roughly that if I have two waves in some area you just add them together to get the total ( the phase takes care of interference ). That is often honoured by reality. Certainly for light if the energies aren't too high ( else we start creating particle/anti-particle pairs ... ). For gravitational waves, no. Einstein's GR equations are non-linear. Though they are often modelled as linear ( especially well away from the source ). Linear maths is much easier so is a preferred hammer. Or at least the first approximation used, before one refines ....
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
Here's yet another way to
)
Here's yet another way to view the velocity of the wave. Take any two arbitrary points in ( one dimensional ) spacetime. Call them A and B.
For A the phase of the wave is :
k * x_A - w * t_A
and for B :
k * x_B - w * t_B
now the difference in phase for these points is :
( k * x_B - w * t_B ) - ( k * x_A - w * t_A )
= k * ( x_B - x_A ) - w * ( t_B - t_A )
Now suppose I want to say that these two points represent the same phase value, or if you like they are samples of the same wave front. Then I set that phase difference is zero, so
k * ( x_B - x_A ) = w * ( t_B - t_A )
which re-arranges to
( x_B - x_A ) / ( t_B - t_A ) = w / k
You'll recognise the left hand side as a velocity ( a distance divided by a time interval ) and w / k = wavelength * frequency as before. If you consider a left going wave, you'd have a plus for the w * t term within the phase, and end up with (-1) * w / k. So this derivation makes the direction/sense of the wave's travel explicit.
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
RE: Ahh, this I did not
)
If you travel at light speed, you must have zero ( rest ) mass. And vice versa. This is required to be consistent with relativity, but probably could well reflect something deeper too. Time doesn't pass for a photon, meaning that at light speed clocks stop ( or time and clocks don't have meaning ). If you have a rest mass and increase your speed then you'd get faster and faster but never actually reach c. You're kinetic energy just grows and grows without limit. As KE = m * v^2 / 2, then m = 0 means KE = 0. If m > 0 then KE will grow if v increases, but by then you have to use another formula for KE. Or you can say mass increases with speed .... I think SLAC had to double it's beam energy for a particular upgrade just to get a further 60 mph closer to c. So it used just as much energy to gain that extra 60 mph, as it did to get the first 179,000 or so mph !! So 'counter-intuitive' is right on!!! :-)
Yup, it's utter BS ..... it just levers the force of your own muscles to squeeze the tube. Golly gee .... :-)
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
In brief... (Still puzzling
)
In brief... (Still puzzling about hammers, cause, effect, theories, and... Then there's logolopolis* ;-) )
Do you need time to pass for something to be able to exhibit mass?
That is, as delta t -> 0, mass -> 0, or below some limit of delta t, mass becomes in effect 0 ?
Regards,
Martin
* A Dr Who story in which mathematicians have religiously dedicated themselves to reshape the universe by working through their mental calculations. A sort of exercising the equivalence principle in that if the mathematics faithfully describe the universe, then manipulating the mathematics should also manipulate that universe itself... (Which might be true within a simulation :-) )
See new freedom: Mageia Linux
Take a look for yourself: Linux Format
The Future is what We all make IT (GPLv3)
RE: RE: Ahh, this I did
)
I thought that as you approach the speed of light... your mass approaches infinity..
There are velocities that can be greater than the speed of light.. Microwave phase velocities in a wave guide can be greater than the speed of light..
There might be a savings ... Were you ever hungover in the morning and squeeze to much toothpaste on your brush..:-)
As a matter of fact everybody uses to much toothpaste..
There are some who can live without wild things and some who cannot. - Aldo Leopold
RE: RE: ... Or you can
)
Indeed so. As shown in the SLAC example above.
Also such as the speed of gossip and the speed of anticipation... Similarly so for the 'end' of a quickly sweeping radar beam...
Except ofcourse there is no 'physical' entity or form of communication that is actually superluminal in those examples.
For your phase velocity example, is it just not a case that there is a 'blob' travelling at a finite (sub-luminal) speed that itself changes shape and so gives the illusion of a superluminal shift of the feature that you are looking for?...
Regards,
Martin
See new freedom: Mageia Linux
Take a look for yourself: Linux Format
The Future is what We all make IT (GPLv3)
RE: RE: RE: ... Or you
)
Thats right.. (so far :-)) [url=http://en.wikipedia.org/wiki/Dispersion_(optics)] Dispersion [/url]
There are some who can live without wild things and some who cannot. - Aldo Leopold
RE: In brief... (Still
)
Don't forget the guy who hit himself on the head repeatedly with a hammer. He said he did it because it felt so good when he stopped! Thinking about physics can be rather like that! :-)
Yes, actually. In the sense that mass is an inertial quantity. In F = ma it's the amount that tells how much ooomph produces such and such a change in motion. To measure an actual mass amount I have to interact over some time interval and compare before and after. Force is the time rate of change of momentum. Thus before I kick a particular soccer ball lying on the ground I don't yet know if it is a cleverly painted balloon, or a concrete sphere. My toes will no doubt tell me ... :-)
Ditto for measuring mass via gravity. Scales and the like. You'll always find the need for before & after comparisons.
Ah, they'd fit right in with Roger Penrose - he goes for that Platonic correspondence b/w math & reality. Was that the episode where they became trapped in an Escher like recursion? Leaving by the right door brought them back in on the left, or by going upstairs you came out of the cellar? And it got worse so that with time the effective distance around a 'loop' reduced. I really enjoyed that story. I recall Peter Davison was the doc then.
In middle age you can do that without moving.
I got a tachyonic message last week, sent this week, saying someone would bring that up. :-)
So I wrote :
You have to find out which c they are talking about. The one they can actually measure or the value they put into the wave equation. The group velocity is dw/dk, but the phase velocity is w/k. These are identical for a single photon. But in a mix of photons not necessarily so. What these superluminal phase velocities effectively refer to is that if the packet/group changes 'shape' - by becoming a narrower pulse, say - then we can deduce that some of the photons 'must have caught up to the pack' to achieve that. But only the transit time of a pulse, and it's width, was really measured over some span. The distance traveled divided by the time to do it does not come out as superluminal.
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
RE: ... so good when he
)
Ouch?
... And light behaves masslessly and yet is a packet of energy (and so should have an associated mass). Particles gain infinite mass as they approach the speed of light... And light is timeless with photons surviving the entire life of our present universe...
There's something rather tantalising there methinks...
Logopolis
So did I.
That one is "Castrovalva" although I remember it as "Recursive Occlusions" and it was very cleverly done. A key plot feature was that the diarist for the inhabitants scrupulously recorded the day's events day by day in a large diary. There was also a second diary that had been filled with the history prior to the present diary. Both diaries, old history and new, both looked by the condition of their covers and the pages to be very new...
Cheers,
Martin
See new freedom: Mageia Linux
Take a look for yourself: Linux Format
The Future is what We all make IT (GPLv3)