The periodic table is arranged according to the number of 'external' electrons that an atom has. These are like having a certain number of fingers to connect to other things with. A bit like LEGO.
There is another table of interest here. It is the table of nuclides which rather ignores the electrons and focuses on the contents of the nuclei. There are many versions of this table, this is one of the simpler ones :
... the number of protons is along the horizontal axis, the number of neutrons along the vertical axis. Each possible nucleus - denoted as having Z protons and N neutrons here - is represented as a wee square. Such a square is then color coded to the key on the right. So there is this avenue of stability, in the darker colors, going up the middle of the band of known nuclei with less stable nuclei to either side. Generally there is an excess of neutrons required with the heavier nuclides in order to remain stable.
That's an interesting feature : a lone neutron will decay but you need them to make nuclei more stable. The logic for that is pretty straightforward. Each time you add a proton or a neutron then one does add to the nuclear force attraction b/w it and existing members of the nucleus. But with a proton you add positive charge so electrical repulsion ( between existing protons in the nucleus ) is increased, and that doesn't happen with neutrons. Clearly there is some compromise here between the relative effects of the nuclear forces and electromagnetic forces.
But you can't just keep adding neutrons indefinitely, for a given number of protons. You reach what is called the 'neutron drip line' where any neutron you add will just 'drip out' of the nucleus in short order. There is a corresponding 'proton drip line' of similiar nature. These drip lines are roughly outlined above as the margins between the main band of colored squares and the white background. Now what is really happening - in horrible detail - is up quarks interacting with down quarks in various proportions. It's just that we parcel quarks together in labelled bunches of threes with the names of 'proton' and 'neutron'.
By the time you get to Uranium ( 92 protons ) then one needs about 140+ neutrons to keep things relatively stable, and the exceptions are quite famous. You'll note that after about Z = 80 and N = 120 ( far upper right of picture ) we lose any dark squares. That's about where the aforementioned Francium is. There just aren't any really long term stable combinations.
[ so when I said '... an extra neutron or two ...' earlier I meant with regard to each alpha sub-unit ]
[aside]
What do we mean by 'neutron star' then ?
A great gob of neutrons evidently. In a normal atom you will have vast reaches of empty space. Consider this following anthropomorphic pseudo-explanation : if I was down at a Helium 4 nucleus - two protons and two neutrons - hanging & chillin', I could have a chat with them, share an apple cider, do a couple of snaps to Twitter with etc. If I asked 'where are your electrons' their answer would be 'out there somewhere' with a vague wave in any old direction. So if I got my super-duper binoculars out and scanned for a while I might see something whizzing around in the far distance. The ratio of the nuclear diameter to the atom's diameter is around 1:10,000.
Now imagine a form of matter where virtually everyone's a neutron, but with almost no intervening space. Jammed in. Cheek by jowl. In all dimensions/directions. And gravity is now very much a player. Indeedy do. Each cubic meter is a million billion tonnes of matter and that is three times the density of nuclei that we have hereabouts on Earth. We have nuclear forces acting b/w the neutrons, or quarks/whatever. This is the very centre of a neutron star and the question now becomes 'how do you hold up against gravity ?' Gravity always adds in attraction, never repels. If you have enough matter it will dominate.
There was this puzzle book I had when a kid. It had these weird physical questions ( & alleged answers ) within it. My favorite was 'what happens when an immovable object meets an irresistible force'. As a language construct of course you have a contradiction by the choice of words. But there was a deeper aspect which I pondered about .... in the real world, what wins in the end ?
Now for the centre of a neutron star you have gravity on the one hand as the irresistible force. On the other side you have quantum mechanics which states that fermions - here neutrons - just cannot be stacked one atop the other. They are the immovable objects. So this is the realm of 'a quantum theory of gravity' :
Who wins ? :-) :-)
[/aside]
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
I've delayed answering this because I've had to think 'well, what is the problem here?'. Exactly why* does action-at-a-distance ( call it AAAD ) fail ? I'm going to have a longer think about that before replying. I want to identify and isolate the key components better ...
It is time. Not simply time to answer this question, but to realise that like it or nay time is an embedded property of this universe. So we have to discuss the basis of what is called 'relativity' which alas has a plethora of meanings in modern culture up to and including 'anything goes'. Which relativity - the word as used in physics - isn't. I think there is some confusion with the philosophical phrase 'moral relativity' which roughly means anyone/everyone has a valid viewpoint so a dog's breakfast awaits any meeting of disparities there-of ..... this being a good example of 'I have a hammer in my hand, thus everything starts to look nail-like'.
So we have to be more precise and/or bounded in our discourse in order to make analytical/predictive headway in physics. Hence one needs to leave pre-conceptions at the doorway. We begin with what follows as the definition of an inertial observer or reference frame :
#1 - a data collection system extended in time and/or space sufficiently for the purpose at hand.
#2 - differences in position coordinates are independent of time.
#3 - the time of an event is that reading upon the clock situated at that event.
#4 - all clocks in the frame are suitably synchronised.
#5 - all clocks remain in synchrony.
#6 - at any given constant time, space is Euclidean.
Notes :
#1 -> implies that we don't need to talk of cognition, intelligence or lack of it. So an observer is not some guy sitting at some point ( call it the origin ) looking around with a pair of binoculars and making notes.
#2 -> implies some rigidity of the distance measure.
#3 -> in practice one can reasonably interpolate b/w clocks and places, provided the measures obtained are 'transitive' ie. consistent amongst different paths to the same single event.
#4 -> the trick to synchonising clocks is to claim one clock as the 'master' eg. the one at the distance origin, and divide round trip light travel time by a factor of two to set the other clock readings.
#5 -> it turns out this will imply that an inertial frame is not accelerated, otherwise the clocks within a given frame would run at different rates and vice versa ( if the clocks don't keep time then you must be accelerating ).
#6 -> Pythagorus' Theorem holds so the metric or distance measure is the one you are familiar with, but only if you make a spacetime slice with a given time coordinate ( once the frame has been properly setup ).
generally -> it is a matter of experiment to determine if such frames exist. They do ... :-)
Please don't panic about these statements. I mention them not to seem a clever dick but to emphasise what is often not made plain : you have to have a working definition of what is meant by simultaneous events occurring at different places. Because if you don't have that then you can't track cause and effect because time ordering is crucial ie. cause comes prior to effect. That is a supreme principle in all force discussions, fields or particles or whatever ....
... specifically when we say 'light has a fixed speed ( in a vacuum ) for all inertial observers' then that means a finite speed within any particular measurement system. Thus all information transfer within a frame is subject to delay but we 'regularise' that issue by #4 and #5 above. Note that we haven't gotten around to discussing measurement comparisons made by two different frames yet.
That'll do for today.
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
The main take-home message is that all information from separated positions must be time delayed at the rate of ~ one nanosecond per foot of travel. That's the speed of light. Fast for sure but not infinite. There is much more that flows from the constancy of the speed of light etc, but this is the prime concern : All news is old news ! :-)
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
Now if one looks at conditions #1 thru #6 of the inertial frame definition, one can isolate #3, #4 and #5 as the ones that depart from the action at a distance idea ie. they talk of time delays. Condition #6 is still true for Newton AAAD as space is Euclidean for all time and thus quite irrespective of any particular time. In what follows I am not going to retrace/derive Special Relativity results or deductions rigorously as such, but rather I present a heuristic argument by analogy to convince you hopefully of the merit of thinking of time delays and the special importance of velocities in that discussion.
Velocity you will recall is some distance traveled divided by the time taken to do that, but with a vector quality so that the direction of travel is important too.
Gun-laying
Let's pretend that we are the crew of a gun emplacement on a shoreline. Our job is to accurately hit some naval target passing by within our range. To be polite suppose it is peacetime and we practice alot using some drone vehicle which is maneuvered on some suitable course on the water surface. For our training. Also just consider the horizontal distances and not be perturbed by all that up and down stuff. Of course gravity matters but we will ignore that. We will concern ourselves with geometry in the plane and arbitrarily but conveniently place ourselves at the coordinate system origin. We are not going to use a fully fledged inertial frame. Just think of your everyday classic Newton :
... looking down from above. Cases :
(A) Static drone. Just plonk the craft in some fixed position with respect to the gun and get into it. If we're any good then the path of the winning shell looks something like this :
... where here I've indicated the speed of the artillery round to be c. Just a random choice of variable name right ? :-)
Consider thus that shell speed c. What is the value ? In the real world, and due to air resistance especially, it wouldn't be constant.
Quote:
Those of you who have done late high-school physics or math applications however would have been taught that the horizontal components of velocity for this type of problem would be constant. That's typically phrased as because, in the free flight phase after firing :
(i) gravity ( which we are ignoring anyway ) only acts vertically, and
(ii) we are in the horizontal plane perpendicular to the line of gravity, and
(iii) with no forces in that horizontal plane eg. air resistance discounted, then
(iv) velocities in that plane remain constant.
It is a marvel of The Universe that such orthogonal dimensions may be considered independently that way, but there you have it !! :-)
By now you know I'm drawing an analogy to light. At Newton's time there was the concept that something did go from place to place to illuminate things. That something went into our eyes and that's why we saw things at all.
Quote:
Isaac himself probed to the side and behind of his own eyeball - with a blunt instrument in the space between the eye and the surrounding socket - to demonstrate that pressure at various spots on the outside of his eyeball would alter what he saw accordingly. That would have caused shocking pain! Do not do this at home!
The issue of light speed did arise. Some French guy* tried to time the interval b/w masking and unmasking of lamps on separated hillsides, but that was dominated by human reaction times though. Ole Roemer found a cyclical variation in the timings of the eclipsing of Jupiter's moons and attributed that to a finite speed of light across the varying distances from there to here. His estimate was pretty good actually. So for a long while and for most purposes light was assumed to travel very, very fast. Effectively at infinite speed.
Question for next time : if the speed of the shell is constant and finite then how ought my gun-laying change when the target drone is moving ?
Cheers, Mike.
* Sorry, Galileo thought of it, tried it but to no avail. Fizeau and Foucault separately demonstrated using similar apparatus - stroboscopic or light beam chopping - the correct value to within ~ 0.5%
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
I was an Artillery Forward Observer in the Army : )
Quote:
By now you know I'm drawing an analogy to light. At Newton's time there
was the concept that something did go from place to place to illuminate things.
That something went into our eyes and that's why we saw things at all.
AAAAH Wait a Minute ! .... That ain't what happens ???
Way to go Bill ! So that means you're actually deaf then ? What ? :-)
To put you on the spot then : with suitable artillery how would you ( in generality ) deal with target movement for a given fixed rate of shell movement ?
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
Way to go Bill ! So that means you're actually deaf then ? What ? :-)
To put you on the spot then : with suitable artillery how would you ( in generality ) deal with target movement for a given fixed rate of shell movement ?
Cheers, Mike.
Allright then ) ...
I would attempt to calculate (or Guess ) a convergence point
between the moving target and the artillery taking into account ...
A. The speed and direction (of movement) of the target ...
B. The TOF (Time of Flight) of the Howitzer shells.
There may be some other things to consider but,
I'll leave it at that for now )
The periodic table is arranged according to the number of 'external' electrons that an atom has. These are like having a certain number of fingers to connect to other things with. A bit like LEGO..........
Now for the centre of a neutron star you have gravity on the one hand as the irresistible force. On the other side you have quantum mechanics which states that fermions - here neutrons - just cannot be stacked one atop the other. They are the immovable objects. So this is the realm of 'a quantum theory of gravity' :
Who wins ? :-) :-)
[/aside]
Cheers, Mike.
I finally got back from my vacation. Thanks Mike for all of this work. I am still here to listen.
With your comment above 'So this is the realm of 'a quantum theory of gravity':
Would the quantum people then believe that we won't find a gravitation wave?
Also,
If they say that fermions can't be stacked, how can they explain neutron stars?
Why don't the neutrons in neutron stars decay into protons like you said in one of your prior comments (in about a half an hour)?
merle
What is freedom of expression? Without the freedom to offend, it ceases to exist.
The periodic table is
)
The periodic table is arranged according to the number of 'external' electrons that an atom has. These are like having a certain number of fingers to connect to other things with. A bit like LEGO.
There is another table of interest here. It is the table of nuclides which rather ignores the electrons and focuses on the contents of the nuclei. There are many versions of this table, this is one of the simpler ones :
... the number of protons is along the horizontal axis, the number of neutrons along the vertical axis. Each possible nucleus - denoted as having Z protons and N neutrons here - is represented as a wee square. Such a square is then color coded to the key on the right. So there is this avenue of stability, in the darker colors, going up the middle of the band of known nuclei with less stable nuclei to either side. Generally there is an excess of neutrons required with the heavier nuclides in order to remain stable.
That's an interesting feature : a lone neutron will decay but you need them to make nuclei more stable. The logic for that is pretty straightforward. Each time you add a proton or a neutron then one does add to the nuclear force attraction b/w it and existing members of the nucleus. But with a proton you add positive charge so electrical repulsion ( between existing protons in the nucleus ) is increased, and that doesn't happen with neutrons. Clearly there is some compromise here between the relative effects of the nuclear forces and electromagnetic forces.
But you can't just keep adding neutrons indefinitely, for a given number of protons. You reach what is called the 'neutron drip line' where any neutron you add will just 'drip out' of the nucleus in short order. There is a corresponding 'proton drip line' of similiar nature. These drip lines are roughly outlined above as the margins between the main band of colored squares and the white background. Now what is really happening - in horrible detail - is up quarks interacting with down quarks in various proportions. It's just that we parcel quarks together in labelled bunches of threes with the names of 'proton' and 'neutron'.
By the time you get to Uranium ( 92 protons ) then one needs about 140+ neutrons to keep things relatively stable, and the exceptions are quite famous. You'll note that after about Z = 80 and N = 120 ( far upper right of picture ) we lose any dark squares. That's about where the aforementioned Francium is. There just aren't any really long term stable combinations.
[ so when I said '... an extra neutron or two ...' earlier I meant with regard to each alpha sub-unit ]
[aside]
What do we mean by 'neutron star' then ?
A great gob of neutrons evidently. In a normal atom you will have vast reaches of empty space. Consider this following anthropomorphic pseudo-explanation : if I was down at a Helium 4 nucleus - two protons and two neutrons - hanging & chillin', I could have a chat with them, share an apple cider, do a couple of snaps to Twitter with etc. If I asked 'where are your electrons' their answer would be 'out there somewhere' with a vague wave in any old direction. So if I got my super-duper binoculars out and scanned for a while I might see something whizzing around in the far distance. The ratio of the nuclear diameter to the atom's diameter is around 1:10,000.
Now imagine a form of matter where virtually everyone's a neutron, but with almost no intervening space. Jammed in. Cheek by jowl. In all dimensions/directions. And gravity is now very much a player. Indeedy do. Each cubic meter is a million billion tonnes of matter and that is three times the density of nuclei that we have hereabouts on Earth. We have nuclear forces acting b/w the neutrons, or quarks/whatever. This is the very centre of a neutron star and the question now becomes 'how do you hold up against gravity ?' Gravity always adds in attraction, never repels. If you have enough matter it will dominate.
There was this puzzle book I had when a kid. It had these weird physical questions ( & alleged answers ) within it. My favorite was 'what happens when an immovable object meets an irresistible force'. As a language construct of course you have a contradiction by the choice of words. But there was a deeper aspect which I pondered about .... in the real world, what wins in the end ?
Now for the centre of a neutron star you have gravity on the one hand as the irresistible force. On the other side you have quantum mechanics which states that fermions - here neutrons - just cannot be stacked one atop the other. They are the immovable objects. So this is the realm of 'a quantum theory of gravity' :
Who wins ? :-) :-)
[/aside]
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: I've delayed answering
)
It is time. Not simply time to answer this question, but to realise that like it or nay time is an embedded property of this universe. So we have to discuss the basis of what is called 'relativity' which alas has a plethora of meanings in modern culture up to and including 'anything goes'. Which relativity - the word as used in physics - isn't. I think there is some confusion with the philosophical phrase 'moral relativity' which roughly means anyone/everyone has a valid viewpoint so a dog's breakfast awaits any meeting of disparities there-of ..... this being a good example of 'I have a hammer in my hand, thus everything starts to look nail-like'.
So we have to be more precise and/or bounded in our discourse in order to make analytical/predictive headway in physics. Hence one needs to leave pre-conceptions at the doorway. We begin with what follows as the definition of an inertial observer or reference frame :
#1 - a data collection system extended in time and/or space sufficiently for the purpose at hand.
#2 - differences in position coordinates are independent of time.
#3 - the time of an event is that reading upon the clock situated at that event.
#4 - all clocks in the frame are suitably synchronised.
#5 - all clocks remain in synchrony.
#6 - at any given constant time, space is Euclidean.
Notes :
#1 -> implies that we don't need to talk of cognition, intelligence or lack of it. So an observer is not some guy sitting at some point ( call it the origin ) looking around with a pair of binoculars and making notes.
#2 -> implies some rigidity of the distance measure.
#3 -> in practice one can reasonably interpolate b/w clocks and places, provided the measures obtained are 'transitive' ie. consistent amongst different paths to the same single event.
#4 -> the trick to synchonising clocks is to claim one clock as the 'master' eg. the one at the distance origin, and divide round trip light travel time by a factor of two to set the other clock readings.
#5 -> it turns out this will imply that an inertial frame is not accelerated, otherwise the clocks within a given frame would run at different rates and vice versa ( if the clocks don't keep time then you must be accelerating ).
#6 -> Pythagorus' Theorem holds so the metric or distance measure is the one you are familiar with, but only if you make a spacetime slice with a given time coordinate ( once the frame has been properly setup ).
generally -> it is a matter of experiment to determine if such frames exist. They do ... :-)
Please don't panic about these statements. I mention them not to seem a clever dick but to emphasise what is often not made plain : you have to have a working definition of what is meant by simultaneous events occurring at different places. Because if you don't have that then you can't track cause and effect because time ordering is crucial ie. cause comes prior to effect. That is a supreme principle in all force discussions, fields or particles or whatever ....
... specifically when we say 'light has a fixed speed ( in a vacuum ) for all inertial observers' then that means a finite speed within any particular measurement system. Thus all information transfer within a frame is subject to delay but we 'regularise' that issue by #4 and #5 above. Note that we haven't gotten around to discussing measurement comparisons made by two different frames yet.
That'll do for today.
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
Howdy Mike ! OK .... Got
)
Howdy Mike !
OK .... Got it .... sort of :-)
Bill
RE: Howdy Mike ! OK ....
)
Oh well done ! :-)
The main take-home message is that all information from separated positions must be time delayed at the rate of ~ one nanosecond per foot of travel. That's the speed of light. Fast for sure but not infinite. There is much more that flows from the constancy of the speed of light etc, but this is the prime concern : All news is old news ! :-)
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
Now if one looks at
)
Now if one looks at conditions #1 thru #6 of the inertial frame definition, one can isolate #3, #4 and #5 as the ones that depart from the action at a distance idea ie. they talk of time delays. Condition #6 is still true for Newton AAAD as space is Euclidean for all time and thus quite irrespective of any particular time. In what follows I am not going to retrace/derive Special Relativity results or deductions rigorously as such, but rather I present a heuristic argument by analogy to convince you hopefully of the merit of thinking of time delays and the special importance of velocities in that discussion.
Velocity you will recall is some distance traveled divided by the time taken to do that, but with a vector quality so that the direction of travel is important too.
Gun-laying
Let's pretend that we are the crew of a gun emplacement on a shoreline. Our job is to accurately hit some naval target passing by within our range. To be polite suppose it is peacetime and we practice alot using some drone vehicle which is maneuvered on some suitable course on the water surface. For our training. Also just consider the horizontal distances and not be perturbed by all that up and down stuff. Of course gravity matters but we will ignore that. We will concern ourselves with geometry in the plane and arbitrarily but conveniently place ourselves at the coordinate system origin. We are not going to use a fully fledged inertial frame. Just think of your everyday classic Newton :
... looking down from above. Cases :
(A) Static drone. Just plonk the craft in some fixed position with respect to the gun and get into it. If we're any good then the path of the winning shell looks something like this :
... where here I've indicated the speed of the artillery round to be c. Just a random choice of variable name right ? :-)
Consider thus that shell speed c. What is the value ? In the real world, and due to air resistance especially, it wouldn't be constant.
By now you know I'm drawing an analogy to light. At Newton's time there was the concept that something did go from place to place to illuminate things. That something went into our eyes and that's why we saw things at all.
The issue of light speed did arise. Some French guy* tried to time the interval b/w masking and unmasking of lamps on separated hillsides, but that was dominated by human reaction times though. Ole Roemer found a cyclical variation in the timings of the eclipsing of Jupiter's moons and attributed that to a finite speed of light across the varying distances from there to here. His estimate was pretty good actually. So for a long while and for most purposes light was assumed to travel very, very fast. Effectively at infinite speed.
Question for next time : if the speed of the shell is constant and finite then how ought my gun-laying change when the target drone is moving ?
Cheers, Mike.
* Sorry, Galileo thought of it, tried it but to no avail. Fizeau and Foucault separately demonstrated using similar apparatus - stroboscopic or light beam chopping - the correct value to within ~ 0.5%
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
NOW you're talkin closer to
)
NOW you're talkin closer to home !
I was an Artillery Forward Observer in the Army : )
AAAAH Wait a Minute ! .... That ain't what happens ???
I guess I belong back in Newtonian Times (
Bill
Way to go Bill ! So that
)
Way to go Bill ! So that means you're actually deaf then ? What ? :-)
To put you on the spot then : with suitable artillery how would you ( in generality ) deal with target movement for a given fixed rate of shell movement ?
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: Way to go Bill ! So
)
Allright then ) ...
I would attempt to calculate (or Guess ) a convergence point
between the moving target and the artillery taking into account ...
A. The speed and direction (of movement) of the target ...
B. The TOF (Time of Flight) of the Howitzer shells.
There may be some other things to consider but,
I'll leave it at that for now )
Bill
PS: To be sure of hitting the
)
PS: To be sure of hitting the target, shoot first and call whatever you hit the target : )
Bill
RE: The periodic table is
)
I finally got back from my vacation. Thanks Mike for all of this work. I am still here to listen.
With your comment above 'So this is the realm of 'a quantum theory of gravity':
Would the quantum people then believe that we won't find a gravitation wave?
Also,
If they say that fermions can't be stacked, how can they explain neutron stars?
Why don't the neutrons in neutron stars decay into protons like you said in one of your prior comments (in about a half an hour)?
merle
What is freedom of expression? Without the freedom to offend, it ceases to exist.
— Salman Rushdie