1

Just Chat! / Theories to start a new world.

« on: 30/11/2024 15:26:16 »

Hi.

    So, in Britain a few years ago there was a radio show where someone chooses the three music discs that they would take with them to play if they became stranded on a desert island, that was called "Desert Island Discs".

     Let's do a science version of that.   Moreover, why doesn't the TNS radio show do a version of this? 

     Due to some problem, civilisation is leaving earth and will try to colonise some other planet and start a new world.   You can take the material that describes three theories in science.   Which three theories would you choose to take?


    Thinking time allowed:   I don't mind but 5 minutes is adequate, it's fun not something that is happening.   Yes, you will be critically judged based on your answers but it's better than doing some personality quiz.   I may give out the prestigious award of a "thankyou" mark for the first few answers and possibly the more prestigious award of a "best answer".   Then again, I may not but instead just thoroughly deride the response you make.   Life must have some risk.

Best Wishes.   

2

Just Chat! / The fair use of LLM and AI in education.

« on: 14/04/2024 02:45:59 »

Hi.

      Did you know that a lot of Universities run quite a lot of submitted material, like essays, through a computer to check for plagiarism?   You probably did know that.   
      Did you know they now also include a quick assessment of the probability that this content was substantially created by some LLM  (Large language Model - like Gemini, ChatGPT etc.)?   You may have known that but LLM's are quite new so they've only recently started it.
     If you submit an essay with a high chance of having been generated by a LLM then it can be rejected or the person could be called in for a viva examination.
     However, it seems to be bit one sided.   There's one student I know who felt strongly that the feedback and comments on their essays were very generic and not especially useful.  They ran the feedback through a LLM checker and - well, you guessed it.   Perhaps they should reject the feedback and insist the marker comes in for a face-to-face meeting where the essay is properly discussed for 10 minutes?

    On the other hand, perhaps it's not all bad.   Eduaction may end up becoming a game or a test to see who can game the system better - but we will have grauates who can play the game very, very well.  Students will be working not just to prevent triggering an LLM detection but to also get future iterations of their LLM assisted essays adjusted in line with output generated by the markers LLM system.  This will help the markers AI system pick up key elements and hopefully grade it more highly.   We'll have future graduates who are highly skilled with this new LLM technology.
    That will be important because LLM and AI will only continue to develop, so our new graduates will need to be good with this technology.  There's got to be a bright side to everything.

Best Wishes.

3

Physics, Astronomy & Cosmology / How many spots are produced from Stern-Gerlach apparatus that rotates?

« on: 15/03/2024 15:01:23 »

Hi.

      Hopefully, some of you have heard of Stern-Gerlach apparatus.



Image taken from:  https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment    where some more information is also avaialble.

     Basically, we could send some electrons through a piece of Stern-Gerlach apparatus aligned in the z-axis direction and they would have their path deflected up or down dependng on whether they have a z-component of spin +1/2   or  -1/2.   We only end up with two spots or locations on the screen rather than a smeared out line - suggesting that this spin is quantised.  I expect you've seen or heard the usual explanations.
    Similarly we could turn the appratus sideways, so that the magnetic field is aligned in the y-axis.   Then we have two spots separated left and right instead of up and down.
     More interestingly we can send the electrons through a z-axis aligned apparatus and then send them through a y-axis aligned apparatus.   What we find is that electrons with the z-component of spin +1/2   will still have an equal chance of having the y-component of their spin reported as being + or - 1/2 when it is measured.   Overall, we end up with  four spots or locations for the electrons at the end with an equal intensity on the screen:   1/4  went up and left,    1/4 went up and right,  1/4 down and left,  1/4 down and right.

    If you were able to trace the path of an electron throughout the whole experiment then you expect to observe electrons that were near the North magnetic pole of the first apparatus to be deflected left or right with equal probaility in the second apparatus.   Similarly, those near the South pole of the first apparatus were deflected left or right with equal probability in the second appratus.     At the end of the experiment then,  the electrons near the North pole of the last appartus were not necessarily near the North pole of the first appartus, they could have come from the South pole in the first apparatus.    I hope this makes sense, even if you need to read it twice.    The electrons can move in the two directions independantly in both pieces of apparatus.   Those which are on the Left in the final apparatus could have had a total movement that was  Up then Left   or   Down then Left.

    Now, what happens if you do the experiment slightly differently?   Instead of having two pieces of apparatus, with one just in front of the other,   we will use just one very long Stern-Gerlach apparatus and slowly rotate the apparatus while the electrons are travelling through it.    Initially the apparatus would be aligned in z-axis direction when the electrons enter it,  it would then be rotated so that the magnetic field was aligned in the y-axis direction by the time the electrons exit from it. 
     You would expect the electrons to get deflected according to their spin as usual.   What path will the electrons actually take now?   If an electron had started to move toward the North pole of the appartus when it entered the apparatus, that means it had z-component of spin +1/2.  In principle it can still have a y-component of spin that is + or -1/2 as shown in the original experiment, which could suggest it will move away from the North pole and toward the South pole of the apparatus when the apparatus is rotated and now measuring the y-component of spin.
   On the other hand, perhaps it ALWAYS stays near the North pole of the apparatus even during the rotation.   Will we only get two spots on the screen when the electrons exit the apparatus?     If it's still just the usual four spots on the screen, then you've got to ask yourself some questions:   Will some electrons that were at the North pole initially or early on, move to the south pole later in the experiment,  while an equal number that were at the South pole move to the North pole?  (i.e. so you may have equal total numbers at the North and South poles of the apparatus but some electrons have switched sides during the experiment?)
    I honestly don't know what we will get and would like some opinions.   I suspect we are only going to get two spots on the screen at the end and the situation will be similar to sending polarised light through polarising filters.   (Birefly recall experiments where polarised light is sent into a polarising filter.   If you use one polarising filter at 90 degrees to the incoming light, then you get nothing through.   If you use two polarising filters, the first at 45 degrees orientation to the incoming light, the second at 45 degrees to the first (so now a total of 90 degrees to the original light) then you do get some light through at the end.   The more filters you add and the more gradually you ask the photons questions about the orientation of their polaristaion, then the more light will be passed through at the end).

Best Wishes.

4

Just Chat! / Are the first year lectures the best?

« on: 13/03/2024 01:40:41 »

Hi.

     Recall the first year at University, college or whatever it was called that you may have gone to?    The lectures seemed great.

   In the later year(s), the lectures did not seem as good.   Why?

Is it these things:
   (i)   Many of the well established staff have become involved in the first year lectures.   They were often presented by lecturers that had been running the course for years and had a lot of good material, maybe practical demos, video clips etc. ready and good to go.
       By comparison, in the later years, the course may only run every other year instead of every year and the lecturers assigned may not be the most experienced staff.  While they were certainly competent and sufficiently experienced in the area, they just would have had some teaching time left to allocate while other staff may not.   As mentioned, many of the professors were already allocated to the compulsory courses with the really big numbers of students and, I suspect, did genuinely enjoy introducing the topic(s) to the new students and running those courses.

    (ii)   The beginning of everything just always will seem more interesting.  There are so many directions to go off in and you will see many snippets of more specialised things that are genuinely interesting and seem attractive.
     By comparison, when you're actually doing the specialised courses, you find that although there are some genuinely interesting and elegant bits, a lot of it isn't so elegant.    The whole area may still be quite near the frontier of knowledge and the technqiues will be much more practical, based on numerical approximations, computer simulations or basically "clumsy", messy and inelegant.   It will take some years before some of it is refined into something more elegant and the bits that may have been going in the wrong direction are discarded.   By which time, of course, this version will have found its way into the courses in the earlier years - so the stuff in the specialised courses will always tend to be the less refined and raw stuff. 

    ----  Anyway, I don't know... maybe it's something else.    I'm now watching a few lectures online and I've noticed the same trend again:   The later years lectures are just not as good or as well polished.   Is this just how it is all the time and everywhere?

Best Wishes.

5

Physics, Astronomy & Cosmology / What is included in a configuration space?

« on: 01/03/2024 17:00:25 »

Hi.

     Consider a Newtonian system of some particles moving in space.  Let's use conventional Cartesian co-ordinates to describe locations of the particles and there will also be some velocity for each particle,  both of these  things (position and velocity) are functions of time.

Is "the configuration space" for the system just the set of possible co-ordinates for the system     OR
the set of positions AND velocities (or momenta if you'd rather use that)?

Let's say we have 1 particle in the system.   Is "configuration space"  R³   =  just the possible positions
  OR   is the configuration space  R⁶  =  possible positions and possible velocities.

Wikipedia seems to be suggesting it is just the space of possible co-ordinates:
In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the space defined by these coordinates is called the configuration space of the physical system.
....   ...  Example: a particle in 3D space
The position of a single particle moving in ordinary Euclidean 3-space is defined by the vector q = ( x , y , z ) , and therefore its configuration space is Q = R³

See https://en.wikipedia.org/wiki/Configuration_space_(physics)   for more info.

I was fairly sure that "configuration space" included both positions and velocities of the particles - but maybe I have just mis-remembered this.

---- End of the main question  --- a more advanced or developed question follows -----

   Now, let's take a more specific case:   Suppose that the state of a system cannot be described adequately just by knowing the positions of the particles.   For example, suppose there is some force acting on a particle that isn't just a function of the positions of particles but it is also dependant on the velocities of the particles.   [ A fully concrete example:  There is a magnetic field in our system in addition to some electrostatic forces and the particles in our system are charged - so the force acting on a particle depends on both its velocity through a magnetic field and also on its position in an electric field ].    Do we now declare that since we must know both positions and velocities of the particles to ascertain the state of the system, the configuration space is now R⁶ⁿ   (with n = number of particles) instead of  R³ⁿ ,  i.e.  that velocities do have to be considered ?
    I don't know..... maybe we still don't include the velocities as part of the generalised co-ordinates we would require because, for example, provided we have the position of each particle at each moment of time, then we can derive the velocity anyway just from this.    Although if that's what we would assume, then "the configuration space" is a bit more than just a description of all possible generalised co-ordinates - it is no longer enough to know a particle was at  (1, 1, 1) and also  (2, 2, 2) we must know what times it was actually at these places if we are to derive the velocity.

    Just to be clear I need to know what the official definition of "configuration space" is supposed to be.   Is it always just the set of possible generalised co-ordinates and never something that includes the set of generalised momenta (or velocities)?   Are "the generalised co-ordinates" something which we assess on a sliding scale - it must be possible to describe the state of the system using only the generalised co-ordinates,  so that if we HAD to know something about velocity then velocity would have to be included as a generalised co-ordinate?

     The Wikipedia definition of "generalised co-ordinate" is less than usefull (to me):

In analytical mechanics, generalized coordinates are a set of parameters used to represent the state of a system in a configuration space. These parameters must uniquely define the configuration of the system relative to a reference state.
   [  From:   https://en.wikipedia.org/wiki/Generalized_coordinates ]

The first sentence makes for a circular or useless definition,  we must already know what our configuration space is in order to know what our generalised co-ordinates should be.    The second sentence, however, does seem to suggest that our generalised co-ordinates must be sufficient to uniquely define the state of our system.

Best Wishes.

6

Just Chat! / What is the difference between Beer, Lager and Ale?

« on: 26/02/2024 20:48:52 »

Hi.

    What is the difference between Beer, Lager and Ale?
Seems to have a different colour with Lager being a bit more see-through,  Ale is just Beer they drunk in the old days - but overall they're all just the same thing aren't they?   Although for some reason people seem to get upset when you bring them the wrong one.

    Perhaps there's some chemical or biological difference?   One made with yeast, the other made with some other microbial organism - maybe natural yoghurt?

     I did try a quick Google search but it was incredibly dull.   Websites spend for ever talking how something like using an Oak barrel will matter.  As far as I can see, they are all basically the same thing with such minor differences it really shouldn't matter a lot.

Best Wishes.

7

Technology / What are the assumptions of the hydrogenic model in semiconductors?

« on: 24/02/2024 01:19:03 »

Hi.

    I have a question and the Tech section hardly gets used, so I thought I might use it.   It's a question about semiconductors and that's vaguely "technology" stuff.   It may also require some background, which can be boring for others to read, so we'll break it into pieces and stop.   I'll have a check to see if anyone is following the topic so far, if they aren't, I'd be better off asking elsewhere and you would be better off not having to read more background.

Background, part I:

   We have some Gallium Arsenide.   That's an intrinsic semiconductor with this sort of crystal structure (often described as Zinc blende):



During formation you can dope the semiconductor with Silicon.    The overall crystal structure is essentially the same but some Si atoms will replace some of the Ga atoms,  that's a group III to group IV element switch,  so you have a spare electron whenever this happens.    This gives us a donor energy level in the semiconductor and we have an n-type doped semiconductor.    That's the background (part I) complete.   I'm going to guess I still have half the original audience, so I'll continue to part II.    That's almost chemistry and I suppose the post could have gone in the chemistry section - but it had to go somewhere and the tone or topic is going to shift to something more physics based very soon.

Background, part II:

    Now we have an electron we're interested in.   It's one of those "spare" or almost spare electrons from where a Si atom has replaced a Ga atom in the crystal lattice.    We're mainly interested in how it might be bound, where it is located and how available it may be to become de-localised and go off elsewehere in the crystal lattice and contribute to the electrons we would have in the conduction band.   In other words, the standard stuff that would make the doping useful for the usual purpose of creating an extrinsic n-type semiconductor.
     There is a standard model that is used to describe or estimate these things,  it's usual called the Hydrogenic model for donor impurities in a semiconductor  or just "the Hydrogenic model".
    Here's a short description summarised by (someone) of Glasgow university:
http://web.eng.gla.ac.uk/groups/sim_centre/courses/hydrogenic/hydro_1.html
    It's good because it's short and doesn't make much apology for anything that was done.  It hardly attempts to justify what was done or make many claims about the basic or fundamental physical assumptions that may have been made when proposing this model.   (It also has some minor typing or display errors - but you can't have everything).
    I'll provide a short summary of the procedure below:
(i)   We have a model for the Hydrogen atom already.
(ii)   So we have a formula for the ionisation energy of H atoms and the Bohr radius of H atoms.   Those formulae involve ε₀,  the permittivity of free space,   and also m_e , the ordinary or sometimes called "bare" mass of an electron when semiconductors are discussed.
(iii)  Just take those formulae and replace  ε₀    with  ε for the semiconductor environment   and replace  m_e   with  m_e*,  the effective mass of an electron in the semiconductor.
(iv)  That's it,  you've got your estimates.

    That's pretty much the end of part II of the background.   I'm going to stop soon and check if anyone is still following.
It's probably vital that I actually present the main question I have, so let's do that.   It still may not make perfect sense without some more background BUT it's a forum and it's all about getting some discussion and not just presenting some (possibly) factual information.

The question:
      What are the fundamental assumptions that were made or are required when proposing the Hydrogenic model?

I do already have some thoughts of my own but that will wait for a later post.  For now, I just need to check if anyone is still following or may be willing to discuss the hydrogenic model.

Best Wishes.

8

Just Chat! / Fault on the NS server 17/2/24

« on: 17/02/2024 19:51:32 »

Hi.

    Just a minor note that although the forum is working when you go directly to   https://www.thenakedscientists.com/forum  ,    your main homepage     www.nakedscientists.com    is not.

   Since the home page is where Google will take you if just type  Nakedscientists  into the navigation bar,  this means people will assume that nothing is working.    (When I say people,   I mean that's what I had assumed - but it's less embarassing if I say "people" rather than admitting it may just have been me).

Fault existed:   17/02/2024   approx.  11 am ~  now (7:70 pm)    British time.
late editing:  7:70 doesn't look quite right but maybe that's how we fit some extra time into each day.  I guess it was 7pm and some tens of minutes.

Best Wishes.

9

Just Chat! / Is there a change afoot?

« on: 02/02/2024 01:56:40 »

Hi.

Is something changing?
    When I logged on I was asked to make a cookie selection.
    Any chance whoever is adjusting the website will also switch  LaTeX support back on for use in the forum posts?

Test run:    This is supposed to be the sum of n terms in a geometric progression:

 and this is the formula for free beer:


   That's just a load of numbers for some gif image that never gets created isn't it?   Probably no great loss.

Best Wishes.

10

New Theories / New theories

« on: 19/01/2024 02:22:37 »

Hi.

    I've decided that a TOE  (Theory of Everything) is overrated.   What we need is a system that is realistic ; easily implemented and  will make the world a better place.

This is what I propose:

(i)    We have a collection of theories.
(ii)    Different theories will cover different bits and pieces of stuff that arise here and there.
(iii)   Theories are judged on their usefulness and ability to make predictions, especially if these can be tested.
(iv)   Some elegant thories will also be kept beause we're human and it's inevitable we will do this.
(v)   Chips or "fries" cannot be served with the potato skin left on, it's not better.

- - - - - - - - - - - - -

Best Wishes.

11

Just Chat! / Short puzzle, just for fun.

« on: 17/01/2024 18:57:59 »

Hi.

   Who doesn't love a short puzzle?    [Approximate time:  4 minutes,  Calculators and Google allowed].

    Suppose you have a rope that was long enough, while on the ground, to go around the circumference of the earth but there was only a few metres to spare.
   Now lift the rope 1 metre above the ground everywhere.  How much extra rope would you need to go around the earth?

[You can ignore hills and velleys and assume the earth is a sphere.   You can look up whatever else you may want.]



Best Wishes.

12

Geek Speak / What IT person did this nonsense and what can I do about it?

« on: 09/01/2024 19:27:46 »

Hi.

I've got an email account operated by Microsoft and I tend to use Outlook to view and manage my emails.
I couldn't send/receive anything because my email folder was full.   I've been a bit lazy in making deletions.
Anyway... the solution (you would have thought) was to delete some old emails.
I did that.
Still couldn't receive any mail,  apparently there still isn't any space.
Ah...ha....  I found the deleted emails in the "deleted items" folder.... so they were still there and still taking up space.  They wouldn't be deleted for 30 days.
So I selected all the mail in the deleted items folder and chose to have it deleted immediately.
That should work you would think.
It didn't.... there still isn't any space.
I did some research and it seems this is the system that Mcrosoft employ:


email folders.jpg (122.29 kB . 905x887 - viewed 674 times)

There are 3 different folders for deleted emails.   The first is called the "deleted items" folder and this makes sense and email in here is easily recovered.
   The second is called the "deletions" folder,  it's a folder where stuff is... idk....  more gone than it was but still not gone in any way.... and could be recovered.
    The third is called the "purges" folder,  and it's where the system is declaring "I'm serious, this time, this stuff will be gone" and you have your very last chance to go in and recover that email.
    After the purges folder the stuff is actually deleted.
    There is a delay of at least 14 days between movement to each new folder.

I can delete an email and then empty the deleted items folder.... so I can push stuff as far as the  "reasonably gone folder" but no further.   Only the system will push it into the  "seriously gone folder" when it's good and ready (that'll be14 days later) and it will only delete it from here another 14 days after that.   

So, unless there is something I can do to speed up the movement to the "actually gone state",   then I can't receive any email for about 1 month.

Any help or advice would be appreciated.    Otherwise, I'll just have a moan and ask who invented this system of  the many stages of deleted-ness for emails?

Best Wishes.

[Spoiler:]

13

Just Chat! / Merry Christmas (with trivia and a joke).

« on: 25/12/2023 02:22:27 »

It's just gone midnight where I am.   So I would like to wish everyone a merry Christmas.   

Minor Note:  I don't wish to cause offence to anyone of any religon.   If you don't recognise Christmas as any special occassion, that's fine.  I would just wish you a good day.

Piece of trivia:   Friedmann is famous for his work in Cosmology.   The name Friedmann can be written in many ways.   It is not a spelling mistake to write it as  Friedman (with one n)  or as Fridman (no e) and you can find all of these variations used in the literature.
     The scientist was Russian and the name should be written in the Cyrillic alphabet (and if this forum supports it then the only correct way to spell the name is as follows:    Фри́дман   ).   A direct transcription to the Latin alphabet is then problematic.  The other scientists working in this area at the time were German and they found that the sound comes over more accurately when it is written as Friedmann and so that spelling became prevalent.

Joke:   Why is Eibniz an acceptable spelling of the mathematician who inventend calculus?

 ..... (this one takes a moment to think about - but when you see it it will sleigh you)...... 

Spoiler: show

.....   It has  'No L'  in it.   

Best Wishes.

14

Physics, Astronomy & Cosmology / What is a Fermion?

« on: 18/12/2023 01:40:59 »

Hi.

What is the current definition (or defining property) of a Fermion?   

    I thought Fermions could be defined as particles with half integer spins.   I mean it turns out they also follow Fermi-Dirac statistics rather than Bose-Einstein but you did not have to define them as particles which follow the Fermi-Dirac statistics       OR     by some definition such as particles where no two Fermions could not have identical quantum numbers.
    Just to be clear I though the following were all equivalent:

     Particle has half integer spin   <=>   particle is a Fermion  <=>  no two of these particles can have the same Quantum numbers.

      However, there seems to be some shift toward defining a Fermion purely as a particle which follows Fermi - Dirac statistics  and/or the Pauli exclusion principle and a removal of the half-integer spin characteristic.     Take this definition from Wikipedia:

    In particle physics, a fermion is a particle that follows Fermi?Dirac statistics. Generally, it has a half-odd-integer spin: spin 1/2, spin 3/2, etc.      [ From  https://en.wikipedia.org/wiki/Fermion ]

   What is the word  "Generally" doing in there?   Is there a Fermion with integer spin   and   similarly do we now know of a Boson with half-integer spin?

Best Wishes.

[Spoiler:]

15

Physics, Astronomy & Cosmology / QM puzzle: Is a measurement being made in the 2 slit experiement all the time?

« on: 29/11/2023 23:10:39 »

Hi.

    I have another "problem", "concern" or "puzzlement" of a scientific nature today and I'm asking for some other opinions and/or discussion   (you know... what a forum is meant for).   Don't spend too long here,  I know I'll be busy for a few days and may not make much reply for a while.

Background:
    This is Quantum mechanics.   It concerns "the double slit experiment" which I'll assume you are familiar with.   Basically, if you fire a single particle (say an electron) at a double slit then and have a detector screen at the far side (say a screen which is phosphorescent, something that will glow when an electron hits it),   then you do observe single glow spots on the screen.  The electron seems to behave like a particle at the time it hits the screen.     HOWEVER   when you repeat the procedure you will start building up the usual pattern where the number and location of hits on the screen does correspond to the usual wave diffraction pattern through a double slit.    The general conclusion being that the electron was behaving as a wave or QM object until it hit the screen -  it had a wave function and that was propagating through the space before it hit the screen.

    Now we're not here to discuss whether the electron did move as a wave or not.   Let's just assume that the usual QM stuff does apply and I'll choose the Copenhagen interpretation of QM for this problem.   So the electron always has a wave function, it evolves according to the time dependant Schrodinger Equation UNTIL a measurement is made.   On measurement the wave function is immiediately updated (collapses), so that it is now definitely in an eigenstate for that measurement.

    The question is:   Isn't the phosporescent screen always making a measurement?   If the screen does not have a glowing spot at time t,  then the electron is not at the screen at time t.   We should update the wave function,  it cannot be in any state where there was even a small probability to find the electron at the screen.    Conversely, if the screen does glow at time t, then the electron is there,  the wave function has collapsed in a much more dramatic way (to something like a dirac delta function of position δ(x-x₀) in position representation, furthermore we can now remove the electron (from the computer model I'm building - which I may talk about later).   It has been absorbed by the screen and will not propagate any further.

     The situation is very similar to "Quantum Zeno effect" which you can Google if you want some more background.   Specifically isn't it possible that by constantly making a measurment, the phosphorescent screen ensures that the electron's wave function cannot collapse to the state where it would be at the screen?   An easier to read background is obtained by Googling  "Zenos Arrow" but you MUST take a quantum mechanical discussion of that and not the original Greek philosophy by Zeno, there are YT videos on this if you don't even want to read.   Here's just one:
   

Why am I asking?
   Too long... I'll put this under a spoiler... it's not essential.

Spoiler: show

    I've been dabbling with a bit of computer coding lately.   Just to be clear - I'm not doing anything that will be new to the world but it's just new to me and has my interest.   I've made fair progress on a simulation of a wave function propagating through space in 1 dimension and encountering various potential barriers.   I'm ready to move it to 2 (or 3) dimensions.   What I'm using as a test case is the double slit experiment because we already have a good idea of the results that you should get.   I'll have the barrier represented as a region in 2-D space (let's say a thin rectangular region running parallel to the y-axis) of very high potential with "slits" that are 0 potential regions through that barrier.    I'll be modelling the electron as a Gaussian wave packet, the details don't really need to concern anyone but a Google search will furnish you with the details if you're interested.   It's enough to know that the wave function is known initially (at t=0) and we can give it a momentum to represent the electron being fired toward the barrier.   That wave function will evolve according to the time dependant Schrodinger equation, which we can do numerically on the computer.   
     Then we place a "screen" or detector at the far side of the barrier.   We are interested in what that screen will collect.   We would think (OK, I would but it's more natural to keep using the third person)) that the probability of the screen having a spot glow (i.e. having absorbed the electron) at  a given position and time,   (x,y,t),   will be proportional to the probaility density of wave packet at (x,y,t).   We can make this more precise,  the probability of a position on the screen between (x axis values)  x and x+dx  and  between (y axis values) y and y+dy  detecting the electron (starting to glow) in the time interval between  t and  t+dt is     
         ~    |ψ(x,y,t)|² .dt.dx.dy

     So with just a bit of integration we can find the probability of a given position on the screen glowing after, say 1 minute from when the electron was fired.   We can start to build up the expected pattern of hits on the screen directly from this.
     It seemed and still does seem natural to assume that once the screen has glowed, the electron has been located on the screen and absorbed.  It can be removed from the simulation (and we're ready to fire the next electron).    It was only after a bit more thought that I realised what we're really doing here is recognising the wave function collapse and thus updating our information immediately.   This is when it dawned on me that we have information ALL the time, if the screen hasn't glowed yet then the electron is NOT there, why don't we immediately update the wave function to show that instead of just continuing with evolution by the Schrodinger Eqn?

Best Wishes.

16

Physics, Astronomy & Cosmology / Temperature and k.e. : Does a substance cool down if particles break apart?

« on: 11/11/2023 05:29:17 »

Hi.

    Just had a minor thought about temperature which seemed a bit odd, so I would like to have it checked by others.

Background:   
   Temperature, T, is a measure of the average kinetic energy  < 1/2 mv² >   of some particles in a substance.
For an ideal gas we can assume the usual relationship:
      The average kinetic energy of one particle =  (3/2) K.T        [with K = Boltzman constant,  T = temperature in kelvin]

The problem:
   Now suppose you have an ideal gas in an insulated container so that no energy gets in or out.   So that's a big box full of little particles like peas and they have some temperature T, that is to say the peas are moving around.   The exact kinetic energy of a given pea varies but on average we have the usual relationship:   The average k.e. = 3/2 kT.
    The problem is that you didn't buy high quality peas, you got the "two-for-one" bargain peas.   If you bounce them around then they just break in half.   Now, the new half-sized peas are what you have bouncing around in the box.  Those are the new particles you have, each identical and for simplicity exactly half the size of the original particles BUT there are, of course, twice as many of them.

   Now the question is - does the temperature T change at the moment when the peas (particles) split into two?

This is my reasoning:
   Energy is conserved, the container is insulated.
   Initial total kinetic energy = E and this remains the final total k.e.  of all the particles at the end.
   So  the average k.e. of a particle at the end (when there were 2n particles instead of just n) is   E/2n,    while it was  E/n  initially.
   Now just re-arrange the usual formula     (average k.e. of one particle) = (3/2)kT     using E/n    and  E/2n  for the initial and final averge energy of a particle.

   So ,  initially we have   T_i =  (2/3k) .(E/n)
    At the end we have,   T_f  = (2/3k) . (E/2n)    =     T_i  / 2

The temperature must fall to half it's initial value when the particles split into two.   (Have a think about it, seems a bit odd to me - but it keeps coming up any way that I look at it).

- - - - - - - - - -

Some other things to consider:
      Since each of the final particles is precisely half the mass of the initial particles,  we have that the average speed of a particle does not change.   
[Briefly,     (2n).  (1/2) m_f V_f ²     =    E      =      (n).  (1/2) m_i V_i ²,
substitue  m_f = final particle mass =  (1/2) m_i     to obtain   V²  is unchanged and hence  |V| is unchanged  ]
    So you can imagine that two halves of a pea started off just by holding hands to make one large pea.  In that state the gas had a temperature T_hot.  If the two half-peas just decide to let go of each others hand, then it's not as if they need to abruptly part ways with some significant relative velocity like a Uranium nucleus undergoing fission.   Just drifting along at much the same velocity will change the temperature to T_cold  just because the total number of individual particles has changed.

- - - - - - - - - -
Why it matters:
   Well, I just read a school chemistry book that was talking about releasing energy when N₂ is formed from atomic Nitrogen.   It said an increase in temperature is evident in the reaction   N + N --> N₂. 
   The number of particles present has halved so you'd expect the temperature to double even if no energy was released during bond formation.
   Furthermore, going back to Uranium and run-away nuclear fission reactions, once everything is hot enough to be gaseous or genuinely atomised, the effect of doubling the number of particles on each fission helps to prevent any further rapid increases in temperature.   That's quite nice, although it's already hot enough to be a bit of a problem but you've got to be grateful for small things.

   I'd be grateful if someone could check this reasoning.

Best Wishes. 
     

17

Physics, Astronomy & Cosmology / Which bit of the Shell theorem is not working?

« on: 13/10/2023 16:23:45 »

Hi.

    I'll assume you're familiar with the Shell theorem.    https://en.wikipedia.org/wiki/Shell_theorem

    Now supppose you're considering a simple model of star formation in the early universe.   We'll have a perfectly uniform distribution of Hydrogen gas spread out over space  AND  we'll also assume that space is infinite.   [NOTE:  It is not necessary or guaranteed that the universe is or was infinite,  that doesn't matter, for this hypothetical situation we are having an infinite space].    For a star to form, some hydrogen has to clump together under gravity and form an overdense region of Hydgrogen.

     We can choose to put an origin somewhere and draw a sphere of radius r around that.   Now, consider a particle of Hydrogen on the boundary (surface) of that sphere.   By the shell theorem, we can see that the Hydrogen particle is attracted to the origin by gravity.  We also see that we can ignore the attraction to anything outside that sphere of radius r.   Why?   We can draw hollow shells of radius R > r and the shell theorem tells us that since the Hydrogen particle is inside those spheres, it expereinces no net force due to those larger shells.   All of space is just a collection of hollow spheres of radius R > r    plus the solid sphere of radius r,   so we have considered all of space.     So there is just a net force toward the origin and we can even calculate this if we wish.        F =   GMm / r²       with m = Hydrogen particle mass,     M is the Mass contained in the sphere of radius r, so M = 4/3.ρ.π.r³   for some density ρ which we assume to be uniform across space atleast until some movement of Hydrogen particles to one place does start to happen.

   Now, of course, the puzzling thing is that we chose to put the origin somewhere and we could just as easily have put the origin somewhere else.   Measure the distance from the new origin to the same Hydrogen particle, that is your new value of little r you will use.  We could repeat the argument with the shell theorem (the particle is on the surface of a sphere of radius new r from the new origin etc.)  We obtain the resut that the same Hydrogen particle is no longer being pulled toward the old origin, it is only being pulled toward the new origin location we have now selected.
    Obviously, the Hydrogen particle cannot have a net force in TWO different directions.   It can't be accelerated  ---> that way and also   <---- that way  and also   /  this way,   \ this way  and every other way you can imagine.

    Which thing went wrong?   Which bit of the shell theorem broke down and why?

Best Wishes.

18

Geek Speak / Complaint about Windows 11

« on: 12/10/2023 21:18:17 »

Hi.

    Why are the things you can adjust in "settings" not joined up to the things you can adjust in "control panel"?

   I guess I'm just too old now.   In the good 'ol days, whenever you wanted to adjust anything you could always get to it through control panel.   These days, you can't.    I wanted to switch my camera on.   I can do that by going through "settings" (which could be accessed straight from the windows icon on the strip at the bottom) but if you went through control panel then it seems there are no links or routes you could take to get to that setting.

   Why do they have to keep changing everything?  I liked the old days of Windows XP where you turned the computer off by clicking on "Start" instead of anything called "End".   Those days made sense.

Best Wishes.

19

Physics, Astronomy & Cosmology / What happens to the surplus electrons after an alpha decay?

« on: 07/10/2023 22:20:57 »

Hi.

   So assume you have an atom that decays by alpha emission.    Example:

²⁴¹ Am ₉₅  ----->     ²³⁷ Np ₉₃  +   ⁴ He ₂
Americium decays to Neptunium.   It's tricky to get mass and proton numbers both lined up properly on the LHS so I hope you'll forgive me putting them left and right.

The Americium started off as a neutral atom, so it had  95 electrons.    On completion the Neptunium only wants 93 electrons.    The decay is an essentially nuclear process, the electrons were never really involved or changed.   So what happens to the surplus electrons?  Do they just drift off somewhere?

Best Wishes.

20

Physics, Astronomy & Cosmology / Why do kettles make a whoooarr sound?

« on: 06/07/2023 03:25:31 »

Hi.

   So I went to start making a cup of tea but I couldn't remember if I had switched the kettle on.   I went back out to the kitchen and soon knew because I could hear the kettle making a gentle "whooo / roar" sound.   It's mid-range rather than being high pitched but some people do say the kettle is "fizzing"  (There are little bubbles of gas rising and I think people mistakenly describe what they can see instead of what they can hear).
    Why does it make that sound?   (I mean long before the water has reached the boil).

Best Wishes.