1

New Theories / Re: Where does quantization of energy of electromagnetic radiation come from?

« on: 05/06/2023 17:01:50 »

Hi.

Can it describe interaction between two permanent magnets?
How about a magnet and a small ferromagnetic material?

   In general Maxwell's equations are used for Magnetostatics.  As @paul cotter  stated,  some are more relevant than others and the Biot-Savart law is useful.    You can get the Biot-Svart law out of Maxwell's equations with minimal assumptions.

    They won't model the force between permanent magnets and ferromagnetic materials on their own.   You need to make a few additions:
   (i)  Assign a magnetic substance a (vector) Magnetisation  M.   This depends on the properties of the material.   LaTex still isn't working so you can't have any formulas, only words.     It is the vector sum of magnetic dipole moments per unit volume of the material.
    (ii)  You also have to understand what a magnetic dipole is.   In general they can always be modelled as being equivalent to a microscopic loop of current.   (We have terminology like "bound current" to describe the equivalent current that would create the dipole that exists in a place.   Sometimes that can be thought of or identified as an actual current, e.g. an electron whizzing around an atom.  Sometimes it can't.  Bound current is not usually an actual current but just a way of modelling a magnetic dipole).
    (iii)   Make assumptions about how magnets and magnetic materials behave.   The microscopic explanation doesn't necessarily need to concern us (but there is one, with varying degrees of sophistication and accuracy).   For the macroscopic behaviour you only need to know how the Magnetisation,  M,  of a magnetisable material will vary with an applied field.    So, for linear materials we have   M  =  χ_m H   with  χ_m = a constant called the magnetic susceptibility.    The H field for a simple linear material is just a linear multiple of the B field,   B = μH  with μ being the permeability of the material (rather than μ₀ as for a vacuum).

   I think that's enough additions.   With that you will be able to determine the forces between magnets and/or simple linear magnetic materials.   Basically all magnets are just a collection of magnetic dipoles and magnetic materials become a collection of dipoles in their Prescence.   So the final determination is entirely based on the fields and forces exerted on and by magnetic dipoles.

    I think there was a previous post or two that discussed non-linear materials.  That's more complicated.

   As outlined by @alancalverd ,  dipoles don't follow an inverse square law for the field strength they produce.   At large enough distances, it's an inverse cube law.   (To be honest I'm surprised Alancalverd uses a 1/r² law as an approximation at any range - but very close it isn't a perfect 1/r³ law,  which we both agree on)
   To further complicate it, in addition to the thing that created the field being a dipole, the thing that is acted on by the field is also a dipole.   So it experiences a force that depends on the gradient of the B field instead of being directly proportional to B (we have F = Bm for a simple monopole of magnetic charge m    but  F = ∇(B.m) for a dipole moment m).   
    So at large distances a dipole experiences a force from another dipole that falls off ~  1/r⁴.  This assumes that both dipoles were permanent and unchanging dipoles.   If only one had been a permanent magnet and the other is merely a magnetisable material, then  (by the relationship M = χ_mH )  the magnetisable material becomes less magnetised the further away it gets from the permanent magnet.  So the force existing between the permanent dipole and the magnetisable material falls off with an even higher power (~ 1/r⁷ ).

I know formulas are not always displaying well.  See  https://en.wikipedia.org/wiki/Force_between_magnets#Magnetic_dipole%E2%80%93dipole_interaction
for some discussion of constructing  the 1/r⁴  formula for the force between two magnetic dipoles. 

Best Wishes.

2

Physics, Astronomy & Cosmology / Re: Talking about Physics

« on: 05/06/2023 15:05:30 »

Hi.

    Your discussion of LRC circuits and analogies is interesting and many textbooks will exhibit that analogy.   Indeed, it is commonly said that as a student of physics all you will do is study the harmonic oscillator in ever increasing levels of complexity and detail.   They are ubiquitous across most of physics.
    So rather than just go along with that I thought it would be worth taking a moment to consider a different viewpoint:   Perhaps it is mainly that human beings go looking for such simple relationships.

   

An electromagnetic force is the analog of a Newtonian mechanical force; there's a symmetry in the equations of motion for an LRC circuit and a simple pendulum.

    There is some analogy between how a LRC circuit behaves and how a pendulum or harmonic oscillator behaves but you've been very human in finding this analogy.   You've ignored the thousands of electrical circuits and situations where Current was not like velocity and/or there wasn't anything like mass or inductance.   Instead you've identified a situation where analogies can be made, assumed that would be important and run with it.    That's ok in that sometimes these analogies and ideas will lead somewhere and turn out to be very useful in very general situations.   However, sometimes they remain just happy co-incidences - an analogy that existed for that one situation only.
    Given enough time human beings will identify ways in which any two things are similar or analogous.   The way my dog eats spaghetti is going to be analogous to the way the moon orbits the earth,  I just need to find some quantities I can calculate or measure which will show a suitable correspondence (and ignore all the things I could measure that don't).   For example, the square of the orbital time period is proportional to the cube of the semi-major axis.   Given enough time and effort we will find something about the spaghetti eating that will have the same correspondence.

This only tells you that Newtonian momentum has an electromagnetic equivalent, which is inductance multiplied by the current.

     Does it?   It's an analogy you can make for an LRC circuit but not necessarily for other electrical circuits or for all things involving electromagnetism.
    For example, an electromagnetic field does contain a perfectly conventional Newtonian momentum, it has to be there and it has nothing to do with a current being observed anywhere.   If you considered current as a quantity analogous to a velocity then this means there can be a non-zero momentum where there is zero velocity  (i.e. the analogy seems to break down).
When you started this thread you ( @varsigma ) were interested in a Feynman lecture, so you might like section 27-6 of the Feynman lecture documented here:  https://www.feynmanlectures.caltech.edu/II_27.html
In that lecture it discusses precisely how much momentum is contained in the E and B fields.   In any region with non-zero E and B fields, there is a  momentum density  g  =  (1/c² ) .  E  x B .   That's all we need - just a non-zero E and B field, no current has to flow from somewhere to anywhere for momentum to exist in the electromagnetic field.   (Minor note:  It's commonly said that the momentum is "in the field" but I would prefer to say only that it is in the space permeated by those fields -  i.e. avoid suggesting that the fields could hold it, just that momentum is in the space somehow when the fields are in that space).

   It is possible to analyse and think about the LRC circuit in terms of how it changes the momentum of the space around the inductor and between the capacitor plates.  As you know, the E and B fields are changing in those components, so the momentum in the space around those components is changing (see the Feynman lecture above).  The pendulum had a mechanical component (a mass or bob) which shows a change in momentum as it swings back and forth, the LRC circuit has space (or the fields within that space) as the equivalent component showing a change in momentum.   This might take a moment to think about, so I'll say it again:   When the E and B fields change, the momentum in the space is changing,  so it is exactly like the electrical components are applying a force onto space - pulling and pushing it.
   Now, as mentioned earlier, we human beings will eventually identify a similarity or analogy between any two phenomena if we spend enough time and ignore all the things that just didn't show the correspondence we wanted.   I wouldn't exclude my own suggestion from that.   I think it's interesting to imagine an LRC circuit as being exactly like a pendulum - it just has space as the component swinging back and forth instead of the pendulum bob - but I wouldn't encourage anyone to run too far with that idea. It works nicely for this situation.

Best Wishes.

3

Physics, Astronomy & Cosmology / Re: Talking about Physics

« on: 05/06/2023 14:11:45 »

Hi.

   I seem to have a bit of time and have tried to read some of the later posts.   I thought I'd start with some questions.

the electromagnetic field is a connection in a fiber bundle over spacetime.

    I'm willing to put my hand up and say that I don't understand that sentence.  I'm no expert and not too worried about looking ignorant - it was ambiguous and confusing to me.
    The main problem is understanding what is meant by a "connection" and the possibility that "a fibre bundle over spacetime" meant the usual one associated with general relativity.   A "connection" would then be understood as an "affine connection".  However, you probably didn't mean that but just used the word "connection" to imply some relationship or link between elements of a fibre bundle that just has 4-D spacetime as a base space.
    Overall, I'm not really sure what that sentence meant.   If the sentence was important then it needs some references or further development.

 The next sentence is equally uninformative for me:

A photon is representative of the field in that it has the same dimensions as the field.

    What dimensions does the field have?   Do you mean length, time, mass  - those sorts of dimensions    OR   the dimension of some linear space (the number of vectors in a basis etc.)     OR    a measurement of just space occupied ( 3 cm x 10 cm x 12 cm )     OR  something else?    i.d.k.

Best Wishes.

4

New Theories / Re: Where does quantization of energy of electromagnetic radiation come from?

« on: 02/06/2023 16:40:59 »

Hi.

No. They apply to any medium if you substitute  ε_m and μ_m for ε₀ and μ₀.

   I would more or less agree with that.   Let's do the "more" bit first:
You can exhibit the propagation of an e-m wave through a simple material with a speed 1/√(μ_mε_m) < c    when you reformulate Maxwells equation by replacing the E and B fields with D and H fields where necessary.    For a simple dielectric material,  the relationship between the electric polarisation, P, of the material and an underlying E field should be linear (so you will have the constitutive relationship  D  =   ε_m  E etc.).   Similarly for a simple magnetic material the magnetic susceptibility of the material should also remain constant so that you have a linear constitutive relationship B = μ_m H between the B and H fields.   
    Overall then,  what you ( @alancalverd ) are saying is that provided you consider "Maxwells equations" to be the version which is often called "Maxwells equations in matter"  rather than "Maxwells equations in a vacuum" then everything works fine and you can exhibit a wave that propagates as required with an appropriate speed for the medium.    I would agree with that - for simple linear materials.

So that brings us to the "less" bit:

To make life easy, we measure and publish dimensionless relative permittivities and permeabilities for various materials (including air and metamaterials) so you can just multiply the vacuum value as appropriate.

    There are some materials for which we just can't - there isn't a simple scalar relating E and D fields  OR  the B and H fields.

    1.  Hard Ferromagnetic material can retain a Magnetisation even when the H field is reduced back to 0 after first being a strong non-zero field in some direction.  So the relationship between  B and H fields inside the material is not the simple linear relationship we would want,  instead it can depend on the history of the fields the material has been exposed to.

    2.  Superconducting materials also have complicated relationships between B and H fields:   For example, in Type-I superconductors we can have Magnetic susceptibility χ_m = -1 throughout some critical range of the H field (giving a relative permeability μ_r =  1 + χ_m = 0 ) but then undergoes a discontinuity and we have  χ_m = 0   (and hence μ_r immediately changing to 1)  outside that range.

    3.   Similarly, not all dielectric materials will be simple linear materials (where the D and E fields would be linearly related).   I've not studied it but I have been informed that sometimes the dielectric polarisation of a material isn't even in the same direction as the applied E field (e.g. in some crystalline structures we require a rank-2 tensor, T, to relate the (vector) E field to the (vector) D field:   D  = T E     )

    I would not vouch for how (or even "if") an e-m wave can propagate through some of these non-linear materials.   For all I know, the propagation of an e-m pulse through some non-linear materials could be extremely unusual:
1.  A pulse of e-m radiation sent into the material could travel through the material along path(s) that may not be straight lines.
2.  It may not always take the same path but instead may depend on the prior history of E and B fields that were applied to that material.   Since the e-m wave is itself changing the E and B fields inside the material when it passes through, the first part of the pulse may exit the material in a different place to where later parts of the pulse exit the material.

Best Wishes.

5

Chemistry / Re: How do "all in one" dishwasher sachets work?

« on: 01/06/2023 14:45:22 »

Hi.

 I don't know but I have built a theory while doing housework.    Some of the all-in-one tablets have 4 fairly separate looking chambers full of fluid, powder and some solid ball of stuff.   The walls of the chambers can be made to dissolve at different rates thus releasing detergent, salt or rinse aid at different times in the cycle.    Even when the walls have dissolved, the ball of solid stuff is only slowly dissolved into the water throughout the whole cycle.
     Experience based on:    Seeing what happens to these tablets if you have accidently picked them up with wet hands and then returned them back to the packet for later use;    Putting the dishwasher on a fast wash cycle that is just too fast and having gloopy stuff and undissolved bits left in the bottom (while other bits do seem to have dissolved) etc.
     Theorised improvements:   Have the walls of the tablet act more like semi-permeable membranes that don't dissolve away at all quickly.  Water should get into the membrane eventually and the internal concentration should then be maintained at ~ saturated with solute.  Meanwhile, outside the tablet the concentration ~ 0,  so you have a fixed concentration gradient over a semi-permeable membrane and thus a fixed rate of diffusion across the membrane throughout the wash cycle.

Best Wishes.

6

New Theories / Re: Where does quantization of energy of electromagnetic radiation come from?

« on: 30/05/2023 16:12:29 »

Hi.

    I've always thought that Quantisation is fairly odd and can only be used with caution.  Although we can use Quantum mechanics to establish that quantisation should be there,  we then quickly establish that we cannot observe a perfect example of it.   Instead what we will typically observe is a frequency that could fall anywhere within some continuous range, with just some statements we can make about the probability distribution or spread of what is typically a continuous random variable.

     An atom with an electron in an excited state, should eventually have that electron fall back to a lower energy orbit but we don't really know exactly when that will happen.  Although the transition from one orbit to another should be quantised, there is an uncertainty relation between the time the atom takes to transition (remains in the excited state before falling back to the lower energy state) and the energy of the photon released.
    See  https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.03%3A_The_Heisenberg_Uncertainty_Principle
   for some discussion  (especially the section around equation 7.3.2 and example 7.3.3).

   As a consequence, all atomic spectral emission / absorption lines have some non-zero width rather than being perfect spikes at precisely one frequency.   There is another theoretical limitation that can be considered:  We also have a position - momentum uncertainty relation.   The atom which emitted the photon along with the detector that captured and identified it can be moving relative to the lab frame and a Doppler-shift in frequency is inevitable.   
    In practice there are also limitations on the accuracy of the equipment and random experimental errors that appear.   Even if you overlook those experimental limitations, the theoretical limitations from uncertainty relations cannot be avoided.   Overall, there should be some precise quantisation BUT you can't observe it in any single measurement.   Theoretically, we can only assert that the expected frequency of a photon emitted by an excited atom should correspond to the difference in the energy between the two states of the atom.   There is nothing we can do to remove all of the randomness and spread of the actual frequency that is really detected from any one atom and one emission.

Best Wishes.

7

New Theories / Re: A Quandary about Accelerated Motion in Special Relativity

« on: 28/05/2023 00:51:22 »

Hi.

If you disagree with any of my above statements, identify the first such statement that you disagree with

This one:   

But that contradicts special relativity

and tell me exactly why you disagree with it.

   Because I think it's wrong.

You seem to have said much the same thing in your last 3 posts and I know I've been trying to say much the same thing, just in some slightly different ways, in a few of my last posts.    I'm not sure it's going to be very productive for me to say the same stuff again  or vice versa.
     
You said, in one of your very earliest posts, that the diagram had been hanging on your wall for the last 20 years.   I was guessing that you had studied Special Relativity at that time.   If that's not correct, that's fine - I know I learn a lot of stuff and certainly wasn't born with much knowledge of anything.   However, it suggests an alternative course of action would be sensible - perhaps we should cover some basic principles of SR  before trying to tackle the tricky example of Bell's spaceship paradox.    On the other hand, you may just have reached an alternative understanding or point of view and remain quite firmly set in that view.   That's also fine, there's no law against it.   I don't think I will easily change your opinion and equally, I don't think you'll change my opinion.   If you bring something new then I may read it  BUT on the short term I've already spent a lot of time here and I am way behind on other tasks.

   What-ever happens I wish you well.

8

Physics, Astronomy & Cosmology / Re: What star will humans witness to go out first: Antares or Betelgeuse?

« on: 27/05/2023 14:57:43 »

Hi.

I don't know.   As you've indicated we only have approximate time estimates where getting the order of magnitude right is about all we're expecting.

We think various stars have gone supernova and been observed already.   See https://en.wikipedia.org/wiki/History_of_supernova_observation   for a discussion of several observed astronomical phenomena that could have been Supernova events from  about 4500 B.C.   through to 1604 AD.   Evidence and records are very unreliable for the earliest dates.    The earliest event that we're reasonably certain was a supernova was observed by Tycho Brahe in 1572.

Best Wishes.

9

New Theories / Re: A Quandary about Accelerated Motion in Special Relativity

« on: 27/05/2023 02:31:36 »

Hi.

I'm just not able to follow you, Eternal.

   That's ok.   It's probably my fault.   Also the entire Bells spaceship paradox is quite tricky.

Each rocket has an attached accelerometer, and those two accelerometers always show exactly the same acceleration. (That is part of the initial specification of the scenario).

    This part is ok.   It's best to assume the accelerometers show a constant acceleration at all times.   Have the acceleration shown on the accelerometer = a(t) = a = a constant, independent of how long the rocket has been in flight.

The INITIAL diagram says that the inertial observers who are stationary wrt the rockets immediately before the rockets fire, say that the separation of the rockets doesn't vary.

   Yes.  That is the space-time diagram you would have for the rockets if they follow the prescribed behaviour (both rockets have the same acceleration a, showing on their accelerometers).   In the frame of reference of those observers (which I will call the lab frame from here onwards),  the worldlines of the two rockets are exactly as you've shown in your first diagram.
   In the lab frame the separation of the two rockets would not vary with time.

But THAT violates special relativity:  special relativity says (via the length contraction equation) that an inertial observer MUST conclude that a yardstick moving away from himself (in the direction of its length) is shorter than his own yardsticks.

    It doesn't violate special relativity.   Yardsticks with some non-zero velocity in the lab frame would show contraction - but there weren't any yardsticks hanging between the two rockets, so it's not an issue.
    Hypothetically you can imagine there were yardsticks between the rockets and indeed, if those yardsticks were to move with the rockets, then as the rockets accelerate, those yardsticks have to take up less space (contract) in the lab frame.   That doesn't change the space between the rockets in the lab frame, that will be whatever is shown on the diagram (it is always measured along a straight line parallel to the x-axis and in our diagram that will be a constant).  However, it does mean that using a frame of reference that moves with the rockets will disagree about the distance that exists between the rockets.   An (instantaneous) rest frame for the rocket (i.e. a frame that moved with the rocket) shows that the space between the two rockets is bigger than that reported in the lab frame.
    I know that was complicated so let's say the same thing again but in a different way:  We have a lab frame, that's where all the rockets were at rest before the engines were started.    Yardsticks that remain at rest in the lab frame, will remain 1 yard long in the lab frame for ever.  So if you already had these yardsticks nailed up and held in the background of space, then as the two rockets race past them you could still see that at every moment of time, there were (say) 100 yard sticks between the rockets.    Meanwhile, yardsticks that aren't at rest in the lab frame do show length contraction in the lab frame.  Since these yardsticks are moving with the rockets you can't just have them nailed up on the background of what you're considering static space in the lab frame.   Instead you need some other system where they do move along with the rockets.   Do that by whatever system you care for, for example have a million other mini-rockets at your disposal, each mini-rocket precisely 1 yard long (proper length, or length measured when that rocket was stationary in the lab frame) and have them race after the two main rockets we are interested in and try to get themselves lined up nicely head-to-toe in-between the those two main rockets.    You would find that you do need more than 100 of those yard-sticks (the moving ones, the 1-yard mini-rockets) to bridge the gap between the two main rockets.  Indeed the faster the two main rockets go, the more that a yardstick or 1-yard mini-rocket undergoes contraction in the lab frame -  so you'd find that more of the mini-rockets need to move in and join the line of mini-rockets bridging the gap between the two main rockets.
      I hope that makes sense.
     There has been no violation of special relativity required so far.    The observers who remained in the lab frame were not "forced" to conclude the distance between the two main rockets was reducing.  Instead all they notice is that while the distance stays the same in their frame of reference (which they can see by looking at the stationary yard sticks nailed up in the background), it can't be staying the same in a frame of reference that moved with the rockets (because more 1-yard mini-rockets had to be used to bridge the gap).

Best Wishes.

10

New Theories / Re: A Quandary about Accelerated Motion in Special Relativity

« on: 26/05/2023 19:31:55 »

Hi.

WHEN you do that, then the original diagram (that hung over my desk for 20 to 30 years) violates special relativity ... because the inertial observers who are stationary with the rockets immediately before the rockets are fired, claim that the separation between rockets is constant.

     It doesn't violate special relativity and it's not impossible for that to be the motion and corresponding worldlines of the rockets.    Are the observers who were "stationary with the rockets immediately before the rockets were fired" going to observe those worldlines for the rockets or not?   That is a choice you have.    Decide how the rockets will move in this frame (which I'll call the lab frame).   You can make this choice - but then it will determine what happens to a piece of string that connected the two rockets.

Special relativity (via the length contraction equation) says that any inertial observer will conclude that yardsticks that are moving (in the direction of their length) wrt himself are shorter than his own yardsticks (by the gamma factor).  I.e., if gamma = 2.0, the yardsticks are only half as long as they would be if they weren't moving relative to the inertial observer.  So the inertial observers who are stationary with the rockets immediately before the rockets are fired MUST (according to special relativity) say that the two rockets get closer together as their speed increases.

   There weren't any rigid connections like yard sticks between the rockets.  If you do put a rigid connection rod between them (e.g. the rope or piece of string in Bell's spaceship paradox) then you do find there is a problem, exactly as you have outlined.
      If the motion of the rockets was as originally described (constant separation in the lab frame), then the string must break.

      Alternatively you can start the problem the other way round.  Stipulate that a string of fixed length was attached between the two rockets and it did not break as the rockets accelerated.   Then the motion of the rockets (in the lab frame) could not have been as previously described,  it would have been different.  The motion of the rockets in the lab frame would be exactly as you have described later in the post - the observers who stay in the lab frame would see the rockets getting closer together as time progresses.   One consequence of this is that, in the lab frame, the rockets did not have the same acceleration at every moment of time.

I hope that makes some sense.   You can choose how the rockets move in the lab frame   OR   if the string will break.   However, you can't choose to have the rockets accelerate equally at every moment of time in the lab frame AND ALSO avoid the string breaking  --->   That's a combination that is not possible.

Best Wishes.

11

New Theories / Re: A Quandary about Accelerated Motion in Special Relativity

« on: 25/05/2023 19:28:57 »

Hi.

Show me where in the above I have changed anything.

 
You said this:

The important thing to understand is that the diagram, as shown, is INCORRECT.  It does NOT show the correct viewpoint of that first set of inertial observers.

    If it doesn't show the situation you wanted to discuss, then don't show it.  Show the diagram that does show the situation you wanted to discuss.
     There is a diagram that corresponds to the situation you wanted to discuss.
A diagram like this one, for example:

Diagram from  https://math.ucr.edu/home/baez/physics/Relativity/SR/BellSpaceships/spaceship_puzzle.html 

If you had shown a diagram like that and had the rockets experience the appropriate accelerations to create that,  then exactly as you have stated:

That correct diagram shows that, according to the given inertial observers, the two rockets get closer together during the acceleration, and therefore the string does NOT break.

We're all in agreement with that.

   You seem to be suggesting that the original situation, with the original diagram you did supply was just outright impossible - it isn't, it is a possible situation but just a different one to the situation you are describing later.
1.    There is a situation (where the rockets experience a certain pattern of acceleration) where the distance between the rockets stays constant in the lab frame AND then the string must break.
2.    There is another situation (a different pattern of acceleration) where the string does not break but then the distance between the rockets would be seen to reduce in the lab frame as time progressed.

    This comment was made in a much earlier post from me:

Notice that they (ucr.edu website on Bell's spaceship paradox) do end the discussion with a diagram showing a very different pair of worldlines the objects could have traced out in the lab frame  (the one you called IRF in your posts),  where the people in the rockets now would find that the distance between the rockets remains constant - but the person in the lab frame no longer does.

    Just to be clear then, both situations are possible.   They require a different pattern of acceleration for the rockets.   The first situation is not made "impossible" just by talking about the second situation.

Best Wishes.

12

Just Chat! / Re: Fast buck hack

« on: 25/05/2023 10:44:32 »

Hi.

If the forum rules don't explicitly forbid promotion of illegal activities please update them.

   They do...

We are all bound by law, and we cannot host material that contravenes the law.

Acceptable Usage Policy.   https://www.thenakedscientists.com/forum/index.php?topic=8535.msg99453#msg99453

   Although this is in the "Just Chat" section so you'd have to assume it was just light-hearted discussion.

Best Wishes.

13

Physics, Astronomy & Cosmology / Re: Talking about Physics

« on: 25/05/2023 10:33:43 »

Hi.

Friendly grumble:  I'd reserve quantity for something that can be associated with a numerical value

    Agreed and it was agreed originally.

Even the word "quantities" is an issue since in the English language one tends to think of something you can count and number.   Overlooking that....

    Since Feynamn said ".... Energy is a numerical quantity...",  it was much more natural just to change one word in that and have   numerical quantities    vs.     non-numerical quantities     rather than changing everything and talking about      numerical data   vs.    non-numerical data.

Best Wishes.

14

New Theories / Re: A Quandary about Accelerated Motion in Special Relativity

« on: 25/05/2023 10:19:41 »

Hi.

If you're loosing an argument, change the subject.

    That seems to be what you ( @MikeFontenot ) have done.     You CAN have a situation where the two rockets get closer together in the lab frame and the string between them does not break.   However, that wasn't the situation you originally described or what was shown in your original diagrams.
     Change the original situation and you will change the final consequences.  I think we're all in agreement with that.  It doesn't make the original situation an impossible situation to have, just one that you didn't really want to be examining.

Best Wishes.

15

New Theories / Re: What makes Riemann's Hypothesis Hard to Prove?

« on: 24/05/2023 11:59:19 »

Hi.

I don't know if you've noticed but some of the old posts are going wrong.
Example:   Examine the section in quotes in post #39:

It’s not likely that a single line will pass through all of them

Presumably you once had an apostrophe but it's changed to an accented letter a,  one Euro currency symbol and finally a Trade Mark symbol.

Sometimes pictures or diagrams just go missing.   If there were any mathematical symbols produced with LaTeX coding, then they've almost certainly gone.   Overall the forum is having a problem  (see other discussions like https://www.thenakedscientists.com/forum/index.php?topic=70438.msg705025#msg705025 about a server migration due to excessive costs).   There's no guarantee of anything in this thread (or any other) being safely stored or maintained in a way capable of being read by someone else in the future.   
    I'm not staff but I just thought you might like to be aware of the problem.

Best Wishes.

16

Physics, Astronomy & Cosmology / Re: Talking about Physics

« on: 20/05/2023 00:08:08 »

Hi.

I've noticed that plenty of people seem to be able to make what they please of what Feynman said in that lecture.

    Yes, that's what people will do when they read a document that is about 3 pages (or listen to lecture of about 1 hour),  they will summarise and/or condense it.   Different words are bound to be used by them.
    If you read that lecture I don't think there is a compact sentence that is held up high as the perfect definition.   There isn't a single sentence that you should try to utilize as a self-contained definition of energy.   He takes an entire lecture to make his point and provide examples.  He is frequently telling you what energy isn't instead of attempting to tell you what it definitely is.   Overall, a scientist should have some appreciation of what energy is and isn't by the end of that lecture.
   Split the lecture into thirds:
1st section:   Smash pre-conceived ideas.  Illustrate that all we know is that energy is some abstract numerical quantity.
2nd section:   Provide some examples.   Illustrate that what we have understood is enough to do a lot.
3rd section:    Explain that it is even more complicated than this lecture suggested and even more things are going on.

   Example phrases from the 3rd section:  There are many other forms of energy, and of course we cannot describe them in any more detail just now.  ;     independence of time has to do with the conservation of energy*   ;  we should note that available energy is another matter?.... The laws which govern how much energy is available are called the laws of thermodynamics and involve a concept called entropy 
   
* - In a previous post I've already taken some extracts out of his discussion of conservation laws and time translation invariance.   I haven't taken extracts from lectures on thermodynamics or many other things but they are there.

I think he was trying to uncover the big secret about physics;

   OK, sure.   I wasn't looking that deeply.  On the face of it, he was just presenting a lecture to educate his students.   So trying to introduce them to some of the big ideas in physics or uncover the big secrets etc. is precisely what he was trying to do.   Although, in the wider sense, his own motivation for studying and teaching physics may very well have been trying to discover some of the fundamental questions he has himself (why are we here?, what is the nature of our world? etc.)

I can't see that therefore taking away the idea that he says "energy is a number", when he actually says "energy is a conserved numerical quantity", follows at all.

   OK.  Although you asked about it in post #107, so you got a reply.

Do you think he's saying energy is just a number?

    There is at least one sentence where he does DIRECTLY talk about energy with the word "number":
...it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same...     
    However, I am not advocating that you take just that sentence as a definition,  the whole point is that you can't, you need the whole lecture (and more).   However, if you did "take away" the idea that energy is a number then that's OK and you're not wrong (although it is only a small portion of what is in the lecture). 

If we don't know what energy "really" is, and if mathematics doesn't tell us beyond it being conserved (numerically), that's as far as it goes.

    As discussed previously.  Feynman is not the only source of information about what energy is or isn't.   However, just confining our attention to this one lecture,  yes,  that is pretty much what he was saying here.  Well done.

Numbers are entities because they have properties or attributes, right? Numbers most certainly don't have a physical existence, all they have is a value.

   I'm not sure I can discuss the nature of numbers in a small amount of space and this post has already taken too much time (to write or to read).

Best Wishes.

17

Physics, Astronomy & Cosmology / Re: Talking about Physics

« on: 19/05/2023 14:26:37 »

Hi.

I think you need to be careful about the phrase "numerical quantity" that Feynman uses. My opinion of it is that he's reminding everyone he also used an analogy of counting up 'abstract' children's toy blocks.

   You are free to make of Feynman's lectures what you please, however there are some conventional understandings of what was said and intended.   Feynman wasn't really using language or addressing his lectures to an audience of philosophers, he was aiming at scientists and that particular lecture was an early one for the students (in their progress through undergraduate studies).  So he was aiming to break some misconceptions from school and provide a good introduction to undergraduate level physics.
   
    Given the audience, it's fair to say that Feynman was attempting to communicate something different when he said "Energy is a numerical quantity".   He meant that it is a quantity AND ALSO it has numerical properties.

     Most people would assume the natural division was between numerical quantities and non-numerical quantities.    Even the word "quantities" is an issue since in the English language one tends to think of something you can count and number.   Overlooking that, a numerical quantity is one where a number is assigned to it.  A non-numerical quantity is something that doesn't meaningfully behave like a number.
   How many people are in this room?   How long is this string (in inches)?    Those are numerical quantities.
   What is the name of this person?   What is the colour of this t-shirt?   Those are non-numerical quantities.

Numerical quantities follow all the properties you expect of things that are numerical.   For example you can order them,  4 (people in this room) is more than  2 (people in this room).      You can also multiply and add them meaningfully,   a room with 4 people in really does have  2 times the number of people as a room with 2 people in it.   Similarly you can add the people from two rooms together and you will get a number of people that is the sum.

At best, non-numerical quantities can be ordered but they do not have all the properties of numbers.  Quite often you can't even order them.    Example:    "Pink" is not more than "Blue", there is no natural order relation on non-numerical data like colours.    If you assessed peoples size as "Small", "Medium" or "Large"  then that data actually is partially ordered but it still lacks all the other properties of numbers,   for example  you cannot add small people together and end up creating a medium person.   Meanwhile, if you had actually measured the mass of the person, then that would be a numerical quantity.

What Feynman was saying is that Energy has the properties you expect of a numerical quantity rather than being some qualitative or descriptive data only.   So, it's not as if at the start of an experiment all we can say is that the total energy was "medium" and at the end of the experiment the amount of energy was also "medium".   Energy isn't just any old sort of descriptive quantity, it is a numerical quantity.   So you can meaningfully add two energies together   AND  write a conservation law as a conventional mathematical expression:   
    The numerical sum of all energies at the start  =   the numerical sum of all energies at the end.

It can't be that nobody knows what energy is, but we know it's a number, because . . . we then know what it is.

    It is commonly understood that what Feynman was saying is that all you (his students) should accept about energy is just it is a numerical quantity which seems to be conserved (does not change with time) in all experiments and observations.  Just don't make any further assumptions about it - because you can't.
   As discussed in an earlier post,  Feynman did have more to say about energy in some later lectures.  So these are not the last or final word from him but I am confining my attention to the spirit and meaning of just this lecture.
 
Best Wishes.

18

Physics, Astronomy & Cosmology / Re: Talking about Physics

« on: 19/05/2023 02:31:42 »

Hi.

I'd like to canvas some responses, about the subject of energy and how this is understood.

   There was a fairly recent (end of 2022) discussion in this thread:
https://www.thenakedscientists.com/forum/index.php?topic=85721.0

I don't suppose anyone would mind discussing it again but there's already quite a bit of information and opinion in that thread.   It's recent enough that many of the regulars will remember a little about it.

@alancalverd said this:

In simple terms, there isn't a simple explanation or even a simple definition.  Energy is one of the quantities that is conserved in classical physics, and very few adults have any idea what that means.

@Bogie_smiles said this:

In the simplest terms, I have always understood energy as the ability to do work.

@paul cotter  said this:

To return to the original question, I propose the following: energy is the capacity to do work with the limitation that in the case of thermal energy some or all( worst case ) will  not be able to do useful work.

@Eternal Student  (me) said stuff that took a lot of space and I'll just try to summarise here:
    1.   School level definitions don't really do it (Energy) any justice.
    2.   Energy is that which appears in Noether's theorem and as such it can only be identified as a conserved quantity in systems with time translation symmetry.  For example, in our expanding universe, there isn't a conserved quantity you can call energy.   (To condense that severely:  What most people think of as Energy is not conserved).

- - - - - -

One more detail: Feynman says that energy is a conserved numerical quantity. What's your opinion of that? Do you think he's saying energy is just a number?

    Yes, that is pretty much the gist of what he was saying in that lecture.
    There were some other lectures discussing symmetries and conservation laws but they are more specialised.  He discusses symmetry and conservation laws mainly in the context of Quantum Mechanics:
You see, therefore, the relation between the conservation laws and the symmetry of the world. Symmetry with respect to displacements in time implies the conservation of energy;...

[Taken from Feynman 17-3  between eq. 17.24 and 17.25.  https://www.feynmanlectures.caltech.edu/III_17.html ]   

    In the time of those lectures the relationship was mainly used just in Quantum mechanics but that particular relationship is much more general and not just limited to QM.

Best Wishes.

19

Famous Scientists, Doctors and Inventors / Re: Are some scientists unique and only they could have made the discovery?

« on: 18/05/2023 21:33:07 »

Hi.

   There has recently been a statement made by Chris here:
https://www.thenakedscientists.com/forum/index.php?topic=70438.msg705025#msg705025
    Where a server migration is discussed.

Best Wishes.

20

Famous Scientists, Doctors and Inventors / Re: Are some scientists unique and only they could have made the discovery?

« on: 17/05/2023 04:33:10 »

Hi.

Y'all know about the DONATE button on thenakedscientists.com website, Right?

   Yes I know about it.
- - - - - - - - - - - - -

What is a reasonable expectation and what do TNS need?
    The information on the donate page is suggesting 5 pounds every month, is that still sufficient or has the situation changed?

   I'm wondering if a "storage fee" would be reasonable and could be enforced without significantly altering the original purpose of the forum.   If forum posts were deleted after (lets say) 4 weeks that will keep the need for online servers down and reduce running costs.  It doesn't prevent the use of the forum for discussion or for getting questions answered.  It's controversial and may alter how people use the forum but not all of those changes would be negative.
If money is getting that tight then "controversial" is what might be required.   My stuff wouldn't be exempt - it can go.
   Another option is to put an internal message out to all the users:  "You've been using the site for a week,  please consider donating" etc.   My message box wouldn't be exempt.
   Wikipedia are quite skilled at analysing cookies and noticing even just when you have visited them a few times,  fire messages out to anyone who browses the site even without logging-in directly.   My computer won't be exempt.
    If you (TNS) just can't provide the forum free of charge then you just can't, economics has laws just like physics has laws.  So you could make a payment compulsory for people who want to use the site.  (As always, I won't be exempt).

    They're all controversial options but is it time that TNS staff did update people on the current situation and possibly ask for opinions  or, since it's your website and your money that is limited, just state what will be necessary.

Best Wishes.