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  4. Can a scalar have a negative value?
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Can a scalar have a negative value?

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Offline alancalverd

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Re: Can a scalar have a negative value?
« Reply #20 on: 05/04/2025 22:59:44 »
What happened before the Big Bang is at best irrelevant and at worst unknowable. My comments pertain to the observable universe "as is", and AFAIK there are no processes that do not conserve charge.

Now if we accept that charge is a scalar, then all the evidence is that the total, i.e.the sum of all positive charges minus the sum of all negative charges, is zero, though the number of charged particles can be anything you like, as is the number of separated charges at any instant.

The idea of a primordial black hole is appealing and consistent with one I've held since a dinnertable discussion in 1963 about the observed expanding universe being merely the current state of an oscillatory universe, which is consistent with some of the ideas in Hawking's "Black Holes and Baby Universes". But it still allows for zero net charge!
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Offline paul cotter (OP)

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Re: Can a scalar have a negative value?
« Reply #21 on: 06/04/2025 10:16:06 »
In reply to #17, i'm all up for expanding the tangent space.
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Offline Bored chemist

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Re: Can a scalar have a negative value?
« Reply #22 on: 06/04/2025 13:38:09 »
" Such as when the water has already been reacted with something else previously."
So... not water.
Where's a "roll eyes" emoji when you need it?
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Offline Eternal Student

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Re: Can a scalar have a negative value?
« Reply #23 on: 08/04/2025 02:49:25 »
Hi.

     Please don't roll your eyes @Bored chemist ,  try to look upon things as half-full rather than half-empty.   It took a lot of time for me to pick another example and set up the images in the forum (for the double-pendulum).  I did that because it's a better example than K + H2O.    Specifically, I completely acknowledge that the potassium water example is not a good one.   
   None-the-less thank you for time, you don't have to read anything or spend time making any comments.  I can be left here talking to myself.  Thank you.
- - - - - - - - - - - - - -

Quote from: alancalverd on 05/04/2025 22:59:44
What happened before the Big Bang is at best irrelevant and at worst unknowable.
   Let's try it this way:   YES that's absolutely right.  Well done.

You have also gone on to talk about what seems to happen in the universe now.   Indeed, much as you suggested charges do seem to be created so that the overall charge is conserved.   However, we need to step back for a moment and recognise that it's irrelevant - if you genuinely appreciate what you are saying yourself.   Quite possibly some BH were just always there, they did not evolve following the laws of physics as we have them now - they were under no obligation to conform with current physics and leave some equivalent positive charge somewhere if they themselves are negatively charged etc.

------------
Going back a bit further @alancalverd said the following:
    ..(The Universe).. has as far as we know, exactly equal numbers of positive and negative charges, and always will be overall electrically neutral. Experiment confirms this.

    Perhaps we should look upon in this way:    It has some positive charges, that much we can probably all agree on.   It also has some negative charges.   However, jumping straight away to the notion that an overall neutral charge in one place provides a net 0 force on a test particle is  NOT  something that is written into the basic laws of electrostatics.

   Don't get me wrong, we can often obtain that result:  We can look at the force produced by the positive charges, then look at the force produced by the negative charges, then finally make a vector sum of the whole lot.   For a finite set of positive and negative charges, distributed equally so that the net charge is treated as 0 everywhere around the test particle, then this calculation is perfectly feasable and produces the result we expect:   Where there is net neutral charge, even if that consists of several positive and negative charges either in exactly the same place or as much as possible so that we can treat a small region of space as having net 0 charge, then there is a net contribution of 0 to the force on a test particle from this little bit of space.   We can also generalise the result, it holds even if we allowed a continous distribution of charge(s) through space and perform appropriate integrals  ( ∫ dV )   instead of  sums  ( ∑ ) to determine the net force acting on the test particle,  PROVIDED we confine ourselves to a finite volume of space OR insist that the density of both the negative and positive charges  → 0   fast enough  as  the disatnce, r, from the test particle tends to infinity.   (For example,  having the density of those charges fall off as  1/r   would be acceptable,  see earlier posts).

     It's very hard to find an article describing what is NOT in a basic theory of electrostatics,  so instead I've got to present just a snippet of what IS in a basic theory of elctrostatics:.....

                   - - - - - - - - - - -

* Electrostatics.jpg (146.39 kB . 951x645 - viewed 737 times)
                   - - - - - - - - - - -
[Extract from  "Introduction to Electrodymanics", Griffiths ].

   As discussed in earlier posts there are just two basic axioms or tenets:
    (i)   Coulombs law for the force from one charge.
    (ii)  A superposition principle,  we sum over all charges.

     There's nothing in this book that I know of that puts any extra axioms into the theory.   For moving charges... stuff is added...,  for electrostatics, what you see written up there - that is all there is.

   So we don't really need to concern ourselves with whether space is typically of net 0 charge everwhere, we can't use that information anyway.  Instead we HAVE to be concerned about the idea that there are some positive charges  (or negative charges) in space, space may be infinite and these charge densities may not fall off as you increase the distance from the test particle.   We have to be able to determine the contribution from all the charges and sum them.

   I hope you can see the essence of what I'm saying.   If we add a new axiom  (probably two related axioms) to basic electromagnetic theory then we might be OK.   Those two axioms would be something like this:

    (Extra Axiom 1):   Spatial Symmetry rules.   Where charges are symmetrically placed around a test particle, we can immiediately discount all the charges in this set and conclude there is no net force on the test particle from these.   This holds for an arbitrary (possibly infinite) set of charges, we demand only that a suitable symmetry exists and place no limit on the number or cardinality of this set of charges.
     (Extra Axiom 2):   Numerical Symmetry of opposite charges.     Provided a small region of space,  δV,   has an equal magnitude of positive and negative charges in it, then we can also discount any contribution to the net force on the test particle from that region of space.

    We don't really need any of those extra axioms if we keep everything finite, we can just deduce them from the more basic tenets of the theory  BUT for an ininfinite set of charges we HAVE to have them.

   Anyway, that's the bottom line that appears ---->    We can't just declare that the net force acting on a test particle is given by  Coulombs Laws  (or Newton's law for gravity if you're working with gravity)   AND  a principle of superposition.    Instead we have to add a bit more, a bit more "fudge factor":  We have to admit these two basic tenets are not sufficient for, or capable of, determining the force acting on a particle in the universe.   Our simple notions must be overridden and give way to arguments of symmetry where it occurrs.

    That might sound a relatively minor, unimportant alteration but it isn't:    If we just had the two basic tenets of electrostatics, then we can say or think to ourselves that we understand something about what is causing an electric force on a particle in the universe.   Specifically, we can say that every other charge acts on it in a way we know  AND  we just sum these.    However, it is NOT that.   In an infinite universe the net force acting on a given particle cannot be that sum.

Best Wishes.
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Offline alancalverd

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Re: Can a scalar have a negative value?
« Reply #24 on: 08/04/2025 09:41:27 »
Axiom 1 demands absolute symmetry. we have no reason to believe that the universe is symmetric, and indeed we observe asymmetry whenever we look upwards, so, in the absence of temporarily induced static charges, the lack of detectable force on our test particle suggests no net charge.

Axiom 2 needs a little amplification. It is true that there will be no net force on a test particle outside the element δV, but if charges inside are separated, there will be local E fields that will polarise our test particle and possibly cause it to move.   
 
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Offline paul cotter (OP)

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Re: Can a scalar have a negative value?
« Reply #25 on: 08/04/2025 18:09:42 »
Caution, simplistic argument. If the universe had a net charge either + or- then we would find a repulsive force between two samples of matter, assuming that this net charge was evenly distributed. This would be in opposition to gravitational force. The fact that ε can be modified by the use of dielectric materials would allow differentiation of these two components of the total force in such a situation. The fact that placing a dielectric between two masses does not have any effect suggests neutrality.
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Offline Eternal Student

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Re: Can a scalar have a negative value?
« Reply #26 on: 09/04/2025 12:18:16 »
Hi,

Quote from: paul cotter on 08/04/2025 18:09:42
Caution, simplistic argument.....

It's interesting.
There are some complications.  For example, the universe is expanding,  so in general two bits of space (or space and the matter in it) that are well separated actually will have the distance between them increase and would appear to be accelerating away from each other.

   None the less, it is an intersting idea.   Thank you.

Best Wishes.
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Online Halc

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Re: Can a scalar have a negative value?
« Reply #27 on: 09/04/2025 15:59:05 »
Quote from: paul cotter on 08/04/2025 18:09:42
If the universe had a net charge either + or- then we would find a repulsive force between two samples of matter, assuming that this net charge was evenly distributed. This would be in opposition to gravitational force.
Thought about this and decided not. Suppose we have a net glut of electrons.  All matter with evenly distributed negative charge would push their excess electrons to the surface (much as what occurs on a neutron star, but for different reasons).  This cloud on the surface would be mutually repulsive and would flee the uncharged mass below. The excess electrons would find their way into intergalactic space and would push on each other, but not so much on the fairly uncharged mass collections. So no particular repulsion between two masses like planets.
The electron cloud would get evenly distributed kind of like how dark matter sort of is, except the latter does collect near mass (galaxies not heavily accelerated) and the electron cloud would have little reason to collect significantly like that.
« Last Edit: 09/04/2025 16:01:52 by Halc »
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Offline paul cotter (OP)

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Re: Can a scalar have a negative value?
« Reply #28 on: 09/04/2025 18:42:00 »
Electrons are not quite that mobile. To free electrons from a metallic surface there are three methods: (1) thermionic emission which requires heating to red heat or more, (2) incident radiation with enough energy to overcome the metals work function and (3) field emission(thanks Alan!) which requires a very high field strength. As regards freeing electrons from insulators and semiconductors I have no knowledge. Also if there was to be a deficit of electrons resulting in a net positive charge there would be no charge carriers with mobility. I will finish by again stating that this is a simplistic argument and may well have more holes than a sieve.
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Offline alancalverd

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Re: Can a scalar have a negative value?
« Reply #29 on: 10/04/2025 16:23:08 »
Quote
Suppose we have a net glut of electrons........
Then intergalactic or interplanetary space would have a negative charge, for which there is no evidence.

And whence came this glut of electrons? All the reactions we have observed in stars, involve neutral atoms and net zero charge conservation.
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Offline Wellwisher

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Re: Can a scalar have a negative value?
« Reply #30 on: 06/05/2025 16:39:28 »
Quote from: paul cotter on 01/04/2025 14:26:03
I have been involved on the periphery of an argument on a different forum. A question has arisen as to whether a scalar can have a negative value, leaving out trivial examples such as temperatures below freezing point of water. What say ye?

Scalar is more like the magnitude, while the vector shows a sense of direction, such as plus and minus temperature relative to the freezing point of water. If we are at -10C, this is a sense of direction and therefore a vector for this temperature system.

Absolute zero in degrees K avoids the minus vector, since all temperatures are a positive vector, and is assumed within the scalar. In that sense, a scalar can have a positive value and imply its own 1-D default vector. Although ΔT or a change in absolute temperature has a vector for heating and cooling using only positive scalars.
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