[TommyJ]

"the ability to do work" should really be a description only of Free Energy

School variant.
If a body or several interacting bodies (a system of bodies) can do work, it is said that they have energy.
Potential energy is called energy, which is determined by the mutual position of interacting bodies or parts of the same body.

'Hotter and colder' are rather relative notions. 'Hotter has more hot energy'.
And same about charges.

When we talk about energy of a system, which work was done to put the system into the state is not mentioned.

[yor_on]

ES  "  [gravitational potential energy is not needed in the stress energy tensor  ---> this is close to suggesting gravitational potential energy is fundamentally not required but I'll leave that for another day and another post].  "

That one is something you actually need to clarify :)
And don't you try to avoid it.

I always questioned the idea of potential energy. It irritates me.

[alancalverd]

Back to Newton.

Objects accelerate when subject to a force.

Suppose a given object has a property called mass, m. By experiment (altering m or F)  we can see that F = ma.

We see the apple accelerate so there must be a force attracting the apple to the planet. 

Since the gravitational acceleration of all small objects (i.e. m_obj  << m _planet) is the same*, the gravitational force must be proportional to the mass of the object. We can demonstrate this with a beam balance. Call the constant of proportionality g, with the dimensions of acceleration.

Now define work as force x distance moved. If we lift the apple with force mg through a height h, we have done work = mgh.

Experimentally we find that the apple reaches a speed v when dropped such that gh = ½v². This should come as no surprise dimensionally because g is after all an acceleration. The interesting point is that something seems to be conserved: by experiment, gh = ½v² for all values of h.

Now m hasn't changed, so the work we put in, mgh, has the same value as ½mv². For convenience, to distinguish between the conserved quantity before and after the apple falls, we call them potential (because it hasn't started falling yet)  and kinetic (i.e. moving) energy. 

If you want to move away from Newton's apple (m<<M, r <<R) you can look at Cavendish's experiment which showed that for commensurate values of m and M, the attractive force between objects is actually F = GmM/r². And now we are talking about gravitational fields (ah, the beloved inverse square law!) rather than an empirical observation.   


*a good point at which to raise Galileo's thought experiment: what happens if we glue the little rock to the big rock? Does the little one slow down the big one, or does the big one speed up the little one? Either statement contradicts the other, so g must be constant for all objects.

[yor_on]

Well, I have some different ideas. One of them is that a gravitational acceleration is coordinate dependent, as I understand it defined in relativity. Or as Pete used to describe it, by changing coordinate system you can 'transform away' gravity. Locally non-existent, 'globally' as from another coordinate system existing.

In all 'free falls' gravity is non existent, locally defined. I've seen is treated as 'field' of 'energy' but 'energy' is just a coin of exchange. you can state is as the apple falls to earth due to gravity, you can also state it as earth accelerating towards the apple or as both, as a sort of 'system', are acting upon each other.

I'm guessing ES refers to the stress energy tensor there? And possibly treating gravity as a field?
=

eh, well, looking again, that is what it says :) the quote I took from him.

This one is also about 'energy'

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

[yor_on]

It becomes kind of strange thinking of the Higgs field. How does it define a free fall? Doesn't it create a golden standard if it defines it as being at rest relative that field, as you then become weightless. It's not the same as mass, I know that but when thinking of that analogy to a 'molasses' giving particles part of their mass?

What molasses, and what happens when you become weightless? Doesn't motion change it? Relative or accelerating.
=

'Real' accelerations differs from a gravitational in that you will notice yourself gaining a 'gravity' locally defined. A gravitational acceleration becomes the opposite, you gain no mass from it, instead you become 'weightless' . All locally defined.

(as per Einsteins equivalence principle, the original one)

spelling
=

potential energy is overall a very tricky subject in that, the way I see it, you can define yourself to have a infinite amount of simultaneous 'potential energies' just as you can define yourself to have a infinite amount of time dilations, or speeds, just by defining it relative something else.

[Eternal Student (OP)]

Hi again.
   This thread has been busy with several people posting.  I hope everyone is well and thank you all for spending some time.

   @evan_au
   I quite like and agree with with most (possibly all) of what you've said.  The main thing is that you're thinking about  (and making me think about) energy and some of the problems we have understanding it.
   One of the things you didn't mention at all was that just changing reference frames can change the kinetic energy you would associate with an object even in the most simple Newtonian system.
- - - - - - - - -
   @TommyJ
   That's also quite good and quite interesting.

Potential energy is called energy, which is determined by the mutual position of interacting bodies or parts of the same body.

   That's OK for most uses of the term "potential energy" that school age pupils may encounter.  However, they also encounter terms like "chemical potential energy".
- - - - - - - - -
   @yor_on
   It's very kind of you to state that you are interested in hearing more.  I might talk a bit more about gravitational potential energy but this forum (and especially this section) isn't my personal website or "Blog".  I'm trying not to lecture or preach here.   I think forums work better when there is discussion between people and that's what I was hoping to get here. 
   It also takes hours to write something carefully, accurately, use Mathematical notatation in it and correctly identify references to back up some issues.  To be honest it's taken me hours just to write this post because I wasn't at all sure what I was going to say and how best to say it.
     Finally, please remember that I learnt General Relativity from a book.  I'm not an expert in very much.  With this in mind, I'll try and comment on what you've written but it's not like my opinion matters a lot, it's just all I can offer.

..I have some different ideas.  One of them is that a gravitational acceleration is coordinate dependent, as I understand it defined in relativity. Or as Pete used to describe it, by changing coordinate system you can 'transform away' gravity. Locally non-existent, 'globally' as from another coordinate system existing.

   This is mostly OK.  There is some need to keep Newtonian definitions of "gravity" seperate from G.R. definitions of "gravity".  In Newtonian theory, "gravity" is a force.   In GR  "gravity" is a curvature in a manifold.  You have blended the two theories together when you started talking about a "gravitatonal acceleration" and then ended the sentence with "as I understand it defined by relativity".  You don't need relativity to remove acceleration by choosing the right co-ordinates.  However, you can almost get away with blending these two theories in this case because of something very special that happens...
1.     When you said  "gravitational acceleration" is co-ordinate dependent it's better to state that any acceleration (regardless of what you think caused it) is co-ordinate dependant.  So we can find co-ordinates in which this acceleration is 0.  This doesn't require anything more complicated than Newtonian mechanics.
2.     The second half of your sentence is based on the idea that we can find co-ordinates (the LIF or Local Inertial Frame) so that every manifold behaves like the flat Minkowski manifold (although only in a small region).  Newton didn't really care about Riemann manifolds, why would you want to find co-ordinates so that this nonsense happens?  It doesn't seem related to anything useful.
3.      The amazing thing is that, if you construct the appropriate manifold, then in the right co-ordinates (the LIF) both these things (1) and (2) happen at once.  The acceleration required in the Newtonian theory drops to 0 and also the manifold behaves like the the flat Minkowski manifold.  This is one of the things that suggested to Einstein that gravity could be modelled as curvature in a Riemannian manifold.

    Now, as a consequence of this it is possible to state that "we can remove gravity" by choosing certain co-ordinates and it doesn't matter how you are defining "gravity".   We can use the Newtonian concept of gravity as an acceleration     OR  the  GR concept of gravity as curvature.
     You have qualfified (restricted) the statement adequately by stating that this only holds "locally".

 

I'm guessing ES refers to the stress energy tensor there? And possibly treating gravity as a field?

   Maybe.  Although I think there's two different fields we might be talking about here. 
1.    GR can be considered as a reasonably self-contained field theory all on its own.  This is a classical field theory not a quantum theory and "the field" of interest here will be "the metric field".
2.    It's also possible to consider gravity as one of the fundamental fields in Quantum Field Theory and then the field of interest here will be "the graviton field".   * [Late editing:  Note that Gravitons have not been discovered and QFT is not a fully comprehensive quantum theory of gravity.  In particlular QFT within a framework of curved spacetime would be something different again].

    The metric field is not the same as the graviton field, they are from two separate theories. Some of the more recent posts in other threads have been talking about  Q.F.T. and some have been talking about the metric field and classical General Relativity.  I know more about Classical GR rather than QFT.   Personally, I think the metric field is a fundamental field that exists in space - but I use the word "fundamental" only in the ordinary way.  It is basic, essential and naturally inherent in space.   In particular it describes the geometry of spacetime.
    Other people reserve the word "fundamental" to refer to the fundamental forces and/or fundamental particles in Physics and then a fundamental field is one that models those particles - so they would consider fundamental fields to be those fields used in QFT.   I think some of your ideas about a description of gravity as a field of energy originate from some articles about QFT you may have read.  I'm not sure that I can help much with QFT (sorry). 

   @alancalverd   Thanks for your recent post.

For convenience, to distinguish between the conserved quantity before and after the apple falls, we call them potential (because it hasn't started falling yet)  and kinetic (i.e. moving) energy. 

   I think this is very much how the subject was originally developed (the real historical development).  It's good in that it just directly presents what we observe and why we would start to think that terms like potential energy are useful.   Indeed, they are useful in simple systems modeled with Newtonian mechanics but their origins were purely mathematical - there was a quantity that seemed to be conserved,  we gave it a name and some years later, more meaning or importance has been attached to this concept then it deserved.  You know you are almost suggesting that the entire law of conservation of energy should be presented differently to children:  "We speculate that energy can be usefully defined in every system and we speculate further that this will be conserved   BUT  it's mainly an extrapolation based on something that we knew for a small number of special cases".
Personally, I'd be happy to present that version of the law of conservation of energy to children.

Best Wishes.

[alancalverd]

As an aside, I once watched a gorilla in Chessington Zoo discover, in five minutes, what took homo sapiens 2000 years, the murder of Bruno and the excommunication of Galileo, to work out.

He had two apples, one about twice the diameter of the other.

He dropped them both at the same time and noticed that they hit the ground at the same time.

Even without reading the student laboratory guide, he repeated the experiment.

Having obtained the same result, he changed hands and did it again.

Satisfied that h = kv² {∀ m,h} , he ate the apples.

So how come the National Curriculum still makes a pig's ear out of it?

[TommyJ]

gorilla in Chessington Zoo discover

It didn't articulate it to others.)

[alancalverd]

I don't speak gorillaese, so I'll take your word for it for the time being. I do however have a friend who is an expert on primate behavior and communication, so the question is worth putting.

Obviously gorillas teach their young and communicate about things that matter to the family. It will be interesting to see whether they do indeed discuss mathematical abstractions at GCSE level - it's clearly beyond the ability of most humans. 

[alancalverd]

It didn't articulate it to others.)

...and wouldn't have been burned at the stake or forced to recant if he had.

[Eternal Student (OP)]

Hi.   TommyJ + Alancalverd.

   About the National Curriculum  --->  Obviously it's nasty thing but we should also mention one positive thing about it.
It's an "entitlement curriculum".  Pupils are protected from the bias of teachers to some extent.
For example, a Biology teacher must teach the children about Darwinian evolution.  They can also talk about something else if they wish but Darwin must be there and it should be clear to the pupils that this is what they will be examined on.   In the same way, we can (and probably should) spend some time talking about our own understanding of energy and interpretations of the conservation of energy BUT the pupils are protected from outrageous whimsy and corruption to some extent.

Even where the National Curriculum just gets things plain wrong - at least later institutions have a reference standard to use.   They know that this piece of junk is what the pupils will be coming in with, regardless of which village community they were taught in.

Best Wishes.

[yor_on]

Thanks for the reply ES

Yes, a lot of things discussed. and I will have to go through them all methinks :)  I will assume that you by using the 'metric field' refer to the geometry of SpaceTime? And I don't think I will discuss it in form of QFT, aka, gravitons. I find them quite questionable myself.

[yor_on]

It seems as we have two different approaches to reality in physics. One is looking for 'grains' as 'photons', 'gravitons', or f.ex the 'Higgs boson'. the other becomes when we define it from 'laws' and 'properties' as f.ex 'spin'. That one is very abstract. And I think that one is more correct myself.
=

Which btw makes your definition of it as a metric field very acceptable to me. You could say that me wondering about a Higgs field, and the way it is supposed to give particles mass, versus, the way relativity differs between accelerations, giving you a gravity, aka a added mass on a scale, and 'relative motion' comes in as part of that.

It's about the reality of nature. Is it 'grains' creating it, or are those 'grains' just a result of something else. A perfect example is lights duality.

[TommyJ]

Thanks for the replies ES and yor_on.

While I was my the last years at school, I had to study physics deeply with PhD. Technical mentor additionally. And somehow he managed to put the knowledge within consumable time and level.
It is not trivial to explain to a school student not only physics, electrodynamics .. literature. To transform it to the limited math and understanding.
Some professors tell to university newcomers: 'Forget everything that you were taught at school'.

[Colin2B]

gorilla in Chessington Zoo discover

It didn't articulate it to others.)

It did demonstrate the principle however. A good student watching could learn something 

[yor_on]

No ES. "  I think some of your ideas about a description of gravity as a field of energy originate from some articles about QFT you may have read.  I'm not sure that I can help much with QFT "

They doesn't, I've seen it used describing stress energy tensors. It seems to come from that formula used to describe the equivalence between mass and energy.  Then stretched to 'gravitational fields' and the 'energy' they contain.
=

I also remember Pete looking at in much a similar way. I don't know to what degree he had studied Relativity, but I found him quite proficient in it .And the way he looked at mass, all included, was in form of 'energy'. And I think he used it also to describe those 'fields' from. Forms of 'energy'. Myself I don't know, if we use the metric of SpaceTime then it exist, and it's also observer dependant. I use to differ between a abstract 'global' definition of the universe, versus a local definition. From the abstract we all have a 'same universe', the same metric. Locally I don't see it as we do, speeds, accelerations and its equivalence, mass. F.ex, using a extreme, what is the metric of a 'photons' propagation through our abstract definition of a universe. Does it exist, and if so, from whose definition?

 ( I agree to the difference there between dependent and dependant btw, thanks for that one ES, will blame that on my lack of knowing enough nuances in english. Always something new to learn :)

It can become very tricky if one wants to define it through the universe containing a 'energy'

Just read this  http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

He uses a redshift of light as one example. And states that it proves that 'energy is not conserved'.  And we might assume that this means that light must 'propagate'. But I don't think it necessarily needs to be so. We could just as easily refer to it as laws and properties defining it without using a propagation. It gives us a logic any which way. Just as using a duality does, without locking it to neither waves nor 'photons'. So I'm of two minds when it comes to fields, but I do know that the 'metric of SpaceTime' exist, with or without it being a 'field of energy'.

And yes, assuming laws and properties to define it instead of a propagation makes it possible to define it as 'energy' is conserved, 'globally' defined. Well. as I think of it for the moment.

You can turn it around also and then define all energy as different types of 'mass'. That would probably suit those looking for 'grains' more than the opposite.

I seem to remember Sabine being somewhat of a devotee of  'Super Determinism'. In that view, and as far I've looked it up, everything becomes predestined. And if it would be that way energy has to be 'conserved' from a 'global' standpoint. It can't lose anything, everything becomes 'locked up', as far as I see?

Found a link    https://backreaction.blogspot.com/2019/07/the-forgotten-solution-superdeterminism.html

[Eternal Student (OP)]

Hi again.

I also remember Pete looking at in much a similar way.

   I'm sorry but I don't know Pete.  I think he used the forum before my time here.  I've heard from other posts that he has passed away.  I'm very sorry. 
   What you're describing about energy and the stress-energy tensors does sound like the standard or main approach to General Relativity but I don't really know exactly what it was that Pete did or was intending to do.
   There are online lecture notes from Sean Carroll that describe GR and show how all the components of the theory are defined and constructed.  (This is the same person that you gave a link to in your post).
https://www.preposterousuniverse.com/spacetimeandgeometry/
   I learnt about GR from the textbook written by Sean Carroll which is based on those lecture notes (but the book will cost you a lot of money, while the lecture notes are free if a little outdated).
   I'm not going to re-present the theory of GR here, it would take too long and I really can't do it any better than the myriad of other courses and textbooks that are already out there.   However, I'm fairly sure bits and pieces will be mentioned occasionally.

The link you gave:   "Energy is not conserved" is a good article that I'm familiar with and I've recommended it to others in the past.   The main point made in it is exactly as stated in the title -  Energy is NOT conserved and the example is exactly as you have described.  I'm glad you mentioned here because it is obviously relevant to this thread.   It is certainly something that everone should read before they start telling children about the conservation of energy.
 

...'Super Determinism'. In that view, and as far I've looked it up, everything becomes predestined. And if it would be that way energy has to be 'conserved' from a 'global' standpoint. It can't lose anything, everything becomes 'locked up', as far as I see?

    The first part seems right.  Super Determinism  does generally imply that everything is predestined.
    The second part may be true.  I haven't studied Super Determinism much since it isn't one of the more popular interpretations of Quantum Mechanics.  However, it seems that  Super Determinism  does not prevent  the expansion of space and the red-shift of photons exactly as you described in your link  "Energy is not conserved".   So, it doesn't force energy to be conserved if we were defining energy in the same old-fashioned way  (as the ability to do work).   I'm sure you can define energy in a different way  (some consider energy as information and information is conserved in quantum mechanical systems).

   Oh yes... and I didn't have my spell check switched on.    Dependent and Dependant are different but I'm not sure I did that deliberately, sorry.

 - - - - - - - -  -
I think it's time for another question:
   How much energy does it take to make a magnet?

You've probably made a permanent magnet in school.  You might have stroked a piece of iron with an existing magnet or else placed some iron between some coils of wire and passed electricity through the coils for a time.
It seems clear that some energy was used to create the permanent magnet.  It's probably not much.  maybe you used an electromagnet drawing 1 KW  of electrical power for about 5 minutes.  I don't know, something like this.

Anyway, once you've got this permanent magnet it will start attracting other bits of Iron.   There's quite a lot of Iron in the universe, possibly an infinite amount.   To use Evan_au's favourite way of visualizing a potential energy, there's now a magnetic potential well available and we can use this.
   Ignoring friction and other inconveniences as usual, we can allow all the Iron in the universe to come to our new magnet.  How much kinetic energy can we harvest at the magnet?  Where did all this magnetic potential energy come from?

Best Wishes.

[yor_on]

That was somewhat funny ES. You introduced the new 'term' by mistake if I get it right? :) English is a very nuanced language. Dependent or dependant. Both have their importance. and yes, a spellchecker is useful but mine is so old by now that it mostly gets it wrong. It shouldn't be able to change but it does, or it might just be me getting sloppy when I write.
=

You wrote " Super Determinism  does not prevent  the expansion of space and the red-shift of photons. " and I think it doesn't matter how the universe is expected to behave if it would be predestined. The only thing that would make it weird, to me then, would be if it behaved 'magically', aka if we could find no logic explaining it, no rules, no laws and no properties. One could of course argue that what we can't explain, as 'spin' and 'probability' in quantum mechanics are just such factors. But I would still say that a overwhelming part of the universe has a logic that we can follow. And that we find a logic in quantum mechanics too.

There might be a subtle point to that. For Creationists the universe is something 'created'. If we assume that a 'God' can do whatever he/she/it please, then logic doesn't matter for it, in a choice between what I call a magical universe or one logical . So the logic's we find existing, assuming this to be correct, does not point in a creationist direction.

[Eternal Student (OP)]

Hi everyone.  I hope all is well.

But I would still say that a overwhelming part of the universe has a logic that we can follow.

    Yes, I agree.
   Although you could also argue that we (human beings) are just extremely good at finding patterns and very likely to forget about something that didn't make sense or follow a pattern.
   You will notice that two things do seem to be related and remember it.  This is useful for your survival.  Meanwhile, there could have been 100 other things that were not related in any way.  You won't notice or remember those.

     Let's take some examples:
1.  We can see a relationship between electricity and magnetism.
2.  We can't see a relationship between  "what you eat for breakfast"   and  "what the weather will be in France".

  We remember  1.    We forget about 2.   We don't even ask the question why isn't the weather in France related to my choice of breakfast?

[Eternal Student (OP)]

Can I push this question again, please?   Maybe I should put it in another thread.

How much energy does it take to make a magnet?

You've probably made a permanent magnet in school.  You might have stroked a piece of iron with an existing magnet or else placed some iron between some coils of wire and passed electricity through the coils for a time.
It seems clear that some energy was used to create the permanent magnet.  It's probably not much.  maybe you used an electromagnet drawing 1 KW  of electrical power for about 5 minutes.  I don't know, something like this.

Anyway, once you've got this permanent magnet it will start attracting other bits of Iron.   There's quite a lot of Iron in the universe, possibly an infinite amount.   To use Evan_au's favourite way of visualizing a potential energy, there's now a magnetic potential well available and we can use this.
   Ignoring friction and other inconveniences as usual, we can allow all the Iron in the universe to come to our new magnet.  How much kinetic energy can we harvest at the magnet?  Where did all this potential energy come from?

    I'm keen to get some answers.

Best Wishes to everyone.