Capiert

Capiert, to save further argument over terminology I suggest you research

 

Momentum Transport

 

This is the technical term I think you are trying to portray.

 

There is a whole branch of engineering science about this

 

https://en.wikipedia.org/wiki/Transport_phenomena

Good suggestion. Thank you, for putting a name on it. e.g. translating, identifying it.

Empirical evidence aside,

& to hear that (line) from a scientist.

What a disgrace for science.

 

unless you can find at least a few physics textbooks that teach momentum flow, I don't see how you can claim that you are being unmistakably clear.

If someone says "flow" to me, I sure do have to ask myself, "of what?".

You didn't bother with the word (at all) as though it did not exist.

You ignored the description, even if a standard naming exists.

That's ignorance.

 

You don't have to budge,

if you don't want.

You don't have to do anything

if it makes no sense to you

(even if it does for others.

A question (just down the road) of puzzlement

did not come from you, to clarify misunderstandings.

I'd evaluate that as not really interested.)

That's your choice, not mine.

 

MIT seems to have a meaning for momentum flow,

if you don't.

 

http://web.mit.edu/16.unified/www/FALL/fluids/Lectures/f07.pdf

"When material flows through the surface, it carries not only mass, but momentum as well. The momentum flow can be described as

momentum flow = (mass flow) × (momentum /mass)"

 

to say it awkwardly.

 

It doesn't look like anyone is bold enough to call momentum flow a force,

although the variable is swapped

from the acceleration (speed (velocity) per time)

to the mass per time.

With viscous friction,

speed won't remain constant.

e.g. a bullet thru air.

 

I still see a momentum transfer,

e.g. flow,

no matter what way you look at it,

mass or speed as constant.

Thus can be equated (somehow, someway).

 

https://www.av8n.com/physics/euler-flow.htm

"We (temporarily) assume there are no applied forces (i.e. no gravity etc.) and no pressure (e.g. a fluid of non-interacting dust particles). We also assume viscous forces are negligible. Then, the only way a momentum-change can occur is by momentum flowing across the boundary:

∂ Πi/∂ t = ∫(ρ vi) v · dS = ∫(ρ vi) vj djS (8)

We are expressing dot products using the Einstein summation convention, i.e. implied summation over repeated dummy indices, such as j in the previous expression."

 

It seems like some people can make sense

of the idea of momentum flow.

Why you couldn't or can't is beyond me.

(..other than doing a number on me. =Giving me the "treatment".)

 

 

Standard terminology of basic concepts is found in introductory textbooks.

Yes, a "sea" of liturature exists. You guys (& gals) have the roadmaps. (The shortcuts, to efficiency (I hope).)

It may come from specialists but it's available to the novice.

Yes, but then accessible, when known (e.g. where).

That's the difference, whether it can be used.

 

As technology advances, new nomenclature will be developed.

However, what names become popular, (especially when old names exist (multi_naming, multiple names),

or which become outdated: what's IN, & what's OUT,)

it is all written in the wind, what the future will bring.

 

E.g. Speed of light symbol

was once V,

now it's c.

Who changed it? When? Where? & why?

(I don't know that, but am curious.)

 

Identification, is where it's at.

Recognizing.

"No one said momentum is a force."

You did, just a few posts back.

"If we equate flow of momentum with force".

I don't recognize momentum's "flow" (a statistic, e.g. change)

& momentum as the same thing.

I reject your accusation, as not true. I did not say momentum is a force.

I said the "flow" of momentum could be seen as a force, in that sentence, not momentum (as no flow, at all).

You obviously missed:

flow of momentum=(momentum's) "flow".

That is actually unmistakeably clear.

Please don't push the blame on me,

that wouldn't be fair.

 

Momentum doesn't flow,

Does it not?

What is a change of e.g. momentum

wrt to a location (or position)?

I would say flow.

 

so if you meant something different, you failed in expressing it.

ajb & Strange (seem to have) got the most out of it,

you apparently the least.

 

No, our answers are basically the same.

The same?

You started with the anti_thesis,

boalstering as thought I said something wrong,

(as a correction)

when you were not even on topic (thesis);

& then say it's basically the same.

You came in the back door,

& are covering it up.

Bravo: Anti_thesis, then thesis.

Not a word false there;

only the sequence is mixed up (=reversed),

giving away the (correcting=correction) intent.

(You obviously misinterpreted. No tragedy. Mistakes happen.)

Say it right the 1st time, please.

 

Um, no, not because they "Want" to.

To be fair, what then?

Newton had a talent for making formulas.

When Hailey visited Newton

with a problem,

the answer was already prepared

in a manuscript.

I get the idea Newton worked on (some) things he wanted to,

because a contract for that problem had not existed.

 

Current is the amount of charge passing a point per unit time. If the current is constant, there is a constant amount of charge in any given region.

Yes, but it's moving.

 

How would you have an amount of momentum passing by you?

If someone shot at me, but missed.

 

Momentum doesn't really "accumulate" as if it were a substance.

But it is a "property" that can accumulate.

The bottom line here is that you are using non-standard terminology. Don't place the blame elsewhere if you are misunderstood, because by using your own version of the language you are making it easy to misunderstand you.

I'll try to improve, but I'm amazed how many understand, & also how many are not able to understand.

Standard terminology comes from the specialists. I look to them that they can bring things into context,

to make things understandable,

considering they know what their specialty is all about.

But can the specialists communicate with the public?

Nobody is perfect.

It is rediculous to expect that I know your specialty,

especially as good as you.

Otherwise I'd be sitting in your place.

Momentum is not force, change in momentum per unit time is. You can't just equate things because you want to.

 

"No one" said momentum is force.

It seems ajb #16 understood the question & answered it better, & more appropriately than you.

But I wonder why both your answers are (almost) opposite.

Physicists have been equating things (=the things they can) for centuries,

simply because they want to, e.g. Newton.

Without that creativity, we would be nowhere, a big zero!

Change of charge per time is current "flow".

I don't find my question was extraordinary,

but the answer seemed a bit rude.

(If you can't, it looked like ajb could.)

Perhaps "accumulation" was not obvious,

& that irritated you.

e.g. if we charge a capacitor,

(the charge accumulates at a final destination

inside the capacitor).

If momentum flows into a mass (in 1 direction),

then I would expect the mass to accelerate.

 

If the mass stays in equilibrium,

with no accumulation (of momentum),

(e.g. current flow analogy similar to a wire conductor)

then maybe it (the situatation)

is as Strange described #18,

as pressure (force per area).

 

Recognition is the 1st step to improvement.

Review: SR was (originally) done

without Heaviside's (not Maxwell's) 4 equations.

Y/N?

 

So I can conclude:

SR (1905) (originally) did NOT use Heaviside's 4 equations (1884).

 

 

Sun 2016 06 19 12:31 PS Wi, 14 C drizzle, ..23:59

 

No getting around it,

a bit of a grammatical inconsistency

led me to (distracting) ambiguity,

 

("much" infinitive vs plural;

& singular "1 of them" belonging from the plural, not infinitive)

 

I needed to exclude, by rewriting.

Such sentences are too tricky for me,

as my brain starts dancing off

in 2 directions.

(It's like SSB single side band transmission to me,

that's exclusive (high tech).)

 

You're obviously staying on track,

but (for me) as a newcomer

I'm too easily sidetracked

by other possibilities

if some words are not well defined enough.

The sentence becomes too vague, or abstract

for me too follow, &/or I get lost (in the sauce).

E.g. I've never heard anybody say Maxwell's "theory"

when discussing Heaviside's 4 formulas (equations).

Usually I hear about (Heaviside's) "Maxwell's equations", instead of (Maxwell's) "theory";

& I hear about SR's "theory".

(That's a real sidewinder, for me.)

So the word "theory" was ambiguous (Heaviside (not Maxwell) or SR's?),

for obviously Heaviside's (not Maxwell's), intuitively (=guessed, assumption).

 

The amazing thing is that there is so much (=so many "things") in Heaviside's [not Maxwell's] 4 equations of 1884 that were not understood or appreciated at the time (of SR development 1905). "One of them" is that the Heaviside's (not Maxwell's, [not SR?]) theory varies (=is [not in]variant) under the Galilean transformations (the symmetry of classical mechanics).

(That's an obvious sign something has gone wrong, when consistent results don't happen.)

Later it was recognized that it is the Lorentz group ((c*t )^2 -x^2 -y^2 -z^2) that is important there (with only the relative velocity (as) parameter).

(That experimental particle physicists use opposite polarity (away) from the theoretical relativists, already indicates a break in the branches of physics, as a discontinuity, that something is wrong, theory doesn't agree with experiment, but (that difference=disagreement) is talked away as (opposite (polarity)) "preferences".

 

Now that's cool! There is no mistake, & nobody is wrong, by being an egoist (if the facts are straight). I.e. "Subjective" (view) relativity frame. E.g. "Your point of view is just as valid as mine", because there is no preferred perspective (=frame). The challenge is setting up the convers(at)ion (table, equations, setup e.g. communication) so each can see the others viewpoint (=frame).)

 

Other things that are written into Heaviside's' (not Maxwell's) (4) equations include

(I have to put a few word in to keep a eye on this, complex stuff)

 

gauge symmetry

(non_measurable particle's force fields, in equilibrium)

and

conformal symmetry

(15 degrees of freedom: 10 for the Poincaré group, 4 for special conformal transformations, and 1 for a dilation),

(an extension of the Poincare symmetries

(same duration interval,

e.g. counting in seconds).

 

(Oliver Heaviside had an incredible overview (for (producing) his 4 equations, now (wrongly) called Maxwell's) & he (=the dumb Heaviside, he couldn't hear right, &) wasn't even a physicist (nor mathematician), just a telegrapher. It seems his 4 equations are 1 of the most stablest & dependable, throughout physics & mathematics, without (enough) recognition. You need & depend on his stuff (to the core of sub_atomic nuclear physics, & beyond (.. (even) our capability)), but who he was?, hmm, give it to Maxwell instead (to maintain the (questionably accurate) tradition). Heaviside wasn't (even) a Ph.D, so his fame doesn't interest us (much). He's insignificant*.)

All these things are at the forefront of field theory today.

Yes it's amazing, what ya can build (=program) into (compact) equations,

for others (not as advanced) to find years later.

 

Pink finger nails, half deaf, stone furniture,

"sarcastic humor, anti_quarterionist, scandal" lover.

 

A (brutal) editor of Maxwell.

e.g. He shortened Maxwell's formulas to a minimum.

 

Bizarre? Hm, More eccentric (=decided),

he knew what he (himself) liked,

& what fascinated him(self).

 

But at least Maxwell recognized Heaviside,

& so Oliver rewarded him with those 4 equations,

for that (recognition).

 

A real "crack"(er) on formulas. Oliver Heaviside.

(Nephew of Kirchhoff.)

(Or should I say Kirchhoff is his uncle.)

 

Formula: condenser, compacter, editor.

=revisor. Reformulator.

& author.

He even meddled with (operational) calculus, successfully,

against everybody's understanding,

(using algebra,

causing great controversy).

[self taught electrical engineer!,

dare we (also) say mathematician?]

 

*Sarcasm. It seems:

Maxwell's stomach (tummy) aches are more interesting for us,

than Heaviside's humor.

 

People probably hated (life ruining) quarterions

because they dealt with angle,

& that nobody knew that,

a ("partial") polarity problem.

 

Although against the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science for years to come.[2]

https://en.m.wikipedia.org/wiki/Oliver_Heaviside

Probably because ya can't get much [accomplished or] changed,

by agreeing all the time.

---

 

Heaviside's (not Maxwell's, 4 equations) theory varies (is [not in]variant)

under Galilean transformations

(which are classical mechanics' symmetry).

Later, the Lorentz group was recognized to be stable (& important)

there;

it had only 1 parameter, relative speed (vector).

(Heaviside's 4 equations had too many parameters,

so that linear (consistent) results could not be expected

when using Galilean transformations.)

 

PS:

Does that also mean they (=Heaviside's' 4 equations, not Maxwell's)

vary (=stay [non in]variant)

for SR? Yes.

 

(I suspect your answer will be NO,

although you will state neither yes nor no,

(indirect y/n, avoids arguements)

but tend to a no (to make the point that we didn't understand

completely back then (which I almost missed)),

with the correct following consequence of the)

 

Anti_Thesis: How is it they (=Heaviside's 4 equations, not Maxwell's)

suddenly become constant=reliable (=invariant)

near light speed?

(SR has the advantage of working right for "slow" & fast speeds

thus correctness is guaranteed at slow speed too.

A sudden change does not exist, at 1 particular speed, near c.)

Somewhere there must be a gray zone from yes to no. ?

Or at what particular speed do things magically happen (=stabilize, to become reliable)?

 

Anti_Thesis: How is it they (=the 4 Heaviside equations)

suddenly become invariant near light speed?

 

ajb:

The Lorentz transformations have only 1 parameter - the relative velocity.

So th(os)e transformations hold for all relative velocities,

not just those near the speed of light.

Galilian transformations (=approximations) are (only) ok for slow speeds

(non_near light speeds).

There are recent papers that perform very similar experiments with modern measuring devices and techniques.Herrmann, S.; Senger, A.; Möhle, K.; Nagel, M.; Kovalchuk, E. V.; Peters, A. (2009). "Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level". Physical Review D 80 (100): 105011. arXiv:1002.1284. Bibcode:2009PhRvD..80j5011H. doi:10.1103/PhysRevD.80.105011.No aether influence detected down to 1 part in 10^17. Awfully little wiggle room left, there.

Yes, quite astounding(ly little). I noticed Michelson said less than 1% so I gave up hoping to find anything significant, yesterday.

You've confirmed that. Thanks.

Time is needed as a vector coordinate in order to model the combination of time dilation and length contraction on a given coordinate system.

Aren't you skipping the point?

What you need, & what things (really) are, are 2 different things?

I can't make a male into a female, I'm not a surgeon

& it won't change all the chromosones in their body

to hide the fake.

I can't make time (into) a dimension.

Time never was a dimension, never is a dimension, & never will be a dimension.

The 4 *4 matrix are necessary when you fully understand GR.

I never questioned (=never doubted) that you need them.

You need of them is your justification,

(because) you can't do without them

if you did not have them.

But that's the back door,

=the end of the story.

The first of the story also has to be true too.

Is it?

The fact is we know time isn't the same for all observers so you need to account for this

It's fine that you can start with (virtually) what you need. I wish I could (do that), but can't.

The closest account I can offer for time would be derived from that Pythagorean equation, meantioned above, not a Lorentz group.

 

The Lorentz group does not look like it demonstrates the equality;

instead (it looks to me) like it scatters that.

Hi ajb!

The amazing thing is that there is so much in Maxwell's equations that were not understood or appreciated at the time. One of them is that the theory is not invariant under the Galilean transformations (the symmetry of classical mechanics).

Nice point.

Does that also mean they stay non invariant for SR? Yes.

Anti_Thesis: How is it they suddenly become invariant near light speed?

Somewhere there must be a gray zone from yes to no. ?

Or at what particular speed do things magically happen?

Later it was realised that it is the Lorentz group* that is important here. Other things that are written into Maxwell's equations include gauge symmetry and conformal symmetry (an extension of the Poincare symmetries). All these things are at the forefront of field theory today.

*I'm sorry, I can't really see the connection (yet) why we construct a 4x4 tensor matrix, with an unrelated variable time, as 1 of the 4 properties. A balanced equation of L^2=, (c*t)^2=x^2 + y^2 + z^2, seems more reasonable, & symmetric to me, (than a Lorentz group, e.g. distortion?). Minkowski shamed the physicists into hanging on an extra variable, time, that didn't belong. He indirectly accused you of being lazy if you didn't (do what he recommended. But I see no advantage to the method, instead disadvantageous, mixup, & non_reversability. To say it worst, screwball method. Time is NOT a vector, it's not a dimension like x,y,z are. Time does not belong there in that type of construction. Maybe in a different construct, but not so; as far as I can see, the basis is wrong (or could be?). Am I wrong?

It is complicated: https://arxiv.org/ftp/arxiv/papers/0908/0908.1545.pdf

 

It's fascinating that we have so little accurate information about something that happened just over a century ago.

It's interesting, that we are getting different stories, even from Einstein.

But I think, he couldn't have avoided the M&M experiment, & eventually was trying to, .. work on the next level, distracted by the optimistic solution. In other words he tackled the (same) problem (completely) differently.

The mind has a tendancy to complete things (errors happen too). No sense staying in a rut.

(That's only my (meager) opinion, so I'll have to drop it. Otherwise I'll never get a chance to read all the goodies, you sent me.)

So what if the experiment is "old?" Which is a very relative term anyway.

 

Copernicus' discovery of a heliocentric solar system and not a geo-centric one predates the M&M experiment by a good 300 years.

 

Newton; Kepler; Jennings; Curie; Rutherford. All old by your standards I guess?

 

Yet the M&M findings of there being no Aether ARE correct. So maybe instead of calling it old and inaccurate we should instead say they were ahead of their time? LOL

Go out & look at this planet, even after a rainshower, the jungle, forests, cliffs & seas!

It's all ancient! Just because it sparkles & is clean, everybody thinks that's new.

No, it wasn't. Einstein, for example, wasn't aware of the Michelson-Morley experiment (and, if I recall correctly, later said that if he had been he wouldn't have paid it any attention).

I would have said, Einstein got it (the M&M ether dilemma) indirectly. Lorentz had 19 of the 20 GR terms, in 1904; 1 year befor Einstein published SR.

Lorentz was quite aware of the M&M experiment('s problem). Einstein, however, decided to solve ((the constant light_speed) controversy) differently.

He was probably aware of the relativity issue, because of the attention it was getting, that's why he joined in. Light's_speed was accused of being constant (that was a major consequence of the M&M experiment,

even if he didn't know who did the experiment.

If everybody was bickering about whether the ether existed, he decided he knew how to solve things (& kill the arguementation)

with a method without using the ether (at all). 1905 he said he will not use the ether.

He didn't say it did not exist, only that he was not going to use it, in SR. That certainly stopped a lot of fights.

Effectively, all Einstein did was say (virtually), "if that's what the experiments says, then we'll use that status". The average (back & forth) speed of light was then declared to be used for c, but he didn't call it an average. Nobody did.

 

If anything, Maxwell's equations were the fork in the road. So it all depended on Faraday "playing" around with "wires" and "magnets".

Good description, it really brings it to the point.

 

Everything that Einstein, Poincare, Lorentz, et al. did was just derived from applying Maxwell's equations and reaching the obvious and inevitable conclusions.

Wasn't SR originally, without Maxwell? I mean Maxwell's 20 equations, were the basis for Heaviside's 4 equations, which everybody calls Maxwell's, but they are not. Didn't Maxwell propose the experiment, that Michelson decided to do in 1887? Didn't application of Heaviside's 4 equations come later (after SR), into GR?

 

At which point, anyone looking at the results of the M-M experiment would have said, "well, obviously."

At that point, looking back, obviously. Who could avoid, the connection?

But I think Maxwell's proposal for the M&M experiment, was the indirect inscentive for Einstein's SR theory, trying to end the feuds?

Einstein wanted to end the constant c controversy,

something that came out from the M&M experiment.

You might say Maxwell used his equations, to propose the M&M experiment (setup)?

Absolutely not; I loved studying History of Science (I probably did better in that than I did in my science studies!).

Hey!, that's nice to hear!

 

I just think it is fascinating that certain experiments capture the imagination far beyond their actual significance.

Well we got stuck there, didn't we? Michelson & Lorentz found it difficult to accept. Everything that came later, depended on that experiment. It was a fork in the road. It's not a wonder that people will question its significance, & search for what caused our present situation. Maybe imagination, is the safety valve, for helping us to deal with our reason(ing). That experiment is a pivot point, it seems to be very significant.

 

But that's human nature, I guess.

It's obvious that some things become very significant to us.

You're right we cannot always follow the reason why.

Your rating "actual" significance,

does seem to indicate

there is another rating system being used by us,

which we are not all aware of.

Otherwise there would be no difference between the 2.

You've made a good observation.

The next challenge would be,

what (exactly) is that other natural rating system we use,

considering people are equipped with brains (computers)

& using them. What's causing the extremes?

Something is out of sync, or out of wack?

Super!, Strange. Thank you!

I wonder why people are still so fascinated by such an old and relatively inaccurate experiment...

I don't know, maybe it's the nostalgia, & pioneer spirit of hands on experience.

We can relive those discovery moments, of history like a Jules Verne novel.

Everything had to "start" from somewhere, to get the ball rolling.

Maybe those past clues, awaken in us things, we recognize, for a specific time (frame).

I don't believe in time travel back into the past, because it has not been experimentally proven, to film a clock going backwards. So I've dropped that hypothesis til someone can. But maybe that grasp, or inkling, to ponder in the past (memories) will in someway

help us get a clue to how to do time travel, as some form of experience platform. Til then it's only speculation. I think its the spirit, that counts, that flavour.

Lovers of the future go in the opposite direction, towards maximum accuracy (quality), quantity (statistic) & variation.

 

Absolutely super! for the following:

 

This page has one of the most detailed analyses I have seen: http://www.relativitycalculator.com/Albert_Michelson_Part_II.shtml

 

Or this one: http://spiff.rit.edu/classes/phys150/lectures/mm_results/mm_results.html

(The author of this one is, I think, very active on another science forum.)

 

A copy of the original paper here: https://www.aip.org/history/exhibits/gap/Michelson/Michelson.html#michelson1

Historically, I get many tidbits from the side, it conjures up many impressions,

of how the people lived, & what went on back then, when following the style.

(It helps fill (in) & complete the (unique) picture.

See it maybe, as a data (number) check, each time incident has it's own unique style (signature),

that fits (the whole picture) or doesn't. A coding.)

A real fantasy ride. Something you probably, would prefer to exclude,

because you are interested in only the facts.

But historians & history lovers, do exist.

It's just another enjoyment, like the love for a modern fast motorcycle,

or any other advancement. We like, because it works for us.

 

The past errors, set (=confirm) the authenticity,

for the (past) time period;

& the accuracy (achievable) sets (=determines, the limits for) the future timestamp ((technological) capability).

Each time period is unique in its own way, displayed thru a (data) quality like that.

It's (=the amount of quality is) a continuum, of facts.

 

At least that's how I see it (could be), now.

 

P.S. The neat thing about modern,

is we can take an old or primitive idea,

& improve it,

to get the bugs out,

making that technology comfortable

for us.

Call it a revision, if you want.

Does anyone have a link or editable file (.docx, .pdf)

to the thorough calculation (comprehensible)

for the Michelson & Morley experiment 1887?

I noticed or suspect the 2nd mirror's 2nd coordinate

might be at rest, & I just wanted to check the official calculations

to be sure that is not the case.

A historical rundown (briefing) would also be helpful

as to what Lorentz did. E.g. Status report.

Indirectly (re)states the bipolar, pair law.

 

Strange said something

about a zero momentum frame

that bugs me, (=drives me nuts, up the wall)

because it is so naive.

 

"There is (always) a frame

where the net momentum

is zero."

 

Big deal!

Whoopy do!

 

1. Can we measure it?

That idea is in his head,

science is (about) measurement.

Reproducing methods

& facts,

not just silly ideas (in our heads).

 

Does it tell us anything? Yes. (Almost nothing! It's so naive!)

 

2. If New york & china are both near dusk,

1 experiences sunrise

while the other (experiences) sundown,

then the (earth's) net speed to & from the sun is zero.

Conclusion: does the earth still rotate?

 

3. I have a gas pressurized in a bottle,

it's net momentum is zero.

Thus, no pressure?

 

4. The net force is always zero (Newton's 3rd law, reaction).

How much do I weigh?

I can tell you, anybody's net weight is zero,

the scale always counteracts.

The net force in the universe or anywhere is always zero.

The net momentum anywhere, is always zero, everywhere.

Boy have I said a lot.

What have we learned? Next to nothing!

Forces are always created in pairs.

Momentum is always created & destroyed in pairs.

(The same applies to energy, although physicists don't want to agree.

Restated agreeably for them:

physicists don't want to agree, that bipolar energy also exists,

although Gibb's (free) energy is used in chemistry.

Somebody has managed to polarize energy,

if physicists can't.)

 

Telling me the net is zero, only tells me the pair law. Naive(ly).

It doesn't tell me anything (else), quantitatively.

It doesn't tell me how much.

Strange's net zero momentum frame

doesn't tell (about) the constant (unstable) jitter (that happens),

as the direction differences & amounts continually change!

The (momentum formula) statement

mom-mom=0

is so naive

& meaningless

because stated so

it assumes

the total momentum (macroscopically)

has already cancelled,

which it hasn't.

Microscopically, each molecule

is moving

in it's own direction

at its own speed.

At worst, the equation should read

mom=mom.

(Or just plain momentum,

without an equation.)

In other words

the entropy**=k*mom

of all coordinates

(e.g. both of all 3 (xyz), =6 axii directions)

not just the silly net (is zero),

(that) says something more

than just zero. (=Such stupidity,

we still love ya Strange, but that's too little

for me to be fascinated with.

I can't hang that (zero) out as useful, for telling the details.

Stating the pair law (so)

says next to nothing. (=Too naive.)

 

**The thermodynamic mom (non polar)

(cause for temperature, & pressure

of a gas volume)

says something (quantitatively);

instead of (naively) nothing.

 

 

Feel free to attack, this hubris, you would call (it so).

Maybe you can change my mind?

(You've locked just about everything you can get your hands on from me.)

I appologize for the rude style, in advance,

but I don't know how to get the message across better.

10. Don't listen to anything, do what you want to do.

Go for your calling.

I would find it a pity, that you did not follow what makes you happy, with such a love & dedication.

But be prepared for a very difficult way, to overcome poverty (& master). Choose the most harmonious way.

Right now doctors are (over) demanded, but as technology develops, physicists will be needed, to solve future problems.

Doctors will need physicists. Perhaps think of a joint major biology & physics. Your plans will change in the future, nothing is static, everything changes, we must adapt. Interests change. We become more choosey, & we cannot plan our whole life, only part of it.

Something new always comes along. Later you will be more mature, to get a better scope, for the next direction. Decide to enjoy, & learn a lot. There is so much to choose from. The world & beyond will be available to you, not just greece. Nitches have to be found (=discovered), that special place where you fit in exactly, or to the best possible.

Maybe you can start in physics, full gas, the 1st year, & migrate to medicine 2nd or 3rd later years, but those are lost years financially, but for a love, worth it. It seems more & more surgeons are operating on distant patients thru telecomunication lines. Good solid technical knowledge is needed, for the future challenges & difficulties. You would have the advantage (that can mean more money when you can do what others can't, you will be in demand. It depends how you sell yourself & if you want?) Take care. Try to please all (don't forget the love for your fellow man, they will help you, some at least), but most yourself. Remember in the end, you are responsible for what you do & decide. In the end you (alone) must deal with (all) the difficulties that await you, including caring for your family & their difficulties (that come). It would be nice to find the perfect package, the best selection, mix that works best with the most advatages, & least disadvantages. Concentrate on your strengthes, to support your weaknesses. Not everyone is capable of all things. Each person has at least 1 talent. That is a natural thing. Some say god given. Use it!

 

 

(We are here to help each other, because we cannot live alone, completely on our own, without that. We need others help. E.g. Everything that is produced for us, to buy &/or for free.)

There has to be a force on an object in order to have it move in a circle.In the presence of a net force, momentum is not conserved. F = dP/dt

If we equate flow of momentum with force, could you elaborate there?

Yes, there certainly are.

 

Consider an object of mass m moving at a speed v in a circle of radius r. Energy will be conserved; here we simply have kinetic energy. 1/2 mv². But momentum will not be conserved*, because circular motion requires a centripetal force, and forces change momentum. The force does no work, however, because it is is always perpendicular to the motion.

What happens to the momentum there*? Is it safe to say momentum is continuously transferring from x to y axii & visa versa (when z is the rotational axis)? In other words we never have a (permanent) stable value of momentum for any coordinate. Instead we have a varying flow of momentum. The momentum value is always changing, but in a complementry way, so that what 1 axis looses, the other axis gains, & visa versa. ?

Have we forgotten something (that might help explain)?

 

https://www.physicsforums.com/threads/scalar-quantity-can-it-be-negative.407547/

 

Scalar is the magnitude

of a vector.

I think that's the best description,

(that they described)

it excludes the direction part of a vector.

In other words if you had to describe,

"both" parts of a "vector",

1 is its amount, the scalar (quantity);

& the other is its (orthogonal=90 degree)

"bidirection" (="double" 90 degree or orthogonal as)

possibility.

 

That is a subtle (2+1=3) triple meaning,

buried hidden inside.

We're dealing with (double) 90 degrees,

without saying it.

Instead (we say) 180 degrees (for the bidirection, minus).

 

At least, that is the most meaning(ful) definition for me.

 

As soon as we set (define) where zero is,

for a negative polarity,

we can have minus (=180 degrees).

 

But the unique thing about vectors is

they are about "direction", (in 3D space);

that's not just position.

It has to do with that 90 degree concept (orthogonal)

of the axii (x, y, & z)

to each other.

 

That has the most meaning,

in my definition (perspective, =way of seeing things).

It distingushes what it's all about,

by taking a specific example

for a/the example,

to explore & test the concept,

& help (self)define it.

 

Anti-thesis:

 

Then if we take temperature (called a scalar)

we can see that [it] has no (x,y,z) direction. e.g.

if we rotate the thermometer thru the (different x,y,z) axii a bit,

for the negative temperature (e.g. -10 C),

the negative temperature stays the same,

it does not depend on 1 of "6 directions" (+/- x,y,z).

(Celsius) Temperature does not depend on (+/- x,y,z, 90 degree) "direction",

although it has negative (=180 degree=opposite) polarity.

 

That's just taking practical examples to help (explain) define

what it's all about.

In the end, we find out we are dealing with 6 main directions,

written in a very compact form (+/-x,y,z).

That's what vectors are all about, (wrt zero).

 

Ruffly said.

 

Back to the basics.

 

(Strange I can feel your criticism,

is this website tapped?)

As you say: it is theory which, in science, means that it is based strongly on evidence.

Yes, it's based on evidence, (that's nothing really remarkable, it's rather common, we observe (often=most of, all the time) how things go, thus also get an idea, of how they don't go too. Putting formulas to them helps reassure us even more,) it doesn't have to be perfect as can be seen but it is an attempt to fit things correctly into the picture of reality. How close we get to an accurate picture is another thing, qualitatively.

It didn't come from thin air. It came from measurements of energy and temperature and their relationship. It is already practical.

Yes, to a fair degree (=mostly). But sometimes you have to iron the bugs out. Or can you say it's 100% accurate, everywhere, all the time. The devil is in the details. If you're 95% accurate, most people are happy. 60% is a bit ugly. If 1 extreme of a curve looks good but the other end or the middle doesn't, then it's back to the old drawing board, trying to work the bugs out. It bulges & heaves if the assumptions are wrong, or off. It's a real world, little seems completely (=100%) perfect. It's always better to have some sort of theory than none. But some let sure question, considering the accuracy. I think that's obvious though. We're not perfect, how can our theories be expected to be? It's obvious, we can see (=notice) trends, & we try to describe them as accurately as possible. Theory is intended to help, most of the time (it does).

 

The formula I gave you, for water's boiling temperature also has problems (T^4 vs 3D volume?).

(E.g. Why 2 different exponents ^4 vs ^3?)

I can only guess, (=suspect, & this is a "speculation" website):

Maybe concerning 0 K, although it's (my formula is) in Celsius, having a limited temperature & pressure range (that were not mentioned, i.e. critical point 373.946 C, at 217.7 atm (22.06 MPa) ref Wiki). IAPWS-95, & http://www.iapws.org/faq1/boil.html

It's such a large website, but I find the frequently asked questions, most explainitory, & easiest to follow.

Further menus are available, for depth, if you want.

Thomson calculated the earth's age to be about 1 million years old based on the temperature difference,

wrt depth down into the crust (vs cooling effects), if I remember correctly.

Didn't that premiss affect the calculation for determining 0 K?

Anyway, we all know the earth's age is much older, because of dino fossils, sediments etc.

& Lord Kelvin was no dummy, but his calculation doesn't fit our facts.

(There are lots of paradoxes in science, you or I only have to stubble on them, to find them. Those are the bugs I mean.)

That formula does show my interest in thermodynamics, since I've achieved a simpler formula fit, that is easier than your scientists have. We can squabble about the accuracy, & typos if that is all you want to do.

I used their data to help derive it.

 

Such a frame is guaranteed to exist, so it is not exceptional.

It's not so much the frame's uniqueness, as it is to "how" you want to use it for all cases that is the error in your deduction. You've already excluded, certain things, by choosing only that (kind of) frame. You can not expect me to include those (exclusions) for further applications. That would be breaking the rules.

 

The use of that frame is part of the definition.

Please don't put the cart before the horse. Your priorities are reversed. You're taking a special example (=exception case), having success with it, & then falsely believing you can use the same method for all cases, because it worked well in the exceptional case.

It's like let's look at families with boy girl twin pairs no other extra children (balanced relations for momentum analogy), we conclude they run well (kinetic energy analogy). Conclusions are fine. Now we try to apply it to any type of family with unbalanced boy girl ratios. Doesn't work. The balanced pair was the exception, not the rule. Is that too abstract?

 

You have not shown any such thing (math example).

Yes, I have shown you a math example,

1 of the simplest

with only 1 particle,

but it is "so obvious"

that you ignore it as trivial

& thus wrongly argue that I have not shown it.

You do not acknowledge my calculation, at all,

although you do acknowledge (1 particle failure) independent of me.

That is "Strange" Strange.

That's not something you do not know,

you know it already,

& reject that I remind you.

That's a mind game, against me.

 

It is always true in one frame of reference.

If you mean the special cases that you mentioned,

where total momentum is balanced to zero

& I suspect you do,

I find it difficult to believe "always".

However, to give you the benefit of the doubt,

let's say they did (even if they didn't).

You are still only dealing with a special case.

What are you going to do about other frames that don't have that momentum balance?

Ignore them?

e.g. 1 particle, &/or 2 particle orthogonal.

 

 

Because, as explained, it is irrelevant.

I'll assume you mean by "as explained":

needed effort to understand,

math error momentum was shown to be not (balanced) to zero

for an alone single particle.

There is an effort to understand,

& maintain reasonability.

I'm not biased for no reason.

I've tried to show my reasons for my decisions.

(They are no secret.)

You can attempt to change them (my conclusions) from there.

Only the anti_thesis can change a person's decision,

stuck in their ways.

E.g. You tell them what it isn't.

(But why present, what you do not trust?

Why should I either?)

Can you please provide an example when there is not a frame in which the total momentum of an ensemble of massive particles is zero?

Good (=sly) question. I never assumed a frame had zero total momentum. It's (=zero total momentum is) a nice (neat) idea,

but it's an assumption. I can't say whether the total momentum is zero or is something else, at any time, because I can't measure either, yet. The concept of using large massive particles makes the idea (task) easier. I'll have to give it some thought. But at present, I have no other idea to become an extra example; other than a room of spinning tops, or the the solar systems' spinning planets, or a glass of water from a microwave oven, before the water molecules slow down spinning, from banging into each other, producing random linear motion heat temperature speed.

 

Your example of two particles both with orthogonal momentum, the zero total frame* is moving at 45 degrees to them both relative to the original rest frame.

I'm sorry, I didn't quite follow that*. Maybe I missed a word there?

Are you saying you derive a common frame which is zero speed relative to all particles, in the container?

In that (case), can then, that common frame be moving relative to the stationary container,

& as you said be moving at 45 degrees to both particles?

That's an interesting concept, but it tells me the net momentum in the container is not zero, it is the sum of those 2 particles,

in other words that common frame itself (is the total momentum) (relative to the stationary container).

1st, I consider the earth as the rest (reference) frame, unless otherwise stated.

That's obvious, & redundant (rebose) for me (to state).

Maybe you scientists have other problems I don't know about,

but I'm happy to have my feet on the earth (as ref)

& keep the language simple, if possible,

because it (often) gets too complicated & long.

E.g. If I'm moving in a car, we have a different story,

but if we have a beaker or container sitting in the lab,

what's the bother?

 

Also, when giving speeds you need to state what they're relative to.

Dito, above. Relative to earth('s surface as ref) unless otherwise stated.

I like to think simply, not complicated like you.

(Whether I succede, being so simple is another question. I'm informal.)

Is that ok?

Most of us deal with this by learning when rules apply by understanding the assumptions that go into the rule. That way, it's not an error. The downside is you can't blithely apply a rule or definition all circumstances, but there are none which would work that way anyway, so nothing is really lost in this approach.

 

That's not a bad arguement. I mean we try to do our best, & improve where we can, if possible (rare).

E.g. Zero (e.g learning) to hero (e.g. all), but maybe the gray (steps in) between them too.

Then why claim it is wrong?

Because it's incomplete, its only an exceptional observation, not the full story for a basis of analysis.

My beef is stated further below with what bugs me there. It's incomplete.

 

You cut off the quotes too short to make any sense, sometimes.

So I repeat, I agree that there is a connection between thermodynamics & the kinetic energy of the particles .. of a material. There on that statement I agree with you.

For me that is obvious. Kinetic energy influences their temperature.

You said it, a "clear" connection. =Very obvious.

 

Do try and stick to the subject.

Yes, I think that was a fair question. What did Maxwell work on there concerning thermodynamics, so I can orient? I mentioned Boltzmann because I don't think too many people know how ruthless science can be.

We're dealing with people, representing it. Boltzmann is spelt with 1 l, & 2 n's. (Gosh! I almost spelt it wrong too.)

 

Let me repeat the sentence you claim is incorrect: "The basic kinetic theory of gases tells us that the temperature is the average kinetic energy as measured in the frame for which the total momentum of the gas is zero."

 

There is a frame where the momentum of that particle is zero. There is a frame where the total momentum of two particles is zero. There is a frame where the total momentum of all the particles is zero.

 

You need to read and understand what is said before leaping to claim it is wrong (because you haven't even bothered to read it).

If you want to know what I don't like there (=disagree with) is, first it's pure theory, somebody's idea, it didn't come from thin air, & I begin to start looking for the practical real side of things.

You've stated those frames in which the total momentum is zero, but that does not happen all the time.

You can describe those exceptional circumstances, but that's not enough for me. I can't close my eyes for the other times when the total momentum is not zero. There is more to the story than just the perfect ideal situation. The (almost rare) frames when total momentum is zero is not a basis for me, because it's not the whole picture. It doesn't happen all the time. (That definition was an attempt to eliminate all other motion except random motion for heat & maybe pressure, but it didn't work, it failed, falling on its face in the very first step.) You can do your thermodynamics the way you have been taught, but it's not acceptable for me so. Sorry. It can not be used all the time, as was shown. Zero total momentum, is not always true, so generally it is false. It only has a limited theoretical application, where it is true, & so there it must stay. If you want to do more than that, then you must use something else. Are we making any progress with (some sort of) agreement between you & me? I'm interested in the bigger picture? Are you?

 

 

If it matters to you, then you need to make an effort to understand.

 

Until you either show an error in the mathematics (which despite your wild claims, you have not done)

I demonstrated the math above,

but (ashamed?) you did not quote it.

 

or some evidence that contradicts current theory, it doesn't matter to science.

Your kinetic gas hypothesis has failed from the very beginning for me.

I start with nothing, & then begin with 1 particle,

& work my way up.

That it cannot support the very 1st instance is a total collapse for me.

There is no basis of support. It's a matter of good luck that it works so long.

Pisa's leaning tower was also built on weak foundation, but it still stands!

What a mesterpiece.

 

Water's boiling temperature has been fit to

Tbc=(Pb*Vb/(mol*Rb))^(1/4), [degrees Celsius)

Pb=1 atm pressure

Vb=0.02214 m^3 volume

mol=6.0221367*10^-23 Avogadro's number

Rb=2.2711*10^-5 [Pa*(m^3)/(mol*degrees_C^4)]

 

You might be more familiar with it so

P=mol*Rb*(T^4)/V.

 

The energy

P*V=mol*Rb*(T^4)

is related to the temperature

with 4th exponent;

unlike the ideal gas.

 

Don't be ridiculous.

I'm quite serious. Consevation of energy & momentum.

I don't throw them away before the last particle,

like you want to. I "try" to be consistent.

Temperature is a property of bulk materials, collections of particles. That is the definition. It doesn't apply to single particles.

I don't see why not. The total is added, from the sum.

0+1=1 sum.

The math should be exact.

Anything else is an approximation.

 

If you want to define some other property that does apply to single particles, then go ahead. But I assume that will just be kinetic energy (in some frame of reference).

Exactly. Why reinvent the wheel, when it already exists?

KE & momentum are sufficient, enough.

I need no other property or significance that I know of yet.

Thus it will do.

So because you don't understand what 4-momentum is, you assume it must be wrong. This seems typical of your approach.

 

This, again, seems to be an example of "don't understand therefore wrong".

If you think so. ? This time you are making the conclusion from your assumption, not me.

Btw. Did I say 4-momentum is wrong? Did I say I assume 4-momentum must be wrong?

I'll assume your 1st of 3 assumptions is correct. That's 2 against you.

 

There is a clear connection between thermodynamics and the kinetic energy of the particles in the material.

I don't disagree (=I agree).

This was worked out mainly by Maxwell and Boltzmann I think (this is not a part of history of science that I have studied) and is not an "assumption".

Bolltzmann hung himself, while his family went swimming. Probably too many enemies. They didn't like his stuff (probably) as bad as you don't like mine. Maybe a lot worse.

What did Maxwell do?

 

Please show in appropriate mathematical detail that it does not work.

mom=m*v

only 1 particle in the container has mass m=6.646*10^-27 kg

& speed v=100 m/s moving right, from middle in the stationary cubic container 1 m^3.

The particle's momentum is thus

mom=m*v=6.646*10^-27 kg*100 m/s=6.646*10^-25 kg*m/s.

That is not zero momentum.

Thus the total momentum of the particle cannot be zero.

Proven.

 

Normally we prove something works;

but here for scientists we have to prove they don't work

even when they admit they don't work. (See below.)

That sounds a little crazy to me.

It hints however, the task is possible (=not impossible).

 

Even if I had 2 particles, there could be times when 1 particle could be moving verical(ly up, as example),

while the other moving mostly sideways (horizontally).

Even there in detail we cannot always expect all momentum cancels to zero.

 

Yes. I would suggest that you stop taking your lack of knowledge as the "litmus test"

for whether science is correct or not.

What? Do you mean to turn the the scientists from red to blue? (pun intended).

It doesn't really matter if it makes sense to you or not.

It matters to me. (It's a lousey job, but somebody has got to do it.) So again you are not correct. Sorry.

 

I think everyone agrees that the definition does not apply in the case of a single particle. So I am not sure what your point is.

That was my point. It does not hold for that case, thus the definition is inferior. Throw it out. Don't try to hide its mistake as an exception just to maintain the nonsense. The definition is faulty. You can't win them all. The chain is as strong as the weakest link.

If it doesn't hold, the chain breaks. I don't know why you take pride in keeping an error? It indicates the premiss (assumption) is wrong.

How valueable is that if it leeds you the wrong way (without knowing)?

 

Please allow me to show my spontaineous "reaction" here, we can discuss reasonably later. What is 4-momentum?

Loosley, in special relativity you combine the momentum with energy to build a vector.

That is (for me) crazy, it looks so backwards if combine means something like multiply instead of divide. KE=mom*va.

(Momentum mom=m*v, m=mass, v=v1-v0, va=(v0+v1)/2, v0=initial_speed, v1=final_speed.)

The basic kinetic theory of gases tells us that the temperature is the average kinetic energy as measured in the frame for which the total momentum of the gas is zero.

"Moment!" "Who" came up with that 1 on momentum? It's got to be "somebody's" .. idea (assumption).

That is obviously an error for me to see. To err is human. It doesn't work & everybody is happy with it.

It's trying to say the average momentum (+ & -) adds to zero. But does not apply for only a single particle,

otherwise it would illegally rob that particle of its momentum. "Somebody" didn't think that statement out to the end. They goofed. Or do I see things wrong?

 

So if we have only one particle then this definition has little meaning.

Correct, so we can dismiss that definition (as Strange would say), & start again to reconstruct a more accurate description.

 

I guess one can do lots of things to construct vectors, but that does not mean they all have any physical meaning.

Pity. If we're loosing meaning, then we're off the right track (for physics).

Most mathematics starts with set theory.

 

A set is the posh mathematical name for a collection of (mathematical) objects, although there is some argument about this and the words class and type have also been used.

 

By itself a random collection of objects is pretty uninteresting and useless, mathematically.

 

So we place restrictions on the objects.

 

Usually we require that all the objects are of the same sort (eg all numbers, all vectors all angles )

We often require that there is only one appearance (instance) of any particular object.

 

But this is still pretty boring

 

So we set down a list certain properties that all our object must possess.

Obviously there are many possible lists so centuries of thought has gone into what should be on a particular list.

 

We call such a list 'the axioms of our set'

 

and a space is the set of all objects that obey they axioms.

 

So a vector space is the set of all objects that obey the (8 or 9 ) vector space axioms.

What are those axioms? Are they written only in sentences like Euclid did?

Perhaps with helping formulas too?

We call these objects vectors.

Can those vectors be more than just arrows? length & direction.

Or is the distinguishing idea, the name of the (group) "space"? with only length & direction?

That brings up the question: Is my concept of vector outdated?

Has the definition evolved into something more that only direction, & magnitude?

(E.g. We can't rely on definitions, they change each year? or few (decades)?)

 

This gives the set some useful structure and justifies introducing a new word (space).

Yes, but isn't the word space old, & was already taken (in physics?) meaning something like volume?

E.g. Outer space.

Or is it more intended, like a (e.g. mailbox) slot, where we store info? E.g. Something reserved for info (list). ?

 

This structure allows us to perform mathematical operations on the vectors in the vector space, which is why we go to all that trouble to spout all that terminology.

 

There are many different vector spaces and that part of mathematics devoted to the study of these is called linear mathematics.

This is still probably the largest part of mathematics since most applications are linear.

 

 

You have a knack for digression by introducing new words that you do not fully understand.

Yes, too curious.

 

So it was good that you acknowledged this.

I try.

This post was designed to help there.

Thank you. The vocabulary (syntax) unsures me a bit, that mathematicians can call things the way they like, ignoring previous definitions, from other subjects. Its almost as bad as me? e.g. space, unless I've misunderstood. ?

 

You also made some very good comments on my post 43 (your post 46)

Thank you. It's nice to hear some encouragement, once & while, while the lions roar (=threat) & the sheep say bah! (=disagree, scoff).

 

If you like this post I will return to the subject of momentum, conservation and invariance and those replies.

Oh yes, please do!

 

At the risk of seeming rude, you should really learn some mathematics.

Theme: Just to confirm.

If we just have a vector space, then there is no notion of multiplying vectors together.

I'll assume you mean, empty as a vacuum, in (something like) x,y,z, coordinates. (I don't use polar coordinates much, because they are in angles. ? The idea there is I don't have a simple formula for angle, only a conversion exists &/or Taylor's series or something like it.) Since it's empty (=no structure, yet) no algebra applies. Then it gets interesting. We suddenly talk about something (e.g. algebra, no longer empty space).=

 

If we have further structure, say that of an algebra then we can multiply them.

The context of the structures is important.

If you just mean vectors on R^n

n is normally something like 3 for 3D. ?

My idea was to use a scalar A that also had an exponent ^n.

In other words take a simple scaler B & root it to the n, to get A.

In that way A could be merged with R, so both could be together with 1 common exponent.

An art or kind of scaling, together, if you know what I mean?

B^(1/n)=A, B*(R^n)=(A^n)*(R^n)=(A*R)^n.

It was just a guess (no rigor) if some of that could apply?

Naturally dot product must also recognize the angles between with cos (angle) factor(s).

E.g. That syntax probably does not apply?

Swansont probably wanted to see

the vector dot product as

U*V=u*v*cos (theta)=U1*V1+U2*V2+U3*V3

for the 2 vectors U & V, with lengths u & v

& the angle theta between them

& their components 1,2,3 (for ruffly x,y,z similar).

Vector cross product as

UxV

(U2*V3-U3*V2)*i +

(U3*V1-U1*V3)*j +

(U1*V3-U2*V1)*k

which is a vector

perpendicular to the vectors U & V,

with components postscripted 1,2,3,

& length u*v*sin (theta),

unit vectors i,j,k (again for ruffly x,y,z).

then we do not have a canonical

Please define canonical in a few words please.

My mind flips to different meanings, confusing me.

Please limit the definition to what you mean.

method of multiplying vectors.

This* is one of the axioms of a vector space... you should know this.

Are you saying yes, scalar multiplied by vector gives a vector?

I simply need a bit of confirmation, to the things I heard long ago, to get started.

That's why I say assume. I seemed to have lost track, what this* was, & got a glimse later what it could be.

One day I'll pluck up courage and look at non-Euclidian geometry.

Enjoy it!

 

Einstein said:

Work+Fun=Success.

 

Cheers.

Up till now whenever I see the word "Non-Euclidean" I switch off. I have not even attempted to master that yet. Have you understood it fully?

Hi, I'm fascinated with your observation, even if the rest aren't.

Euclidean geometry is straight line geometry.

So non-straight geometry is curved.

It doesn't have to be an exact circle, either.

They** (=the math world) make the distinction, because straight line is easy y=m*x+b, known.

(It's linear, x is the culprit, with a factor m which makes the slope (affecting the angle);

& hang_on "+b" which is the offset (raising it) up the y_axis.)

But things can get a bit squirrelly when they start to curve.

A circle is relatively easy (=known, uses rooting which begins to get complicated), but things get more complicated when they are not exactly obeying pythagorus r^2=x^2+y^2.

In fact very many curves have nothing to do with circular geometry.

Best wishes to all.

 

Theme: (non)Euclidean.

 

** If I said we, it wouldn't be in laymans terms. Informal to get the idea across.

 

Euclid was a greek & invented it (straight line (=Euclidean) geometry) with only sentences

(observations written down, now known as laws or axioms, something like that.)

So they named it (his work) after him.

 

non_Euclidean: It's everything else, which is not straight (no exceptions).

How are you measuring your speed - you are measuring with respect to the road. There is no such thing as intrinsic velocity- ie velocity which can be measured without reference to something else.

 

Yes, I think you are only repeating what was agreed upon in #52 & #53.

All speeds are relative, no exceptions.

I do not know why you are doing that repeat. Did I miss something you wanted to say? Please explain. Maybe I missed something? Do you know what it is?

At the risk of seeming rude, you should really learn some mathematics.

I will try to take it to heart. With all you say below you make me curious. My problem is finding a book .pdf that will maintain my interest. Perhaps I need a fly over & then details, to maintain perspective.

If we just have a vector space, then there is no notion of multiplying vectors together. If we have further structure, say that of an algebra then we can multiply them. The context of the structures is important. If you just mean vectors on R^n then we do not have a canonical (rule) method of multiplying vectors.

(Why not A^n factor as well? So you can combine A with R before exponentiating? Or am I too far off, naive?) Is there any reason why you use the church word canonical? Or am I astray again? Referring to a canon (e.g. ball) instead?.

This is one of the axioms of a vector space... you should know this.

If you say, I wish I did. I just haven't made the connection. I know too little.

 

Even your word vector space confounds me because I think of lines or arrows filling a volume.

I begin thinking about filling a volume with points instead.

I do not bring the math vocabulary in connection with reality.

 

Let us first get the orientation correct (standardized) & say northward is positive, & southward is negative.

I will quote your text with that correction made.

So if a car going up the motorway from South to North has 700kJ of kinetic energy does a car on the opposite carriage way (going down, North to South) have -700kJ of kinetic energy?

Yes, (it is the same way as) how would you describe the momentum (while ignoring KE for the answer).

The momentum would have similar polarities. We determine that (direction) based on our earth reference seen to us as stationary. For all practical purposes. We have created the math construct, not nature. It's our job to make some sense out of what we do, not natures.

 

As both the cars started from being parked - with no kinetic energy the car travelling north must have somehow used its engine and petrol in its fuel tank to gain 700kJ of KE; but hang on,

(to what? pun intended)

the car travelling South has -700kJ (that's) less energy than it started with - has the fuel tank refilled itself?

No, obviously not. You don't seem to be adhering to the rules of vectors. If KE is a vector, then you must also use those vector laws to explain its behaviour. KE is bidirectional. Dealing with it as though it is (only) a scalar is not acceptable. That won't work.

 

(Chemical energy, is expressed as Gibb's Free energy, in "both polarities", for determining if a chemical reaction will happen spontaineously. Negative difference is spontaineous. E.g. burning carbon with oxygen is only spontaineous beginning at a specific hot temperature. The chemists seemed to have taken this (bipolar energy) concept further than you Physicists. It's not new, just for you maybe?)

 

Look at it so, (I know it's not a good example because a lot more happens than I will simply say, but let me simply say it).

Please change the energy of both cars so they are going very fast (MJ?, GJ?) each ~100km/h & opposite directions.

 

If each car started near the (geo) pole(s), & a (thick) wall was at the equater,

then each car would receive a dent when colliding against the wall.

 

If there was no wall, & both cars collided together,

then each car's dent would be, let's say double so deep.

Their energies, would have added, similar to the way it would have added with momentum.

 

There is really not much of a difference between the 2 concepts energy & momentum,

because they both use the same 2 units, (m & v)

but with different amounts,

thus they are scaled differently,

that's all.

KE is simply scaled momentum.

The scaling "factor" is va.

KE=mom*va

Mom is the vector.

KE must obviously be a vector also.

But va is also a vector, instead of scalar.

 

I can't say it very well,

but maybe you can get what I mean?

Please restate it in your own words,

I'm sure you'll do a better job at it, than me.

 

Is that ok?

You need to think what multiplication of vector means... you need to brush up on the basic notions in linear algebra -- I have written a book on this! (almost I have some lecture notes that are not polished)

Yes. I said I do not know much about vectors. I need a few pointers. You may correct my assumptions. (There is not really much there.) I have only tried to make use of that little I know. For I know it is better to do much with less, than little with much.