1. Sub Quantum Echo Particles...(SQEP's) & Sub Quantum Echo Particle Kinetic Resonance Flux

[Imagine Everything]

 

It dawned on me during the last half hour, that perhaps my idea or the name of the 'thingy' is paradoxical as it stands. I have called this a 'nameless particle'.

But if DM or space or whatever that invisible stuff is can't be measured, then it couldn't be a particle or I'm sure you guys would have measured it?.

So I'll think about another term for it, I'm not sure what yet but in my unskilled brain I am wondering if 'nameless non particle' might be more apt for now.

Anyway so, I can't help but feel I am very very wrong about this but I keep seeing the resting position line of a wavelength in my head. Maybe I just need to put this to bed or maybe it's a 'something'. Either way I need to know so I can exclude it or not, when a wave length is at rest and it shows as a flat line (I'm guessing that how it's seen, sorry if it's a bad wag) could this resting position be interpreted as actually the possible non measurement, measurement of the 'nameless non particle' dm/space/other?

It seemingly isn't doing anything except simply 'being' (to me anyway without knowing more) and isn't that what space/dm seems to do?  (again without knowing more)

A wavelength can pass through a resting position which is energy? being moved?

In one of my many many weird and wonderful creation thoughts, I can visualise 'space/dm/other' as the resting position for everything else to pass through and be created within or even with.

And this coupled with the endless thought of 'something' not being able to be 'nothing'

Or ultimately I guess, maybe I am just reaching too far without the necessary knowledge to know I'm wrong lol.

 

I don't want to or mean to come across as spamming my own thread (is that possible?) but I'm going to add another part of this idea and how I see this 'nameless non particle' happening/working between people. Which I will do in a while so that it doesn't get added to this post.

 

Edited Saturday at 02:07 PM by Imagine Everything

[Imagine Everything]

ugh sorry, I wrote 'test' to see if the page was ready for me to write another post without adding it to a previous one but it took me so long to write the next bit that I couldn't edit the 'test' bit and post the following LOL.

 

 

 

The following is part of a chapter that was induced by the idea originally posted as SQEPKRF.

The simple State 1 BC1 next to State 2 BC2 exchange/merger/creation idea progressed into more areas/chapters and this next bit is from one of those areas/chapters. I still don't know if this idea is feasible or not and I'm still obviously trying to learn more so that I can prove or disprove it.

BC refers to Boundary Condition

The personal aura.

I referred to this as a resonance before but perhaps, knowing more now, I should refer to it as aura.

So I see this BC exchange as being within all state BC's meeting. From fundamental particles all the way up to the more massive masses in our universe.

Regarding people, I don't know the entire physiology of the body but I see this 'nameless non particle' as being created within us as well, and within everything that makes our body that makes us, us and for this bit, I will refer to just 2 people and the 'space' between them.

So starting from the quantum level and then all the way through the different items that make our personal bodies, I see this as being produced through State BC exchange and that alone is significantly numerous and also unique and different for all of us or we would all be the same.

Thoughts for you to ponder...have you ever looked at your phone or thought about someone 'randomly' only then for that person to ring you a few moments or minutes later?

Have you ever met someone or seen someone and been repulsed or attracted to them for a seemingly unknown reason? You just simply 'feel' it.

A couple or close friends perhaps that have spent a long time together seem to know what the other is thinking or about to say.

Or even said something at the exact same time?

I see this 'nameless non particle' as the possible reason this happens. I see us having our own unique aura and this interacts all the time, everywhere with the 'nameless non particles' outside of our bodies and that the 'nameless non particles'? also act as a conduit/medium of sorts that also connect to another persons, personal 'nameless non particle' unique aura.  And possibly a lot more.

I see this as happening all the time, everywhere and perhaps if I may use it analogously, we only feel or think about the other person when we see or think about them but only then, superpoistioned if you will until we 'measure' it.

By measure I mean looking or thinking about the other person. And when that happens, we 'realise' or tune into that connection on a very deep, quantum level.

On a quantum level, I see this as information being passed between each persons nameless non particle' aura and being collected and then processed by our brain into thoughts and or feelings.

I see it as basic information which is interpreted and made sense of by our brain allowing us to form an opinion (for want of a better word) from it.

I see this as potentially covering illness too. I know that there are physical reasons for being ill but even those physical reasons have to start somewhere, on a quantum level whether fast or slow, such having a limb cut off (fast) or getting a virus (slow).

 

That's a very very short version of  this area from this nameless non particle' idea. I just wanted to show you I guess that I see this idea working in many many ways.

If I zoom out a bit as it were and incorporate more than 2 people, the idea gets even more very complex (if it isn't already lmao)

I mentioned quantum travel too I think originally but hmm, perhaps that part really is a wag, having found out more about atoms, fundamental particles and fields since then.

I still haven't proved this and without being able to prove it yet one way or the other, I think the idea itself and what I see it as doing could and perhaps will fall down like a house of cards. If the original simple idea is wrong then I suppose so is the rest of it lol.

To be honest, I really thought it would fail instantly when I posted it. I was pleasantly surprised that it didn't. And also humbled by not being seen as the 'usual crank' you sometimes get on this forum.

I am also still gratefully surprised that I am able to still be talking with you about it and also the things I need to learn. Thank you for that, all of you.

I would just add that the word aura is borrowed from my short time in a few spiritualism groups and perhaps better describes the definition than 'personal resonance'.

I won't post another chapter, I still have @Phi for All wisdom in my head about keeping it as short as possible.

And I have tried to, honestly.

 

 

@swansont Just a quick question, going back to my hypothetical hanging in space, trying to understand better what you told me, would that mean that the spacesuit I'd be wearing would have gravity and that my mass would be producing it? Even on a very small scale.

Edited Saturday at 04:20 PM by Imagine Everything

[Genady]

31 minutes ago, Imagine Everything said:

to see if the page was ready for me to write another post without adding it to a previous one

It takes 1 hour.

[studiot]

Just now, Imagine Everything said:

would have gravity

Not a good way to think of it.

It takes two to tango.

Gravity is a phenomenon that takes place between two or more objects.

Since most objects have an actual size, the various parts of that object display that phenomenon between each other.

Gravitational Potential is an imaginary field that records the strength and direction of that phenomenon at any point in the field, were we to place a material object there. But until we do it remains imaginary, which is why it is called potential.

Edited Saturday at 05:25 PM by studiot

[swansont]

1 hour ago, Imagine Everything said:

Just a quick question, going back to my hypothetical hanging in space, trying to understand better what you told me, would that mean that the spacesuit I'd be wearing would have gravity and that my mass would be producing it? Even on a very small scale

Your mass and that of the spacesuit each would have gravity, owing to the mass of each. Your attraction to the suit would be small compared to the gravity just outside the suit, because inside there would be cancellations. If the suit were spherically symmetric, the cancellation would be complete and the suit would exert no gravitational force on you.

[Imagine Everything]

54 minutes ago, studiot said:

Not a good way to think of it.

It takes two to tango.

Gravity is a phenomenon that takes place between two or more objects.

Since most objects have an actual size, the various parts of that object display that phenomenon between each other.

Gravitational Potential is an imaginary field that records the strength and direction of that phenomenon at any point in the field, were we to place a material object there. But until we do it remains imaginary, which is why it is called potential.

Thanks @studiot, your answer helps me understand it better. Also didn't know it was a relationship between 2 or more objects. That's quite interesting. Always thought of it as being something that held things down, rather than interacting with other objects. Starting to think a little differently about BH's now. But that is of course a whole other ballgame.

I don't know if you saw btw but I answered your question about a wave colliding with particles. I only mention it here as I seem to have buried it with my last few posts.

 

44 minutes ago, swansont said:

Your mass and that of the spacesuit each would have gravity, owing to the mass of each. Your attraction to the suit would be small compared to the gravity just outside the suit, because inside there would be cancellations. If the suit were spherically symmetric, the cancellation would be complete and the suit would exert no gravitational force on you.

Thanks @swansont,  it gives me a better formation of it in my mind now.

[studiot]

Just now, Imagine Everything said:

I don't know if you saw btw but I answered your question about a wave colliding with particles. I only mention it here as I seem to have buried it with my last few posts.

Did you mean this ?

 

Just now, Imagine Everything said:

A wavelength can pass through a resting position which is energy? being moved?

 

Not quite sure what you mean, but yes I did say that waves could travel through material objects.

 

Incidentally the word particle has special significance in Physics.

Very many different areas on Physics have models or theories that rely on the interactions of huge numbers of very tiny elements which are called particles. They are the smallest bodies or bits of the subject theory that we can consider as acting as individuals and interacting with each other to produce the observed physical phenomena. These theories don't inquire as to what is inside the particle, just how it interacts with the others.

We spent nearly 2000 years developing th idea that the smallest piece of matter is called an atom.

Then at the end of the 19th century scientists began to realise that the atoms may be made up of yet smaller bits., which became known as sub atomic particles.
That is the famous history.

But in the 1930s a quiet revolution occured that is not so famous but perhaps even more startling and revolutionary.

They found out that there are 'particles' small enough to be sub atomic, but that never appear as part of an atom.

 

[Imagine Everything]

2 hours ago, studiot said:

Did you mean this ?

No sir, you said this and then asked a question at the end

Collisions are also interesting.

Being scientific about it you can ask what happens when two (or more)    something or anothers collide.

When matter alone is involved damage, deflection, chemical action, coalescence and many other results occur.

On the other hand when two waves collide, the waves can pass right through each other and come out the other side, undeflected, undamaged and apparantly unaffected.

So what do you think might happen if a wave collides with some matter ?

 

This was my attempt at an answer

Ok so I had a look on google and I think it is telling me that a wave is the vibration of a field.

So trying to answer your question, if a wave collides with matter then a few things go through my head.

The collision will create vp's and more vibration/Ke/waves? Which returns the vp energy to the colliding wave making it stronger? Slightly perhaps analogous to mixing different colours.

And then this is turn can create or decay particles if vibration is key to how everything is created in respect to their respective fields.

I'm kind of guestimating this but would that in turn also change the wave and then create a different field in the colison.

Is this then also why everything is superpositioned and then relative to the measurement of the wave looked at from different perspectives as they are all seemingly mixed up with each other like the inside of a golf ball.

 

Quick thought, is a wave a scalar and a field a vector?

2 hours ago, studiot said:

7 hours ago, Imagine Everything said:

A wavelength can pass through a resting position which is energy? being moved?

 

Not quite sure what you mean, but yes I did say that waves could travel through material objects.

On this part, I was wondering if a resting position line in a wavelength was similar toto the way space/dm/or another something' might work as particles/wavelengths can pass through space easily? (I dk if I shouldn't say that or not, I'm looking at particles ( as wavelengths, it's easier for me to visualise in my head. Is it wrong for me to think this way? Am I just confusing myself?

I went more in depth with it but I'm sure you guys might have had enough of my endless writing today.

It's the first post on this page. I was trying to ascertain as to whether a resting position of a wavelength (particle?) could also be a measurement but of something else. The actual line itself as opposed to the peaks and troughs.

My wonderful imagination is working overtime to try and possibly find out where or what my proposed 'nameless non particle' might be or how it might look if it could be measured.

If you measure a particle or vibration and then take the wavelength away and are left soley with the resting position.

One of the tests my idea has to pass is to be able to be created by every single particle wherever it is, whatever is creating it.

I'm nowhere near as knowledgeable as you guys so maybe that's a really stupid thing for me to say, Idk.

I see DM or whatever DM might be as being everywhere, going through everything, maybe a bit similar to a neutrino.

I'll admit I really haven't studied or looked at neutrinos much so far but after saying what I did directly above, could neutrino's be DM?

I do have a maths question for you too please

I'd really like to understand how this character works.

∑

What is the reference that goes on the top of the ∑ when writing an equation/formula?

What is the reference that goes underneath the ∑ when writing an equation/formula?

What do both top and bottom references represent? I have seen that this symbol itself represents 'sum' and I'd like to learn more so that I can use it or add it to my knowledge and perhaps come up eventually with an equation? formula? for how I see my 'nameless non particle' being created.

5 hours ago, Genady said:

It takes 1 hour.

Thanks btw, good to know.

Edited Saturday at 09:49 PM by Imagine Everything

[studiot]

Just now, Imagine Everything said:

I do have a maths question for you too please

I'd really like to understand how this character works.

∑

What is the reference that goes on the top of the ∑ when writing an equation/formula?

What is the reference that goes underneath the ∑ when writing an equation/formula?

OK so the symbol is the greek capital letter sigma and represents what is called a continuous sum.

It is really an instruction not an equation by itself, although it can form part of an equation.

Some examples might help.

[math]\sum\limits_{n = 1}^4 {formula\;involving\;n} [/math]

This is an instruction to form the sum of the squares of the foirst 4 integers  ( 1², 2² ,3² and 4² )

[math]\sum\limits_{n = 1}^4 {{n^2}} \;which\;is\;1 + 4 + 9 + 16 = 30[/math]

n is an index for the formula and runs from n = 1 through to  n = 4

Lazy folks may abbreviate this a bit to

[math]\sum\limits_1^4 {{n^2}} [/math]

This is a finite sum (n is finite) comprising only 4 terms.

Sigma may also be used to symbolise an infinite sum or sum to infinity.

[math]\sum\limits_{n = 1}^\infty  {formula\;involving\;n} [/math]

This sum may be used in an equation if there is a formula that gives you the answer directly

[math]\sum\limits_{n = 1}^4 {{r^2}}  = \frac{1}{6}\left( n \right)\left( {n + 1} \right)\left( {2n + 1} \right)[/math]

 

Note capital sigma should not be confused with little sigma which is used for an entirely different purpose.

 

Sigma is for summation.
There is similar symbol for multiplication  called continuous products.

This uses the greek capital letter pi insteat of sigma, but works in the same way.

I am using the star to indicate multiplication

[math]\prod\limits_{n = 1}^4 {{n^2}} \;which\;is\;1*4*9*16 = 576[/math]

 

[Imagine Everything]

15 hours ago, studiot said:

This is an instruction to form the sum of the squares of the foirst 4 integers  ( 1², 2² ,3² and 4² )

∑n=14n2whichis1+4+9+16=30

Man this is tricky for me but I think I understand.

So the ref above the sigma represents how far the integers go.

And the ref under the sigma tells me the value of the random? letter used to give a value.

The by placing the n²  directly in front of the sigma, this tells me the power? of the sum?

So it stops at 4 and it then adds what n is up to that 4?

If I understand this, if I changed it to n1 in front of the sigma then this would become

1 + 2 + 3 + 4 = 10 ?

Though I guess (from vectors I've seen) that I could just simply put n in front of the sigma instead of n1 as they are the same?

 

The ref above the sigma is just how far it goes and the ref underneath states the value of the random? letter used for the sum?

Or is n specific to something in this respect, like nth represents infinity in vector equations?

Hmm, just a thought just occurred to me. Is the n²  in front of the sigma a scalar?

If it is a scalar, is that how sigmas' always appear? With the scalar in front?

 

What's the difference between summation and multiplication? Do they not both end up with a total of the accrued maths?

 

I tried using the charmap on windows but it's a bit shit to be honest, unless I'm using it wrong of course. Is there such a thing as a physics keyboard with all the relevant char's I can buy somewhere?

Or a website perhaps that I can copy and paste from?

I don't know if this is a strange question or not but after n2 for instance is there an n3?

And if so is, 3² the same as 3ᴈ? =9?

The following I'm not sure I understand much at all

This sum may be used in an equation if there is a formula that gives you the answer directly

∑n=14r2=16(n)(n+1)(2n+1)

 

I've noticed too that when I quote (copy n paste) you guys sums, they come out very differently to how you originally wrote them.

Lol, literally just found the superscript button. I feel like a bit like...

Edited yesterday at 02:58 PM by Imagine Everything

[studiot]

Just now, Imagine Everything said:

Man this is tricky for me but I think I understand.

Don't worry, it is tricky. So I haven't told you all of it. I am trying to do it in bite sized chunks.

When you get to the level of Einstein you can dispense with the sigmas altogether, using what is known as the einstein convention. Sadly this is where you will most likely come across the need.

Anyway.

Just now, Imagine Everything said:

So the ref above the sigma represents how far the integers go.

And the ref under the sigma tells me the value of the random? letter used to give a value.

Yes you can use any letter, but n is by far the most common, followed by i.

Remember they are the index, which tells you how many terms you are adding up or how many times you are repeating the formula with differnt values.
That is why they have to be integers.

Yes the bottom one is the start point (0 is often acceptable but adding zero doesn't add much)

And the top one is the last or end one  (unless it is infinity where this is no end)

Just now, Imagine Everything said:

If I understand this, if I changed it to n1 in front of the sigma then this would become

1 + 2 + 3 + 4 = 10 ?

Yes that is correct,

Gold star point.

Just now, Imagine Everything said:

Though I guess (from vectors I've seen) that I could just simply put n in front of the sigma instead of n1 as they are the same?

I will come onto vectors because that is your most likely use.

Just now, Imagine Everything said:

Hmm, just a thought just occurred to me. Is the n²  in front of the sigma a scalar?

No it is simply a number, but I call it after the sigma not infront of (ie not before)

 

Just now, Imagine Everything said:

What's the difference between summation and multiplication? Do they not both end up with a total of the accrued maths?

Yes they do end up with a single output, but you will see when I do vectors the formulae are more complicated.

Just now, Imagine Everything said:

Is there such a thing as a physics keyboard with all the relevant char's I can buy somewhere?

I wish . I did invent one once and actually thought about going into production. But there are too many obstacles in blighty.

Just now, Imagine Everything said:

Or a website perhaps that I can copy and paste from?

https://editor.codecogs.com/

or

https://www.sciweavers.org/free-online-latex-equation-editor

[Imagine Everything]

4 hours ago, studiot said:

When you get to the level of Einstein you can dispense with the sigmas altogether, using what is known as the einstein convention. Sadly this is where you will most likely come across the need.

Well hmm, maybe if I live for anther 300 years and study 25 hours a day, 9 days a week lol

 

4 hours ago, studiot said:

I wish . I did invent one once and actually thought about going into production. But there are too many obstacles in blighty.

What a  shame, imagine you would have sold quite a few.

 

I see 'n' being used a lot throughout what I've watched or read so far, is it because it doesn't interfere with other character used to mean something else?

I see that a dot for instance is used (1^.4 =4) instead of 1x4 =4 for mulitplication and sometimes the 'x' or ^'.'  just seems to be implied.

4 hours ago, studiot said:

4 hours ago, Imagine Everything said:

What's the difference between summation and multiplication? Do they not both end up with a total of the accrued maths?

Yes they do end up with a single output, but you will see when I do vectors the formulae are more complicated.

Mmmm I can sort of imagine it will be. I've seen a few chalk boards on a few lectures I watched and the formulae/sums seem so bewilderingly complex.

4 hours ago, studiot said:

4 hours ago, Imagine Everything said:

If I understand this, if I changed it to n1 in front of the sigma then this would become

1 + 2 + 3 + 4 = 10 ?

Yes that is correct,

Gold star point.

Thank you so much, I don't know if a gold star means anything other than you giving me praise but the fact that you even said that as someone as studied and clever as you are, means an awful to me  

I think I understand the pi ref a bit better now too. Whenever & wherever I saw it used/mentioned before, I kept thinking 3.142 etc and I almost pooped myself wondering how you used that to calculate stuff. But if I do indeed understand what you said, it is merely a symbol representing multiplication?

∑n=14r2=16(n)(n+1)(2n+1)

Whats the r²  in front of the sigma in this formula and how does the whole formula work please?

I understand the 1st sigma part now but after that is confusing to me.

+1 to you too btw for teaching and also being patient enough to someone who knows or knew nothing beyond dartboard level maths. Did I just put you off me by saying that lol?

I can't physically give you anything in return for your help but there is one thing I can offer. I'm too bad a poet and if you ever want one for whatever reason, anniversary, birthday? please feel free to pm me a few details about what you'd like in it and I'll write you one. The same offer goes to you other guys/gals that have helped me. I don't want anything in return, it's just me trying to balance out the help you have all given me.

I really do & can imagine a lot, perhaps too much lmao.

 

Ty too for the website links.

hahaha I once again find myself writing for England so I'll stop there for now.

Edited 23 hours ago by Imagine Everything

[studiot]

Just now, Imagine Everything said:

∑n=14r2=16(n)(n+1)(2n+1)

Whats the r²  in front of the sigma in this formula and how does the whole formula work please?

I understand the 1st sigma part now but after that is confusing to me.

I wondered if you would notice that so wel spotted.

If you will indulge me until next time we will return to the more difficult uses of sigma and its whys and wherefores.

 

I mentioned vectors and einstein last time so please take a look at this webpage which is the source of this picture about vectors in 3 dimensions and their components, using XYZ axes

http://emweb.unl.edu/negahban/em223/note4/note4.htm

 

There lots of useful graphics, but can you spot the difficulty (clumsiness really) they get into using XYZ ?

Don't worry about the rest of the maths, but it is a good page to refer to in the future.

Note they make use of sigmas.

 

We can then return to answer your question about r2 and also see if we can improve on the XYZ issue.

 

We can use it

[Imagine Everything]

I had to quickly remind myself of the i and j, sorry I guess I slightly cheated on my answer rather than getting it from my head.

46 minutes ago, studiot said:

I can see that the y in this image should be x and the z should be y. Is that right? I'm not sure about where the z should be. Should z be where x is? Is that how 3d vectors are drawn?

Another way to put it, j should be where k is and i should be where j is and k should be where i is.

So, forgive the simplified way I write this please, it should be x/i horizontal line, j/y vertical line and z/k RHR.
 

 

46 minutes ago, studiot said:

And the same in this one? Should z be where x is in the image? And also y should be x and z should be y.

Is that how 3d vectors are drawn?

I'm afraid I'm very 2d ish still and also still haven't figured the following out

The matrix is

4 1 3

0 2 4

3 2 1

I get to the 3 small det and so far so good but I don't understand the sum below. I think I confuse myself and this is probably an easy example too lol.

= 4 (-6) -1 (-12) +3 (-6) = 30

I will take a look at the website more in depth but probably tomorrow now if you don't mind.

Gotta get things ready for work tomorrow etc now.

Have a good night. See you tomorrow.

Edited 23 hours ago by Imagine Everything

[Imagine Everything]

18 hours ago, studiot said:

There lots of useful graphics, but can you spot the difficulty (clumsiness really) they get into using XYZ ?

I'm afraid if you're referring to the cosine part, I still don't know much at all about sine cosine. I did look the other day but didn't understand it much. I think my takeaway was that both might relate also to infinite somethings?

Looking more at that website now.

I noticed also that the sigmas they use don't have integer above or value below.

But is that because they initially wrote Fr before the sigma?

And I dont actually see an F vector for them to have obtained it in the image for them to have referred to if as they say

Addition of vectors: The resultant vector F_R obtained from the addition of vectors F₁, F₂, …, F_n is given by

To be honest, I only vaguely recognise a few things. I clearly need to learn more to understand it.

I don't think I could tell you, aside from what I've said, what could be wrong or right.

 

 

 

 

Edited 5 hours ago by Imagine Everything

[studiot]

I believe I said don't woryy about the rest of the maths, there is more there than we need for now.

The main message is about splitting a vector into components one parallel to each axis. (hence the i, j, k)

Or if you prefer components combining components to make a single vector ( they call the single vector A on that webpage)

[Imagine Everything]

2 minutes ago, studiot said:

I believe I said don't woryy about the rest of the maths, there is more there than we need for now.

The main message is about splitting a vector into components one parallel to each axis. (hence the i, j, k)

Or if you prefer components combining components to make a single vector ( they call the single vector A on that webpage)

Yes you did, whilst the format seems familiar, I didn't realise I was talking about the maths sorry, I think I need to go back and look at some more vector lectures and get to understand components better.

2d seems to be so much easier than 3d.

I'm sure I could look it up but I trust your word more than google, could please explain cosine and sine please?

 

[studiot]

Just now, Imagine Everything said:

2d seems to be so much easier than 3d.

In many ways this is true and indeed there is even a great deal of theory in science and engineering that take great advantage of this.

However we do not live an a 2D world. In fact such a world is incomplete as we can deduce the exsistence of at least a 3rd dimension mathematically. So there are times when it is necessary for 'solid' thinking.

Just now, Imagine Everything said:

I'm sure I could look it up but I trust your word more than google, could please explain cosine and sine please?

Ok we will do some trigonometry when we have done the next bit about sigmas.

And perhaps reinforce stuff about vectors as we go along.

I take it you are happy with labelling the axis with X, Y and Z  in some order or other ?

We will deal with the order in a minute.

The diagram shows that we can create or imagine vectors i ,  j  and  k respectively parallel to or along the 3 coordinate axes, X Y and Z. (bold letters are often used to denote vectors)

Further we make each of these vectors of magnitude exactly one.
So i ,  j  and  k each have magnitude exactly 1.
We then call these unit vectors in the directions of the axes.

Having done this we can create any vector whatsoever that is parallel to one of these axes by invoking the first law of vectors.

That is a larger (or smaller) vector is a scalar times a vector.

So if I have a scalar a and a unit vector i  then the larger (or smaller) vector is ai

 

That is the meaning of the second figure I posted where  the vector A is the sume of the three components

A = a_xi  +  a_yj  + a_zk   -   where a_x, _ay and a_z are usually different

say a₁, a₂ and a₃

So  our vector, A = a1i  +  a2j  +a3k

 

 

 

Note they have used capital As where I have use small ones.

 

OK to move on one stage further

Instead of naming the axes X, Y and Z as we learn in school we can call all the axes X-something.

If we call them X₁, X₂, and X₃

something rather clever happens.

We can bring in the sigma notation

A  =  [math]\sum\limits_{n = 1}^3 {{a_n}} {X_n}[/math]

Where the index, n runs from 1 to 3 for both the coefficient scalars and the axes.

 

My reference to Einstein was that he proposed to simplify even further and for get the sigma alltogether

So

A  =  [math]{a_n}{X_n}[/math]

Where the summation is 'understood'.

And there you have your first @Mordred type tensor.