28.05.17 // new week, new window 💭

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28.05.17 // new week, new window 💭

n roots of unity

When one is dealing with complex numbers, it is many a times useful to
think of them as transformations. The problem at hand is to find the n
roots of unity. i.e

As is common knowledge z = 1 is always a solution.

Multiplication in the complex plane is mere rotation and scaling. i.e

**Now what does finding the n roots of unity mean? **

If you start at 1 and perform n equal rotations(

because multiplication is nothing but rotation + scaling), you should again end up at 1.We just need to find the complex numbers that do this.i.e

This implies that :

And therefore :

**Take a circle, slice it into n equal parts and voila you have your n roots of unity.**

**Multiplication by 1 is a 360 ^{o} / 0^{o }rotation.**

When you say that you are multiplying a positive real number(say 1) with 1 , we get a number(1) that is on the same positive real axis.

**Multiplication by (-1) is a 180 ^{o} rotation.**

When you multiply a positive real number (say 1) with -1, then we get a number (-1) that is on the negative real axis

The act of multiplying 1 by (-1) has resulted in a 180^{o} transformation. And doing it again gets us back to 1.

**Multiplication by i is a 90 ^{o} rotation.**

Similarly multiplying by i takes 1 from real axis to the imaginary axis, which is a 90^{o} rotation.

This applies to -i as well.

so on and so forth,

Have a great day!

The central new notion introduced by quantum mechanics is not indeterminism, nor uncertainty, but wholeness. This new feature has been described by phrases such as “the non-separability of spatially separated systems”, or more briefly as “quantum non-locality”. These terms are actually inadequate expressions of the radical implications of the notion of wholeness and reflect a strong desire to cling to a reductionist philosophy. A radically new approach is needed, an approach that does not depend upon the Cartesian Order, but requires the introduction of new orders such as the implicate order and the generative order. Mathematical descriptions of these new orders are under active development at present.

It is now quite clear that if gravity is to be quantised successfully, a radical change in our understanding of spacetime will be needed. We begin from a more fundamental level by taking the notion of process as our starting point. Rather than beginning with a spacetime continuum, we introduce a structure process which, in some suitable limit, approximates to the continuum. We are exploring the possibility of describing this process by some form of non-commutative algebra, an idea that fits into the general ideas of the implicate order. In such a structure, the non-locality of quantum theory can be understood as a specific feature of this more general a-local background and that locality, and indeed time, will emerge as a special feature of this deeper a-local structure.

It is now quite clear that if gravity is to be quantised successfully, a radical change in our understanding of spacetime will be needed. We begin from a more fundamental level by taking the notion of process as our starting point. Rather than beginning with a spacetime continuum, we introduce a structure process which, in some suitable limit, approximates to the continuum. We are exploring the possibility of describing this process by some form of non-commutative algebra, an idea that fits into the general ideas of the implicate order. In such a structure, the non-locality of quantum theory can be understood as a specific feature of this more general a-local background and that locality, and indeed time, will emerge as a special feature of this deeper a-local structure.

—
Relativity, Quantum Gravity and Space-time Structures, research group at Birkbeck, University of London

*Alan never got the chance to tell Christopher he loved him.*

* Christopher died not knowing that Alan loved him.*

*When Alan learned of the passing of his first love, his life had never truly been the same since.*

^planning and studying🍭^ [28/05/2017]🍌

- all the studying you are doing will be worth it in the end.

Yet another timelapse - **here’s me doing some Physics exercises!**

*I really like these, because I can’t get distracted by my phone. The exam is tomorrow but I feel relatively confident. Had a lovely, sunny weekend.* (Countdown to Summer: 42/75)

Hello studyblr world!

I want to introduce myself to all of you, knowing facts about me you’ll probably connect easily to me.

**Why I started this blog:**

I wanted a place where I could:

- reblog pictures or post pictures myself about school, since it takes up so much time from my life ;)
- motivate myself and others through the posts
- meet people who also attend high school (or uni)
- have tips for studying

**Basic facts:**

My name is Elisa, you can call me Liz

I’m 17

I come from Italy (which has other cities after Milan and Rome)

I attend the ‘liceo linguistico’, which means I study languages, and I’m at the third year (corresponds to a junior in American High School)

The notion of a permanent object with well defined properties can no longer be taken as basic in physics … Rather, it is necessary to begin with the event as a basic concept, and later to arrive at the object as a continuing structure of related and ordered events.

—
David Bohm

Writing my HL Physics I.A. 👩🏻💻

This contain all the equations for Physics we need to know in Yr10. To me it’d an efficient way because I can look back at them whenever, and it’s really easy to carry it. The different colours are different topics, and there is a little heading on top of the equationd to kmow what to use them for.

I hope some of you feel inspired to do this, even if it’s not with the same design.

Earth with rings, what?

Why don’t we have a ring like Saturn? why is it so, let’s find it out;

Our moon is big very big the diameter of our moon is 2159 miles which is very big. Our moon is too far from earth it is about 361747 km from earth because of our moon is big that is why we can see the moon clearly. As it is so far from earth that is why we have a solid one piece moon if our moon gets closer to earth the gravity of earth will rip the moon apart creating a ring like Saturn but if our moon gets closer to the earth which it is never going to happen.

guys, please feel free to let me know what you wanna read next

Physics notes from yesterday!! I think these came out looking pretty nice, though they are simple. Sorry for my messy handwriting, I wasn’t focusing much on the look of the notes for this, but rather getting all the info down. Have a great day!

At present quantum physicists tend to avoid the issue by adopting the attitude that our overall views concerning the nature of reality are of little or no importance. All that counts in physical theory is supposed to be the development of mathematical equations that permit us to predict and control the behaviour of large statistical aggregates of particles. Such a goal is not regarded as merely for its pragmatic and technical utility: rather, it has become a presupposition of most work in modern physics that prediction and control of this kind is all that human knowledge is about.

—
David Bohm

“Something’s come up, concerning Morcom.”

**“Why am I here…?”**

“…Christopher is dead.”

**“…I don’t understand…”**

**28/5/17** || Maths physics is confusing for a non-physics person (。ヘ°) How can something be at rest but still accelerating??

Some of the best signs from the science day march.

Science appreciation post

Reblog if u think science is cool (and deserves some rad funding)