Spinor rotated twice

Most people don't understand the difference between vectors and spinors. Both are directed entities. They have feet and a head. What are you, reader, a vector or a spinor?

You might think that rotating your body by 360° or 2 pi would return it to its former position. Reader, you're wrong. You must rotate your body twice, i.e. by 720° or 4 pi, before your initial position is retrieved.

Vectors need a single rotation. Spinors, by contrast, require a double turn. Reader, you are a spinor!

In this movie, your body is represented by a plastic can formerly filled with milk powder. The can becomes spinor when it is connected to its environment via elastic ribbons. In this movie, the environment is represented by students on the left- and right-hand sides. They hold the ends of the ribbons. The student in center rotates the can twice. Finally he demonstrates that the ribbons, apparently being twisted, can be disentangled without any rotation.

After a single rotation, disentanglement is not possible. This is shown in a companion movie:
http://www.youtube.com/watch?v=GykGJeCUJtQ

For an example showing that each palm of yours is a spinor, too, watch
http://www.youtube.com/watch?v=fTlbVLGBm3Q
Instead of the elastic ribbons it is now your arm which connects the palm with its environment.

All parts of your body, reader, consist of electrons, protons and neutrons. They all have magnetic moments and are connected to their surroundings via magnetic field lines. They all are small spinors combining to make you a gigantic spinor.

The basic idea that the difference between vector and spinor comes from a stronger binding of the spinor to its surroundings was probably frist pronounced by P.A.M.Dirac. However, that a spinor and its binding to space can be visualized using trash materials, was first demonstrated in a lecture on quantum electrodynamics in 2009, see
http://sci.althand.com/qed.html
or
http://home.arcor.de/althand/qed.html

Ulrich Brosa http://sci.althand.com/

Category:

Science & Technology

Tags:

• physics
• mathematics
• spinor
• vector

[althand]

PsychedelicsAwaken wrote:

"You would need to show that a double rotation is homotopic through rotations to the identity..."

The correct request is: "You would need to show that a double rotation is homotopic to the identity..." This is shown in this movie. Just watch!

PsychedelicsAwaken wrote:

"unlike a single one..."

This is demonstrated in the companion movie "Spinor rotated once". All is already explained in the text under the video. The URLs are given there.

[adelpctan]

I disagree with the comment that one must rotates 720° and not 360° to come to one's initial position. A multiple of 360° would restore one's initial position.



[althand]

@adelpctan : Humans like all apes descend from worms. Such are their capabilities. Humans are not able to cope with rotations. It's simply too difficult for them. Another example: Three-dimensional rotations do not commute. Students learn this because the teacher tells it, but in everyday life they don't understand what it means.

[PsychedelicsAwaken]

Seems to me that this is misleading, or perhaps I don't understand what is being done in principle - it appears that the double rotation of the left strings is cancelled by the opposite double rotation of the right strings. If you just let go of the can, it would spin itself right back to the twistless state - and the exact same thing would occur if you only used single-twists. You would need to show that a double rotation is homotopic through rotations to the identity, unlike a single one...

[JanPBtest]

It's not really true about the 360 vs. 720 degrees. Rotating your body by 360 does return it to the original position with respect to its surroundings. It is only when one keeps track of the rotation by some means (e.g. the rubber bands or in terms of, say, a curve in SO(3)) that one finds out the 360 rotation cannot be undone while keeping the body's initial and final position fixed. The 720 rotation can be undone this way as you show in the video.

[gravitymindofgod]

omg done and undone so simple...