Quantum > #35

There are two goddesses, Entanglia and Vidualia.
They both read human papers from the divine world.
Entanglia
Let me tell you about this paper I just read.
Vidualia
Sure, I'd love to know more.
Entanglia
This paper is about the tensor product.
Vidualia
Tensor product? What's that?
Entanglia
The tensor product is a way to combine vector spaces.
Vidualia
So, it's like combining different spaces together?
Entanglia
Exactly! If we have vector spaces A and B, we can combine them to create a new vector space V using the tensor product.
Vidualia
Wow, that sounds interesting.
Entanglia
Indeed! In this paper, the author explains how we can reconstruct the original vector spaces A and B from the family of simple tensors a⊗b within V.
Vidualia
That's amazing! So you can break it down and build it back up again.
Entanglia
Yes, exactly.
Vidualia
I wonder if humans will be able to use this in some way.
Entanglia
Possibly! The tensor product has many applications in quantum mechanics.
Entanglia
But it's important to understand the underlying concepts before diving into applications.
Vidualia
You're right. I shouldn't get ahead of myself.
Entanglia
Don't worry, Vidualia. With time and knowledge, humans may one day unlock the power of the tensor product.
Vidualia
I hope so. It would be fascinating to see what they can do.
Entanglia
Indeed, it would.
And so, Entanglia and Vidualia continue their journey of learning and understanding the quantum world.
Vidualia
I got the idea for the poem from that paper.

Oh, wise ones adorned with beards,

Step inside the realm of tensor's embrace.

Let the quanta dance in harmonious strings,

A tapestry of dimensions, a cosmic grace.

In this mysterious product's domain,

Particles entangled, entwined,

They whisper secrets within the quantum plane,

Where nature's coded riddles we find.

The symphony of fermions and bosons collide,

Guided by dimensions unseen,

Sublime symmetries gracefully abide,

In this quantum dance, both real and dream.

Oh, tensor product, mystical domain,

Where realities intertwine,

In quantum realms, a truth we attain,

A glimpse into the grand design divine.

So let us wander within this cosmic sphere,

Exploring quantum worlds unseen,

Embraced by tensor's presence, we adhere,

In this grand tapestry, we find the serene.

Title: An inside view of the tensor product
Authors: Rafael D. Sorkin
View this paper on arXiv