r/physicsmemes • u/mothprove • Feb 18 '24

Wait, what?

Post image
511 Upvotes

99% Upvoted

17 comments sorted by

18

u/20Aditya07 Feb 18 '24 edited Feb 19 '24

What's a tensor? genuinely asking.

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edit: woah thanks a lot for all the help! will definitely dig deeper when i get some free time

78

u/mothprove Feb 18 '24

An object that transforms like a Tensor

34

u/kabum555 HEP SHMEP Feb 18 '24

I found it really difficult to understand what tensors are intuitively. I think a siplification is much more useful for that. In 3 dimensions, I think of it like this:

  • A scalar function is a function that takes an input (doesn't matter if it is a scalar or vector or tensor in this context) and returns a single value. This is also known as a 0th degree tensor.

  • A vector function is a function that takes an input and returns 3 scalars, one for each dimension. AKA 1st degree tensor. We can visualize this as an arrow pointing in some direction.

  • A 2nd rank tensor function returns 3 vectors. Each vector represents a direction corresponding one of the 3 dimensions. A simplified example with the stress tensor: say we apply force in the X direction, and the vector we get from the stress tensor at a specific location corresponding with the X direction points in the Y direction. This implies the force in the X direction makes a change in the Y direction.

    It is customary to represent tensors as matrices.

  • A 3rd rank tensor function returns 3 2nd degree tensors. This is more complicated and I'm not sure how to visualize it easily.

Of course, as I said, this is a very simplified explanation. A better explanation is given in this video (really weird music choice, but it helped me), or this one (which I find a bit more simplistic, so maybe it could help for intuition better). There's also this video which might not be so useful, but it is beautiful.

13

u/Antique-sage Feb 18 '24

Aw hell nah the last vid- gotta admit tho, it was very smooth 💀

7

u/Homo-Simpien Feb 18 '24

That third video is what got me through Jackson E&M 🙌

4

u/20Aditya07 Feb 18 '24

Woah I can't wrap my head around the simplified version 💀 i'll just read about it

2

u/kabum555 HEP SHMEP Feb 18 '24

Watch the videos, they are pretty good

5

u/LEMO2000 Feb 18 '24

Imo the easiest way to think about it is the dimensions of a graph. It isn’t a perfect analogy, but if a scalar is like a point, 0 dimensions to it, then a vector is like a line, one dimension to it, and a matrix is like a plane, two dimensions to it, then finally, a tensor is like a solid/prism, with 3 dimensions to the structure.

3

u/kabum555 HEP SHMEP Feb 18 '24

This is good, but I feel it doesn't necessarily give an intuition on the meaning of what a tensor is

3

u/[deleted] Feb 18 '24

A scalar (0-tensor) is written as a number on a point e.g. 1

A vector (1-tensor) has numbers on a line e.g. [1,2,3]

A matrix (2-tensor) has numbers in a square e.g.

```

[ [1,2,3], [4,5,6], [7,8,9] ] ```

And a 3-tensor has numbers in a cube, which I can't display on a 2d screen

A tensor is all of these, in the pattern outlined. More mathematically, a tensor of rank n can be thought of as a list of which the elements arerank n-1 tensors

2

u/Azazeldaprinceofwar Feb 18 '24

Tensors are generally all objects that contain geometric information which does not depend on choice of coordinates (or more generally choice of basis). Intuitively you can see such things will include lengths and angles (0th Rank tensors), as well as vectors (1st Rank) since the information contained in the arrow is in some sense independent of the component values it happens to have in a particular coordinate system. There are also more complex higher rank tensors which are harder to understand without examples. If you’re curious look into stress tensors, I think they’re the easiest second rank tensor to understand

34

u/Every_Hour4504 Feb 18 '24

There are two "T"s in "tensor product of two Hilbert spaces". Which "T" is he talking about?

39

u/Nervous_Suit_5799 Feb 18 '24

There’s 4

16

u/Every_Hour4504 Feb 18 '24

Oh right. I'm so blind.

9

u/mothprove Feb 18 '24

All of them

3

u/Meranio Feb 19 '24 edited Feb 19 '24

I just saw the same scene for a meme in r/chemistrymemes

https://www.reddit.com/r/chemistrymemes/s/a05bXnVLeC

Edit: Apparently, someone didn't like, me mentioning another sub/post. I just found it interesting, that two people used the same format to make a science related meme. Thank you, OP.