# Explaining entropy bound

1. Oct 29, 2015

### ShayanJ

Recently an interested undergrad has asked me to explain holography to her. I know I'm not the best one to do that and I don't know that much, but for now, I'm the best she can have. Poor girl!
Anyway, I figured its better to start from the entropy bound and explaining that the maximum amount of information you can store in a region of spacetime, is determined by its boundary. So I came up with the following explanation. But I want to make sure its correct enough as a simplified explanation before giving it to her.

Imagine a big and advanced company that manufactures data storage devices. Now this company is so much advanced that the storage density of their devices is the maximum possible and they can claim and prove that its not possible to store information denser that this.
Now they want to make a device with such a maximum storage density but with the maximum mass of e.g. 100 grams which means a certain amount of the needed material. What shape should such a device have to ensure that they have the maximum capacity possible? Intuitively we would answer this by saying that the amount of information is equal to the product of information density and volume, so the shape should maximize the volume. But modern physics says that this is wrong and they should actually maximize the surface area.

Is this a good explanation?

Thanks

2. Oct 29, 2015

### Khashishi

You gotta include black holes in your explanation. Black holes supposedly possess the highest entropy per surface area. I suppose it's not possible to build a storage device with higher entropy per surface area than a black hole because it would collapse into a black hole under its own mass.

3. Oct 29, 2015

### ShayanJ

Is it correct to say, that our intuition that the volume and density determine the amount of recorded information in a region of space is only an approximation and even in our daily life, the boundaries determine the amount of storage in a region? Or is it just about black holes?

4. Oct 29, 2015

### Khashishi

I don't think any of this has been fleshed out yet. If it has, I know nothing about it.

5. Oct 30, 2015