In summary: The entropy is independent of the choice of how 0s and 1s are represented, in particular exchanging the state representing 0 for the state representing...1 does not change the entropy.
Is digital information that travels across the internet massless? If we were to take out the cables(and maybe the electrons)from the equation, is the digital information taking up physical space?

Information is encoded in the state of some physical object, it doesn't have any weight. It's like using a stick to write in the sand, the information is encoded in the troughs and hills of the sand.

Information can be stored on a USB stick, try weighing one and see if it has changed its weight before and after the information is saved to it.

The same is true for information transmitted in a wire or wirelessly. The information is encoded in the state of the electrons flowing through the wire or in the frequency or amplitude of the wireless electromagnetic signal.

Here's a discussion of frequency modulation an example of how information can be encoded onto an electromagnetic signal.

https://en.m.wikipedia.org/wiki/Frequency_modulation

Last edited:
jedishrfu said:
Information is encoded in the state of some physical object, it doesn't have any weight. It's like using a stick to write in the sand, the information is encoded in the troughs and hills of the sand.

So digital information is classified as a non-physical object? And does a hard drive then almost lose mass when you put a program on it then?

Last edited:
So digital information is classified as a non-physical object? And does a hard drive then almost lose mass when you put a program on it then?
Odd concept. You can count objects and you can measure objects (like your fingers). You can also use objects to convey information (sign language, used to communicate with the deaf). Your fingers do not increase in mass when using sign language...

It depends on whether 0s and 1s weigh the same . If 1s correspond to a higher energy state, then the more ones you have, the heavier the memory storing it. If you have an optical fiber, if no signal is going through it, then it is lighter than when light (and hence information) travels through it.

DrClaude said:
It depends on whether 0s and 1s weigh the same . If 1s correspond to a higher energy state, then the more ones you have, the heavier the memory storing it. If you have an optical fiber, if no signal is going through it, then it is lighter than when light (and hence information) travels through it.
But do they have to be "different" energy states? If you store information in a capacitor, you can choose a capacitor voltage of >0.1V as "1" and a capacitor voltage of <-0.1V as 0. Or (fast-forward 20 years or so) store information in the electron spin state? As for data communication, we always try to code information in such a way that the mean voltage/current/lightflux across a symbol is 0 (see for example https://en.wikipedia.org/wiki/Manchester_code and https://en.wikipedia.org/wiki/8b/10b_encoding).

Svein said:
But do they have to be "different" energy states?
No. That's why I started the sentence with "It depends." You can easily imagine systems where 0s and 1s correspond to the same energy, such that information itself has no weight.

This reminds me of an article in the Annals of Improbable Research, where someone suggested the following compression algorithm: considering that in binary, only the ones actually carry information (since 0 corresponds to no information), then one can compress a binary file by removing all the zeros .

Moreover, you can express that compressed file as the number of 1s in it, resulting in a binary number. Again, compress that resulting file by removing the zeros. Repeating the process, you end up with 1, so any binary file can be easily compressed to a one-bit file. Maximum compression!

nsaspook
@berkeman pointed me to an earlier thread at PF that discussed this issue

https://www.physicsforums.com/threa...rd-drive-weigh-more-than-an-empty-one.419343/

The notion is equating information with the entropy of the system and the information has mass by virtue of the entropy in describing the state of the system.

I am troubled by this definition since for digital information, we make an arbitrary choice as to what state constitutes a ONE and what state constitutes a ZERO. Consequently, the same information would have differing masses depending the choice of states and the medium it's stored on.

In any event, this is one of those questions with no easy answer.

berkeman
jedishrfu said:
The notion is equating information with the entropy of the system and the information has mass by virtue of the entropy in describing the state of the system.

I am troubled by this definition since for digital information, we make an arbitrary choice as to what state constitutes a ONE and what state constitutes a ZERO. Consequently, the same information would have differing masses depending the choice of states and the medium it's stored on.
The entropy is independent of the choice of how 0s and 1s are represented, in particular exchanging the state representing 0 for the state representing 1 (i.e., flipping all bits) doesn't change the entropy of the memory.

jedishrfu
Also on a given storage medium or communication path you never have "more" or "less" information. You simply different information. A "full" storage has all of its information relevant where an "empty" storage has little of its information relevant but the irrelevant information still occupies space.

BoB

Saw this post when it was posted, and it kind of stuck in my head. So I guess a discharged battery weighs less than a charged one. Also, the discharged battery has higher physical entropy. Relating that information entropy, it should take more information to exactly specify the state of the discharged battery than to specify the state of the charged one. So in that situation, information has a "negative weight", though that's quite a stretch, and it seems backwards.

I did find this:
https://en.wikipedia.org/wiki/Landauer's_principle
Which is about the lower bound of energy consumption in computation. An interesting tidbit is that any irreversible computation (like an AND gate) must increase the physical entropy of the system as data is erased. So in this case information has a relationship with the ability to do work, reverse of my speculation above. Also, the Wikipedia article mentions the energy needed to flip a nano bit as 3 zeptojoules. A truly tiny mass over the speed of light squared, but information must have a physical manifestation, and if there's energy and mass equivalency...

## What is digital information?

Digital information refers to any data or content that is stored, transmitted, or accessed in a digital format. This includes text, images, videos, audio files, and any other type of information that can be represented by binary code (0s and 1s).

## What are the benefits of digital information?

Digital information offers many benefits, including ease of storage, access, and transmission. It also allows for faster and more efficient processing, sharing, and analysis of data. Additionally, digital information can be easily replicated and backed up, reducing the risk of data loss.

## What are the potential risks of digital information?

One of the main risks of digital information is the threat of cyber attacks, which can compromise the security and privacy of sensitive data. Digital information is also vulnerable to technical issues such as hardware failures and software malfunctions, which can result in data loss or corruption.

## How is digital information stored?

Digital information is typically stored on electronic devices such as computers, external hard drives, and cloud servers. It is stored in the form of binary code, which is a series of 0s and 1s that represent different types of data.

## How is digital information transmitted?

Digital information can be transmitted through various means, including the internet, satellite communication, and wireless networks. It is sent in the form of digital signals that can be decoded and interpreted by receiving devices, such as computers or smartphones.

• Programming and Computer Science
Replies
1
Views
1K
• Programming and Computer Science
Replies
19
Views
2K
• Programming and Computer Science
Replies
10
Views
3K
• Programming and Computer Science
Replies
7
Views
1K
• Programming and Computer Science
Replies
1
Views
1K
• Classical Physics
Replies
18
Views
2K
• Programming and Computer Science
Replies
3
Views
1K
• Programming and Computer Science
Replies
4
Views
2K
• Programming and Computer Science
Replies
13
Views
4K
• Computing and Technology
Replies
8
Views
2K