# Weight difference between an empty and a full memory stick

• Rebu
In summary, the weight difference between an empty memory stick and the same memory stick with data can be proofed. This is due to the energy stored in the information on the memory stick, as well as the energy associated with entropy. The amount of information stored can also affect the mass of the device. However, the exact change in mass may be difficult to measure accurately.
Rebu
Problem:
"What is the weight difference between an empty memory stick and the same memory stick when it contains data?"
Can the answer to the previous question be proofed?

Rebu said:
Problem:
"What is the weight difference between an empty memory stick and the same memory stick when it contains data?"
Can the answer to the previous question be proofed?

Just a quick note to the General Physics regulars. This is a continuation/retry of a thread from earlier tonight. The OP has clarified the question that he wants to ask, and to me, it's actually an interesting physics question that I'm curious about the answers to as well.

In addition, from my experiences with flash memory technology, some flash drives store information in differential cells, so there is no difference in stored energy, but there is a difference in stored information. I don't know if that makes a difference in the final physics/relativity answers, but I think it's an interesting angle to the OP's question.

So if there is a difference in the energy stored in information storage on a flash memory stick or chip, does that change the mass of the device? What if there is a difference in the information stored, but not in the amount of stored energy it takes to encode that information?

berkeman said:
Just a quick note to the General Physics regulars. This is a continuation/retry of a thread from earlier tonight. The OP has clarified the question that he wants to ask, and to me, it's actually an interesting physics question that I'm curious about the answers to as well.

In addition, from my experiences with flash memory technology, some flash drives store information in differential cells, so there is no difference in stored energy, but there is a difference in stored information. I don't know if that makes a difference in the final physics/relativity answers, but I think it's an interesting angle to the OP's question.

So if there is a difference in the energy stored in information storage on a flash memory stick or chip, does that change the mass of the device? What if there is a difference in the information stored, but not in the amount of stored energy it takes to encode that information?

why was my reply deleted =p.

It looked like you were saying that you expected this thread to be locked as an unauthorized repost of the other problematic thread. I've been working with the OP to morph this into a valid thread where we can all learn something. That's why. Oh, and txt speak is not permitted here ;-)

Seems it would depend if all 0 bits or all 1 bits would be heavier than some specific pattern.

It's an interesting question and the answer will come from first defining exactly what you mean by "information".
If all the bits were set to "0" would that be information? How much? If they were all set to 1 would that be information. If half are 0 and half are 1, is that information and how much more or less information is it compared to the other cases?
What is held in the memory stick may be information to one person, but not to another.
Information only has meaning or existence in conjunction with the one who is observing or decoding it.
From a consideration of these questions, it could be possible that the memory stick could hold different amounts of information to different people.
Information is not a form of energy, and as such, the information has no "weight". On the other hand, if storing the 1's and 0's involves a gain in stored energy, then of course there is a change in weight.
Just my thoughts.

Well one of the memory sticks would be unpartitioned and the other would contain a FAT32 partition with some music files on it.

Can the change in weight, if there is one, be proofed?

http://en.wikipedia.org/wiki/Flash_memory

Hmmm... I guess this would take a little more info. does a memory device with '000000000000000000000000000000000' stored store more energy than '1010101001011110101010110101010101'? If so, by E=MC^2, it should be more massive.

Rebu said:
Problem:
"What is the weight difference between an empty memory stick and the same memory stick when it contains data?"
Can the answer to the previous question be proofed?

This is an interesting question, but the question should refer to 'mass' rather than weight.

If there is a difference in energy required to have a '1' or a '0', then the answer is clear (yes, because of E = mc^2)

If there is no difference in energy, there is still be energy associated with the entropy: kT ln(2) per bit of information, and again, there will be a change in mass.

So, my 8 GB memory stick at room temperature has a maximal information difference of 8*2^9*kT*ln(2) joules of energy (about 1*10^-17 J) which corresponds to 4*10^-17 fg. Not much.

Can you explain the energy associated with entropy? And how you do relate entropy with information on a microscopic level?

Andy Resnick said:
This is an interesting question, but the question should refer to 'mass' rather than weight.

If there is a difference in energy required to have a '1' or a '0', then the answer is clear (yes, because of E = mc^2)

If there is no difference in energy, there is still be energy associated with the entropy: kT ln(2) per bit of information, and again, there will be a change in mass.

So, my 8 GB memory stick at room temperature has a maximal information difference of 8*2^9*kT*ln(2) joules of energy (about 1*10^-17 J) which corresponds to 4*10^-17 fg. Not much.

How do you define a change in amount or quantity of information?
In a single memory byte location, which of these has the most "information"?
00000000
11111111
00001111
11110000
If you claim to be able to allocate "mass" to information, which state has the most "mass"?

Ok I just measured it at about 10^(-17) kg heavier with music. That's for a 4GB memory stick. I'm not sure of the measurement error though as I used my kitchen scales.

Stonebridge said:
How do you define a change in amount or quantity of information?
In a single memory byte location, which of these has the most "information"?
00000000
11111111
00001111
11110000
If you claim to be able to allocate "mass" to information, which state has the most "mass"?

I'm not an expert in information theory, but IIRC, a string of identical bits has *zero* information (and zero entropy), because of the way information is encoded in a signal. See the way entropy of a signal is defined here:

http://en.wikipedia.org/wiki/Information_theory

If all 00000000's has the same mass as all 11111111's, then any combination in between should have the same mass I am guessing.

Andy Resnick said:
I'm not an expert in information theory, but IIRC, a string of identical bits has *zero* information (and zero entropy), because of the way information is encoded in a signal. See the way entropy of a signal is defined here:

http://en.wikipedia.org/wiki/Information_theory

"The entropy, H, of a discrete random variable X is a measure of the amount of uncertainty associated with the value of X."

According to that link, entropy is a function of your expectations. If your options are 1 and 0 and you don't know which you're going to get, you have maximum entropy. The values that you actually get, 00000, 01101, etc, don't (typically) change the entropy level.

If you know that the sum of your bits is odd, you have 5 total bits, and you know what the first 4 are, then you can predict the final bit - there is no entropy or uncertainty associated with it. It is only when your bits are correlated like this that the actual series of bits has anything to do with total entropy.

This type of entropy doesn't have anything to do with physical E=mc^2 energy though. If it did, gaining knowledge about what's on my flash drive would change its mass. If my drive has all 0s and I expect a random sequence of 1s and 0s, it is at maximum entropy. If my drive has all 0s and I expect it to have all 0s then it has no entropy. You don't need a physical change to change your information entropy, so it can't be related to mass.

There's no inherent "amount of information" in a string of bits, no matter what they are. It all depends on what you are expecting - what algorithm you are using to encode or decode your bits.

The mass would change if the drive physically has more electrons on it when storing 1s or 0s and your density of 1s and 0s changes. That's the only way I can think of it changing though.

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IMP said:
This might be an interesting read, and seems to be related. It is an article on the similarity between information energy and dark energy:
http://arxiv.org/ftp/astro-ph/papers/0603/0603084.pdf

Interesting, but not quite related . The theory is that the universe is inherently discrete and made of some physical equivalent of bits. We don't exactly have the technology to make flash drives that store information at the qubit level (if there is such a level). We can't just count how much mass it would take to get 8gb worth of qubits (is there even a straight conversion?). Even if we could, we would have to know the mechanism by which the 1s and 0s are encoded into qubits. Which particle property corresponds with a 1 and which corresponds with a 0? Does the particle mass change when we change between these expressions of properties? Is compression used?

The real questions still are, how exactly are 1s and 0s physically encoded, and does the physical 1 have more mass than the physical 0.

On another note, a formatted flash drive and a full drive will typically have about the same random amount of 1s and 0s. Flash bits can only be flipped so many times, so the drive won't be reset to all 0s when it is formatted. The key file system data will be reset, and the rest of the bits are just left randomly set to whatever they are. This is the same as doing a "quick format" vs a full format in Windows.

The only exception is when you first get the drive from the manufacturer, and then it might all be 1s or 0s. Even then, smart drives will use all of the empty space before going back and resetting the used space, so all of those initial values are relatively quickly overwritten.

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You could build a "flash drive" out of wood. It could have 1000 levers. Any levers in the up position are 1's, any in the down position are 0's. Why would the position of the levers change it's mass? All down, all up, any combination in between should have the same mass. Now the 32GB one is rather large...

Initially I made a guestimate based on typical structure of modern flash memory of about 10^3 electrons per floating gate (that is, per bit). Stupidly I took the mass increase to be the mass of these electrons (approx 10^(-27) kg per bit). That's nonsense of course, as each cell remains overall charge neutral and the electrons are just redistributed from one plate of the capacitor to the other.

Looking at it again I'll say approx $n\, q_e\, V\, /\,(4\,c^2)$ kg per bit. So based on n approx 10^3 electrons per bit and assuming V is a few volts, I get about 10^(-33) kg per bit as a serious guestimate for modern flash memory.

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IMP said:
You could build a "flash drive" out of wood. It could have 1000 levers. Any levers in the up position are 1's, any in the down position are 0's. Why would the position of the levers change it's mass? All down, all up, any combination in between should have the same mass. Now the 32GB one is rather large...

I think one part of the OP is whether having more or less energy stored ber bit would make a difference. So we could simplify that aspect of the question, and ask, is there more mass in a compressed spring, compared to an otherwise identical uncompressed spring?

kote said:
<snip>
There's no inherent "amount of information" in a string of bits, no matter what they are. It all depends on what you are expecting - what algorithm you are using to encode or decode your bits.

<snip>

That's not true: entropy is a quantitative measure of the number of equivalent (micro)states. The sequence of bits, when assigned in order to store specific information (however they are assigned), is of lower entropy than a state of "thermal equilibrium" specifically because it is not random.

In order for the sequence to contain information, it cannot be random. Random (thermal) sequences have maximal entropy. Thus, energy is removed from the memory stick when a bit is assigned a specific value (by the amount kT ln(2)).

IMP said:
You could build a "flash drive" out of wood. It could have 1000 levers. Any levers in the up position are 1's, any in the down position are 0's. Why would the position of the levers change it's mass? All down, all up, any combination in between should have the same mass. Now the 32GB one is rather large...

Because in order for you to move a lever, you must perform work on the lever, adding energy to the system.

Andy Resnick said:
That's not true: entropy is a quantitative measure of the number of equivalent (micro)states. The sequence of bits, when assigned in order to store specific information (however they are assigned), is of lower entropy than a state of "thermal equilibrium" specifically because it is not random.

In order for the sequence to contain information, it cannot be random. Random (thermal) sequences have maximal entropy. Thus, energy is removed from the memory stick when a bit is assigned a specific value (by the amount kT ln(2)).

Whether or not information is random or meaningful is 100% a function of your encoding algorithm. What seems random to you is pure information to the right algorithm.

A drive of 100% 0s can be meaningless, or, given the proper algorithm, it can be used to reconstruct the encyclopedia or whatever else you want. The fact that anyone bit sequence itself can have varying levels of information/entropy depending on your expectations is proof that the information/entropy has absolutely nothing to do with mass.

See http://en.wikipedia.org/wiki/Information_theory#Entropy. Entropy is a function of the probability of seeing a certain result, and not the actual result itself. Whether or not you have a 1 or a 0 is irrelevant to the entropy. Entropy is defined by the probability alone.

If I tell you every bit on your drive has an equal chance of being a 1 or a 0, then entropy is maximized for the drive regardless of the actual sequence of bits. If I tell you truthfully that the drive is 100% 0s, then it contains no information and it has 0 entropy. The exact same sequence of bits can have no entropy or maximum entropy depending on the context.

Hey, how about the spring question?

This is very simple way of looking at it.
Does the light switch on the wall weigh more when it’s on or off?
I think the Memory stick is nothing but many off and on switches.
I don’t think there is a difference in weight.
I would say that information does not have weight.

I don't get the focus on the "information" in this thread.

Would the slight change in chemical structure to represent a 0 or 1 bit in a flash memory result in some slightly different binding energy state that would show up as a very tiny difference in mass?

kote said:
<snip>

If I tell you every bit on your drive has an equal chance of being a 1 or a 0, then entropy is maximized for the drive regardless of the actual sequence of bits. If I tell you truthfully that the drive is 100% 0s, then it contains no information and it has 0 entropy. The exact same sequence of bits can have no entropy or maximum entropy depending on the context.

That is not true. Besides, information is stored as a *sequence* of bits, not individual bits considered individually.

berkeman said:
Hey, how about the spring question?

heh... if you put work into the system (because a spring by itself will just rebound), the mass increases.

So would a page of paper on which is written some information, have more mass than the same page on which is scribbled nonsense using the same mass of ink?
If the "information" was encoded so that it meant nothing to you, but I could understand it, does that mean that the mass of the sheet would depend on who is looking at it?
Concentrating on data bits in a computer might be clouding the issue a little.

Andy Resnick said:
That is not true. Besides, information is stored as a *sequence* of bits, not individual bits considered individually.

From http://en.wikipedia.org/wiki/Information_entropy:
In information theory, entropy is a measure of the uncertainty associated with a random variable.

A sequence of bits and individual bits are both treated as random variables, so the distinction is irrelevant.

Definition

The entropy H of a discrete random variable X with possible values {x1, ..., xn} is

$$H(X) = \operatorname{E}(I(X)).$$

Here E is the expected value function, and I(X) is the information content or self-information of X.

I(X) is itself a random variable.

Entropy is a function of what you expect a random variable to be, not what it actually is. See http://en.wikipedia.org/wiki/Expected_value for a description of the expected value function used to define entropy.

Again, Shannon entropy, which is entirely different than thermodynamic entropy, is a function of probability. Fair coins and weighted coins can produce the same sequence of heads and tails while having different entropy due to the different probabilities of forming that particular sequence.

If you are going to claim as fact that the mass of an object depends on how it is interpreted symbolically, please provide some support. There certainly isn't any support for your claim in information theory. You might begin with http://www-ee.stanford.edu/~gray/it.pdf.

Regarding the spring question, it's correct that the spring will gain mass when compressed. This is because the work you do to the spring is stored as potential energy in the system. It is not correct that when you flip a (horizontal) light switch or lever that its mass will increase. This is because when you flip a switch the switch itself does not store any energy. The switch immediately does the same amount of work, through friction and air displacement, to its environment. Any heating of the switch during this process will increase its mass, but that heat (and mass) will dissipate to the environment, leaving the switch with same energy and mass that it started with.

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Stonebridge said:
So would a page of paper on which is written some information, have more mass than the same page on which is scribbled nonsense using the same mass of ink?
If the "information" was encoded so that it meant nothing to you, but I could understand it, does that mean that the mass of the sheet would depend on who is looking at it?
Concentrating on data bits in a computer might be clouding the issue a little.

Sigh. If the entropy is different, the mass must also be different.

kote said:
<snip>

Again, Shannon entropy, which is entirely different than thermodynamic entropy, is a function of probability. <snip>

Ugh. What do you think the statistical-mechanical interpretation of entropy is?

Andy Resnick said:
Stonebridge said:
So would a page of paper on which is written some information, have more mass than the same page on which is scribbled nonsense using the same mass of ink?
If the "information" was encoded so that it meant nothing to you, but I could understand it, does that mean that the mass of the sheet would depend on who is looking at it?
Concentrating on data bits in a computer might be clouding the issue a little.

Sigh. If the entropy is different, the mass must also be different.

To be clear, are you telling us that the mass of a book depends on the native language and educational level of its reader?

Let's say you had a drive with all 0s and re-wrote it so they were all 1s. In both cases the entropy is zero. So if the mass increases then conservation of energy has been violated, no?

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