Uh, you are confusing mass and weight. You have the same mass no matter where you are in the universe, but your weight is relative to gravity. They are completely different.
Silly Scott, I do not mean weight. I mean mass.
At an infinite distance from the Earth (pretend there is nothing in the universe besides you and Earth), your body has some given mass. You also have 0 potential energy. As you move towards the Earth, your potential energy goes negative. This energy gets released, in the form of you losing mass, because energy is conserved. A carbon-12 atom has less mass than 6 protons + 6 neutrons + 12 electrons. Science.
When I say configuration, I mean how the coin is physically positioned with respect to the Earth. That does change their mass. A coin at sea level has less mass than a coin 1000 miles up.
True story. It's actually any potential field (e.g. electric field), not just gravity. Everybody knows the equation, but nobody seems to know what it means:
E = mc2
where E is energy, m is the mass of an object, c is the speed of light. This means matter and energy are the same thing. Energy is the same thing as mass. If you change the energy of an object, the mass will change accordingly.
where E is energy, m is the mass of an object, c is the speed of light. This means matter and energy are the same thing.Energy is the same thing as mass.If you change the energy of an object, the mass will change accordingly.
Wow, very interesting discussion on entropy and information. It is very hard to understand why a laptop full of zeroes weighs less than a laptop full of structured information. It gets even harder to understand when you realize that the most information you can cram in there is when everything is compressed perfectly. But perfect compression is indistinguishable from random noise, which contains no "information" as we generally think of it, but contains maximal information from a statistical and energy content view.
Interesting stuff!
And right on time, regarding the original question of computational resources, Slashdot has an article about this on the limits of computational speed. If people are interested I may be able to get hold of the original scientific article (abstract).
Edit: Scott is right though, in real world situations, the energy content of information is insignificant compared to e.g. the energy used by the system housing said information.
Edit2: I just back-of-the-envelope calculated the difference in mass of an empty 1TB drive vs a full drive. The result is 1.84*10^-23 Kg or about 11 000 protons. The reason why this is so small when compared to the drive is that the drive uses a gigantic amount of mass per bit of storage. As technology advances the mass necessary for storing one bit will decrease so the relative mass fraction of the information itself might catch up. E.g. for a Trillion terabytes the mass is already 0.02 micrograms :-).
Edit2: I just back-of-the-envelope calculated the difference in mass of an empty 1TB drive vs a full drive. The result is 1.84*10^-23 Kg or about 11 000 protons. The reason why this is so small when compared to the drive is that the drive uses a gigantic amount of mass per bit of storage. As technology advances the mass necessary for storing one bit will decrease so the relative mass fraction of the information itself might catch up. E.g. for a Trillion terabytes the mass is already 0.02 micrograms :-).
I just want to clarify something. As we've already discussed, the "bits" in a magnetic hard drive are represented by sectors that are either magnetized or demagnetized. Are we then saying that the full drive is one that is entirely magnetized or one that is entirely demagnetized? Or are you saying that a full drive is one that is full of data? Are you then saying that a 1TB drive which contains 1TB of videos has more mass than one which is all 1s or all 0s? Please clarify.
Also, how does this apply to flash storage, or how about optical storage?
From my understanding, the logic gates that flash drives work on are held open (that is, in the "1" position) by a captive electron. This electron is forced into place by a process known as hot carrier injection. So, the more 1s are needed to represent your file on a flash device, the more electrons are needed to hold the gates open. Thus, more weight.
optical storage?
EDIT: Thought I had this one right, but no. I was wrong. The info on flash storage should be correct.
Or are you saying that a full drive is one that is full of data? Are you then saying that a 1TB drive which contains 1TB of videos has more mass than one which is all 1s or all 0s? Please clarify.
Yes, this is what Timo is saying - his argument is based on entropy and information theory. I'm still thinking about the details, myself.
I just want to clarify something. As we've already discussed, the "bits" in a magnetic hard drive are represented by sectors that are either magnetized or demagnetized. Are we then saying that the full drive is one that is entirely magnetized or one that is entirely demagnetized? Or are you saying that a full drive is one that is full of data? Are you then saying that a 1TB drive which contains 1TB of videos has more mass than one which is all 1s or all 0s? Please clarify.
Basically yes. Although what I am saying goes even beyond that, in that it doesn't matter whether the information is stored by magnetization, phase changes in a crystal lattice, or very well trained beavers (answering your question about flash etc). I am talking about the energy of Information itself, or rather the relation of statistical entropy to thermodynamic free energy (wiki article).
In thinking about this it is also very important to differentiate between "information" in the statistical sense, and "information" in the philosophical sense, these are not the same (see Kolmogorov complexity for some discussion). Finally it should be noted that, even though it is made on a sound theoretical basis, the statement "a laptop weighs more when full than when empty", is made slightly tongue in cheek and could be contended by experts in thermodynamics based on minutia of the actual system. Mainly this is to do with the transfer of statistical entropy (which can be calculated for anything) and thermodynamic entropy (which is well defined only in macroscopic physical systems) and how the two can be exchanged.
For a physical object, such as a laptop, the statement stands.
HAH! Some kurazii Japanese physicists think they figured out a way of getting energy from pure information, which (as I said) was the major malfunction in my derivation of "a 1TB drive full of zeroes weight 11k proton masses less than a drive full of information".
Comments
...Can't let you do that, Starfox.
E = mc2
where E is energy, m is the mass of an object, c is the speed of light. This means matter and energy are the same thing. Energy is the same thing as mass. If you change the energy of an object, the mass will change accordingly.
Interesting stuff!
And right on time, regarding the original question of computational resources, Slashdot has an article about this on the limits of computational speed. If people are interested I may be able to get hold of the original scientific article (abstract).
Edit: Scott is right though, in real world situations, the energy content of information is insignificant compared to e.g. the energy used by the system housing said information.
Edit2: I just back-of-the-envelope calculated the difference in mass of an empty 1TB drive vs a full drive. The result is 1.84*10^-23 Kg or about 11 000 protons. The reason why this is so small when compared to the drive is that the drive uses a gigantic amount of mass per bit of storage. As technology advances the mass necessary for storing one bit will decrease so the relative mass fraction of the information itself might catch up. E.g. for a Trillion terabytes the mass is already 0.02 micrograms :-).
Also, how does this apply to flash storage, or how about optical storage?
Also found this: Rest Mass Versus Relativistic Mass.
Is there a good article explaining where the 'extra' mass comes from when dealing with relativistic mass?
I'm still thinking about the details, myself.
In thinking about this it is also very important to differentiate between "information" in the statistical sense, and "information" in the philosophical sense, these are not the same (see Kolmogorov complexity for some discussion). Finally it should be noted that, even though it is made on a sound theoretical basis, the statement "a laptop weighs more when full than when empty", is made slightly tongue in cheek and could be contended by experts in thermodynamics based on minutia of the actual system. Mainly this is to do with the transfer of statistical entropy (which can be calculated for anything) and thermodynamic entropy (which is well defined only in macroscopic physical systems) and how the two can be exchanged.
For a physical object, such as a laptop, the statement stands.
Now excuse me while I go patent Maxwell's Demon.