I suspect that the relativistic mass of a memory stick depends more on the ambient room temperature than how many bits are set to one...

How is 'information' in the universe (presumedly describing the physical configuration of mass-energy?) encoded on any physical medium? EM charges? Virtual particles? CMBR distribution? What processes decode any stored information - translating it into physical energy configurations?

The additional mass thought necessary to account for the discrepancies between the observed rotation curves of spiral galaxies and those predicted based on standard methods of gravitational evaluation ranges from 6-10 times typical mass estimated for luminous galactic matter. That would have to be some really 'heavy' information!

Likewise, the inferred mass of cosmological 'dark matter' is thought to be around 6 times that of 'ordinary' matter...

@Tamas. In physics, when we talk about information we are not talking about semantic meaning as your chalk example suggests. We are talking about physical information, which is different and related to entropy.

Tamás,

"... or if it is information about a physical object, all properties belong to that object."

Yes but, like your cat, no object 'knows' of any information that may be known about it and, as I understand, there is no (even hypothetical) process that causally relates any information to any property of matter. For example, in the case of quantum entanglement, if information is either communicated between or shared among particles, what particle process can cause the physical reconfiguration of the entangled particle to align with the detected particle's measured property state?

Actually, the bit states of any data storage device only relates to information to the extent that some intellectual processes attribute some specific meaning to them. IMO, information related to physical systems exists only in the mind of an observer...

Derek,

"In physics, when we talk about information we... are talking about physical information... related to entropy."

Actually, the concept of information is used and misused in a large variety of ways by physicists, resulting in a great deal of misinformation and confusion. Please see http://en.wikipedia.org/wiki/Physical_information

IMO, any variation in the relativistic mass of a memory storage device due to the charge state of any bit domain has absolutely nothing to do with any physical energy or mass related to 'information' - the question is based on (common) misconceptions.

Derek,

I think I understand how did you arrive at your great question. We know the equivalence of mass and energy, thanks to Einstein. It seems natural to think that those two attributes are not enough to understand the world around us, we certainly need the information, too. Therefore, IMHO, it is likely that the next great breakthrough in physics will be to establish a relation like the one below:

E/(mc^2) = (1/2) [ 1 + exp(I\pi)],

where "I" is information, of course, and the factor \pi is present just for the elegance.

As I'm known as a guy with good ideas, but - unfortunately - without equally good final touch, then don't forget me, please, after you are nominated to the Nobel Prize for proving the above formula;)

Marek,

In the mass-energy equivalence equation, the terms are quantifiable - measurable physical aspects of matter in the universe. How does one quantify 'information' in your suggested equation - by the number of bits required for representation? If I assign a value of '1' to the existent state of the universe and '0' to the non-existent state, is that bit of information equivalent to the spin state of an individual particle?

As I hope I've explained, there is no mass-energy that can be physically attributed to information - even when some minute quantities can be attributed to the physical storage and processing of data bits.

IMO, the concept of physical information is a projection of human intellectual conception onto the universe, akin to considering what forces a particle 'feels'. Particles feel and know nothing - they only respond to physical effects imparted to them. It is we who produce information from data.

Hi Derek,

I don't follow the logic leading from the statement :

" I slightly increased the inertial mass of the particle, by raising it."

To this conclusion :

"Therefore, the weight of a flash memory should be different if I write information to the memory."

On the other hand, I've found this interesting paper :

http://arxiv.org/abs/0711.1197

In my view there's no connection between information and mass/energy.

Information, since Shannon, is a measure of the entropy of the system not necessarily related to its total energy.

James,

I forgot to add at the end of my message "Don't ask me what is information". This is fully compatible with Norbert Wiener view of entropy, when he advised Shannon on how to call his expression "p*log(p)".

Essentially I agree with your point of view: particles feel and know nothing. Note, however, that in order to describe their evolution you have to know their initial conditions, i.e. positions and velocities, after Laplace, if I'm not mistaken. Today we perhaps should add more degrees of freedom, like spin. This is, in my opinion, the information, the one being an essential component of reality. That means indeed many, many bits, not just one - as you suggest. Such an information may reside in our minds, but this is by no means necessary. It is the mindless particles who "process" the information, while our minds merely register it.

If you think information is merely a concept, not reality, not able to drive purely physical processes, then what would you say about DNA double helices? They all consist of always the same 4 amino acids, yet after some time you have a tree, a human, or a fish. Isn't it the result of information hidden somewhere in a single DNA helix?

Marek,

Yes, information can be difficult to define...

My intended point is that, it is we require at least data regarding position and velocity, for example, to predict the motions of particles using equations that represent the physical processes that produce them. Particles are not aware of their initial conditions and do not employ equations or information processes to determine their motions - they, in very general terms, respond mechanistically to conditions and interactions. That their motions correspond to the the products of our equations is the measure of our collective intellectual capabilities.

Yes, we would require an enormous amount of data and informational processes to accurately predict the behavior of the physical universe, but IMO the components of the universe only respond to the conditions that are presented to them in the ways that they must.

I think that living systems are well outside the boundaries of strictly physical processes and systems. DNA decoding may be a relatively straightforward process of producing proteins, to the extent that I understand, but the biological processes that ensue are extremely complex. The encoding of DNA involves reproduction success within populations, based on the biological characteristics imparted to individuals, etc.

I have been over-stringent in my attributing information processes to solely human intellect - to some extent all animals process sensory data relating to the immediate environment in some reductive process to produce information that can be used in decision systems to determine present and future actions. However, only humans have clearly developed systematic methods of symbolic reasoning applied to conceptual abstractions. Certainly it is through informational processes and mathematical reasoning that physicists have been able to usefully represent the physical processes that actually determine the dynamical properties of the universe and its components. As I see it, the universe does not require information about what it's doing in order to determine what to do...

Derek, interesting question!

It seems clear that macroscopic bound systems like a memory chip should have the

same mass whether the stored bits represent noise or contain information. Energy is

required to change the memory cells creating heat that momentarily increase mass

before it is dissipated to the surroundings. Total entropy thereby increasing.

If the high and low bits contain different charge, potential energy etc. mass will change, but that is a very different problem from mass contribution of information itself.

The situation is different if the chip is put in a closed adiabatic system and left to

deteriorate over time. Left on it own, entropy will increase and information will be

lost. The mass will then as I understand it be constant over time.

In order to maintain or increase the information contained inside a closed adiabatic

system over time, energy is needed to be put in from the outside. This energy then

contributes to the total mass of the system.

A simplified adiabatic system of molecules with a defined number of freedoms is

probably a much better model of what is going on than any macroscopic systems.

Then it can be argued that information itself has weight since most ordered molecular structures capable of being interpreted as information have a higher potential than disordered ones. The question is then whether this can be generalized to more macroscopic and open systems.

What seems clear is that energy input is needed to maintain or increase information

density in any closed system. Then a closed system with constant information density should need to increase its mass over time.

How can the physical properties of recorded noise vs. music or any other data be distinguished? Information can only be retrieved or stored by a intellectual process that applied a coding method to interpret data. As such, the physical properties of meaningless random data are indistinguishable from encoded data.

In the case of DVD-RW devices, for example, binary data is recorded by modulating the amplitude of laser light to produce a amorphous or crystalline structure in a medium of metal alloy. The two phases of metal have differing reflective properties that can be probed by low powered laser light and a detector. Obviously, writing and reading storage locations involve heating to varying degrees, but once cooled to ambient temperature - how would the disk mass vary based on the informational value of any recorded data? How would that mass differ from randomly recorded noise?

Encoding of a signal into a physical structure of some kind changes its properties in a similar way as to the properties of the signal itself. For macroscopic structures this may not be so obvious. On a molecular or nano level, when coming closer to the (classical) limits of information density, encoding structured information will increase order and locally decreases entropy. One way to look at it is that the small molecules will interact, while the memory cells of a macroscopic memory are spaced so far apart as to not affect each other much. Ordered structures tend to be at a higher potential than disordered ones. This gives plausibility to the idea that information may have weight.

If the signal is baseband white noise, no extractable information is encoded and it can be argued that the entropy is at maximum. If the signal is a sinewave or any other information it can be detected equally both in the recorded signal and in the medium itself. Correlation analysis of an unknown structure or signal is one way to do this. Information in this context could be defined as any order imposed on a physical system that can later be decoded. By clever encoding schemes information content can be optimized. There are of course many possible definitions of "information".

This is a bit different from the question - does information itself have weight?

This is much more difficult to answer. What seems to be the case is that molecular information carrying systems tend to have higher energy than disordered ones, and therefore more weight. Also encoding information will require energy to maintain it in a closed system over long time periods. If the system is closed, this means that temperature will increase over time eventually reaching a limit destroying the information inside...

An information carrying system would then always seem to need some energy input and cooling in order to maintain its information content intact over long timeperiods.

I do not think dark matter could be composed of "information". It would mean that the mass of hyptetical information would greatly exceed the 5% mass of ordinary matter carrying this information. But perhaps some fractonal mass in bound systems like galaxies could be considered to consist of "information".

Data has no inherent meaning - even the symbols contained in this message have meaning only to an intelligent process (you, the reader) that imparts a specific method of interpretation to extract information from it. Whatever the mass of the preceding symbols might be, the following symbols' must have similar mass-energy while having no informational value: xxxx xx xx xxxx xx xxxxxx xxx x x xxxxx...

Dear Tamás,

Yes, I think we are in general agreement (although I will quibble about information being a strictly mathematical construct - by combining sensory data sources, animals are able to aggregate threat assessment information, conclude that they are in danger and respond appropriately, for example). Anthropomorphization is a critically appropriate term here!

In the context of quantum physics, as I understand it has been suggested that quantum (particle) information is (somehow) retained (at the event horizon of black holes) for ingested particles and even that information about all mass-energy is holographically encoded throughout spacetime. While I cannot fully evaluate these arcane propositions, there seems to be a fundamental failing in their not recognizing the requirement for systematic processes that transcribe abstract information regarding mass-energy configurations, encoding and somehow storing associated data in the environment. Likewise, there is no recognition of the requirement for processes that decode any such recorded data in order to physically configure quantum particle mass-energy.

IMO, the fanciful 'storage' of 'bits' of quantum information servers no useful purpose without some physical processes to extract & encode, and decode and implement any abstracted information related to physical systems in the universe. It is for these reasons that I may vehemently object to what I consider to be misconceptions about abstracted information and its relation to natural physical systems - I believe the processes of information abstraction are being anthropomorphilogically ascribed to the physical universe by physicists!

I do apologize if I offend anyone...

@James & Tamás

I disagree with most of Your statements if You claim that You are discussing information theory in context of the posters question related to physics. How information is interpreted by intelligent beings is a question for other sciences such as psychology and philosophy, certainly very interesting and relevant subjects in them self. But information as usually defined in physics is a much wider subject concerned with encoding, decoding, storage and transmission of information. Information is related to encoded complexity that can be decoded by some means. If it is actually decoded or not or by whom does not matter. We decode optical and radio astronomy information teaching us most of what we know about the universe at large. the information is there whether we chose to decode it or not.

A simple mechanical key opening a lock decodes the the information in the key in the process. No intelligence is involved. Similar simple designs are possible in nature by trial and error, such an example is the subject of evolutionary programming and in biological evolution itself. Information encoding and decoding in communication channels can hardly be considered requiring intelligence.

A sequence of noise is easily discriminated from one rich in encoded information. A simple correlation analysis will do this. The question is probably more about what complexity do you require in order to define something as "information". The smallest unit as far as I understand the subject is a digital bit set to true or false. What this bit then represents can be very different, but that does not affect the way it behaves in a certain physical storage media.

I am not able to define exactly what information is, there are many possible definitions even if we just stay in a non quantum classical physics context. Perhaps somebody more knowledgeable could update us on the more recent opinions on this in modern information theory? My knowledge of the field is probably quite outdated, from the late 1880:es...

The subject in this post relates more to properties of dense information rich systems that can be discussed in thermodynamic terms. A disperse system has very little interaction between the information carrying elements.

Erik,

I disagree entirely - as I think I've repeatedly explained. IMO, 'information' in physics is discussed far too broadly - far beyond its "encoding, decoding, storage and transmission of" - data bits! As I mentioned, information is even referenced in cosmological terms, absurdly in the posted question as a potential explanation for the perceived missing mass in the universe (my apologies, but the suggestion is absurd). Again, in that case, information would have to represent about six times the total mass of ordinary baryonic matter in the universe! Is the Earth becoming more massive as a result of the vast amount of information we've very suddenly accumulated?

Do you really consider the flash memory device mentioned in the posted question to be a "dense information rich system"? How is it a "disperse system", having "very little interaction between the information carrying elements"?

Please consider these questions I posted earlier:

In the case of DVD-RW devices, for example, binary data is recorded by modulating the amplitude of laser light to produce a amorphous or crystalline structure in a medium of metal alloy. The two phases of metal have differing reflective properties that can be probed by low powered laser light and a detector. Obviously, writing and reading storage locations involve heating to varying degrees, but once cooled to ambient temperature - how would the disk mass vary based on the informational value of any recorded data? How would that mass differ from randomly recorded noise?

I don't know offhand whether it is the reflective property of the amorphous or crystalline structure is used to represent a '0' or a '1' - but either one could be (i.e. the '0' and '1' specification, could be exchanged). In that case, any physical differences in mass between amorphous and crystalline pits might be associated with either the value '0' or '1' - inverting any connection between bit storage mass and any information represented.

Similarly, in charge state memory systems (without any media exchange capability), whether a charge exceeding the threshold value or one that does not represents a '1' for example, is strictly a matter of internal device specifications. As a result, any relation between 'bit' charge state and information mass is strictly coincidental.

I agree with Tamás and James that information is an abstract concept, in my opinion having features similar to entropy. The difference between the two, I think, lies in fact that entropy has no sense for any "simple" single object, be it photon or electron, while such object may (and should!) carry an information, not even a single bit. If so, then its "mass equivalence" is probably very small, of order of Planck mass. No wonder it cannot be easily detected in our today's information storage devices. But at galactic scale things may be different. On the other end, the information may be the true cause of a "zero point energy" of a quantum harmonic oscillator. Just hints, pointing that some day we will see the "mass-energy-information conservation law".

Very well said, Tamás! It's real pleasure to red your contribution.

Tamás,

Yes - well put!

I must say IMO, that if the properties of matter or physical 'parameters' are to be considered information, they must be used by some information process that mediates between physical states and that information. Having state information encoded holographically upon the event horizon of a black hole (in order to avoid a perceived information loss paradox), for example, is only meaningful and useful if some process can retrieve 'ingested' particles from the retained 'information' along with perhaps some eventual reprojection of their energy...

BTW - IMO, as long as the energy is retained energy conservation is preserved. I do not understand why it's thought that all past configurations of energy be maintained as 'information' - why it's thought that this information must be conserved in the universe. That seems like saying that all motion within the universe must be reversible... After all, motion and velocity also affect relativistic mass!

@James

I made the same argument as You do regarding dark matter in relation to baryonic matter previously in this thread, so on this we agree...

I assume Derek used the memory chip as a metaphor to make the point of his question. Perhaps it should be reformulated "Does the information content (density) of a closed physical system affect its mass?" or similar. The density of information in a DVD or flash memory is likely so low that no internal interaction between memory cells takes place, as I wrote earlier in the thread. I also agree that the absolute potential of the cells probably should not matter much in this context.To me it is what happens to the interaction between the particles/states and internal energy change for the system as a whole when information content changes that seems interesting. Then it makes sense to discuss this in terms of thermodynamics, which gives the stored information properties similar in concept to any adiabatic ordered system that can be modeled using thermodynamic methods. Any hypothetical mass effects will likely be most evident at high information densities.

@Tamás

I like Your discussion about what information is to us and I agree with much of it. Perhaps it is partly a semantic problem, As human being we use the word in one sense and in different scientific disciplines we mean something different. Perhaps we need new words. Maybe a good definition of subsets relevant in different contexts (as You sort of indicate in Your text) could be made.

But whatever we chose to call it, any imprinted or existing order imposed on a physical system can represent information according to more restricted definitions of what information is. In a classical context the physical system will exist in its state whether we look at it or not. (A quantum system is of course different situation) If this is meaningful to us or not depends on the coding and/or decoding of the imprinted information in different situations. But the physical information content will nevertheless be the same. And speculations about the properties of this particular physical system and its information content, like in this thread, therefore seem relevant. These speculations then also apply to more restricted definitions, whether these definitions are meaningful to us in a certain context or not....

I have a problem with considering abstract thinking as information or data, even assuming a simple mechanistic process. Abstraction requires processing of information, which is different. A much simpler example is data reduction of repetitive patterns etc. requiring processing in addition to memory.

@Marek

Just to split some hairs - even purely abstract constructs will need to be encoded into something physical, at least into our brains...

An attempt to identify some of the several interesting questions being discussed in this thread, perhaps deserving threads of their own....

Is energy required to maintain information over time?

What is information and which definitions of information make sense in different contexts?

What makes information different from a random data sets and noise?

What is the distinction between data/information and processing of the same?

What are the possible cosmological implications if information can carry mass?

See here for an interesting discussion on the topic:

http://www.ece.tamu.edu/%7Enoise/research_files/IEEE_information_mass.pdf

Dear all, thanks for many interesting insights in this discussion; what is yet missing is the aspect about how complex information structures humanity produces (as self-evolving system?!) manifestate in time and space, and also energy flow.

Seems that the terms "semantic  entropy" and "semantic weight" are not yet completely explored. I put a couple of relevant papers towards these topic in the following RG thread:

https://www.researchgate.net/post/Foundations_for_semantic_weight_and_semantic_entropy

Btw looks like that there now a formula to calculate the mass of information:

https://www.researchgate.net/publication/260922976_The_mass_of_a_bit_of_information_and_the_Brillouin's_principle

Article The mass of a bit of information and the Brillouin's principle

Entropy: A concept that is not a physical quantity

https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity