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We can observe an object with mass as it has a well defined boundary but it is not the same with energy.

What may happen to the information or data that exists with an object and is needed to constitute an object when mass is converted into energy.

When we see matter as objects around us it has details. For example a ball has structure of elements and molecules constituting it, its shape, size etc. If suppose it was converted to energy it should still posses the information about its constitution, its identity as information cannot be destroyed.

And when we talk about other objects and forms of matter that are complex, say those with life. They have much more information associated with them. What can possibly happen to all this information if suppose it was converted to energy. There has to be some way to store all the information associated with an object be it any form. A energy counterpart for every particle counterpart? For example if it were a chemical reaction and water vapor was converted into water the molecules are still intact.

When there is a nuclear reaction and mass is converted into energy the information associated should still be present in some way.

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Take a look around you. What you see is seen through the electromagnetic field, which obviously contains a great deal of information. Whether one wants to count it as just energy or a particular kind of matter (composed of photons) is mostly a issue of convention. A deep reason is that there is no true distinction between matter and energy, as shown by relativity theory. Energy doesn't have to be featureless, and can carry information.

A neat example is Alonso-Serrano and Visser's paper On burning a lump of coal, where they point out that burning a lump of coal or encyclopedia must, because of the unitarity of quantum mechanics, produce radiation that actually encodes the information in photon-photon correlations (with on average $3.9 \pm 2.5$ bits per emitted photon). Presumably the same thing happens if you do other processes converting matter to energy (e.g. fuse it in a star or drop it into an accretion disk).

The one possible exception is black holes. Black hole information paradox is all about the apparent lack of unitarity in converting encyclopedias to Hawking radiation by dropping them into black holes. One popular answer is that the information is still there, encoded in correlations in the radiation, but there have been big theoretical arguments back and forth on this.

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