is matter eternal ?
We don't really know. Proton decay has never been observed, but may be a possibility. However I don't think electrons are believed to ever decay, so they may outlast protons and be truly eternal. But we simply don't know is the only accurate answer I can give you.
Drakkith is right. Some particles do spontaneously decay, but so far there is no indication that basic building blocks like proton and electron decay.
You would have to be more specific about what you mean. Do you include light energy (photons) as a form of matter? Do you include black holes?
You have to give some practical meaning to your question. Black holes do evaporate but very very slowly, producing radiation. Light is gradually redshifted out of existence. Photon is still there but so feeble that no practical means of detecting it. Do you care, if it can't be detected?
I guess one could imagine that in trillions of trillions of years all of what you call matter falls into BHs and all the BHs evaporate and there is nothing but light, which is getting longer and longer wavelength (because of expansion) so existence slowly wimps out. Don't know how realistic that is. I doubt ALL the matter could fall into BHs.
Also do you mean merely future-eternal or do you mean past-eternal as well? Some models of cosmos have expansion starting with a BOUNCE---a rebound from a prior classical universe contraction phase. Matter in some form could have undergone such a bounce, and so have a history that goes back before start of expansion.
So maybe you could think of ways of making your question about "eternal" less abstract and give it a more practical meaning. then maybe even if we don't have a complete ultimate answer we could say SOMETHING.
Protons obviously tend not to decay over time spans equaling the age of the universe. We see little evidence of any significant variance in the baryonic mass of the universe over the past ~14 billion years.
An interesting read: Future of an Expanding Universe
What is matter? What is eternal?
I have not found a quantitative definition of matter anywhere. Neither is there a quantitative definition of eternal.
You appear to be asking about the limits of a conservation law. There is conservation of energy, conservation of momentum, conservation of electric charge, and other conservation laws. Some scientists have been analyzing the general validity of some conservation laws.
The phrase "conservation of matter" used to apply to a law now called "conservation of mass." However, mass is now known to be equivalent to energy. Therefore, matter can no longer be equated with mass.
There is currently no unambiguous definition of matter. If there is an unambiguous definition of matter, then the definition would be of scientific interest in itself. Similarly, it would be interesting if there was a quantitative definition of eternal. Without knowing what these things are, one can not answer your question.
There is no definitive definition of matter. Therefore, it is meaningless to ask whether matter is eternal.
The word eternal is sometimes associated with the mathematical concept of infinity. Eternal is sometimes defined as infinite time. However, infinite quantities by definition can't be measured.
Infinity refers to asymptotic limits. Infinity is sometimes a useful concept when estimating the accuracy of certain physical expressions. However, there is no way to measure an infinite quantity even in principle. Therefore, the question of what is infinite and what is eternal has no physical meaning.
Your question is purely philosophical rather than scientific. There is no measurement that can answer your question, even in principle. If one can't measure something even in principle, then one can't discuss it scientifically.
The policy of this forum excludes purely philosophical questions. Therefore, the moderator may soon block the thread. However, before the moderator does that I suggest that you rephrase the question.
One can scientifically ask about the accuracy and reliability of a conservation law. If you rephrase your question with regards to a conservation law, then the discussion could continue. For example, you may start a thread asking about the limits of validity of the conservation of energy. I don't think the moderator could object to that.
Also, present some of your own work. For instance, how would you set up an experiment to determine if anything is eternal?
Separate names with a comma.