Marcos, you know that's an interesting question. I have often thought that in the past. But, the question itself is 'rather loose'. Still, I'm pretty sure I get your meaning.

OK, let's look at it this way. As you probably already know, Albert Einstein's famous equation E = MC^2, where E is the equivalent energy, M is the mass of the object (read that 'matter') of interest, and C^2 is the proportionality constant, equal to the speed of light in a vacuum squared. It's this correspondence that causes people to say things like "Is matter condensed energy?"

So, how do physicists know this is true? Consider nuclear fusion. Let's fuse a proton and a neutron together to make a Deuterium nucleus by slamming them together at some great speed. We must also keep track of the kinetic energy of the incoming particles and the out going nucleus. If you sum the mass of the proton and the neutron separately and then compare that number to the measured mass of a Deuterium nucleus, you will find that the mass of the nucleus is less than the sum of the parts. That difference in mass goes into the kinetic energy gained by the out going nucleus.

Wow, that's pretty obscure huh?

Let's look at another reaction. Let's combine a proton and an anti-proton. In this reaction, the proton and anti-proton TOTALLY ANIHILLATE. That is, they convert 100% of their mass into energy. They don't just break apart or anything like that, they totally convert into a gamma ray photon with energy equal to that predicted by Einstein. This is a well known and often measured reaction in the laboratory (e.g.: CERN's Large Hadron Collider).

Well, both these reactions are actually showing how matter can 'evaporate' into energy. (Speaking VERY loosely!). But the original statement is about 'condensation'. Does that really happen? Can we take just energy and produce matter? The answer to that question is 'yes'.

Aside from considering what happened at the beginning of the 'big bang', where pure energy created all the mass of the entire universe, is there a more practical example? Yes, this is also done frequently in particle accelerators. Heavier particles that have very short lifetimes (and therefore are not readily available for study in the laboratory) are synthesized/created on demand by slamming two particles together at very high speed (that is, having large energy). With some degree of predictability, a much heavier particle is created. Need a heavier particle? Go faster (more energy).

In a now famous example, this is how the Higgs particle was synthesized and detected at CERN. The Higgs particle is hundreds of times more massive than any conventional sub-atomic particle. So, in order to create one, the two particles that are collided must have fantastically high energies. And, that's why CERN's Large Hadron Collider cost so much money, took so long to build, and literally spans two countries.

I hope this helps.

Marcos, where did you get this sentence from? According to Albert Einstein, energy of any object is equivalent to its mass, not to matter. Matter is a rather loosely defined term.

Hi Sergei

Any forums and blogs that disclose about physics is customary to have someone that puts the sentence. An example: http://my.opera.com/urzmath/blog/2012/10/07/matter-as-condensed-energy.

There would be a confusion or misinterpretation to equate mass and matter?

http://my.opera.com/urzmath/blog/2012/10/07/matter-as-condensed-energy.

Marcos, you know that's an interesting question. I have often thought that in the past. But, the question itself is 'rather loose'. Still, I'm pretty sure I get your meaning.

OK, let's look at it this way. As you probably already know, Albert Einstein's famous equation E = MC^2, where E is the equivalent energy, M is the mass of the object (read that 'matter') of interest, and C^2 is the proportionality constant, equal to the speed of light in a vacuum squared. It's this correspondence that causes people to say things like "Is matter condensed energy?"

So, how do physicists know this is true? Consider nuclear fusion. Let's fuse a proton and a neutron together to make a Deuterium nucleus by slamming them together at some great speed. We must also keep track of the kinetic energy of the incoming particles and the out going nucleus. If you sum the mass of the proton and the neutron separately and then compare that number to the measured mass of a Deuterium nucleus, you will find that the mass of the nucleus is less than the sum of the parts. That difference in mass goes into the kinetic energy gained by the out going nucleus.

Wow, that's pretty obscure huh?

Let's look at another reaction. Let's combine a proton and an anti-proton. In this reaction, the proton and anti-proton TOTALLY ANIHILLATE. That is, they convert 100% of their mass into energy. They don't just break apart or anything like that, they totally convert into a gamma ray photon with energy equal to that predicted by Einstein. This is a well known and often measured reaction in the laboratory (e.g.: CERN's Large Hadron Collider).

Well, both these reactions are actually showing how matter can 'evaporate' into energy. (Speaking VERY loosely!). But the original statement is about 'condensation'. Does that really happen? Can we take just energy and produce matter? The answer to that question is 'yes'.

Aside from considering what happened at the beginning of the 'big bang', where pure energy created all the mass of the entire universe, is there a more practical example? Yes, this is also done frequently in particle accelerators. Heavier particles that have very short lifetimes (and therefore are not readily available for study in the laboratory) are synthesized/created on demand by slamming two particles together at very high speed (that is, having large energy). With some degree of predictability, a much heavier particle is created. Need a heavier particle? Go faster (more energy).

In a now famous example, this is how the Higgs particle was synthesized and detected at CERN. The Higgs particle is hundreds of times more massive than any conventional sub-atomic particle. So, in order to create one, the two particles that are collided must have fantastically high energies. And, that's why CERN's Large Hadron Collider cost so much money, took so long to build, and literally spans two countries.

I hope this helps.

There is a fork in the conceptualization of matter. Along one fork, matter is infinitively divisible. The equation E = mc2 appears to be consistent with that pathway. However, what controls the balance point between matter and energy? How can the expression of energy go from an apparent velocity of zero to c and vice versa? If matter is infinitively divisible, how does one reconcile a supposedly continuum of mass components with the distinct constituents in the hierarchical patterns of matter that we observe? For example, encounters between positrons and electrons, under appropriate conditions, appear to result in their mutual annihilation or disappearance and a release of energy in the form of and at a specific photon level. In the converse situation, photons of the same precise energy level fired into the environment of a bubble chamber “appear to” create electron-positron pairs. Why isn’t there an analogous sequence for each species of photon?

If the path toward an ultimate particle is taken, it conceptually undermines the contemporary interpretation of the relationship E = mc2. It distinguishes the motion (energy) associated with particles from matter itself. Why have scientists missed elucidation of the ultimate particle? It is proposed that its experimental accessibility is associated with the “crossover zone”. In the crossover zone small, unit-like entities cannot be elevated to a sufficient energy level to be detected individually. As a consequence, experimental measurements can only be associated with the collective energies of populations. Thus the illusion of an energy source without a matter carrier is manifested. Particles in this zone are collectively designated “crossons”. See [http://www.pivotalconceptsinscience.com] for an elaboration of the argument that matter and energy are different entities.

Marcos, be careful with non-physical blogs (especially called "Little Mathematician") discussing physical issues. In my opinion, an assumption that "matter is condensed energy" is simply meaningless, even though this phrase was coined based on quite correct interpretation of Einstein's formula. Indeed, a "small amount of matter can release a vast amount of energy". The successful realization of atomic bomb is based on this known fact. However, "matter" in this interpretation is tantamount to "material" (e.g., atom of uranium). I also agree wth the above conclusion of William: matter and energy are different entities. Let me just mention that in order to explain the evolution of our Universe, two separate entities have been introduced: dark matter and dark energy.

“Snakes In a Box”

As a young kid my Uncles told me that my Grandfather had found two snakes eating each other. Each had the other’s tail in its mouth. He placed them in a secure box and when he opened the box the next day, it was empty. The snakes had eaten each other! Try as hard as I could, I could not visualize how it could have happened. But it had to be true, my trusted Uncles had told me.

I entered college with the same faith in my professors and encountered concepts such as the dual nature of light that I could not reconcile. (Scientists, who act as our mentors, have felt justified in ignoring logical flaws simply because of the vast success of contemporary theories.) Later, an acquaintance asked: “Why do you think you are wrong and are just unable to grasp such foundational concepts?” From that point my quest has become to understand: What is the structure of the Universe that makes our laws and theories useful? This approach is somewhat different from directly trying to prove or disprove a law or theory, a process that often leads to a recycling of contemporary arguments.

Listed are some pet “Snakes in a Box”.

1. Matter and energy are inter-convertible, i.e. E0 = m0c^2. (The Marcos snake.)

2. The speed of light c is independent of the relative motion of the source and observer.

3. Light is both a wave and a particle – the dual nature of light.

4. A light signal traveling in a vacuum at c undergoes a reduction in speed when it enters a transparent medium, but resumes the speed c upon exit back into the vacuum.

5. Regardless of the intensity of a source, the velocity of energy released never exceeds c, and the radiation component from a source only occurs at c.

Snakes 1-3 might also be considered pivotal concepts of contemporary science. See http://www.pivotalconceptsinscience.com.

In equation E0=m0c^2, m0 = mass, not matter. Therefore, the interpretation would be "mass and energy are inter-convertible". Or am I wrong?

You are right, Marcos. Mass is a well-defined measurable property of physical bodies. Einstein's equation means that any body having mass has an equivalent amount of energy. At the same time, you may say that m0 in that equation means mass of a particular form of matter (e.g., electron or our planet Earth). That is why we may say, for example, that the total mass of the observable part of our Universe is of the order of 10^{52} kg. Alternatively, we may formulate the same statement by saying that the total mass of all the matter existing in the observable part of our Universe is of the order of 10^{52} kg. Though both sentences are formally correct, the mentioning of matter in the second sentence seems a bit redundant.

It is very important to get our terminology correct. However, the conceptual question that I sensed from Marcos’s original question is how can, an at rest entity (mass or matter), be converted into motion such that a predictable quantity of the entity disappears? All motion that we directly observe is associated with a change in positions of mass components. The induction of such motion in some situations is attributed to electromagnetic radiation. An example is the boiling of water when sunlight is focused on it. Is radiation pure energy, conveyed by a massless particle or does it have a matter component? Is there a substructure to photons?

Hi, Marcos.

Probably the claim is not true in this wording. If one formulates the question as you did, (as you had seen elsewhere), without mentioning about what kind of matter and what kind of energy are we talking, the claim is not valid.

We have several types of matter: Sergei mentioned that matter is loosely defined and Patrick used in his excellent example a matter-antimatter reaction. As the antimatter will not fall upward in a gravitational filed (claims held also by many amateur bloggers), the mass of antiparticles will add up in the process of annihilation. So, "normal" matter is made of fermions represented by quarks (feels strong force, so the form nuclei e.g protons, neutrons) and leptons (let go hang color force, e.g. electons, neutrinos, etc). All these particles have theri anti-matter counterparts (anti-quark, anti-electron, etc) formed together in the BigBang By a not fully explained method the particles which we call normal outnumbered the antimatter particles - so, luckily, we were left with galaxies formed mostly of our normal matter. Oh, the antimatter particles has the same mass as their normal counterparts.but opposite charges

Problems arise if we really try to understand the interaction of these particles. Sooner or later we will arrive to the concepts of virtual particles. These are terms belonging to the perturbation theories of quantum field theories, representing excitations of the quantum field which realizes the interactions between "real" particles - belonging to matter and antimatter particles. Virtual particles - although conserving energy - usually does not carry the same mass as it's real counterpart.: the mass depends on the length of the particle's temporal existence. So if you may say that mass is energy in case of normal particles, in case of virtual particles you may say mass is time.

But don't feel relieved. We have other types of matter also in our bestiarium. To be sincere, we can speak only about a fifth of the matter present in our Universe. The rest is composed mostly of dark matter - and we can not speak very much about dark matter. What we know is that DM does not interact with our EM radiations but feels gravity and has mass. As it lies beyond our Standard Model's concepts, we prefer not to discuss more for the moment.

And don't forget exotic matter: this falls upward in a gravitational filed and this is needed to build the walls of wormholes to realize time-travel.I prefer not to discuss it for now.

The situation is much worse in terms of energy.

We have some descriptions and ways to calculate the quantities related to the energies of the matter and antimatter. But this energy is negligible compared to the Dark Energy of the Universe - which makes up to 70% of the Universe's mass. And you may guess: I prefer not to discuss here the relations of dark energy with the abovementioned forms of matter.

So, Marcos, maybe your question should be reworded to get rid of the dark side of the Universe to a formulation like

Is barionic matter and antimatter bright energy condensed?

Hi Marcos, Interesting question this one! More interesting is the fact that Both matter and energy are ill-defined concepts in physics although they are the very sum and substance, the very bread and butter of physics. All definitions are circular in the ultimate analysis. Matter is a concept of the phenomenal world as perceived by us. Matter in the form of neutrinos continuously flow unimpeded through our heads and through the earth to the other side because they very weakly couple to other forms of matter.

If we say, Anything that has "mass" is matter, obviously we have to define mass, and this is not easily defined, even with the help of the Higgs boson!

Energy is even more difficult to define, It is easily classified though.

If we say, energy is the ability/capacity to do work, we have to define "ability/capacity" and "work" without any reference whatsoever to energy and surely, we cannot escape circularity.

Therefore, Matter, (as ordinarily understood) can surely be said to be energy (as understood in physics) "condensed" (E=m.c^2), without any hiccups, provided "condensed" means "a relatively more tangible or palpable or ponderable manifestation (all these as ordinarily understood!)" as the case may be.

Hi, Rajat.

In the first part of your post you demonstratee how difficult is to define matter.

The second part deals with the circularities in the definition of energy.

Both parts are tenable.

Than in the third finale you ruin your strongholds, affirming that matter can surely be said to be energy.

My hiccup would be: along this logic, if one makes a corespondence between two undefined terms, it also could surely be said that mind is soul condensed.

And what is mind?

Simple!

A mysterious form of matter secreted by the brain. Its chief activity consists in the endeavor to ascertain its own nature, the futility of the attempt being due to the fact that it has nothing but itself to know itself with. From the Latin mens, a fact unknown to that honest shoe-seller, who, observing that his learned competitor over the way had displayed the motto "Mens conscia recti," emblazoned his own front with the words "Men's, women's and children's conscia recti."

(Mind's definition from Ambrose Bierce: The devil's dictionary)

Hi Andras,

It seems you missed the bracketed phrases in the last para of my post. My position is quite clear. The confusion pointed out by you exists in the original question itself.

Work and energy(esp. heat) evolved as distinct concepts till the beginning of nineteenth century, when it was realized that they were one and the same thing. For example, the work-energy theorem states that the work done by the forces equals the change in Kinetic energy.When you subtract final K.E. from initial K.E. , you should get logically, an energy, but you get work! Thus they are equivalent and to define "energy" as capacity to do "work" becomes truly a circular definition.

Similar is the case with definition of matter.

Yes, Keeping aside the tricky issue of definitions, You are right in saying that the mind(as understood ordinarily) is the condensation (as understood ordinarily) of the soul (as understood ordinarily).

Science (as understood ordinarily) should make affirmations (as understood ordinarily) about interactions (as understood ordinarily) of well-defined entities (as understood ordinarily) in order to explain (as rarely understood ordinarily) a mechanism(as understood ordinarily), to make a prognosis(as understood ordinarily) or know-how (as understood ordinarily) of some natural or artificial processes. (as understood ordinarily).

Science can not trick definitions.

Science starts with definitions.

What is ordinarily understood, is rarely science.

Hi Andras,

Good post ! I laughed a lot !

If science starts with definitions, we should not be having trouble with defining everyday scientific quantities like mass or energy after even four hundred years of dealing with them. No one can deny the fact that a definition cannot be completely free from terms which retain their meaning as they are ordinarily understood, since the definition in order to make sense must have elements(words) having their ordinary meanings intact (check it with any definition). However it should not happen with the keywords (like work in energy ) entering the definition, which may (and often does) result in circularity. To better appreciate the difficulties with the foundations of science you may refer to Feynman or Eddington who looked critically and very open-mindedly at science and its methods.

Anyway, It seems we have drifted too far away from the original question. Let's put the original question this way:

Did all forms of matter (dark varieties included) originally exist as matter at the Bigbang (say), or were they in the form of energy?

if we take up this issue on the basis of current scientific models, the best and well- accepted understanding is that massive particles got their masses through the process of spontaneous symmetry breaking and all of them ( whether fermions or bosons ) were fundamentally massless. Even string theory and M-theory support this view which belongs originally to the standard model. So it is energy that is more fundamental and thus masses have emerged (call it condensation or what you like) out of energy which is the ultimate form of all phenomenal existence.

Unless, dark matter and dark energy force us to drastically modify our current understanding of the emergence of mass (matter), matter can certainly be said to be a condensed(as ordinarily understood!) form of energy.

Hi, Rajat.

I have to admit, your post sounds convincing.

However I'd like to maintain my position about the importance of definitions in science.

You say, that after 400 years of dealing with mass and energy we should not have difficulties defining them.

In my oppinion if someone comes tomorrow with a definition of mass and energy here on RG, that will not lead to the close-down of RG and will not obligate all the scientist of the world to pack in their tea-baskets and toys to go home because science is complete and game is over. Allegedly that was some american congressmen's position after Edison forwarded his patent for the light-bulb - they considered that everything is invented what is worth to be invented.

That will be not the case with mass and energy, because every definition has its domain of validity. That is also part of a definition's definition.

Concerning the importance of definitions to foundation of science I would like to complete the list of the eminent scientists who made an important contribution with Kurt Godel's case: the list would be complete only if it will contain Godel's incompletness theorem.

Wow, wait a minute. That makes the complete list incomplete. Never mind! List it!

Back to the original question.

The chance of two undefined terms to be equal is inversely proportional with the number of their possible values. As some definitions will make a constraint on the number of possible values, the chances are starting to rise from 0 toward 1. In case of a perfect definition and match we have the idealistic value of 1.

In your post you joust for the acceptance of the term " as usually understood =AUU" to be a valid definition. So, energy AUU is matter AUU condensed AUU.

I could not withold myself to demonstrate that matter and energy has other forms, where the AUU definitions are not holding. They are certainly not holding in case of virtual particles and exotic matter. It is unknown in the dark part of the Universe.

The dark side of the Universe is more than 95 % of it's mass.

So, scientifically speaking, we can not make valid statements about energy and mass, because our knowledge and imagination does not enable us (yet) to understand them in general. We can try to summarize some of our observations concerning mass and energy - AUU - made in the last 400 years, on some 5% of the mass of the Universe. 400 years of our observations is 1/300.000 part of the 13.7 bld years from the Big Bang - so we are on track and advancing.

But to foretell the equivalence of matter and energy based on our present knowledge is like announcing the result of a plebiscite after counting 5% of the polls.

I would say let's hear what those entities has to say, which are living on the dark side.

I believe what's missing from that view (matter as condensed energy) is the informational or structuring side of the Universe. There are reasons to believe that the Universe has a structuring and non-spatial component responsible for the organization of "matter", which has remained uninvestigated so far (because our measurement instruments were not designed for this purpose.)

There is something lurking here, below the equation E = m c^2. The concept of energy is well defined in classical mechanics because of the work energy theorem that follows from the fact that f = m a is a differential equation that can be solved with respect to the second derivative and does not include the velocity. Then the method of order reduction can be applied to obtain a first order equation, which is what is done to solve Kepler problem or the harmonic oscillator: m d^2 x + k x =0 implies m d^2 x d x + k x dx = 0 or d ( 1/2 m (dx)^2 + 1/2 k x^2) =0. This means that 1/2 m dx^2 + 1/2 k x^2 = E is a constant of motion, the so called mechanical energy. When we say that mechanical energy is conserved in classical mechanics we know what we are talking about. We know what energy is! When we talk about energy in relativity we don't know what it is and, as a consequence we don't know what we are talking about!

In the statement E = m c^2, we knows what is m (the amount of matter), we know what is c (the speed of light). Who knows what is E?

There is another equation E = h v. We can eliminate the undefined term and write h v = m c^2. We might want to write this in the form m = h v / c^2 and take this as as the definition of mass.

This is fascinating! "E" has several definitions depending on the context. In the case E0 = m0.c ^ 2, "E" and "m" is the relativistic energy as "m" is mass relativistic. The same for E = pc and E = hv (photon energy). So "E" and "relativistic energy" can be used in the classic context in which is defined as "the ability to do work?". Energy in the relativistic contexto (rest energy) seems a property of matter (such as mass) or rather, the physical system.

In the case of the explosion of the atomic bomb is the relativistic energy (rest energy) or binding energy from protons and nêutrons adding its kinetic energy (nuclear fission) that is "doing work"?

Do not know if everyone understood me?