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From physics, we know that energy interacts with matter, and can be converted into matter.

From this, if energy can be converted into matter, does this imply that energy and matter are two expressions or modes of the same underlying "ontological substance" (analogously, just like how H2O can be expressed through liquid, gas, and and solid forms). The implication of this would be a type of monism with real distinctions where the universe is composed of a single unified ontological substance. Perhaps our brains partly create the hard differentiation of this as they process stimuli and input from reality.

Is this notion or reasoning erroneous? Are there any different approaches to this that could counter this conclusion?

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    In terms of the science there are a number of problems here, chief of which is that "matter" is no longer the clear distinct concept that we once thought it was in the 19th and early 20th century. For instance does a photon count as matter? It is a wave, doesn't have mass or take up space but OTOH it is also a particle, does have energy, momentum, locality and have independent existence. And photons are easy compared to others (quarks, gluons, weak bosons, neutrinos, etc.) which can have crazy combinations of these attributes. Commented Aug 3 at 16:32
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    My high school chemistry teacher stated that E = mc^2 proves that matter and energy are two forms of the same thing.
    – EvilSnack
    Commented Aug 3 at 20:27
  • See 'Is the idea that "Everything is energy" even coherent?' philosophy.stackexchange.com/questions/85899/… The TLDR is, energy is more like a unifying language that can speak to both fields & particles in the same terms.
    – CriglCragl
    Commented Aug 4 at 9:31
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    @RBarryYoung: Photons have a scattering cross-section, which is basically what we mean by taking up space en.wikipedia.org/wiki/Gamma_ray_cross_section Electrons are point-like particles, but we can still meaningfully talk about them taking up space.
    – CriglCragl
    Commented Aug 4 at 9:35
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    @CriglCragl I was referring to the Pauli Exclusion Principle and the distinction between "occupying" space vs. "taking up" space. Being bosons, any number of photons can "occupy" the same space, which is not true for fermions which can be said to "take up" space. This has been the traditional reason for some to identify fermions as "matter" and bosons as "not matter". But since some bosons have mass and worse, most of the normal mass we perceive doesn't come from fermions but from their binding energy in nucleons, it makes the concept of matter hard to define. Commented Aug 4 at 14:50

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It would be wrong to say that the universe is made of "matter" on the one hand, and "energy" on the other, as if they were two distinct substances that can be converted into each other. The universe is made of matter (particles that have mass) and non-matter (particles that do not have mass), and both matter and non-matter have energy.

Energy is not a substance of its own, it's a property that systems (including systems made of matter) can have.

A photon can have a certain amount of energy. But a photon is not energy; a photon is a particle, or alternatively a disturbance in the electromagnetic field. A gas molecule can have kinetic energy. But the gas molecule is not "made of" energy. It's made of atoms.

Note that the energy a photon (or gas molecule) has depends on your own speed. The faster you are traveling towards the source of the photon, the more blueshifted the photon will be, and the more energy the photon will have from your frame. So the energy can't be a substance that the photon has a fixed amount of. Energy is only conserved with respect to a given inertial frame; if you change the frame, the kinetic energy of everything in the universe changes.

Matter has energy deriving from its rest mass. It always has this energy. You can change the matter into other forms; you can (in theory) turn the matter into photons, or turn the photons back into matter. But the matter had just as much energy as the photons have, which is to say, neither are energy, they just both have the property of energy.

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  1. The story begins earlier. In the 19th century physicists discovered that heat is a form of energy. This unification was made precise by the formula which converts numerically one form of energy into the other.

  2. A further and deeper step was Einstein formula E=m*c^2 from special relativity. The theory showed that it is not the energy. Instead, it is the combination (E,p)=(energy, momentum vector) which is independent from choosing the coordinate system (frame of reference): The scalar E^2-p^2=m_0^2, the square of the rest mass, is the coordinate independent physical quantity.

    The analogue with the different phases of H_2O-molecules is not complete. During a phase transition the water molecules due not change. It is their configuration which changes.

  3. To embed concepts from physics into an ontology is a questionable task. We do not know what energy, mass, gravity etc. are. We know how to measure these quantities, we know conservation theorems, we know how to relate the concepts. But what a philosopher might want to know “What is its essence?”, this question physics does not answer.

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    "...this question physics does not answer" - but is there still a sensible, serious, relevant (answerable) question left after physics has answered? (i.e. ignoring the fact that there are always remaining open physics questions and that answers may have to be corrected)
    – mudskipper
    Commented Aug 3 at 15:28
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    @mudskipper I think the question for the essence remains. But possibly the question is delusive. Because the question expects the answer to be expressed by concepts we are used to. Due to our meso-cosmic experience and intuition. - While physics has long stepped beyond the limits of meso-cosmos into the domain of micro-cosmos and macro-cosmos. There we do not have approved perceptions and reliable concepts.
    – Jo Wehler
    Commented Aug 3 at 20:01
  • @mudskipper: Essence is not meaningful in physics, it's just concerned with measurements & observations. Kant's noumena idea explicitly addresses the idea of 'thingness' that cannot be measured or encountered, but only appriximated & moved towards. Even if you disagree with Kant, he makes something meaningful for scientists with the idea, even if it's outside science. The interpretations of quantum mechanics also seem to be unfalsifiable. Our inability to understand quantum-gravity is forcing physicists into deeper thinking about ontology, eg Loop Quantum Gravity.
    – CriglCragl
    Commented Aug 4 at 9:55
  • @JoWehler: Do you know David Deutsch's book 'The Fabric of Reality'? He tries to essay what our complete cosmology is, with four strands, many-worlds QM, information theory, natural selection, Popperian epistemology. In the sense of this kind of work, physics concepts can absolutely be embedded into ontology. We don't need the distractions of assessing what is 'really real', we only need to be working towards a general assessment of how to situate ourselves towards the cosmos. Ontology is just a way of grouping ideas within that, not magic sauce with the power to reveal the really real.
    – CriglCragl
    Commented Aug 4 at 10:02
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Mass and energy are both the same thing: momentum in spacetime. Energy has momentum only in space, and mass has momentum in time.

All mass is is momentum in the direction of future time, and it isn't anything else. I didn't make that up. Feynman told me in disk 5 of the Australia lectures and in his easy pieces book.

That cup sitting on the table is moving through time at c. It looks like it's standing still because we're moving in the same direction at the same rate

If you push it, you're changing the direction of its 4D motion. You're rotating it away from speeding into the future, to speeding through space. Its speed through time slows down, and we see that in GPS satellites as time dilation.

GEEKS ONLY!
If you're curious, acceleration in n dimensions is always rotation in n+1 dimensions. Like, if you look at a candle on the edge of a rotating turntable in a dark room, the candle looks like it's accelerating back and forth in 1 dimension. But if you look at it from above, in 2 dimensions, you can see that the really, the candle is part of a system that's rotating.

That's what happens in 4 dimensions when you accelerate mass. You're really rotating it's momentum vector slightly away from future time and into motion through space.

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  • There are particles, & fields, both have energy. If the candle is in a linear vibration, it's still linear when you look from above. While in the general case there will be rotation, still an elliptical path with a short axis of zero is not rotation.
    – CriglCragl
    Commented Aug 4 at 9:45
  • If it takes time to rotate, then in 4D Lorentzian spacetime, the short axis is nonzero. Commented Aug 4 at 12:24
  • Mass is not “the same thing” as energy. Mass is the Lorentz-invariant length (in Minkowski space, using natural units) of the energy-momentum four-vector. Energy is the temporal component of this four-vector. Thinking that they are the same thing is as wrong as thinking that the hypotenuse of a right triangle is the same thing as one of its sides.
    – Ghoster
    Commented Aug 5 at 19:09
  • Ghoster from the physics stax! Yaay! Yes, momentum looks different in the time direction (when it's mass) and when it pushes stuff around in a space direction. But they're both the same thing. You can tell because you can convert one into the other just by smoothly rotating the 4-vector. Turn mass into energy, accelerating the remaining mass -- It's all momentum, just pointed in different directions. Commented Aug 5 at 21:08
  • @Ghoster "thinking that the hypotenuse of a right triangle is the same thing as one of its sides" Great analogy that shows understanding. They are the same because they share the same metric. All 3 sides are distances in spacetime. One just has the opposite sign on the magnitude. That sign flip in the signature is the ONLY difference between distance and elapsed time. Commented Aug 5 at 21:32

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