I have long been interested in physics as (working toward) a description of absolute truth and, as a consequence, have had a number of discussions with people with religious and metaphysical beliefs far from mine own. These conversations often turn toward ontology, the study of existence vs. non-existence. It seems to me that the fundamental ontology in physics is characterization of mass/energy.

For example, when textbooks work through solving basic quantum mechanics problems, they describe the case where the wave equation equals 0 as the "trivial" case because it means that the particle doesn't exist. If a particle has a non-zero wave function, then it also has an energy (even if not entirely well defined) described by the Hamiltonian operator operating on that wave function. Similarly, the creation and annihilation operators represent the "creation" or "annihilation" of a particle by adding or removing a unit of mass/energy to the system. Even within a Newtonian system, for an object to have an effect it must have either mass and/or energy.

Granted, field theories appear to be an exception in the sense that the magnetic, electric, induction, displacement, etc. fields are often treated as real entities that do not have any intrinsic energy. Nonetheless, texts often explicitly warn students not to be concerned with the "reality" of these fields but to use them as a descriptive tool. Modern theories that incorporate virtual and exchange particles do away with these fields and suggest a description more in line with the mass/energy paradigm.

Recognizing that there is not universal consensus on the point, in what sense does the philosophical foundation of physics imply that existence is contingent upon the "posession" of mass/energy?

Equivalently, does it make sense to say that something may exist without mass or energy?

  • I would say that existence is entirely dependent on mass-energy. This would be why existence cannot be fundamental. I don't know what 'religious' views you have examined but I'd suggest you have a look at mysticism, specifically as explained by Nagarjuna and 'Middle Way' Buddhism, for which nothing really exists and nothing ever really happens. This would say that space and time are required for existence (and for mass/energy) but avoids the ontological difficulty by denying the metaphysical existence of anything at all. Ontology then becomes a lot easier! .
    – user20253
    Commented Feb 17, 2018 at 12:54

8 Answers 8


The answer, for a materialistic physical viewpoint, which is what is commonly assumed in the field, is no it does not exist (depending on what you mean by exist). You correctly identify that objects that have neither mass nor energy are actually not anything at all. (Edit: because, for example, for them to have any effect on anything they'd have to violate the laws of conservation of energy or momentum.)

However, this is not terribly profound philosophically for two reasons. First of all, it doesn't answer the question about whether, say, mathematical objects exist. An equilateral triangle "exists" in the sense that you can write down a logically coherent set of properties for that triangle (unlike a triangle with three right angles), but it cannot exist in that it cannot possibly be instantiated exactly (because of quantum mechanics, atomic nature of matter, etc.). Philosophically (or semantically) controversial categories of existence remain just as controversial.

Secondly, we can identify things like a cold spot as existing, which actually have less energy than their surroundings; or like a printed triangle, which has the same energy as many other configurations of ink on paper. So although you need mass and energy as a substrate, it is convenient to make distinctions about what exists on the basis of no difference in energy or a reduction of energy. These sorts of distinctions tend to be richer and more complicated than whether or not there is any matter at all, and so the insight that no matter and no energy is nothing does not get one very far.

  • I like the first paragraph and am curious if you could provide justification for your thermo argument. As a physicist, I disagree with the statement ”an equilateral triangle exists.” A great deal has been written on the history and anatomy of werewolves but a better description does not make them more real. It is true that phenomena of existent objects occur and are said to exist, but the meaning in the sense physicists use is different. Commented Oct 1, 2011 at 12:11
  • I also disagree that recognizing the contingency of existence on matter is not profound. It does, for example, prohibit an omnipresent God, which is a foundational belief for most of the world population. Commented Oct 1, 2011 at 12:24
  • @AdamRedwine - You do not agree that an equilateral triangle exists in some sense that a triangle with three right angles does not? I also changed from the 2nd law (where you could at least potentially create a Maxwell's demon by using an unmoved mover to push things together) to conservation of energy and momentum, which should be obvious enough to not require explanation. And I don't think there's anything profound; one just says, "Well, God breaks physics any time He feels like it", and there's no problem any more.
    – Rex Kerr
    Commented Oct 1, 2011 at 18:52
  • Neither triangle is any closer to existing than the other. The logically coherent model of an equilateral triangle is more useful, but not more real. And no, you can't just say God breaks physics, you must say he breaks logic. Commented Oct 1, 2011 at 20:44
  • @AdamRedwine - Fair enough; I've edited to take that perspective into account.
    – Rex Kerr
    Commented Oct 2, 2011 at 3:22

I have long been interested in physics as (working toward) a description of absolute truth

I wish you luck with this, but I think you're going to find the gap between physics and metaphysics to be unbridgeable. Absolute Truth is not the domain of physics.

That being said: from a philosophical perspective, to exist is reducible to possessing causal efficacy; in other words, for something to be said to exist, it needs to be capable of having some kind of detectable effect on something else.

So, the question for a physicist would then be: is it possible for something to possess causal efficacy without having mass or energy? I don't see how this would be possible, but I'm not a physicist.

So, I suspect that the answer to your question (Does the philosophical foundation of physics imply that existence is contingent upon the "posession" of mass/energy?) is "Yes"-- but I stand prepared to be corrected by a physicist.

  • I have difficulty reconciling your hypothesis that the gap between physics and metaphysics is unbridgable with your statement of the philosophical definition of existence as causal efficacy. It seems to me that that definition does indeed bridge the two. Commented Oct 1, 2011 at 13:33
  • And what makes you say that absolute truth is not the domain of physics? Physics is exactly that. After a photon passes a polarizing lens, it is ABSOLUTELY TRUE that a subsequent measure of its polarization before an interaction will yield the initial value. There is no question or doubt involved. Commented Oct 1, 2011 at 13:38
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    @AdamRedwine: I'm not sure of the wisdom of the attempt to reduce the philosophical notion of absolute truth to the measurement of photon polarization [cf en.wikipedia.org/wiki/Absolute_(philosophy) for a brief sample of what is entailed] , but even if one were to go down those lines, the example of Heisenberg ought to serve as warning enough. Commented Oct 1, 2011 at 14:19
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    It's certainly possible that I misunderstand the uncertainty principle, not being a physicist, but my layman's understanding echoes Wikipedia-- that there is "fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known." As for philosophical navel-gazing-- I'm not a fan of it either. I find the philosophical notion of Absolute Truth to be quite absurd (I did my thesis on Nāgārjuna) and as I said earlier, Absolute Truth is not the domain of physics. Commented Oct 1, 2011 at 15:47
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    I assumed (perhaps foolishly) that what you meant by absolute truth was the standard philosophical notion of that description. In answer to your question: No, I absolutely do not know of (nor am capable of imagining) any entities that have causal efficacy that are not governed by the fundamental forces of physics; I am quite happy to say that anything existing possesses mass or energy (or both)-- but, as I said, I am not a physicist. Commented Oct 1, 2011 at 16:05

I can't really say I've read many philosophers who have spoken directly about matter or energy, at least, in the intertwined sense the physicist speaks of them. However, many philosophers speak of substance, although they might not speak of it in the precise manner I think you are looking for.

In regards to other notions within physics:

  • Philosophical determinism certainly speaks to Newtonian physics to some extent. See also this in depth SEP article for an interesting read. Quantum mechanics, as it stands, actually speaks against determinism, and the implications for belief in such a notion are outside the scope of my knowledge.
  • Some philosophers, such as Immanuel Kant, have offered explanations for the necessity of space and time in physics.

    Kant, in the Critique of Pure Reason, described time as an a priori notion that, together with other a priori notions such as space, allows us to comprehend sense experience. Kant denies that either space or time are substance, entities in themselves, or learned by experience; he holds rather that both are elements of a systematic framework we use to structure our experience. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantitatively compare the interval between (or duration of) events. Although space and time are held to be transcendentally ideal in this sense, they are also empirically real, i.e. not mere illusions. (Source)

You might be interested in looking at the course list of Columbia University's M.A. in the Philosophy of Physics. Also check out the brief Wikipedia article on the Philosophy of physics if you haven't already.

  • I would be interested in the program though my desire for a job outweighs my interest. :-) Commented Oct 1, 2011 at 12:06
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    Though the subject is a complex one, I would not say that quantum mechanics speaks against determinism. QM is a theory of absolutely defined indeterminacy, not indeterminate uncertainty. That is, in QM you always know exactly how likely an outcome is; and sometimes that likelihood is 100%. Commented Oct 1, 2011 at 12:32
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    At this point I tend to take Einstein and Rosen's position that our knowledge of QM is simply incomplete, and we will find at some point wholly deterministic mechanisms to fill in the "gaps" of current quantum theory. Oh, and regarding the course list, I was recommending you look at it because the course list descriptions list the topics of discussion in each class, as well as some authors who discuss philosophy of physics, so you could use those names and topics to aid you in your search for information in the field. :P
    – stoicfury
    Commented Oct 1, 2011 at 16:19
  • @AdamRedwine - With determinism like that, who needs indeterminacy? (Utterly unpredictable-within-the-expected-probability-distribution non-local determinism is not in any practical way different from indeterminism.)
    – Rex Kerr
    Commented Oct 1, 2011 at 18:56
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    @stoicfury: "Indeterminant" and "unpredictable" are not the same thing. Indeterminacy can indeed be absolutely defined through statistics. It is possible to say that a quantum event has a 50% probability of outcome A and a 50% probability of outcome B. Such a description is absolutely defined in the sense that it contains all information about the system, i.e. only those outcomes with those probabilities are possible. It is indeterminant in that the outcome could be either A or B. Commented Jan 16, 2012 at 19:47

Frege was of the opinion that there must be a realm of mathematical objects. Hence, according to this view, mathematical objects exist, but they do not have energy or mass in the physical sense.

This actually makes more sense than one might think.

For example, it is undeniable that the programming language Java exists. After all, many thousand people make money everyday writing programs in that language. Java is a member of the infinite set called "context free languages", hence also this set does exist. And so forth.

Note that a programming language is not the same as the software that implements it, or the books that describe it, just like a cake is not the same as a recipe for baking it. Hence the argument "a programming language exists physically in the form of bits on some hard disk" does not hold water.

By the way, Frege used as example the Pythagorean Theorem and says it is of "timeless truth, independent of someone recogizing it as true". And he continues "It does not need a medium". Here is what he told in german:

Ein drittes Reich muß anerkannt werden. Was zu diesem gehört, stimmt mit den Vorstellungen darin überein, daß es nicht mit den Sinnen wahrgenommen werden kann, mit den Dingen aber darin, daß es keines Trägers bedarf, zu dessen Bewußtseinsinhalte es gehört. So ist z. B. der Gedanke, den wir im pythagoreischen Lehrsatz aussprachen, zeitlos wahr, unabhängig davon, ob irgendjemand ihn für wahr hält. Er bedarf keines Trägers.

  • This is a little unclear. Software takes up energy/mass; just because an entity is predominantly 'logical' doesn't mean it has no physical instantiation. And in passing can you please try to back up your claim about Frege?
    – Joseph Weissman
    Commented Jan 7, 2012 at 18:05
  • A programming language is not just software. The compiler and the language description may exist in the form of software. But you wouldn't say that the recipe for a cake is the same as the cake, would you? -- Regarding Frege, it's in "Der Gedanke.", unfortunately references for this seem to exist only in german, for ex: de.wikipedia.org/wiki/Drittes_Reich_(Frege)
    – Ingo
    Commented Jan 7, 2012 at 23:06
  • I'm not sure I follow. Should I take your analogy to imply a recipe doesn't take up mass or energy? Regardless of the substrate (neural, physical, logical) doesn't a cooking recipe, or a program, or programming language, or operating system, etc. exist in a clear and strong sense, instantiated as a physical system involving matter and energy? Since I concede I may be missing your point here, I'm just hoping you could clean up your answer somewhat to address this.
    – Joseph Weissman
    Commented Jan 7, 2012 at 23:11
  • @Joseph, I edited my post. I didn't say a recipe has no mass or energy. I did say it is not the same as the cake. Likewise, software that implements a programming language is not the same as the programming language.
    – Ingo
    Commented Jan 7, 2012 at 23:22
  • Thanks for improving it! It's much clearer now. Welcome to Phil.SE, by the way!
    – Joseph Weissman
    Commented Jan 7, 2012 at 23:28

I am not a physicist, mathematician, or philosopher, but my common sense tells me that dead brains can’t have thoughts. The source of all thoughts is electrochemical activity, which is energy. I suspect that a super smart neuroscientist could pick out a number or section of the brain’s active neurons and credit them with the singular thought of a triangle. So – everything including thoughts must have energy to exist.

  • A thought of a triangle requires mass/energy to exist. Why do so many people pass around this concept of 'triangle'? If all humans died, and a new intelligent race of cockroaches evolved, they would independently begin thinking of 'triangles'. Does the concept of triangle have some sort of causal effect, even though it doesn't have matter or energy? Or, instead of 'triangle', substitute any physical or mathematical law, no matter how simple, that is an abstract conclusion about how matter/energy behaves. Does 'two' exist? Commented Dec 29, 2017 at 19:05

Supposing mathematical objects are real and not fiction - then they have no energy - they cannot as they are not in this world. Yet as ideas in our own minds they visibly have causal efficiency.

But we never see the bare mathematical 5, say; it is always incarnated within a mind. This is the position, roughly of fictionalism.

But given that your standard of truth is Physics - let me take an example from there: We never see the bare quark; Nature has arranged it such that we see them in triples. Their bare existence is only inferred. But existence, by general consensus has been awarded them. So, by analogy - can we say that although numbers are never seen on their own, but hosted by a mind in a human body - can we then award bare numbers existence. Perhaps not, but it is at least thought-provoking (if not provocative).

We can go a step further. Does thought or qualia have energy? Descarte famously divided thought from matter and philosophers struggled to put them back together again. Spinoza made an attempt where they were two modes out of an infinite number of modes of a substance that he identified as God.

In Islamic theology, the world is a creation of Allah and returns to him. Does energy apply to Allah? The theologians would say not - as energy is a created concept.

In Taoism, the Tao is eulogised and described. Does the Tao have energy? It has causal efficiency as it can be known and experienced; but also it does not - causal efficiency is a term from Western Philosophy and sits very uneasily with how the Tao is said to govern.

  • The thought of a mathematical concept has causal efficiency, the concept itself need not exist for that to be so. With respect to quarks, it is not necessary that we observe bare quarks in order for quarks to exist. A quark confined to a nucleus is very different from the thought of a number in a person's mind; I think your analogy is too tenuous. The philosophical naval gazing and religious pontificating is also beside the point as the stated paradigm of the question is that of physics and the real world. Commented May 13, 2013 at 12:04
  • @AdamRedwine: Well this is a philsophy Q&A and you've phrased your question a little ambiguously if you're looking for a purely physics orientated answer by mentioning absolute truth and ontology. Feynman wrote in his book The Character of Physical Law that this question of fundamental ontology escapes its grasp. Yes, I realise the analogy is tenuous, this is why I remarked that it was thought-provoking. Commented May 13, 2013 at 12:33
  • As for the religous mumbo-jumbo, if you look into Islamic Ash'arite theology you may care to note that they carried the greek atomists project further - whereas they only atomised matter - they also atomised space & time. This idea has only become current quite recently with ideas of spin networks and spin foam. Obviously in quite a different form and with no direct connection to the Ash'arite ideas. Still its indisputable that they got there first. Commented May 13, 2013 at 12:34
  • I was looking for a purely physics oriented answer, I originally posted this question on the physics stackexchange and it was migrated here. I disagree with Feynman; I believe it is perfectly reasonable to ask questions of ontology within the paradigm of physics. And, no, it is not indisputable that the Ash'arite's "got there first"; I dispute that claim. To say that their philosophizing means they "got there first" is to totally misunderstand the nature of scientific investigation and the foundation of knowledge. It is perfectly plausible to write a computer program... Commented May 13, 2013 at 14:01
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    To be honest - I think your question is too philosophical for physics; and too physical for philosophy. Commented May 13, 2013 at 14:35

In physics, for a thing to exist it must interact, therefore it must have mass and/or energy. Using Einstein's famous equation e=mc^2, the two can be considered interchangeable. However, in philosophy, there are many things that exist that do not have either; Dreams, beliefs, opinions and equilateral triangles. All exist in the thoughts of the philosophers, and those thoughts require brains, which require mass and energy. So the question becomes, what does it mean to exist? And does that differ depending on who is asking the question?


What does it means "something to exist"? Intuitively you are asking if something is observable but this is different from something to exist. If something do not have energy and mass it will not participate in any of the known to us interactions and there is no way to observe it with the current technology, but even so it may exist, just we can not "see it" with our tools.

If you consider a volume of absolutely empty space without energy, mass or particles it exists but can not be observed because there is nothing there. So the short answer to your question is that the empty space-time itself exists without energy/mass. The long answer is that the Zero wave function means that the space do not contains any particles expressed by the QM wave equations, but still there may be other particles not described by wave equations. For example gravity field is not described by wave functions but still has energy, mass. According to Einstein's STO however the gravity fields permeates anywhere in the Universe and 'distorts' space-time. This is one of the biggest myths in physics and dilutes the very basic concept of empty space. So the confusion that something can not exist without energy mass comes actually from the STO not QM. Since we can not observe an "empty space" with current technology this is impossible to be proved of disproved.

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