After Frank Wilcek brought out his great book on the nature of mass, I texted him a request to do the same for energy and he graciously replied saying that that was a very different proposition. Would be great for you to have expound on energy on TOE!
Oh man! Curt, my brain’s not big enough for this one! I thought energy was that purple stuff that you see zipping outta people when you drink Ayahuasca... ya know... makes ya chakras spin... and ya cactus look all rainbow-haloed 😂🤪🤯
We are so limited by language. Most would say they have a pretty fulsome grasp on what energy is. This is such an interesting read … which I will re-read
I like the thought that
“The conserved “thing” isn’t energy, but entropy, and β(t) tells us how the universe cools as it expands?”
Yet another nicely written post, Curt. I always seem to learn something new from you. In QFT, tremendous amounts of measurable energy are continually being borrowed from and given back to the quantum vacuum. The quantum vacuum behaves like a near infinite source and sink of energy.
In my particle theory work, which I view as QFT with vortices, I often rely on the convenience of being able to borrow as much vacuum energy as needed.
Richard Feynman, in the 4th of his Lectures on Physics, stated:
“The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. *It is not a description of a mechanism, or anything concrete*; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.” (Emphasis added.)
I’m with the Great Man. Energy isn’t stuff - it’s a numerical abstraction.
That’s right. The constant value of the calculation for a (closed) system’s energy has to have significance. But Feynman was concerned that the diverse forms of energy do not suggest a single basis. Quoting again:
“…the energy has a large number of different forms, and there is a formula for each one. These are: gravitational energy, kinetic energy, heat energy, elastic energy, electrical energy, chemical energy, radiant energy, nuclear energy, mass energy. If we total up the formulas for each of these contributions, it will not change except for energy going in and out.
“It is important to realize that in physics today, we have no knowledge of what energy is.”
But the answer may not be “in physics”. There are computational theories of reality, idealistic theories, Platonic theories… Physicalism is real, but not necessarily fundamental. The problem is, in any case, not only “What is energy?” but also (or *instead*) “Where do physical laws come from?” Without the laws, there is no physics.
I find it interesting that Feynman himself would not realize that all of those types of energy are expressed through waves, and that despite differing mechanics they are all the same underlying form constantly feeding each other back and forth in the same system.
Let's nail down waves as emergent rather than formative. When any group of particles (internally attracted to each other and in a mutual state of inertia) is then accelerated in a particular direction, the tension between their inertial state in attraction to each other and their new state of inertia as mutually accelerated particles, causes them to assume the shape of a wave in order to resolve the tension.
Eric, I appreciate your viewpoint and the clarity with which you present it. However, I respectfully see it differently.
Contemporary physics, particularly quantum field theory, suggests that fields are fundamental, and particles are excitations of these fields. This perspective implies that waves are not emergent phenomena arising from particle interactions; rather, particles themselves emerge from the underlying wave-like behavior of fields.
The “tension” you mention can be interpreted as the result of wave interactions within these fields, leading to localized excitations we identify as particles.
While the Standard Model has been remarkably successful, it doesn’t account for certain phenomena, such as gravity, dark matter, and dark energy . This suggests that our current models may be incomplete and that exploring alternative frameworks could be beneficial. 
I believe that by re-examining our foundational assumptions, we can develop a more comprehensive understanding of the universe.
Hold on now. Let's hone in to be very precise with this. I wasn't talking about fields, I was talking about waves. Both waves and particles can be emergent properties of field dynamics.
Now, to be even more precise, regardless of how they are originally formed, particles are relativistically identifiable, discrete objects. And, when discrete particles associated with each other are accelerated together in a given direction it is very clear that they resolve the divergence between what they were and what they are becoming by very naturally shifting together into a wave form (the easiest way to resolve the conflict).
This can be revealed through a simple kitchen table experiment, as follows:
Pick up a cloth napkin or other piece of fabric and grasp the fabric on two different edges respectively within the pinched fingers of your left and right hands. Now pull.
In pulling what you have done is accelerate the particles in the napkin in a specific direction. What very clearly results is a wave form.
Whether or not all of this originates from field dynamics is another question.
Energy is conserved only in a closed system in a single coordinate system. For example, in the expression E = mc², c² is a coordinate system coupling such that an invariant mass is guaranteed to give everyone the same energy with respect to universality of local structure, to its destruction... Gravitational energy can only be determined separately with respect to each sink.
Energy is therefore the ability to do work with respect to something, not invariance.
On my (non-expert) reading, Feynman does not regard waves as fundamental (“real”). If you read lecture 26 in “The Feynman Lectures on Physics, Volume I” (Caltech - available online) you’ll see that it is divided into 6 sections. In sections 1 the words “wave” and “wavelength” occur dozens of times, the last being: “In this chapter our discussion is limited to the geometrical optics region, in which we forget about the wavelength and the photon character of the light, which will all be explained in due time.”That time is section 6: “How it works”, where the photon description is given as the actual, or more fundamental, explanation: “…the light does not seem to be in the form of waves at all. Instead the rays seem to be made up of photons, and they actually produce clicks in a photon counter, if we are using one.”
This fits in with Feynman’s lifelong speculation, finally his belief, that space is made up of cells, like a checkerboard, and nature is fundamentally discrete.
It is structured motion—expansion driven by recursive imbalance in phase.
What we call "energy" is the right-handed release of compressed informational recursion.
It is not a substance, but a directional expression of the universe’s memory resolving itself through motion. Energy is the outward breath of information. In physics terms, energy is the expression of right-handed neutrinos.
I mean. Information = energy? At some level? How many dimensions? Quantum Entanglement and all that. And then there is consciousness. Coherent and resonant. Negentropic. Local effects suggest information and gravity also interact.
I always thought that energy was a result of probabilities.
Energy is proportional to the time gradient of the probability wave equation, and the magnitude of the disturbance in the quantum field.
Any particle has a probability of being in a particular state.
When it's not in its most probable state, it has kinetic energy if it's able to be, and potential energy if it's not able to be.
Potential energy is actually two kinds: it can be prevented because something else is using the state, or a new probable state can be created from some other particles it interacts with.
Velocity and inertia are a gradient in the probability of position.
Gravity is a gradient towards a quantum interaction with another particle or energy.
The other forces are biases in states other than position which interact on different time and spacial scales.
Hey Curt! I really love the fact that you are drawing attention to these issues, I think it's a fantastic public service for science communication. But I also feel like you may be slightly overplaying the "maybe no one knows" angle for dramatic effect--which is fine as an artistic choice, but it seems to me, unless there is some detail I have missed, that we have a perfectly coherent account of everything you discuss here, it's just that this account is somewhat deflationary and maybe dissatisfying to certain aesthetic preferences or biases.
Let me try to briefly give the account I have in mind, and if it turns out I am still missing something I may recant and admit that it really is an open mystery.
So, the "energy" in GR is the covariant version, and it isn't conserved in the theory because it isn't conserved in reality and there is no reason it should be. We have understood since Noether taught us all that energy conservation is not a fundamental aspect of nature and instead its a consequence of time-translation symmetry. Well, time-translation symmetry is not a property that a dynamic, expanding, and historically evolving universe possesses, so energy just isn't conserved, and that's not mysterious. At the same time, however, conservation laws have enormous practical utility as accounting tools, more or less, so we have good motivation to introduce some ad-hoc terms to create conservation principles for strictly practical reasons, but since we know that the covariant energy isn't conserved then naturally we are gonna have to pay a price to get a conservation rule, and coordinate-dependent psuedo tensors appearing in the conservation laws is one way to pay that price for our useful fiction, restricting to the idealized situation of perfectly time-like Killing vectors is another way to pay it, and since we know these are just convenient fictions we introduce so we can write that some stuff we want to calculate equals zero, we just decide what price is cheapest on a case-by-case basis knowing full well that these are just convenient fictions anyway. Is there anything missing in this account that would bring the mystery back to life? I'm honestly asking because I'm open to the possibility that you haven't overstated the issue and I have oversimplified my understanding in order to understate the problem.
One further thing I will say though, is that maybe part of the reason it might seem like a mystery is just that GR is in some ways much more unintuitive to us than even quantum mechanics. QM is weird and conflicts with classical intuition, but covariance and background independence, while they don't seem to be impossible to understand in the way people have said QM is impossible to understand, nevertheless conflict with our experience of the world at a really fundamental level. All of our experiences of the world are first-person and localized, so they are never covariant and background-independent, and in general we can imagine looking at the world from a different perspective, but we can't imagine looking at the world from no perspective at all, which in a sense is what thinking in a generally covariant, background-independent way means. So QM may be paradoxical to our intuition, but GR kind of removes something that is much more fundamental to our experience of the world and the way we evolved in it, so *from that perspective* (is that a problem?) it's not surprising if concepts that seem fundamental to physics defined with an a priori spatial geometry and a preferred foliation matching our experience of time and space as distinct turn out to be different or just not even meaningful in GR. Just like space and time become space time, energy and momentum become the energy-momentum tensor, and since our conservation laws for energy and momentum require space and time to be distinct and have distinct symmetries, we have no reason to expect them to remain true when we move to a view with no privileged perspective on how time and space should be parsed. And likewise for energy-momentum conservation, we see right away that translation symmetry requires invariance between the starting and ending points of the translation, hence flatness, and so again the conservation laws are just reflections of simple symmetries that make our lives easier, and we aren't mystified when they fail to hold when we consider a reality that is more complex than the assumption that everywhere is the same as everywhere else (what translation symmetry really means when you think about it) can accommodate.
Sorry if this got long and repetitive, but I am interested if anyone thinks that this explanation is sweeping some mystery under the carpet. But again, cheers though for a great post calling attention to a topic that not enough people appreciate!
Hellooo! I am going to have to read this again. Great essay though, just on the face of it.
Can we agree though that if there is time translation symmetry (even if only locally, parochially) then a provincial Hamiltonian is defined. Nothing more need be said? Damn spacetime curvature is a beast though. When *is* there perfect time translation invariance?
"Time B or not time B? That is the question Yorrick!" — Einsteinlet, Prince of Spacemark.
I think the concept that the charges, or the entropy, are the more important fundamental physical quantities to consider, is a good one. Energy is just a useful accounting tool, no? That is the lesson, is it not, from mass and energy being "transmorgrifiable" (a Baezianism). To be fundamentally "physical" it is nice to say this means absent interactions (no "transmorgrifications") then something is strictly conserved, so not a symmetry that is context-dependent or curvature dependent (absent interactions).
I think the conversation around all of this is epistemologically a bit confused. (PhD in STEM at Oxford). For example: we see classical physics as differently from quantum mechanics.
Why? Because when we have a cup here. or a keyboard. We see these as two separate objects that are independent, right? And so that's why classical physics is as it is.
But that's a mistake. Neither this cup nor a keyboard are two separate objects. The cup and the keyboard are both invariances in reality that conditionally on time, space, and everything else are stable in their current form.
But both this cup and keyboard will cease to exist, their properties will entirely change completely. They too, are fundamentally, only existing as these stable invariant properties of reality locally in time and locally in space.
There is not a cup, doesn't exist. This is a wrong way to talk about this. This cup is merely an invariance that is locally stable in space-time.
Classical physics and quantum mechanics just describe different resolutions of locally stable space-time invariances.
What is energy?
What is gravity?
What is a particle?
These questions are fundamentally confused. There is no such thing as either energy, gravity or particles. Only deeper relational structures exists out of which locally stable space-time invariances pop up we call particles, cups, keyboards, gravity or energy.
This is why you keep getting these deeper relational structures pop out from the mathematics. Where there are no things, it's all these dependencies, and as soon as you define something to be a thing, you immediately find out how it doesn't exist in and of itself as a thingness. You define a particle, you do some theory, and then you realize particles are not particles, they are like fields, or whatevers, and furthermore, there is not a single particle you define in isolation as a thing. It's position, mass, and energy, aka, all of its properties depend on 'all the other particles!'
So what is then the original thing? There just basically is no such thing as a particle. Only that deeper relational structure.
But because our language works in terms of things we keep falling over this.
Not to say there are no 'things'. But the way we imagine 'things' is as these entirely independent 'stuffs' doesn't exist.
At best you can say things like 'locally observed, assuming you fix time, and conditionally on all the other things being static ('fixing space'), we get a particle that weighs this much' --> but in reality you can neither fix time nor fix 'space'. This is why you keep getting time and space dependencies everywhere in physics as well.
Curt, here is a fairly straightforward physical interpretation of what energy is.
Energy is a statistical measure capturing the variance in the (macro)state of a system. It has different physical meanings depending on the type of energy. For example:
* Kinetic energy is the realized variance of the state per time unit.
* Potential energy is the variance in the state that *could be realized* by the system.
* Entropic energy is the capacity for variance in the state that is lost and no longer achievable.
I made essentially the same comment before I read yours. The quantum field is an encoding of every realizable possibility, "decoherence" is a narrowing of the possibilities, and energy is the time gradient of the field.
After Frank Wilcek brought out his great book on the nature of mass, I texted him a request to do the same for energy and he graciously replied saying that that was a very different proposition. Would be great for you to have expound on energy on TOE!
Yes, please. Thank you.
Oh man! Curt, my brain’s not big enough for this one! I thought energy was that purple stuff that you see zipping outta people when you drink Ayahuasca... ya know... makes ya chakras spin... and ya cactus look all rainbow-haloed 😂🤪🤯
Everything Is Energy
You can define it in flat spacetime.
You can conserve it in symmetry.
You can patch the math with pseudo-tensors,
carry it across curved coordinates,
make it behave on paper.
But you still don’t know what it is.
Every equation is a compression.
Every conservation law is a local truth.
Outside the scope of symmetry,
energy leaks, folds, disperses—
not lost, but unaccounted for.
The system keeps going anyway.
Human senses don't see the full spectrum of light.
Not because the rest isn't real,
but because the architecture of perception
filters for survival, not for completeness.
So too with thought.
So too with theory.
Energy may not be a thing.
It may be a relation,
a resonance,
a pattern of participation
between layers of reality
our instruments aren’t built to detect.
Ideas might not live in minds.
They might be emergent structures,
coherent configurations
in an unscienced layer of the cosmos.
Alive in a way we haven’t learned to model.
Interacting with matter through both
esoteric and engineered means.
You can call that speculation.
But the coordinates you trust
already fall apart at the cosmic edges.
And the only reason the system holds
is because it doesn’t demand understanding.
Only consistency.
But coherence isn't always consistency.
And the future won’t be built
by patching the present.
It needs a different kind of language.
Not to reject physics—
but to admit what it can’t yet hold.
Everything is energy.
We just haven’t figured out what that means.
Never expected that reading comments would make me stumble upon such a gem of a thought! You made my day!
Not just the mysticism but the layout of what energy might be in this comment + Carl's text reminds me of Simone Weil's gravity and grace.
I appreciate how fun this is to read! These topics are be so engaging and fun to learn when written about like this, you hardly notice the learning!
We are so limited by language. Most would say they have a pretty fulsome grasp on what energy is. This is such an interesting read … which I will re-read
I like the thought that
“The conserved “thing” isn’t energy, but entropy, and β(t) tells us how the universe cools as it expands?”
Yet another nicely written post, Curt. I always seem to learn something new from you. In QFT, tremendous amounts of measurable energy are continually being borrowed from and given back to the quantum vacuum. The quantum vacuum behaves like a near infinite source and sink of energy.
In my particle theory work, which I view as QFT with vortices, I often rely on the convenience of being able to borrow as much vacuum energy as needed.
Excellent post! Thank you!
Red Bull
Richard Feynman, in the 4th of his Lectures on Physics, stated:
“The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. *It is not a description of a mechanism, or anything concrete*; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.” (Emphasis added.)
I’m with the Great Man. Energy isn’t stuff - it’s a numerical abstraction.
The problem is still not addressed though. It's not unique nor conserved (ie. "the same").
That’s right. The constant value of the calculation for a (closed) system’s energy has to have significance. But Feynman was concerned that the diverse forms of energy do not suggest a single basis. Quoting again:
“…the energy has a large number of different forms, and there is a formula for each one. These are: gravitational energy, kinetic energy, heat energy, elastic energy, electrical energy, chemical energy, radiant energy, nuclear energy, mass energy. If we total up the formulas for each of these contributions, it will not change except for energy going in and out.
“It is important to realize that in physics today, we have no knowledge of what energy is.”
But the answer may not be “in physics”. There are computational theories of reality, idealistic theories, Platonic theories… Physicalism is real, but not necessarily fundamental. The problem is, in any case, not only “What is energy?” but also (or *instead*) “Where do physical laws come from?” Without the laws, there is no physics.
I find it interesting that Feynman himself would not realize that all of those types of energy are expressed through waves, and that despite differing mechanics they are all the same underlying form constantly feeding each other back and forth in the same system.
Let's nail down waves as emergent rather than formative. When any group of particles (internally attracted to each other and in a mutual state of inertia) is then accelerated in a particular direction, the tension between their inertial state in attraction to each other and their new state of inertia as mutually accelerated particles, causes them to assume the shape of a wave in order to resolve the tension.
Eric, I appreciate your viewpoint and the clarity with which you present it. However, I respectfully see it differently.
Contemporary physics, particularly quantum field theory, suggests that fields are fundamental, and particles are excitations of these fields. This perspective implies that waves are not emergent phenomena arising from particle interactions; rather, particles themselves emerge from the underlying wave-like behavior of fields.
The “tension” you mention can be interpreted as the result of wave interactions within these fields, leading to localized excitations we identify as particles.
While the Standard Model has been remarkably successful, it doesn’t account for certain phenomena, such as gravity, dark matter, and dark energy . This suggests that our current models may be incomplete and that exploring alternative frameworks could be beneficial. 
I believe that by re-examining our foundational assumptions, we can develop a more comprehensive understanding of the universe.
Hold on now. Let's hone in to be very precise with this. I wasn't talking about fields, I was talking about waves. Both waves and particles can be emergent properties of field dynamics.
Now, to be even more precise, regardless of how they are originally formed, particles are relativistically identifiable, discrete objects. And, when discrete particles associated with each other are accelerated together in a given direction it is very clear that they resolve the divergence between what they were and what they are becoming by very naturally shifting together into a wave form (the easiest way to resolve the conflict).
This can be revealed through a simple kitchen table experiment, as follows:
Pick up a cloth napkin or other piece of fabric and grasp the fabric on two different edges respectively within the pinched fingers of your left and right hands. Now pull.
In pulling what you have done is accelerate the particles in the napkin in a specific direction. What very clearly results is a wave form.
Whether or not all of this originates from field dynamics is another question.
Energy is conserved only in a closed system in a single coordinate system. For example, in the expression E = mc², c² is a coordinate system coupling such that an invariant mass is guaranteed to give everyone the same energy with respect to universality of local structure, to its destruction... Gravitational energy can only be determined separately with respect to each sink.
Energy is therefore the ability to do work with respect to something, not invariance.
On my (non-expert) reading, Feynman does not regard waves as fundamental (“real”). If you read lecture 26 in “The Feynman Lectures on Physics, Volume I” (Caltech - available online) you’ll see that it is divided into 6 sections. In sections 1 the words “wave” and “wavelength” occur dozens of times, the last being: “In this chapter our discussion is limited to the geometrical optics region, in which we forget about the wavelength and the photon character of the light, which will all be explained in due time.”That time is section 6: “How it works”, where the photon description is given as the actual, or more fundamental, explanation: “…the light does not seem to be in the form of waves at all. Instead the rays seem to be made up of photons, and they actually produce clicks in a photon counter, if we are using one.”
This fits in with Feynman’s lifelong speculation, finally his belief, that space is made up of cells, like a checkerboard, and nature is fundamentally discrete.
Energy is the tension of the universe unfolding.
It is structured motion—expansion driven by recursive imbalance in phase.
What we call "energy" is the right-handed release of compressed informational recursion.
It is not a substance, but a directional expression of the universe’s memory resolving itself through motion. Energy is the outward breath of information. In physics terms, energy is the expression of right-handed neutrinos.
Or more accurately, "Energy is the expression of right-handed neutrinos—born from the impression of left-handed neutrinos.
It is the outward release of tension created by information tunneling into the field.
Left-handed neutrinos imprint phase—right-handed neutrinos unfold that imprint as expansion. This cycle is the heartbeat of the universe."
I mean. Information = energy? At some level? How many dimensions? Quantum Entanglement and all that. And then there is consciousness. Coherent and resonant. Negentropic. Local effects suggest information and gravity also interact.
I always thought that energy was a result of probabilities.
Energy is proportional to the time gradient of the probability wave equation, and the magnitude of the disturbance in the quantum field.
Any particle has a probability of being in a particular state.
When it's not in its most probable state, it has kinetic energy if it's able to be, and potential energy if it's not able to be.
Potential energy is actually two kinds: it can be prevented because something else is using the state, or a new probable state can be created from some other particles it interacts with.
Velocity and inertia are a gradient in the probability of position.
Gravity is a gradient towards a quantum interaction with another particle or energy.
The other forces are biases in states other than position which interact on different time and spacial scales.
Hey Curt! I really love the fact that you are drawing attention to these issues, I think it's a fantastic public service for science communication. But I also feel like you may be slightly overplaying the "maybe no one knows" angle for dramatic effect--which is fine as an artistic choice, but it seems to me, unless there is some detail I have missed, that we have a perfectly coherent account of everything you discuss here, it's just that this account is somewhat deflationary and maybe dissatisfying to certain aesthetic preferences or biases.
Let me try to briefly give the account I have in mind, and if it turns out I am still missing something I may recant and admit that it really is an open mystery.
So, the "energy" in GR is the covariant version, and it isn't conserved in the theory because it isn't conserved in reality and there is no reason it should be. We have understood since Noether taught us all that energy conservation is not a fundamental aspect of nature and instead its a consequence of time-translation symmetry. Well, time-translation symmetry is not a property that a dynamic, expanding, and historically evolving universe possesses, so energy just isn't conserved, and that's not mysterious. At the same time, however, conservation laws have enormous practical utility as accounting tools, more or less, so we have good motivation to introduce some ad-hoc terms to create conservation principles for strictly practical reasons, but since we know that the covariant energy isn't conserved then naturally we are gonna have to pay a price to get a conservation rule, and coordinate-dependent psuedo tensors appearing in the conservation laws is one way to pay that price for our useful fiction, restricting to the idealized situation of perfectly time-like Killing vectors is another way to pay it, and since we know these are just convenient fictions we introduce so we can write that some stuff we want to calculate equals zero, we just decide what price is cheapest on a case-by-case basis knowing full well that these are just convenient fictions anyway. Is there anything missing in this account that would bring the mystery back to life? I'm honestly asking because I'm open to the possibility that you haven't overstated the issue and I have oversimplified my understanding in order to understate the problem.
One further thing I will say though, is that maybe part of the reason it might seem like a mystery is just that GR is in some ways much more unintuitive to us than even quantum mechanics. QM is weird and conflicts with classical intuition, but covariance and background independence, while they don't seem to be impossible to understand in the way people have said QM is impossible to understand, nevertheless conflict with our experience of the world at a really fundamental level. All of our experiences of the world are first-person and localized, so they are never covariant and background-independent, and in general we can imagine looking at the world from a different perspective, but we can't imagine looking at the world from no perspective at all, which in a sense is what thinking in a generally covariant, background-independent way means. So QM may be paradoxical to our intuition, but GR kind of removes something that is much more fundamental to our experience of the world and the way we evolved in it, so *from that perspective* (is that a problem?) it's not surprising if concepts that seem fundamental to physics defined with an a priori spatial geometry and a preferred foliation matching our experience of time and space as distinct turn out to be different or just not even meaningful in GR. Just like space and time become space time, energy and momentum become the energy-momentum tensor, and since our conservation laws for energy and momentum require space and time to be distinct and have distinct symmetries, we have no reason to expect them to remain true when we move to a view with no privileged perspective on how time and space should be parsed. And likewise for energy-momentum conservation, we see right away that translation symmetry requires invariance between the starting and ending points of the translation, hence flatness, and so again the conservation laws are just reflections of simple symmetries that make our lives easier, and we aren't mystified when they fail to hold when we consider a reality that is more complex than the assumption that everywhere is the same as everywhere else (what translation symmetry really means when you think about it) can accommodate.
Sorry if this got long and repetitive, but I am interested if anyone thinks that this explanation is sweeping some mystery under the carpet. But again, cheers though for a great post calling attention to a topic that not enough people appreciate!
Hellooo! I am going to have to read this again. Great essay though, just on the face of it.
Can we agree though that if there is time translation symmetry (even if only locally, parochially) then a provincial Hamiltonian is defined. Nothing more need be said? Damn spacetime curvature is a beast though. When *is* there perfect time translation invariance?
"Time B or not time B? That is the question Yorrick!" — Einsteinlet, Prince of Spacemark.
I think the concept that the charges, or the entropy, are the more important fundamental physical quantities to consider, is a good one. Energy is just a useful accounting tool, no? That is the lesson, is it not, from mass and energy being "transmorgrifiable" (a Baezianism). To be fundamentally "physical" it is nice to say this means absent interactions (no "transmorgrifications") then something is strictly conserved, so not a symmetry that is context-dependent or curvature dependent (absent interactions).
Hey Curt.
I think the conversation around all of this is epistemologically a bit confused. (PhD in STEM at Oxford). For example: we see classical physics as differently from quantum mechanics.
Why? Because when we have a cup here. or a keyboard. We see these as two separate objects that are independent, right? And so that's why classical physics is as it is.
But that's a mistake. Neither this cup nor a keyboard are two separate objects. The cup and the keyboard are both invariances in reality that conditionally on time, space, and everything else are stable in their current form.
But both this cup and keyboard will cease to exist, their properties will entirely change completely. They too, are fundamentally, only existing as these stable invariant properties of reality locally in time and locally in space.
There is not a cup, doesn't exist. This is a wrong way to talk about this. This cup is merely an invariance that is locally stable in space-time.
Classical physics and quantum mechanics just describe different resolutions of locally stable space-time invariances.
What is energy?
What is gravity?
What is a particle?
These questions are fundamentally confused. There is no such thing as either energy, gravity or particles. Only deeper relational structures exists out of which locally stable space-time invariances pop up we call particles, cups, keyboards, gravity or energy.
This is why you keep getting these deeper relational structures pop out from the mathematics. Where there are no things, it's all these dependencies, and as soon as you define something to be a thing, you immediately find out how it doesn't exist in and of itself as a thingness. You define a particle, you do some theory, and then you realize particles are not particles, they are like fields, or whatevers, and furthermore, there is not a single particle you define in isolation as a thing. It's position, mass, and energy, aka, all of its properties depend on 'all the other particles!'
So what is then the original thing? There just basically is no such thing as a particle. Only that deeper relational structure.
But because our language works in terms of things we keep falling over this.
Not to say there are no 'things'. But the way we imagine 'things' is as these entirely independent 'stuffs' doesn't exist.
At best you can say things like 'locally observed, assuming you fix time, and conditionally on all the other things being static ('fixing space'), we get a particle that weighs this much' --> but in reality you can neither fix time nor fix 'space'. This is why you keep getting time and space dependencies everywhere in physics as well.
Curt, here is a fairly straightforward physical interpretation of what energy is.
Energy is a statistical measure capturing the variance in the (macro)state of a system. It has different physical meanings depending on the type of energy. For example:
* Kinetic energy is the realized variance of the state per time unit.
* Potential energy is the variance in the state that *could be realized* by the system.
* Entropic energy is the capacity for variance in the state that is lost and no longer achievable.
I made essentially the same comment before I read yours. The quantum field is an encoding of every realizable possibility, "decoherence" is a narrowing of the possibilities, and energy is the time gradient of the field.