Why the Flow of Time Is an Illusion

That's always a good question!

Since we're talking about General Relativity (the top of the thread introduces the stress-energy tensor, and a particular solution to the Einstein Field Equations) let's talk in those terms. We can also talk in those terms because it is the more-fundamental theory from which Special Relativity (which gives the famous E=mc^2) can be derived.

The "stress-energy tensor" determines the curvature of spacetime. It goes by other names: the matter tensor, the energy-momentum tensor, and so forth, largely depending on how one wants to interpret the tensor components in a particular problem.

Three quick paragraphs with some reference to the mathematics:

You can write the energy-momentum tensor's components as a 4x4 matrix where each cell represents a flux of momentum from one direction to another. Momentum which "hangs around" flowing only from the past to the future corresponds to the m in "E=mc^2" either very locally or more globally in a spacetime which has no gravitation whatsoever. Since a nonzero "m" represents a nonzero value of the energy-momentum tensor, and since the energy-momentum determines the curvature of spacetime, "E=mc^2" is really just an excellent approximation that is better when m is small.

The fuller Special Relativity relation is E^2= (mc^2)^2 + (pc)^2 where we square to get rid of sign problems and where p represents linear momentum; if there is no momentum and the mass stays at the spatial origin (moving only in time) in our reference coordinates, then all but one component of the energy-momentum tensor is zero, and the one remaining one is totally determined by "m".

If we (non-gravitationally) impart momentum onto our m then p becomes nonzero and so does at least one other component of the energy-momentum tensor.

Summing up: mass sources energy-momentum, which determines curvature. Moving mass sources even more energy-momentum, and so greater curvature.

In your question about the cup, let's apply a restriction: we use the same number of water molecules at all times.

As we heat the ice or water, the motion of the water molecules relative to the centre of the coffee cup (or the overall centre-of-mass or the overall centre-of-momentum) increases. Increased motion means increased momentum. This in turn means a greater curvature is sourced by the heated molecules, or if you like, that there is a greater "active" gravitational interaction for the hot water than for the cold water or ice. "Active" in the sense of small things falling towards it. It virtually certianly also has an identically larger "passive" gravitational interaction, where "passive" is in the sense of falling towards an object that makes it seem like a very small thing. (We have excellent experimental evidence that passive and active interaction strengths are effectively identical, and the underlying theory demands it, ignoring some details about gravitational back-reaction which even experts won't want to think too hard about.)

So if we use a very sensitive scale we can measure that the hot water with exactly N molecules of hot water weighs more than the exactly N molecules of cold water. Ignoring gravitation again, we see that E is greater in the hot water case, but because there is a larger average value for p (momentum) for each of the molecules. The "m" remains effectively the same in the hot and cold water. Rest mass (m_0) is properly determined by the count of water molecules when they are completely free of momentum (including internal momentum, right down to the momentum of photons, electrons, quarks and gluons), which gives you the answer to when E is lowest for the cup of exactly N molecules of water. (It's at absolute zero!)

Back to gravitation: the minimum influence on the curvature of spacetime by the N molecules of water is when they are at absolute zero.

The difference is very tiny at the sorts of temperatures you're asking about. However, if we could somehow confine the N molecules of water into a magical box of the volume of the coffee cup, and heat the water molecules to the point where the molecular bonds break, the atoms all ionize, the oxygen nuclei disintegrate into protons, the protons disintegrate into a quark-gluon plasma, and keep going through several orders of magnitude (wherein we may discover new subatomic physics!) then as we go the "active" and "passive" gravitational interactions of the confined matter will grow substantially. It will become very heavy (passive interaction: hard to hold above the lab's floor, assuming the ultra high energy stuff didn't vapourize everything around it) and noticeably start affecting the trajectories of ever larger things (dust, pencils, lab assistants...). In the extreme, we can add so much momentum to to the stress-energy-momentum tensor the magical container encloses that it collapses into a black hole.

In essence this is what happens in the cores of neutron stars when they collapse into black holes: the internal pressure and temperature gets so high that an event horizon forms. The "container" is a few solar masses worth of incredibly dense "nuclear pasta" and other exotic stuff we don't know much about yet, and is more the size of the city the magical-container lab is in than the lab itself.

One last thing: the total value of the stress-energy tensor at a given point is observer-independent -- an ultrarelativistic observer passing by the lab and a scientist standing still in the lab will both agree on the total stress-energy-momentum of each container of water. However, different observers may prefer to split the total tensor value into its sixteen components in different ways; indeed, any single observer is free to do so because the splitting is coordinate-dependent and one is free to select from an infinite set of systems of coordinates in describing spacetime or a small patch thereof.

Because of this sort of coordinate- and observer- independence ("general covariance", technically) modern physics uses tensor fields as fundamental objects and either copes with the heavyweight mathematics that requires or reduces tensors by imposing special conditions on coordinates and on how coordinate-dependent vector-values are extracted from the tensors.

Finally, the stress-energy-momentum tensor is contributed to by all the fields of matter, so this would (where not excluded for convenience) include the classical electromagnetic tensor field, or the fields of quantum electrodynamics, or the fields of the Standard Model of particle physics. The contribution to stress-energy for known matter is always non-negative. So when considering classical or quantum matter fields, where there are nonzero field-values there is nonzero stress-energy. In heating up the water molecules we are also creating [a] more photons and [b] higher-momentum photons. Photons carry nonzero momentum and so contribute to the "p" term in E^2=(mc^2)^2+(pc)^2 or more fundamentally they add to the total tensor-value of the energy-momentum tensor.

I hope this is a helpful answer.

PS: I should have said that absolute zero is probably not physically achievable in our universe, but to the extent things can get very close to absolute zero (attokelvins or colder) we can always describe a relatively-moving observer who will think the object is warmer than someone at rest with respect to it (and some ultrarelativistic observers might think it's rather hot, spraying out a thermal bath of kilokelvin photons!). Nobody knows what the quantum chromodynamics equivalent of absolute zero would be, so that's always happening, and the momenta of the quarks and gluons thus don't completely vanish.

I don't claim to be special - what I'm describing goes for all conscious beings, after all (and it could very well be that there are conscious animals). It seems to me you are trying really hard to make it seem like I'm uncomfortable on a personal or emotional level with the concept that consciousness can arise from matter only; please belive me when I say I am not. But on an intellectual and rational level I find the idea untenable. I don't understand why this is so hard to accept for you?

Your argument about the complexity of computers would have weight if I had been claiming that the reason consciousness cannot be found outside humans is because nothing can be as complex as the human brain; I am not claiming that. Hence you can make computers as complex as you want - you still haven't answered how subjective experience can arise from matter.

There is nothing about me in particular that is special, but every conscious being does possess a quality or is inhabited by a phenomenon that is unlike anything else in the universe that we know of. That makes it pretty damn special, yes.

But again, it's not the feeling of feeling special that I am talking about here. It is the phenomenon of subjective experience.

As someone who isn't that familiar with the physics behind it, this comment was just as an intriguing read, if not even more than the original article. Thanks for taking the time to write an in-depth response.

>Thanks for trying to explain your belief to me. If we concentrate on exactly your last post, maybe you can understand how I see it: I see again that you claim that you came to that conclusion "intellectually and rationally" but everything else contradicts that. I see the claim to uniqueness of conscious beings (and I still haven't heard from you if you consider only humans "conscious") as a "the phenomenon of subjective experience." That is, because you "subjectively experience" it, that means to me "not rationally" and I still conclude it's your "feeling of being special."

I think we already here have some deep reasons for disagreement: If I understand you correctly here, you're saying that no conclusion reached on 'subjective' grounds can be rational - maybe you would even go so far as to say that what is rational is identical to knowledge gained via the scientific method? If so, I would disagree with your definition of what is rational.

(I don't know whether animals are conscious in the same way we are - I would have no problems either way. As I said, it's not about humans (or myself) being special, it is that the phenomenon of consciousness is special).

> If you would really approach your claims "intellectually and rationally" you'd understand that that "subjective experience" which you see as something special is an emerging property.

This is a really bold claim, and it is indeed the locus of our disagreement, so again I'd have to say I disagree :) Emergence is not a magic wand you can wave and make every problem go away; for all phenomena where 'emergence' have been invoked as an explanation, we are really just talking about very complex phenomena that are very very hard to reduce to their base 'constituents' (elementary particles and their force transmitters), but which we can at least imagine can be reduced to these constituent parts - in other words, I can imagine starting from some basic building blocks of matter and, through some very complex patterns of organization, I can imagine moving from that starting point to the end result - conceptually, even if I cannot trace all the steps with my current understanding.

But this is not something I can imagine with the phenomenon of subjective experience. (An aside here: It seems you take me to say that 'because of my subjective experience that I cannot imagine this, this cannot be true' - what I am saying is that it is subjective experience itself that is what we're trying to explain here. So referring to earlier people not 'subjectively experiencing' an understanding of how e.g. planets can move is not really on target: My concern here is with the phenomenon of subjective experience itself).

What I mean is that in order to explain, say, my subjective experience of how an apple tastes, it's not just a matter of saying 'well, now your neurons are firing in this way and we know this is the taste center of your brain, so that's why you have a sensation of taste'. That is showing a correlation. What I'm saying is that this is not an explanation, and to me it shows that it will be impossible to move from a purely materialistic account of this experience to my actual subjective experience of the thing. How can we ever translate the firing of the neurons in my brain into the subjective world my consciousness inhabits? How can atoms, no matter how sophisticately arranged, give rise to this type of phenomenon?

Let me try to say it in another way: You could measure the activity of the brain and give an 'objective' account of what happens to a person: Now they're angry, now they're cold, now they're slightly hungry, etc. But it stops there! How will you move from this objective description to the actual experience of these feelings and states of mind?

Sean Carroll is a great physicist, and it's great that he engages with these questions, but he is mainly a physicist, not a philosopher of mind, and he does exhibit the same hubris that many of our ilk (yes, I'm a physicist too) have when it comes to other fields. The question I'm raising here is far from being unanimously agreed upon, and when Carroll writes stuff like "To persuade anyone otherwise, you would have to point to something the brain does that is in apparent conflict with the Standard Model or general relativity.", it's either disingenous or just a bit lazy. Giving a materialistic account of consciousness is non-trivial no matter whether the brain violates SM or GR or not, and whether it does or not will have little bearing on this problem.

If you're interested in reading more, and indeed seeing that I'm not the only one who sees this as a big problem of a materialistic account of the universe, here is a book I can recommend: https://www.amazon.com/gp/product/1851683763

Ok, I think we either have some communication issues or philosophical differences (if I understand you correctly, you're saying that subjective experience is an illusion? Which to me just shows the absurd lengths one has to go to in order to rule out any question that cannot be answered by science. Your own subjective experience is literally the starting point for any investigative endeavor you might attempt in this world, so I'd be careful with claiming it is only your imagination) or a combination of both, so maybe we should recognize this and leave it here.

You have provided ample examples of emergent properties, which are interesting in their own right for sure, but if you really imagine that Conway's game of life and the unknowable future of that game is analogous to the phenomenon of subjective experience, we either are miscommunicating or there is a quite insurmountable barrier of understanding between us.

Either way, thanks for engaging!