It’s often said that in quantum physics, everything that can happen will happen.
One way this comes up is in something called a path integral, used to calculate the probabilities of quantum events. If you want to find what happens to a particle traveling from point A to point B, you have to add up a contribution for every path, no matter how windy, that goes between A and B. These contributions mostly cancel out, and matter less the further they are from a straight line, so the straight-line path is, for the most part, a good description of what happens. But in principle, all of the other paths matter too.
The same thing happens in quantum field theory, in more elaborate form. Instead of a path from one place to another, the paths are from one configuration of quantum fields to another, via all the different ways fields can in principle interact. We are almost never able to take account of all these possibilities mathematically, so we have to approximate, organizing the interactions into more and more complicated pictures called Feynman diagrams, each with a smaller and smaller effect.
In principle, these diagrams need to contain every single combination of interactions that might result in the end-state we’re interested in. These combinations can have a Rube Goldberg flavor, with one field activating another, which activates another, only to all cancel out in the end. Because of this, any field that exists, any particle no matter how rare, can matter, if only a little.
And from that, physicists can learn something.
Because absolutely everything matters, physicists get to reason about absolutely everything that exists.
The best example involves something called an anomaly. These aren’t the anomalies of experimental physics, unexpected results that have a tendency to go away with better measurements. Instead of something unexpected, a theorist’s anomaly is something impossible.
Anomalies are combinations of particles that, if they were to show up together in a sum of Feynman diagrams, would break the rules that the theory was made with in the first place. If they show up, they’re a sign of an inconsistent theory, one that doesn’t obey its own rules and thus doesn’t make sense.
In order to have a theory without anomalies, different calculations involving different particles need to cancel. For example, it might be that the charge of different particles has to add up to zero. This means that if you’ve only discovered a few particles, and their charges don’t add up to zero, then you know you’re missing one. There is an extra particle there, which you haven’t observed, that together makes charge add up to zero.
This logic actually works! It was used to predict the top quark. Before the top quark was discovered, the list of quarks, electrons, and neutrinos had electric charges that didn’t add up to zero. One particle was missing, with the same charge as the up quark and charm quark. It was found in 1995, after being proposed almost 20 years earlier.
4 gravitons 
This logic was used to predict the charm quark. The bottom and top quarks were predicted as an explanation of the CP symmetry breaking.
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Ah, I may have the history wrong here. Wikipedia cites Conlon’s “Why String Theory?” for the claim that the top quark was predicted from anomaly cancellation, and doesn’t list anomaly cancellation as one of the arguments used to predict the charm quark. Can you point me to a primary source? Might be good for someone to edit those pages if they’re in error.
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Feynman’s short series of four lectures on this topic, given in New Zealand and edited and collected in a book called “QED” is a truly excellent way for a layman to get a good working understanding of what is going on with this and to understand Standard Model physics at a deeper level, without taking too much time or requiring too much of a mathematically challenging foundation. No other text written before or after it strikes such a perfect balance of being informative yet accessible. If someone is going to read just one book on modern quantum physics, this is the one to read.
It is all the more impressive for being written by someone who did some of the core science work in this field himself and created some of this physics, people who often have trouble explaining their work to laymen, rather than a science communicator who is not actually primarily a scientist.
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Hi!
I can’t stop myself from pointing out that not every anomaly is bad. Really, only the anomalies that lead to the breakdown of the gauge symmetries are what signify inconsistency. As a matter of fact, the most prominent case of the anomaly is the conformal anomaly present in practically every quantum field theory. The classical pure chromodynamics is conformally invariant, whereas the quantum one is not. The most famous chiral anomaly plays the crucial role in the spectrum of the light mesons as well as allows a two-gamma decay of the pion. Also, if the electroweak baryogenesis works after all (if some new physics changes the nature of that phase transition), the baryon number anomaly may be one of the things that allow us to exists at all.
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Very true! I felt like it would be too tricky to explain the difference between a gauge anomaly and a global anomaly in this post, but yes, what I said only applies to the former.
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Re your article in the New Scientist: 100-year-old assumption about the universe may soon be overturned
This is a really interesting direction, particularly the idea that departures from FLRW might resolve tensions like evolving dark energy or discrepancies in the expansion rate.
One thing I find intriguing is that once large-scale homogeneity is relaxed, it becomes less clear what global structure we should assume in its place.
A natural possibility seems to be that spacetime is not only inhomogeneous, but composed of many finite expanding regions embedded within a larger background. If spacetime is infinite and governed everywhere by the same physical laws, then Big Bang–like expansions may not be unique, but could occur throughout it.
In that context, the “lumpiness” you describe would not just be a deviation from FLRW, but a reflection of fundamentally different regions at different evolutionary stages. Observables like expansion rate or effective dark energy could then be sensitive to our location within that structure, rather than representing a global average.
I’m also curious whether, in such scenarios, interactions between regions — for example via gravitational collapse leading to black hole–dominated phases — could play a role in shaping large-scale observables, rather than treating regions as completely isolated.
Do you think current or near-future data (e.g. distance measures or large-scale structure) could realistically distinguish between “mild departures from FLRW” and more radical global pictures like this?
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The more dramatic picture you’re describing sounds a bit like concepts like eternal inflation, where things like the inflaton have different values in different places, or there are more dramatic differences in phases in different areas (you mention black-hole dominated phases, for example). The impression I get is that that kind of thing would have to exist on a larger scale than these people are measuring, because they’re mostly basing their analysis on astronomical measurements of things like supernovae where we don’t see black-hole dominated regions or anything like that. So that’s not to say that it’s impossible that things are inhomogeneous even more dramatically on larger scales, but it’s not really part of what these people were addressing.
Also, I’d encourage you to challenge this thought:
“One thing I find intriguing is that once large-scale homogeneity is relaxed, it becomes less clear what global structure we should assume in its place.”
An important question that tends to get overlooked is, should we assume any global structure at all? Obviously for practical reasons people do. But part of the motivation of the people I covered there was to try to assume as little as possible, and I think they’ve got the right idea there. As much as possible we should try to see what the observations imply without assuming anything we don’t need to.
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Thanks — that’s a really helpful clarification, especially the point about trying to minimise assumptions and let observations lead.
I think the place where my thinking differs slightly is in what follows from taking a minimal set of assumptions seriously at large scales.
If one assumes:
spacetime is unbounded (effectively infinite)
and the laws of physics are the same everywhere
then it seems difficult to avoid the conclusion that processes like Big Bang–like expansions are not unique, but could occur in multiple regions.
At that point, some form of global structure isn’t being imposed so much as emerging from those assumptions.
I completely agree that current observations are probing scales far smaller than anything like black hole–dominated phases or inter-region interactions. But it raises the question of whether departures from FLRW are simply local effects, or early indications that our observable region is not representative of the whole.
Do you think it’s possible, in principle, to remain fully agnostic about global structure if those minimal assumptions are taken seriously, or does some broader picture become unavoidable?
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Ah, I see what you’re asking.
I’m not a cosmologist by training, so I’m not 100% sure of this, and would welcome an actual cosmologist chiming in. I think the concerns you’re bringing up are to some extent already present in mainstream cosmology, but with caveats. At the largest scales we can observe today, most of the universe seems like it shouldn’t have been in thermal contact early enough to give rise to the level of inhomogeneity that it observably has, which is what motivated the idea of inflation. So I think some amount of large-scale inhomogeneity is actually expected. However, the earlier you go the smaller the scale factor gets, and more and more is in contact, so there is a limit to how dramatically areas can vary (that loosens the further out you go). Since you can’t get bounces or the like without some exotic physics, you’d still have a picture where everything we see has big bang-like conditions around the same time. But it gets much harder to reason about areas much further from our visible universe, and I don’t see any obvious reason why one wouldn’t expect them to be quite different, up to that limit.
It’s also important to note that we don’t actually know the universe is infinite, we just know it’s substantially bigger than the visible universe. It may turn out to be finite.
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Thanks — that makes sense, and I agree that we don’t know the universe is infinite. Perhaps the better way to phrase my assumption is not “we know spacetime is infinite,” but “if no physical boundary is observed or required, infinite extension may be the simpler extrapolation than a finite totality with an unexplained boundary.”
My difficulty with a finite universe is that any boundary seems to raise the question of what defines it. If it has no edge because it is closed, that is mathematically possible, but it is still a specific global assumption. If it has an edge, then the boundary appears to require a further explanation. So I’m not claiming infinity is proven — only that it may be the least additional assumption.
On inflation, the framework I’m considering would try to avoid needing it by making the Big Bang a transition from a finite, long-lived progenitor. If such a progenitor existed before expansion, it could have had time to equilibrate, so the observed CMB uniformity would be inherited rather than produced by inflation.
On the “exotic physics” point, I agree that some non-singular collapse mechanism is required. But there are already serious ideas in that direction: Gaztañaga’s work explores collapse and rebound using the Pauli exclusion principle within GR; Planck-star models suggest quantum-gravity effects may halt collapse; and fuzzball ideas also replace singular interiors with finite physical structure.
So my thought is not that bounces are established, but that singularities are probably the least physical option. If black holes are finite systems rather than literal infinities, then their long-term role in cosmology may be much larger than standard heat-death pictures assume.
I suppose my core question is: would you regard “infinite spacetime plus universal laws” as an excessive assumption, or as a reasonable limiting case to explore when no boundary is observationally indicated?
Why did my first post have my name and the second one have my email? I prefer my name.
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I had the impression that usually people consider a finite universe with no boundary.
Whether that’s an additional assumption or not, eh. In general, you seem to be reaching for a kind of argument where you establish some Occam’s razor-favored default, and argue that should be assumed pending further evidence. I’m skeptical of that approach overall. I don’t think Occam’s razor is a good guide on the scale of the entire universe, because it’s fundamentally based on our day-to-day experience of which things are more likely than others, and the notion of counting how many assumptions you’re making is just a simplified heuristic for that messier judgement process. And I think in general it’s best to think of things as genuinely unknown when the evidence isn’t particularly strong, rather than to argue for one default or another.
Regarding your comments, that’s all handled on WordPress’s side, and I don’t know the details. My guess is you signed in for one of the comments and not the others, or you entered your info slightly differently. But it’s also possible the back-end updated in between your first comment and your latter two and changed how it processes your info.
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That’s a fair point — and I agree that framing something as the “default” based on Occam’s razor probably isn’t the right way to approach questions at this scale.
A better way to put what I’m trying to do is simply to explore one side of a basic dichotomy.
Either spacetime is finite (with some global structure, whether closed or otherwise), or it is not. My interest is in taking the second possibility seriously and following its implications.
In that case, the argument isn’t that infinity should be assumed, but that if spacetime is unbounded and the laws of physics are the same everywhere, then processes like Big Bang–like expansions need not be unique, and a broader structure naturally follows from that.
What I find interesting is that this possibility isn’t usually developed very far in cosmology, where the focus tends to stay on models that are effectively self-contained.
So I suppose my question is less “which assumption should we prefer,” and more: do you think the “unbounded spacetime” branch is underexplored, or are there existing frameworks that already push it as far as it can reasonably go?
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There are of course lots of cosmologists doing lots of different things, so I don’t know whether there’s any precedent for the particular things you have in mind. But just in terms of how many people explore which ideas, I think you can break things down in the following way:
Most cosmologists do not actively work on models of the universe dramatically outside our Hubble volume. Most cosmologists are in fairly tight dialogue with observation, and aren’t interested in speculating about the universe outside of the area that can be tested.
Most cosmologists trust inflation, with a minority of dissidents of various stripes proposing different things or dismissing the problem altogether.
Most cosmologists are skeptical about exotic effects on the scale you would need to support the long-lived progenitor state you mentioned. (I don’t know this about your specific proposal, but it’s the usual objection to cyclic universe models, which is one of the bigger groups of the “dissidents” I mentioned in 3.)
So putting all that together:
The majority of cosmologists aren’t actively engaged in the question of what the universe looks like on the very largest scales, far outside our Hubble volume.
The minority that do think about those scales mostly favor inflation over scenarios involving more exotic effects, so they mostly work on eternal inflation.
Many of the people who distrust inflation are cyclic universe people, who would have a different picture of the overall behavior where there are genuine universe-wide big bangs and crunches.
Many of the others are inhomogeneous cosmology people, who are often distrustful of exotic physics, and thus wouldn’t be in favor of the kind of long-lived big bang progenitor states you’re envisioning.
So yeah, I think the particular direction you’re talking about would be a minority of a minority. Whether that means it’s under-explored depends on how much it deserves to be explored, which is not really something I can judge. 😉
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That’s a very helpful breakdown — and I think your summary makes the situation much clearer.
I agree that what I’m describing would sit in a “minority of a minority,” particularly because it combines:
So the real question isn’t whether it’s a mainstream direction, but whether there’s any reason it should be explored.
The motivation I have in mind isn’t primarily speculative, but structural. If spacetime is unbounded and governed by the same laws everywhere, then Big Bang–like expansions need not be unique. Once you take that step, the question becomes whether those regions remain isolated, or whether interactions between them could have cumulative effects over long timescales.
That’s where I think it diverges from most existing approaches — not just in being “outside the Hubble volume,” but in treating different regions as potentially connected rather than independent.
I completely take your point about skepticism toward exotic physics. My intuition is that the key issue may actually be the status of singularities — if black holes are finite physical systems rather than true infinities, then their long-term cosmological role might be very different from standard expectations.
So I suppose the real question becomes:
Do you think there is any principled reason to rule out interaction or mixing between such regions in the long-term evolution of spacetime, or is it simply that current frameworks don’t extend that far?
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It feels like we’re getting to a point where you’re asking me for detailed feedback on your idea, and at that point you really ought to talk to a cosmologist, not an ex-particle physicist turned science writer. 😉
For example, for this question, of course regions can only interact or mix if they’re in causal contact, and if the universe expands enough regions fall out of causal contact with each other. So you’d need to make that quantitative: how much mixing, on what time and distance scales, what you’re assuming or not about dark energy, etc.
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