In an infinite multiverse, the need to calculate if our universe is typical leads directly to the devastating three-layered measure problem: ad hoc measures are bad ideas to begin with, all intuitive measures don’t work, and even if multiverse scientists were to find a contrived measure that did work, it would beg the question of what fine tuned and designed it?
While multiverse theory is plagued by many issues, the measure problem is unique. It conclusively demonstrates the multiverse’s failure to explain fine tuning and, for that matter, to explain anything at all. Once you understand the full scope of this problem, you’ll see why the multiverse fails as a good scientific theory, even in multiverse scientists’ framework.
Highlights of this essay:
From a Naive Multiverse to the Measure Problem
Since this essay is the culmination of our main attack on the multiverse, it’s so important to see how it naturally follows from the line of reasoning that started a few essays ago with a naive multiverse. In that spirit, let’s review the line of reasoning from the past four essays.
First, we discussed a naive multiverse that argues that since in an infinite varied multiverse everything must happen somewhere, there must be at least one universe with fine tuned constants. We showed that since using such a naive multiverse to explain fine tuning could equally be used to explain anything at all, it suffers from three crippling problems and is therefore not maintained by any serious scientists.
Next, we explained that a complete multiverse theory could theoretically explain fine tuning and avoid these problems by making a true prediction - that we are typical observers in a typical universe.
We provided compelling reasons to believe that this sole prediction of multiverse is false. Specifically, the Boltzmann Brain and Grand Universe problems indicate that we aren’t typical. That being said, in the last essay we showed that there’s an even more fundamental problem with the multiverse making any prediction whatsoever.
Since the multiverse posits an infinite number of universes, there is also an infinite number of copies of every universe. Therefore, there’s no straightforward way to determine what the predicted typical universe is. This is a major problem because if the multiverse can’t make any prediction, it reduces to a flawed naive multiverse theory.
To avoid this failure, multiverse scientists introduce a new metalaw called a measure that allows them weight the probabilities of the different universes. Since there are many potential measures that would yield different predictions about the typical universe, multiverse scientists must try to find the right measure that predicts that our universe is typical.
The Three-Layered Measure Problem
In this essay, we’ll clearly show the deep flaws that emerge from multiverse’s dependence on measures. We’ll explain how the three-layered measure problem is an intrinsic flaw with multiverse theory that renders scientists’ attempt at explaining fine tuning into nothing other than a naive multiverse.
The measure problem, together with other problems, ultimately led physicist Paul Steinhardt, a key contributor to inflationary cosmology, to reject inflation altogether as it leads to a fundamentally unsound infinite multiverse.
While this essay will develop the three layers of the measure problem, for further elucidation we highly recommend reading Steinhardt’s 2011 Scientific American article, The Inflation Debate, as well as Alan Guth’s 2007 paper, Eternal Inflation and its Implications. Incidentally, Steinhardt, Guth, and Andrei Linde all won the 2002 Dirac Medal for their work on inflation.
1. Ad Hoc Measures
The first layer of the measure problem is the intrinsic problem with the unjustified introduction of a measure.
To appreciate this problem, it's important to realize that a measure is conceptually very different from any known law of physics. It’s an entirely new type of metalaw that scientists design to enable them to calculate probabilities in an infinite multiverse. In other words, any measure that multiverse theorists select doesn’t naturally emerge from inflation or string theory, but is rather an ad hoc, external constraint added to the theory in order to render our observed universe typical. In Steinhart’s words, “the introduction of ad hoc measures is tantamount to an admission that eternal inflation on its own does not explain or predict anything.”
To illustrate this point, let’s reexamine last essay's analogy of trying to order an infinite row of silver and gold marbles. To enable us to compute probabilities and determine the typical marble, we initially chose an ordering of a million silver marbles for every one gold marble. However, such an ordering is an ad hoc external addition to an infinite row of marbles - there’s nothing about the original setup of an infinite number of silver and gold marbles that naturally tells us how to order them. Since there is an infinite supply of both gold and silver marbles, we could have ordered them in any way we wanted. We could have just as easily declared that the pattern should be 2 silver marbles for every 9 gold marbles, or 372 silver marbles for every 151 gold marbles.
Obviously, these different declarations would result in different probabilities. Since any ordering of the infinite row of marbles is an unjustified artificial addition, one can argue that in an infinite row of marbles, it simply doesn't make any sense to compute probabilities or determine the typical marble.
The same is the case with introducing a measure to weight the infinitely many universes of the multiverse. Since there’s no indication from any scientific theory that a measure even exists, we could very well argue that even if the infinite universes of eternal inflation were real, there’s still no reality to a measure. Perhaps all that exists is an infinite number of universes for which the probability of any particular universe simply can’t be calculated. If so, there’s no such thing as a typical universe, and the proposed complete multiverse reduces to a flawed naive multiverse.
Just to clarify, we understand why multiverse scientists need to posit a measure - after all, without a measure, the whole idea of an infinite varied multiverse having a typical universe is baseless, and hence eternal inflation’s cogency as a legitimate scientific theory is undermined.
Yet, just because scientists need to calculate probabilities to justify the Typical Universe Premise doesn’t mean that the hypothetical metalaws of the multiverse must respond to this need.
To summarize, the first layer of the measure problem is that there’s no justification for positing any ad hoc measure whatsoever. But it doesn't end there. Let’s move on to the second layer.
2. Intuitive Measures Don’t Work
The second problem begins with the realization that even if we ignore the first layer of the measure problem and grant the existence of a measure, there’s still a significant difficulty in choosing the right measure that actually governs the distribution of universes in the infinite multiverse.
You might be wondering what determines a particular measure to be the right measure. Well, first of all, the right measure must obviously end up with the prediction that our observed universe is typical. Otherwise, our observation of an atypical universe would falsify the multiverse. But is that enough?
Not really. There should also be a good intuitive reason why this particular measure is chosen as the measure for the multiverse. Yet, because measures don’t organically emerge from the theory of inflation or string theory, multiverse scientists face a real challenge in choosing a measure that isn’t completely arbitrary. Since they can’t lean on any fundamental law of physics to select the right measure, multiverse scientists try to find a measure that is based on some simple principle that justifies giving more weight to one type of universe over another.
Using our analogy of the row of marbles, there seems to be no intuitive reason why you would choose the ordering of a million silver marbles for every one gold marble. However, if a gold marble were to cost a million times as much as a silver marble, then it would be intuitively plausible to use an ordering of a million silver marbles for every one gold marble, so that the total monetary value of both classes of marbles would be equal.
Likewise, multiverse scientists attempt to construct arguments to justify the claim that some measures are more intuitive than others. Taking this path, they hope to find a measure that is both intuitive and leads to the conclusion that our universe is typical.
This brings us to the second layer of the measure problem. The problem is even though multiverse scientists need to justify selecting a particular measure, the intuitive measure approach simply doesn’t work. Though eternal inflation theorists have been trying since the 1980s to seek out intuitive measures that would justify the Typical Universe Premise, every semi-intuitive measure that they’ve tried has failed to result in our universe being typical.
In their article Measure Problem for Eternal and Non-Eternal Inflation, Andrei Linde and Mahdiyar Noorbala, describe some of this history. While we'll cite the quote, once again it’s not important to follow all the details. Just try to get the main idea.
They wrote as follows:
Since that time, dozens of different candidates for the role of the probability measure have been proposed, most of them giving different predictions. It is impossible to give a full list of different proposals here...Out of all of these measures, the original proper time cutoff measure is the simplest. However, this measure suffers from the youngness problem…This measure exponentially rewards parts of the universe staying as long as possible at the highest values of energy density. As a result, this measure exponentially favors life appearing in the parts of the universe with an extremely large temperature, which contradicts the observational data.
The details of the youngness problem don’t matter for us. The main idea is that the original and simplest choice of measure didn’t work because it contradicted observational data. This sort of problem isn’t unique to this particular measure but has plagued the dozens of measures that followed. The failure of all the many intuitive measures to render our universe typical undermines multiverse scientists’ attempt to explain fine tuning via an infinite varied multiverse.
More fundamentally, the inability to find an intuitive measure that works undermines multiverse’s very legitimacy as a scientific theory. This is because without a measure, the multiverse can’t make any prediction whatsoever. This is the second layer of the measure problem.
There are two reasons why multiverse scientists must seek an intuitive measure and can't just select any contrived measure that makes our universe typical.
First, the right measure, whatever it may be, is ultimately the fundamental metalaw that governs all reality because it determines which universes are more probable than others. Just as scientists didn’t want to posit that 25 seemingly arbitrary constants are the bedrock of reality, so too they don’t want the most fundamental metalaw of all to be a mysterious, contrived, arbitrary measure with no rhyme or reason.
Additionally, if multiverse scientists attempt to support the Typical Universe Premise by positing a highly contrived measure with no intuitive justification, the problems with naive multiverse will reemerge. This is because multiverse scientists can in theory explain any observation whatsoever if they’re willing to accept a contrived measure - they just have to seek out the “right” measure that renders that observation typical.
It would be no different from positing a contrived measure for anything one would like to imagine. We can just see it now. The featured topic at a future Naive Multiverse conference: The Search for the Fire-Breathing Dragon Measure.
While that's just a joke, according to actual multiverse scientists, there really is a universe that has that conference. In fact, there are infinitely many of them.
Let’s bring the point home. Now that we see why multiverse scientists need to find a measure that is both intuitive and that renders our universe typical, we can summarize the second layer of the measure problem. The problem is that all intuitive measures that have been tried thus far have failed to make our universe typical. Let’s now move to the third and final layer of the measure problem.
3. Fine Tuned Measures
The final layer is the fine tuned measure problem. This problem emerges from the new approach that multiverse scientists take to deal with the fact that all intuitive measures fail to make our universe typical. Namely, they work backward, beginning with the premise that our universe is typical and then look for a measure with the right qualitative and quantitative features that makes it so.
Even using this retrospective method, they have thus far failed to find a measure that makes our universe typical. Nevertheless, they’re hopeful that they will find it at some time in the future.
An example of this optimistic attitude can be found in the article we mentioned last essay, Boltzmann brains and the scale-factor cutoff measure of the multiverse. Guth, Linde, Vilenkin, and the other authors acknowledge that while the scale-factor cutoff measure might not work, they will nevertheless continue to search for new measures that can avoid the Boltzmann brain problem. In their conclusion, they write as follows:
On the other hand, if we do not find a sufficiently convincing theoretical reason to believe that the vacuum decay rate in all vacua in the landscape is always greater than the fastest Boltzmann brain production rate, this would motivate the consideration of other probability measures where the Boltzmann brain problem can be solved even if the probability of their production is not strongly suppressed.
In short, if a given measure doesn’t work, they’ll keep searching for another.
While the strategy of seeking out a measure with the right qualitative and quantitative features that make our universe typical keeps multiverse scientists optimistic, this whole approach falls prey to the logical fallacy of begging the question.
This is because even if multiverse scientists were to find some contrived measure to make our universe typical, it wouldn’t be intuitive or self-justifying. After all, there are clearly dozens of more intuitive measures that could’ve theoretically existed but have demonstrably failed to make our universe typical.
Any handpicked measure, or metalaw, that multiverse scientists may discover that would happen to make our universe typical would have fine tuned quantities and specially designed qualitative features. Therefore it would be subject to the all-important question: What meta-metalaw chose the fine tuned and designed measure that rendered our complex universe typical as opposed to all the other possible measures that wouldn’t have rendered it typical?
Steinhart gets to the essence of this problem as follows:
Measure enthusiasts take a trial-and-error approach in which they invent and test measures until, they hope, one will produce the desired answer -- that our universe is highly probable. Even if they someday succeed, they will need another principle to justify using that measure instead of the others, yet another principle to choose that principle, and so on.
Because of this problem, Steinhardt rejects the entire attempt to find just the right measure that would render our universe typical. He ultimately rejects inflation altogether because, without a legitimate measure, it naturally leads to a theory of infinite universes incapable of making any scientific prediction.
Steinhardt’s critique is especially relevant with regard to the question of whether an infinite varied multiverse and its fine tuned measure can explain fine tuning and design without an intelligent cause. It clearly can’t!
Positing a measure with fine tuned quantities and specially designed qualitative features to explain our observed fine tuned constants and designed laws does nothing at all to solve the problem presented by fine tuning and design. All it does is take the question of “What fine tuned the constants and designed the laws?” and push it back one step to “What fine tuned and designed the contrived measure?” The point is that even if the search for the right measure were successful, it wouldn’t undermine the fact that fine tuning indicates an intelligent cause.
Let’s spell this out clearly because it’s so important. Let’s suppose that an intelligent agent (in this case, a multiverse scientist) handpicks a particular measure that actually renders our fine tuned universe typical. If so, it would turn out that from the set of all possible measures, the one measure that actually governs the distribution of universes in the infinite multiverse happens to be fine tuned and designed such that the typical universe is as highly complex, structured, and ordered as our own. Had the metalaw that ultimately determines the most typical universe been any other measure, we would’ve been intelligent observers in a much simpler universe; in fact, we would’ve been Boltzmann brains.
Even if intelligent multiverse scientists were to discover such a special measure this would still leave us with the same essential question of fine tuning and design: What caused the multiverse’s all-important measure to be so fine tuned and designed to make our fine tuned and designed universe typical? It simply pushes the same question back to an earlier level of the universe’s development without answering anything whatsoever.
The bottom line is that fine tuning and design indicate an intelligent cause - whether it’s in the constants or in the measure. When all is said and done, the introduction of measures does absolutely nothing to explain away fine tuning and design without an intelligent cause. So, to summarize the third layer of the measure problem: even if multiverse scientists work backward to find the right measure that makes our universe typical, it ultimately leads back to the fine tuning problem in the form of a fine tuned contrived measure instead of the fine tuned constants.
The Scope of the Measure Problem
Before concluding, let’s consider the full scope of the measure problem. First, we’ll address whether the measure problem is limited to being an attack on just the eternal inflation/string theory multiverse, or whether it's a more general problem for all infinite multiverse theories that attempt to explain fine tuning by chance alone.
After we do that, we’ll address whether a finite multiverse can avoid the measure problem.
The Measure Problem Applies to Any Infinite Multiverse
We’ll start with infinite multiverse theories. Once scientists posit any theory of an infinite varied multiverse, they will naturally fall prey to the three problems of a naive multiverse that boil down to the fact that it can explain anything and everything. To get around these problems, they must limit the explanatory power of the infinite multiverse by making a prediction that our universe is typical - a claim that can only be tested by computing probabilities.
But to calculate probabilities in an infinite multiverse, scientists must use extraneous measures that aren’t naturally part of any other physical theory. This leads directly to the measure problem, because these measures are ad hoc, contrived, and ultimately fine tuned to render our one complex, ordered universe typical.
Since the measure problem emerged as a direct consequence of positing the existence of an infinite number of universes, we can clearly see that the measure problem will apply to all infinite varied multiverse theories, and not just the eternal inflation/string theory multiverse that’s currently in vogue.
Problems with a Finite Multiverse
Since the measure problem is a consequence of attempting to take probabilities in an infinite multiverse, one may think that perhaps multiverse scientists can simultaneously explain fine tuning and avoid the measure problem by positing a very large but finite multiverse. We will explain why this doesn't work in three steps.
First, as we explained in essay one, because fine tuning is evidence that indicates an intelligent cause, it doesn’t suffice for multiverse scientists to merely speculate that there exist an enormous number of unobservable universes - they must support this assertion. The only ways to do so are either by observing all these parallel universes - which is obviously impossible - or by showing that their existence naturally emerges from some physical theory that’s derived from our one universe.
This is where eternal inflation came in. Its foundation, the theory of inflation, has scientific grounding; and, eternal inflation is the simplest model for this theory. The catch is that eternal inflation predicts an infinite multiverse, leading directly to the measure problem.
If scientists choose to reject eternal inflation and its infinite universes, they can avoid the measure problem. However, this comes at the cost of losing their support for the Infinite Multiverse Premise and being left with one fine tuned universe that points directly to an intelligent fine tuner. There is simply no evidence whatsoever for a finite but enormous number of unobservable parallel universes. This leads to the second step.
Even if we generously grant that multiverse scientists could simply posit a very large finite number of unobservable universes without any evidence or support, they’d still run into the Boltzmann Brain and Grand Universe problems. This is because even in a finite but extremely large varied multiverse the typical observer in a typical universe wouldn’t be anything like us, but would be a single brain surrounded by total chaos.
To get around these problems, they would need to show, through a genuine calculation, that our universe is typical in this huge but finite multiverse. The problem is that if this conjectured finite multiverse would simply be granted to multiverse scientists without any justification at all, it would be impossible for them to calculate whether we are typical observers. Since all the granted parallel universes don’t emerge from any actual physical theory but from mere speculation, scientists would have no knowledge about them and would be unable to make any actual calculations of their probabilities. This leads to the final step.
The only possibility remaining for multiverse scientists is the implausible dream that maybe scientists will one day find a real physical theory that legitimately predicts an enormous finite number of alternate universes (but not an infinite number of them), and in addition, it will turn out that genuine calculations will happen to show that we’re typical observers in that finite multiverse.
Think about just how dubious this dream is. There’s no reason to believe that there ever will be a scientific theory that somehow generates other universes, stops creating them once it makes the incredibly large number that is needed to explain away fine tuning by chance and that according to this dreamed-about finite multiverse theory, our grand universe will end up being more typical than a Boltmzann brain surrounded by total chaos.
For multiverse scientists to simply speculate that they will one day discover such a finite multiverse theory is once again falling into the naive-multiverse-of-the-gaps problem. If they can use this strategy to explain away fine tuning without an intelligent cause, why can’t they explain away anything in the same manner?
For example, maybe one day they’ll discover a finite multiverse theory in which voices from heaven or fire-breathing dragons are typical.
The common idea of all three steps is that multiverse scientists need real justification to posit other unobservable universes and calculate that our universe is typical. Because multiverse scientists know this point, they use eternal inflation as the justification for the existence of other universes. Unfortunately for them, eternal inflation doesn’t lead to a huge finite number of universes but to infinitely many such universes.
And in an infinite multiverse, the need to calculate if our universe is typical leads directly to the devastating three-layered measure problem that can be succinctly stated as follows: Ad hoc measures are bad ideas to begin with, all intuitive measures don’t work, and even if multiverse scientists were to find a contrived measure that did work, it would beg the question of what fine tuned and designed it?
The Significance of the Measure Problem
We want to emphasize that the measure problem isn’t some small issue that we or Steinhardt are nitpicking at but is a formidable problem recognized by multiverse scientists themselves. In fact, at the end of Leonard Susskind’s book, The Cosmic Landscape (pg. 370), he notes that the measure problem could very well turn out to be the ultimate undoing of the core idea of his book - the eternal inflation/string theory multiverse.
He wrote as follows:
The measure problem…has vexed some of the greatest minds in cosmology, Vilenkin and Linde especially. It could prove to be the Achilles heel of Eternal Inflation. On the one hand, it is hard to see how Eternal Inflation can be avoided in a theory with any kind of interesting Landscape. But it is equally hard to see how it can be used to make scientific predictions of the kind that would establish it as science in the traditional sense.
The proper conclusion to draw from the three-layered measure problem is to reject attempts to use ad hoc, contrived, and fine tuned measures to explain away the fine tuning of the constants. Finding a contrived measure that’s specifically chosen to yield the desired outcome that our universe is typical would do nothing to explain away our universe’s fine tuning, design, and order without an intelligent cause. Whether it’s the fine tuned constants themselves or a fine tuned measure that’s responsible for the fine tuned constants, our universe’s fine tuning clearly indicates an intelligent fine tuner.
At this point, you may sense a logical problem with our argument. We argued that explaining our fine tuned constants with a measure doesn’t explain anything because it ultimately leads to the question of what fine tuned the measure itself. But can’t that same exact question be asked about God? In other words, if we invoke an intelligent fine tuner to explain our fine tuned constants, then aren’t we left with the problem of what fine tuned the intelligent fine tuner itself? If so, positing God doesn’t ultimately help explain fine tuning any more than positing a measure!
That’s a great question. While we’ll take it up in depth in our next series about God, the short answer is that if someone were to argue for a complex god with parts, that would indeed beg the question of what fine tuned its parts. Just as a complex measure has fine tuned parts, so too a complex god has fine tuned parts. And because they each have fine tuned parts, they’re both bad solutions to fine tuning.
But we’ll demonstrate that series one’s arguments from fine tuning and design naturally point to the idea of one simple God with no parts. Because God has no parts, you can understand clearly why such an idea is intrinsically not subject to fine tuning and design.
We know that might not make a lot of sense when we say it in a couple of sentences, but in the next series, we’ll fully develop this line of thought with clear language and helpful analogies. In fact, questions like this are one of the major reasons why we need the next series about God to truly complete our argument. If we only attack the multiverse but don’t answer questions about God, it’s dishonest to conclude that modern physics points to God.
But we can’t do everything at once. If we tried to explain fine tuning, the multiverse, and God, all in the same series, everything would just become confused. It might take us some time, but we’ll get to every significant issue in its proper place.
Now that we’ve fully explained the measure problem, the Achilles heel of the multiverse, you might think we’re done with this series. But there’s something even bigger and crazier coming next essay.
We’ll discuss how multiverse scientists move beyond the fine tuning of the constants and posit the Mathematical Multiverse to explain away the design of the laws of nature. If you think you’ve heard it all, just wait until the next time.
And we’ll show how the Mathematical Multiverse necessarily leads to the ultimate measure problem: the meta-measure problem. All that and more is coming in the rest of this series. So stay tuned!
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