Next Monday, November 17th at 7pm, I’ll be at the Harvard Bookstore with particle physicist and author Daniel Whiteson. Professor Whiteson and his co-author Andy Warner have a nice new book, for the general science-aware reader, exploring an age-old and unanswered question: how universal is the knowledge and understanding that we call “physics”? How much of modern physics is actually telling us about the universe, and how much of it is created by, or an accident of, the humans who have helped bring it about?
For instance, if we started all over again and reran history from scratch, would the physics (and science more generally) of this re-run culture look much like our own, or might it turn out very differently? If another culture on Earth had had time to develop highly mature science (or something like it) in its own direction, independent of Western Europe’s influence, how different might that science be? (Indeed, would our word “science” even be translatable into their worldview?) Or if we encountered aliens with far greater understanding of the universe than we have, would we be able to recognize, parse, grok, appreciate, comprehend, and/or otherwise make sense of their notions of scientific knowledge?
Whiteson and his co-author, wanting to write a popular book rather than a scholarly one, and desiring nevertheless to take on these serious and challenging intellectual questions, have set their focus mostly on the aliens, accompanied by amusing cartoons and a generous helping of dad jokes (hey, some dad jokes are actually very funny.) They’re looking for a broad audience, and hopefully they will get it. But don’t let the light-hearted title (“Do Aliens Speak Physics?“) or the charmingly goofy cover fool you: this book might well make you laugh, but I guarantee it will make you think. Whether you’re just curious about science or you’ve been doing science yourself for years, I suspect that, within the vast array of problems and issues that are raised in this broad-minded book, there will be some you’ve never thought of.
Among scientists and philosophers, there are some who believe that any aliens with the capacity to reach the Earth will obviously “speak physics” — that math and physics float above contingencies of culture and species, and will easily be translated from any intelligent creature to any other. But are they perhaps flying too high? It’s clear that Whiteson and Warner are aiming to poke some holes — lots of holes —- in their hot-air balloon, and to do so in a way that a wide variety of readers can appreciate and enjoy.
I tend to agree with Whiteson on a lot of these issues, but that won’t stop me from asking him some tough questions. You can ask him some tough questions too, if you like — just come to the Harvard Bookstore at 7:00 on Monday and join the conversation!
As many of you are no doubt aware, in the past few days the US Congress voted to make major cuts to scientific research, and the president signed the bill. The government’s National Science Foundation has been cut by more than half, which means that its actual science budget has been cut by much more than that after you account for fixed costs. So vast, sudden and draconian are these cuts that it will take a long time for me and others in the field to figure out what has actually happened.
The reductions seem extreme, quite arbitrary and very poorly thought out. As an example, half of the LIGO observatory (the Laser Interferometer Gravitational-Wave Observatory, whose amazing discoveries, such as this one and this one, earned the United States a Nobel Prize in 2017) is being hit hard. There are currently two interferometers, one in Washington state and one in Lousiana, but one has been largely defunded in this bill, if I understand correctly.
I can see the logic: the scientists have two interferometers, but in tough times they ought to be able to get along with just one, right?
Well, that’s like cutting off one of a runner’s legs. Two were built because two were needed.
With just one, the signal from most gravitational wave events is so weak that you can’t distinguish it from noise. Other interferometers around the world just aren’t working well enough to make up for throwing away one of LIGOs. (And besides, you need three or four interferometers around the world to be able to know precisely in the sky where the waves are coming from, knowledge which can make other major discoveries possible.)
According to Science magazine, “In a two-sentence email to Science, an NSF spokesperson said the plan reflects `a strategic alignment of resources in a constrained fiscal environment.’ “
This is not strategic. This is stupid. The amount of money saved, less than 10 cents per year per US citizen, is very small compared to what we as a nation have already spent on this wonderful facility, and cutting LIGO in half makes it dramatically less than half as good — so this is actually a big waste of money both past and future. The decision to make this cut in this way is nothing short of ridiculous and incompetent.
[Not to mention that “constrained fiscal environment” is quite a phrase when you’re increasing the budget deficit rather than shrinking it.]
I fear there are many other similar examples to be found.
The United States’ government is waging an all-out assault on Harvard University. The strategy, so far, has been:
Cut most of the grants (present and future) for scientific and medical research, so that thousands of Harvard’s scientists, researchers and graduate students have to stop their work indefinitely. That includes research on life-saving medicine, on poorly understood natural phenomena, and on new technology. This also means that the university will have no money from these activities to pay salaries of its employees.
Eliminate the tax-advantageous status of the university, so that the university is much more expensive to operate.
Prohibit Harvard from having any international students (undergraduate and graduate) and other researchers, so that large numbers of existing scientific and medical research projects that still have funding will have to cease operation. This destroys the careers of thousands of brilliant people — and not just foreigners. Many US faculty and students are working with and depend upon these expelled researchers, and their work will stop too. It also means that Harvard’s budget for the next academic year will be crushed, since it is far too late to replace the tuition from international undergraduate students for the coming year.
The grounds for this war is that Harvard allegedly does not provide a safe environment for its Jewish students, and that Harvard refuses to let the government determine who it may and may not hire.
Now, maybe you can explain to me what this is really about. I’m confused what crimes these scientific researchers commited that justifies stripping them of their grants and derailing their research. I’m also unclear as to why many apolitical, hard-working young trainees in laboratories across the campus deserve to be ejected from their graduate and post-graduate careers and sent home, delaying or ruining their futures. [Few will be able to transfer to other US schools; with all the government cuts to US science, there’s no money to support them at other locations.] And I don’t really understand how such enormous damage and disruption to the lives and careers of ten thousand-ish scientists, researchers and graduate students at Harvard (including many who are Jewish) will actually improve the atmosphere for Harvard’s Jewish students.
As far as I can see, the government is merely using Jewish students as pawns, pretending to attack Harvard on their behalf while in truth harboring no honest concern for their well-being. The fact that the horrors and nastiness surrounding the Gaza war are being exploited by the government as cover for an assault on academic freedom and scientific research is deeply cynical and exceedingly ugly.
From the outside, where Harvard is highly respected — it is certainly among the top five universities in the world, however you rank them — this must look completely idiotic, as idiotic as France gutting the Sorbonne, or the UK eviscerating Oxford. But keep in mind that Harvard is by no means the only target here. The US government is cutting the country’s world-leading research in science, technology and medicine to the bone. If that’s what you want to do, then ruining Harvard makes perfect sense.
The country that benefits the most from this self-destructive behavior? China, obviously. As a friend of mine said, this isn’t merely like shooting yourself in the foot, it’s like shooting yourself in the head.
I suspect most readers will understand that I cannot blog as usual right now. To write good articles about quantum physics requires concentration and focus. When people’s careers and life’s work are being devastated all around me, that’s simply not possible.
We’ll get back to measurement, interference and the double-slit experiment just as soon as I can get my math program to produce pictures of the relevant wave functions reliably. I owe you some further discussion of why measurement (and even interactions without measurement) can partially or completely eliminate quantum interference.
But in the meantime, I’ve gotten some questions and some criticism for arguing that superposition is an OR, not an AND. It is time to look closely at this choice, and understand both its strengths and its limitations, and how we have to move beyond it to fully appreciate quantum physics. [I probably should have written this article earlier — and I suspect I’ll need to write it again someday, as it’s a tricky subject.]
The quantum double-slit experiment, in which objects are sent toward a wall with two slits and then recorded on a screen behind the wall, creates an interference pattern that builds up gradually, object by object. And yet, it’s crucial that the path of each object on its way to the screen remain unknown. If one measures which of the slits each object passes through, the interference pattern never appears.
Strange things are said about this. There are vague, weird slogans: “measurement causes the wave function to collapse“; “the particle interferes with itself“; “electrons are both particles and waves“; etc. One reads that the objects are particles when they reach the screen, but they are waves when they go through the slits, causing the interference — unless their passage through the slits is measured, in which case they remain particles.
But in fact the equations of 1920s quantum physics say something different and not vague in the slightest — though perhaps equally weird. As we’ll see today, the elimination of interference by measurement is no mystery at all, once you understand both measurement and interference. Those of you who’ve followed my recent posts on these two topics will find this surprisingly straightforward; I guarantee you’ll say, “Oh, is that all?” Other readers will probably want to read
When do we expect quantum interference? As I’ll review in a moment, there’s a simple criterion:
a system of objects (not the objects themselves!) will exhibit quantum interference if the system, initially in a superposition of possibilities, reaches a single possibility via two or more pathways.
To remind you what that means, let’s compare two contrasting cases (covered carefully in this post.) Figs. 1a and 1b show pre-quantum animations of different quantum systems, in which two balls (drawn blue and orange) are in a superposition of moving left OR moving right. I’ve chosen to stop each animation right at the moment when the blue ball in the top half of the superposition is at the same location as the blue ball in the bottom half, because if the orange ball weren’t there, this is when we’d expect it to see quantum interference.
But for interference to occur, the orange ball, too, must at that same moment be in the same place in both parts of the superposition. That does happen for the system in Fig. 1a — the top and bottom parts of the figure line up exactly, and so interference will occur. But the system in Fig. 1b, whose top and bottom parts never look the same, will not show quantum interference.
Fig. 1a: A system of two balls in a superposition, from a pre-quantum viewpoint. As the system evolves, a moment is reached when the two parts of the superposition are identical. As the system has then reached a single possibility via two routes, quantum interference may result.
Figure 1b: Similar to Fig. 1a, except that when the blue ball is at the same location in both parts of the superposition, the orange ball is at two different locations. At no moment are the two possibilities in the superposition the same, so quantum interference cannot occur.
In other words, quantum interference requires that the two possibilities in the superposition become identical at some moment in time. Partial resemblance is not enough.
The Measurement
A measurement always involves an interaction of some sort between the object we want to measure and the device doing the measurement. We will typically
For today’s purposes, the details of the second step won’t matter, so I’ll focus on the first step.
Setting Up
We’ll call the object going through the slits a “particle”, and we’ll call the measurement device a “measuring ball” (or just “ball” for short.) The setup is depicted in Fig. 2, where the particle is approaching the slits and the measuring ball lies in wait.
Figure 2: A particle (blue) approaches a wall with two slits, behind which sits a screen where the particle’s arrival will be detected. Also present is a lightweight measuring ball (black), ready to fly in and measure the particle’s position by colliding with it as it passes through the wall.
If No Measurement is Made at the Slits
Suppose we allow the particle to proceed and we make no measurement of its location as it passes through the slits. Then we can leave the ball where it is, at the position I’ve marked M in Fig. 3. If the particle makes it through the wall, it must pass through one slit or the other, leaving the system in a superposition of the form
the particle is near the left slit [and the ball is at position M] OR
the particle is near the right slit [and the ball is at position M]
as shown at the top of Fig. 3. (Note: because the ball and particle are independent [unentangled] in this superposition, it can be written in factored form as in Fig. 12 of this post.)
From here, the particle (whose motion is now quite uncertain as a result of passing through a narrow slit) can proceed unencumbered to the screen. Let’s say it arrives at the point marked P, as at the bottom of Fig. 3.
Figure 3: (Top) As the particle passes through the slits, the system is set into a superposition of two possibilities in which the particle passes through the left slit OR the right slit. (The particle’s future motion is quite uncertain, as indicated by the green arrows.) In both possibilities, the measuring ball is at point M. (Bottom) If the particle arrives at point P on the screen, then the two possibilties in the superposition become identical, as in Fig. 1a, so quantum interference can result. This will be true no matter what point P we choose, and so an interference pattern will be seen across the whole screen.
Crucially, both halves of the superposition now describe the same situation: particle at P, ball at M. The system has arrived here via two paths:
The particle went through the left slit and arrived at the point P (with the ball always at M), OR
The particle went through the right slit and arrived at the point P (with the ball always at M).
Therefore, since the system has reached a single possibility via two different routes, quantum interference may be observed.
But now let’s make the measurement. We’ll do it by throwing the ball rapidly toward the particle, timed carefully so that, as shown in Fig. 4, either
the particle is at the left slit, in which case the ball passes behind it and travels onward, OR
the particle is at the right slit, in which case the ball hits it and bounces back.
(Recall that I assumed the measuring ball is lightweight, so the collision doesn’t much affect the particle; for instance, the particle might be an heavy atom, while the measuring ball is a light atom.)
Figure 4: As the particle moves through the wall, the ball is sent rapidly in motion. If the particle passes through the right slit, the ball will hit it and bounce back; if the particle passes through the left slit, the ball will miss it and will continue to the left.
The ball’s late-time behavior reveals — and thus measures — the particle’s behavior as it passed through the wall:
the ball moving to the left means the particle went through the left slit;
the ball moving to the right means the particle went through the right slit.
To make this measurement complete and permanent requires a longer story with more details; for instance, we might choose to amplify the result with a Geiger counter. But the details don’t matter, and besides, that takes place later. Let’s keep our focus on what happens next.
The Effect of the Measurement
What happens next is that the particle reaches the point P on the screen. It can do this whether it traveled via the left slit or via the right slit, just as before, and so you might think there should still be an interference pattern. However, remembering Figs. 1a and 1b and the criterion for interference, take a look at Fig. 5.
Figure 5: Following the measurement made in Fig. 4, the arrival of the particle at the point P on the screen finds the ball in two possible locations, depending on which slit the particle went through. In contrast to Fig. 3, the two parts of the superposition are not identical, and so (as in Fig. 1b) no quantum interference pattern will be observed.
Even though the particle by itself could have taken two paths to the point P, the system as a whole is still in a superposition of two different possibilities, not one — more like Fig. 1b than like Fig. 1a. Specifically,
the particle is at position P and the ball is at location ML (which happens if, in Fig. 4, the particle was near the left slit and the ball continued to the left); OR
the particle is at position P and the ball is at location MR (which happens if, in Fig. 4, the particle was near the right slit and the ball bounced back to the right).
The measurement process — by the very definition of “measurement” as a procedure that segregates left-slit cases from right-slit cases — has resulted in the two parts of the superposition being different even when they both have the particle reaching the same point P. Therefore, in contrast to Fig. 3, quantum interference between the two parts of the superposition cannot occur.
And that’s it. That’s all there is to it.
Looking Ahead.
The double-slit experiment is hard to understand if one relies on vague slogans. But if one relies on the math, one sees that many of the seemingly mysterious features of the experiment are in fact straightforward.
I’ll say more about this in future posts. In particular, to convince you today’s argument is really correct, I’ll look more closely at the quantum wave function corresponding to Figs. 3-5, and will reproduce the same phenomenon in simpler examples. Then we’ll apply the resulting insights to other cases, including
measurements that do not destroy interference,
measurements that only partly destroy interference,
destruction of interference without measurement, and
