As part of my post last week about measurement and measurement devices, I provided a very simple example of a measuring device. It consists of a ball sitting in a dip on a hill (Fig. 1a), or, as a microscopic version of the same, a microsopic ball, made out of only a small number of atoms, in a magnetic trap (Fig. 1b). Either object, if struck hard by an incoming projectile, can escape and never return, and so the absence of the ball from the dip (or trap) serves to confirm that a projectile has come by. The measurement is crude — it only tells us whether there was a projectile or not — but it is reasonably definitive.
In fact, we could learn more about the projectile with a bit more work. If we measured the ball’s position and speed (approximately, to the degree allowed by the quantum uncertainty principle), we would get an estimate of the energy carried by the projectile and the time when the collision occurred. But how definitive would these measurements be?
With a macroscopic ball, we’d be pretty safe in drawing conclusions. However, if the objects being measured and the measurement device are ultra-microscopic — something approaching atomic size or even smaller — then the measurement evidence is fragile. Our efforts to learn something from the microscopic ball will be in vain if the ball suffers additional collisions before we get to study it. Indeed, if a tiny ball interacts with any other object, microscopic or macroscopic, there is a risk that the detailed information about its collision with the projectile will be lost, long before we are able to obtain it.
Amplify Quickly
The best way to keep this from happening is to quickly translate the information from the collision, as captured in the microscopic ball’s behavior, into some kind of macroscopic effect. Once the information is stored macroscopically, it is far harder to erase.
For instance, while a large meteor striking the Earth might leave a pond-sized crater, a subatomic particle striking a metal table might leave a hole only an atom wide. It doesn’t take much to fill in an atom-sized hole in the blink of an eye, but a crater that you could swim in isn’t going to disappear overnight. So if we want to know about the subatomic particle’s arrival, it would be good if we could quickly cause the hole to grow much larger.
This is why almost all microscopic measurements include a step of amplification — the conversion of a microscopic effect into a macroscopic one. Finding new, clever and precise ways of doing this is part of the creativity and artistry of experimental physicists who study atoms, atomic nuclei, or elementary particles.
There are various methods of amplification, but most methods can be thought of, in a sort of cartoon view, as a chain of ever more stable measurements, such as this:
- a first measurement using a microscopic device, such as our tiny ball in a trap;
- a second measurement that measures the device itself, using a more stable device;
- a third measurement that measures the second device, using an even more stable one;
- and so on in a chain until the last device is so stable that its information cannot easily or quickly be erased.
Amplification in Experiments
The Geiger-Müller Counter
A classic and simple device that uses amplification is a Geiger counter (or Geiger-Müller counter). (Hans Geiger, while a postdoctoral researcher for Ernest Rutherford, performed a key set of experiments that Rutherford eventually interpreted as evidence that atoms have tiny nuclei.) This counter, like our microscopic ball in Fig. 1b, simply records the arrival of high-energy subatomic projectiles. It does so by turning the passage of a single ultra-microscopic object into a measurable electric current. (Often it is designed to make a concurrent audible electronic “click” for ease of use.)
How does this device turn a single particle, with a lot of energy relative to a typical atomic energy level but very little relative to human activity, into something powerful enough to create a substantial, measurable electric current? The trick is to use the electric field to create a chain reaction.
The Electric Field
The electric field is present throughout the universe (like all cosmic fields). But usually, between the molecules of air or out in deep space, it is zero or quite small. However, when it is strong, as when you have just taken off a wool hat in winter, or just before a lightning strike, it can make your hair stand on end.
More generally, a strong electric field exerts a powerful pull on electrically charged objects, such as electrons or atomic nuclei. Positively charged objects will accelerate in one direction, while negatively charged objects will accelerate in the other. That means that a strong electric field will
- separate positively charged objects from negatively charged objects
- cause both types of objects to speed up, albeit in opposite direction,
Meanwhile electrically neutral objects are largely left alone.
The Strategy
So here’s the strategy behind the Geiger-Müller counter. Start with a gas of atoms, sitting inside of a closed tube in a region with a strong electric field. Atoms are electrically neutral, so they aren’t much affected by the electric field.
But the atoms will serve as our initial measurement devices. If a high-energy subatomic particle comes flying through the gas, it will strike some of the gas atoms and “ionize” them — that is, it will strip an electron off the atom. In doing so it breaks the electrically neutral atom into a negatively charged electron and a positively charged leftover, called an “ion.”
If it weren’t for the strong electric field, the story would remain microscopic; the relatively few ions and electrons would quickly find their way back together, and all evidence of the atomic-scale measurements would be lost. But instead, the powerful electric field causes the ions to move in one direction and the electrons to move in the opposite direction, so that they cannot simply rejoin each other. Not only that, the field causes these subatomic objects to speed up as they separate.
This is especially significant for the electrons, which pick up so much speed that they are able to ionize even more atoms — our secondary measurement devices. Now the number of electrons freed from their atoms has become much larger.
The effect is an chain reaction, with more and more electrons stripped off their atoms, accelerated by the electric field to high speed, allowing them in their turn to ionize yet more atoms. The resulting cascade, or “avalanche,” is called a Townsend discharge; it was discovered in the late 1890s. In a tiny fraction of a second, the small number of electrons liberated by the passage of a single subatomic particle has been multiplied exceedingly, and a crowd of electrons now moves through the gas.
The chain reaction continues until this electron mob arrives at a wire in the center of the counter — the final measurement device in the long chain from microscopic to macroscopic. The inflow of a huge number of the electrons onto the wire, combined with the flow of the ions onto the wall of the device, causes an electrical current to flow. Thanks to the amplification, this current is large enough to be easily detected, and in response a separate signal is sent to the device’s sound speaker, causing it to make a “click!”
Broader Lessons
It’s worth noting that the strategy behind the Geiger-Müller counter requires an input of energy from outside the device, supplied by a battery or the electrical grid. When you think about it, this is not surprising. After the initial step there are rather few moving electrons, and their total motion-energy is still rather low; but by the end of the avalanche, the motion-energy of the tremendous number of moving electrons is far greater. Since energy is conserved, that energy has to have come from somewhere.
Said another way, to keep the electric field strong amid all these charged particles, which would tend to cancel the field out, requires the maintenance of high voltage between the outer wall and inner wire of the counter. Doing so requires a powerful source of energy.
Without this added energy and the resulting amplification, the current from the few initially ionized atoms would be extremely small, and the information about the passing high-energy particle could easily be lost due to ordinary microscopic processes. But the chain reaction’s amplification of the number of electrons and their total amount of energy dramatically increases the current and reduces the risk of losing the information.
Many devices, such as the photomultiplier tube for the detection of photons [particles of light], are like the Geiger-Müller counter in using an external source of energy to boost a microscopic effect. Other devices (like the cloud chamber) use natural forms of amplification that can occur in unstable systems. (The basic principle is similar to what happens with unstable snow on a steep slope: as any off-piste skier will warn you, under the correct circumstances a minor disturbance can cause a mountain-wide snow avalanche.) If these issues interest you, I suggest you read more about the various detectors and subdetectors at ongoing particle experiments, such as those at the Large Hadron Collider.
Amplification in a Simplified Setting
I’ve described the Geiger-Müller counter without any explicit reference to quantum physics. Is there any hope that we could understand how this process really takes place using quantum language, complete with a wave function?
Not in practice: the chain reaction is far, far too complicated. A quantum system’s wave function does not exist in the physical space we live in; it exists in the space of possibilities. Amplification involving hordes of electrons and ions forces us to consider a gigantic space of possibilities; for instance, a million particles moving in our familiar three spatial dimensions would correspond to a space of possibilities that has three million dimensions. Neither you nor I nor the world’s most expert mathematical physicist can visualize that.
Nevertheless, we can gain intuition about the basic idea behind this device by simplifying the chain reaction into a minimal form, one that involves just three objects moving in one dimension, and three stages:
- an initial measurement involving something microscopic
- addition of energy to the microscopic measurement device
- transfer of the information by a second measurement to something less microscopic and more stable.
You can think of these as the first steps of a chain reaction.
So let’s explore this simplified idea. As I often do, I’ll start with a pre-quantum viewpoint, and use that to understand what is happening in a corresponding quantum wave function.
The Pre-Quantum View
The pre-quantum viewpoint differs from that in my last post (which you should read if you haven’t already) in that we have two steps in the measurement rather than just one:
- a projectile is measured by a microscopic ball (the “microball”),
- the microball is similarly measured by a larger device, which I’ll refer to as the “macroball”.
The projectile, microball and macroball will be colored purple, blue and orange, and their positions along the x-axis of physical space will be referred to as x1, x2 and x3. Our space of possibilities then is a three-dimensional space consisting of all possible values of x1, x2 and x3.
The two-step measurement process really involves four stages:
- The projectile approaches the stationary balls from the left.
- The projectile collides with the microball and (in a small change from the last post, for convenience) bounces off to the left, leaving the microball moving to the right.
- The microball is then subject to a force that greatly accelerates it, so that it soon carries a great deal of motion-energy.
- The highly energetic microball now bounces off the macroball, sending the latter into motion.
The view of this process in physical space is shown on the left side of Fig 2. Notice the acceleration of the microball between the two collisions.
On the right side of Fig. 2, the motion of the three-object system within the space of possibilities is shown by the moving red dot. To make it easier to see how the red dot moves acrossthe space of possibilities, I’ve plotted its trail across that space as a gray line. Notice there are two collisions, the first one when the projectile and microball collide (x1=x2) and the second where the two balls collide (x2=x3), resulting in two sudden changes in the motion of the dot. Notice also the rapid acceleration between the first collision and the second, as the microball gains sufficient energy to give the macroball appreciable speed.
The Quantum View
In quantum physics, the idea is the same, where the dot representing the system’s value of (x1, x2, x3) is replaced by the peak of a spread-out wave function. It’s difficult to plot a wave function in three dimensions, but I can at least mark out the region where its absolute value is large — where the probability to find the system is highest. I’ve sketched this in Fig. 3. Not surprisingly if follows the same path as the system in Fig. 2.
In the pre-quantum case of Fig. 2, the red dot asserts certainty; if we were to measure x1, x2 and/or x3, we would find exactly the values of these quantities corresponding to the location of the dot. In quantum physics of Fig. 3, the peak of the wave function asserts high probability but not certainty. The wave function is spread out; we don’t know exactly what we would find if we directly measured x1, x2 and x3 at any particular moment.
Still, the path of the wave function’s peak is very similar to the path of the red dot, as was also true in the previous post. Generally, in the examples we’ve looked at so far, we haven’t shown much difference between the pre-quantum viewpoint and the quantum viewpoint. You might even be wondering if they’re more similar than people say. But there can be big differences, as we will see very soon.
The Wider View
If I could draw something with more than three dimensions, we could add another stage to our microball and macroball; we could accelerate the macroball and cause it to collide with something even larger, perhaps visible to the naked eye. Or instead of one macroball, we could amplify and transfer the microball’s energy to ten microballs, which in turn could have their energy amplified and transferred to a hundred microballs… and then we would have something akin to a Townsend discharge avalanche and a Geiger-Müller counter. Both in pre-quantum and in quantum physics, this would be impossible to draw; the space of possibilities is far too large. Nevertheless, the simple example in Figs. 2 and 3 provides some intuition for how a longer chain of amplification would work. It shows the basic steps needed to turn a fragile microscopic measurement into a robust macroscopic one, suitable for human scientific research or for our sense perceptions in daily living.
In the articles that will follow, I will generally assume (unless specified otherwise) that each microscopic measurement that I describe is followed by this kind of amplification and conversion to something macroscopic. I won’t be able to draw it, but as we can see in this example, the fundamental underlying idea isn’t that hard to understand.
24 Responses
Thanks again for your updates.
An article that your non-PHD readers such as myself might find interesting is in the latest issue of Discover magazine.
N
Several comments, including 4gravitons’, motivates this observation.
Questions often carry presuppositions. The answer you give to “What is a measurement?” suggests this. Other debates involving physics would question the anthropomorphization of physical processes. A more neutral question might have been:
“How can one formulate an analogy between vestigial evidence of physical interactions and measurements obtained using devices in controlled experiments?”
Of course, I would never expect this usage to become popular… people like short and sweet. I bow to pragmatic choices here.
4gravitons remark mentions counterfactuality. In your list of elements intended to make the analogy, you conclude with “interpretation.” It is difficult to see how physical processes interpret.
Although, again, it would be unwelcome, an expression like “nonveridical counterfactuality” seems appropriate as a substitute. Wikipedia mentions veridicality in temporal context. I had a harder time finding a general modal context. Nonveridicality in a modal context means that “p is true” in some worlds and “not p is true” in others.
Your premeasurement metastability and postmeasurement stability suggests that your comparison had been intended to conform with consistent histories. So, the threshold aspect of the “interpretation” element seems to coincide with differentiating a counterfactual. The modifier “nonveridical” is simply intended to suggest that such an interaction constitutes a branch point for possibilities.
This is not intended to be critical, and, I know your focus is on presenting the explanation of the physics carefully.
Like NF, I am very grateful for what you are doing here.
Niels Bohr (supposedly) once said “Clarity and truth are complementary variables”, to which Alain Aspect replied “Perhaps Bohr’s answer is true but I am certain it isn’t clear.”
Given the choice, I think I’d prefer more clarity.
Traditional logic relies upon classifications. Consecutive Stern-Gerlach apparatuses violate that mode.
As for Bohr,
“The entanglement between the object and the measuring apparatus prevents the object as well as the detector from having a well-defined, independent state. Hence, the entanglement prompted Bohr to think that the use of classical concepts depended on the experimental context and that was therefore complementary.”
from
https://plato.stanford.edu/entries/qm-copenhagen/#CompDecoProb
Apparently, Bohr is, unfairly associated with the Copenhagen interpretation. Philosophers of science who revisit his papers explain that he understood how quantum physics introduces ambiguity between epistemic order and causal order. That ambiguity had also been a concern of Ernst Mach when criticizing Newton’s absolute space and time.
This ambiguity is why it is important to devise the analogy between measurement and irreversible histories.
I think I understand most of what you’re saying. What precisely is the meaning of “epistemic order” and “causal order” here?
I’m also not sure what you mean by “irreversible histories”. My knowledge of the jargon used in quantum foundations circles is still quite limited.
This goes back to skeptical arguments. The modern skeptical argument, apparently defensible in every way, is by David Hume. Immanuel Kant accepts it and tries to recover a basis for “objective knowledge.” Problematically, this may be summarized as “saving science at the expense of scientific realism.”
Within this framework, causality has to be assigned to human faculties. It is thus bound to epistemology.
Ernst Mach had rejected Kant’s approach in favor of Humean empiricism. Yet, Mach retains the traditional ground for empiricism — subjective experience. Ultimately, this places him at odds with the statistical methods of Boltzmann. Angela Collier’s “edutainment” video,
https://m.youtube.com/watch?v=DM5qBRwU5EU&list=PLlKeLhFiZ6hYZXSzBW9eItF44x82ldgZ9&index=27&pp=iAQB
attributes Einstein’s interpretation of Brownian motion as the key interpretation undermining Mach’s position.
At this point, physics becomes formally divorced from traditional empiricism. Modern science must clearly demarcate “empirical science” from “empircism.” This has many consequences. Statistical inference needs to be distinguished from statistics. Typical associations of statistical inference with Aristotelian inductive logic must, instead associate such inference with “abductive reasoning complemented by non-monotonic defeasibility.”
Jonathan Faye has a decent paper on Mach’s principles suggesting that Mach’s awareness of the conflation between causality and epistemology motivated his views on physics,
https://jonathanfay.com/wp-content/uploads/2023/12/fay-2023-machs-principle-and-machs-hypotheses.pdf
Interestingly, MOND as modified inertia also suggests “retrocausality.” Mach’s demand that inertia be understood strictly by empirical data is extremely problematic.
Zingernagel has a decent paper working toward rehabilitating Bohr from association with the Copenhagen Interpretation,
https://arxiv.org/abs/1603.00353
The simplest way to understand the failure of traditional logic relative to the experiments motivating quantum mechanics is through sequential Stern-Gerlach experiments. That two ‘z’ beams appear after a ‘z-x-z’ sequence violates the kind of classificatory reasoning of Boolean partitioning by “properties.” After blocking a component of the first ‘z’ apparatus, traditional classification would not admit two ‘z’ beams after the terminal ‘z’ apparatus.
Bohr seems to have understood complementarity as an epistemic problem because the description of experiments and phenomena is communicated with classical reasoning.
A great deal is made of “quantum computing.” This, however, is not the same as quantum logic, if one takes the latter as originating with the attempts of Birkhoff and von Neumann. For one thing, quantum logic effectively discards the potential theory.
A result from studies in quantum logic which seems significant appeared 30 years ago. Classical logic need not be Boolean. To the best that I can tell, no one from any relevant community has been looking at it.
A very long reply…. I hope it helps to clarify a few things.
At least, it may help you understand my appreciation for your careful methodology. It is extremely hard work to sort out the important issues from philosophical residues of historical developments.
I appreciate the long anwer, but the challenge here is that I need more focus on particular issues, not longer answers with more issues. The latter just leaves me with too many questions to establish any knowledge.
Let’s stick with Stern-Gerlach. I’m not convinced this interpretation is right, because as so often happens, we have left out the measurement devices from the state function. When we include them, I don’t know how we apply Boolean partitioning. In other words, letting devices 1, 2 and 3 each have states r,a,-a for “ready to measure”, “observed along the axis” and “observed opposite the axis”, and putting square brackets around the state we plan to block, we have four stages from the beginning of the measurement to the end:
(x,r1,r2,r3) to
(z,a1,r2,r3)+ [(-z,-a1,r2,r3)] to
(x,a1,a2,r3)+(-x,a1,-a2,r3) + [(x,-a1,a2,r3)+(-x,-a1,-a2,r3)] to
(z,a1,a2,a3)+(-z,a1,a2,-a3)+(z,a1,-a2,a3)+(-z,a1,-a2,-a3) + [(z,-a1,a2,a3)+(-z,-a1,a2,-a3)+(z,-a1,-a2,a3)+(-z,-a1,-a2,-a3)]
In other words, it is perfectly fine for (z,a1,r2,r3) to evolve to (-z,a1,+a2,-a3) and (-z,a1,-a2,-a3), independent of whether (-z,-a1,r2,r3) is blocked.
We can only apply Boolean logic to these results if we neglect the states of the devices. But to do so makes no sense to me; we are then conflating different states of the world as though they were the same states. To say it another way, by integrating out the devices and ignoring what they say, we are taking pure states and turning them into mixed states, aren’t we? and if that’s right, we are not justified in asking logical questions about the measured spin as though it were in a pure state.
What’s wrong with this counterargument?
Nothing. It is just counterintuitive to realize that there are different logics. And you have the benefit of a vetted modern perspective — Bohr did not.
Boolean logic is not temporal. So, evolving states would be meaningless. All of that “eternal truth” stuff…
One would treat “electrons” as a class of linguistic subjects. Then:
1) Some electrons are spin up.
2) Some electrons are not spin up.
3) Some electrons are spin down.
4) Some electrons are not spin down.
5) All electrons that are not spin up are spin down
6) All electrons that are not spin down are spin up.
From this, the blocked beam would yield only one type of electron through the remaining tests.
That there are now many logics currently being studied is precisely because this did not make sense to a significant number of mathematicians.
What Birkhoff and von Neumann tried to capture had been:
1) ‘The electron is spin up’ and ‘The electron is spin down’ may both be false
2) ‘The electron is spin up or the electron is spin down’ is true
This affects the distributivity property of Boolean logic.
Relative to lattice theory, every Boolean order appears in quantum logic, if orthogonality stands for negation. Every non-Boolean lattice order for this logic has a 6-element suborder called MO2,
https://www.researchgate.net/publication/357262875/figure/fig1/AS:1103987222810625@1640222473990/Orthomodular-lattice-MO2-39.png
which is the defining feature of the non-distributive nature of the logic.
From what I can tell, the reappearance of the ‘z’ component in the last measurement is correlated with the non-distributivity which motivated Birkhoff and von Neumann.
Anyway, this is not physics, and, I apologize for bringing it up.
Or at least one should find the state where the uncertainty in each is minimized, which is not currently the case in my opinion.
I don’t know if it is a matter of perspective, but it seems like the red dot and the ‘blob’ in figs 2 and 3 doesn’t travel toward decreasing values of x2, in the end of the interaction.
On that point, x1 is decreasing, x3 is increasing, but x2 seems to be increasing when the blue dot is traveling backward.
I agree it is hard to tell how things are moving at the end, especially since the motion in x2 is slow. There may be better ways to make these specific figures, but images of 3d spaces are always hard to design well.
A quick question, the way the ‘blob’ is drawn in the second scenario suggests that its spread remains the same during both collisions. Is this correct or will it alter over time? I have the intuition it should be squashing and stretching somehow.
I haven’t been careful about this. At some point I’ll do some precise solutions to the Schroedinger equation and we can explore this. Right now I’m more focused on logical issues.
It *will * alter over time, although how much depends on the object masses, the original wave function, etc, as you can see in https://profmattstrassler.com/2025/02/11/elementary-particles-do-not-exist-part-2/ . An explicit example of how things might spread out is shown in https://profmattstrassler.com/2025/03/06/can-a-quantum-particle-move-in-two-directions-at-once/
Hi, Matt,
I’ve been enjoying this series a lot! I’m a mathematician who’s been trying to learn some physics in my spare time for a while. There’s something about the quantum measurement story that’s always confused me a bit, and this seems like as good a time as any to ask about it.
The schematic story I’ve been exposed to is that when you measure the spin of an electron, you model the initial state of the system as a tensor product of some two-dimensional vector representing the electron’s initial state and some other, enormous vector representing the initial state of the rest of the universe.
After the measurement, the state is entangled, but because decoherence something something, it’s close to being a linear combination of two states that could be interpreted as “the electron has spin up and my measurement device said spin up” and “the electron has spin down and my measurement device said spin down”.
It seems like there’s a lot of ideas about what to make of that final state, but there’s one possibility I think I’ve ever seen mentioned, so I assume there’s something wrong with it. Suppose we perform this experiment and our measurement device says “spin down”, corresponding to the second term in the sum described above. What if I decided that that second term “actually was the state the whole time”, so the “real” initial state was the state you’d get by taking that term and running it backwards with the Schroedinger equation to the initial time? In this picture, my original description of the initial state was incomplete, and by performing this measurement I’ve acquired new information that lets me describe it more accurately.
What is problematic about this story? Is the initial state you’d get by running time backwards on the measurement outcome you actually see somehow unsuitable as a description of the state of affairs before the measurement happened? I hope this question makes sense!
You have to chain measurements together to start seeing what goes wrong.
Let’s consider states (up), (down), (left), (right), where the (up) state is a linear combination of the states (left) and (right): literally (up) = 1/sqrt[2] [(left) + (right)].
For instance, suppose you have a state (up) to start with, and you measure and thus confirm that the state is undeed (up).
Next we measure whether the state is left or right, and find (right).
If we now say that the state was (right) all along, and we just didn’t know it, then how do we explain the fact that we already confirmed the state was (up) in our previous measurement?
Thanks for the quick reply! I think I might be asking something slightly different from this, though. I’m pretty sure I understand why it doesn’t work to say that the electron itself really was in the state (up) the whole time.
The suggestion (which, again, I’m sure falls apart for some reason) is rather to take the state of the whole universe after the measurement, which we might schematically write as 1/sqrt(2)[(up)(we measured up) + (down)(we measured down)], take just the (up)(we measured up) part of it, and run *that* backwards to the pre-measurement time and say that that was the “real” initial state.
I’d imagine that the resulting state no longer cleanly splits up as (up)(something), so in that sense I’m not claiming anything about the state of the electron by itself; probably it’s some horrible entangled mess. But it would seem to at least partially resolve the question that feels like it’s behind a lot of the philosophical hand-wringing about quantum measurement — the question about whether there is anything at all about the initial state of the universe that predicts that we would get the measurement outcome “up” when we do the measurement. In this story, there is, but the information isn’t locally stored “inside the electron” — which definitely doesn’t work — but it would be encoded in some way in the state of the electron and the measurement apparatus together.
Well, (up)(we measured up) isn’t a suitable initial state. (up)(we haven’t measured anything yet) is the appropriate initial state. Otherwise we simply replicate the problem: if the measurement’s outcome was predetermined *even in the external world*, then in what sense did any measurement get made?
More convincing perhaps is the fact that we can see that this is not the way the equations work. Even in this example, keeping only the microball and forgetting the macroball for a moment, and remembering that the microball is the measuring device, the initial state is (projectile moving right)(ball is stationary [no measurement has been made]), and the next state is (projectile is moving left)(ball is moving right [measurement detects that the projectile was present]). Would it be meaningful to say that the intitial state was really (projectile is moving left)(ball is moving right)? The whole point of physics is to describe the evolution of physical states.
If you now include the macroball and view that as the “rest of the universe”, you see that things are no different from what I just said, other than being more complicated to write down.
Again, you have to chain events together to see the problem. Suppose we did accept that the state (projectile is moving left)(ball is moving right [measurement detects that the projectile was present]) is the state that we should say was the real initial state. But there’s another part of the system that was used to generate a projectile that was moving right, and measured it to be so. What happens to that part of the system when we include it? Do we say that even though we have a gun that shoots projectiles that move right, the fact that the projectile moves left after the measurement by the microball means that the state of the universe is one in which it was always moving left?
I don’t really see this as an issue of philosophical hand-wringing. I see this as an issue of taking a final state and asserting it is also the initial state, and that evolution of physical objects is just a tautology, not actual evolution. Once you do that there’s no evolution over time.
It’s a fact that a deterministic wave equation like the Schroedinger equation tells you the past state given the future state, and so you can assert that the future state is the past state in some philosophical sense, since the evolution is just a determined path. But it’s not true in the mathematical sense; there is an evolution equation, which does implement evolution over time. What you’re asserting is not consistent with what it actually does.
I’m pretty sure the problem is on my end but I think there might still be a failure of communication going on here. I appreciate your patience and I hope this question isn’t too annoying!
I’m not saying (up)(we measured up) should be the initial state. Let’s write U_t for the run-the-Schroedinger-equation-forward-by-t operator. Say, in the usual model, the electron starts in the state (left), so that the initial state is (left)(we haven’t measured anything). My understanding of the measurement story is that, if t is the length of time it takes for the measurement to finish, then
U_t[(left)(we haven’t measured anything)] = 1/sqrt(2)[(up)(we saw up) + (down)(we saw down)].
Since the U’s are linear, it would be equivalent to say that
(left)(we haven’t measured anything) = 1/sqrt(2)[U_{-t}[(up)(we saw up)] + U_{-t}[(down)(we saw down)]].
In other words, it’s equivalent to say that our initial state is a linear combination of a state that will eventually evolve into (up)(we saw up) and a state that will eventually evolve into (down)(we saw down).
Now, suppose I actually do this measurement and I see “up”. The question I’m trying to ask is: what is wrong with taking this as meaning that we can drop the second term from the above expression, and say the initial state was actually U_{-t}[(up)(we saw up)]? This is presumably quite different from (up)(we saw up) itself; I imagine it’d be basically impossible to describe explicitly, but it would at least answer the question of why we saw up rather than down.
It was maybe not the best turn of phrase, but the “philosophical hand-wringing” I was referring to is the question of what to make of the (down)(we saw down) term in light of the fact that we saw “up”. Some philosophers of physics take this as evidence of some many worlds picture, some try to add on extra degrees of freedom like in Bohmian mechanics, some imagine that wavefunction collapse is a real physical process that picks out the outcome we see, et cetera. I’m asking this question because, at first glance, it seems like this offers a way out of the problem, but obviously things can’t actually be this simple.
So, it’s quite possible that the following is overkill (if it is Matt will likely chime in and say so), but in some sense what you’re proposing appears to be what’s known as superdeterminism. And the cost of superdeterminism is that you lose the ability to state counterfactuals regarding measurement choices.
The normal way a physicist would think of the experiment is that you could have chosen to either measure up-down or left-right, and you want to be able to state, given each choice, what you would have observed. Your trick only works for one of those choices: you can set the initial state to U_{-t}[(up)(we saw up)], but you can’t simultaneously set the initial state to U_{-t}[(right)(we saw right)] or U_{-t}[(left)(we saw left)] because they aren’t commuting measurements. And yet, you could have made either measurement.
This definitely does boil down to philosophical hand-wringing, to be clear! A superdeterminist would say that you couldn’t have made either measurement, your measurement choice was fixed by the initial conditions. But at that point, you’re giving up on the ability to ask “what should I do to achieve X outcome”, which is in some sense the whole reason science is useful, and you’re positing large correlations between the outcomes of specific particle physics experiments and the arrangements of big macroscopic measurement apparatuses and possibly human brains, which sounds like a wacky conspiracy theory to most physicists. Those aren’t physics objections, they’re philosophy objections, but they do feel like pretty strong ones to me.
Thanks for the clarification on what you are asking. The details do matter in this business, and now you have stated your question clearly enough that I understand the details.
There is something in what 4gravitons is saying, so you shouldn’t ignore it. But one of the large problems here is that neither you nor I has been specific about how these states were actually prepared, and about issues of causality being forward in time.
The answer I’m about to give is probably not my final answer; like you, I am thinking these things through and learning as I go. But here is what is bothering me at the moment.
To prepare an experiment in which the object to be measured is (up) and in which the rest of the universe is in the state (we have not seen up or down but we are ready to do the measurement) takes effort: the measurement device must be carefully prepared, using a protocol that leaves us unbiased as to whether we will see up or down, and so that if we send in a beam of up particles we will always measure up, so that if we send in a beam of down particles we will always measure down, and if we send in a superposition of the two (let’s say, “left” particles) we will measure up and down in the correct ratio of probabilities. Preparing the beam is done independently of preparing the device, and it is perfectly possible for its orientation to be effectively random chance (but fixed during the experiment) by briefly coupling the beam’s settings, say, to a thermal bath. Now, what you are suggesting is that the result of the experiment tells us what the world’s state was at the time of the measurement. I’m telling you that the preparation of the experiment — of the device and of the object(s) to be measured — tells us what the state was at the time of the measurement. We cannot have it both ways.
If we have it your way, and we repeat the experiment 10^6 times, the initial state requires 10^6 pieces of information, telling us the 10^6 results of the up-down measurements on our randomly oriented beam. If we do it my way it requires 1 — the orientation angle of the beam.
Causality tells us that things naturally become more correlated over time, not less; that careful preparation is needed to create the conditions for an experiment, in which the measurement device and the object of measurement are uncorrelated; that measurement is a process of correlation between observed and observer. You want to say the correlation was already there in the initial state, with all the complex patterns of correlation that would accompany repeating the experiment 10^6 times and getting an unpredictable pattern of 10^6 results. I’m saying that’s teleological; you’re using the future to determine the past, which is not logically impossible but is not physically useful.
Great, yes, I agree that we’re now on the same page! And I think this answer and the one from 4gravitons do a lot to answer the question. Talking about this stuff sometimes makes me feel like everything I’m saying is nonsense — as a mathematician I have some experience reading pseudo-mathematical nonsense on the Internet and I don’t want to produce the physics version of the same thing — so I really appreciate that you were willing to stick with it long enough for me to get the question across.
Thanks, and I look forward to reading whatever it is you end up producing on this topic going forward.
Measurement is an interaction. Concept of “measurement” is needed for humans to explain “wave function collapse”. Wave function collapse is one of the dominant anthropic interpretation of events in micro-world.
The problem is that quantum world is a permanent interactive environment surely well without humans. So wave function collapse is an artificial anthropic construct. New theories needed.
I’ll discuss wave function collapse very soon.