# What operators can we measure directly?

1. Jun 8, 2009

### Fredrik

Staff Emeritus
Some time ago, someone in this forum asked how you measure momentum. One of the answers said that if it's a charged particle, you can let it pass through a bubble chamber and a magnetic field, and measure the curvature of the bubble trail. But this isn't really a direct measurement of the momentum. The bubbles appear at locations where the particle has interacted with the liquid, and each interaction that produces a bubble is an approximate position measurement. So what we actually do here is to make a series of approximate position measurements, and infer an approximate value of the momentum.

Consider a Stern-Gerlach apparatus. A beam of silver atoms is sent through an inhomogeneous magnetic field and is split in two. How do we measure the spin? We put detectors at the locations of the outgoing beams so that we can tell if a particle has been detected there or not. Then we infer the value of the spin from the fact that we have prepared the system so that the spin eigenstates are entangled with states that almost have a well-defined position.

In a recent thread, someone talked about measuring wavelengths by sending a photon into some sort of cavity, which will absorb the photon if it has the "wrong" wavelength. If we're able to detect the photon there, then we infer that it had the "right" wavelength. (I don't know the details of this experiment, so I could be wrong about some of it).

In all of these situations, the measurement device really just says "yeah, it's here", and we use our theoretical knowledge of the state preparation procedure to infer the value of the quantity we're really interested in. My question is, are all quantum physics experiments like that? Is there any way to measure an observable directly? Are there any measurements that have an actual number as a result, or are all the numbers we think of as measurement results inferred from "yes" and "no" answers about a particle's position from our measuring devices?

Last edited: Jun 8, 2009
2. Jun 8, 2009

### ytuab

Spin magnetic moment of one electron is measured directly by the Penning trap.

But we can not directly watch the spin of electron.
And probably No one believe that spin is a real spinning of electron.
So There is a possibility that this magnetic moment is caused by a simple circular movement of an electron.

Only Stern-Gerlach experiment can't show that the spin angular momentum is 1/2 hbar.

Stern-Gerlach + Shrodinger equarion show this.
(If we forget Shrodinger equation, there is a possibility that spin angular momentum is hbar. If angular momentum is hbar, is it really spilitted into three? )

3. Jun 8, 2009

### ZapperZ

Staff Emeritus
You need to define what you mean by "directly". What exactly, even in classical measurement, would you consider to be measured "directly"? How do you determine, for example, the speed of a vehicle? What instrument would you use and how exactly do you arrive at a number, even in such a classical case? Would you consider this as a "direct" measurement?

Zz.

4. Jun 8, 2009

### Fredrik

Staff Emeritus
After reading the wikipedia article about the Penning trap, my conclusion is that it's no different than the other setups I described. The apparatus produces a bunch of signals and each of them is really just saying "hey I just interacted with a particle".

That's a good point. In SR, we take one of the axioms of the theory to be "A clock measures the proper time of the curve in Minkowski space that represents its motion". "Proper time" is defined mathematically. "Clock" doesn't get a formal definition. This makes it pretty clear what a direct measurement of time is. What about length? We could use a similar axiom that tells us how to use a ruler to obtain a number that corresponds to the proper length of a spacelike curve, but I prefer to use clocks, light and a mirror. The exact statement isn't important here. The point is that it's natural to postulate that we measure lengths using clocks (and some other stuff). So in the axiomatic formulation of SR that I prefer, not even lengths are measured directly. If we use a clock, we're really measuring length by measuring time and inferring the result. If we use a ruler instead, that's even less direct, because the axiom defines length measurements in terms of the times displayed by clocks, so we would actually have to use our theoretical understanding of concepts such as "Born rigidity" and "local Poincaré invariance" to interpret the result as a measurement of length.

I haven't thought all the details through when it comes to including axioms about measuring other physical quantities, but I suspect that we can measure everything with clocks...and of course something similar to what I talked about in #1, a device that sends us a 1-bit message every time it participates in the interaction it's designed to detect. Without something like that, we wouldn't even know when to start and stop our clocks.

I guess it's pretty clear that this is how measurements work in all theories. It's all about creating a situation where a single bit of information tells us everything we need to know. I'm just surprised by the fact that I haven't thought of this before. Makes me wonder how many other simple things I haven't thought of yet.

Last edited: Jun 8, 2009
5. Jun 8, 2009

### ZapperZ

Staff Emeritus
But even with your "clocks", you still need to determine some sort of position, and from that position, infer the velocity. Compare that with the statement you made in the OP.

So would such a thing be considered to be a "direct" measurement for you?

Zz.

6. Jun 8, 2009

### Fredrik

Staff Emeritus
Agreed.

No.

I thought my second post made it clear what my answers to questions like these would be, but I guess I didn't make it clear enough. My current position on these matters is that the only direct measurements in physics are the ones that tell us that a specific interaction has happened, and measurements of proper time (which can tell us both where and when the interaction occurred).

I don't see how it could be any different. Maybe if we completely redefine what we mean by "measurement" or "time", but I doubt that a new definition of those concepts will ever be useful. Yes, a new theory of gravity would probably describe time in some weird way, but when we calculate its predictions about the results of experiments, we would only consider experiments performed over a time scale at which time doesn't have any noticable exotic properties. Just like when we test the predictions of QM, we only care about predictions about the behavior of measuring devices which are effectively classical.

7. Jun 8, 2009

How come people think we can measure voltage directly? We only see a number on the multimeter and infer that some interaction has taken place due to the set up of how we prepared our multimeter. :)

8. Jun 8, 2009

### ZapperZ

Staff Emeritus
Maybe you should give a specific example of what you consider to be a direct measurement. A direct measurement of "time" doesn't quite do it for me.

Zz.

9. Jun 9, 2009

### Fredrik

Staff Emeritus
Seems like a strange thing to ask for, considering that I said that there are no direct measurements except for a) measurements of proper time, using a clock, and b) measurements that indicate that a particular interaction has taken place, using a device that's designed to be an indicator of the particular interaction we're interested in.

However, deadbeef's simple example had me wondering if I'm making a mistake. (Thanks deadbeef). Let's consider an analog ammeter that consists of a pointer, held in place by a spring, with a copper wire wrapped around it to make a coil.

The current flowing through the coil produces a magnetic field, which interacts with an external magnetic field, and the interaction turns the pointer one way or the other. This device seems to be doing more than just tell us that an interaction has taken place. It doesn't just tell us that electrons are flowing through the wire. It also tells us how many of them are passing through per unit of time.

One way of thinking about this is to consider each possible number of electrons flowing through the wire a different interaction. If we think of it that way, this device is just a device that tells us that an interaction has taken place. It just happens to be able to detect many different interactions.

Another observation worth making here is that it's the position of the top of the pointer that indicates to us what the current is.

10. Jun 9, 2009

### strangerep

red/green/blue but I suppose that could be reduced to a microscopic position
measurement amongst the particular cells in the retina.

In any measurement, it seems to me that we have to set up a collection of
reference states and then compare the experimental state under investigation
against these reference states. Ideally, only one of the reference states gives
non-zero when we take its inner product with (a single copy of) the
experimental state. Our set of reference states must be both stable and
distinguishable somehow when we set them up, ready for a experimental run.
IMHO, there's not much choice but to use position to distinguish them.

11. Jun 9, 2009

### mn4j

Not if you are color-blind. Actually our eyes do not measure color. They measure the wavelength/frequency of light. When you talk of measurement, the "thing" being measured has to be separable from the measuring device. However, color is a property of the joined "eye" + "photons" system.

There are manything we can measure directly, such in the analog ammeter example, we are measuring "the position of the pin" directly! In this case, though, the measuring device is not the ammeter but the human eye. However, since we are not interested in the pin but in the current, we have to infer what the current is from the position, by carefully preparing the system (ie the ammeter), in such a way that we can separate the thing we are interested in (current), from the ammeter. In this case, the measurement is indirect.

12. Jun 9, 2009

### ZapperZ

Staff Emeritus
How exactly do you measure "time" directly? What makes this a "direct" measurement?

Zz.

13. Jun 9, 2009

### ytuab

I think it is impossible to measure the mass and charge directly without any interaction.

Because the bare mass and charge are infinit.

The instant they interact with other (photon or other particles), they become definit.
These values are not real things.
( though I doubt this fact.)

14. Jun 10, 2009

### Demystifier

All we ever measure are SPACE POSITIONS of something. In fact, this is the main reason why the Bohmian interpretation (where particle positions are preferred observables) is compatible with standard QM. Nevertheless, there is also an interpretation independent explanation of the fact that we allways measure positions. This is because all the interactions are local in space, so decoherence always occurs in a basis of states well localized in space.

15. Jun 10, 2009

### Fredrik

Staff Emeritus
OK, that's a good question. Hm, I think I'm going to have to change my mind. There are no direct measurements, of any observables. Every "measurement" is reducible to a series of events where a specific interaction causes a signal that indicates that the interaction has taken place. Those events should be thought of as "detections", not as measurements. It's the whole series of events that can be described as a "measurement".

This means that a precision measurement of time isn't going to be more "direct" than a precision measurement of any other observable. (By "observable", I mean "something we can measure". I don't care if it corresponds to a self-adjoint operator in QM). Time does however have a special role to play in the process by which our brains become aware of their environments. I'm going to talk about that for a bit, mostly because I think this is interesting.

The only way we can become aware of something in our environment is through our sensory organs. They are devices that send signals to our brains indicating that some specific interaction has taken place. We can clearly build devices that are extensions of our sensory organs in the sense that when they participate in a specific interaction, they send a signal to a sensory organ. This signal causes an interaction in the sensory organ, which then sends a signal to the brain.

Our brains are clearly able to distinguish between these signals. (For example, a signal from a cone in the retina which is sensitive to "red" light causes a different experience than a signal from a cone that's sensitive to "blue" light). This is of course absolutely necessary in order for our brains to be able to simulate the world around us, based only on those signals. Such a simulation is of course what we would usually call an "experience".

Our brains are clearly also able to process information. This is something that takes time. That gives our brains a way to keep track of (roughly) how much time has passed. So the information that the brain can use to create a simulation of the world around us consists of a) signals that indicate that "an interaction of type X has occured", and b) the approximate "timestamps" on those messages, added by our "internal clocks". (Those timestamps are very inaccurate, but at least we have some idea when the signals arrived).