Through the looking glass

Studying physics ultimately changes the way one sees the world. This is probably true for any subject but with physics, this change goes deeper than with biology or history. One starts to see some very basic things very differently. At least that is what I think.

Take the simple act of measurement, for example. You want to know what the weather is like? You check the thermometer. Want to know whether you lost weight? You step on the scale. In any case, the act of measurement is just a way of obtaining some information that already exists. There was a particular temperature outside before you looked and it does not depend on whether you look or not.

Then you start learning quantum physics and your understanding of measurements dramatically changes. You want to measure a position of a particle? Sure, you can do that. But unlike in normal world, it does not make much sense to talk about the position before you measure. The particle was not here or there before you measured, there was only certain probability for it to be there.

At first, this might seem similar to your everyday experience — when you are looking for lost keys, you do not know where they are so there is only a certain probability to find them at a particular place. But there is an important difference; although you are unaware of the exact position of your keys, they are lying at a particular place. A quantum particle, however, is literally at several places at once. Only by measuring its position you localise it at a particular place. It is as if you are looking at the thermometer changed the temperature outside.

Since the particle was not at a particular position before the measurement but it is at a specific position afterwards, the measurement changes the behaviour of the particle. If you now let the particle move freely (i.e., without observing it), it will behave differently than if you did not look at it in the first place. To use the analogy with measuring temperature, it is as if the weather during a day depended on whether you looked at the thermometer in the morning.

If that is still not enough for you, you can go deeper and ask how the measurement process works. First of all, you will find that people know surprisingly little about that. They will tell you that the system you are measuring (such as the particle whose position you want to measure) interacts with a second, meter system in such a way that some variable of the meter contains information about the measured system and can give a strong, classical measurement signal. But what determines whether a system is classical and can be used to measure other systems or whether it is quantum and can be measured by other systems? Not a clue.¹

Even with this little knowledge about measurements, people can describe what is going  on surprisingly well. Because the system and the meter have to interact for some time, a lot can happen during the measurement. If you try to measure the position of a particle, the particle will continue to move while you are measuring. Measure too quickly and you will not know where exactly the particle is because you do not collect a strong enough signal. Measure too long and the particle will move too much during your measurement.

In the end, you can never measure as precisely as you would like. There will always be a small uncertainty in the position of your particle. And this gets even weirder when you try to look at the position later again. Quite surprisingly, the better you know the position at an early time,the more blurred the measurement will be at a later time. This is the result of Heisenberg uncertainty relation between position and momentum but that is a story for another time.²

Another thing you can do is measure really slowly so you need a long interaction time between your system and the meter. At any given time, you do not have a complete information about the state of your system, i.e., you never know exactly where your particle is, all you can have is a guess. The measurement then becomes an inherent part of the evolution of your system and can be used to steer it. There is now certain randomness in the evolution (remember, all we can talk about before the measurement are only probabilities of each outcome and the measurement is thus random at heart) but that does not matter that much since you know what the random measurement outcome is.

If you do not like this randomness, you can use the information you get from the measurement to control your system. You can, for instance, use the result of the position measurement to keep a particle pinned to a particular position. Every time it tries to move a bit (and everything moves a lot in the quantum world), your measurement will tell you so and you can push it back. We thus came to the notion of measurement feedback I already talked about before.

Realisations that such simple things as measurements have such rich and complex internal structure are one of the things I love about physics. Where most people see a simple (and a little boring) way to get some information, I see an incredibly complex process people still don’t understand after studying it for decades. More than that, measurements are for me a tool that we can use to control and manipulate quantum systems. And there is nothing boring about that!

¹ I am, of course, simplifying things a bit here. There is a lot that we know about measurements (and a lot we don’t!) but it all involves a lot of counterintuitive things and complicated maths. There is no room for the details in a blog.

² Here, I am mixing the notion of single-shot measurements (i.e., measurements you only do once) and repeated measurements (which can be used to obtain statistics). But since even a single-shot measurements takes up a finite time, it is, in a way, a statistical matter. I will try to get to this problem in a later post.