Simultaneous measurements of 1 observable

In summary: If yes, then will the eigenvalue be equal in both measurements?The answer is yes, provided the measurements are performed with a sufficiently precise apparatus. If the two measurements are performed with slightly different methods or with a slightly different apparatus, then the eigenvalues may be different.if they will be the equal, why will they be the equal?This question is a little more complex. If two observers make measurements of a system at different times, then the results of the two measurements will be "frame-independent." In other words, the values of the variables (like momentum and velocity) will be the same in any two frames of reference that observe the system at the same time. However, the
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Ghost Quartz
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some doubts about the measurement of observables
Hi. I'm new to the forum and and I am currently studying quantum mechanics.
According Sakurai, page 24, "When the measurement is performed, the system is" thrown into" one of eigenstates of observable". This raised some questions for me:

Is possible two measurements simultaneous of one observable?
If yes, then will the eigenvalue be equal in both measurements? if they will be the equal, why will they be the equal?

If not, then why not? I do not remember it well, but I believe I have heard somewhere that it is impossible for two photons to interact simultaneously with an electron. Is there any relation?

i am not a graduate student in physics, then I don't know the correct level of this thread. When in doubt I put A, sorry for this.
 
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Ghost Quartz said:
i am not a graduate student in physics, then I don't know the correct level of this thread. When in doubt I put A, sorry for this.
”I” for general college level is about right, and it’s no problem - just a few mouse clicks to change, probably the most common edit I make.
 
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Ghost Quartz said:
According Sakurai, page 24, "When the measurement is performed, the system is" thrown into" one of eigenstates of observable". This raised some questions for me:

Is possible two measurements simultaneous of one observable?
If you think of QM as describing nature at an elementary level, then it's not possible. Two observers can independently and simultaneously measure the velocity and position of a car, for example, because the car can be bombarded by light from all directions without significantly changing its position or momentum.

You can't do that to a electron. The position measurement of an electron must be deduced indirectly by the scattering of a single photon, say. That's a whole different game.

The role of measurement in QM is subtle and somewhat problematic. For the time being, I would assume that a system in QM is subject to one measurement at a time.
 
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1. What is the concept of simultaneous measurements of 1 observable?

The concept of simultaneous measurements of 1 observable refers to the ability to measure the value of one observable property of a system at the same time. This means that multiple measurements of the same observable can be taken simultaneously, allowing for a more accurate and comprehensive understanding of the system.

2. Why is it important to perform simultaneous measurements of 1 observable?

Performing simultaneous measurements of 1 observable is important because it allows for a more precise and complete understanding of a system. By taking multiple measurements at the same time, any variations or changes in the observable can be captured and analyzed, leading to a more accurate interpretation of the data.

3. What are some examples of observables that can be measured simultaneously?

Some examples of observables that can be measured simultaneously include temperature, pressure, flow rate, and concentration. These are all properties that can be measured using various instruments and techniques, and their simultaneous measurement can provide valuable insights into a system.

4. How are simultaneous measurements of 1 observable performed?

Simultaneous measurements of 1 observable are typically performed using specialized instruments or equipment that can measure the desired property at the same time. This may involve using sensors, probes, or other devices that can collect data in real-time and display it in a meaningful way.

5. What are the benefits of using simultaneous measurements of 1 observable in scientific research?

The benefits of using simultaneous measurements of 1 observable in scientific research include increased accuracy and precision, the ability to capture changes and variations in the observable, and a more comprehensive understanding of the system. This can lead to more reliable and robust conclusions and findings in scientific studies.

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