What is the meaning of a measurement expressed as 2.0 cm -/+ 0.05 cm?

In summary: The +/- 0.05 cm indicates the uncertainty in the measurement. In other words, the actual measurement could be anywhere within that range.
  • #1
Quarlep
257
4
Hi I saw something in Wikipedia and I am confused. I saw something like this
2.0 cm -/+ 0.05 cm Whats that mean?
My first opinion Between 1,5 and 2,5
My second opinion 1,5 cm or 2,5 cm
 
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  • #2
Quarlep said:
Hi I saw something in Wikipedia and I am confused. I saw something like this
2.0 cm -/+ 0.05 cm Whats that mean?
My first opinion Between 1,5 and 2,5
My second opinion 1,5 cm or 2,5 cm

It means the error is between the value written after -/+, so for example 1.0 km -/+ 0.5 km. That means we are not certain that the measurement is 1.0 km as given by whatever instruments we have. The real value can range between 1.5 km and 0.5 km.
 
  • #3
Quarlep said:
Hi I saw something in Wikipedia and I am confused. I saw something like this
2.0 cm -/+ 0.05 cm Whats that mean?
My first opinion Between 1,5 and 2,5
My second opinion 1,5 cm or 2,5 cm

Your first thought ("between") is right, but have you dropped a decimal place in there? ##2.0{\pm}0.05## means between 1.95 and 2.05, not 1.5 and 2.5
 
  • #4
I think of the +/- as the uncertainty in the measurement in a statistical sense. This may be a subtlety different view to that posted above. I don't interpret those bounds as definitely encompassing the 'true measurement'. Usually I'd take it to mean that there's a 68% chance (1 sigma) that the true measurement is in that range, assuming 'normal' statistics of course. Just my view, others may disagree!
 
  • #5
Quarlep said:
Hi I saw something in Wikipedia and I am confused. I saw something like this
2.0 cm -/+ 0.05 cm Whats that mean?
My first opinion Between 1,5 and 2,5
My second opinion 1,5 cm or 2,5 cm

Seydlitz said:
It means the error is between the value written after -/+, so for example 1.0 km -/+ 0.5 km. That means we are not certain that the measurement is 1.0 km as given by whatever instruments we have. The real value can range between 1.5 km and 0.5 km.
As Nugatory points out, the error portion is ##\pm## 0.05. Also, the units involved are centimeters, not kilometers

Nugatory said:
Your first thought ("between") is right, but have you dropped a decimal place in there? ##2.0{\pm}0.05## means between 1.95 and 2.05, not 1.5 and 2.5
Quarlep, the measurement is between 1.95 cm and 2.05 cm.
 

1. What is the "Measurement Problem" in physics?

The "Measurement Problem" refers to the philosophical and theoretical challenge in quantum mechanics where the act of measuring a quantum system causes it to change or collapse from a superposition of multiple states to a single observed state. This phenomenon is known as the "collapse of the wave function."

2. How does the "Measurement Problem" relate to the uncertainty principle?

The "Measurement Problem" is closely related to the uncertainty principle, which states that it is impossible to simultaneously know the exact position and momentum of a particle. This means that the very act of measuring a particle's position or momentum will inevitably disturb its state and cause it to collapse.

3. What are some proposed solutions to the "Measurement Problem"?

One proposed solution to the "Measurement Problem" is the many-worlds interpretation, which suggests that every possible outcome of a measurement actually occurs in a different parallel universe. Another solution is the Copenhagen interpretation, which states that the wave function only collapses when it is observed by a conscious observer.

4. How does the "Measurement Problem" impact our understanding of reality?

The "Measurement Problem" challenges our understanding of reality and raises questions about the nature of the universe. It suggests that our traditional understanding of cause and effect may not apply at the quantum level, and that there may be multiple realities or dimensions beyond our current understanding.

5. What are the implications of the "Measurement Problem" for future scientific research?

The "Measurement Problem" continues to be a topic of debate and study in the scientific community. It challenges scientists to further explore the nature of quantum mechanics and how it relates to our understanding of the universe. It also highlights the need for more advanced measurement techniques and technologies to better understand and observe quantum systems without disturbing them.

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