Measuring Length, Area & Volume: Classical vs Quantum Physics

In summary: Lengths are still the same, but you need to use integrals to find areas and volumes.In summary, the concept of length, area, and volume is based on measurements of length and the use of mathematical operations like multiplication. This applies to both classical and non-classical physics, where measurements can differ depending on the theory being used. In special relativity, lengths are relative and can be measured using a beam of light, while in general relativity, the concept of volume can be more complex due to the curvature of space and spacetime.
  • #1
geordief
215
48
I am talking about length area and volume.

As I reason it out in my own mind area (and volume) is based on length and involves 2 random measurements of length that are combined (with multiplication as the device of convention - could any other function be used to work as well and as usefully?) to give a measurement of area (or Volume with 3 measurements).

Now I understand that this would be seen as reflecting the Classical Physical view of the world and so I am wondering if ,in this limited but easily generalised case , there would be a corresponding approach in non-Classical physics .

In other words , maybe , how do you measure "length" in quantum physics?

If I am talking garbage please tell me !
 
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  • #2
Quantum physics uses the same concept of space as classical physics. Use a ruler or anything similar, measure the distance.

In special relativity, it is a bit trickier, as lengths are relative. Use a beam of light emitted at one point, measure the time it requires to reach the other point, and you get the distance between the two points in your reference frame. Areas and volumes are the products of lengths.

In general relativity, volume is tricky, too, as space and spacetime can be curved.
 

Related to Measuring Length, Area & Volume: Classical vs Quantum Physics

1. What is the difference between classical and quantum physics when it comes to measuring length, area, and volume?

Classical physics deals with macroscopic objects and uses continuous measurements to determine length, area, and volume. Quantum physics, on the other hand, deals with subatomic particles and uses discrete measurements to determine these quantities. This means that in classical physics, we can measure length, area, and volume with infinite precision, while in quantum physics, there is a limit to the precision of these measurements.

2. Can the classical and quantum approaches be used interchangeably to measure length, area, and volume?

No, the classical and quantum approaches cannot be used interchangeably. While classical physics is accurate for macroscopic objects, it breaks down when dealing with subatomic particles. Quantum physics, on the other hand, is accurate for subatomic particles but does not apply to macroscopic objects. Therefore, the two approaches cannot be used interchangeably to measure length, area, and volume.

3. How does the uncertainty principle affect our ability to measure length, area, and volume in quantum physics?

The uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. This means that in quantum physics, our measurements of length, area, and volume are subject to uncertainty. The more precisely we measure one of these quantities, the less precisely we can measure the others.

4. Can quantum measurements ever be as precise as classical measurements?

No, quantum measurements can never be as precise as classical measurements. This is due to the inherent uncertainty in quantum measurements, as described by the uncertainty principle. While classical measurements can be infinitely precise, there is a limit to the precision of quantum measurements.

5. Are there any real-world applications of quantum measurements of length, area, and volume?

Yes, there are real-world applications of quantum measurements of length, area, and volume. For example, quantum computing relies on precise measurements of subatomic particles to perform calculations. Additionally, quantum measurements have been used in industries such as medicine, GPS technology, and cryptography. As our technology and understanding of quantum physics continues to advance, we may discover even more applications for these measurements in the future.

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