# Differences between perturbation/variation of an object?

• I
• troglodyte
In summary: So there is not a consistent use of the word. The next question is, what is the scenario in which you are seeing the word used? That should determine how it is being used.
troglodyte
Gold Member
Hello Guys,

everyone use the word "perturbation" but no one explain it in a consist manner .So,If I perturb a system it is equivalent to vary a system?
Maybe someone can explain it to me in a clear way .

Thank You,
troglodyte

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You perform a perturbation on a system if you change some parameters that define the state of the system. For example, imagine you are measuring the water flow rate outside of a tank. If you add some water to the tank or if you change the pressure inside the vessel, or if you change the dimension of the hole where the water flows out, you are perturbing the system which you were studying before and in fact the outcome of the new measurement (of the water flow rate) will be different from before.

In physics the world "perturbation" may also refer to the technique known as "perturbation theory".

troglodyte
..which means through a perturbation of a system i change the state of system from an initial state to a final state.Therefore, to vary a system one needs a perturbation.So, both concepts are not not equivalent.There exist a kind of implication from perturbation theory to variational theory. Not vice a versa, right?

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I think one difference are the quantities which I perturb .In variational problems i perturb geometrical objects like curves ,areas..On the other hand ,in perturbation theory the perturbed objects are physical quantities of the systems, which I definitely know.

troglodyte said:
..which means through a perturbation of a system i change the state of system from an initial state to a final state.T
The perturbed state is not necessarily the final state.

Consider a ball initially at the bottom of a valley. We perturb it by moving it away from the bottom, then let go. In the final state it returns to the bottom. The goal of the problem might be to see whether or not it returns to the initial state.

troglodyte
troglodyte said:
in perturbation theory the perturbed objects are physical quantities of the systems, which I definitely know.
Hold on, I didn't say that perturbation theory is about perturbing stuff... In fact this is a pretty misleading way to put it. The word "perturbation" in "perturbation theory" has a different meaning. I just said that so that you don't confuse those terms but apparently it backfired

The term "variation" is generally used when there is a random component that causes random variations. The term "perturbation" is generally used there is a planned, hypothesized, or one-time, change to a system. But I do not think that there is an official rule that applies.

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sophiecentaur
FactChecker said:
The term "variation" is generally used when there is a random component that causes random variations. The term "perturbation" is generally used there is a planned, hypothesized, or one-time, change to a system. But I do not think that there is an official rule that applies.
I think that makes sense and it's how I would look at things.
We're into that region of classification of terms again.
If you are searching then, rather than risk missing out on some information because the title / summary of a source may not be following the name convention, look deeper into any document before rejecting it merely on the basis of the use of one or other of those terms.

FactChecker
sophiecentaur said:
look deeper into any document before rejecting it merely on the basis of the use of one or other of those terms.
Maybe you have a good reference.As I have stated before.The literature is not consistent in this case .Most of them uses the word "perturbation"but without introducing the concept and without telling what they concretely mean by this.

troglodyte said:
Maybe you have a good reference.As I have stated before.The literature is not consistent in this case .Most of them uses the word "perturbation"but without introducing the concept and without telling what they concretely mean by this.
So there is not a consistent use of the word. The next question is, what is the scenario in which you are seeing the word used? That should determine how it is being used.

## 1. What is the difference between perturbation and variation of an object?

Perturbation refers to a small change or disturbance in the state of an object, while variation refers to a difference or deviation from the expected or average state of an object.

## 2. How are perturbation and variation related?

Perturbation can cause variation in an object's state, as it introduces a change or disturbance that can alter the expected state of the object.

## 3. Can perturbation and variation be measured?

Yes, both perturbation and variation can be measured using quantitative methods such as mathematical models, statistical analysis, or experimental data.

## 4. What are some examples of perturbation and variation in the natural world?

Perturbation can be seen in natural phenomena such as earthquakes, climate change, and genetic mutations. Variation can be observed in the diversity of species, changes in weather patterns, and differences in physical characteristics among individuals.

## 5. How do perturbation and variation impact scientific research?

Perturbation and variation are important factors to consider in scientific research, as they can provide valuable insights into the behavior and characteristics of objects. They can also help scientists understand the effects of external influences and identify patterns and trends in data.

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