Increasing confidence in theoretical calculations

In summary, a theoretical physicist would go through various checks to ensure the results of their calculation are correct. They would check for dimensional consistency, physical reasonableness, unusual behaviour, and scale invariance. They would also check for consistency with similar problems and for what the result means. Lastly, they would ask what next should be done.
  • #1
ergospherical
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How can one maximise one's confidence in the results of a theoretical calculation? After long and fiddly calculations I often encounter an uneasy feeling where I find it difficult to confirm whether the fruits of all that labour are actually correct. The first ports of call are always:

- dimensional consistency;
- physical reasonableness; is the behaviour unusual? are there different regimes? extreme cases?
- does the result depend on the variables I expected it to? symmetry considerations? scale invariance?
- consistency with similar problems? does the solution reduce to those of special cases?
- does the computer agree with your maths? (did you miss a minus sign on line 37...?)

Some less conclusive tests are:
- "niceness"; a short, tidy answer inspires confidence, but a long, messy answer is not necessarily incorrect.
- peer-review; ask your friend - did (s)he get the same thing?

I'm especially interested to hear about how a theoretical physicist would go about verifying his/her results before publication to a journal/competition etc.
 
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  • #2
In addition to your list, I would add...
- comparison with alternate approaches? - use another method to try to get the same result (and compare advantages and disadvantages... in particular, understand its limitations... where would your approach fail?
What was tried by others in the past? Why did those succeed or fail?)
- clear presentation? - crudely, a storyline to present to someone else who might not follow all of the details; clear definitions and terminology? good notation?
- what does it mean? Is it valuable? - does anybody care? (If not, can one make them care about it?)
- (anticipate follow up questions... what next?)
 
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  • #3
ergospherical said:
I'm especially interested to hear about how a theoretical physicist would go about verifying his/her results before publication to a journal/competition etc.

Comparison with experiment?
 
  • #4
gmax137 said:
Comparison with experiment?
Whilst true in principle, I ought to have clarified that I am only here concerned with analytical techniques (think sitting at a desk with only a pen/paper/laptop, solving a theoretical problem). In other words it's out of the question to perform an experiment, for reasons of feasibility/equipment/expense/time/etc.
 

1. What is the importance of increasing confidence in theoretical calculations?

Increasing confidence in theoretical calculations is crucial for scientific research as it allows for accurate predictions and explanations of natural phenomena. It also helps in the development of new technologies and advancements in various fields.

2. How can we increase confidence in theoretical calculations?

There are several ways to increase confidence in theoretical calculations. One approach is by using advanced mathematical techniques and computational methods. Another way is by conducting experiments and comparing the results with the theoretical calculations to validate their accuracy.

3. What are the limitations of theoretical calculations?

Theoretical calculations are limited by simplifications and assumptions made in the mathematical models used. They also rely on accurate input data and can be affected by errors in the calculations or measurements. Additionally, theoretical calculations may not account for all factors and variables in complex systems.

4. How do scientists validate theoretical calculations?

Scientists validate theoretical calculations by comparing them with experimental data, conducting sensitivity analyses to assess the impact of different variables, and performing cross-validation with other established theories or models. Collaborating with other scientists and peer review also play a crucial role in validating theoretical calculations.

5. What are the benefits of constantly improving theoretical calculations?

Constantly improving theoretical calculations leads to more accurate and reliable predictions, which can have significant impacts on various fields such as medicine, engineering, and climate science. It also allows for the discovery of new phenomena and the refinement of existing theories, leading to a deeper understanding of the natural world.

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