How to check theoretical point of view

In summary, the goal of mathematics is to understand the universe at a deeper level. This can be done by studying higher abstract mathematics, which may result in new number theory. However, this is not always the primary motivation for studying mathematics.
  • #1
Saturnine
9
0
I'm reading Frederic's Paugam "Towards the Mathematics
of Quantum Field Theory."
I'm also interested in higher structures in mathematics which could have applications in physics.
How to check theese theories with the experimental data ?
For example the data in LHC. Where can I find experimental results to check QFT from theoretical point of view ?
 
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  • #2
Saturnine said:
Where can I find experimental results to check QFT from theoretical point of view ?
You can find experimental results in the publications of the collaborations of the experiments. Usually those results include comparisons to theoretical predictions.

The interesting raw datasets are available to members of the collaborations only, but some older data is made public sometimes.
 
  • #3
Saturnine said:
I'm reading Frederic's Paugam "Towards the Mathematics
of Quantum Field Theory."
I'm also interested in higher structures in mathematics which could have applications in physics.
How to check theese theories with the experimental data ?
For example the data in LHC. Where can I find experimental results to check QFT from theoretical point of view ?
When "higher" structures in mathematics (such as categories) are applied to physics, usually such results cannot be compared with experimental data. As a rule, the experimental data are associated with "lower" mathematical structures. If you want a book on QFT containing many comparisons with experimental data, one good choice is Donoghue Golowich Holstein:
https://www.amazon.com/dp/0521476526/?tag=pfamazon01-20
But this book is 20 years old, so if you prefer something very recent, see Nagashima
https://www.amazon.com/dp/3527409629/?tag=pfamazon01-20
https://www.amazon.com/dp/3527409661/?tag=pfamazon01-20
 
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  • #4
But what are then foundations to use for example category theory and modern math ?
Whre can I get the data of LHC or some other particle accelerator ?
 
  • #5
Saturnine said:
But what are then foundations to use for example category theory and modern math ?
Pure mathematicians study these things for the sake of mathematics itself. Those who try to apply this stuff to physics hope to gain deeper understanding of physics, but deeper understanding is not the same as comparison with experiments.

Eventually, deeper understanding by higher abstract mathematics may result in new numbers which can be compared with experiments, but that is usually not the primary motivation for studying abstract mathematical formulation of physics.
 
  • #6
Demystifier said:
Eventually, deeper understanding by higher abstract mathematics may result in new numbers which can be compared with experiments, but that is usually not the primary motivation for studying abstract mathematical formulation of physics.

Isn't the goal to have some application of higher mathematics in sciences ?
What is primary motivation ?
 
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  • #7
Saturnine said:
Isn't the goal to have some application of higher mathematics in sciences ?
What is primary motivation ?
It's all individual. Different people have different motivations and goals.

There is no such thing as a "goal of science". There are only particular goals by particular scientists.
 
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  • #8
How to work in theoretical field but also do some experiments with your work ?
 
  • #9
In particle physics?
Typical theory positions won't give you hands-on work. You might come in contact with the mess of data-analysis if you work together with collaborations. If you count that as "do some experiments", ...
Experimental positions can span the whole range from "I solder together stuff in the lab" to "I improve a mathematical method used in data analysis" or "I use this theory model to calculate the cross-section in this region of phase-space".
 
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  • #10
mfb said:
In particle physics?
Typical theory positions won't give you hands-on work. You might come in contact with the mess of data-analysis if you work together with collaborations. If you count that as "do some experiments", ...
Experimental positions can span the whole range from "I solder together stuff in the lab" to "I improve a mathematical method used in data analysis" or "I use this theory model to calculate the cross-section in this region of phase-space".
Can you give me some books or tutorial for data analysis which is used in collaborations.

For example, in the "Towards the Mathematics of Quantum Field Theory" I would like to test everything what I can. Can I test it in crystals and lasers for example. So, the data I can collect, how to use it in higher mathematics.
Thx
 
  • #11
Google "data analysis high energy physics" -> Data Analysis in High Energy Physics: A Practical Guide to Statistical Methods
I didn't read it, but it looks good.
Individual analyses might use more specialized publications, but it is impossible to read all of them.

Saturnine said:
Can I test it in crystals and lasers for example.
Test what, why, how?
Saturnine said:
So, the data I can collect, how to use it in higher mathematics.
How do you want to use experimental data in mathematics? Mathematics does not care about measurement results.
 
  • #12
Saturnine said:
I'm reading Frederic's Paugam "Towards the Mathematics
of Quantum Field Theory."
I'm also interested in higher structures in mathematics which could have applications in physics.
How to check theese theories with the experimental data ?
For example the data in LHC. Where can I find experimental results to check QFT from theoretical point of view ?

It is unlikely you will make any useful progress comparing to LHC data, even supposing you could get it. This is a drastically specialist area. You would need to have a detailed understanding of a huge amount of context and detail of the specifics of he lab and the detector you had data for. This would involve, probably, many months of intense effort just to get the background. And unless you are in a graduate program actually working on the project, you are going to have trouble getting anybody to help you to the extent you would need. The people working in these labs are very busy.

You will likely do better by looking at some of the "standard" experiments that form the foundation of quantum mechanics. For example, you could start with such old-time enjoyments as black body radiation, the double slit experiment, the Hydrogen atom spectrum, and Rutherford scattering. If you get to the point where those seem too easy, you could move on to things like the Lamb shift and Compton scattering. These are all such standard things that you will find them in many standard textbooks.

Reading the jacket text on the book you mention, it says he gives examples from experiments. What experiments does he refer to?
 

1. How do you determine the theoretical point of view in a scientific study?

The theoretical point of view in a scientific study is determined by identifying the underlying assumptions, concepts, and principles that serve as the basis for the research. This involves critically evaluating existing theories and frameworks in the field and selecting the most appropriate one to guide the study.

2. What is the purpose of checking the theoretical point of view in a study?

The purpose of checking the theoretical point of view in a study is to ensure that the research is grounded in a well-established and relevant theoretical framework. This helps to provide a strong foundation for the study and ensures that the findings are valid and reliable.

3. How do you know if the theoretical point of view is appropriate for your research?

The appropriateness of the theoretical point of view for a research study can be determined by considering its relevance to the research question, its compatibility with the research design and methods, and its ability to explain and predict the phenomena being studied. Consulting with experts in the field can also help to validate the suitability of the theoretical framework.

4. Can the theoretical point of view change during the course of a study?

Yes, the theoretical point of view can change during the course of a study. This could happen if new evidence or perspectives emerge that challenge or contradict the initial theoretical framework. In such cases, researchers may need to modify or even change the theoretical point of view to better fit the data and findings.

5. Is it important to have a theoretical point of view in all scientific studies?

Yes, having a theoretical point of view is essential in all scientific studies as it provides a framework for understanding and interpreting the data. Without a theoretical point of view, research may lack direction and coherence, making it difficult to draw meaningful conclusions and contribute to the existing body of knowledge in the field.

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