Theoretical Physics Can Be Hella Frustrating

Andrew Dotson
11 Jun 201805:07
EducationalLearning
32 Likes 10 Comments

TLDRIn this video, the speaker, who humorously clarifies they are not Andrew but possibly his little sister, shares their recent experience with a challenging task during their theoretical physics internship. They recount spending three hours searching for a missing 'factor of four' in an equation involving integrals, tensors, and Fourier transforms. The frustration stems from the complex nature of the math and the difficulty in pinpointing errors. The speaker discusses the concept of the transition amplitude, an invariant quantity, and the confusion that arises from the notation used in physics literature, which led to their search for the elusive factor. They also touch upon the benefits of being able to switch between coding and mathematical problem-solving within their field of study. The video concludes with a reflection on the commonality of such frustrations across different fields and an invitation for viewers to share their experiences in the comments section.

Takeaways
  • ๐Ÿง‘โ€๐Ÿฆฑ The speaker is not Andrew, but an impostor, possibly his little sister, as indicated by the absence of a beard.
  • ๐Ÿ•’ The video is short because it mainly discusses the speaker's experience of spending three hours searching for a mathematical factor.
  • ๐Ÿ” The speaker talks about the challenges faced during an internship in theoretical physics, particularly with the mathematical intuition required for complex equations.
  • ๐Ÿงฎ Despite being capable in math, the speaker finds it difficult to track all components of an equation involving integrals, tensors, and Fourier transforms.
  • ๐Ÿ“š The process of deriving the differential cross-section equation led to a deeper understanding of the subject matter.
  • ๐Ÿ”— The transition amplitude, an invariant quantity, is central to the discussion and is related to, but not identical to, the lepton tensor and hydronic tensor.
  • ๐Ÿงฉ The speaker struggled to identify a '4pi cubed' factor in the hydronic tensor, which was a source of frustration.
  • ๐Ÿ”‘ There was a misunderstanding regarding the convention used in the literature, which led to the confusion about the '4pi cubed' factor.
  • ๐Ÿ’ก The realization that the tensors referred to matrix elements, not the tensors themselves, helped clarify the convention used.
  • ๐Ÿ’ป The speaker enjoys the flexibility of being able to switch between coding and doing math on paper during their theoretical physics internship.
  • ๐Ÿ” The video ends with an invitation for viewers to share their experiences of frustration or enjoyment in their fields, especially in experimental work.
Q & A
  • What was the main challenge the speaker faced during their internship in theoretical physics?

    -The main challenge was dealing with complex mathematical equations involving integrals in both coordinate and momentum space, tensors, and Fourier transforms, which made it difficult to keep track of all the components.

  • What specific equation did the speaker work on deriving?

    -The speaker worked on deriving the differential cross-section in terms of the leptonic tensor and hadronic tensor.

  • What is the transition amplitude in the context of the speaker's discussion?

    -The transition amplitude is an invariant quantity that is usually written in terms similar to the leptonic tensor and hadronic tensor, but it involves summing over all possible states and includes a delta function.

  • Why was the speaker searching for a factor of 4pi cubed?

    -The speaker was looking for the factor of 4pi cubed because it was missing from their equation, and they were trying to understand where it came from in the context of the conventions used in theoretical physics literature.

  • What does the speaker mean by 'convention' in the context of their work?

    -By 'convention,' the speaker refers to the standard or accepted way of representing or calculating something in a field, which can differ from one person or paper to another.

  • How does the speaker feel about switching between coding and doing math on paper?

    -The speaker appreciates the ability to switch between coding and doing math on paper as it provides a break from one activity when they get stuck or frustrated, allowing them to maintain a fresh perspective.

  • What was the speaker's attitude towards their day of work in the video?

    -The speaker expressed frustration for spending a significant amount of time searching for a mathematical factor but also acknowledged the value in the exercise for gaining a deeper understanding of the equation.

  • Why does the speaker apologize at the end of the video?

    -The speaker apologizes because they realize that not everyone may be interested in the mathematical details of their work, but they felt the need to discuss it as part of their daily vlogging routine.

  • What does the speaker suggest as a positive aspect of doing a theory internship?

    -The positive aspect is the flexibility to switch between coding and mathematical problem-solving, which can be a relief when one becomes too challenging or frustrating.

  • What does the speaker invite the viewers to do in the comments section?

    -The speaker invites viewers to share in the comments section what frustrates them about their field of work or what they enjoy doing.

  • What was the speaker's plan for the rest of the day after recording the video?

    -The speaker planned to spend a little more time working on their cone (likely referring to a specific project or problem) and then relax.

Outlines
00:00
๐Ÿง Frustration in Theoretical Physics Internship

The speaker shares their experience of spending three hours searching for a factor of four in a complex equation during their theoretical physics internship. They express the difficulty of keeping track of numerous mathematical elements such as integrals, tensors, and Fourier transforms. The video focuses on the derivation of a differential cross-section equation, which involves the transition amplitude, a quantity that is invariant and typically written in terms of the lepton tensor and hydronic tensor. The speaker discusses the challenge of understanding the convention used in literature, which assumes a certain level of familiarity with summing over states and the inclusion of a Delta function. They also mention the frustration of not having an intuitive grasp of the math and the process of identifying conventions that are not immediately clear to a newcomer. Despite the challenges, the speaker finds satisfaction in the deeper understanding gained from the exercise and appreciates the flexibility of being able to switch between coding and theoretical work when one becomes too challenging.

Mindmap
Keywords
๐Ÿ’กTheoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions to explain natural phenomena. In the video, the speaker discusses their internship in theoretical physics, which involves complex mathematical equations and concepts. It is the main theme of the video as the speaker shares their experiences and challenges in this field.
๐Ÿ’กFactor of Four
The 'factor of four' refers to a specific mathematical element the speaker was searching for in their work. It symbolizes the meticulous and sometimes frustrating process of solving equations in theoretical physics. The speaker mentions spending three hours looking for this factor, indicating the depth and complexity involved in their calculations.
๐Ÿ’กTransition Amplitude
Transition amplitude is a concept in quantum mechanics that describes the probability of a system transitioning from one state to another. In the context of the video, the speaker discusses this concept in relation to the lepton tensor and hadronic tensor, emphasizing its importance in the equations they were deriving.
๐Ÿ’กLepton Tensor
The lepton tensor is a mathematical object used in quantum field theory to describe the interactions of leptons, which are elementary particles like electrons and neutrinos. The speaker uses the lepton tensor as part of their equation derivation, highlighting its role in theoretical physics calculations.
๐Ÿ’กHadronic Tensor
The hadronic tensor is another mathematical construct used in quantum field theory, specifically to describe the interactions of hadrons, which are composite particles made up of quarks. The speaker's mention of the hadronic tensor illustrates the complex interplay of different particle interactions in their work.
๐Ÿ’กFourier Transforms
Fourier transforms are mathematical techniques that decompose signals or functions into sinusoidal components. In the video, the speaker discusses the use of Fourier transforms in the context of their equations, indicating their utility in analyzing and solving problems in theoretical physics.
๐Ÿ’กDifferential Cross-Section
The differential cross-section is a measure used in physics to describe the probability of a specific outcome in a scattering process. The speaker mentions deriving an expression for the differential cross-section, which is central to understanding collision events in particle physics.
๐Ÿ’กCoding
Coding is the process of writing computer programs to perform specific tasks. The speaker contrasts coding with their mathematical work, describing it as a different but complementary aspect of their theoretical physics internship. They appreciate the ability to switch between coding and mathematical problem-solving as a way to maintain productivity and avoid burnout.
๐Ÿ’กConventions
In the context of the video, 'conventions' refer to the standard practices or notations used in a particular field of study. The speaker expresses frustration with identifying and understanding the conventions used in theoretical physics literature, which can be non-intuitive for someone new to the field.
๐Ÿ’กIntuition
Intuition is the ability to understand or know something without conscious reasoning. The speaker discusses the lack of intuition for the mathematical aspects of their work, which can make it challenging to identify errors or navigate complex equations in theoretical physics.
๐Ÿ’กMatrix Elements
Matrix elements are quantities in quantum mechanics that represent the result of an observable for a specific transition between states. The speaker's reference to matrix elements in the context of the transition amplitude highlights their role in quantum mechanics and the calculations they are performing.
Highlights

The speaker spent three hours searching for a factor of four in their theoretical physics work

They discuss the challenges of not having a strong intuition for the complex math involved in theoretical physics

The speaker talks about the frustration of identifying and understanding conventions used in the field that are not conventional to them

They derive the differential cross-section in terms of the lepton tensor and hadronic tensor, leading to a deeper understanding

The transition amplitude is introduced as an invariant quantity, which is written in terms of quantities similar to the lepton and hadronic tensors

The speaker was trying to create a factor of 4ฯ€^3 out of thin air, which was missing from their equations

They explain the convention of writing the transition amplitude in terms of matrix elements, which was unfamiliar to them

The speaker mistakenly obtained a ฯ€^2 term instead of the full expression, but does not go into detail about the mistake

They express their enjoyment of being able to switch between coding and doing math on paper when one becomes too frustrating

The speaker contrasts the quantifiable nature of theoretical physics with the more ambiguous sources of error in experimental physics

They encourage viewers to share in the comments what frustrates them about their field or what they enjoy doing

The speaker plans to spend the rest of the day working on their cone and then relaxing

The video serves as a candid look at the struggles and thought processes of someone working in theoretical physics

The speaker provides a detailed walkthrough of their work deriving the differential cross-section

They discuss the importance of understanding the conventions and notation used in the field, even if it is not intuitive at first

The video highlights the value of persistence and attention to detail when working through complex theoretical problems

The speaker's candidness about their struggles and mistakes provides a relatable perspective for viewers facing similar challenges in their own work

The video emphasizes the importance of switching between different modes of thinking, such as coding and doing math by hand, to maintain productivity

The speaker's enthusiasm for theoretical physics and their willingness to share their thought process makes the video engaging and informative

Transcripts
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