Prove 4 Vectors: Last Hope for Finding an Answer

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In summary, the conversation discusses the proof that velocity (dx^{i}/dt) is not a 4 vector, while du^{i}/ds and momentum are. The suggestion is to test the properties of a 4-vector using the formula \mathrm{d} \tau as a scalar, and dividing it by ds = cdt \sqrt{1-(v^2/c^2)}. This will result in the 4 components of U, which can be confirmed as a 4 vector.
  • #1
M. next
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In books, it is always posted that velocity (dx[itex]^{i}[/itex]/dt) is not a 4 vector. While du[itex]^{i}[/itex]/ds and momentum are 4 vectors.. But it is never proved.

How to prove this?? I am not finding anyway to it.

You're my last hope!
 
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  • #3
Thank you for the reply, but can you tell me which one to use? I mean which formula from the two links?
 
  • #4
Do not apply formulas - test the properties of a 4-vector.
If you do not know how a 4-vector transforms, then learn and revisit the problem of a proof later.
 
  • #6
Oh thank you! You mean that if I took the proper time and divided that by ds = cdt [itex]\sqrt{1-(v^2/c^2)}[/itex] I should get the 4 components of U. And I say that yes, these looks like (dA^0, dA^1, dA^2, dA^3) as in your link so it is a 4 vector. Right?
 
  • #7
sorry I meant if I took Ui and divided that by ..
 

What is the concept of 4-vectors?

4-vectors are mathematical objects that have four components and follow certain rules of transformation under Lorentz transformations. They are used to describe physical quantities in special relativity, such as position, momentum, and energy.

How are 4-vectors used in physics?

4-vectors are used to describe physical quantities in special relativity, such as position, momentum, and energy. They are also used in other areas of physics, such as quantum mechanics and general relativity, to describe the behavior of particles and fields.

What is the importance of 4-vectors in finding answers?

4-vectors are important in finding answers because they allow us to accurately describe and analyze physical phenomena in different reference frames. They also help us understand the relationship between space and time in special relativity.

How do 4-vectors differ from ordinary vectors?

4-vectors differ from ordinary vectors in that they have four components instead of three, and they transform differently under Lorentz transformations. Additionally, 4-vectors are used to describe physical quantities in special relativity, while ordinary vectors are used in classical mechanics.

What are the challenges in using 4-vectors for finding answers?

One challenge in using 4-vectors is understanding the mathematical concepts and rules that govern their transformations. Additionally, it can be difficult to visualize and interpret 4-dimensional space and time. Another challenge is accurately applying 4-vectors in complex physical systems and equations.

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