Undergrad Understand Relativity w/o Math: A Different Framework

[kent davidge]

Is there any way of obtaining the exact same theory of Special/General Relativity but using a completely different framework? That is, without manifolds, without vectors, etc...

 

[Nugatory]

Is there any way of obtaining the exact same theory of Special/General Relativity but using a completely different framework? That is, without manifolds, without vectors, etc...

"Any way" covers a lot of ground. I knew someone who wrote a complete recursive descent parser generator (BNF in, ALGOL code out) as a TECO macro. (I chose a more traditional programming language for this exercise).

But you'd have to do classical physics without those tools first, because SR builds on classical physics, and classical physics including electrodynamics without vectors makes about as much sense as my classmate's self-defined compiler compiler project.

As an general rule, if you see a physicist using math you can reasonably assume that they had no easier way of solving the problem at hand.

 

[martinbn]

Is there any way of obtaining the exact same theory of Special/General Relativity but using a completely different framework? That is, without manifolds, without vectors, etc...

Why?

 

[Dale]

Is there any way of obtaining the exact same theory of Special/General Relativity but using a completely different framework? That is, without manifolds, without vectors, etc...

With math it is always possible to do something in a more complicated way.

 

[kent davidge]

Why?

Because I'm almost giving up! Trying hard since end of last year and can't understand some fundamental stuff regarding manifolds

 

[Dale]

Because I'm almost giving up! Trying hard since end of last year and can't understand some fundamental stuff regarding manifolds

What source have you been using?

It will only become more difficult without manifolds and tensors, not easier.

 

[robphy]

What are your specific goals for understanding relativity? You may not really need manifolds from a purely mathematical viewpoint to understand the physics of special relativity, etc...

Sometimes “understanding” is not a linear sequential process... skip over what you don’t get now and move on... returning to the parts you missed later, if you need to and if you happen to be ready for it...

 

[Daverz]

Without vectors?! No. You can't even do freshman physics without vectors.

A lot of the physics can be covered without too much formalism. Some examples:

Hartle, Gravity
Dray, Differential Forms and the Geometry of General Relativity

 

[Sorcerer]

Is there any way of obtaining the exact same theory of Special/General Relativity but using a completely different framework? That is, without manifolds, without vectors, etc...

Special relativity was done before Minkowski got ahold of it and introduced Minkowski space, so I don’t see why you couldn’t get pretty much all of SR without all that.

A big chunk of it is here, by Einstein, and it’s all undergraduate math, and not even the hardest undergraduate math. http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdfBut good luck with that with GR.

 

[Nugatory]

Special relativity was done before Minkowski got ahold of it and introduced Minkowski space, so I don’t see why you couldn’t get pretty much all of SR without all that.

Yes, but without vectors?

A big chunk of it is here, by Einstein, and it’s all undergraduate math, and not even the hardest undergraduate math.
http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf

Is it any easier that way than using Minkowski space? The required math background is the same either way - you don't even need any calculus if the examples are properly chosen so we're comfortably in the realm of high-school math. For example: spaceship flies away from Earth at .5c for a year, turns around and returns to Earth two years after it left. How much time passed on the ship? Try solving this problem using the methods Einstein used in his classic paper (top of page 11). Now compare with the Minkowski approach: spacetime interval out is $\sqrt{3}/2$, spacetime interval back is the same, total time is $\sqrt{3}$ years.

 

[Sorcerer]

Yes, but without vectors?
Is it any easier that way than using Minkowski space? The required math background is the same either way - you don't even need any calculus if the examples are properly chosen so we're comfortably in the realm of high-school math. For example: spaceship flies away from Earth at .5c for a year, turns around and returns to Earth two years after it left. How much time passed on the ship? Try solving this problem using the methods Einstein used in his classic paper (top of page 11). Now compare with the Minkowski approach: spacetime interval out is $\sqrt{3}/2$, spacetime interval back is the same, total time is $\sqrt{3}$ years.

Oh, I’m not saying Minkowski didn’t make things cleaner or easier. Just saying you can get the theory just using algebra and calculus (and to be honest I find calculus easier than linear algebra, tensors and all the rest). As for vectors, I don’t see how you can escape vectors in physics unless you work only in terms of energy, and correctly if I’m wrong, in SR you’re STILL working with vectors (4-vectors) when talking about energy.

 

[Ibix]

Because I'm almost giving up! Trying hard since end of last year and can't understand some fundamental stuff regarding manifolds

The question is where do you want your complexity? You can hide it behind a standardised notation with standardised tools for manipulating it, or you can put it out front and handle it yourself. Sure, there's a learning curve for the tools (still climbing it myself), but it more than repays itself by saving you from errors trying to do the book keeping manually.

It's like using a spreadsheet instead of pen and paper. There's nothing you can do with a spreadsheet that you can't do with pen and paper, but there's a lot less room for transcription errors with the spreadsheet. Similarly, a single tensor equation is easier to grasp and quality assure than sixteen separate algebraic statements.

As @robphy says, skip the bits you don't understand and come back later.