Does the Lorentz factor aid understanding of SR, or obscure it?

[Trysse]

I had a look at a number of books that deal with Special Relativity.

Many, if not most, textbooks on the theory of Special Relativity introduce the Lorentz factor $\gamma$
$$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$
Different textbooks introduce $\gamma$ differently; some use it only as a shorthand to replace the mathematical expression above. Some introduce it with a historic reference to Hendrik Lorentz. And others again dive more deeply into how $\gamma$ relates to relative speed.

However, some textbooks do not introduce $\gamma$ as a distinct symbol. In these books the authors simply use $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ or $\sqrt{1-\frac{v^2}{c^2}}$ wherever needed.

And of course $\gamma$ pops up in many discussions here on PF.

So would like to know what you think:

If you were to write a textbook, would you use $\gamma$ or not? If yes, how? If you teach SR, do you use $\gamma$? Do you think $\gamma$ was helpful when you learned SR?

To me, the benefit of $\gamma$ is that almost everybody knows it. So when I say $\gamma$ everybody knows what I mean. I don't need to explain it. But I don't think it's helpful for understanding Special Relativity. I actually think it hides how special relativity works.

Do you have an opinion? Or is this a topic you have not yet thought about?

 

[weirdoguy]

I actually think it hides how special relativity works.

How? It's just a notation. Writing down this square root explicitly every single time is tiring. That's all to this.

EDIT: You've had similar thread about this: https://www.physicsforums.com/threads/lorentz-factor-in-textbooks-on-special-relativity.1078774/

 

[vela]

I use it mainly for the same reason @weirdoguy stated. It's a pain to keep writing the square root down, and not using it makes the equations look unnecessarily complicated. Another reason is that I find my students are notoriously bad at calculating things. If they can calculate $\gamma$ just once and use that value elsewhere, I'd wager it results in fewer errors than if they had to evaluate the square root in every single equation.

I'm not sure how using $\gamma$ hides how SR works. I think the best way to see how SR works is to write the equations in terms of rapidity.

 

[sbrothy]

Isn't it at the very core of SR? That velocities don't add but rapidities do?

How can you talk about time dilation and not reaching light-speed without the gamma-factor?

 

[Trysse]

How can you talk about time dilation and not reaching light-speed without the gamma-factor?

I am not sure if this was meant as a rhetorical question. But I think this is the right question to ask. I would reformulate it slightly:

Is the Lorentz factor i.e. the expression
$$\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$
fundamentally necessary to do the math of Special Relativity?

 

[sbrothy]

I think so yes. I'm not as strong in math but I think that was essentially what I meant. I can't remember the particular equation but it goes something like this:

γ = 1 / Sqrt[ 1 - (v2 / c2) ]

which looks suspiciously like yours!

EDIT: I'm just not so strong in Latex.

EDIT: But thinking about who I'm "discussing" with you're probably right. It was, in all likelihood, rhetorical.

 

[weirdoguy]

I am not sure if this was meant as a rhetorical question. But I think this is the right question to ask.

And the answer is yes, whether you write gamma, or write square root explicitly. You can't avoid it.