Relativistic calculations - when to use them?

[Darth Geek]

This is less of a strict math problem than me thinking my online teacher is wrong. I will, however, format the question as per PF's requirements, and I think it should be in this forum because it involves my coursework.

1. The problem statement, all variables and given/known data

Essentially, when should I use relativistic calculations (considering gamma in equations like momentum, speed, length, etc.)?

2. Relevant equations

γ = 1/sqroot(1 - v^2/c^2), and dependent equations

3. The attempt at a solution

My teacher says that this should only be used for cases where "it makes a difference", and uses "like, 99% of c" as his example. I was given a problem on a quiz in which a particle was traveling at 16% of c, I used the relativistic momentum (I was finding the De Broglie wavelength), and got the answer wrong (presumably because I used the relativistic momentum). In the example the problem showed, it used the regular definition of momentum.

SO- who screwed up? My answer was wrong enough for it to be counted wrong, which pretty much justifies my argument. The value of gamma at 16.6% of c is 1.014, which I think is an appreciable difference (1.4 percent). At 50% of c, which my teacher also seems to be discounting, gamma is 1.1547. 15.5% is definitely an appreciable difference.

What do you all think?

[rock.freak667]

I think if you work out \gamma and it is approximately 1, you don't need to use relativistic equations.

[MeJennifer]

This is less of a strict math problem than me thinking my online teacher is wrong. I will, however, format the question as per PF's requirements, and I think it should be in this forum because it involves my coursework.

1. The problem statement, all variables and given/known data

Essentially, when should I use relativistic calculations (considering gamma in equations like momentum, speed, length, etc.)?

2. Relevant equations

γ = 1/sqroot(1 - v^2/c^2), and dependent equations

3. The attempt at a solution

My teacher says that this should only be used for cases where "it makes a difference", and uses "like, 99% of c" as his example. I was given a problem on a quiz in which a particle was traveling at 16% of c, I used the relativistic momentum (I was finding the De Broglie wavelength), and got the answer wrong (presumably because I used the relativistic momentum). In the example the problem showed, it used the regular definition of momentum.

SO- who screwed up? My answer was wrong enough for it to be counted wrong, which pretty much justifies my argument. The value of gamma at 16.6% of c is 1.014, which I think is an appreciable difference (1.4 percent). At 50% of c, which my teacher also seems to be discounting, gamma is 1.1547. 15.5% is definitely an appreciable difference.

What do you all think?
If the answer was correct in that you applied relativistic calculations your teacher ought to reward, not punish you, for that.

People are still wondering why after 100 years relativity is not mainstream. The answer is simple, because of the educational system. Youngsters can learn and understand relativity just fine if only they were taught!

[Barny]

I'm sure this changes between different teachers and the like, but we have always used relativistic calculations for anything over about 10% of the speed of light.


I suppose the limit where you draw the line can be context dependent, some problems can be more sensitive to these things then others, as well as sometimes perhaps the physics isn't altered enough to bother with a fully relativistic solution. However, I'd question my teachers/colleagues if they started doing classical mechanics or whatever at 0.5c.

[Gear300]

If you did your relativistic calculations right, then you should have gotten the answer right not wrong. Your answer is more accurate than when classically done.

[Darth Geek]

Thanks. We had been over relativistic effects in chapter 13.1, and this question appeared in 13.2, which is why I was confused about why the course was being so anal about it.

I'm questioning him too- the 1.4% that I used was quite a lot to dismiss in a measurement like a De Broglie wavelength.

And yeah- if only this were taught in schools and I didn't have to use an Apex (not) Learning summer course- thereby trying fruitlessly to do 2 semesters in 2 months. I think the educational system would be a lot better if it was stricter. I had to learn relativity and its effects (mathematically, and not counting my Trekkie fanatic background) on one day. 13.2- Atomic Structure, and 13.3- Fission and Fusion, also took one day. However this is nothing compared to the entirety of unit 12: Physical Optics (Diffraction and the like) being crammed into two days, including the unit test. I still feel that I understand the basic concepts of each of these. Physics isn't the incredibly difficult ordeal everyone makes it out to be.

OK. Rant over. I probably won't call the teacher on it since it's only one point out of 1.9 thousand, but I feel justified in that I was right. Thanks everyone. :)