General purpose thread where Kitty advises posters on whatever they ask

[Elok]

Hmm. So in this context, .55 + .55 = .8? How does that work? Does it have to do with the way time slows down as objects approach C?

[Ramo]

Slightly more than .5c + slightly more than .5c = slightly more than .8c.

And sort of. The basic idea behind special relativity is that the laws of physics are the same in every inertial reference system. Shift everything by a uniform velocity, and nothing changes (if I crash my car, my wind shield shatters whether you're inside or outside of it). In classical mechanics, you can relate two reference frames with a certain kind of transformation of the coordinate system called the Galilean transformations.

Einstein applied this principle of relativity to the equations which describe electromagnetism, and arrived at the conclusion that the speed of light in a vacuum is the same in every inertial reference frame. So if I'm moving at a different speed from you, and a light flash goes off, we see the light travel at the same speed.

Work you a little bit of algebra, and you can figure out a different (Lorentz) transformation between our coordinate systems, which affects spatial and temporal coordinates. This is where you get time dilation, BTW. Take time derivatives of these transformations, and you get expressions for how velocities transform.

Incidentally, the velocity addition law (for oppositely directed velocities u and v) is (u + v)/(1 + uv/c^2).

[KrazyHorse]

Inane physics question: if two objects collide while each traveling at a little over half the speed of light, they have a combined velocity greater than C, right? It's like an object traveling faster than light ran into a stationary object. Might there be any trippy side effect to "bending the rules" that way? Aside from the massive flash of light when the two objects crashed together at that speed, I mean, which would be pretty cool in itself. I'm thinking of Cherenkov radiation here (stumbled across its Wiki page a while ago).

No. In fact, the lorentz transformations allow you to derive a velocity transformation equation. This velocity transformation equation has the necessary property that given any two objects A and B each traveling at velocity less than c in some given frame of reference the velocity of B as viewed from somebody standing on A is less than c.

For your example we have that the velocity of one with respect to the other is

(c/2 + c/2)/(1 + (c/2)*(c/2)/c^2) = c/(5/4) = 4c/5 < c

[KrazyHorse]

Yes, I know Ramo answered but this is my thread.

[KrazyHorse]

The interesting case appears, with that velocity transformation equation, when you transform the velocity of an object traveling at c. In that case, all observers see the transformed velocity of the object as c as well.

The difference between the "Galilean transforms" where velocities simply add and the true Lorentz transforms was first directly observed in the Fresnel-Fizeau experiment of 1850, which I recreated as a lab project when I was 19. My partner and I were able to exclude galilean velocity transforms to 3 standard deviations and measure the speed of light to within 3% (under the correct lorentz theoretical framework) using equipment built for less than 2000$ and sitting on a tabletop. It is still one of the most elegant tests of special relativity.

[TCO]

I did 3-5 days for each of my written exams (one each on Stat Mech, Classical, Quantum and EM), a week for my oral exam and 2-3 weeks preparing my presentation and studying for my thesis proposal.

Great particular example. (Serious.)

Would you generalize it as advice? (per the question?)

[KrazyHorse]

I would generalize with the caveat that I am talking about solid 12-14 hour days in each of those cases. And an efficient learner at the wheel.

[Elok]

So, is there any way to "cheat" the speed-of-light limit in a vacuum? I'm guessing "no."

[KrazyHorse]

Not really.

[Krill]

Physics, breaking maths since 194...ugh, thanks Einstein.

KH, how long should it take me to learn to drive? I started to learn 3 years ago, and was starting to get OK at it, looking towards my test, but then I stopped learning when went to teh US for 5 weeks and then returned and left for uni. I'll have a care to learn to drive in over the summer from early July, but would it be possibly to have passed both the written and practical tests by the beginning of September?

[Theben]

When using neodymium magnets, about how much "pressure" from like poles being positioned towards each other would be necessary in order for one of them to realign?

[KrazyHorse]

When using neodymium magnets, about how much "pressure" from like poles being positioned towards each other would be necessary in order for one of them to realign?

Insufficient information given.

[KrazyHorse]

Physics, breaking maths since 194...ugh, thanks Einstein.

KH, how long should it take me to learn to drive? I started to learn 3 years ago, and was starting to get OK at it, looking towards my test, but then I stopped learning when went to teh US for 5 weeks and then returned and left for uni. I'll have a care to learn to drive in over the summer from early July, but would it be possibly to have passed both the written and practical tests by the beginning of September?

I passed my actual driving exam after ~25 hours practice. As long as there are no bureaucratic delays or minimum waiting times that should be plenty of time, as long as you get hold of somebody with a car who's willing to let you drive it.

[Theben]

Insufficient information given.

Okay, FE 2 100g magnets are set (+-)(-+) 1cm apart. Will the field generated be strong enough to force one of them to realign, and if so how quickly?

Hopefully that's all you needed. Assume no other forces are acting on them.

[KrazyHorse]

From a couple of quick calcs, no. Even though Nd magnets have low Curie point they have high BH. At room temp. you'd need the field of one magnet at the other to get you to ~BH/2 before the new "Curie temp under applied field" (not sure what this would be called) would flip the magnet. That stills seems too high.