Enter the Relativity Challenge

An anonymous reader writes "Any slashdotters wanna pick up a lazy 25,000 Euros? All you have to do is explain Einstein's theory of relativity in a five minute multimedia presentation. The Pirelli Group have laid down this 'Relativity Challenge' to anyone as part of the International Year of Physics. Entries close on 31 March 2005."

Comments

Like Dirty Harry said:

[R2.0]

"A Man has got to know his limitations."

I found mine in Physics 21 when we hit Relativity. I just flat out don't get it. I can do the math, and get the right answers, but I couldn't truly explain it.

Re:Like Dirty Harry said:

[Randolpho]

I had the same problem.

After several years of thinking about it, I've decided that the reason is because I kept asking "why".

I've never seen an adequate explaination for *why* a Lorentz Transformation is necessary and, since everything about relativity hinges on it, the entire theory breaks down for me at that point.

Of course, as soon as I finally understand why, I'll probably go "duh! of course!!!!" or something like that. ;)

Re:Like Dirty Harry said:

[Anonymous Coward]

It's very simple.

The speed of light remains constant regardless of the motion of the person observing it.

Let's compare how light is differnt than a physical object.

First, take an object (let's say a bullet). You have a friend standing still, while are you moving away from him at 500 glorps (arbitrary unit for velocity) per second. Someone fires a bullet in the same direction you are moving at 1000 glorps per second. Your friend will measure that bullet moving at 1000 glorps/s. YOU will measure it moving at 500 glorps/s since you are moving in the same direction. If you were going the opposite direction, you would see it as 1500 glorps/s.

Now a beam of light is different.

Once again you have a friend standing still. You are moving at 1/2 the speed of light. Someone sends a beam of light in the same direction as you are moving. Your still-standing friend will of course view light as going full light speed. The strange thing is YOU will also measure that same beam of light as going full light speed. Even though you are moving at 0.5c (relative to your "stationary" friend), light still will measure at full light speed.

It's not very intuitive, but once you understand what it means that light has the same velocity regardless of your inertial reference frame (read: difference in speed), the other stuff (slowed time, descreased width, and increased mass) can begin to make sense.

Re:Like Dirty Harry said:

[wowbagger]

OK, let's see if I can help.

Maxwell's equations of electro-magnetic theory show the speed of light in a medium to be determined by 2 properties of that medium. For vacuum, those two properties are fundimental constants - thus the speed of light is fixed.

Now, if I take a squirt gun with a fixed exit velocity and squirt it at you, the water will be moving slower if I am backing away from you and quicker if I am running at you. That fits with our day-to-day experience.

But for light in a vacuum that does not happen - if I now use a light-gun, you will measure the speed of all three beams of light (me backing away, me standing still relative to you, me running at you) as the same.

And curiously, so will I - I will measure the speed of light leaving my light-gun as the same, no matter what.

Now, the ONLY way you can get both my measurements and yours to agree is if things like length, mass, and time change based upon my motion relative to you - hence the need for the Lorentz transformation.

Then, you get into the "twins paradox" - Take 2 twins. Kick one of them up to nearly the speed of light. Wait till the other one has aged 10 years. Bring the high-speed twin back.

From the stationary twin's perspective, the high speed twin slowed down. From the high speed twin's perspective, the stationary twin (who wasn't stationary from the high speed twin's perspective) slowed down. Yet both cannot be true.

So Einstein reasoned out that the ONLY difference between the twins was who felt the acceleration - that twin would slow down.

But if I lock you in a box, you cannot tell if you are setting on a planet or in free space being accelerated - so gravity must be like acceleration.

That's GR in a nutshel.

Why

[GigsVT]

Einstein's work was already in very simple laymen's terms. I don't know what the point is in trying to make it into braindead powerpoint.

Twins Paradox

[jgoemat]

Numbers are for example, I didn't take the time to figure out the equations...

You can't just wave it off saying the one that experienced the accelleration will have their clock slow down. If you want to calculate how much less one person aged, you go by how long (time and distance) they were travelling at that speed. For example, if I accellerate to 0.999999c in about a year (I think that's about 1g accelleration) and travel 10 light-years and back, then 24 years will have passed on Earth (20 travel + 4 for accelleration), but I will have aged only about 4. If I undergo the same accelleration but travel 10,000 light-years and back, then 20,004 years will have passed on Earth, but I will still have aged only about 4. The accelleration didn't make time pass more slowly, it was the period while I was tavelling at high speed that made it pass more slowly. Take both examples together and the one would seem to have 4 years pass and the other would seem to have 19,984 years pass, even though they experienced the same accellerations.

This also leads to an absurd result from my point of view. I will have only seen 2 years go by, but I will have travelled 20,000 light-years. From my point of view I would have been travelling 10,000 times the speed of light. How can this be?

I think it has to do with contraction. Lorentz contraction is one thing I haven't understood, how you can measure the length of something that is going nearly the speed of light? Apparently, when you are going nearly the speed of light, everything else contracts in the direction of your travel. For instance, if you were going a certain speed and passed a meter stick, it would appear to be only 1 millimeter long, although a stationary observer by the meter stick would see it as 1 meter long.

Now as for how fast you are going, that is all relative as well. If I take off from earth and accellerate to 0.999999c for about a year and travel 10 light-years, I don't think I'm going 10 light years. Space and the galaxy will seem to contract along the direction of my motion. When I get 10 light-years in space, it will appear to me like I have travelled a much shorter distance.

Here's a more concrete example. Let's say that I pass Earth going at velocity V, which slows down time for me to 1/10th normal. Then I travel to a space buoy that you have measured from earth as 10 light years away. Not only will I reach that buoy in about a year, but I will think I have travelled much less than 1 light-year because space along my direction of motion has contracted. During that time, an earth-based observer thinks 10 years have passed. The reason that his clock doesn't appear to slow down for me is because I don't think he's travelling that fast. To me, he has travelled much less than 1 light-year because space contracted and I think it was in 1 year, so he is travelling much slower than the speed of light and subject only to minor relativistic effects.