Homework Help: Reletivity question

This is a basic problem in relativity. To understand it with no math, you have to remember that relativity also "generates" (the word isn't correct because the effect would also exist if we hadnt discovered SR !) time dilatation and lenght contraction.

Where you think there should be different speeds, there is only one, and this is easily explained when you remeber those effects : the distance light has to travel is in fact a bit shorter and time is dillated.

Moreover, the well-knnown formula v(total) = v1 + v2 to add velocities is false in SR. vtotal = (v1 + v2) / (1 + (v1 * v2)/c²)

Sorry if my message is a bit confusing but it's 1.30am in France and i am quite tired :(

PS : Be careful, you cannot travel at the speed of light, and you cannot use SR in frameworks going at the speed of light.

 

Excuse me?

Let's say the spaceship is going past the person at .99C, than the light from the flashlight is passing the spaceship at the speed of light. The light from the flashlight is moving away from the "stationary" person at the speed of light also. That's why there is time dialation.

 

If you shine a flashlight on earth, you can measure it to be going exactly what we think it would go. If you do the same on a the moon, you would see it is the exact same velocity as it was on earth, yet the moon is not stationariy relative to the earth. If you understand the concept that the speed of light will always be going the same exact velocity relative to anything, you may be closer at understanding a lot of things.

Or, if you are drifting in space, you may feel as if you were stationary. You shine a flashlight and you measure it to be exactly what it is on earth. Yet, relative to certain stars, you could be going extremely fast.

 

Think for a second about the reason this is true. It does seem intuitively obvious because the low speeds we constantly deal with in every day life do behave this way, but is there any real reason to believe this is the way the universe should behave? Is it a priori (something you know independent of experience) or a posteriori (something you know because of experience)? It may be hard to accept, but it turns out that the Galilean addition of velocities law ([itex]v_{AC}=v_{AB}+v_{BC}[/itex]) is not independent from experience. We know we can add velocities only because it works so well in every day activities.

However, Einstein showed us that the Galilean equation for the addition of velocities is only an approximation. The way relative velocities truly compare in our universe is similar but not quite Galilean:

[tex]v_{AC}=\frac{v_{AB}+v_{BC}}{1+\frac{v_{AB}v_{BC}}{c^2}}[/tex]

Using this equation we can see that if observer C is moving 2 km/h relative to observer B ([itex]v_{BC}=2 km/h[/itex]) and observer B is moving 10 km/h relative to observer A ([itex]v_{AB}=10 km/h[/itex]) then observer C is moving extremely close to 12 km/h relative to observer A ([itex]v_{AC}{\approx}12 km/h[/itex]) since the speed of light is so large ([itex]c=1,079,252,848.8 km/h[/itex]), but as [itex]v_{AB}[/itex] or [itex]v_{BC}[/itex] gets closer and closer to [itex]c[/itex], the more the Galilean answer starts to deviate from the relativistic addition of velocities. And as you can see, if you fill in either [itex]v_{AB}=c[/itex] or [itex]v_{BC}=c[/itex] then [itex]v_{AC}[/itex] will always equal c.

 

just curious, why was this moved to the homework section? it didnt sound like homework to me..