Calculating Apparent Speeds of Objects at Light Speed

[you878]

I've noticed that when driving down a road, cars passing in the opposite direction appear to be going much faster than if viewed from a stationary position. I asked my friend how you could calculate how fast the other car appeared to be going and he said you just add your speed and the other car's speed.
I thought about this, and then had a question: if one object was going 75% the speed of light and an object going in the other direction was going 75% the speed of light as well, the apparent speed of the other object from the view of the first object would be 150% the speed of light. Since I know this is not possible, something has to change, but my friend is certain about his answer. What is the change?

 

[alphawolf50]

Your friend is wrong :)

If there are two ships, A and B, and they are traveling at .75c relative to a stationary observer C, then both A and B believe they are approaching the other at .96c. The formula is:

$$v=\frac{w - u}{1 - wu/c^{2}}$$

in other words (btw, since we're using "natural units", we can simpify the speed of light to 1):

$$v=\frac{.75 - (-.75)}{1 - (.75(-.75))/1}$$

Which simplified is:

$$v = \frac{1.5}{1.5625} = .96c$$

More on this here:http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html"

And here: https://www.physicsforums.com/showthread.php?t=16948"

 

[seto6]

well your friends is somewhat correct WRT very low speeds... when speed is fraction of c then galileo's works goes crashing and special relativity comes in.

 

[JDługosz]

he said you just add your speed and the other car's speed.

On another thread in the recent past, I posted the result of adding 60 MPH and 60 MPH using the full relativistic formula. It's so close to 120 MPH that a regular calculator won't show the difference. Try it yourself using the formula posted in this thread. See how the "normal" way is close enough at human scale speeds, and why it's silly to make it more complicated in this regime?

 

[pmacias]

Your friend is correct in that the apparent speed of an object can be calculated by adding your speed and the other object's speed. However, this calculation only applies to objects moving at speeds much slower than the speed of light.

According to Einstein's theory of special relativity, the speed of light is the maximum speed at which any object can travel. This means that no object can travel at a speed greater than the speed of light, including the apparent speed of an object.

In your example, if two objects are both moving at 75% the speed of light in opposite directions, their apparent speeds from each other's perspective would not be 150% the speed of light. Instead, the apparent speed would still be less than the speed of light, but it would be distorted due to the effects of relativity.

In order to accurately calculate the apparent speed of an object at the speed of light, you would need to use the equations of special relativity, which take into account the distortion of time and space at high speeds. These equations show that the apparent speed of an object at the speed of light would actually be equal to the speed of light, regardless of the observer's perspective.

So, in conclusion, the change that needs to be made in your friend's calculation is to take into account the effects of special relativity when dealing with speeds close to the speed of light.