# When adding up velocities, is it possible to produce 1+1=1?

1. Aug 1, 2009

### Duchovnik

Forgive me if the question sounds ignorant and petulant, but I am very curious about this and woefully undereducated in physics. I was browsing a debate board and the topic was whether or not logic is a human construct.

One of the arguments posited by someone was that everyone would logically deduce that 2+2=4, but that if you started adding up velocities under relativity you would get 1+1=1. I would just like to know if this is true or not.

It came from post #10 on this page:

http://www.4forums.com/political/worldviews/7480-how-do-atheists-account-laws-logic.html [Broken]

Appreciate anyone's time, and thanks for reading.

Last edited by a moderator: May 4, 2017
2. Aug 1, 2009

### hkyriazi

It seems to me that the "1+1=1 according to Special Relativity" statement is true. Think of Einstein's example of someone shining a flashlight on a train moving at almost the speed of light. (For the latter, it'd be something like 1+0.99=1.) But, I'm just an amateur physics enthusiast. I'd be curious what an expert in SR would say.

3. Aug 1, 2009

### Staff: Mentor

Velocity addition is, of course, something of a misnomer. 1+1 still equals 2, but if the velocity of something is measured as u in one frame, then in a frame moving at v the velocity of that thing is (u+v)/(1+uv/c²). This is obviously only equal to u+v in the limit of uv<<c².

It would be more correct to call it "velocity composition" instead of "velocity addition" with the understanding that in Galilean relativity velocity composition is simple addition and in Special Relativity velocity composition is the more complicated expression given above.

4. Aug 1, 2009

### Dadface

In addition to the above velocity is a vector and in classical physics when two vectors of numerical value unity are added vectorially(taking directions into account)the resultant vector can have any numerical value between zero(when the vectors are in opposite directions and cancel) and two(when they are in the same direction and add)

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