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

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Discussion Overview

The discussion revolves around the concept of adding velocities in the context of Special Relativity and whether it is possible to arrive at a situation where 1+1=1. Participants explore the implications of relativistic velocity addition and the nature of velocity as a vector.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the validity of the statement "1+1=1" in the context of Special Relativity, seeking clarification on its truth.
  • Another participant supports the idea that "1+1=1" can be interpreted through an example involving a moving train and a flashlight, suggesting a relativistic perspective.
  • A third participant clarifies that the term "velocity addition" is misleading, explaining that the correct formulation involves a more complex equation that accounts for relativistic effects, specifically (u+v)/(1+uv/c²).
  • Additionally, a participant notes that in classical physics, when adding two unit vectors, the resultant can vary between zero and two depending on their directions, which adds another layer of complexity to the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of velocity addition in relativity, with some supporting the notion of "1+1=1" and others emphasizing the complexity of the mathematical formulation. The discussion remains unresolved regarding the validity of the initial claim.

Contextual Notes

The discussion highlights the limitations of terminology, such as "velocity addition" versus "velocity composition," and the dependence on the definitions used in different frames of reference. There is also an acknowledgment of the conditions under which the relativistic equation simplifies to classical addition.

Duchovnik
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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

Appreciate anyone's time, and thanks for reading.
 
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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.
 
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.
 
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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