Why is the speed of light an exception? (same to all observers)

  1. say you are in a car travelling at 60 mph, and another car beside you is travelling at 80 mph about to overtake..If a third really fast car was to zoom past at 200 mph (in a third lane), to me he is effectively travelling at 140 mph and to the overtaker 120 mph..

    But the speed of light would be the same to all of us, if a car travelling at the speed of light was to whizz past also...why? why is it an exception? and exactly at what speed threshold can we stop subtracting speeds like I did above? c-2 kph? c-3 kph?
  2. jcsd
  3. D H

    Staff: Mentor

    If you want, I can post the relativistic velocity addition formula. (Or you can google it.)

    This formula applies at all speeds, not just relativistic speeds. When both of the two velocities to be added are very small in magnitude compared to the speed of light, the relativistic velocity equation simplifies to the our everyday velocity addition rules.

    For example, you are a passenger in a car going 60 mph and you shoot a sling shot which sends a rock flying in front of you at 60 mph relative to you. A stationary observer on the ground will see that rock as going at 119.99999999999904 mph, not 120. That difference is so very small that it is essential 120 mph.

    There is not a special point at which one can stop adding velocities per our everyday velocity addition rules. What happens is that discrepancy between our everyday velocity addition rules and the rules per special relativity grows as velocities approach the speed of light.
  4. Or in a different sense. Einstein's theory of special relativity begins on the determination of synchronous events. He does so by introducing a thought experiment suggesting that if a beam of light is sent from position A to position B and reflected back again, while another beam of light is sent from B to A and reflected back again, that if they were to arrive simultaneously, than the events (clocks) are synchronized. Say that tA is the time at which the beam leaves A, tB similarly, and tA' is the time at which the beam is reflected from B. Then:

    tA - tB = tA' - tB and,

    2AB/tA'-tA = c

    Thus by definition, the speed of light is a measurement of synchronous events or of time itself. In our Universe, as we know it, the constant of the speed of light (c) is simply that, a constant. Everything else, including space, time, energy etc. is relative between observers.
  5. I am not a physicist but for years I was uncomfortable with this concept.

    No matter how much people said, "well it's a constant: distance/time = c," I was not satisfied. Common phrases such as, "it's based on our unit of measure," or "it's how we define things," did nothing to convince me.

    What finally gave me a comfortable feeling, as naive as it may be, was the concept of the fine-structure constant.

    When I think of this in my layman's head, it makes me think: If we were to change the speed of light, the interaction distance of various forces (EM, strong, weak, gravity) would change. If this changes then our sense of distance would change. If our sense of distance changes, then the way we measure speed changes, and in the end arrive at the same number, c. So changing the speed of light has no impact.

    It's kind of fun to think about how arbitrary our sense of distance really is. We could change our length scale and change the speed of light (compact our universe into an atomic nucleus). But with a constant fine structure we would never know it – the amount of time for information to travel a given distance stays the same.

    On the other hand changing the fine structure constant would change things, I believe it would make a change to our length scale or change our concept of time. My understanding however is that matter would then no longer be stable.

    I would appreciate if an expert repudiates/adds precision to what I am saying. I am a lowly engineer.
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