Peeter Joot's (OLD) Blog.

Math, physics, perl, and programming obscurity.

Why is the speed of light the limiting velocity that a particle can travel. Attempt to answer with (almost) no math.

Posted by peeterjoot on April 30, 2011

My dad asks

” I’ve googled some data about “c”, the speed of light, but found really no data about why this is the speed limit that a particle can travel. It is just stated to be so but no allusions ( except Einstein’s smoke and mirrors) were indicated as to why this was the case.”

Here was my attempt at answering.  I liked it and share it here.

For light itself, this is an observed quality.  Light in vacuum hasn’t been observed travelling at any other velocity.  There have been lots of experiments attempting to show otherwise, and none of them worked.  Where people get hung up is that they think of light as a thrown object, like a ball tossed out of a car window.  If you are (the passenger) in a convertible (let’s say this is a Porsche for fun) that is zipping down the street at 90mph, and toss a baseball at 50mph somebody on the sidewalk will see that ball travelling at 140mph.  If you through it backwards, an observer will see it moving at just 40mph.  We have lots of experience with “addition of velocities like this”.

With light, something that’s already tricky to measure because it is so fast, we don’t have a lot of experience.  However, when an experiment like this is done carefully, from a fast moving object, it is carries a light pointing in its direction of motion, an observer will see the light emitted go at the speed of light, regardless of the speed of the object.  If you imagine a rocket that’s moving at 1/2 the speed of light itself, it’s headlight emits light that seen to travel at c (not 1.5c), and it’s taillight is seen to emit light that travels at c (not 0.5c).  This is very different from the ball and the car example.

The way that I think of this is that the light was not, then is.  At that point of creation, it moves at speed c, but this motion is never associated with the speed of any nearby objects (ie.  this light at the point of creation was never carried by the object that’s travelling in its vicinity).

Since we have this phenomena that always appears to have a fixed velocity, we can use it as both a measuring stick and as a clock.  If light is bounced off of a mirror and returns (assuming that the delay for the interaction with the mirror is negligible), then if we’ve counted out the distance to the mirror (say d), then we would know that an interval of time 2d/c has passed.  Similarly, if clocks are synchronized at two points in space, with you standing by one clock and your buddy standing by another with an agreement to turn on his light at 12:00, and you observe that his light signal gets to you at 12:00:000003, then the distance between you is .0003 seconds x c = 90km.  The basic idea is that you can use light signals as a mechanism for both time and space depending on what you know.

What Einstein did was argue very carefully that there is no such concept as simultaneity.  Events that are simultaneous can be observer dependent and we have to alter the way that we describe time and space to account for this.  Light ends up having a place as a measuring stick for this new way of describing time and space.  When space and time and motions in space and time are treated carefully, to ensure that notions of time and distance are related to the observer and the observers own motion, there are some interesting consequences.

One of these consequences is that velocities don’t add like the ball and car example.  There is a very very small correction required, and if one were to able to measure the speed of the ball thrown forward over the front windshield of the Porsche, you would find that it is actually a tiny bit less than 140mph.  That correction gets bigger and bigger, as the speeds of the objects are increased.

If you had a rocket turbocharger on the Porche and was able to launch it into space at .75 c, and then tossed the ball into a turbocharged baseball pitching device that could propel it at 0.5 c, then you’ll see the ball moving at 0.5 c, but an observer will NOT see it moving at 0.75c+0.5c=1.25c.  It will actually be observed to travel at less than 1.0 c.  There is a lot of math involved and this can be thought of as Smoke and Mirrors if you like (and perhaps justifiably so since it’s not terribly easy math to learn), but again this is something that is backed up by experiment.  It takes a lot of care to measure things when interactions happen at such high velocities (velocities that are significant factions of the speed of light), but when you do velocities are never seen to add to more than the speed of light, regardless of the motion of the observed interactions.  This is why in a very real way: it has never been observed to be otherwise.


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