Relatively Fast Horses

I have written elsewhere about the balance between speed and accuracy when devising a scoring system for horseback archery.  I have also written about the application of Einstein’s special theory of relativity on the sport.  It’s time to put them together.

Lightspeed and Spacetime

Those who have read my previous articles on relativity (search for “Einstein” to read these articles) will recall that physics has shown through repeated experiment that c, the speed of light, is the same to all observers.  The usual demonstration of this is that if you stand on a train travelling at 100mph and throw a ball forwards at 100mph then the ball will appear to you to be going at 100mph but to somebody on the platform it is going at 200mph.  If you shine a beam of light, however, you and the person on the platform will both measure the light as travelling at the same speed: c.  .

Even in these ill-educated times I feel justified in saying that every schoolboy knows that speed = distance/time.  Since the two observers register the same speed but different distances (the person on the train only sees the movement along the train but the person on the platform sees that plus the movement of the train), it follows that they must measure different times for the ball’s travel.  It turns out that the faster you travel relative to somebody else, the slower time will pass for you than for them.  This fact has also been demonstrated repeatedly.  Methods include flying atomic clocks around the world and registering the fact that they measure different times.  More prosaically, the GPS system relies on special relativity.  The clocks in the satellites are set to run at a different rate from those on the ground to allow for the time-altering effects of relativity.  Without this adjustment satnavs would be hopeless: the tiny alteration in clock speed amounts to a change of about 10km per day.  (Most of this adjustment is due to the fact that time also runs differently under different strengths of gravity, but the speed of the satellites is also factored in.)

The corollary of the above effect is that space contracts at high speed.  If a moving and a stationary observer both see a photon (particle of light) travel from A to B then they will age on the speed (c) but disagree on the time (because their speeds are different relative to the photon).  They must therefore disagree about the distance traveled.  Experiment and theory agree: as you move, space becomes shorter in the direction of your travel.  Like time dilation, this effect is basically non-existent at everyday speeds but gets bigger close to the speed of light.  In a calculation that seems to make a mockery of the very concept of lightyears as a unit of distance, it can be shown that if we were to go at 99.9999999% of the speed of light we could travel 3 million lightyears (the distance to the Andromeda galaxy) in 50 years.  This is because the distance between us contracts at those high speed.

The general theory of relativity combined space and time into a single entity called (not very imaginatively) spacetime.  The predictions made by this theory have been confirmed so often and in so many different contexts that it must be considered the closest thing to “fact” that physics currently has about reality.

Can’t We All Just Agree?

The mathematics of spacetime provides a solution to the seeming chaos of time and distance being so malleable.  The solution is this: although different observers will disagree about time and space, they will agree about distances in spacetime.  This being the case, the week also agree about speed in spacetime.

Through a piece of mathematics that is a little beyond what I want to call with while typing on a touchscreen tablet after dinner, it can be shown that the relationship of time dilation and observed speed fit together in spacetime to demonstrate that everything, from photons to the stars that emit them (and everything in between, including you and me and, crucially to the title of this piece (which you have probably forgotten, given how loosely it connects to the subject matter), horses) travels at the same speed.  Thus we get to possibly my favourite physics fact: we are all traveling at the speed of light.

WTF?

You read that right.  We are all moving at the speed of light.   More correctly, we are all moving at speed c.  The reason we don’t notice that is that we are moving through spacetime and we use our allocation of speed through space and time differently.  If you sit still, i.e. you don’t move in space, them you move through time at the speed c.  If you are a massless particle such as a photon then you move entirely in space and time does not pass for you at all. If you move at any lesser speed through space then your movement through time is such that your total speed in spacetime is c.

Fast Women and Slow Horses

George Best, a successful footballer and notorious drinker, once said “I blew a lot of my money on slow horses and fast women.  The rest I just squandered”.  Many horseback archers would sympathise about slow horses, having missed out on speed points.  I shall make no comment about fast women and horseback archers…

Technically speaking, there are no slow horses.  There are just horses that travel more in the time dimension than others.  A fast woman is presumably one who will go further while time seems to pass more slowly. 

I’ll leave it there…

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Technically, all three of these horses are traveling at the same speed…

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