∆ 3 How far to the Moon.

Measuring the distance to the moon without clocks or calculations.

(The 'super-moon' over Glastonbury Tor - Guardian News)

If you get caught between the moon and Apache observ-atory

I know it’s crazy..       But it’s true  ♫


Apollo 11 Dropping off a 'corner cube' reflector.

Light hitting the corner cube is sent back in the direction it came from...very handy.

The Apollo 11 astronauts left a special 'corner cube' mirror array on the surface of the moon, designed to reflect back any light received in the same direction that it came from.

You have probably seen how this odd effect works for yourself when you notice how your own reflection seems 'trapped' wherever you look directly at 2 mirrors meeting in a corner.

In the Apache Point Observatory in Sunspot, New Mexico (USA) they can calculate the distance from the Earth to the moon to millimeter accuracy by 'timing' the journey of a high powered pulse of laser light travelling from the Earth, off the Luna mirror, and back to the observatory.

 The highly accurate results obtained when doing this may seem to be a proof of the existence, measurement, passing, and practical use of time… But there’s a simpler way of looking at things…

Typically we would say the distance to the moon can be calculated by first ‘timing’ how ‘long’ it ‘takes’ a laser pulse to complete the journey from the Earth, to the moon, and back. (excuse emphasis).

 If we do this our clock might display say 2.68 seconds as the pulse is detected coming back from the moon. We then halve this ‘time’, 1.34, and multiply the result  ‘time’ by the speed of light, 300,000 kilometres per second…

  So we get an accurate distance from the Earth to the moon of 1.34 * 300,000 which equals 402,000km. (Around 250,000 miles  -  all values are approximate for simplicity).

 Given that the speed of the laser pulse is effectively constant (being the speed of light), the accuracy of this calculation, will depend almost entirely on the accuracy of the ‘clock’ used to measure the photons round trip. At Apache point observatory they use a cesium atomic clock because the vibrations within cesium atoms occur very rapidly ( 9,192,631,770 times per 'second') and at highly regular rate, and their effects can be accurately detected and counted.

 Seeing how time appears to be used completely indispensably and highly effectively in this highly scientific operation, seems to directly demonstrate that time really must exist, and must be genuinely measurable and tangible in some real way.   However, while this operation and its calculations seem to use, and prove time, we could get the same figure for the distance to the moon in far fewer steps, and without using anything that need be called a ‘clock’.

 To do this we just construct a special ‘light box’ containing two parallel and opposing mirrors. The device is set up so that the mirrors are exactly half a metre apart, and such that a particle of light repeatedly bouncing between the mirrors, causes a counter on top of the box, to be incremented by one as the trapped photon hits the top mirror.

This setup is of course generally known as an Einstein ‘light clock’. But, we call it a ‘Light Box’ here, being wary of casually using the word clock – and thus thoughtlessly stirring up the false logic, that just using the word clock counts towards a proof that time exists. If this was legitimate, then calling a stick a ‘wand’ would count towards proof  that ‘magic’ exists’.

Diagrammatically simplified, we can imagine a single laser creating and spiting a single pulse of light, one half of the pulse is trapped, constantly reflecting between 2 mirrors 1 metre apart - while the other half reflects between Earth and a mirror on the moon. In essence both light paths are the same, one is just longer than the other.

Counting the number of metres the trapped photons travel as they oscillate gives us a clear indication as to the number of metes the freer photons must also be travelling.

This may just seem like a simplistic way of explaining the actual Apache Observatory distance to moon calculations, but the difference is here I make no reference to a 'clock' or to the idea that there is a 'past', or a 'future', or a thing called 'time' that exists and flows between them. Whereas every typical explanation f this, and similar experiments, will infer that a 'clock' measures the 'time' the experiment takes - and this implies without saying - that time, and the past and the future all exist.


We could modify the light clock/box slightly so we could launch a single  laser pulse such that half its beam heads straight off for the mirror on the moon, and the other half is trapped bouncing between the opposing mirrors.

In this way as half the photons headed for the moon the other half would be steadily causing the light box counter to keep incrementing its display by ‘1’ on every round trip between the mirrors.  Because we set up the mirrors so the round trip was precisely 1 metre then the counter shows us directly, without any calculations needed, the distance in metres that the trapped photons have covered.

(In reality at Apache point they don't just send one or two photons, but around (four ?) a 'quadrillion' in a pulse just a few centimetres in length, of all of these photons only one or two may make it back to the detector.)

And of course, ignoring minute atmospheric or gravitational effects for simplicity, the distance the trapped photons cover is basically the same distance any other photons cover, in particular the ones heading to the moon.  Now we just leave the device running, but with the small addition of ‘light detector’ set up to stop the light box counter if any laser light is received from the direction of the moon.


Figure - As a Laser pulse travels to the moon and back, a trapped photon travels the same distance between 2 mirrors. Calibrating the mirrored device in terms of 'seconds', and expressing what happens in terms of 'time taken for the round trip' is misleading.

In this way, if we trigger of the device, the light box counter will very rapidly count up the total metres traveled by the light trapped within it. And stop, when light back from the moon is detected. So of course the display will simply show the total distance to the moon and back, in metres.  We can half this total distance for clarity, or better still, double the distance between the mirrors, so the distance indicator just shows the effective distance to the moon without us having to do any calculations at all.

 Is 'time' the same by any name?

 Now all of the above may just seem like a long winded way of describing the same experiment but with words chosen to avoid direct reference to time. But the difference between the two explanations of the same experiment are that the ‘timeless’ version doesn't claim to prove the existence of anything that is not directly observed...

While the ‘time’ based explanation suggests that ‘throughout the entire universe, as photons or anything else pass from one place to another, an invisible thing called ‘time’ also passes – from the future, to the past, in a fourth dimension (so to speak) - and it can be measured as it does so’! 


Timeless motion.

That the ‘timeless’ version works perfectly well - while only assuming that matter and motion exist, and can move and interact. It also shows very cleanly, that all we are actually doing is comparing two examples of motion, to get our final distance to the moon.

 We happen to be using light in our example. But if we could bounce, or ‘echo’ sound between Earth and the moon, and the opposing mirrors, or any other effect, or object, at any consistent speed, the experiment would still work.

 Critically, the timeless version also makes no mention of the need for a future or a past to exist for the operation to work, or for some ‘interval’ of time to pass… at the speed of light, through an infinitely thin three dimensional slice of four dimensional space time!  


Time-based motion.

The time-based example however first relies on counting the consistent oscillations of cesium atoms and then displaying, and naming, the count as ‘seconds of time passed’.

 The speed of light is then considered in terms of how far a photon travels ‘in’ a second – and a calculation based on how far light could have travelled ‘in the time’ - ‘taken’ gives a number in Km, that does indeed correlate to the correct distance to the moon.

 So the time based version gives the correct distance to the moon, but also suggests, implies, or assumes, that…


  • Time exists and ‘passes’.
  • Things ‘take’ time to move.
  • ‘Clocks’- ‘measure’ time.


And in doing this, it is also suggested that, ‘as time exists’, (and because certain four dimensional equations work), then…


  • The future exists,
  • The past exists,
  • The present exists as an infinitely thin, constantly changing  ‘3 D moment’ travelling though time at the speed of light, between the future and past.
  • Time is in some or other way, a fourth dimension.


… given that both versions of the measurement make sense and give the same answer, but that the ‘time’ based version seems to suggest the existence of a great deal of mysterious ‘things’ that are not seen, or apparently required for the correct figure to be reached, perhaps the extra unseen features of the universe it suggests should not be just accepted without further proof.

 (if you saw a ‘magic’ show you may come away with two explanations of what you saw. A –you just saw some skillful misdirection, B - magic exists. If A or B is actually true then that is the correct explanation. But having two possible explanations doesn't mean you can choose the one you like and declare it to be true.)

>> 05 The Arrow of time.