# About time for a reflection

As I stood in front of a mirror a few days ago I saw wrinkles on the man in the reflection. Sadly the wrinkles weren’t from the mirror itself, but an unwelcome sign of my increasing age and my ongoing one-way movement along the time line.

I’m sure they weren’t there a few days ago…but what’s a few days in the scales of the infinity of time?

It got me thinking…

In a guest post I wrote a couple of years back, I commented that we perceive a reflected ray of light as an extension into and beyond that of the reflective surface. In other words, the reflection is a construct which our brain has put together. What this means for time and time travel is outlined in the full article on the Quantum Time Travel Institute.

In this post I’d like to revisit this idea of light rays and their parallels with the time line.

Admittedly this post is a little long as I briefly describe a couple of optical properties, but you can jump straight to the time travel bit here if you wish! (Time is a precious commodity, after all!)

## Commutative

Reflection is commutative – in the same way that the order of the factors in multiplication is irrelevant (e.g. 2 x 3 is the same as 3 x 2), the same can be said for the direction of a light ray. i.e. the angles of incidence and reflection are interchangeable.

Or to put it another way, the direction of the light beam can go along either pathway – from source to destination, and the vice versa.

Here’s a practical example: shine a torch at a mirror in the dark, and you’ll see an illuminated spot on the wall where the light beam from the torch has been reflected. Now shine the torch from the illuminated spot on the wall onto the same spot on the mirror, and the new reflected spot will be in the place where you were just standing. Source and destination are interchangeable!

Note that the same principle also holds true for refraction, where a ray of light (partially) enters another medium of a different optical density and follows a different direction.

## Total internal reflection

In optics there’s a condition called “total internal reflection” where a ray of light doesn’t enter and refract into a medium of a different optical density, but is instead reflected within the same medium as it’s source. More simply put, the interface between the two optical mediums becomes a mirror, even though this particular mirror can under other conditions allow light to pass through it.

Incidentally, this is the principle behind fiber optics – the light stays within the optic because it’s totally internally reflected (it doesn’t pass out of the fiber optic cable).

It’s also the principle that a certain 7 year old tried putting into practice by sticking a torch in his mouth and taking a leak in the dark to see if the fruit juice he’d just drunk glowed in the dark when it came out… I’ll let you conduct the experiment yourself if you’re interested in knowing the outcome…! ðŸ˜‰

## Critical angle of incidence

Between reflection and refraction there’s an interesting phenomenon.

As the angle of incidence away from perpendicular is increased, there comes a certain angle (the “critical angle”) where on meeting the second medium there is a line of light which is reflected along the interface. The light ray doesn’t bounce away, and it doesn’t penetrate through – it simply zooms of sideways! It’s explained well in Mr Cutlife’s Web Pages where I also found the image below.

Recall from commutativism (?) that the torch in the above graphic can be moved to the top of the picture and the rays would propagate downwards.

## And put it all together…

Now this is the juicy bit!

Let’s take that case third from right in the above image. The torch shines from the blue side, and the resulting ray travels along the boundary. But we know that light rays are commutative, so we can expect that if we now place the torch on the line between the blue and the white and aim it to the left, the ray of light will bend down and enter the blue.

Here’s the thing: at what point along the boundary (and how) does the ray of light change its horizontal direction downwards?

This is a paradox, because actually that single point is undefined – it can be anywhere at any and every point along the light ray. And further, what physical mechanism exists to cause the light ray to change its direction? It’s scientifically possible but (currently) inexplicable!

(My high school physics teacher tentatively suggested there’s a small irregularity on the reflecting surface, but I disagree – the effect occurs with a perfectly smooth interface.)

Arguably, the above paradox could be considered to be an inverted version of the scientific explanation of time travel mechanics in physics; there’s nothing in physics to say that it can’t happen, but we don’t know how it can happen – let alone know how to explain it!).

## Finally…the time travel bit!

Now let’s compare the line of light to the time line.

The time line is probably the simplest model of time that there is – that time progresses linearly from past, through present and into the future.

Many mechanisms for time travel in science fiction refer to a ‘river of time’ where it’s a little easier to visualise the flow of time in one direction. It allows for certain modifications and adjustment to the simple time line model, thus providing ways to allow time travel. For example, inserting loops and meanders into the river of time, creating eddies, or just getting out the river completely, walking along the river bank and jumping back in again.

(I’ll momentarily interrupt myself here to point out that moving away from the traditional time line has been discussed in my imaginary yet complex post post.)

In short, we have some form of time travel if we’re able to deviate away from the regular and unbroken) linear flow of time.

Using our light ray example, can a fiber optic be seen as a parallel with a time machine, causing us to jump out of a time line?

Such a time machine would maintain the basic principle of optical / temporal straight lines, yet provide a physical mechanism for the same net result as a departure from the linear condition.

## Timewarp – a change in reference

There’s another way we can add curves to our time line – by changing the viewing reference.

Now after a very complimentary comment on my post about complex time I do feel quite self conscious about my following example which this time, yes, I read from Stephen Hawking (“The Grand Design“).

This particular example examines the view which a goldfish has of the world whilst viewing it the confines of his goldfish bowl. The water and curved glass make straight lines outside of the bowl appear distorted and curved, but for the fish, that ‘means’ straight. That’s his reality and a question of perception.

(You might be interested to read my guest post on Mihir’s Theory of Space Time blog on the Perception of Time).

Perhaps we can imagine the life of a goldfish more readily when we see the wobbly shadow of a straight stick on the rippled surface of a beach. From the sun’s view, that wobble is a straight line because the dimension of (sand ripple) height is projected – and to use the Matlab programming term, squeezed – onto the 2D surface of the Earth; it becomes hidden in perspective. As our viewing angle changes, that third dimension comes of out hiding and becomes visible.

Going full circle and coming back to the mirror – or at least going on a trip to the funfair and visiting the hall of mirrors – we put ourselves into a kind of goldfish bowl; an altered state of fixed reference where normal images and lines appear distorted thanks to optical trickery and misdirection of rays of light.

If we consider travel between two points on that warped image, where they’re stretched apart if follows that travel between them will take longer. The inverse is true for points which have been compressed or squeezed together. Of course we know that these points aren’t really at differing spatial distances and the speed between them must be constant. Yet we see them differently.

But could we consider a possible explanation in having a change in local time to account for these differences in speed? This is covered in General Relativity.

Can we achieve time travel by changing our point of reference?

Like most things, it’s easier said than done. We can’t jump into the mirror and become the reflection, although we can certainly influence it’s behavior. And recall that a reflection, after all, is a construction from our own perception of optical rays of light based upon our knowledge that it always travels in a straight line. Maybe if it’s in our head we can totally immerse ourselves after all.

But perhaps our analogy with time may still hold.

Aside from the synergistic view, we can assume that the total travel time of all light rays must be equal to the sum of the individual components from all directions. By definition, the average speed will then be the baseline norm given with a flat mirror where all light paths are straight and parallel to each other. But if we could get a handle on local variances in the speed of time effectively trading moments of low speed for high speed (or vice versa depending on your point of view) then maybe time travel would be within our reach.

Oddly, this brings us back to the optic fiber based time machine I mentioned earlier. The paths of individual some rays of light will be longer than others, depending on the number of internal reflections it’s suffered. Whether all travel durations take the same amount of time, or that we simply cannot perceive the fractional differences in arrival speed from within the fiber is a question best directed to general relativity specialists.

Is there a future with optic fibers and warped mirrors as time machines? Or are these just some random thoughts from a wrinkly old man day dreaming in front of a mirror?

Paul

[lastcall]