## About time for a reflection

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

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…! 😉

## 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

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## Quantum or steam powered time travel with a kettle

A watched kettle never boils. Does this make it a quantum or even just a steam powered time machine?

A watched kettle never boils. Does this make it a quantum or even just a steam powered time machine?

That said, the kettle in our work kitchen takes ages even when you’re not there to grow old with it.

Indeed, the kettle takes so long to boil I may as well go off and make a cup of tea whilst I’m waiting for the water to reach boiling point.

Many colleagues walk away whilst it hopefully brings the cold / tepid water inside to boiling point, and come back later to make their drink, but this brings about a moral dilemma; when I get to the kitchen to make a tea and see a kettle recently boiled and still full of water I’m faced with two options: first (and the most polite) is to hang around indefinitely until the person who switched it on comes back for his water, or secondly, add more water to the kettle so that there’s enough for both of us, and switch it back on again.

But this means another long wait.

Personally, I go for the third option – take the water. I kind of think that if you can’t invest time in a good cup of tea, then you don’t deserve it and deserve to wait until those of us who do are ready.

I wonder if people of the future would have a similar dilemma if they saw a time machine parked outside and no-one there to use it…

Paul

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## How to move a time machine

A time machine needs to move itself in time as well as its inhabitants because otherwise it would be a portal. But how does it do that without bootstrapping?

One of the most commonly asked questions in time travel would probably be – Is time travel possible, and if so, how do you build a time machine to transport the occupants to another time?

I’ve got another question which I think should also be considered: How does a time machine move itself (in time)?

For a time machine to work it needs to move itself in time as well as its inhabitants because otherwise it would be a portal of some ilk which requires a similar device at the ‘other end’. In such a portal, a temporal field modifier (or whatever!) is generated by the device and applied to the time traveller to be. But in a ‘regular’ time machine, the force is generated internally and applied to internal occupants, moving both time traveller and machine.

But the idea of a time machine moving itself is almost a literal example of “bootstrapping” (though paradoxically, not a paradox!). Bootstrapping is a little bit like living in the ‘cartoon world’ where Newton’s third law doesn’t exist (“For every action there is an opposite and equal reaction”).

This is where you can sit on a yacht and blow yourself along, or as the name suggests, lift your whole self up by tugging on your boot laces (or straps). Or, as it would seem here, lift a time machine into another time by using an internally generated force.

Further, if a time machine remains moves through time then it is effectively present in space through all of the intermittent time steps between the moment of departure and the time of arrival. You’d think this would increase the chances of us coming across a time traveler (or at least his time machine), though they seem to be in short supply…

But maybe there is a paradox. Saying that a time machine will take you some place else in time but not actually move itself it much like saying you’ll get into a car which will take you somewhere, but it doesn’t move itself because it has no wheels. (Come to think of it, that does sound like my own car!).

So we’ve some full circle; a time machine needs to be transported. But how?

Paul

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## Journey or destination

Some time travel novels focus more on the journey to another time, and how it’s done, than the destination itself. Other novels focus only on the “when” and pretty much ignore the time *travel* element. Which kind of novel works best?

“It’s not about the destination…it’s the journey”

Sometimes I think this is especially true for time travel novels.

## The “Journey novel”

I absolutely love The Man who Folded Himself (…the book ;)) which primarily focuses on time travel paradoxes and various complications arising from them. The journey through time and its implications are central to the read.

Running in the same vein are novels which focus on the actual mechanics of time travel itself.

These journey novels have the juicy stuff and work to separate time travel novels from other genres.

## The “Destination novel”

On the other hand, I was extremely disappointed with Time and Again where someone goes back in time and pretty much nothing happens after that. The Mirror is a similar example of a time travel novel where nothing happens.

In these destination novels time travel is used to get a character into a different period and the historical or futuristic setting is described. The story is based in that period and the time travel takes a secondary role at best. It’s barely more than a scene setter.

This kind of book is interested mostly in the temporal destination and I don’t see how these destination time travel novels differ from a ‘regular’ novel. For me, these books aren’t ‘real’ time travel novels. (And I must admit to finding them rather dry, descriptive and not interesting…as you’ll see from my ratings.)

Time and Again could have missed out the time travel element and have simply taken place in its entirety in 1882 New York. Whether the character started out in present day New York and went back in time to 1882, or whether the book started off with “Once upon a time there was a man in 1882” makes no difference.

The destination novel can be about anything. It can use a time machine to go back (or forward) in time, or a car or plane to go to another place. The temporal and spatial mobility devices serve only to change the setting…from somewhere/when to…who really cares?

## Preference

So for me it’s clear – I need time travel in a time travel novel to be more than a transporter. Some level of thought into the time travel element. But at the same time, would reading a novel concerned only with the nuts and bolts of time travel be like reading an instruction manual for a car, for example? Or is it chavvy to obsess about a vehicle and not care where/when it goes?

Characters must surely do something during or after their journey. I had a friend at university who was studying French. We used to tease him that without learning about anything else, he could go to France but do nothing. I think it’s a bit the same with time travel novels; you can go back to the past or forwards to the future, but once there surely something needs to actually happen.

So a bit of both, then. I like the science, the nuts and bolts, complications – and philosophy – of time travel…but given all of that, something actually needs to happen too!

Paul

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## Time travel warning

Cartoon with a warning for time travellers – take note!

A warning for time travellers!

Paul

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## Time is money? No…it's greater!

“Pay me peanuts and I’ll work like a monkey.”

I recently started a new job; they pay me peanuts, but it’s worth it. Why? Because it’s research in a fascinating subject and not an unchallenging position where I’m reduced to clock watching. (Please note I’d like to think that I’m capable enough to perform this work with a greater statistical likelihood than an infinite number of monkeys producing the works of Shakespeare 😉

My previous job was a bore. I’d sit in the office staring at my watch just waiting for the tedious hours to pass. Waiting to spend my time in the way I want it, where I wanted it.

Was spending 8 hours a day like this worth the money?

At the time I thought it was, but from my new present position I must say that I have really learnt that time spent wisely is worth so much more then money. Money can be hard to come by, but it’s even harder (for now) to get more time.

For now, I love what I do…but I still wish someone would hurry up and invent that time machine!

Paul

## Watch the time machine!

Place a thermometer into boiling water, and it will read 100 degrees centigrade. Now plunge the same thermometer into a bucket of ice. The difference in temperature is (at least) 100 degrees, but there is a lag with the thermometer reading. It won’t immediately read 0 degrees, but it will go through the intermediate temperatures (albeit quickly) from 100 degrees, down to 0.

It can easily be argued that the thermometer is in part reading the temperature of itself – it’s own internal temperature, rather than the true ambient temperature.

Keep this in mind as we take an instantaneous journey through time in a time machine…

In an earlier post I demonstrated how the progression of time through space is instantaneous. But how does time progress in a time emachine?

Consider this. A person goes in a time machine and is instantly placed from the present to say 100 years into the future (as far as “instant” is possible…let’s call it experienced time).

Will the watch he’s wearing read t = 0 and instantly transform to t = 100 years? Or like the thermometer, will it pass through all the intermediate times like the thermometer read intermediate temperatures? Will he?

It might seem that a watch, by changing from one state of time to another, intrinsically needs to go through the intermediate times. But this implies a non instant travel. It sounds a little paradoxical that instant time travel means travelling [instantly] through all times in between!

Alternatively, does the watch measure the moment of ambient time, such as a GPS receiver ‘checking in’ to a satellite clock signal? Or does it measure the progression of experienced time?

I mentioned that this particular time machine operates instantaneously. That is to say that the “experienced time” is zero. Ambient time, therefore undergoes an instant change. This raises the question of how is an instant change in time possible?

Let’s pause for a moment on a slight detour and consider a well known thought experiment. On a train.

A train is traveling at a constant speed of 125 mph towards the west. A fly is buzzing in exactly the opposite direction, on a collision path with the train.

The collision inevitably takes place, and I think it’s fair to say that neither the train or the fly are aware of the event.

Now let’s consider the movement of the train and the fly.

The train is moving to the west at constant speed, collides with the fly, and continues its movement to the west (with a very slightly reduced velocity owing to increased combined mass with the fly).

The fly was flying towards the east. It collides with the train, then moves with the train towards the west. This means that the fly’s velocity changes sign, i.e. it goes from an arbitrary positive, through zero, to negative.

At the moment that the fly had zero velocity, it was in contact with the train. It might seem logical to assume that the train must therefore also have a zero velocity…but we know from experience that this is not the case.

We have therefore defined an infinitesimally small moment in time, but how to explain it? (Aside – this is the great thing about time travel – one question leads to another! 🙂 )

I was spinning on a roundabout with my daughters last week trying not to retch. They were fine; they were sitting near the middle, whereas I was on the outer rim. How was it possible that I had a greater linear velocity than they, and yet we were all in contact, much like the fly and the train?

The clue is that we were sitting on the same roundabout, undergoing the same angular velocity. Even the infinitesimally small point in space in the dead centre…was still rotating at the same rate as the rest of us.

And there it is. Angular velocity. I suppose that it’s not for nothing that people talk about the wheel of time! 😉

So back to our question of how is local ambient time experienced in an instantaneous time machine. Could it be that the local time is compressed or contracted to a point of ‘zero time’, (not to be confused with t = 0, an arbitrary reference time point) and regrows back to a new time? This zero time point would be analagous to the ‘fly point’ of zero velocity, or the zero space point on the roundabout.

Progression along the radius of the roundabout maintaining constant angular velocity showed that these zero points are possible. How that can be translated to time, or get it to regrow again…well there lies the magic of a time machine!