## Time’s Arrow

“The Arrow Paradox” and “Time’s Arrow” work in space and time respectively and each have limitations. Can they be reconciled to allow time travel?

## Seen the movie?

When I watched “Clock Anti-clock” by Deepak Sharma (Paragravity Films) it made me think about an altered state of physics.

Just last week I stumbled upon a description of the “Arrow Paradox” (sometimes called “Fletcher’s Paradox”) which is a much more succinct way of putting what I think I was trying to get over!

In my earlier post there was a snapshot of a plane in flight. A photo, or snap shot, is independent of time because time is essentially reduced to zero duration. I made the point that physics must be behaving differently if there’s no time; the plane which we see in the photo is stationary in the air. Velocity is a function of time (and there’s no time in a snap shot), and with no speed there can be no lift.

With no lift the plane must fall (OK, admittedly this would be a velocity, or a reaction to the force of gravity (acceleration – another function of time)), but we don’t see that happening (or expect it). We assume that the plane will continue to carry on its original flight path.

## Now read the theory

The Arrow paradox follows a similar argument, using an arrow in flight as an example, and ultimately concludes that motion is impossible. It’s a clever argument – but flawed because we know that motion through space is possible.

## Mix and retreat

You’ve probably seen the link coming a mile off – The Arrow of Time and the Arrow Paradox.

The Arrow of Time is a basic model of time which says that time can ‘move’ only in one direction. There’s a brilliant video describing it here:

But does having a limitation on (the direction of) motion sound familiar? 😉

I’ve noticed that many authors play the H.G.Wells ‘trick’ and twist the space and time dimensions around when it comes to conjuring up a method for time travel. And I must admit that I have also played around with a few ideas in the past wondering that if space and time can be considered equal in terms of dimension then by space’s analogy we can think up some interesting temporal counterparts.

But I was interested to read a statement by Arthur Stanley Eddington (this is the astronomer who came up with the concept of Time’s Arrow):

“I shall use the phrase ‘time’s arrow’ to express this one-way property of time which has no analogue in space.” – Arthur Stanley Eddington

What does this mean for us then? That time is bound to a single direction whereas this isn’t true in space? I suppose this is nothing new – it’s our base position because it fits in with our everyday experience in life. We can walk to the bar, have a drink, and walk back home again. But we can’t go back in time and wish we hadn’t got into that bar fight.

Maybe the clue isn’t in the direction of travel within a dimension, but in exploring the number of dimensions. Space has 3 (“length”, “width” and “height” – which I’ll label here as “X”,”Y” and “Z” respectively) and Time has one (“time” – let’s call it “T”.)

Even if we move along only the X axis in space, we know that movement along Y and Z is also possible. These are at right angles to X and effectively constitute a move into imaginary space. And if that’s possible then moving in a negative direction is child’s play.

With time it’s different. Having only one temporal dimension means that we’re restricted to movement only within that dimension along that one axis (and apparently, only along one direction).

Given that string theory is able to come up with as many as 26 dimensions this seems a little unfair! How come time only has one?

According to superstringtheory.com time was introduced by Einstein as a dimension “…to describe an event in spacetime” – in other words, so that things can move (in space) and happen at a given time. Or in Einstein’s own words (possibly…) “…the reason for time is so that everything doesn’t happen at once.”

Of course, I’m not one to argue with Einstein (because that would require a working time machine… 😉 ) but I’d like to question his empirical approach where he’s constructed a set of parameters which describe what we have. Is there space (or time, *giggle*) to keep searching within string theory to find another temporal dimension?

Being at the back of the list, number 27, I expect it’s going to be tricky one to find. But that’s the thing when it comes to finding the secret of time travel, isn’t it? 😉

## A (Re)call to View

Time’s Arrow dictates that we cannot go backwards in time the same way that we can in space. This of course assumes that we can go backwards in space – though I’m sure that physics would take a funny turn…

Meanwhile, here’s the link to “Clock Anti-Clock”. If you recall, I mentioned this movie at the start of this post. Memory? Isn’t that the only way we can currently go back in time? 😉 (see header image!)

Enjoy! 🙂

Paul

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## Clock Anti-Clock – a time travel short movie

How does time flow in Clock Anti-Clock? Is there personal time, is it a matter of perception of time, or does time actually flow backwards?

Clock Anti-Clock is a time travel movie produced by Deepak Sharma (Paragravity) with the simple premise of a time traveler who meets himself. But there’s a twist…

I’ve only got one issue with this movie, and I only noticed it because it accentuates the first of a few of my thoughts when I watched Clock Anti-Clock: Is time personal?

It relates to the construction; when the character is experiencing a backward flow of time, he stares at everything running backwards; it’s strange, it’s unusual – it deserves a good look.

But why was no-one staring at him? Relative to their time frame he’s also walking backwards etc. and would be strange to look at. He seems to be in a personal time bubble.

## Personal time

In my post A Unique Signature of Time I alluded to the question: Is time personal?

In Clock Anti-Clock the question is very relevant because I think it explains a situation at the end of the film where otherwise there’d be a paradox.

We hear the door knob rattle. He puts his glasses on and from then on it seems that time runs backwards from around 12:00 pm. This is inside the room where we see the clocks going backwards, and also outside where he observes people walking backwards, taps dripping upwards, etc..

By the end of the movie we have a better perspective on what’s going on outside. The ‘experienced’ version of the character tries to open the door (causing the door handle to rattle), and realising it’s locked, walks away.

But here’s the thing: if time is running backwards for the guy inside his room and opening the door (to find no-one there) why hasn’t he seen the guy outside walking backwards back towards the door and trying the handle?

In other words, time appears to be flowing in different directions by the door – or at least, in different directions for each character.

I think it’s clear by the end of the movie we’ve figured out that it’s the glasses which cause the change of flow direction for time (though whether time actually flows backwards, or that things look like they’re going backwards can be questioned!). Since only one person can wear a single pair of glasses at the same time, it seems reasonable to assume that time is indeed personal and that there is a time bubble or something around our guy. After all – he’s still walking forwards whilst everyone else is walking backwards.

## The Perception of Time

The flip side of this is that no matter what direction time flows, we perceive it as forwards – rather like applying a modulus function on time ( -2 seconds becomes 2 seconds).

This already happens in physics; I remember a cretinous teacher who took joy in deducting a mark from me when I was calculating “work done”, given as force times distance. We were told that distance was measured positive from left to right, but in the example the force was applied to an object moving in the opposite direction, so I gave it a negative sign. Of course, this gave me a negative product, but since work done cannot be negative I applied the modulus and gave the final work done as a positive number.

Mr Cretin took a mark away because he didn’t even want to see the negative number in a work done calculation. I still disagree with him. But the point remains – having a closed mind and removing a negative sign completely, or being a budding scientist to be and applying the modulus are just 2 ways in which direction is made a non factor.

So why not with time? Maybe wearing these glasses “opens our eyes”!

(As an aside, you might like to read my guest post on the perception of time and its relevance in time travel on the Theory of Space Time blog.)

## Time running backwards

The question of time either being personal and acting under its own rules within personal space, or being perceived to be so, brings me onto my final point – time actually running backwards.

Time travel seems to be obsessed with moving from one point in time to another, but for the large part, time flows in one (forwards) direction. It’s often referred to as the “Arrow of Time” – a term developed by astronomer Arthur Eddington which basically says that there’s an obvious direction or flow of time reference: Wikipedia.

(Sometimes we experience time appearing to move backwards from the viewpoint of a time machine making a backward trip, but I’d suggest that this is little more than illusion – parked cars don’t really move backwards when we walk forwards alongside them, for example.)

So how does physics work when time runs backwards? For example, we saw in the movie a plane flying backwards because time flows backwards. But for the plane to remain in the air, complete with its aerodynamic design, surely physics must have changed to keep it airborne?

To the left is a snapshot of the plane in the sky. It’s not falling, yet it’s not defying gravity. The force of gravity is an acceleration so has a time term, but here in this snapshot time has simply been removed from the equation. Is the gravitational force now working in the opposite direction so keep the plane airborne?

Physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time. Reference: Wikipedia

In practice, I don’t know what this actually means and how that relates to the (macroscopic) plane, but I wondered further about the sign of time in vector physical equations. For example, velocity. Where speed (a scalar) is concerned only with how fast something goes, velocity is more specific; direction is also important.

Usain Bolt is the fastest human on the planet and ran 100 m in 9.58 seconds (reference: Guinness World Records). (That’s a speed of 10.43 m/s – he can run further in 1 second than he can fall if he fell off a cliff in the same time!) But Usain wouldn’t have won the Olympics unless he ran in the right direction – i.e. from the start line to the finish line. He needed to have the fastest velocity.

Where speed can’t be negative, velocity can (e.g. if Usain ran in the opposite direction). We’re back to my work done calculation here…where we can switch the sign for distance and come up with a negative velocity, can we not equally change the sign of time instead? We’d end up with negative velocity – and it would explain why everyone would be walking backwards…

## Personal, perception or actual?

So how is time flowing in Clock Anti-Clock? Is there personal time, is it a matter of perception of time, or does time actually flow backwards?

The more I think about this movie, the more intricacies I find. And getting someone to think can only be a good thing!

You can see more of Deepak’s productions on his website (paragravityfilms) and follow him on Facebook and on Twitter (@deepaktrivadi).

Paul

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