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?

Times Arrow by Arthur Stanley Eddington

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.

Plane doesn't fall
Plane remains in air with 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! 🙂


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Author: Paul Wandason

I love astronomy and science fiction, but I love my family more. So I love time travel too!

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