The Man Who Stopped Time-Travel

Time travel is much used in fiction, since H G Wells's excellent book about its possibilities. I suspect, when writers get a mental block or the budget is tight, it is rolled out as a way to kill an hour.

But does time does flow? Stephen Hawking thinks it does and invented imaginary time. The brief word on time is that it goes neither back nor forward. The elusive "atoms of time" don't exist. Time has no direction, and, since one can't determine a relative position of anything to anything at an instance in time, there is no such thing as an object accelerating or having velocity in the first place. Time is an interval, not an instance. It is the order of events that matter to us when we speak or consider or calculate time. Brilliant isn't it. So simple. Time someone came up with that explanation. Yes, its that man Lynds again. I wrote about Peter Lynds's work on time recently.

So, since time does not flow, one can't travel through it. Lynds stopped time-travel in its tracks.

Lynds' time is what passes when events transpire and, since what matters to us is the order of events, we perceive the illusion that time flows. When I rewind a VHS tape, it is like looking back through time. I am winding back through events, in reverse order. When I look at a photograph of past times, I am looking at what an order of events resulted in. Its about as close to time-travel I am going to get, if Lynds is right. It all stems from his notion that dynamic objects have no relative motion at any instance of time, only over an interval of time. Since instances of time for moving objects is undefined, time can't move forward or back, flow or vector at angles. It would be like dividing by zero.

Lynds says that it is fortunate that Nature choice continuity rather than certainty as the foundation of the Universe. Not knowing for certain where a dynamic object is, allows it to move in the first place. Einstein and Lynds would have some deep discussions about thought experiments, I think.

But back to Sci Fi and the loss of time-travel stories - no more Dr Who. But better stories in most films, I expect.

The excellent Battlestar Gallatica (TV) does not have risible aliens or time-travel stories. Just humans and satanic robots. Maybe that is why it is so good. It is not even set in the future; it is set in another galaxy at anytime.

When is a paradox truly beyond belief?

A paradox is "a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth". Now, key is the word "possible".

Victor Meldew in the comical One Foot in the Grace TV sit-com had the catch-phrase, "I don't believe it!" when he met something unbelievable or beyond belief. A birthday card said the same thing when I opened it on my fiftieth. It was funny because the paradox was self-evidently true.

Oscar Wilde said that a paradox was a 7-lettered way of spelling truth, and once quipped: "I can believe anything, provided that it is quite incredible". The special thing about a paradox is that one feels that if one chews on it long enough, some pearl of wisdom will emerge from the metaphysical mastication. A paradox tests our personal belief system.

Many people argue that intelligent design explains human existence better that evolution because evolution powered by the natural selection argued by Darwin and Wallace since the 19th century can't overcome the paradox of the cell. All life is founded on the cell. How did it evolve? It seems self-evident that a designer was needed. Moreover, how could complex organs such as the eye or the liver evolve? Evolutionists, argues that huge time periods enabled evolution, but much of mankind often can't comprehend such eons of time, let alone how natural selection works, so are deluded into crediting God as creator. God is a paradox: what created God, they ask? The meaning of life and how we got here - this blog digs deep. Let's surface for a moment...

Consider a race between a man and a tortoise that caused (and still causes) consternation after thousands of years. It can be argued that a man can't catch a tortoise in a race, if it is given a head start. This famous paradox is one of Zeno's from ancient times: the Achilles and the Tortoise paradox. Briefly, it says that a man who runs twice the speed of a tortoise, say 10 m/s, can't catch up to it after giving it a head start of 10 m. The reasoning goes that the tortoise moves 1/2 the speed of his pursuer. When the reptile has moved 5 m, the man will have reached the tortoise's starting point, but will be 5 m behind. This goes on for ever because the head start means that the tortoise is always a fraction(decreasing, but positive) ahead. An infinite series exists and it is maintained, the paradox assets, where the man will always be behind the tortoise, so can never catch it.

Today, using GCSE physics, an easy rationalisation is to state that the man (whose velocity is 10 m per second) will travel 20 m in 2 seconds. In 1 second the tortoise will travel 5 m, but be 10 + 5 = 15 m from the start position; so in 2 seconds it will be 20 m from the start. Clearly after 2 seconds, the reptile and man are the same distance from the start, and the man has caught the tortoise. So the paradox is refuted - well, at least for continuous and uniform motion.

Calculus and limits were popular mathematical "solutions". The notion is quite simply (and correctly) that a sum of infinite parts does not need to sum to an infinite number. As an analogy, 3.33 recurring aggregated 3 times sums three infinite numbers to a finite value of 1. As the competitors get closer to each other, the fractional distance from each other becomes less significant, tending to zero. It does not really address the fundamental issues that Zeno is raising though, just as the v=d/t manipulation doesn't. Anyway, Achilles catches the tortoise because the tortoise is big enough relative to the decreasing fractional distances to be caught in a particular time and space.

I think that young Peter Lynds's solution is the best explanation to refute the paradox. (Indeed I like the way he dismisses Professor Hawking's notion that time flows as just wrong, and imaginary time, as, er, imaginary!) The notion that there is an infinite series is artifice. Just because there are notionally an infinite parts to an apple does not mean that the apple is infinite; it is a matter of perception and what one is trying to measure at a particular moment. And a moment is an approximation for what matters to us. A moment with ones hand in boiling water is more significant than when it is not. The significance of the moment is the event of hand-scalding; the longer the moment, the worse the likely damage to tissue, and the louder the scream. As Lynds argues, time is an interval in Physics, not an instance. When we measure intervals of time, the paradox fails because the assertion that there are an infinite number of instances where the man and the tortoise have relative positions never happens!

It is interesting how the paradox does indeed challenge what we believe; what we reject and new ideas and concepts that we take on trust.

Zeno's arrow paradox seems so stupid at first, but that is what paradoxes are famous for. This one says that an arrow in flight does not actually move and can't move because at any instant of time it is stationary. Sum the infinite "instants of time", and you have infinite motionless. However, we all surely know that movement is about covering distance over a period of time, not about summation of imagined instance of time. The arrow moves not over an instant of time but a period of time. Even if an instant of time exists in reality (which I doubt), as framed the "paradox" is specious. I thought that before I read Lynds, but he explains it by simply rejecting the notion that an arrow is ever stationary during its movement, even for an instant. If instance of time for dynamic objects existed where they had relative movement, Lynds says, Zeno would be correct in saying that an arrow could not move and could not even start to move.

Speaking of arrows ... in Buffy the Vampire Slayer (TV Show), the heroine is told by a monster awakened after centuries of sleep that no arrow or spear forged by the hand of man can harm him. She shoots him with an anti-aircraft rocket launcher and blows him to smithereens, with the phrase: "That was then, this is now!"

A later blog is going to deal with a stunning outcome from Lynds' hypothesis: time-travel is impossible because time does not have direction and does not flow. Time is an interval during which an order of events takes place. Bad luck for Dr Who fans.

Had I come across Zeno's paradox 10 years ago, it would probably have bemused me. Today, I can furnish arguments that dismiss its power. I have education to thank for that, and a world of information and technology the likes of which the ancients could only dream about. I am grateful to paradox for stimulating my intellect and reminding me that the adventure that life is continues afresh each new day - quotidian hopes.

I believe in paradox. And that a person can outrun a tortoise.

Paper by Lynds, a Timely Solution to Zeno's Paradoxes.