Relatively going back to the future with Doc Einstein

I didn’t join in the Back to the Future fun the other week, on Back to the Future day. I mean, when it comes to time travel, I can join in now. Right?

Packard: 1935. Building: 1932. Photo: 2015.
Packard: 1935. Building: 1932. Photo: 2015. Maybe.

It was a pretty cool series. I never saw the second one, but I saw the first and the third – the latter a couple of times. And I got to thinking. Can you actually time travel? Stephen Hawking says no – in a 1992 paper he proposed that, despite various possible exotic solutions in Einstein’s equations, the laws of physics actually prevent time-travel at macro-scale.

But that doesn’t stop us thinking about time. A lot of the way we think about time is actually to do with a collision between our perception and the laws of physics. There are actually several ways we can perceive and think about time. Only one of them is what our friend Dr Einstein knew about.

So time is just an illusion?

This darling of the pop-quantum set pops up, often. Apparently time doesn’t exist, it’s all in the mind. The idea flows from the way our consciousness operates – you know, six hours spent doing something interesting moves faster than six hours spent doing a maths exam. Or you can tick away the dull days, frittering and wasting the hours, only to find that ten years have somehow disappeared.

Mix that with pop-misunderstandings of the way quantum physics works (a conflation of the way the observation paradox is presented, versus the way it actually works) and the stage is set to suppose time doesn’t exist – it’s all in our minds. Right? Wrong. Yes, we have varying perceptions of the passage of it, and our sense of it passing is also informed by our memory. But this ‘personally conscious perception’ isn’t the time that Einstein knew about.

But at least you can travel through time like you can through space?

Not according to Stephen Hawking. Still, this is the quintessential core of every sci-fi time travel story, from H G Wells’ The Time Machine to Dr Who and, of course, that trilogy of movies that return to the future. And a lot more besides. But the idea has a few problems. One of them is that it violates the laws of conservation of energy. The other is a practical one. Remember that scene in Back to the Future III where they’re pushing the DeLorean along an 1880s railway track that ends in an abyss? According to Doc, the car won’t plunge because the bridge exists in the time it’s going to. Clever, right?

Actually…no. Earth moves – and fairly quickly (it’s whipping around the Sun at around 30 km/sec, the Sun moves, the galaxy moves…yah). Jump forward a century in the same spatial point, and you won’t end up rolling across a bridge. You’ll be in deep space – Earth is long gone from that spatial point. To travel through time properly, your time machine also has to be a space machine – something, in fact, that can travel through Time And Relative Dimensions In Space. I know what I said.

What time actually does according to Dr Einstein

Albert Einstein lecturing in 1921 - after he'd published both the Special and General Theories of Relativity. Public domain, via Wikimedia Commons.
Albert Einstein lecturing in 1921 – after he’d published both the Special and General Theories of Relativity. Public domain, via Wikimedia Commons.

Both the ‘pop-quantum’ and ‘science-fiction’ versions of time, generally, suppose that it is some kind of separate entity – one way or another. But it isn’t. Not according to Albert Einstein, who analysed the whole thing in his theories of Special and General Relativity, over a century ago. Space and time and entwined elements. Bend space with sufficient mass or energy, and the rate at which time passes shifts. Accelerate towards the speed of time – which is also the speed of electromagnetic energy – and the same thing happens.

Time, in short, is integral to the universe – and that’s why we refer to Einsteinian ‘space-time’. But there’s more. According to Einstein, we are moving through time at light-speed, as if down a road. The future, by implication, is determined: but more crucially, the rate at which time passes varies, depending on your relative velocity to each other (these theories were all about relativity…)

This stuff was worked on by several physicists before Einstein got to it, including Hendrik Lorentz. Einstein crystallised them in his theory of Special Relativity, coming up with:

\Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}

What this means is that if you’re moving at 99.999 percent of light-speed away from Earth, an observer on Earth (assuming they could see you through the diabolical red-shift) would note your time, relative to Earth time, had slowed some 246.947881351 times. This number – which varies by relative velocity – is known as the Lorentz number.

The critical thing is that this isn’t the same thing as your personal perception of time. In fact, you wouldn’t notice the difference at all – if you were moving away from Earth at 99.999 percent of light-speed, you’d personally perceive time moving normally. However, if you look at Earth you’d see time moving at nearly 247 times your rate.

The thing about it, though, is that time in all its relative ways presents as one-directional. Einstein’s equations solve equally well if you suppose time is moving in the opposite direction from the one we suppose. However, as Arthur Eddington suggested in 1927, time does move in the direction we suppose – not least because of entropy.

Quantum physics, too, shows that time moves in one direction only – that direction is fundamental to the one-way collapse of the wave function. However, what has physicists exercised is that quantum physics demands that the future is indeterminate. This doesn’t play nicely with Einstein’s determinism – and yet both theories have been proven to be right. The problem has yet to be solved.

Neither, however, quite allow travel in what we might call the DeLorean sense. I mean, being able to travel through time if you’re adding a velocity vector just 88 mph faster than your reference frame? That’s silly.

Copyright © Matthew Wright 2015

6 thoughts on “Relatively going back to the future with Doc Einstein

      1. I take your point in the article about our perception of time (slowing down when we’re bored etc), but the difficulty I’ve always had with the measured effects of time slowing down, the mathematcs, the clocks detecting it on board accelerating aeroplanes and so on, is how are we sure acceleration close to the speed of light isn’t affecting the mechanisms we use to observe and measure time?

        I always use a simple, some might say naieve example, of a steel ruler left outside on a hot day. The heat will make the ruler expand, but no one says heat affects spatial dimension. The kilometre doesn’t expand 0.00001 mm for every increase in degree celsius. But we observe changes to mechanisms, physical and molecular, at high speeds and say those mechanisms are unaffected; it’s time that is altering.

        In your reply, you’ve thrown me a curveball mentioning the collapse of the wave function. It means I’ll have to go and look that up on a Sunday morning when I should really be reading about New Zealand’s win yesterday.

        1. Oh – I can explain that now! In quantum physics, when a particle is in one or another of two possible states, once it’s observed the state becomes known. That is the collapse of the wave function, and it can ONLY happen causally – that is, going from an unknown to a known state. This is proof, therefore, that time must pass – and that it also passes directionally.

          The length issue is interesting. According to Special Relativity, at high relativistic speeds length (let’s say of a spaceship) appears to contract in the direction of motion, relative to an outside observer. This is known as ‘Lorentz-Fitzgerald’ contraction. According to Einstein, this is all relative – those on the spaceship won’t notice anything different. The equation for calculating the apparent shift of length is the same as that for calculating time – the curve is identical. It’s another indication of the fact that what we call space-time, really, is a single thing.

          I have to confess that I find this stuff a lot more interesting than NZ’s rugby!🙂

  1. So, what you’re really saying is, we need a faster DeLorean?

    And regarding time during a Math exam…I always felt time was speeding up with those, as I never had enough time to write down all the answers. Sociology exams, on the other hand…

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