Classical physics States that at the present moment one can predict the future and reconstruct the past. New scientific work shows that this is not always the case, and it’s not the limitations of our knowledge or are not sufficiently powerful computers. The universe ceased to be predictable enough three black holes.

Details are set out in the scientific article published in the journal Monthly Notices of the Royal Astronomical Society.

Into the future and back

the laws of physics, whether the equations of classical mechanics or General relativity, describe how the system state changes with time. They allow us to know in advance what kind of second after the throw hits the ground or a stone where there will be planets in the Solar system in a thousand years. These patterns help to look not only into the future but into the past.

for example, Consider the movement of Mars. We have the same success can serve two purposes. First, you can take his current position for the source and calculate where he will be after the Millennium. Secondly, you can take for the initial data coordinates of Mars from March 26, 3020 and figure out where he was for a thousand years before. As a result, we must obtain its current location. This is a key property of physical laws is called the reversibility of time. It mathematically follows from the formulas expressing these laws.

Power of chaos

this is the case, if all the required data are known with absolute precision. However, in reality this does not happen. Every instrument has measurement error. It can be incredibly small, but it will never be strictly equal to zero.

what this means? The answer depends on what kind of system we investigate.

suppose, for example, it consists of stars and only orbiting her planet. Such a pair behaves very predictable. If we know the current position of the planets with an accuracy of, say, up to a meter, and the future of her whereabouts at any time time we can calculate with a similar error. And if you take these future coordinates for the original data and the “back in time”, we get the current position of the planet with precision again to a meter. In other words, a small error in the knowledge of the present has equally small error in the forecast for the future.

But there are systems that behave much more unpleasant. Differences from the forecast caused by inaccuracy of initial data, is increasing over time, and extremely quickly (exponentially). In the end, even a tiny error in the measurements leads to what is predictable is only the near future. Such systems are called chaotic, and the phenomenon of dynamic chaos.

that is why weather forecasts are really accurate only when done for the next few days. An inevitable error, which meteorologists measured the desired quantities, make forecast for the month ahead is a waste of time. During this time the behaviour of the atmosphere over our heads is certainly drastically deviates from the calculated one, and no one knows in what direction.

of course, forecast with precision “finger in the sky” does not allow to demonstrate the reversibility of time. Taking as a starting point is the future and with the help of calculations “rewind time back”, we hardly come to the current state of the system. This is not surprising, because the real future will probably be quite different, but what remains a mystery.

it Turns out that in chaotic systems the reversibility of time is not executed de facto. But, perhaps, still hope for a more precise measurement instruments and more powerful computers for calculations? In the end, the Universe less than 14 billion years old. If the period for which you can look into the future and the past, was able to increase to this value, then the dynamic chaos would not be a hindrance in treatment time, even for astronomers. What can we say about the scientists working with smaller temporal scales.

Such ambitions, however, does not can be realistic even for the next century. Now experts have shown that this problem is unsolvable in principle. For fairly simple systems exhibit unpredictability (and, hence, the irreversibility of time) on scales of tens of millions of years. The latter, in astronomical terms, the term is quite modest. To avoid this effect, it would take precision measurements above the limit apparently set by physical laws.

Black holes don’t want to be predictable

the authors of the new research work was to model the motion of three massive black holes that are subject to the gravity from each other.

One simulation began with the fact that the body was in motion towards each other. After complex motion one of the black holes leaves the company, leaving the remaining two to enjoy fellowship with each other.

In the second simulation, these results were taken as a starting point. Astronomers tried to track the evolution of the system backwards in time and to come to the state, which began with the first simulation.

But there it was. Even the calculations accurate to tens of decimal places helped to step into the same river twice. For example, if the system was given to the evolution of 40 million years or more (and it is a hundred times less than the age of the Sun), the differences between the starting state of the first simulation and the final state of the second was noticeable, that is, to the naked eye.

the Researchers varied the parameters of the system, trying to understand, what precision is needed for the reversibility of time. In other words, how to make video simulation (predicting the future) has given such a correct prediction that the inverse simulation (healing the past) would return from this forecast to the starting point. And it turned out that in 5% of cases the answer is disappointing: such accuracy do not exist.

namely, this would to measure the coordinates of objects with an accuracy of less than the Planck length (about 10-35 metera). By the way, this value is as many times smaller than an atom, how many times the observable universe more than a two-story house.

moreover, many theorists believe that the Planck length is a kind of minimal bit of space. In other words, smaller distances is basically impossible.

However, these theories not yet proven (need experiments are far beyond our technical capabilities). Nevertheless, they have considerable authority. And if this build is correct, then no measuring device can have a measurement error less than the Planck length.

This means that humanity will not be able to reliably predict the behavior of the three black holes in astronomical terms, even if you learn how to put out the stars and remake the galaxy. It is fundamentally impossible. The unpredictability of the future and the transcendence of the past is rooted in the very nature of such systems.

it

the Study demonstrated that there are systems that are future and the past which will remain forever for mankind a mystery. But this does not negate the fact that in many other situations projected future perfect, the past is restored and the reversibility of time is performed. Planes and cars regularly moving us from point a to point B, the telephones communicate with each other, and switches the lights because it is very predictable devices.

moreover, it is not necessary to think that if a small part of the system cannot be forecast, then it is all the more a whole is unknowable.

that is why the wrong narrow-minded argument “scientists can’t predict the weather for a month, and undertake to judge global warming”. For the climate no matter what the weather will be in April 2020. It is only important how it will change the long-term average temperatures. Similarly, for the future of the Galaxy is insignificant, how will three naughty black holes. Has the value of the average behavior of hundreds of billions of stars.

So, otvlekatü from irrelevant details, we can move away from unpredictable systems (weather or trio of black holes) and get much more convenient for analysis (climate or Galaxy). So with each new scientific discovery past and future of the Universe is becoming more comprehensible to humanity, in spite of the tricks of chaos.

By the way, earlier “Conduct.Science” (nauka.vesti.ru) wrote about the uneasy relationship of black holes with the principle of causality.

Text: To.Science