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Entropic Measure of Time, and Gas Expansion in Vacuum

Leonid M. Martyushev, Evgenii V. Shaiapin
The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is introduced with the help of Boltzmann’s classic entropy. It is shown that, in the general case, this measure of time proves to be nonlinearly related to the reference measure assumed uniform by convention. The connection between this result and the results of other authors investigating measure of time in some biological and cosmological problems is noted…
Read more at https://arxiv.org/ftp/arxiv/papers/1605/1605.06969.pdf

A Clock that Will Last Forever

Berkeley Lab Researchers Propose a Way to Build the First Space-Time Crystal

Imagine a clock that will keep perfect time forever or a device that opens new dimensions into quantum phenomena such as emergence and entanglement.

Imagine a clock that will keep perfect time forever, even after the heat-death of the universe. This is the “wow” factor behind a device known as a “space-time crystal,” a four-dimensional crystal that has periodic structure in time as well as space. However, there are also practical and important scientific reasons for constructing a space-time crystal. With such a 4D crystal, scientists would have a new and more effective means by which to study how complex physical properties and behaviors emerge from the collective interactions of large numbers of individual particles, the so-called many-body problem of physics. A space-time crystal could also be used to study phenomena in the quantum world, such as entanglement, in which an action on one particle impacts another particle even if the two particles are separated by vast distances.

A space-time crystal, however, has only existed as a concept in the minds of theoretical scientists with no serious idea as to how to actually build one – until now. An international team of scientists led by researchers with the U.S. Department of Energy (DOE)’s Lawrence Berkeley National Laboratory (Berkeley Lab) has proposed the experimental design of a space-time crystal based on an electric-field ion trap and the Coulomb repulsion of particles that carry the same electrical charge.

“The electric field of the ion trap holds charged particles in place and Coulomb repulsion causes them to spontaneously form a spatial ring crystal,” says Xiang Zhang, a faculty scientist with Berkeley Lab’s Materials Sciences Division who led this research. “Under the application of a weak static magnetic field, this ring-shaped ion crystal will begin a rotation that will never stop. The persistent rotation of trapped ions produces temporal order, leading to the formation of a space-time crystal at the lowest quantum energy state.”…………
Read more: http://newscenter.lbl.gov/news-releases/2012/09/24/a-clock-that-will-last-forever/

Physicists Predict The Existence of Time Crystals

Read also: Time crystals could behave almost like perpetual motion machines

If crystals exist in spatial dimensions, then they ought to exist in the dimension of time too, says Nobel prize-winning physicist

One of the most powerful ideas in modern physics is that the Universe is governed by symmetry. This is the idea that certain properties of a system do not change when it undergoes a transformation of some kind.

For example, if a system behaves the same way regardless of its orientation or movement in space, it must obey the law of conservation of momentum.

If a system produces the same result regardless of when it takes place, it must obey the law of conservation of energy.

We have the German mathematician, Emmy Noether, to thank for this powerful way of thinking. According to her famous theorem, every symmetry is equivalent to a conservation law. And the laws of physics are essentially the result of symmetry.

Equally powerful is the idea of symmetry breaking. When the universe displays less symmetry than the equations that describe it, physicists say the symmetry has been broken.

A well known example is the low energy solution associated with the precipitation of a solid from a solution—the formation of crystals, which have a spatial periodicity. In this case the spatial symmetry breaks down.

Spatial crystals are well studied and well understood. But they raise an interesting question: does the universe allow the formation of similar periodicities in time?

Today, Frank Wilczek at the Massachussettsi Institute of Technology and Al Shapere at the University of Kentucky, discuss this question and conclude that time symmetry seems just as breakable as spatial symmetry at low energies.

This process should lead to periodicities that they call time crystals. What’s more, time crystals ought to exist, probably under our very noses.

Let’s explore this idea in a bit more detail. First, what does it mean for a system to break time symmetry? Wilczek and Shapere think of it like this. They imagine a system in its lowest energy state that is completely described, independently of time.

Because it is in its lowest energy state,  this system ought to be frozen in space. Therefore, if the system moves, it must break time symmetry. This is equivalent tot he idea that the lowest energy state has a minimum value on a curve on space rather than at a single isolated point

That’s actually not so extraordinary. Wilczek points out that a superconductor can carry a current—the mass movement of electrons—even in its lowest energy state.

The rest is essentially mathematics. In the same way that the equations of physics allow the spontaneous formation of  spatial crystals, periodicities in space, so they must also allow the formation of periodicities in time or time crystals.

In particular, Wilczrek considers spontaneous symmetry breaking in a closed quantum mechanical system. This is where the mathematics become a little strange. Quantum mechanics forces physicists to think about imaginary values of time or iTime, as Wilczek calls it.

He shows that the same periodicities ought to arise in iTime and that this should manifest itself as periodic behaviour of various kinds of thermodynamic properties.

That has a number of important consequences. First up is the possibility that this process provides a mechanism for measuring time, since the periodic behaviour is like a pendulum. “The spontaneous formation of a time crystal represents the spontaneous emergence of a clock,” says Wilczek.

Another is the possibility that it may be possible to exploit time crystals to perform computations using zero energy. As Wilczek puts it, “it is interesting to speculate that a…quantum mechanical system whose states could be interpreted as a collection of qubits, could be engineered to traverse a programmed landscape of structured states in Hilbert space over time.”

Altogether this is a simple argument. But simplicity is often  deceptively powerful. Of course, there will be disputes over some of the issues this raises. One of them is that the motion that breaks time symmetry seems a little puzzling. Wilczek and Shapere acknowledge this: “Speaking broadly speaking, what we’re looking for looks perilously close to perpetual motion.”

That will need some defending. But if anyone has the pedigree to push these ideas forward, it’s Wilczek, who is a Nobel prize winning physicist.

We’ll look forward to the ensuing debate.

technologyreview.com

Refs:  arxiv.org/abs/1202.2539: Quantum Time Crystals

arxiv.org/abs/1202.2537 Classical Time Crystals

Video: How a time cloak could change the past

This video simulates the time cloaking device developed by Cornell University researchers. A ball is trying to pass through a green beam of laser light without being detected. Two short pulses of red laser light change the color of the green light, and since different colors travel at different speeds, a gap is opened in the beam exactly when the ball is passing through. Then the opposite manipulation closes the gap, and two other pulses change the light back to green. Hence, the ball manages to go through the beam without getting detected.

http://youtu.be/GXxzBvN4sKM

British atomic clock ‘most accurate in world’

The clock is responsible for international time

The machine, which is responsible for keeping Britain’s clocks on track and also contributes to the international measure of time, is accurate to within two 10 million billionths of a second.
It is one of a handful of similar clocks which determine the exact length of a second by measuring microwaves as they cause reactions in atoms of caesium, a highly volatile element.
But a number of factors including the shape of the microwaves, the influence of nearby magnetic fields and even the clock’s position above sea level can cause tiny shifts in its measurements.
By tinkering with the clock, physicists at the National Physical Laboratory (NPL) near London, led by Dr Krzysztof Szymaniec, were able to reduce its margin of error to unprecedented levels.
A new analysis of the clock, conducted by NPL scientists and American colleagues, published in the journal Metrologia, established that it will now drop just a billionth of a second every two months, making it the world’s most accurate timekeeper.

http://www.telegraph.co.uk/science

Time need not end in the multiverse

No longer a worry

GAMBLERS already had enough to think about without factoring

the end of time into their calculations. But a year after a group of cosmologists argued that they should, another team says time need not end after all.

It all started with this thought experiment. In a back room in a Las Vegas casino, you are handed a fair coin to flip. You will not be allowed to see the outcome, and the moment the coin lands you will fall into a deep sleep. If the coin lands heads up, the dealer will wake you 1 minute later; tails, in 1 hour. Upon waking, you will have no idea how long you have just slept.

The dealer smiles: would you like to bet on heads or tails? Knowing it’s a fair coin, you assume your odds are 50/50, so you choose tails. But the house has an advantage. The dealer knows you will almost certainly lose, because she is factoring in something you haven’t: that we live in a multiverse.

The idea that our universe is just one of many crops up in a number of physicists’ best theories, including inflation. It posits that different parts of space are always ballooning into separate universes, so that our observable universe is just a tiny island in an exponentially growing multiverse.

In any infinite multiverse, everything that can happen, will happen – an infinite number of times. That has created a major headache for cosmologists, who want to use probabilities to make predictions, such as the strength of the mysterious dark energy that is accelerating the expansion of our own universe. How can we say that anything is more or less probable than anything else?

One procedure physicists are fond of is to draw a cut-off at some finite time, count up the number of events – say, heads and tails – that occur in the multiverse before the cut-off time, and use that as a representative sample.

It seems reasonable, but when tackling the casino experiment, something strange happens. Wherever the cut-off is drawn, it slices through some of the gamblers’ naps, making it appear as if those gamblers simply never woke up. The longer the nap, the more likely it is to be cut off, so if you do awaken, it’s more likely that you have taken a shorter nap – that is, that you flipped heads. So even though the odds seemed to be 50/50 when the coins were first flipped, heads becomes more probable than tails once you and the other gamblers wake up.

“This thought experiment was unbelievably perplexing at first, because it seemed like probabilities were changing from one instant to the next without any explanation,” says Alan Guth of the Massachusetts Institute of Technology, who along with Vitaly Vanchurin of Stanford University in California, came up with the conundrum two years ago.

Last year, Raphael Bousso at the University of California, Berkeley, and colleagues devised an explanation that was effective, if unsettling. The changing probabilities were behaving as if time ends at the cut-off, they said, because time really does end at the cut-off. That’s why the initial 50/50 odds change when you wake up from your nap.

Upon waking, you have new information: you know that time didn’t end. That now means it is more likely that you only slept for a minute than for an hour. After all, time could end at any minute, and an hour has an extra 59 of those to spare. Heads wins.

The idea that time must end for the probabilities to make sense has been bugging Guth and Vanchurin for the last year. Now they say they have developed a mathematical explanation for the multiverse that saves the fourth dimension (arxiv.org/abs/1108.0665).

The essence of the argument is that you don’t need any new information, in this case the fact that you woke up, to understand why the odds are no longer 50/50. In a multiverse that grows exponentially, where each new generation of universes is far larger than the last, younger universes always outnumber older ones. Waking up, you will either be in a universe in which 1 minute has passed (heads), or in a universe in which 1 hour has passed (tails). “The experiment sets up a 59-minute ambiguity in the age of the universe,” Guth says. “You should always bet on the younger one.”

But Bousso doesn’t feel safe just yet: “Nature has often seemed crazy as we discovered how far removed its workings are from our everyday intuition. The end of time may sound crazy, but it is by far the simplest interpretation.” Whether or not time is going to end, there’s a lesson to take from the debate: should you wake up in Las Vegas, bet heads.  http://www.newscientist.com