The Big Crunch Theory

We're all worried about what will happen at the end of our lives. We see other living things die, and we know it will happen to us. Because it's inevitable, we worry about when, where and how it will happen. Many of us also wonder about the fate of Earth. Will it be a hospitable blue ball forever, or will it eventually be consumed by the sun as it swells from a medium-sized yellow star to a red giant? Or perhaps we'll poison our planet, and it will float, cold and desolate, through space. If such a thing were to happen, how long would it take? A hundred years? A thousand? A million?

Some astronomers -- those who call themselves cosmologists -- ask similar questions about the universe. The scale that these scientists work at, of course, is much different. The universe is huge compared to a single planet, even a single galaxy, and its timeline is much, much longer. Because of this, cosmologists can't know with certainty how the universe began or how it will end. They can, however, collect evidence, make educated guesses and establish theories.

One such theory, concerning the future of the universe, is playfully known as the "big crunch." According to this theory, the universe will one day stop expanding. Then, as gravity pulls on the matter, the universe will begin to contract, falling inward until it has collapsed back into a super-hot, super-dense singularity. If the theory holds true, the universe is like a giant soufflé. It starts out small, then expands as it heats up. Eventually, however, the soufflé cools and begins to collapse.

Nobody likes a fallen soufflé, and we shouldn't like a universe that behaves like one. It spells the doom of every galaxy, star and planet that currently exists. Luckily, the big crunch is not a guarantee. Cosmologists are currently engaged in a hot debate. One camp says the soufflé will fall; the other camp says the soufflé will expand forever. It will be billions of years before we know for sure which camp is right.

The Big Crunch is one of the scenarios predicted by scientists in which the Universe may end. Just like many others, it is based on Einstein’s Theory of General Relativity. That is, if the Big Bang describes how the Universe most possibly began, the Big Crunch describes how it will end as a consequence of that beginning.

It tells us that the Universe’s expansion, which is due to the Big Bang, will not continue forever. Instead, at a certain point in time, it will stop expanding and collapse into itself, pulling everything with it until it eventually turns into the biggest black hole ever. Well, we all know how everything is squeezed when in that hole. Hence the name Big Crunch.

For scientists to predict with certainty the possibility of a Big Crunch, they will have to determine certain properties of the Universe. One of them is its density. It is believed that if the density is larger than a certain value, known as the critical density, an eventual collapse is highly possible.

You see, initially, scientists believed that there were only two factors that greatly influenced this expansion: the gravitational force of attraction between all the galaxies (which is proportional to the density) and their outward momentum due to the Big Bang.

Now, just like any body that goes against gravity, e.g. when you throw something up, that body will eventually give in and come back down for as long as there is no other force pushing it up.

Thus, that the gravitational forces will win in the end, once seemed like a logical prediction. But that was until scientists discovered that the Universe was actually increasing its rate of expansion at regions farthest from us.

To explain this phenomena, scientists had to assume the presence of an unknown entity, which they dubbed ‘dark energy’. It is widely believed that this entity is pushing all galaxies farther apart. With dark energy, and what little is known about it, in the picture, there seems to be little room for the possibility of a Big Crunch.

Right now, measurements made by NASA’s Chandra X-ray observatory indicate that the strength of dark energy in the University is constant. Just for added information, an increasing dark energy strength would have supported the possibility of a Big Rip, another universe ending that predicted everything (including atoms) to be ripped apart.

The big bounce take on the life cycle of the universe

Death and Rebirth

Clearly, there's no easy answer when it comes to predicting the fate of the universe. But let's imagine for a ­moment th­at the density of the universe is above the critical value required to stop expansion. This would lead to the big crunch, which in many ways would be like hitting the rewind button on a VCR. As gravity within the universe pulled everything back, galaxy clusters would draw closer together. Then individual galaxies would begin to merge until, after billions of years, one mega-galaxy would form.

Inside this gigantic cauldron, stars would meld together, causing all of space to become hotter than the sun. Eventually, stars would explode and black holes would emerge, slowly at first and then more rapidly. As the end drew near, the black holes would suck up everything around them. Even they would coalesce at some point to form a monstrous black hole that would pull the universe closed like a drawstring bag. At the end, nothing would remain but a super-hot, super-dense singularity -- the seed of another universe. Many astronomers think the seed would germinate in a "big bounce," starting the whole process over again.

That's not the only theory. A few cosmologists, led by Paul J. Steinhardt of Princeton University and Neil Turok of Cambridge University, have recently argued that the big chill and the big crunch are not mutually exclusive. Their model works like this: The universe began with the big bang, which was followed by a period of slow expansion and gradual accumulation of dark energy. This is where we are today. What happens next is highly speculative, but Steinhardt and Turok believe that the dark energy will continue to accumulate and, as it does, will stimulate cosmic acceleration. The universe won't ever stop expanding, but will spread out over trillions of years, stretching all matter and energy to such an extreme that our one universe will be separated into multiple universes. Inside these universes, the mysterious dark energy will materialize into normal matter and radiation. This will trigger another big bang -- perhaps several of them -- and another cycle of expansion.

If you're disconcerted by all this talk of crunching and expanding, you can take comfort in knowing that the fate of the universe won't be determined for billions, maybe even trillions, of years. That gives you plenty of time to focus on things that are a bit more certain, such as your own life cycle of birth, growth and death.

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Tachyon

A tachyon or tachyonic particle is a hypothetical particle that always moves faster than light. The word comes from the Greek: ταχύς or tachys, meaning "swift, quick, fast, rapid", and was coined by Gerald Feinberg. Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. If such particles did exist, they could be used to build a tachyonic anti-telephone and send signals faster than light, which (according to special relativity) would lead to violations of causality. Potentially consistent theories that allow faster-than-light particles include those that break Lorentz invariance, the symmetry underlying special relativity, so that the speed of light is not a barrier.

In the 1967 paper that coined the term, Feinberg proposed that tachyonic particles could be quanta of a quantum field with negative squared mass. However, it was soon realized that excitations of such imaginary mass fields do not in fact propagate faster than light, and instead represent an instability known as tachyon condensation.Nevertheless, negative squared mass fields are commonly referred to as "tachyons", and in fact have come to play an important role in modern physics.

Despite theoretical arguments against the existence of faster-than-light particles, experiments have been conducted to search for them. No compelling evidence for their existence has been found.

Tachyons in relativistic theory

In special relativity, a faster-than-light particle would have space-like four-momentum, in contrast to ordinary particles that have time-like four-momentum. It would also have imaginary mass. Being constrained to the spacelike portion of the energy–momentum graph, it could not slow down to subluminal speeds.

Mass

In a Lorentz invariant theory, the same formulas that apply to ordinary slower-than-light particles (sometimes called "bradyons" in discussions of tachyons) must also apply to tachyons. In particular the energy–momentum relation:

(where p is the relativistic momentum of the bradyon and m is its rest mass) should still apply, along with the formula for the total energy of a particle:

This equation shows that the total energy of a particle (bradyon or tachyon) contains a contribution from its rest mass (the "rest mass–energy") and a contribution from its motion, the kinetic energy. When v is larger than c, the denominator in the equation for the energy is "imaginary", as the value under the radical is negative. Because the total energy must be real, the numerator must also be imaginary: i.e. the rest mass m must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number.

Speed

One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. In particular, approaches zero when  approaches infinity. (For ordinary bradyonic matter, E increases with increasing speed, becoming arbitrarily large as v approaches c, the speed of light). Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, because infinite energy is required to reach the barrier from either above or below.

As noted by Einstein, Tolman, and others, special relativity implies that faster-than-light particles, if they existed, could be used to communicate backwards in time.

Neutrinos

In 1985 Chodos et al. proposed that neutrinos can have a tachyonic nature. The possibility of standard model particles moving at superluminal speeds can be modeled using Lorentz invariance violating terms, for example in the Standard-Model Extension. In this framework, neutrinos experience Lorentz-violating oscillations and can travel faster than light at high energies. This proposal was strongly criticized.

Cherenkov radiation

A tachyon with an electric charge would lose energy as Cherenkov radiation—just as ordinary charged particles do when they exceed the local speed of light in a medium. A charged tachyon traveling in a vacuum therefore undergoes a constant proper time acceleration and, by necessity, its worldline forms a hyperbola in space-time. However reducing a tachyon's energy increases its speed, so that the single hyperbola formed is of two oppositely charged tachyons with opposite momenta (same magnitude, opposite sign) which annihilate each other when they simultaneously reach infinite speed at the same place in space. (At infinite speed the two tachyons have no energy each and finite momentum of opposite direction, so no conservation laws are violated in their mutual annihilation. The time of annihilation is frame dependent.)

Even an electrically neutral tachyon would be expected to lose energy via gravitational Cherenkov radiation, because it has a gravitational mass, and therefore increase in speed as it travels, as described above. If the tachyon interacts with any other particles, it can also radiate Cherenkov energy into those particles. Neutrinos interact with the other particles of the Standard Model, and Andrew Cohen and Sheldon Glashow recently used this to argue that the faster-than-light neutrino anomaly cannot be explained by making neutrinos propagate faster than light, and must instead be due to an error in the experiment.

Causality

Causality is a fundamental principle of physics. If tachyons can transmit information faster than light, then according to relativity they violate causality, leading to logical paradoxes of the "kill your own grandfather" type. This is often illustrated with thought experiments such as the "tachyon telephone paradox" or "logically pernicious self-inhibitor."

The problem can be understood in terms of the relativity of simultaneity in special relativity, which says that different inertial reference frames will disagree on whether two events at different locations happened "at the same time" or not, and they can also disagree on the order of the two events (technically, these disagreements occur when spacetime interval between the events is 'space-like', meaning that neither event lies in the future light cone of the other).

If one of the two events represents the sending of a signal from one location and the second event represents the reception of the same signal at another location, then as long as the signal is moving at the speed of light or slower, the mathematics of simultaneity ensures that all reference frames agree that the transmission-event happened before the reception-event. However, in the case of a hypothetical signal moving faster than light, there would always be some frames in which the signal was received before it was sent, so that the signal could be said to have moved backwards in time. Because one of the two fundamental postulates of special relativity says that the laws of physics should work the same way in every inertial frame, if it is possible for signals to move backwards in time in any one frame, it must be possible in all frames. This means that if observer A sends a signal to observer B which moves faster than light in A's frame but backwards in time in B's frame, and then B sends a reply which moves faster than light in B's frame but backwards in time in A's frame, it could work out that A receives the reply before sending the original signal, challenging causality in every frame and opening the door to severe logical paradoxes. Mathematical details can be found in the tachyonic antitelephone article, and an illustration of such a scenario using spacetime diagrams can be found in Baker, R. (2003)

Reinterpretation principle

The reinterpretation principle asserts that a tachyon sent back in time can always be reinterpreted as a tachyon travelingforward in time, because observers cannot distinguish between the emission and absorption of tachyons. The attempt to detect a tachyon from the future (and violate causality) would actually create the same tachyon and send it forward in time (which is causal).

However, this principle is not widely accepted as resolving the paradoxes. Instead, what would be required to avoid paradoxes is that unlike any known particle, tachyons do not interact in any way and can never be detected or observed, because otherwise a tachyon beam could be modulated and used to create an anti-telephone or a "logically pernicious self-inhibitor". All forms of energy are believed to interact at least gravitationally, and many authors state that superluminal propagation in Lorentz invariant theories always leads to causal paradoxes.

Fundamental models

In modern physics, all fundamental particles are regarded as excitations of quantum fields. There are several distinct ways in which tachyonic particles could be embedded into a field theory.

Fields with imaginary mass

In the paper that coined the term "tachyon", Gerald Feinberg studied Lorentz invariant quantum fields with imaginary mass. Because the group velocity for such a field is superluminal, naively it appears that its excitations propagate faster than light. However, it was quickly understood that the superluminal group velocity does not correspond to the speed of propagation of any localized excitation (like a particle). Instead, the negative mass represents an instability to tachyon condensation, and all excitations of the field propagate subluminally and are consistent with causality.Despite having no faster-than-light propagation, such fields are referred to simply as "tachyons" in many sources.

Tachyonic fields play an important role in modern physics. Perhaps the most famous is the Higgs boson of the Standard Model of particle physics, which—in its uncondensed phase—has an imaginary mass. In general, the phenomenon of spontaneous symmetry breaking, which is closely related to tachyon condensation, plays a very important role in many aspects of theoretical physics, including the Ginzburg–Landau and BCS theories of superconductivity. Another example of a tachyonic field is the tachyon of bosonic string theory.

Lorentz violating theories

In theories that do not respect Lorentz invariance the speed of light is not (necessarily) a barrier, and particles can travel faster than the speed of light without infinite energy or causal paradoxes. A class of field theories of that type are the so-called Standard Model extensions. However, the experimental evidence for Lorentz invariance is extremely good, so such theories are very tightly constrained.

Fields with non-canonical kinetic term

By modifying the kinetic energy of the field, it is possible to produce Lorentz invariant field theories with excitations that propagate superluminally. However, such theories in general do not have a well-defined Cauchy problem (for reasons related to the issues of causality discussed above), and are probably inconsistent quantum mechanically.

History

As mentioned above, the term "tachyon" was coined by Gerald Feinberg in a 1967 paper titled "Possibility of Faster-Than-Light Particles". Feinberg studied the kinematics of such particles according to special relativity. In his paper he also introduced fields with imaginary mass (now also referred to as "tachyons") in an attempt to understand the microphysical origin such particles might have.

The first hypothesis regarding faster-than-light particles is sometimes attributed to German physicist Arnold Sommerfeld in 1904, and more recent discussions happened in 1962 and 1969.



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