Ghost Duniya: physics

Showing posts with label physics. Show all posts

2/21/2015

By Unknown

In: physics

How Can Space Travel Faster Than The Speed Of Light?

Image Credit: ESA/Hubble & NASA, Acknowledgement: Flickr user Det58

Cosmologists are intellectual time travelers. Looking back over billions of years, these scientists are able to trace the evolution of our Universe in astonishing detail. 13.8 billion years ago, the Big Bang occurred. Fractions of a second later, the fledgling Universe expanded exponentially during an incredibly brief period of time called inflation. Over the ensuing eons, our cosmos has grown to such an enormous size that we can no longer see the other side of it.

But how can this be? If light’s velocity marks a cosmic speed limit, how can there possibly be regions of spacetime whose photons are forever out of our reach? And even if there are, how do we know that they exist at all?

The Expanding Universe

Like everything else in physics, our Universe strives to exist in the lowest possible energy state possible. But around 10^-36 seconds after the Big Bang, inflationary cosmologists believe that the cosmos found itself resting instead at a “false vacuum energy” – a low-point that wasn’t really a low-point. Seeking the true nadir of vacuum energy, over a minute fraction of a moment, the Universe is thought to have ballooned by a factor of 10⁵⁰.

Since that time, our Universe has continued to expand, but at a much slower pace. We see evidence of this expansion in the light from distant objects. As photons emitted by a star or galaxy propagate across the Universe, the stretching of space causes them to lose energy. Once the photons reach us, their wavelengths have been redshifted in accordance with the distance they have traveled.

Two sources of redshift: Doppler and cosmological expansion; modeled after Koupelis & Kuhn. Bottom: Detectors catch the light that is emitted by a central star. This light is stretched, or redshifted, as space expands in between. Credit: Brews Ohare.

This is why cosmologists speak of redshift as a function of distance in both space and time. The light from these distant objects has been traveling for so long that, when we finally see it, we are seeing the objects as they were billions of years ago.

The Hubble Volume

Redshifted light allows us to see objects like galaxies as they existed in the distant past; but we cannot see allevents that occurred in our Universe during its history. Because our cosmos is expanding, the light from some objects is simply too far away for us ever to see.

The physics of that boundary rely, in part, on a chunk of surrounding spacetime called the Hubble volume. Here on Earth, we define the Hubble volume by measuring something called the Hubble parameter (H₀), a value that relates the apparent recession speed of distant objects to their redshift. It was first calculated in 1929, when Edwin Hubble discovered that faraway galaxies appeared to be moving away from us at a rate that was proportional to the redshift of their light.

Fit of redshift velocities to Hubble’s law. Credit: Brews Ohare

Dividing the speed of light by H₀, we get the Hubble volume. This spherical bubble encloses a region where all objects move away from a central observer at speeds less than the speed of light. Correspondingly, all objects outside of the Hubble volume move away from the center faster than the speed of light.

Yes, “faster than the speed of light.” How is this possible?

The Magic of Relativity

The answer has to do with the difference between special relativity and general relativity. Special relativity requires what is called an “inertial reference frame” – more simply, a backdrop. According to this theory, the speed of light is the same when compared in all inertial reference frames. Whether an observer is sitting still on a park bench on planet Earth or zooming past Neptune in a futuristic high-velocity rocket ship, the speed of light is always the same. A photon always travels away from the observer at 300,000,000 meters per second, and he or she will never catch up.

General relativity, however, describes the fabric of spacetime itself. In this theory, there is no inertial reference frame. Spacetime is not expanding with respect to anything outside of itself, so the the speed of light as a limit on its velocity doesn’t apply. Yes, galaxies outside of our Hubble sphere are receding from us faster than the speed of light. But the galaxies themselves aren’t breaking any cosmic speed limits. To an observer within one of those galaxies, nothing violates special relativity at all. It is the space in between us and those galaxies that is rapidly proliferating and stretching exponentially.

The Observable Universe

Now for the next bombshell: The Hubble volume is not the same thing as the observable Universe.

To understand this, consider that as the Universe gets older, distant light has more time to reach our detectors here on Earth. We can see objects that have accelerated beyond our current Hubble volume because the light we see today was emitted when they were within it.

Strictly speaking, our observable Universe coincides with something called the particle horizon. The particle horizon marks the distance to the farthest light that we can possibly see at this moment in time – photons that have had enough time to either remain within, or catch up to, our gently expanding Hubble sphere.

And just what is this distance? A little more than 46 billion light years in every direction – giving our observable Universe a diameter of approximately 93 billion light years, or more than 500 billion trillion miles.

Image credit: Htwins

(A quick note: the particle horizon is not the same thing as the cosmological event horizon. The particle horizon encompasses all the events in the past that we can currently see. The cosmological event horizon, on the other hand, defines a distance within which a future observer will be able to see the then-ancient light our little corner of spacetime is emitting today.

In other words, the particle horizon deals with the distance to past objects whose ancient light that we can see today; the cosmological event horizon deals with the distance that our present-day light that will be able to travel as faraway regions of the Universe accelerate away from us.)

Dark Energy

Thanks to the expansion of the Universe, there are regions of the cosmos that we will never see, even if we could wait an infinite amount of time for their light to reach us. But what about those areas just beyond the reaches of our present-day Hubble volume? If that sphere is also expanding, will we ever be able to see those boundary objects?

This depends on which region is expanding faster – the Hubble volume or the parts of the Universe just outside of it. And the answer to that question depends on two things: 1) whether H₀ is increasing or decreasing, and 2) whether the Universe is accelerating or decelerating. These two rates are intimately related, but they are not the same.

In fact, cosmologists believe that we are actually living at a time when H₀is decreasing; but because of dark energy, the velocity of the Universe’s expansion is increasing.

That may sound counter-intuitive, but as long as H₀decreases at a slower rate than that at which the Universe’s expansion velocity is increasing, the overall movement of galaxies away from us still occurs at an accelerated pace. And at this moment in time, cosmologists believe that the Universe’s expansion will outpace the more modest growth of the Hubble volume.

So even though our Hubble volume is expanding, the influence of dark energy appears to provide a hard limit to the ever-increasing observable Universe.

Our Earthly Limitations

Cosmologists seem to have a good handle on deep questions like what our observable Universe will someday look like and how the expansion of the cosmos will change. But ultimately, scientists can only theorize the answers to questions about the future based on their present-day understanding of the Universe. Cosmological timescales are so unimaginably long that it is impossible to say much of anything concrete about how the Universe will behave in the future. Today’s models fit the current data remarkably well, but the truth is that none of us will live long enough to see whether the predictions truly match all of the outcomes.

Disappointing? Sure. But totally worth the effort to help our puny brains consider such mind-bloggling science – a reality that, as usual, is just plain stranger than fiction.

9/24/2014

By Unknown

In: physics

No comments

Angular Mechanics

Angular mechanics is a branch of mechanics. Angular mechanics involves the study of motion of a body in a rotational or a circular way. The angular momentum and torque are the most important and responsible part for angular mechanics. When the force is applied to a body that causes it to rotate then it creates torque. Similar to force, torque also acts to angularly accelerate a spinning object. The equation for torque (expressed as Γ here) looks very much like force in a linear motion (F = ma) because the torque is analogous to the force in rotational motion.
Γ = Iα
Instead of mass, we have rotational inertia(mass and inertia are analogous to each other). Instead of linear acceleration, we have angular acceleration(linear acceleration and angular acceleration are analogous to each other).

Now, if a force is applied linearly to make an object move, its torque is defined as:
Γ = F × r
In angular mechanics, angular momentum, moment of momentum, or rotational momentumis a quantity in a rotational motion is analogous to linear momentum in translation motion. Just as linear momentum is equal o the product of mass and linear velocity, angular momentum is equal to the product of M.I. and angular velocity. It is also a vector quantity.
L = r × p = r × mv,
L =Iw
Where,
r- radius of vector,
P-linear momentum,
m- mass of the body,
v- velocity of a body,
I-moment of inertia,
w-angular velocity
Where there is no net external torque, angular momentum is conserved in a system and its conservation helps explain many diverse phenomena. Let us see one example- the increase in rotational speed of a spinning figure skater as the skater's arms are contracted is a consequence of conservation of angular momentum. The another example is-a very high rotational rates neutron stars. It means, angular momentum conservation has numerous applications in physics and engineering.

9/24/2014

By Unknown

In: physics

No comments

Gravity

An object released from some high above the surface of the earth falls freely with an acceleration. This accelerate motion is due to the force of attraction exerted by the earth on the object. The motion of the moon in a circular orbit around the earth also shows that the earth exerts a force of attraction between the sun and suggest the existence of a force of attraction between the sun and the plant. These observations led Newton to the conclusion that any two material objects always attract each other. This attraction is called gravity or gravitation and the force of attraction is called the gravitational force.
Newton’s law of gravity or gravitation:
The gravitational force between any two material object is given by Newton’s law of gravitation, which is every particle of matter attraction every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of distance between them.
Suppose two particles of masses m₁ to m₂ separated by a distance r them according to Newton’s law of gravitation, these particles attract each other with a force whose magnitude (F) is given by
F::m1m2 / r2
f = Newton’s law of gravity

where G is a constant called constant of gravity.
SI unit of GI is Nm²/kg² its dimensions can be determined
[G] = Newton’s law of gravity

= [M ^-1L³ T^-2]
The gravitational force between two particles act along the line joining the two particles and they form an action reaction pair. The force exerted by the first particle on the second particle is exactly equal and opposite to the force exerted by the second particle on the first.
Newton’s law of gravitation holds good for all material object irrespective of their sizes or distance between them. Therefore it is called a universal law and the constant of gravity G1 is called the universal constant its value is 6.673 x 10^-11 Nm²/kg². In order to explain how to masses attract each other even though there is no physical contact between them, the concept of gravitational field is introduced. According to this concept, there exists a gravitational field in the space surrounding and mass. When another mass is brought into this space, it is acted upon by the gravitational force of attraction.

9/24/2014

By Unknown

In: physics

No comments

Motion

Change in the position of an object with respect to time is the motion of an object is the motion of an object. Motion is one of the most important part of branch of physics called mechanics. Everybody on the Earth moves. The movement might be slow or very very slow. If we are standing on earth then earth moves around the Sun and Sun moves around the galaxy. It means that the movement of a body never stops.
To have a motion of an object or to change its motion, the force should be acted on an object. When some Physicists observe that, how an object moves? , they use some basic terms like the speed or velocity with which an object moves, the mass of an object which also affects on motion of object, forces acting on an object, acceleration(rate of change of velocity with respect to time), energy and the work.
Some basic equations related to motion:
v(velocity) = s(displacement)/ t(time)
a(accelaration) = dv(changes in velocity) / dt(changes in time)
F(force) = ma where, m=mass
Types of Motion:

Uniform motion In this type of motion the direction and the speed of an object are the same and do not change with respect to time. In such case, the object moves in the same direction and travels through equal distance in equal interval of time, however these intervals may be small. Obviously, when the object is in uniform motion, its instantaneous velocity (it is average velocity as the time-interval t becomes extremely small) is the same everywhere along its path. Also its average velocity is the same as its instantaneous velocity.
Variable motion In this type of motion the direction or speed changes with respect to time. In this displacement of an object varies from instant to instant, either increasing or decreasing.
Periodic motion
The motion that repeats and always returns to its original initial position is called periodic motion. Periodic motion repeats in equal interval of time. Examples of periodic motion are a rocking chair, a bouncing ball, a vibrating guitar string, a swinging pendulum, and a water wave, the motion of the Earth in its orbit around the sun.

9/24/2014

By Unknown

In: physics

No comments

Law Of Motion

There are three laws of motion and they were first compiled by Sir Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica, first published on July 5, 1687^. Newton used these laws to explain and investigate the motion of many physical objects and systems. Newton showed that these laws of motion when combined with his law of universal gravitation, explained Kepler's laws of planetary motion.
Newton's laws are applied only to bodies (objects) which are considered or idealized as a particle, in the sense that the extent of the body is neglected in the evaluation of its motion, i.e.,the object is small when compared to the distances involved in the analysis, or the deformation and rotation of the body is of no importance in the analysis. Therefore, a planet is idealized as a particle for analysis of its orbital motion around a star.
Laws of motion are described as follows:

First law: Every body remains in its state of rest or uniform motion (constant velocity) unless it is compelled by an external unbalanced force to change that state. It means that in the absence of a non-zero or the net force the center of a mass of a body either remains at rest, or moves at a constant speed in a straight line.
Second law: The rate of momentum of a body is directly proportional to the impressed force and takes place in the direction of the force. It means a body of mass m subject to a force F undergoes an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force and inversely proportional to the mass, i.e., F= ma. Alternatively, the total force applied on a body is same to that of the time derivative of the linear momentum of the body.
Third law: To every action, there is equal and opposite reaction or the mutual forces of action and reaction between two bodies are equal, opposite and collinear. It means that whenever a first body exerts a force F on a second body, the second body exerts a force -F on the first body. F and -F are equal in magnitude and opposite in direction. This law is usually referred to as action-reaction law with F called the "action" and -F the "reaction".