Astronomy

Why does the sensitivity to GWs drops off inversely proportional to the distance?

Why does the sensitivity to GWs drops off inversely proportional to the distance?


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This answer makes me wonder why the sensitivity to gravitational waves decreases proportionally to the distance.

Since gravitational waves extend in all directions, my (uneducated) guess would be that the same argument can be made as for the decrease in sensitivity for electromagnetic waves. Why is this not the case? Why does the sensitivity to GWs decrease in a linear fashion?


EDIT I'm leaving the original, highly upvoted answer below, but I've had a fundamental rethink about this, prompted by questions from Keith McClary and a helpful clarification from a Physics SE question.

The original answer I gave is the reason that we can detect gravitational waves (GWs) at all. Their coherent nature as single oscillators, means that despite their comparatively low powers, they can be detected right across the universe. In comparison, electromagnetic sources are usually the superposed light from countless incoherent emission sources. On average this has a destructive interference effect that reduces the power (intensity) received; and due to the rapidly changing signal, it is usually intensity that is measured.

However, the answer to the present question is actually just how "sensitivity" is defined.

In order to detect a source, we must identify it in a background of noise. This is done by defining a signal-to-noise ratio. The signal is the product of your source strength (more on that in a minute) and how long you observed it for. The noise is a property of your instrument. The sensitivity of the instrument then is something like the minimum (signal $ imes$ observation time) that will produce a significant detection.

In astronomy it is conventional to express the signal in terms of power received since, due to the arguments given above and in the original answer, power (intensity) is generally what is measured. The sources of noise are therefore also defined in terms of a power and the sensivity has units of something like Watts $ imes$ seconds, or more conventionally, W/Hz.

In gravitational wave astronomy, because it is the amplitude that is directly detected, GW astronomers express their source signal in terms of amplitude (which is proportional to the square root of detected power) and their sensitivities are expressed in terms of gravitational wave amplitude (which is dimensionless) divided by $sqrt{Hz}$ as a result.

i.e. we are not comparing like with like. Doubling the sensitivity of a gravitational wave detector is actually like quadrupling the sensivitity of an electromagnetic wave detector. Thus there is no fundamental difference here, the apparent difference in behaviour is merely a result of how sensitivity is defined. The reason for the different definition is as per my original answer below.

Original answer

The difference is that usually when we detect sources of electromagnetic waves, we are detecting intensity, which obeys the inverse square law.

In contrast, we are detecting the amplitude of gravitational waves, and amplitude only scales as the inverse of distance

Why the difference? Sources of gravitational waves are coherent oscillators. A merging binary produces a single coherent wave train with an amplitude that can be defined and measured. By contrast, when we look at a distant star or galaxy in electromagnetic waves we are seeing the incoherent contribution from countless accelerating particles and atoms and all we can detect is the resultant summed intensity. There is no coherent electromagnetic wave with an amplitude that can be measured.

This difference in behaviour is fundamentally because whilst there are positive and negative electric charges, which require contrived circumstances in which to behave coherently (e.g. in a laser), gravitational waves are produced by accelerating masses, and since there is only one sign of "gravitational charge", the individual parts of a gravitational wave source are able to act in concert quite naturally to produce a coherent waveform that has a wavelength larger than the body itself.

An excellent discussion of these points can be found on the first page of the review article by Hendry & Woan (2007).

In principle, if we were looking at a single coherent source of electromagnetic waves then we can detect the amplitude (for example by the force it exerts on charged particles), and then the sensitivity would just reduce as the inverse of distance. At optical frequencies the electric field varies so rapidly that this cannot be done, but it is possible at radio frequencies. Unfortunately the coherence length and coherence time (the time over which the phase of the wave is predictable) are so short that this is rarely practical in laboratory, let alone astronomical, sources.


Multi-messenger astrophysics

Multi-messenger astrophysics, a long-anticipated extension to traditional multiwavelength astronomy, has emerged over the past decade as a distinct discipline providing unique and valuable insights into the properties and processes of the physical Universe. These insights arise from the inherently complementary information carried by photons, gravitational waves, neutrinos and cosmic rays about individual cosmic sources and source populations. This complementarity is the reason why multi-messenger astrophysics is much more than just the sum of the parts. In this Review article, we survey the current status of multi-messenger astrophysics, highlighting some exciting results, and discussing the major follow-up questions they have raised. Key recent achievements include the measurement of the spectrum of ultrahigh-energy cosmic rays out to the highest observable energies the discovery of the diffuse high-energy neutrino background the first direct detections of gravitational waves and the use of gravitational waves to characterize merging black holes and neutron stars in strong-field gravity and the identification of the first joint electromagnetic plus gravitational wave and electromagnetic plus high-energy neutrino multi-messenger sources. We discuss the rationales for the next generation of multi-messenger observatories, and outline a vision of the most likely future directions for this exciting and rapidly growing field.


What is the AUC - ROC Curve?

AUC - ROC curve is a performance measurement for the classification problems at various threshold settings. ROC is a probability curve and AUC represents the degree or measure of separability. It tells how much the model is capable of distinguishing between classes. Higher the AUC, the better the model is at predicting 0 classes as 0 and 1 classes as 1. By analogy, the Higher the AUC, the better the model is at distinguishing between patients with the disease and no disease.

The ROC curve is plotted with TPR against the FPR where TPR is on the y-axis and FPR is on the x-axis.


AST101 Exam 2 (Ch. 4, 5, 6)

-On Earth the acceleration of g ≈ 10 m/s2 (this is 10 meters per second per second or 10 meters per second squared):

-speed increases 10 m/s with each second of falling.

-Galileo showed that g is the same for all falling objects, regardless of their mass.

The acceleration due to gravity of an object on the surface of Earth depends on what? (Ch.4 quiz)

-Formula:
Momentum = mass x velocity OR p = mv
P=momentum m=mass v=velocity

-only way to change an object's momentum is to apply a force to it

WHAT DO WE MEAN:
-A change in momentum occurs only when the net force is not zero (A net force that is not zero causes an object to accelerate)

-changing object's momentum produces acceleration (means changing its velocity), as long as its mass remains constant

FORCE:
-Anything that can cause a change in momentum
-EX: gravity / electromagnetic forces acting between atoms

NET FORCE:
-the overall force acting on an object

-represents the combined effect of all the individual forces put together

-if two forces cancel each other out then there is no net force [my pwp notes]

-equal to the rate of change in the object's momentum

3. An elevator moving at constant speed: N (the upward speed is being canceled out by the downward force of gravity)

4. A bicycle going around a curve: Y

-an object that is either spinning or moving along a curved path has angular momentum [113]

-FORMULA: m x v x r
(m=mass v=velocity r=radius)

-Earth has angular momentum due to its rotation (rotational angular momentum) and due to its orbit around the sun (orbital angular momentum)

-object's angular momentum can change only when a torque is applied to it

-amount of torque depends not only on how much force is applied, but also where it's applied

What keeps a planet rotating and orbiting the Sun? (pwp question)

Conservation of Angular momentum
-as long as there is no external torque, the total angular momentum of a set of interacting objects cannot change

-an individual object can change its angular momentum only by transferring some angular momentum to or from an object.

-Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely.

WEIGHT:
-the force that an object applies to its surroundings

-the force that a scale measures when you stand on it (force acting on mass)

-depends on object's mass and the forces (including gravity) acting on objects mass. Weight can vary because the forces acting on object can vary

-Weight of object can very because the forces acting on the object can vary

-Objects are weightless in free-fall.

-When in free fall you are floating above the scale so you are not exerting force on the scale or anything else so you are weightless -> there's nothing below you to exert force on.

-Remember that weight is the force applied to an object so you're weightless until you hit the ground

SECOND LAW: Force = mass x acceleration OR Force = rate of change in momentum
EX: a baseball accelerates as the pitcher applies a force by moving his arm. (once the ball is released, the force from the pitcher's arm ceases, and the ball's path changes only bc of the forces of gravity and air resistance)

• He discovered laws of motion and gravitation.

-Interacting objects exchange momentum through equal and opposite forces.

-an individual object can gain or lose momentum only if some other object's momentum changes by a precisely opposite amount

CONSERVATION OF ANGULAR MOMENTUM:
-as long as there is no external torque, the total angular momentum of a set of interacting objects cannot change

-an individual object can change its angular momentum only by transferring some angular momentum to or from an object.

-also explains why objects rotate faster as they shrink in radius.

CONSERVATION OF ENERGY:
-energy cannot be created or destroyed but only transformed from one type to another or be exchanged between objects.

-The total energy content in an isolated system is always the same.

-Interacting objects exchange momentum through equal and opposite forces.

Conservation of Angular momentum
-as long as there is no external torque, the total angular momentum of a set of interacting objects cannot change

-an individual object can change its angular momentum only by transferring some angular momentum to or from an object.

-Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely.

• Radiative (light): Energy carried by light
-EX: sunlight warms surface of earth, light can alter molecules in our eyes

-higher temperature: particles on average have more kinetic energy so they're moving faster

THERMAL ENERGY:
-subcategory of kinetic energy

-The collective kinetic energy of many individual particles (atoms/molecules) moving randomly within a substance (ex:in a rock, in air, in water)

-all objects have thermal energy even when sitting still because the particles within them are always moving

-depends on temperature and density bc higher average (temperature) = higher total energy / higher density = higher total energy

DIFFERENT:
-Thermal measures the total kinetic energy of the particles

-distance object could potentially fall as a result of gravity / the higher it is the more gravitational potential energy

IN SPACE:
-In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts.

• Conservation of energy: energy is always conserved it cannot be created or destroyed but only transformed from one type to another.

1. Every mass attracts every other mass through the force of gravity.

2. Attraction is directly proportional to the product of their masses.
----the strength of the gravitational force attracting any two objects is directly proportional to the product of their masses.

(doubling the mass of one object doubles the force of gravity between the two objects)

3. Attraction is inversely proportional to the square of the distance between their centers.
-----the strength of gravity between two objects decreases with the square of the distance between their centers

(doubling the distance between two objects weakens the force of gravity by a factor of 2^2)

SEE NOTE CARD FOR FORMULA
Fg=Force of gravitational attraction

G= gravitational constant (number given)

M1 and M2= the masses of the two objects

• Applies to other objects, not just planets -> Newton showed that any object going around another object will obey Kepler's first two laws

• Includes unbound orbit shapes: parabola, hyperbola -> Newton showed elliptical bound orbits are not the only possible orbit shape orbits can also be unbound in shape of parabolas or hyperbolas
-BOUND: object goes around another object over and over again
Shape: ellipses
-UNBOUND: paths that bring an object close to another object just once
Shape: parabola or hyperbola

• Objects orbit their common center of mass-> Newton showed that two objects attracted by gravity both orbit around their common centers of mass
-It's the point where the two objects would balance if they were connected
-Equal Mass: center of mass is halfway between them
-Different Masses: center of mass lies closer to the more massive one
-Hugely different masses: center of mass lies inside the more massive one

-It's the point where the two objects would balance if they were connected

Equal Mass: center of mass is halfway between them

Different Masses: center of mass lies closer to the more massive one

GRAVITAIONAL ENCOUNTER: two objects exchange orbital energy when they pass close enough that each feel the effects of the other's gravity
-EX: a comet (with an unbound orbit) passes by a planet, they exchange energy, the comet's orbit changes to bound

WHY WE HAVE 2 HIGH AND LOW TIDES: Earth's rotation carries us through the two bulges each day, giving us two high and low tides each day
Low tides: occur when location is halfway between the tidal bulges
High tides: occur every 12 hours 25 min because reaches its highest point in the sky every 24 hours 50 minutes

EFFECT TO EARTH:
-Tidal friction gradually slows Earth's rotation (and makes the Moon get farther from Earth)

-Earth's rotation tries to pull bulges with it

-the moon's gravity tries to pull the bulges back into line, slowing Earth's rotation

HOW IT EXPLAINS MOON'S SYNCHRONOUS ROTATION:
-The Moon once orbited faster (or slower) tidal friction caused it to ''lock'' in synchronous rotation.

18. I used newtons version of Kepler's third law to calculate Saturn's mass from orbital characteristics of its moon titan.

21. Venus has no oceans, so it could not have tides even if it had a moon (which it doesn't)

22. If an asteroid passed by Earth at just the right distance, Earth's gravity would capture it and make it our second moon

21. Doesn't make sense land can experience tidal friction too

22. Makes sense use explanation of how unbound can become bound

16. Suppose you could enter vacuum chamber on Earth. A feather would fall at the same rate as a rock.

19. If the sun were replaced by a giant rock that had precisely the same mass, Earth's orbit would not change.

20. The fact that the moon rotates once in precisely the time it takes to orbit earth once is such an astonishing coincidence that scientists probably will never be able to explain it

20. Doesn't make sense The moon's synchronous rotation can be explained by tidal friction

[notes]
-compound: molecule with two or more types of atoms (H^2O [water -> 2 hydrogen atoms 1 oxygen atom]

-chemical properties of molecule are different from those of its individual atom (ex: molecular oxygen [O^2] behaves differently from atomic oxygen [O]

-Molecules have additional energy levels because they can vibrate and rotate.

-The large numbers of vibrational and rotational energy levels can make the spectra of molecules very complicated.

ions: atoms with a positive or negative electrical charge

-measured in units of watts: 1 watt = 1 joule/s.

-power can only tell us how fast energy has been transferred, not the total amount

-bc the amount of energy transferred from one object to the other object does not only depend on the rate of the energy flow, which is power, but also depends on how long it has been transferring.

-Interactions between light and matter determine the appearance of everything around us.

Opaque objects block (absorb) light.
• Transmission

Transparent objects transmit light.
• Reflection/scattering

• Emission: the process by which matter emits energy in the form of light
-EX: a light bulb emits visible light the energy of the light comes from electrical potential energy supplied to the light bulb

• Absorption: the process by which matter absorbs radiative energy

Opaque objects block (absorb) light.
- EX: when you place your hand near an incandescent light bulb, your hand absorbs some of the light, and this absorbed energy warms your hand

• Transmission: the process in which light passes through matter without being absorbed
-(glass or air)

Transparent objects transmit light.

• Reflection/scattering:
-Reflection- light bounces off matter all in the same general direction (EX: A mirror reflects light in a particular direction)
-Scattering- when the bouncing is more random (EX: A movie screen scatters light in all directions)

-Red glass transmits red light but absorbs other colors

-EX: light from the sun or a light bulb is often called white light

SPECTRUM:
-Passing visible light through a prism separates it into its "component" colors -> a spectrum

-it's an electromagnetic wave but it also comes in individual "pieces" or particles called photon

-each photon has a precise wavelength, frequency, and energy (the energy depends on its frequency)

-the wavelength, frequency, and energy of light are simply related because no matter what the frequency, wavelength, or energy of an electromagnetic wave, ALL types of electromagnetic radiation (light) travel at the EXACT SAME SPEED! (the speed of light)

-energy is proportional to frequency

-wavelength is inversely proportional to its frequency

• We call this the "Wave-Particle Duality of Light"

WAVELENGTH: is the distance between two wave peaks.

FREQUENCY: the number of peaks passing by any point each second (the number of times per second that a wave vibrates up and down)
-units of hertz or cycles per second

SPEED: how fast the peaks travel / how fast the energy travels from one place to another
-Wave speed = Wavelength × Frequency

RELATIONSHIP:
-energy is proportional to frequency

-wavelength is inversely proportional to its frequency

• High frequency ↔ short wavelength ↔ high energy
• Low frequency ↔ long wavelength ↔ low energy

EX: A wave has a wavelength of 1cm and a frequency of 3 hertz.
-wavelength tells us that each time a peak passes by, the wave peak has traveled 1 cm

-frequency tells us that three peaks pass by each second

-the vibrations of the electric field in an electromagnetic wave will cause any charged particle (electrons) to bob up and down, which is how we tell wavelength, frequency, and speed

RELATIONSHIP:
-because all light travels at the same speed, the longer the wavelength the lower the frequency and vice versa

-energy is proportional to frequency

-wavelength is inversely proportional to its frequency

• High frequency ↔ short wavelength ↔ high energy

-each photon of light carries a specific amount of radiative energy.

-the shorter the wavelength/ higher its frequency the higher the energy of the photons

LIKE PARTICLES:
-can be counted individually

• Reflection can change the polarization of light.

-Electromagnetic radiation: another name for light of all types

• Trends on the electromagnetic spectrum:

• High frequency ↔ short wavelength ↔ high energy

• Low frequency ↔ long wavelength ↔ low energy

Lowest to highest energy / frequency
-RADIO WAVES
-MICROWAVES
-INFRARED
-VISIBLE LIGHT
-ULTRAVIOLET
-X-RAYS
-GAMMA RAYS

Shortest to longest wavelength:
-gamma rays, x-rays, ultraviolet, visible light, infrared, microwaves, radio waves

EXPLANATION:
- energy&frequency the same bc energy is proportional to frequency
-Wavelength different bc wavelength is inversely proportional to its frequency

RADIO WAVES:
-longest wavelength and lowest frequency
-useful for radio communication bc they make electrons move up&down in an antenna
-carry so little energy that they don't noticeably effect our bodies
MICROWAVES:
-wavelength range from micrometers to centimeters
-considered a subset of radio waves

INFRARED:
-lies beyond the red end of the rainbow
-light with wavelengths somewhat longer than red light
-molecules moving in a warm object emit infrared light (why we associate it w/heat)

VISIBLE LIGHT:
-light that our eyes can see
-the particular frequencies that our eyes happen to be capable of detecting (Human eyes cannot see most forms of light.)
-wavelengths range from 400 nanometers at the blue/violet end of the rainbow to 700 nanometers at the red end
-nanometer (nm) is a billionth of a meter
-vision's possible bc receptors in our eyes respond to visible light photons

ULTRAVIOLET:
-lies beyond the blue/violet end of rainbow
-wavelengths somewhat shorter than blue/violet light
-ultraviolet photons carry enough energy to damage skin cells, cause sunburn/cancer

X-RAYS:
-shorter wavelengths than ultraviolet
-can be used to make images of bones/teeth bc x-ray photons have enough energy to penetrate through skin/muscle but is blocked by bones/teeth


Why is cross section inversely proportional to wavelength for interstellar scattering?

The following problem was part of a homework for my Cosmology class:

Compare the probability of interstellar scattering of photons of yellow light (5000 angstroms) and 50 micron infra-red light.

The only explanation my professor provided was: sigma is inversely proportional to lambda (this was written on the board)

In other words the scattering cross section is inversely proportional to the wavelength. (this is my understanding of what was on the board)

However, the units do not match up. Cross section is an area (distance squared) and wavelength is distance. I know that in astronomy we often make 'radical' approximations, but a mismatch on the units seems to be an inconsistency far beyond the "within an order of magnitude" tolerance level.

On a purely conceptual level, it would make sense that the probability of scattering would be inversely proportional to some power of the wavelength, because radio waves (large wavelength) pass through brick walls (object is much smaller than wavelength) while visible light (small wavelength) is stopped by brick walls (object is much larger than wavelength).

I guess my question is: what is the reasoning behind sigma is inversely proportional to wavelength? Was my interpretation of those symbols correct? If so, why don't the units match up? Are there any other ways to solve or conceptualize this problem?


Does Gravity decrease at a steady rate as we go away from the Earth?

Is r radius of earth about 4000 miles, and 2r about 8000 miles?

Is r radius of earth about 4000 miles, and 2r about 8000 miles?

Is r radius of earth about 4000 miles, and 2r about 8000 miles?

”It falls off quickly.”

Grammar Police
Internal Affairs

I am trying to understand several things. Germany started working on the V2 rocket about 1930 but did not launch until until about 1943 & 1944. The rocket had 25 tons of thrust on 75% ethanol 25% water plus liquid oxygen. The engine ran full throttle for 70 seconds that put the rocket 50 miles above earth. The rocket coasted up to a total of 120 miles with no engine thrust before it returned to earth in 210 seconds.

NASA space program was based on German rocket technology the engine had a fuel pump that makes the engines run at full throttle until fuel is gone.

Space X rockets have no fuel pump. They use 300 psi helium to pressurize the liquid methane & liquid oxygen. SpaceX engines run about 1/4 throttle compared to German technology.

I am trying to understand when fuel runs out how far can a rocket coast with no engine thrust before it reaches maximum distance from earth.

I was thinking if I knew and understood gravity, and know a rocket weights 12 tons, travels at 3400 mph for 70 seconds. I could get a better understanding about how far a rocket could be predicted to travel when fuel runs out.

I have an idea that a rocket engine can gradually throttle down at the same rate that gravity degreases and maintain the same speed because at a certain elevation there is no atmosphere and no wind resistance.

In 1930 it is interesting Germany knew with no knowledge of rockets that a rocket would coast 70 more miles up after engine was off. The law of motion probably let then calculate distance assuming they knew the value of gravity at 120 miles up.

I think I answered my own question. I understand something I did not know before. Problem is not much different than a car traveling at a certain speed then running out of gas, how far will it coast before it stops.


Condenser capacity inversely proportional to source voltage - why?

Well, you don't say which formula but I suspect that you mean
C=Q/V, the definition of capacitance.
If this is the case, the capacitance of a given system (capacitor) is not inverse proportional to V. This would be the case if Q were a constant (which it is not). When V changes, Q changes as well.The meaning of the formula is that the ratio between Q and V is a constant and this constant is what is called capacitance.

If you mean something else, please show the formula.

Thanks mate, it's a bit clearer, but still a little over my head since I don't even have high school behind me. It seems to be what I'm looking for though, so I'll definitely educate myself further on the matter. Thanks again!

Well, you don't say which formula but I suspect that you mean
C=Q/V, the definition of capacitance.
If this is the case, the capacitance of a given system (capacitor) is not inverse proportional to V. This would be the case if Q were a constant (which it is not). When V changes, Q changes as well.The meaning of the formula is that the ratio between Q and V is a constant and this constant is what is called capacitance.

If you mean something else, please show the formula.

Yes, terribly sorry, I really should have put the formula to avoid confusion over my original question, C=Q/V is the formula in question.
Though, I would like to know exactly how the change of voltage with a constant charge affects the capacitance. I can understand that, the larger the charge is, the more electrons there are to fit into the capacitor, and therefore the capacitance is larger.
However, thinking it through, I would also assume (leaving aside that the calculations wouldn't work out, more as a thought experiment) that the greater the voltage, the greater will the capacitor's capacitance would be. Let me elaborate why my mind is inclined to think that:

The greater the voltage, the greater would essentially be "electron surplus-shortage" the difference between the power source's poles. I would say that, since one side of the power source is positively charged, therefore the same panel of the capacitor (assuming it's consisted of two panels with an insulator in between, easier for me to explain the situation if we assume this type of a capacitor) would also be positively charged, and the other side being negatively charged, the greater difference would amount to a greater electric force, effectively "pulling in" more electrons to the panel, increasing the capacity, and actually increasing the charge.
I know my logic is terribly flawed, but this is the most reasonable solution I can work out when imagining how this plays out on the microscale in a real circuit. I would really love to find out what exactly is happening inside the capacitor though. Thank you very much for your input!


How can we see the Big Bang?

There is no "epicenter" to the big bang. There is no center to the universe. The big bang was not an explosion that happened at a single point.

I suggest you Google "surface of last scattering" to get a start on understanding what you are asking about, and then come back if you still have questions (as you likely will )

Like the two posters above said, the solution is that there is no one point in our current universe on which the big bang occurred. In other words, it's not like you can point to a direction in the sky and say "the big bang happened that way!". That one point from which all emerged IS our current universe (ALL the infinity of it!). The big bang happened everywhere, because back then, everywhere was only 1 point, that 1 point expanded to be everything that we see! (Actually, one should probably not take the collapse back to the point of the big bang, as the singularity itself is indescribable with our current physics). Admittedly, that is a very weird notion, so it's not your fault that you made this mistake. The light that we see all around is light that came after the big bang, the farther we look (in any direction!), the farther back in time we see.

As it turns out however, we can only see to the "surface of last scattering" (this is the CMBR). This is the radiation from the time when the electrons and protons cooled enough to combine into atoms (this is called recombination for some reason. even though it was the first time this happened) and let all the light out (previously, the light was trapped). This surface corresponds to a time of

400,000 years after the big bang happened. So, currently, we can't see anything that happened before

400,000 years after the big bang because the light couldn't move around before then.

Now, if we could get real neutrino observatories set up and watch the neutrinos produced from the big bang, we would be able to see much farther into our past (I don't know off the top of my head the exact number estimated for a neutrino's "surface of last scattering"). But neutrinos are notoriously difficult to detect, and the signal would be very very faint.

There is no "epicenter" to the big bang. There is no center to the universe. The big bang was not an explosion that happened at a single point.

I suggest you Google "surface of last scattering" to get a start on understanding what you are asking about, and then come back if you still have questions (as you likely will )

Also, here is the link to the essay on the surface of last scattering (forgot to post it in the earlier post).

I'm not much on thermodynamics (MAN I hated that course in undergraduate school) but I think "closed system" doesn't apply to a system that is expanding, which the universe has been doing ever since the singularity.

I hope someone here with a better understanding of thermodynamics can give you a more definitive answer.

I'm not much on thermodynamics (MAN I hated that course in undergraduate school) but I think "closed system" doesn't apply to a system that is expanding, which the universe has been doing ever since the singularity.

I hope someone here with a better understanding of thermodynamics can give you a more definitive answer.

The cooling is a reduction in the energy density due to the expansion, so it isn't an issue for the first law of thermodynamics.

That isn't to say that the expansion of the universe doesn't present problems for the first law of thermodynamics though. The vacuum energy is an issue, but then general relativity doesn't get on too well with it anyway.

The universe is treated as a close system as their is no outside influence. Just prior to last scattering their was a tremendous reheating phase due to the end of inflation. This high energy state allows thermal equilibrium. Different particle species will remain in thermal. equilibrium, only if they interact with each other often enough .Since the Universe expands, particle densities become smaller and smaller, and ultimately the various particle species decouple from each other

First law of thermodynamics: Because energy is conserved, the internal energy of a system changes as heat flows in or out of it. Equivalently, machines that violate the first law (perpetual motion machines) are impossible. Heat is the flow of thermal energy from one object to another.

if this is the law your referring to this law doesn't apply to cosmology as vacuum energy and quantum tunneling. Also the Heisenburg uncertainty principle is involved in quantum virtual particle production processes. Essentially the process is originally described by Allen Guth's false vacuum inflationary model. Which later included the inflaton for chaotic eternal inflation.
In essence a higher energy potential region (true vacuum) can quantum tunnel to a lower vacuum potential (false vacuum)(hopefully I got the sequence correct lol if not I'm positive Bapowell will politely correct me )

Through the above process and the Heisenburg uncertainty principle, its quite possible to have a universe develop from nothing. Lawrence R Krauss has written and supported this process

edit I did get the false vacuum true vacuum sequence wrong lol. the false vacuum is the local minimum but has a higher energy potential than the ground state (lowest energy potential true vacuum.) So tunneling will go from false vacuum to true vacuum


RELATIVISTIC NONLINEAR OPTICS

Raman Scattering, Plasma Wave Excitation and Electron Acceleration

The local phase velocity , described in eqns [98] and [111] , can also vary longitudinally if the intensity and/or electron density does. Local variation in the index of refraction can ‘accelerate’ photons, i.e., shift their frequency, resulting in photon bunching, which in turn bunches the electron density through the ponderomotive force (F), and so on. When the laser pulse duration is longer than an electron plasma period, ττp = 2 π/ωp, this photon and electron bunching grows exponentially, leading to the stimulated Raman scattering instability. Energy and momentum must be conserved when the electromagnetic wave (ω0, k0) decays into a plasma wave (ωp, kp) and another light wave (ω0ωp, k0kp).

From an equivalent viewpoint, the process begins with a small density perturbation, Δne, which, when coupled with the quiver motion, eqn [13] , drives a current J = Δneeve. This current then becomes the source term for the wave equation (eqn [91]) , driving the scattered light wave. The ponderomotive force, due to the beating of the incident and scattered light wave, enhances the density perturbation, creating a plasma wave and the process begins anew. In three dimensions, a plasma wave can be driven when transverse self-focusing and stimulated Raman scattering occur together, a process called the self-modulated wakefield instability.

Two conditions must be satisfied for self-modulation to occur in the plasma. First, the laser pulse must be long compared to the plasma wave, Lλp This allows the Raman instability time to grow, and it allows for feedback from the plasma to the laser pulse to occur. Second, the laser must be intense enough for relativistic self-focusing to occur, P > Pc, so that the laser can be locally modified by the plasma. Under these conditions, the laser can form a large plasma wave useful for accelerating electrons.

As the long laser pulse enters the plasma, it will begin to drive a small plasma wave due to either forward Raman scattering or the laser wakefield effect from the front of the laser pulse. This small plasma wave will have regions of higher and lower density with both longitudinal and radial dependence. That is, the plasma wave will be three-dimensional in nature with a modulation along the propagation direction of the laser and a decay in the radial direction to the ambient density (see Figure 11 ) . The importance of this lies with how it affects the index of refraction in the plasma. In the regions of the plasma wave where the plasma density is lower, the radial change in the index of refraction is negative, ∂n(r)/∂r < 0. This means that this part of the plasma acts like a positive lens and focuses the laser. Whereas regions of the plasma wave where the density is higher, ∂n(r)/∂r > 0, the opposite occurs and the laser defocuses. This has the effect of breaking up the laser pulse into a series of shorter pulses of length λp/2 which will be separated by the plasma period. The instability occurs because of how the plasma responds to this. Where the laser is more tightly focused, the ponderomotive force will be greater and will tend to expel more electrons. This decreases the density in these regions even further, resulting in more focusing of the laser. This feedback rapidly grows, hence the instability.

Figure 11 . The plasma wave generated by a SMLWFA is three-dimensional in nature. Note that the darker regions correspond to areas of higher plasma density. The graphs to the right represent lineouts of the plasma density longitudinally and radially at the indicated points. (Reproduced with permission from Wagner R (1998) Laser–plasma electron accelerators and nonlinear relativistic optics. PhD thesis, University of Michigan.)

The phase velocity of the plasma wave in the case of forward scattering is equal to the group velocity of the beat wave, which for low-density plasma is close to the speed of light, as can be seen from the relation:

where eqn [94] and ω p 2 ≪ ω 2 were used to show that η is close to unity. Such relativistic plasma waves can also be driven by short pulses (ττp). In this case, the process is referred to as laser–wakefield generation, referring to the analogy with the wake driven by the bow of a boat moving through water, but the mechanism is similar (except it has the advantage that the plasma wave is driven linearly instead of as an instability).

In either case, the resulting electrostatic plasma wave can continuously accelerate relativistic electrons with enormous acceleration gradients. The gradient can be estimated from eqn [92] and the fact that because

corresponding to 1 GeV/cm for ne = 10 18 cm −3 . Because this gradient is four orders of magnitude greater than achieved by conventional accelerators (based on fields driven by radio-frequency waves pumped into metal cavities), laser-driven plasma accelerators have received considerable recent attention. They have been shown to accelerate an amount of electron charge (100 nC) comparable to that from conventional accelerators and to have superior transverse geometrical emittance (product of divergence angle and spotsize, similar to the f/# in light optics). However, their longitudinal emittance is currently much inferior, energy spreads of 100%. They have been shown to be useful for much of the same applications: radio-isotope production, radiation chemistry, as well as X-ray, proton, and neutron generation. Once the longitudinal emittance can be reduced, they may be advantageous for, among other applications, injectors (especially of short-lived unstable particles) into larger conventional accelerators for high-energy physics research and light sources, and, as discussed in the section on radiation from relativistic electrons about, as stand-alone all-optically driven ultrashort-pulse duration X-ray sources.

The SIMLAC code has been used to study wakefield generation and laser propagation in the limit a 2 ≪ 1. It draws from nonlinear optics models and treats propagation in the group velocity frame. In this idealized model (which assumes perfect Gaussian beams), the pulse and wake are maintained over long enough propagation distances to accelerate an electron to GeV energy, as shown in Figure 12 . A three-dimensional envelope equation for the laser field was derived that includes nonparaxial effects, wakefields, and relativistic nonlinearities.

Figure 12 . The ‘standard’ resonant wakefield simulated with SIMLAC, a code that moves at the light pulse's group velocity. (Reproduced with permission from Umstadter D (2001) Review of physics and applications of relativistic plasmas driver by ultra-intense lasers. Physics Plasmas 8: 1774.)

The resonant wakefield has been characterized experimentally by temporal interferometry, as shown in Figure 13 . However, this was done only for the tight-focusing case in which the laser spotsize is much smaller than the plasma wave wavelength (r1λp) and thus the transverse wakefield was much greater than the longitudinal wakefield.

Figure 13 . Typical result of a phase shift measurement to study a resonantly excited laser wakefield plasma wave by means of time-domain interferometry. Parts (A) and (B) have different color scales. The bottom graph is a line out of part (B) along the laser axis. (Reproduced with permission from Marquès JR, Dorchies F, Audebert P, Ceindre JP, Amiranoff F, Gauthier JC, Hammoniaux G, Antonetti A, Chessa P, Mora PTM and Antonson J (1997) Frequency increase and damping of nonlinear electron plasma oscillations in cylindrical symmetry. Physics Review Letters 78: 3463. Copyright (1995) by the American Physical Society.)

A typical experimental setup, used to study electron acceleration, is shown in Figure 14 .

Figure 14 . Artistically enhanced photograph of the acceleration of an electron beam by a laser interacting with a gas jet inside a vacuum chamber. The laser crosses the picture from left to right and is focused by a parabolic mirror (right side of the picture). The supersonic nozzle (shown in the middle of the picture) is positioned with micron accuracy with a 3-axis micropositioner. The e-beam makes a small spot on a white flourescent (LANEX) screen, shown in the upper left-hand corner of the picture. (Reproduced with permission from Umstadter D (2001) Review of physics and applications of relativistic plasmas driver by ultra-intense lasers. Physics Plasmas 8: 1774, with permission from the American Institute of Physics.)

Dramatic reduction of the angular divergence of a laser accelerated electron beam was observed with increasing laser power above the relativistic self-focusing threshold, as shown in Figure 15 .

Figure 15 . Images of the spatial profiles of the electron beam measured by a ccd camera imaging a LANEX screen at a distance of 15 cm from the gas jet for various laser powers. The divergence angle of the beam decreases to a value of Δθ=1° at a power of 2.9 TW, corresponding to a transverse geomtrical emittance of just ε ≲ 0.06π mm-mrad. (Reproduced with permission from Umstadter D (2001) Review of physics and applications of relativistic plasmas driver by ultra-intense lasers. Physics Plasmas 8: 1774, with permission from the American Institute of Physics.)


THE BIO-ULTRACARBOFLUID PROCESS

C. Skarvelakis , . G. Antonini , in Biomass for Energy and the Environment , 1996

Results of viscosity regulation

Then, viscosity of slurry depends upon its composition. Generally, it increases with a charcoal or fuel-oil concentration increase and decreases with an increase of water or additive concentration ( Skarvelakis, C., 1992 ).

According to the principle of viscosity regulation described above, two regulators (fluids or solids) are necessary. Viscosity measurement has shown that water could be a good regulator for decreasing viscosity. Althought an additive may decrease viscosity, it is high costmeans that it use unlikely. The solid content increases the viscosity of slurry. The mixture after centrifugation (charcoal/water/fuel-oil), ( Fig. 1 ) is rich in charcoal (55% to 60%) when compared to charcoal concentration in Bio-UCF slurry (40% to 50%) and and therefore appears a better option than charcoal as a regulator. Numerous tests have been performed in order to confirm the regulation process of slurry viscosity.

Figure 3 exhibits an example of Bio-UCF viscosity regulation with the addition of water. An initial volume of water is introduced, destined to incite the first reaction of slurry viscosity. It is shown ( fig. 3 ) that instruction an of 0.150 Pa.s is obtained with very good precision. Water can therefore be used as a fluid regulator for decreasing viscosity. Other tests have been performed in order to increase the viscosity of a very fluid slurry.

Fig. 3 . Viscosity regulation of Bio-UCF

After viscosity regulation, combustion mixture is kept in storage in an agitated tank, in readiness to feed a boiler for combustion tests.


Watch the video: Proportional vs. Antiproportional - einfach erklärt Gehe auf (November 2022).