Higgs Field

 When you step on a scale and look down at the number that shows up, what that number is telling you is how much force the mass of your body exerts on the ground. It's simple Newtonian mechanics. Force equals mass times acceleration. Gravity exerts the acceleration on the mass of your body, which creates a force. That's your weight. So weight is probably easy enough to understand, but mass is a little more nebulous. If you were floating in space, far away from Earth, you would essentially have no weight. But you would still have the same mass as you did standing on that scale. Where does the mass of your body come from? Well, the mass comes from all the atoms in your body that individually have a mass. Where does an atom's mass come from? Well, this is interesting because the mass of atoms at its core is really energy. In fact, all mass is energy. This is exemplified in Einstein's famous mass energy equivalence equation E equals mc squared.

 Massis interchangeable with energy, andthe constant c squared, or speed of light squared, is the conversion factor. So where is the energy of the atom coming from? Well, 99 % of the mass of an atom is contained in the binding energy within the nucleus. This energy is a result of one of the four fundamental forces of nature, called the strong force, which keeps the protons and neutrons glued together in the nucleus of atoms. That's where most of your body's so -called mass resides.

But it turns out that some of your mass, about 1%, is contained in the mass of the subatomic particles that make up the atoms. These are the electrons that form a cloud around the nucleus, as well as the quarks that make up the protons and neutrons. So now the question is, how did these subatomic particles have an intrinsic mass? If mass is energy, then what is the mechanism that confers this energy to these fundamental particles? This is where the Higgs field comes into the picture.

 This field is everywhere in space -time, but most explanations of how this field confers mass can't avoid getting highly technical, talking about symmetry breaking and other advanced mathematical concepts. In this video, I'm going to attempt to explain how the Higgs field confers mass in an intuitive way. So whether you're a math geek or not, you will hopefully get a very good intuitive understanding of what's really going on. That's coming up, right now. I've been wanting to make this video for a while, and I think you're going to find it really interesting. Before we get into it though, I want to thank our sponsor Blinkist that helped make this video possible. This is the one app that saves me more time than any other. Now, as you might suspect, I'm a voracious reader. Blinkist gives me access to over 5 ,500 non -fiction books and podcasts that I can read or listen to in only about 15 minutes. Now, it's not a replacement for reading the whole book, but it allows me to understand the most important things from them.

For example, I just finished listening to a book called The Latte Factor. It's about how making small changes in your life can result in huge outcomes over time, like drinking less latte. What I learned is how life is really a series of baby steps that may not have an immediate payoff, but over time can help you achieve big goals. And my goal this year is to improve my mental and physical health. Blinkist will help me reach that goal, and it can do the same for you. Whatever you want to achieve for yourself is available to you at Blinkist. Right now, Arvin Ash viewers get a whopping 30 % off your subscription, and you can enjoy two memberships for the price of one in a new feature called Blinkist Connect. This allows you to recommend and share your favorite titles with a friend or loved one. Your first 7 days is absolutely free. When you sign up, I highly recommend you click the link in the description. I think you'll be very impressed. Now, where were we? To understand how the Higgs field works, we have to first understand what our best theory describing all the matter in the universe, the standard model of particle physics, is trying to tell us.

 This theory describes all fundamental particles in the universe as excitations in quantum fields. So for example, an excitation of the electromagnetic field would be a photon. An excitation of the electron field is an electron. And an excitation of the quark field would be a quark, etc. These are waves, but when they are well localized as in a measurement, they appear to us as particles. These fields span all of space -time in all directions. The animation you're seeing here is a 2D representation for visualization, but the fields would be in three dimensions. Every type of matter and force particle has its own field. So all the fundamental particles of the standard model would be represented by different fields. All these fields, when they are in their ground state, that is their lowest energy state, even when no excitations or particles are present, always have some vibration. Due to the Heisenberg uncertainty principle, particles are constantly being created and annihilated.

These are virtual particles that exist for such short periods of time that they cannot be measured. They borrow energy from the vacuum when they are created and give it right back very quickly when they are annihilated. But this flurry of energetic activity for each field collectively adds up to zero net real particles. Real particles are created only when enough energy is transferred to these fields from some other field to cause an excitation.

 These excitations are the real particles. And since these are quantized fields, any excitation occurs only in set quantities. So for example, an excitation of the electron field would have to occur in integer multiples of 0 .511 MeV, which is the mass of one electron. So the field can have energy of 1 .022 MeV, which would be the energy of two electrons, or any other multiple of 0 .511, but not for example 0 .7 MeV, which would not be an integer multiple of 0 .511. But the electron only has this intrinsic mass of 0 .511 MeV because of its interaction with the Higgs field. Without this interaction, an electron would be massless. It would have energy, but only in the form of momentum, just like photons. This massless electron would be like a charged photon and move at the speed of light.

 In fact, without the Higgs field, all the other fundamental particles of the standard model would also be massless, with the possible exception of neutrinos. So the question is, how does this mass come about? To answer this, we have to understand the concept of vacuum expectation value of the various fields. What does this mean? Let's imagine for a minute, as if there were no Higgs field. If we then took any of the fields and put them inside an empty box, like the electron field, and if we then weighed that box, we would find that box would have no weight. In other words, the field would have no mass, even though the virtual electrons would be present throughout it. Similarly, all the other fields of the standard model would also have no mass inside the empty box, just quantum fluctuations. But here's the big kicker. There's an exception to this rule. The Higgs field. It's unique because the Higgs field in empty space, unlike every other field, has a net positive mass. Its mass is not zero in empty space. If we were to weigh the box with the Higgs field inside, it would have a weight. The Higgs field in empty space has a mass. This is called the vacuum energy. A more technical term for this is the vacuum expectation value, VEV, of the Higgs field. It is non -zero. It is in fact 246 Giga electron volts, or GeV. This is just the value that we would expect the Higgs field to have when it is in its vacuum state, or in its lowest energy state. Now, as I stated earlier, quantum fields can interact with each other. What this basically means is that anything that interacts with the Higgs field now effectively interacts with this new vacuum expectation value. And that interaction means energy.

And since energy and mass are equivalent, the form this interaction energy takes is indistinguishable from the form of energy associated with a rest mass. So when a fundamental particle interacts with the Higgs field, it gains an energy, or intrinsic mass. Without the Higgs field, forexample, the electron would be massless, like photons, and travel at the speed of light. However, since the electron is coupled to a field with positive value everywhere in the universe, individual electrons are constantly interacting with this Higgs field. This constant interaction effectively slows the electron down. So if you apply a force to an electron, youcan imagine a sort of pushback from the Higgs field that causes the electron to resist acceleration. This property is what we call inertial mass. The electron's behavior in the vacuum is that of a particle with a well -defined rest mass of 0 .511 MeV.

 This rest mass is determined by the strength of the coupling, or interaction, between the electron and the Higgs vacuum expectation value. It's like the mass of the Higgs field is shared with any other field that interacts with it. How much mass an excitation or particle in any given field has depends on its coupling constant. The fields of all massive particles are coupled to the Higgs to some degree.

 The larger this coupling is, the more mass its particles will have. Without the Higgs field, none of the other particles would have an intrinsic mass. The Higgs field is like a thick gravy, and if you try to run a spoon through it, it feels heavy, compared to moving the spoon through the air. So every elementary particle with mass interacts with this gravy in some way. The particles of the Standard Model that have mass such as electrons, quarks, and W and Z bosons are coupled to the Higgs field. While the fields of massless particles, like photons and gluons, are not. So why are some particles coupled, meaning why do some particles interact with the Higgs field, while others do not? We're not sure. This just appears to be the way the universe works. The photon happens to be one of the particles that does not interact with the Higgs field, and so it remains massless and moves at the speed of light.

 The mechanism of the Higgs field giving out mass to other particles is called symmetry breaking. This is a complex subject, but if you want to know more about symmetry breaking, I made a video about it right up here. Now I should add a note about neutrinos. The Standard Model predicts that they should be massless, but measurements seem to indicate that they do have a very tiny mass. We don't know the origin of this mass. It could be that they also interact with the Higgs, but no one really knows for sure.

 Now I want to reiterate what I said at the beginning. The Higgs field is only responsible for about 1 % of the mass of all the matter in the universe that we can see. The vast majority of this mass is due to the energy of the strong force, which keeps the nuclei of atoms tightly glued together. Yet, this 1 % is essential to have the kind of universe we have. In a simple hydrogen atom, for example, the radius of the electron's orbit is inversely proportional to its mass. In a universe with no Higgs field, a massless electron would have an infinite radius, meaning no atoms would form at all. In addition, differences in particle mass are also responsible for the decay of free neutrons to protons. This is called beta decay. Without the Higgs field, the universe may not have any protons at all. So this tiny 1 % mass contribution turns out to be responsible for 100 % of the universe we happen to have.

9th Class || Short Questions/Answers of chapter 8

Why metallic handle of a door is colder than the wood of the same door when touched?

Because, the transfer of heat from our hand to the metallic handle is faster, as compared to wood, thus loosing more thermal energy resulting in our hand feeling colder.

Which type of the clothes do the people of desert wear and why?

The people of the desert wear loose-fitting, long, heavy robes, and head wrappings. 

The loose-fitting cloth prevents sweat from evaporating quickly and allows the air to circulate, hence help the body to retain fluids. These clothes also protect people living in deserts from hot winds and dust storms.

Why does temperature of sea shore cities remain moderate during most of the year?does temperature of land areas vary more during winters and summers? Why

Water has a higher heat capacity than soil and rock, so the ocean takes much longer to heat and to cool than the land. Coastal areas will generally have more moderate temperatures than in land areas because of the heat capacity of the ocean. 

Warm ocean currents tend to raise winter temperatures, while cool currents can lower summer temperatures. Prevailing winds also affect world temperatures. The difference in temperature between the land and the sea in different seasons determines the temperature of the prevailing wind.

During the process of sweating (perspiration), we feel cooling during a hot day. Why? 

That's because cooling your body via sweating relies on a principle of physics called "heat of vaporization." It takes energy to evaporate sweat off of your skin, and that energy is heat. As your excess body heat is used to convert beads of sweat into vapor, you start to cool down.

How a bimetallic strip, made up of copper and iron is used as automatic switch in different devices? Give one example.

Thermal expansion of bimetallic strips used as a heat operated switch in the circuit of automatic equipment's like iron box, fire alarms, electric heater etc. Some thermometers work on the principle of expansion of liquids In automobile engines useful work is done by the expansion of gases. 

How is anomaly in the expansion of water help marine life to survive in extremely cold areas?

The anomalous expansion of water helps preserve aquatic life during very cold weather. When temperature falls, the top layer of water in a pond contracts, becomes denser and sinks to the bottom. A circulation is thus set up until the entire water in the pond reaches its maximum density at 4°C.

Examples of anomalous expansion of water

Bottle Burst: If you put a fully-filled water bottle in the refrigerator and its temperature is below 4 degrees Celsius, then according to the anomalous behavior of water, the water inside the bottle will expand. Therefore, due to no space in the bottle for the expansion of water molecules, water will exert force on the walls of the bottle and it will burst.

Breaking of Rocks: Rocks break during winter because as the temperature decreases below, water inside the rocks starts expanding and hence exert a large amount of force on the rocks and results in the breaking of rocks. 

Aquatic Life: This unique property of water helps aquatic life to survive. With a further drop in temperature, water on top forms ice and becomes a bad conductor of heat. This stops the heat from escaping the water body and helps aquatic life to survive. Hence, aquatic life can survive even when the temperature reaches or falls below. 

Why rollers are used at the ends of steel bridges?

One end of girder is fixed in concrete, but the other end is not fixed into concrete. It is supported on rollers. This is because when temperature increases in summer, the steel girder in a bridge expands and the rollers slide to allow the expansion otherwise the bridge may break. 

MCQs QUESTIONS Chapter 8

1. Temperature is equal to of substance.

A. Average K.E. of molecules

B. Individual K.E. of each molecule

C. Average P.E of molecules

D. Individual P.E. of each molecule

2. Boiling point of water is.

A. 212 °C

B. 212 °F

C. 100 K

D.373 °C

3. J/kg K is the unit of:

A. Specific Heat Capacity

B. Heat Capacity

C. Latent Heat of Fusion

D. Heat Energy

4. At temperature, water has maximum density?

A. 0 °C

B. -4 °C

C. -273 K

D. 4°C

5. Evaporation takes place from of liquid.

A. Surface

B. Bottom

C. center

D. any location

6. Number of divisions on Fahrenheit scale between its reference points are:

A. 100

B. 173

C. 212

D. 180

7. By adding heat at melting point, the temperature of substance does not change. Heat added to substance is used to of substance.

A. increase K.E. of particles

B. decrease K.E. of particles

C. increase the attraction between particles

D. decrease the attraction between particles

8. 336 J/g is latent heat of fusion of a material. How much heat is required to melt 10 g of material at its melting point?

A. 336J

B. 3360 J

C. 33600 J

D. 3.36× 1051

9. Substances with their specific heats are given below. Which of the following substances will cool down quickly if heated for same temperature?

A. Water (4200 J/kg K)

B. Wood (1700)/kg K)

C. Copper (400 J/kg K)

D. Silver (250)/kg K)

MULTIPLE CHOICE QUESTIONS || Thermal Properties of Matter

1. All the bodies expand on heating:

a) Variable

b) Constantly

c) Uniformly

d) All of them:

2. Temperature is the:

a) Mass contained by the body

b) Force of the molecules of body

c) Degree of hotness or coldness of the body 

d) none of above

3. The SI unit of temperature is:

a) °C

b) °F

c) K

d) °K

4. Temperature of 30 °C in Fahrenheit is:

a) 86 °F

b) 80 °F

c) 30 °F

d) 90 °F

5. Human normal body temperature of 37 °C in Fahrenheit is:

a) 98. 6 °F

b) 98 °F

c) 100 °F

d) None of above

6. Boiling point of water in Fahrenheit is:

a) 100 °F

b) 273 °F

c) 212 °F

d) 373 °F

7. Celsius equivalent of O K is:

a) -273 °C

b) -459.4 °C

c) 0 °C

d) 100 °C

8. Fahrenheit equivalent of OK is: 

a) -273 "F 

b) -459.4 °F

c) 0 °F

d) 100 °F

9. Heat is a type of energy: 

a) Kinetic

b) Potential 

c) Mechanical 

d) None of above

10. Linear expansion of a rod occur along- dimension(s):

a) One

b) Two

c) Three

d) All

11. The acteristic of unequal expansion of different metals is employed in a device known as:

a) Thermometer

b) Burner

c) Calorimeter

d) Thermostat

12. Linear expansion depends on:

a) Length of rod

b) Change in temperature 

c) Nature of material of rod

d) All of above

13. Thermostat works on the principle of: 

a) Unequal expansion of solids

c) Anomalous expansion of water

b) Pascal's law

d) Vaporization

THE EXPANSION OF THE UNIVERSE

The evidence for the expansion of the universe comes from the change in wavelength of the light emitted by distant galaxies. We analyzed a similar effect as the relativistic Doppler shift, which we can write in terms of wavelength as

..... 1

where v represents the relative velocity between the source of the light and the observer. Here λ' is the wavelength we measure on Earth and λ* is the wave length emitted by the moving star or galaxy in its own rest frame.

The light emitted by a star such as the Sun has a continuous spectrum. As light passes through the star's atmosphere, some of it is absorbed by the gases in the atmosphere, so the continuous emission spectrum has a few dark absorp tion lines superimposed. Comparison between the known wavelengths of these lines (measured on Earth for sources at rest relative to the observer) and the Doppler-shifted wavelengths allows the speed of the star to be deduced from Equation 1.

      Of the stars in our galaxy, some are found to be moving toward us, with their light shifted toward the shorter wavelengths (blue), and others are mov ing away from us, with their light shifted toward the longer wavelengths (red). 

The average speed of these stars relative to us is about 30 km/s (10^-4 c). The change in wavelength for these stars is very small. Light from nearby galaxies, those of our "local" group, again shows either small blue shifts or small red shifts.

However, when we look at the light from distant galaxies, we find it to be systematically red shifted, and by a large amount. Some examples of these measurements are shown in Figure . We do not see a comparable num ber of red and blue shifts, as we would expect if the galaxies were in random motion. All of the galaxies beyond our local group seem to be moving away from us.

The cosmological principle asserts that the universe must look the same from any vantage point, and so we must conclude that any other observer in the universe would draw the same conclusion: The galaxies would be observed to recede from every point in the universe.

Hubble's Law

In the 1920s, astronomer Edwin Hubble was using the 100-inch telescope on Mount Wilson in California to study the wispy nebulae. By resolving indi vidual stars in the nebulae, Hubble was able to show that they are galaxies like the Milky Way, composed of hundreds of billions of stars. Hubble also was able to observe variable stars in the distant galaxies whose brightness oscillated with periods of days. Using a scale of period vs. brightness for the variable stars in nearby galaxies developed in 1908 by astronomer Henrietta Swan Leavitt, Hubble deduced the distances to the remote galaxies. Finally, plotting his deduced distances against the recessional velocities obtained from the red shifts, Hubble established the empirical relationship between distance and speed known as Hubble's law:

v = H_o d

The proportionality constant H0 is known as the Hubble parameter.

Figure a shows a plot of Hubble's data. Although the points scatter quite a bit (due primarily to uncertainties in the distance measurements), there is a definite indication of a linear relationship. (Hubble's distance calibra tion was incorrect, so the labels on the horizontal axis do not correspond to the actual distances to the galaxies.) 

More modern data based on observing supernovas in distant galaxies are shown in Figure b. There is again clear evidence for a linear relationship, and the slope of the line gives a value of the Hubble parameter of about 72 km/s/Mpc*, within a range of about ±10%. The Hubble parameter can also be determined from a variety of other cosmo logical experiments. These agree with the supernova data, and the best current value is 

The uncertainty in this value is on the order of +4%.

*A parsec, pc, is a measure of distance on the cosmic scale; it is the distance that corresponds to one angular second of parallax. Because parallax is due to the Earth's motion around the Sun, the parallax angle 2a is the diameter 2R of the Earth's orbit divided by the distance d to the star or galaxy. Thus, a = R/d radians, which gives 1 pc = 3.26 light-years = 3.084 x 10¹³ km. One megaparsec, Mpc, is 10⁶ pc. 

The Hubble parameter has the dimension of inverse time. As we show later, H0^-1 is a rough measure of the age of the universe. The best value of Ho gives an age of 14 x 10⁹ y. If the speed of recession has been changing, the true age can be less than H¹.

How does the Hubble law show that the universe is expanding? 

Consider the unusual universe represented by the three-dimensional coordinate system shown in Figure a, where each point represents a galaxy. With the Earth at the origin, we can determine the distance d to each galaxy. If this universe were to expand, with all the points becoming farther apart, as in Figure b, the distance to each galaxy would be increased to d'. Suppose the expansion were such that every dimension increased by a constant ratio k in a time t; that is, x' = kx, and so forth. Then d' = kd, and a given galaxy moves away from us by a distance d'-d in a time t, so its apparent recessional speed is 

If we compare two galaxies 1 and 2,

a relationship identical with Hubble's law, Eq. Thus, in an expanding universe, it is perfectly natural that the farther away from us a galaxy might be, the faster we observe it to be receding.

Notice also from Figure a that this is true no matter which point we hap pen to choose as our origin. From any point in the "universe" of Figure 15.3, the other points would be observed to satisfy Eq. 15.4 and thus also Hubble's law. We can further demonstrate this with two analogies. 

If we glue some spots to a balloon and then inflate it, every spot observes all other spots to be moving away from it, and the farther away a spot is from any point, the faster its separation grows. 

For a three-dimensional analogy, consider the loaf of raisin bread shown in Figure  rising in an oven. As the bread rises, every raisin observes all the others to be moving away from it, and the speed of recession increases with the separation.

The correct interpretation of the cosmological redshifts requires the tech niques of general relativity, which we discuss later in this chapter. According to general relativity, the shift in wavelength is caused by a stretching of the entire fabric of spacetime. Imagine small photos of galaxies glued to a rubber sheet. As the sheet is stretched, the distance between the galaxies increases, but they are not "in motion" according to the terms we usually use in physics to describe motion. However, the stretching of the space between the galaxies causes the wavelength of a light signal from one galaxy to increase by the total amount of the stretching before it is received at another galaxy. This is very different from the usual interpretation of the Doppler formula (Eq). (In fact, for some galaxies the wavelength shift is so large that the special relativ ity formula would imply a recessional speed greater than the speed of light!) At low speeds, the Doppler interpretation of the redshift (that is, calculat ing a speed from the Doppler formula and using that speed in Hubble's law) gives results that correspond with those based on an expansion of spacetime. 

However, for very large cosmological redshifts, a more correct analysis must be based on the stretching model:

where Ro represents a "size" or distance scale factor of the universe at the present time and R represents a similar factor at the time the light was emitted.

The expansion of the universe has been widely accepted since Hubble's discoveries in the 1920s. There are, however, two interpretations of this expan sion. (1) If the galaxies are separating, long ago they must have been closer together. The universe was much denser in its past history, and if we look back far enough we find a single point of infinite density. This is the "Big Bang" hypothesis, developed in 1948 by George Gamow and his colleagues. (2) The universe has always had about the same density it does now. As the galaxies separate, additional matter is continuously created in the empty space between the galaxies, to keep the density more or less constant. This is the "Steady State" hypothesis, proposed also in 1948 by astronomer Fred Hoyle and others. New galaxies created from this new matter would make the uni verse look the same not only from all vantage points but also at all times in the present and future. (To keep the density constant, the rate of creation need be only about one hydrogen atom per cubic meter every billion years.)

Both hypotheses had their supporters, and during the 1940s and 1950s, the experimental evidence did not seem to favor either one over the other. In the 1960s, the new field of radio astronomy revealed the presence of a universal background radiation in the microwave region, which is believed to be the remnant radiation from the Big Bang. This single observation has propelled the Big Bang theory to the forefront of cosmological models.

Statement of Purpose

 

Dear Sir/Madam

I wish to apply for M.S, Ph.D in program name at University name for the year 202_. This program is a solid step towards my future career as a researcher. I earned my bachelor degree from University name, county name in 201_. I am doing a job in job name. Now I have almost no. of years years of  experience. I have gained considerable knowledge during my job and study, but I want to enhance my knowledge by starting for Master degree and research work.

I have searched many countries for this purpose, but I get to know that country name is the best for its education system and research work also. I have found the program offered by your university exactly inline with what I want to do

I feel that getting education in a country other than one’s own is an education itself. Living in such an environment with people having similar goals and aspiration is an enthralling experience in one’s academic life and is of considerable importance in one’s professional career. It is a strong belief in my family that the European education system has the best to offer in the whole world. There are many opportunities and resources for research in country name that are not available in third world countries like Pakistan.

If I can get an opportunity to be a part of that intellectually stimulating environment, I am sure my talent will be put to optimal use. I feel that Master study at an European university is the best for further education, because of the flexibility incorporated in its learning system, its infrastructure and the intense interaction with the industry and exposure to the latest technology. To become a great researcher is my dream. Degree name is the first step towards my goal. My aim is to get knowledge that benefit others. I want to become inspirational person for my people and do something extraordinary for my country. Replete with academic activity and excellent factors, it has motivated me to choose this program to pursue my study.

I am sure that I will be the best choice for you and one day, perhaps, I shall make you proud. 

Sincerely,

Name