m4rc

The parallax method is the method which depends on the least number of assumptions. The red shift method can be used but the only reason that we can assume that the distance is related to the red-shift is that it has been verified using other methods. Another method is to measure the brightness of a star/galaxy and assume the amount of light emitted by that star/gallaxy (absolute brightness). The measured brightness of the star will decrease with distance ([math]1/r^2 [/math] law). In some cases the astronomers can make accurate assumptions of absolute brightness of a star. Red giants, Cepheid variables, Type Ia Supernovae are 3 types of standard candles (see http://en.wikipedia.org/wiki/Standard_candle ). I believe that their distance of some of these were first measured using the parallax method. Using this data, it was noticed that their absolute brigtness was predictable so their brightness could be applied to measure the distances beyond what is possible with the parallax method.

I don't think that the recent discovery of neutrinos mass will change estimates of the mass of the universe. This is because astronomers can estimate the mass of galaxies by observing their rates of rotation (or something like that). For a long time it astronomers came to the conclusion that there was mass could not be accounted for by considering only the visible stars. Therefore they proposed that the galaxies contain a certain amount of unseen matter which they called dark matter. By discovering that neutrinos have mass, they have found an explanation for the dark matter. I'm not sure if this would explain all the dark matter.

The definition that I have given although develloped for solid state physics should still apply for Quantum field theory. I've seen other definitions for the Fermi level. Another is the energy where the probability that a given available electron energy state will be occupied (given by the Fermi function) is exactly 0.5. It is not obvious (even if you know the Fermi function) that this and my previous definition are equivalent. I suspect that you may have found another definition which may be correct as well. I chose my previous definition because, it would be easier to understand and does not resort to any complicated mathematics. You may want to look up: http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html for more information.

The fermi point is an amount of energy. Unless excited fermions, will fill every state available that have energy less than or equal to the fermi point. Usually the Fermi level is used to discuss electrons in semiconductors and metals. In semiconductors at absolute zero, electrons will fill up every available state that have energy of less than or equal to the fermi point. At higher temperatures, some electrons will be excited, so there will be some electrons with energies above the fermi level.

The force between the atoms travels at the speed of light. The atoms themselves move slower This is exactly what happens. Usually the increase in length is too small to notice. It is more noticeable if we use an object that is less rigid like a slinky. A slinky will be at its normal length if no force is applied to it. It you quickly move one end a few centimeters, it will then expand, then soon return to its original length, with the entire slinky having moved a few centimeters. The same thing will happen to a rubber band except the extension of the rubber band will be less because it is more rigid (but still strechable). A steel wire will also behave the same way but is even more rigid. In the case of the steel wire it will be very difficult to measure the extension because it will be very small and for a very short time.

If you move mass then this can be used tosend data. For example, you can have the rod tap out a message in Morse code at the other end. A moving mass does transfer information. However it does not move information faster than the speed of light. As mentioned earlier, the rod is not entirely rigid. The rod is really a collection of atoms bound by electrostatic fields. As you apply a force at one end of the rod, you are only moving the atoms at that end. As these atoms move, their electric feild moves at the speed of light and this is what applies a force on the next atoms in line. So there is always a delay between the motion of one end of the rod and when the far end starts moving. In realistic situation this delay is unnoticeable.

One group managed to get quantum interference patterns from fluronated buckyballs C60F48 as well as other large molecules. See http://physicsweb.org/articles/world/18/3/5.

I just looked up the Excel help files and found out that the LINEST function can give you the result you want. You may need to look it up as well as how to input array formulas. Here is an example of a linear regression with uncertainties using excel assuming that your data are in collumns x and y in rows 1 to 10. 1) Select a 2x2 array. 2) type in the function "=LINEST(y1:y10,x1:x10,true,true)" then press shift, control and enter (this will make the array formula apply to the whole array) 3) The top left value will be the slope, the bottom left value will be its uncertainty. The top right value will be the b value in y=mx+b while the bottom right value will be the uncertainty in b. Hopefully this will work OK.

Try http://www.scienceforums.net/forums/showthread.php?t=18473&highlight=oil+drop

No the uncertainty on the slope has very little to do with the uncertainty in the individual data points. For example, if you had a method of measuring your data that had a large uncertainty, you can get a relatively accurate measurement of the slope by taking lots of data. If you don't want to use the graphical method that I suggested in my previous post, then you can use the method of least squares described in http://www.lsmsa.edu/CMcMullen/Linear%20Regression.doc . Those are the only two methods for determining the error of the slope. You may be able to use software to do the calculation for you. Most computer programs dedicated to producing graphs (like origin, sigmaplot, genplot?) should calculate the uncertainty when they do a linear regression. As far as I know, Excell does not.

Another method to determine the uncertainty on a slope is to draw a line of best fit as well as lines with the minimum and maximum slopes that still adequatly fits the data (although not the line of best fit). The differences between the values will be your uncertainty in the value of the slope. See the last example in http://spiff.rit.edu/classes/phys273/uncert/uncert.html#slope for more details. There is an algeraic method that considers all the points but I don't remember all the details. The advantage of this method is that it considers all of your data and not just the two points that you use to determine the slope.

Interesting question. The answer is not obvious. The best information that i could find that may be relevant is statistics on ship production since 1964 (see http://www.coltoncompany.com/shipbldg/statistics/world.htm ). If we assume that they are all still operative and full of cargo this would add up to 9x10^8 tons (note that GT in the reference means gross tons and not gigaton). This would displace 9x10^8 m^3 of water. If we assume that the area of the oceans is 3.35x10^14 m^2 then these ships raise the level of the oceans by 2.7x10^-6 m or just 2.7 microns. Not much of an effect.

The difference between the two situations will be very small. Heat lost/gained by convection will be the same. The only thing that I can see that would change this is the latent heat gained or loss by evaporation or condensation. If the air is dry, then evaporation off both glasses will cause a reduction in temperature resulting in the hot glass reaching equilibrium first. If the air is very humid, then condensation will occur on the glasses, increasing their temperature, so the cold glass will reach equilibrium first.

E=mc^2 applies to both matter and antimatter. Antimmatter has mass too. It takes 1.022MeV of energy to make an electron and positron pair. Half of the energy becomes the mass of the electron and the other half becomes the mass of the positron.

You need to consider absorption in this case. Because you will absorbe some of the light (otherwise your eyes would not see any light). Initially, you would see yourself like you do using a curved mirror. If there was a small amount of absorption from the mirror and you, as the amount of light in the cavity increases, the temperature you and of the mirror would increase. Everything emits light when hot and this depends on the temperature only (look up black body radiation). For example moderatly warm items are infra-red, while hot items like hot heating coils are red, and very hot items are white. So eventually the blackbody radiation will be the main type of light in the sphere and everthing will be the same colour depending on temperature. After this then the light will either reach equilibrium at some point if heat is radiated outside. Otherwise it willl get hotter, and the light will get brighter and shifted to shorter wavelengths (bluer).

If I understand you correctly, I believe that you are suggesting measuring light intensity using a ccd, then using the light intensity to determine the distance of the light source. This can only work if you know the intensity of the light source. Astronomers are very interested in knowing the absolute intensity (intensity at the source) of various typres of stars in order to determine their distance. For example, I believe that they consider super novas as all emitting the intensity of light. The amount of light measured on earth will depend on the distance between the supernova and earth. They use this to determine the distance to other galaxies. I believe that they may also use pulsars since they know a relation between their absolute intensity and their frequency. For more information you can google terms like "standard candles".

From http://www.wollemipine.com/news/global_launch.php "The average price for a single tree was approximately A$3,600". They also mention that (at least some of) the money raised goes toward various conservative efforts. Many of the botanical gardens in Australia have one or two of these wollomi pines. They are usually protected by a fence/cage, but you can get a good look at it.

Normally in semiconductors, the valence band is full and the conduction band is empty. Despite the name the electrons in both the valence band and conduction bands are mobile and contribute to electrical currents. By absorbing the energy from light, a electron from the valence band can be promoted to the conduction band. When the electron gets promoted to the conduction band, a electron vacancy (usually refered to as a hole) is produced in the valence band. Impurities in solar cells are distributed in the solar cell (more on one side then the other) so that the electrons require less energy to be on one side. As a result, less energy is required for the electron vacancies(holes) to be on the other side. Therefore there will be an excess of negative chages on one side and this junction can be used like a battery. This excess of charges can only be maintained as long as light continued to promote electrons into the conduction band.

If you mean that you would like to see the proof for the rule for determining the derivative of a polynomials then see http://en.wikipedia.org/wiki/Calculus_with_polynomials .

You have noticed a major problem in modern cosmology. The universe is believed to contain a lot more matter than antimatter. As far as we know, there is no way to make matter without making an equal amount of anti-matter. Also as far as we know, there is no way to destroy antimatter without destroying an equal amount of matter. The main way to look for antimatter in the universe is to look for the gamma rays produced during antimatter/matter annihilation. There are no strong gamma ray sources consistent with matter/antimatter annihilation. Although one hypothesis is that the matter and antimatter would be separated. This is not believed to be the case (not certain of the justification for this). Therefore scientists are searching for differences between matter and antimatter to explain the excess amount of matter in the universe. They have found some small differences but so far there has been no adequate explanation. See for example http://www.sciam.com/article.cfm?articleID=000E7C2A-A53B-1C75-9B81809EC588EF21 .

No. You seem to be assuming that if [math]y=x^n[/math] then [math]dy/dx=x^n/x [/math] which is not true. If [math]y=x^n[/math] then dy/dx=nx^(n-1) . For the derivative of many functions see http://mathworld.wolfram.com/Derivative.html

The Heisenburg uncertainty principle states that the product of the uncertainty in a particle's position (dx) and the uncertianty in the particle's momentum (dp) is larger than a certain quantity. (dp)(dx) > h / (2 pi) This mean that is you manage to confine a particle in a small volume (resulting in a small uncertainty in position) then there will be a large uncertainty in the momentum of the particle. The particle will be bouncing around wildly inside it's allowed space. In order to have a particle confined to a singularity (dx=0) will imply an infinite amount of uncertainty in the particle's momentum (dp=infinity) in order to avoid violating the uncertainty principle. This would mean that you would have no idea what the momentum of the particle was. I am not able to comment to space-time jitters at plank length scales.

The second derivative of [Math]x^2-2x-15[/Math] is 2, means that the derivative of the derivative of [Math]x^2-2x-15[/Math] is 2.

no, you calculated the derivative wrong. if [Math]y(x)=x^2-2x-15[/Math] [Math]y(x)=f(x)+g(x)+h(x)[/Math] where [Math]f(x)=x^2[/Math], [Math]g(x)=-2x[/Math] and [Math]h(x)=-15[/Math] [Math]dy/dx=df/dx+dg/dx+dh/dx[/Math] [Math]=2x-2+0[/Math]