Why Witch Sabrina Looks Thinner While Riding On Her Broom.

[Solitary]

Better yet, here is both, in words and math:


SPECIAL RELATIVITY

Central to the discussion of special relativity is the idea of an inertial frame (or reference). This is basically a coordinate system, which might be attached to an observed object or to the observer, which undergoes no acceleration. Consequently, the relative velocity between two inertial frames is necessarily constant, providing what we refer to as uniform motion.

Einstein based his 1905 theory on two postulates:

1. No physical measurement can distinguish one inertial frame from another.

2. The speed of light (in vacuum) is the same in all inertial frames, regardless of any motion of the source.

 
Postulate (1) is also known as the Principle of Relativity and is a generalization of the idea of Galileo: that uniform motion is undetectable by mechanical experiments. This Galilean Principle of Relativity accounts for the fact that there are no obvious effects of the earth's motion through space, as it orbits the sun (at a tangential speed of about 17 000 km/hr !). For example, objects released from the top of a tower fall vertically downwards (towards the centre of the earth), as they would if the earth were stationary and not at some angle which depends on the earth's tangential speed. Einstein thought that Galileo's principle should apply to the whole of physics, including electromagnetic phenomena.


Postulate (2) derives from the idea of Maxwell that light behaves as a travelling wave, containing oscillating electric and magnetic fields which can advance (propagate) in a vacuum at a speed, denoted by the symbol c , which depends only on two basic constants of electrostatic and magnetic theory. The fields require no medium for their existence, unlike the case of sound waves (for example) whose velocity within a gas (or liquid or solid) is affected by any motion of this medium.


Previously, physicists had assumed that light waves behave somewhat like sound, propagating though an invisible medium which they termed the (aluminiferous) ether. Attempts to measure the speed of the earth relative to the ether failed; in particular, the Michelson-Morley experiment (performed repeatedly between 1881 and 1930) showed that light travels with exactly the same speed in two perpendicular directions, which is impossible if the earth is moving (due to its orbit around the sun) through an ether.

Length contraction

From Einstein's two postulates, several properties follow as a matter of pure logic. One of these is an effect called length contraction: the measured length (in the direction of motion) of an object which is moving at uniform speed v relative to an observer is less than if the object were stationary. The length measured when there is no relative motion is called the proper length and all other lengths are called improper. The length-contraction effect can be expressed mathematically as:

 improper length = (1/gamma) (proper length)

where 1/gamma = (1 - v^2 / c^2)^(1/2) and is less than unity; here ^ means to the power of , so ^(1/2) means taking the square root. Since the value of c (= 3.00 x 10^8 m/s) is so large, length contraction is entirely negligible (e.g. 1 part in 2 x 10^12 for v = 1000 km/hr) for objects such a cars, trains and airplanes.

There is no change in dimensions of the object which are perpendicular to the relative velocity v ; therefore it might be expected that a fast-moving cube would appear squashed (in the direction of motion) in a high-speed photograph. However light from different parts of the cube takes different times to reach the camera, so the photograph is not a record of the object at a single instant of time. This illustrates the difference between a true measurement and a simple observation. In fact, the cube would appear as if it had been rotated (through a fixed angle), due to the combined effects of length contraction and the finite (limited) speed of light.

Magnetic force can be thought to arise from electrostatic interaction, plus the length-contraction effect. For example, a metal contains potentially-mobile negative electrons and an equal number of immobile positive charges. In the absence of any electrical current, two parallel wires exert no force on each other because the attractive forces (electrons in one wire attracting positive charge in the other, and vice versa) are exactly balanced by repulsions (electrons in one wire repelling those in the other, likewise for the positive charges).

 With an equal current travelling in the same direction in each wire, the repulsive forces are unchanged (there is no relative motion between the electrons or positive charges) but the attractions are increased, since the positive charge "sees" the distance between the moving electrons as contracted (equivalent to an increase in negative charge per unit length of the wire) or vice versa. This increase is seen as a net attractive force between the two wires, usually attributed to the magnetic effect of the currents. We can say that Special Relativity unites the concepts of magnetic and electrostatic force into a single electromagnetic force.

Time dilation


Another effect predicted by special relativity is time dilation : a clock moving at uniform speed relative to an observer would be measured to run slow, arising from the properties of space-time and not from the finite speed of light. By analogy with the above, we can define an interval of proper time as a difference in the readings of a clock which is stationary with respect to the observer; where there is relative motion, we measure an improper time interval.
 

improper time interval = (gamma) (proper time interval)

 
Since gamma > 1, the interval between ticks of a "moving" (relative to the observer) clock is greater than for a "stationary" clock, so "a moving clock runs slow". This effect has been verified by carrying highly-accurate atomic clocks aboard aircraft and comparing their "readings" with those of an identical clock which remained stationary. Although the difference in elapsed time is miniscule, the extremely high accuracy of the atomic clock has allowed the time dilation effect predicted by Special Relativity to be verified.

A more extreme (but hypothetical) example is the case of two twins: one remains on earth, the other journeys at a high speed (approaching the speed of light) to a distant star and back. Upon returning, the moving twin will have aged less than the twin who stayed on earth. Although this is not a simple situation, since accelerations are necessarily involved in the return journey, detailed analysis shows that Special Relativity gives the right answer for the difference in age.

Relativistic mass


Later in 1905, Einstein published a paper which shows that Newton's second law (F = ma) applies to any object, travelling at any speed v, provided its usual mass (called the rest mass, if measured when the object is stationary) is replaced by a relativistic mass given by:

 
relativistic mass = (gamma) (rest mass)

 
Since gamma > 1, there is a relativistic increase in mass. Therefore, if a constant force F is applied to a stationary object, it initially accelerates at a constant rate a = F/m0 (where m0 is its rest mass) but as the speed v approaches c , gamma becomes significantly larger than unity, the relativistic mass m significantly exceeds m0 and the rate of acceleration (a = F/m) decreases. In fact, the acceleration tends towards zero as v approaches c : no material object can travel at or above the speed of light (in vacuum). At high speeds, the work done by the force F goes into increasing the relativistic mass, rather than the speed. In other words, energy provided by the force is converted into mass. Einstein introduced the concept of the total energy E of an object

E = m c^2 = (gamma) m0 c^2 = K + m0 c^2

as being the sum of its kinetic energy K and its rest energy E0 = m0 c^2 . From this equation, it is easy to show that the correct general formula for kinetic energy is:

K = (gamma - 1) m0 c^2


rather than the classical expression: K = (1/2) m0 c^2 . However, Einstein's general formula is consistent with the classical expression, since for v<<c we can use the binomial theorem:


(1+x)^n = 1 + n x + (1/2)n(n-1) x^2 + ... = 1 + n x (approximately) if x<<1

 
with x = -v^2/c^2 and n = -1/2 , so that gamma = (1+x)^n , giving

 
K = (1 + nx - 1) m0 c^2 = (nx) m0 c^2 = (-1/2) (-v^2/c^2) m0 c^2 = (1/2) mo v^2

For v<<c, Special Relativity gives the same result as Classical Physics, an example of the Correspondence Principle which states that a new scientific theory must give the same predictions as an older theory under conditions in which the older theory has already been found to be correct.


One situation in which speeds comparable to c are routinely achieved is in the acceleration of charged particles, for example electrons in a TV tube, oscilloscope or electron microscope, or other particles in a nuclear accelerator. The particles (charge q) may be accelerated via an electrostatic field, by applying a potential U to an accelerating electrode. The gain in kinetic energy of a particle is then equal to its loss in potential energy: K = - q U . For the electrons in color-TV tube, q = -e = -1.6E-19 Coulomb, m0 = 9.11E-31 kg and U = +20,000 volts, giving K = 3.2E-15 Joules = (gamma - 1) m0 c^2, so that gamma = 1.04 and v = 0.27 c . The electron-optic design of the tube must take into account the relativistic mass increase, and the fact that such designs work as expected is further evidence for the the accuracy of the Special Theory.

 
The conversion of energy into mass leads to the concept that mass and energy are somewhat equivalent, and that it is actually the total which is conserved. The conservation of mass-energy therefore replaces our previous idea of the separate conservation of these two quantities. The reverse process, conversion of mass into energy, is also possible. For example, a star like our sun converts hydrogen into helium and heavier elements within its core, via a nuclear reaction. The products of this reaction have slightly less mass than the original hydrogen and this difference in mass (Dm) accounts for the radiant energy (E = Dm c^2 = 4.0E16 J/s) liberated. The same principle applies to nuclear reactors and nuclear weapons, and even to the energy liberated in chemical reactions (where the change in mass is too small to be measured).

 The math in the special theory wasn't too hard was it?  :roll:  Solitary

[Thumpalumpacus]

And who says I'm treating them equally??? Before writing stupidities, use your head, if you have one!!!

You drew the equivalence, not me.:

I don't believe to be nice to people who are posting erroneous information. No more that I don't believe to be nice to people who believe in unacceptable religious beliefs, like vaginal mutilation.

Thinking that the two issues merit the same treatment is silly.  Own your words, understand that you used hyperbole (by way of implicit comparison) in a stupid fashion, and know that others here read the language for meaning.  

Don't thank me, you're the idiot who blurped some idiocy regarding my post. Next time, mind your own business if you can't make some intelligent comment. You're a waste.

Your opinion of me is none of my business, and your advice none of my interest.  In the meantime, be sure you don't once more draw an equivalence between genocide and an incorrect comment, because it makes you look like someone who cannot tell the difference between a mutilated clitoris and a shitpost.


Don't like my opinion?  There now, pobrecito, you'll live[/backpat]

[Rob4you]

Why Witch Sabrina Looks Thinner While Riding On Her Broom?

You really shouldn't question Witch Sabrina figure, because well... she's a witch so she can do magic, and the least thing you'd want is to anger her and then awake to find out that you've become a frog and now are in her pot!  :shock:

 [-X

[Jason78]

The math in the special theory wasn't too hard was it?  :roll:  Solitary

You've copied and pasted that from //http://web.pdx.edu/~egertonr/ph311-12/relativ.htm.  Anybody can do that.

Care to explain that math in your own words?

[josephpalazzo]

And who says I'm treating them equally??? Before writing stupidities, use your head, if you have one!!!

You drew the equivalence, not me.:

I don't believe to be nice to people who are posting erroneous information. No more that I don't believe to be nice to people who believe in unacceptable religious beliefs, like vaginal mutilation.

Thinking that the two issues merit the same treatment is silly.  Own your words, understand that you used hyperbole (by way of implicit comparison) in a stupid fashion, and know that others here read the language for meaning.  

Don't thank me, you're the idiot who blurped some idiocy regarding my post. Next time, mind your own business if you can't make some intelligent comment. You're a waste.

Your opinion of me is none of my business, and your advice none of my interest.  In the meantime, be sure you don't once more draw an equivalence between genocide and an incorrect comment, because it makes you look like someone who cannot tell the difference between a mutilated clitoris and a shitpost.


Don't like my opinion?  There now, pobrecito, you'll live[/backpat]

Again, which part of "looking at the root causes" don't you understand? When I was comparing I wasn't talking about treatment, as vaginal mutilation is a criminal offense, and that would entail going to the police and get that criminal arrested. If you can't comprehend that my comparison was based on the root cause - that is, ignorance - then blame your limited IQ. And from now on, you are on my ignore list.

[Solitary]

Why Witch Sabrina Looks Thinner While Riding On Her Broom?

You really shouldn't question Witch Sabrina figure, because well... she's a witch so she can do magic, and the least thing you'd want is to anger her and then awake to find out that you've become a frog and now are in her pot!  :shock:

 [-X

Witch Sabrina likes me she wouldn't do that.  Solitary

[WitchSabrina]

:rollin:

[Icarus]

The math in the special theory wasn't too hard was it?  :roll:  Solitary

You've copied and pasted that from //http://web.pdx.edu/~egertonr/ph311-12/relativ.htm.  Anybody can do that.

Care to explain that math in your own words?

Kind of what he does, I asked him to insult me with wit and he plagiarized Shakespeare. Nothing wrong with copy and paste as long as you're citing the source and not attempting to claim it as your own.

[Solitary]

The math in the special theory wasn't too hard was it?  :roll:  Solitary

You've copied and pasted that from //http://web.pdx.edu/~egertonr/ph311-12/relativ.htm.  Anybody can do that.

Care to explain that math in your own words?

Kind of what he does, I asked him to insult me with wit and he plagiarized Shakespeare. Nothing wrong with copy and paste as long as you're citing the source and not attempting to claim it as your own.

If it was that obvious I didn't write it myself, how is that plagiarizing?  :P   I really did want to insult you with my own words, but the sad truth is you wouldn't have understood me.    Solitary

[Solitary]

The math in the special theory wasn't too hard was it?  :roll:  Solitary

You've copied and pasted that from //http://web.pdx.edu/~egertonr/ph311-12/relativ.htm.  Anybody can do that.

Care to explain that math in your own words?

If JosephPalazzo can do it so can I.    Solitary

[Solitary]

The math in the special theory wasn't too hard was it?  :roll:  Solitary

You've copied and pasted that from //http://web.pdx.edu/~egertonr/ph311-12/relativ.htm.  Anybody can do that.

Care to explain that math in your own words?

How can I explain math in my own words when it requires abstract symbols? :roll:  

How about like this without complicating everything like JosephPallazzo does with many formulas that don't show the gist of the theory: Guv=8pituv.  :rollin:  :rollin:  Solitary

[Icarus]

If it was that obvious I didn't write it myself, how is that plagiarizing?  :P   I really did want to insult you with my own words, but the sad truth is you wouldn't have understood me.    Solitary

Really? I have to explain what constitutes plagiarism to an adult? Fine, plagiarism is anything where the author is taking credit for something they did not write. To avoid plagiarism you must cite the source of the quote and show the start and end of said quote. This is taught to every high school student at the start of each course. It's also explained every year, in every course in every university.

Your explanation of why you plagiarized Shakespeare falls short because the quote isn't in modern English. If you think I would understand that better, than how you were planning on insulting me? Were you planning on insulting me in German? French? Swahili?

I expect these kind of responses from teenagers who don't know any better and think they're super geniuses.

If you didn't mean to be intellectually dishonest and weren't trying to sound smarter than you actually are, you should have taken what I said for what it is (not an insult but trying to help someone who doesn't understand intellectual dishonesty). This will help you improve your arguments and quality of posts. If you continue to copy and paste without citing, you've just proven that you are willfully trying to be dishonest.

How can I explain math in my own words when it requires abstract symbols?

Easily, when I explain enzyme mechanics I don't have to use symbols or highly complex terms. An individuals understanding of a topic is measured in how well they can explain it to a layman using their own words.

[Solitary]

If it was that obvious I didn't write it myself, how is that plagiarizing?  :P   I really did want to insult you with my own words, but the sad truth is you wouldn't have understood me.    Solitary

Really? I have to explain what constitutes plagiarism to an adult? Fine, plagiarism is anything where the author is taking credit for something they did not write. To avoid plagiarism you must cite the source of the quote and show the start and end of said quote. This is taught to every high school student at the start of each course. It's also explained every year, in every course in every university.

Your explanation of why you plagiarized Shakespeare falls short because the quote isn't in modern English. If you think I would understand that better, than how you were planning on insulting me? Were you planning on insulting me in German? French? Swahili?

I expect these kind of responses from teenagers who don't know any better and think they're super geniuses.

If you didn't mean to be intellectually dishonest and weren't trying to sound smarter than you actually are, you should have taken what I said for what it is (not an insult but trying to help someone who doesn't understand intellectual dishonesty). This will help you improve your arguments and quality of posts. If you continue to copy and paste without citing, you've just proven that you are willfully trying to be dishonest.

How can I explain math in my own words when it requires abstract symbols?

Easily, when I explain enzyme mechanics I don't have to use symbols or highly complex terms. An individuals understanding of a topic is measured in how well they can explain it to a layman using their own words.

And likewise JosephPallazzo should be able to explain the Special Theory of Relativity in layman's terms.
It's amazing how many people think that helping me when they don't understand what I have written or point out that I don't put something in quotes when it is obviously not my quote is not an insult. There are a few intellectual snobs here that think they know it all and project on to me their intellectual superiority by name calling or being pedantic ass holes apenaaier. "Stop het in je nauwe gaatje droogkloot! Hoed je rotssmoil! " Actually those are in my own words even if it does have quotation marks. lul  Solitary

[Icarus]

And likewise JosephPallazzo should be able to explain the Special Theory of Relativity in layman's terms.
It's amazing how many people think that helping me when they don't understand what I have written or point out that I don't put something in quotes when it is obviously not my quote is not an insult. There are a few intellectual snobs here that think they know it all and project on to me their intellectual superiority by name calling or being pedantic ass holes apenaaier. "Stop het in je nauwe gaatje droogkloot! Hoed je rotssmoil! " Actually those are in my own words even if it does have quotation marks. lul  Solitary

The awesome thing is you actually did learn something. You didn't know what intellectual dishonesty was and now you do! You can't talk about special relativity, then bitch and call people intellectual snobs when they want you to cite your source instead of just an easy copy paste. If the topic was crayon colour, you might have a point. If you did understand special relativity, that would make you an intellectual snob by proxy. What kind of non-intellectual can explain special relativity off the top of their head?

I see that you didn't really address anything in my post but are attempting to deflect by misspelling Dutch. The quote should read, "Stop het in je nauwe gaatje droogkloot! Hoed je rotssmoel!" Those aren't your own words (unless you're just really bad with Dutch) and they're not terribly witty.

You've now proven that you're willfully attempting to be dishonest. That didn't take very long.

[Colanth]

Even dummies can understand an "explanation" that doesn't really explain the theory.

 :-k  #-o  Lets see, an explanation of the special theory of relativity doesn't really explain it if it doesn't have math. Makes sense to me.  8-)  Thanks! Does this mean if someone can't explain the special theory of relativity in a way that a dummy can understand it they are smarter than a dummy?

No, it just means that you can't explain math (which is what SR is) without using math.  And you can't understand math if you don't understand math.

No matter how many non-mathematical "explanations" of SR you can find, they don't actually explain SR, they just give you something that makes you think that you understand something that you don't actually understand.  (Christians used to think that they understood lightning - it was something God did.  It was an explanation, but it was about as close to reality as a non-mathematical "explanation" of SR is.)  It's like the "explanation" of e=mc[sup:1pouv1uc]2[/sup:1pouv1uc] that you posted.  It explains something, but it doesn't explain e=mc[sup:1pouv1uc]2[/sup:1pouv1uc].  It just claims that it does.