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As an exercise, write down the Lorentz transformation that corresponds to a velocity v in the x direction, and apply it to the description of a particle moving at velocity w in the same direction. Find the relationship between the resulting x' and t' coordinates. What do you get?
2. ### Electricity and the Earth

Only if you are connected to something which is connected to the negative wire. They don't. The direction of movement is into the positive source. And the direction of propagation of field changes is completely unrelated to the electrons' direction of movement. The current is established...
3. ### Let's say i'm in einstein's elevator

In Einstein's elevator, the field would be uniform. On a planet, it's not. With decreasing distance to the planet, the non-uniformity becomes more and more apparent.
4. ### Direct Product of Groups

- Closure: This is obvious. a *1 c is a member of G1, and b *2 d is a member of G2. Thus, (a *1 c,b *2 d) is a member of G1 x G2 by definition. - Identity element: If e1 is the identity in G1, and e2 is the identity in G2, the identity in G1 x G2 is (e1,e2). - Inverse element: With a *1 c = e1...
5. ### Why can't we use quantum bit entanglement for FTL information?

"The only people that even know what the corresponding entangled particles mean, is the people who are using them and understand what information they represent. No one else COULD know." "The only people that even know what the corresponding letters in the script to Days of our Lives mean, is...
6. ### Why can't we use quantum bit entanglement for FTL information?

No, what you quoted does not constitute a secure means of communication using quantum entanglement. With only 1 bit measured, it is of course impossible to detect that the message has been tampered with or spied on. In fact, it is not even communication, since no information is transferred from...
7. ### Why can't we use quantum bit entanglement for FTL information?

Well, you really don't get it, do you. The entanglement of the particles has no effect on your scenario. Nothing in your scenario requires that the particles are in an entangled state. You could send him a copy of the script to a Days of our Lives episode, and it would serve the exact same...
8. ### Why can't we use quantum bit entanglement for FTL information?

Oh great, so Mr. junior undergraduate's "cryptography" basically consists of assuming that no one knows where you or your friend are, or how you're communicating. Congratulations on completely missing the point of quantum cryptography. Good luck at university. You'll really impress your...
9. ### Why can't we use quantum bit entanglement for FTL information?

Well, then you obviously can't read. As I said, they would capture your particles, as you try to send them to your friend. They would then generate new entangled pairs of particles, and send one particle from each pair to your friend. When you think you're talking to your friend on the phone...
10. ### Why can't we use quantum bit entanglement for FTL information?

Entanglement is of no consequence in your example. It is no different from any other method involving an one-time pad. It is possible for the police to intercept the particles, measure them, and pass them on, without your friend becoming any wiser. Now, you might think, what if I tell my friend...
11. ### Writer's quantum entanglement Qs (help!)

Entanglement can not be used for communication. Whatever happens to system A cannot effect system B in any measurable way. Entanglement has to do with what you can infer about system B based on your measurement of system A. For example, a source can send particles in two opposite directions in...
12. ### Magnetic force and energy

When an object, such as a lump of iron, is accelerated by a magnetic field, where does the extra kinetic energy come from? Does the object become colder, or is it demagnetized?
13. ### Electrostatic potential from the perspective of an electron

No, by touching a wire, a current will flow into you until you are at the same potential as the wire. At this point, the charge that you have acquired is equal to your capacitance times the voltage. With a wire at thousands of volts, you will therefore feel a jolt. It can seen that it is...
14. ### Absolute value of infinity

\lim_{x \to 0}\frac{1}{x} = \left|\infty\right| This expression is blatantly incorrect and shows that the author has a basic misunderstanding of mathematics. What he probably means, if you could write it like that, is: \left| \lim_{x \to 0}{\frac{1}{x}}\right|=\infty But you can't. An...
15. ### The proliferation of mathematics cranks on the Internet

I've noticed on other discussion boards, that there is a surprisingly high number of people sharing a set of similar, unshakeable beliefs that contradict basic thereoms in mathematics and logic. Usually, these include: - 0.999... not being equal to 1, or not existing - That natural numbers...
16. ### Litle help understanding the point behind Calculus .

No, there may not be a limit at all points. A limit only exists if the function converges to a value as you approach the point. For example, the limits of the expressions \frac 1 x and sin\;ln\;x at x=0 does not exist. Furthermore, a function could have distinct left and right limits, such as...
17. ### Vector perpendicular to the plane

Do you see a 4z in your equation?
18. ### How to solve recurrence relation ?

Yeah, I don't know if there's a simpler way to solve this, but remember that when you take into account the right hand side, the equation has four roots, three of which are 3 and one that is 2. So, the solution must have the form: a_n=A2^n+(B+Cn+Dn^2)3^n
19. ### How to solve recurrence relation ?

When you have multiple roots, you must multiply the term with a polynomial. For double roots, the polynomial is n+1, and for triple roots, it's \frac{\left(n+1\right)\left(n+2\right)}2, etc. We extend the definition of a to the negative domain, and let a_n=0 for n<0. Then we find the value of...
20. ### Filter problem

Oh, nevermind. I had a bug in the program where I accidentally used \widehat{x} for \left|y_{-1}\right| for the next iteration.
21. ### Filter problem

I am trying to graph the frequency spectrum of a signal over time. To do this, for each frequency I use a filter defined by the following equation: y_n = Ae^{i\omega_0}y_{n-1} + x_n This has a frequency response of \frac 1...
22. ### Finding Equivalence Class

http://en.wikipedia.org/wiki/Interval_%28mathematics%29
23. ### Fundamental unit of information

Not really. Although a bit is the smallest amount of information that can be represented, it is clearly possible for a system to represent an amount of information that is greater than 1 bit but smaller than 2 bits.
24. ### X.y=0 but x and y are non-zero numbers

What is the exact formulation of the question in the book?

26. ### Looking for a method to calculate what number are used to make a number

When you have a number in an integer variable, it is already in binary and there is no need to convert it further. Most programming languages have an AND operator which performs an AND operation between the bits of two operands. In the C programming language, the operator is called &. For...
27. ### Creating and using an equation

No, it can't. But if you assume that one liter of water with 1% salt weighs the same as one liter of fresh water, you get the answer 0.5 kg. All you need to assume is the mass of one liter of ocean water (here, they have equated it to 1 kg), and all the other information you need to write down...
28. ### Geometry proofs.

An easier way: Let O be the centre of the circle. Then OC = OA = (AD+BD)/2. Then look at the triangle ODC to find the answer.
29. ### I think this is simple but I just cant work out how!

Think about what value you need to multiply the left hand side with to make it equal the right hand side.
30. ### Trigonometric identity for inverse tan

Do you think the identity should change if you replace the letter x with the letter y? Is the identity invalid for some value of y? What if y = ax? If you agree that it is still valid, what do you get when you put ax in the place of y?