A Little Test

J

Janus

Temporal Navigator
I'm curious to see how much basic physics/general science people in this forum really know. So here's a short quiz, open book of course ;) ; I'll drop by in about a week to see what people come up with.

1) I'm standing on earth. Two spaceships, A and B, are speeding toward me from opposite directions. In my reference frame, I see both moving at 0.5c toward me. What speed does an observer on A see B moving?

2) Using the pseudo-classical Bohr model, what is the energy of the photon emitted when an electron is captured into its lowest energy state around a proton? (hint: this is a progression from the n=infinity 'orbital' to the n=1).

3) If I had a (hypothetical) massless box whose insides were perfect mirrors, and there was some light bouncing around inside, would that system be pulled gravitationally toward the earth?

4) What is a wavelength? An angular frequency? Write down a simple wave equation for light.

5) What is the expectation value for momentum

of a particle with mass m =/= 0 in an infinite square well? Assume Psi(x,t)=exp(iwt). If you want me to explain this further I can.

6) What is the cross product of the two vectors x=(x1,x2) and y=(y1,y2) ?

7) What does a derivative mean, in Classical Newtonian mechanics? For example, what is the meaning of the derivative of position x with respect to time t; (dx/dt) ?

That does it for now - if anyone gets them all, and there are definitive answers for each, which I can give with proof, I'll think up some more. Nothing like a good science quiz to keep the old neurons firing.
 
Dear Janus,
I will writethe answers to the questions you sent as soon as I lookthem up at the library from a physics book. To answer your question I have not recieved a formal education. I have obtained what knowlege I have by consulting physisists and by talking with others. I offered my designs and theories to them after recieving critiques I made corrections. There are still corrections to be made on all theories. I have a question that you may find entertaining none the less. What is the circumferance of an infinite circle. There is a mathematical answer. Good luck it may take you a while but it is a good creative exercize.

cheers,
Edwin G. Schasteen
 
Oh goodie, a science test !

1) Hail "A" via subspace and have them measure it for you.

2) I've been waiting a long time to find this one out.

3) Yes.

4) How long is a piece of string?

5) I didn't know a partical COULD expectate!

Can I stop now I'm really tired.
 
Janus and others:
Math, Science and time travel related: for your neurons, and other parts of your brain.
no physics book required...thinking only. (heheeh) :) goodluck. answers this Friday.

1.Your math professor invites you to her house and she says all of the houses on my side of the street are numbered consecutively in even numbers. There are 6 houses on my side of my block and the sum of their numbers is 9870. You don't know which block I live on and it's a long street but i will tell you that I live in the lowest number on my side of the block. what's the number?


2.You have a coin operated time machine .You have 50 coins totalling $1.00 you drop one down the open drain while tossing the coins in your hand. what is the chance that you have lost a quarter?


3.As a time traveler you need to stay in shape, so You have decided to take your morning run in preparation for the local Marathon at an average speed of 6 miles per hour. Unfortunately, you are not in as good a shape as you thought, and you are running uphill. You find that you complete a half of the run, all uphill, at an average speed of only 3 miles per hour. How fast must you run to make the return trip-all downhill- at an average speed for the entire round trip of 6 miles per hour?


4.The great time traveler detective is hot on the trail of the guilty party who has perpetrated some atrocious puns. "intent to deceive" is the charge, he is now interrogating three suspects. George, the science teacher says,"Im innocent-Jane is too." Jane ,the chemist says"Sally did it,and George is innocent." Sally, the calculus teacher says "Im innocent and Jane did it." The guilty one lied and the innocent both told the truth. who is the perpetrator?

5.You have arrived in a parallel universe and are now lost in Liars and Truthtellers town, you are in real trouble.You need to ask directions from a Truthteller,but how can you tell who is a Truthteller? You stop a group of three women and ask if they are Truthtellers. The first one says "two of us are Truthtellers." the second one says, "Only one of us is a Truthteller." and the third one chimes in, "The last woman who spoke is telling the truth." well, who was or were Truthtellers?

6. On the charts, I remain number one
this position cannot be undone
If I burn, you may get
just a little bit wet
In a zeppelin, Iam no fun.
who am I?
 
Wow! I love tests but yours caused me to have to try and remember formulas I haven't used in years. I'll do my best though:

1) I believe the answer is .8c. Utilize Einstein's equation: (u + v)/(1 + uv/c(squared))

2) Since the electrical potential at infinity is zero, the answer equals the energy contained by the electron in its lowest energy state which can be answered utilizing Bohr's equation for the hydrogen atom (setting Z=1, the atomic number for this atom). I can't remember Bohr's equation off the top of my head though.

3) Yes, since gravity is a curvature of space and even light must follow that curvature and is thought to have an equivalent mass given by Planck's equation E=hv(nu).
Question: If gravity is a curvature of space caused by the mass of an object, why does the object following that curvature have to have mass? Inquiring minds want to know.

4) Wavelength is the distance between two consecutive crests or troughs of a wave. Angular frequency is the number of cycles of a wave or rotational system in a period of time. I can't remember Schroedinger's wave equation (psi formula) off the top of my head but here's an equation defining a wave: y = A sin (w(omega)x + b) where A is the amplitude and b is the phase shift.

5) You'll have to explain this more. All I know is that exp(iwt) = cos(wt) + i sin(wt) per Euler's formula.

6) Since a cross product generates a new vector perpendicular to the previous two vectors, how does this work in two dimensions? The cross product of unit vectors i and j is k, a unit vector along the z axis in three dimensions. I can only imagine that it would be a zero vector in two dimensions since you said they all have answers.

7) Definition of derivative: f'(x)=lim(as x approaches zero)of {f(x+<delta>x) - f(x)}/<delta>x
deltas mean "change in". dx/dt means the instantaneous change in distance over an instantaneous change in time.

I always loved math better though which is why I preferred pamela's quiz. Here are your answers:

1) 1640
2) 2% (The only possibility I come up with is 45 pennies, 2 nickels, 2 dimes, and 1 quarter)
3) 9 miles/hour (assuming this isn't a trick question)
4) Sally (You must like logic questions! Me too!)
5) The last two are truthtellers.
6) Hmmmmmm.... the chart must be the periodic table; it reacts with oxygen to form water; and the last really gives it away since it was responsible for blowing up the Hindenberg. It's plutonium!! Just kidding, we all know it's HYDROGEN!

Now questions for contestant #1:
1) What is the CPT Theorem?
2) What is the photoelectric effect?
3) Is it possible to retreive information from a black hole?
4) What are the fundamental forces?
5) In what order did they separate during the Big Bang from the superforce?
6) What does GUT stand for and what does it do?
7) What keeps a dwarf and a neutron star from collapsing into a black hole?

Answers to be posted Friday...
 
I should rephrase my question I appologize it was not well asked. What is the circumferance of an infinite circle with a radius of infinity?
 
1: An observer on ship A would not see any light from ship B. Any light emmited or reflected from ship B would be "Blue Shifted" out of the visable light spectrum.
2: -13.6eV.
3: Yes, light is effected by gravitation forces.
4: The wavelength is the distance along the x axis after which the shape of the wave begins to repeat itself.
y(x,t) = ym sin(kx – wt) where ym , k, and w are constants. K = angular wave number and w = angular wave frequency
5: (I am lost in this one)
6: (Same for here)
7: A derivative is seen as a limit of a ratio.
 
Victor, seeing how you answered all of my quiz.(I'll give the answers out on friday also.you dont have a couple right.but I was impressed with your answers!)I will try and answer yours. they are kinda short answers though. :)

1. CPT theorum of G Luders-states that a lorentz invariant feild theory is necessary invariant to the product of the three reflections: charge conjugation C. space inversion P and time reversal T.
geez, this is too long too explain..
symmetry C means that the laws are the same for particles and antiparticles. symmetry P means that the laws are the same for any situationand its mirror image. the symmetry T means that if you reverse the direction of motion of all particles and antiparticles
the system should go back to what it was in earlier times.laws same forward and backward.

2. light shinning on certain materials will knock electrons loose from atoms (which make photoelectric cells and solar batteries.)

3. x-rays, high energy particles within jets.that shoot out axis of rotation.(particles dont come from within the black hole but from the empty space just outside the black hole's event horizon.)

4. Gravity, strong nuclear, weak interaction and electromagnetic forces.

5. -43
10 seconds gravity seperated from the three other forces. electromagnetic,strong nuclear and weak interaction.

10-33 3 forces operating electromagnetic, strong nuclear and gravitational
10-10 sec. weak interaction and electromagnetic forces seperated.


6. Grand Unified Theory- linking all four fundamental forces gravity, strong nuclear, weak interaction, and electromagnetic forces. "theory of everything."

7.If a star's MASS is less than the chandrasekhar limit it eventually becomes a brown or white dwarf. If it is above the limit the super giants final gravitational collapse produces a neutron star or black hole.

[This message has been edited by pamela (edited 25 October 2000).]
 
Yay! more questions! thanks, Victor.

1) CPT: charge-parity-time reversal. the theory that either a field theory is invariant on reversal of any of these three properties (eg all matter flipped to antimatter, all right-handed processes flipped to left-handed, the order of events reversed), or more than one of them violates symmetry. Well, obviously the universe isn't time invariant - it came from somewhere spontaneously. so at least one of the other things violates symmetry as well. I recall that some chemical processes violate parity - I don't remember where I heard it, though.

2) Light hits a metal and electrons are ejected. This was central to the development of quantum theory, because the number of electrons kicked out depends on the frequency of the light and not its intensity. They gave Einstein the Nobel for this because they still didn't get relativity.

3) Not inside it, not that I know. Then you'd be able to retrieve info about a naked singularity! That'd be absolutely horrible!

4),5) gravity-strong nuclear-weak nuclear-electromagnetic in that order. :)

6) Grand Unified Theory - the theory that would link the strong and weak nuclear and the electromagnetic forces. If you unified all 4 forces, you'd have a TOE ! (Theory of Everything) I think that's right, the names get silly after a while. Three quarks for Munster Mark!

7) Why, the weak nuclear force! When the gravity isn't enough to overcome the weak nuclear repulsion between neutrons squished so close together, the system reaches a stable equilibrium as a neutron star.

Now, some clarification on question 5) of mine: Psi(x,t) is a probability function for a particle in quantum theory. The momentum operator is p-hat=-i(h-bar)d/dx where d/dx is the partial with respect to x. I really don't have time to explain this more right now, I'll get to it later.

:) you found the trick in 6) :)

pamela- I liked the questions, but they've all been answered ( I know 3) isn't 9 mi/h, but I don't have time to work it out) ! I have some more, when I get time.
 
Well if it isn't my old friend Janus. Hey I thought that once I (a regular joe) beat you, you'd never show your sorry @$$ here again. I guess staying quiet for all these months must of made you feel lonely, being left out and all because nobody liked you :).

Don't worry though, I just have one last thing to tell you. Patronizing the members of this message board to take part of this little test of yours still proves 1 thing. That you still consider your self superior then everyone here, and you know it. That little known fact was what kept you away for so long, and alot of the original members know that. Thanks to me exposing you :).

So I just thought I inform others about this, and allow them to see the true Janus unfold to them over time. As for me, I'm going on a little vacation, just dropped by home to grab a few things. See you all in a few months.

Sincerely,
Javier C.S.
 
Dear Janus,
I will post the answers Friday to my questions, but I thought I'd let you know that Question # 3 is a bit of a trick question. According to current physics, it is impossible to retrieve information from inside a black hole (although black hole evaporation as discussed by Hawking allows for energy to be emitted outside the hole, current theories still believe that this energy can carry no information). I've found a way of looking inside a black hole that is in complete agreement with all laws of physics. I'll let you try and find a flaw in my logic but I don't think you will. The technology required to do this has only been verified in particle accelerators within the last few years. I'll give you a hint: entangled particles...

Dear Pamela,
You almost got all of them right. You might want to check your GUTs :) Pun intended...
 
I missed One??? Darn! Janus cheated from me! heheheh!! Thanks for the questions. :)
Janus, good to see you back!
here's a hint to my quiz...answers to question 3 and 5 are wrong.
question 2 -half right. answers friday. :)
this is fun! heheheh

Victor- cant wait to hear your theory with particle acc. and black holes!

Time 02112- Because you cannot use a wooden leg to photograph anybody......you need a camera! eheheheheheheheh :)

<This message has been edited by pamela (edited 26 October 2000).>
 
Does anyone know where to look on the internet for a collective history of electromagnetic permiability experiments for the last 150 years?
 
Here are the answers to the quiz: :)

1. 1640

2. There are two ways you can have fifty coins totalling $1.00 ---(2 dimes,40 pennies,and 8 nickles.) or (2 dimes, 45 pennies, 2 nickles and one quarter.)
these arrangements are equally probable.,so there is one-half chance you had a quarter to begin with. the probability that you then dropped that quarter from all the coins in your hand is one fiftieth. Therefore, the total probability that you lost a quarter is one half times one fiftieth, or one one-hundreth.

3.You cant do it at all. for example, if your run is 6 miles. you would have to do it in one hour to average 6 miles per hour. However, you've already taken an hour to do the first half of the run, thereby using all the available time.
(victor you were right! you sensed it to be a trick question.)

4.Sally

5.none of them could be Truthtellers.

6. hydrogen

Victor gets a BIG STAR!!!
 
Dear Erwin,
As a circle's radius approach infinity, any arc of its circumference approaches a straight line as I assume the entire circle must do.

Dear Pamela,
Wow! I rarely get math problems wrong! After looking at your questions; yep, you got me. Here are the answers to my quiz:

1) CPT stands for charge conjugation, parity, and time reversal. Simply, it means that if you switch the charges, spatial orientation (i.e. spin direction, etc.), and time flow of a matter particle, it becomes its antimatter equivalent (antiparticle). Electrons become positrons, protons to antiprotons, etc.

2) The photoelectric effect is the production of photons caused by electrons cascading from higher energy states to lower ones.

3) Yes, I'll explain my theory after these answers.

4) Forces: Gravity, Electromagnetism, Strong and Weak Nuclear.

5) Pamela's right (including her timing) Gravity, Strong Nuclear, then the last two from the Electroweak force (the only observed combination of forces so far in particle accelerators).

6) GUT - Grand Unified Theory is the next force combination uniting the electroweak with the Strong Nuclear force. A TOE (Theory of Everything) unites the GUT force with gravity and constitutes the superforce.

7) A dwarf star keeps from collapsing by the electron pressure (the repulsion of electrons from each other). If gravity is sufficient (say about 3 to 5 solar masses), the electrons get crushed into the protons forming neutrons and a neutron star. Now neutrons also exert a repulsion at certain distances from each other referred to as the neutron pressure (which is what keeps neutron stars from collapsing further to a black hole). If gravity can surpass this pressure, no repulsive force remains to stop the gravity's attraction and the result is perpetual collapse into a black hole. Now about seeing inside one...

I once read a book on FTL communication which talked about the use of entangled particles for instantaneous communication. In the past couple years, it has been PROVEN that two photons released from the same electron are said to be in an "entangled" state. When one electron is in a "up" state, the other must be in a "down" state. If I change the state of one electron, the other instantaneously changes to its opposite. There is NO delay (as if the signal from one was travelling at the speed of light to relay the information that its changed state) but the changes are instantaneous in accordance with the laws of quantum physics. This opens up the possibility of instantaneous communication for FTL spaceships and even now would be beneficial to NASA since they no longer would have to wait for the info from deep space probes or calculate how far in advance to send a command so that the probes retrorockets fire on time. Now how does this apply to black holes? Think about the how of it. How do two particles inside a universe where everything is limited by the speed of light break this barrier when sending information. The answer lies in that the reason everything in the universe is limited by light is because this speed limit is built into the fabric of the three spatial dimensions and one dimension of time. Everything travelling within these four dimensions relaying information (including the gravitational and electromagnetic interaction) must be ruled by this speed limit (which accounts for why gravity artificially reproduces the same effects of relativity <which contains the speed of light in virtually every equation> such as spatial contraction, time dilation, etc.). The only way information can be relayed instantaneously is if it is travelling outside these four dimensions, so entangled particles are not only relaying information through a conduit that is fifth dimensional or higher (travelling through compressed dimensions or otherwise), it is also a conduit not affected by gravity since gravity is limited by the speed of light and hence restricted to this universe. This goes along perfectly with Einstein's General Theory that warped space-time is gravity.

THE DEVICE
I set up a digital video camera onto a probe that I'm sending into Cygnus X-1. I have the binary code generated by the camera linked to a controller that manipulates one of an entangled pair of particles so that if it's a zero its in a "down" state and if its a one its in an "up" state. The second particle of the pair is hooked up to a controller that relays the binary data to a monitor on my ship that's staying outside the hole. The controller relays a zero if its in an "up" state and a one if its in a "down" state. The monitor should still be able to relay a perfect picture of what's being viewed by the camera even after it passes the event horizon since the information is being passed by the entangled particles. Not only that, but if the probe can survive through a spinning black hole that, oh say, goes to another universe, you could even see into that universe because the hyperdimensional link would still not be broken. If you find any flaw with any of my logic, please let me know. For you physicists out there, this is not psuedoscience ladies and gentleman. It follows every law of physics and scientific method. This can be built!! Please give me your feedback on this.
 
Dear Janus I believe that is correct that any arc of the circle approaches a straight line as the radius increases to infinity. However if one looks closer mathematically one will notice that if on were to travel an infinite distance on a infinite straight line that one would have an infinite number of zero drops in elevation which is equil to one drop in elevation. Furthermore there are an infinite number of rises in elevation so that at an infinite distance on the infinite circumferance there is a rise of one in elevation. This is equil to an angle of one of the radius. With the tangent of a straight line intersecting the infinite straight line of the circumferance to a drop in elevation of one one may ascertain that and infinite number of drops is equil to a circumferance of 360 degrees on an infinite circle. Therefore the circumferance of an a circle with an infinite radius is equil to r^2 and therefore infinity^2. What do you think ? Does this sound right? I am still going to look up the questions you asked even though they have been answered on this forum. A promise is a promise. inquisitively, Edwin G. Schasteen
 
An infinite number of zeros adds up to one?! By definition, adding the same number over and over again is called multiplication. Therefore, adding an infinite number of zeros is the same as infinity times zero. This is referred to as an indeterminate form, meaning it can take on any value, it doesn't necessarily have to be the value one.
- Victor S.
 
Yes this is true and it actually takes on all finite values I forgot to mention that. The definition of one is any finite value and in this case the set of all finite values at an instant in time. It is therfore also true that all angles in the circumferance of a finite circle from zero to three hundred sixty degrees intersect at the begining and ending of the first infinite tangent of the infinite circle. To us this tangent apears infinitely big and to spann from an infinite distance to the horizon infront of us to an infinite distance to the horizon in back of us so that all the distance in a 360 degree circle appears to be one single straight line so that a single spin on our part would intersect an infinite number of points on an infinite circle that is defined as our entire universe. Of couarse as we have seen that at such a great distance that a curve actually is nothing more then an illussion. Our universe which apears to appears to be an infinitely straight line at it borders but to as apears to suround us to form a circle or sphere if you want to convert this to trhee dimensions. One three hundred sixty degree revolution on our three hundred sixty degree universe is but a single tangent on the circle with an infinite times infinite circumferance. This single tangent which is an infinitely long straight line is an infinitely small point to those outside the circle. This is because the sum of single infinite drops plus the sum of infinite number of single rises on the infinite circle is zero and therefore defined as a dimensionless point to the infinite universe of the third heavens. It is amazing how the universe in the large follows so closely after the finite universe for the same definition of an infinitely small point to us is corresponds to us being within an infinitely small point to a universe surounding our own. I am will to bet you that even this universe is finite. I am begining to be convinced that size itself is as relative as position. I would therefore extend the theory of relativity to include universal size and universal infinity. I would think that there could be an infinite number of universes infinitely smaller then us but have the same mass and density and that there are an infinite number of universes larger then us but of the same size and mass. I would blame the appearance of the size differance as being an illusion when considering the the two universes as closed systems by themselves and as absolute when considering them open and when considering them inconjunction with the universe just larger to them and the universe just smaller to them. I would also equate the appearance of the size differance to the appearance of two parrallel lines getting smaller as they span further and further toward the horizon on an infinitely long flat plane. The portion of the parallel line half way to the horizon appears to be significantely smaller then the portion of the parallel line just in front of us on the infinite plane. If we were to imagine the parallel line beyond the horizon the size of the distance beweet the parallel lines would appear to be smaller then zero and therefore negative. This corresponds to our measurement of the infinitely small universe beyond the centermass of a field or three dimesional mass. It also corresponds the second tangent on the infinitely large circumferance surounding our universe. What do you think does this sound reasonable. I know that perhaps some of the math is not classical. But as far as I know most mathematics in physics has stopped at infinity and no calculations that I know of have been made by plotting the affects at an area greater or less then infinity. Most people conclude that there is no infinite and therfore donnot attempt to experiment to confirm the results and of those who do most if not all interprit there findings as that there is an infinity in the universe... the call this a singularity. However I have heard very little and have read nothing accept Cantorian mathematics that measures infinity in the large although I no there must be alot written and I am sure that it is a science by now. However most of the physisists donnot like to discus infinity and sometimes appear to become offended by one even bringing up the subject. Present company excluded of course. I can understand why this is for to bring up infinity in class might cause others to think I am a "nutty professor". But I still think it is important for I believe that in order for quantum leaps to accur within our technology and scientific understanding will require us to fully accept infinity and analyse no biasedly the affects and nomenclature of the infinite. Until then our progress no matter how significant it may appear will be miniscule in comparison with our potential.


Edwin Gary Schasteen
 
Victor, from what I know about entangled particles there is a problem with your plan. When you generate a pair of entangled electrons, you have two photons. All you know about, say, their spin state is that one must be up and one down - who knows which is which. As soon as one makes a measurement of one of the electrons, the state of the other is locked. But then the two electrons are no longer entangled - they're just normal off-the-shelf electrons again. AFAIK, you can't use these to actually convey information FTL - you don't control which state the electron is in when you measure it, and the other electron has no way of knowing when you measured its twin.

The other trouble was, even if you did have FTL communication, the camera you sent into the black hole would be a) crushed to a point, and b) time would stop for it before it got in far enough to see the inside.

Sorry.


"The definition of one is any finite value <...>" No it's not.

"<...> all angles in the circumferance of a finite circle from zero to three hundred sixty degrees intersect at the begining and ending of the first infinite tangent of the infinite circle." No, only the first 180 degrees. The other side of the circle never intersects the tangent. Or is this some weird infinity thing?

Those were some good questions, Pamela. Here's one along the same vein:

You, the intrepid spacetime adventurer, are deposided by the TARDIS on a remote island. You know that one village is composed entirely of people who speak only the truth, and another village only of those who consistently lie. The Liers have the nasty habit of eating people who ask them more than one question. What is the one question you can ask to quickly determine whether you're in Truthsville or Lieburg?
 
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