timo

The answer to your first question is: Not necessarily. If a, b, and c are real numbers and * is the multiplication of the reals then the statement is true. In case of vectors and the cross product a counter-example would be b = (1, 0, 0) and c = (0, 1, 0) where b is changed to equal (1,1,0). Since I assume that by "the momentum is not zero" you refer to the linear momentum then again the answer to your second question is "not necessarily". Take a radial vector (1,0,0) and a linear momentum (1,0,0). Changing the radial vector to (2,0,0) still leaves the angular momentum at zero. Your statement would work if the angular momentum was not zero, since scaling up the radial vector by a factor (while leaving the linear momentum constant) also scales up the resulting angular momentum by the same factor.

It is a bit hard to give a definite answer without knowing which parameters are given an which are not (your second paragraph suggests the mass of the bullet is given even though your first paragraph suggests it is not, for example). My guess would be the following: Collisions not only need to conserve energy, but also momentum. Additionally, the initial kinetic energy does not need to equal the final kinetic energy, since some of the original kinetic energy can be transformed into deformation energy. Hence, the kinetic energy of the bullet was larger than the energy of the resulting oscillation. Taking this into account (which becomes easy if, for example, you are given the mass of the block and the bullet) should give a correct answer, as far as I can tell.

I'm not sure I get your point. So I'll use an example that is more familiar to me and possibly says the same (or not): If you decide to roll a dice two times, there are 36 possible future outcomes for the dice rolls. After you rolled the first dice, there are only 6 possible outcomes left. The other 30 possible outcomes are destroyed, and the possible outcome of having rolled a different number than you actually did is destroyed as well. Now assume I replace "possible outcome" with "multiverse", rolling a dice with making a decision and the exact numbers in my example with arbitrary other numbers or other mathematical measures: What is the difference between my sentences above and what you said?

You don't. It is a property of squaring a value. If you know that x²=4, you don't know whether x=+2 or x=-2. In a similar sense, the left side could be (a-b)² as well as (b-a)². And both terms of course also evaluate to the same value for any pair of a and b.

I think your way to go is rather straightforward: 1) Prepare for the meeting by trying to get an understanding of what the professor is doing, i.e. the field he or she is working in and the kind of research he or she is doing. For me, being a person who can find an interest in many different things, this automatically leads to ideas, interests and questions. Don't take them too serious, as you are effectively basing them on little information (also see the post of CharonY regarding specific interests). But they are a good preparation for a meeting in the sense that you can contribute to the discussion, rather than being given a monologue about the group's research. 2) Don't be worried about being open about your motives: You want to get some lab research experience in a field that you are hopefully a bit interested in, and you want to ask about opportunities to get this experience in the professor's group. There is nothing wrong with this, and it seems like a good opener to me. The objective of the meeting is finding a path of action that you are both satisfied with. So stating your interest is perfectly fine and helpful, as long as you don't try to enforce it over the professor's interests during the course of the discussion.

I share your feelings that the understanding of the measurement process is not satisfactory on the conceptual level. But my gut feeling is that this might actually lead to the answer to your original question, namely why the Copenhagen interpretation is/became so popular: Physics is all about creating a quantitative description of reality and testing it in experiments. Putting the conceptual annoyance in-between "this is how the system behaves" and "this is how my measurement device works" may be very practical for experiments. You can use your quantum world picture for the system you are investigating and your knowledge of your measurement device for your setup. And you have some magic rule that allows you to calculate what your measurement device sees depending on the state in the quantum world. Putting the annoyance of QM not making sense anywhere else in the interpretation (I am not familiar with other interpretations, but I assume they all have their weirdnesses) may be less suitable for practical work.

x -> 2(x-3)+3 . It's a bijective mapping, so in a sense the two sets have the same number of elements. Sidenote: I don't know what the "infinitesimals" between 3 and 4 are, so I am assuming this thread refers to the real or the rational numbers.

What's wrong with the answer 0? EDIT: That post of mine was less pointless an hour ago when I opened this thread in a new tab and then forgot about it .... .

So is my reply. I even explicitly told you how to solve for the [x y] vector, and why that approach gives you the solution.

If an eigenvector has an associated eigenvalue of zero, then all multiples of this eigenvector solve the equation => find the eigenvectors and their eigenvalues.

x³ - x² = x²(x-1) = x*x*(x-1).

As far as I can see you are calculating mult = a*(a-1)*...*(a-k+1) in that loop. Special cases like k>a+1 and k<2 aside (consider if they can appear in your code), this is the same as mult=a!/k!. You already have a factorial function in your code: Use it, then optimize it with a lookup-table if needed. Note: You are dividing by another k! later on. You only need to calculate it once, of course.

I say it's either 6*6*5 or 42. Probably 42.

Or you call your counter variable "numberOfLinesProcessed" or "linesProcessed" and reconsider if you really need to comment the increment. In my experience, certain circles tend to dislike in-code commenting except for cases where something unexpected happens or a non-obvious choice has to be explained (and both case classes should be avoided). And in recent years I have come to adapt that way of programming. That said, "comment a lot, even in-code" is probably still a good advice for beginning programmers, who I assume are the target audience for this thread. As for a tip I'd have: If in doubt, try it out. Simple examples: What values does a loop over "range(10)" cover? Is "x[1]" the first or the second element in an array x? What is the result of y = A*x, where A is a 2D-array/matrix and x is a 1D-array/vector? You can read the manual. But it takes time and you need to be certain that you understood it correctly. And once you leave language features and go to library-features you also have to implicitly assume that the library behaves according to its documentation (i.e. that it does not have a bug). Or you can just assume something and hope everything goes well. Or you can just try it out and discover the answer for yourself, which is often faster than reading manuals and produces less errors than just assuming some behaviour. And most importantly: It's the most fun variant.

Special relativity is sufficient to describe massless photons. Giving a "reason" why they have momentum but no mass is tricky: What would be the reason that you need mass to have momentum? In non-relativistic physics, there is the relation p=mv, which sais you cannot have non-zero momentum when you have zero mass. That equation no longer applies in relativity. Hence, there is no (mathematical) reason why something with momentum would need to have a non-zero mass. As for the "relativistic mass": The relativistic mass is defined as the energy divided by the squared speed of light. Photons do have non-zero "relativistic mass". But the term "mass" usually does not refer to "relativistic mass" (which is just the energy expressed in different units). The concept that "mass" usually refers to is the mass defined in the equation Swansont posted (the relating equation between energy and momentum). There, a photon's mass is zero.

I don't meditate. But I sometimes let my thoughts go, which may come somewhat close. To me, flow states are kind of the opposite of letting my thoughts go or thinking thinking about a topic. They are characterized by lots of activity and lots of feedback that immediately loops back into activity, whereas the process of letting my thoughts go is characterized by complete lack of activity or feedback. So from my personal experience, I'd say that flow states are the opposite of meditation. I don't think that necessarily means anything about how the amount of meditation a person performs correlates with the amount of flow states, though. Both take well below 50% of one's time, so there is no temporal competition between the two states.

I think prestigious institutions for a PhD are usually overrated by students. Doing your PhD at a less reputable university and doing a good job at it, i.e. developing a good understanding of the field and getting good results, can probably get you quite far. Especially if you know that you want to go for a post-doc and start developing contacts outside the university during your PhD time (e.g. at conferences or by talking to visiting speakers in the seminars). This is just a side-remark, though. I am aware you didn't want to discuss your decision to aim for a prestigious university. I am not super-familiar with the US university system. But I read many, many, really many threads about "my grades are bad but I absolutely have to get into a prestigious PhD program", and I have a bit of common sense. Generally speaking, I think you are in an okay position. The idea of admission is that the committee believes you will be successful in the PhD. Your story of being a bad student that suddenly found his/her passion for science is very cliché. But: Contrary to many of the other people coming along with the story you have the actual proof to back it up. You demonstrated a good performance in the recent past. That will weight higher than your bad performance in the more distant past, especially with the intermediate break and the associated life-experience you gained in that time. As long as you get the 3,0 on average (to avoid being auto-dumped before someone even reads you application) I think you are in a better shape than your total average suggests. Two caveats: 1) I have not understood the concept of "community colleges" so far, so I don't know to what extent that is a disadvantage to <whatever the alternative of a non-community college is called>. 2) I have doubts to what extent a computer science degree prepares you for a neuroscience PhD program. You probably want to approach it from the direction of computational neuroscience, not the biological direction. Summary: Don't give up, yet

I don't think your conclusion about reducing volume and weight by half is supported by what is said in the text you quoted. At best, there is the promise of extended lifetime (by avoiding damaging charging states) or improved charging performance (by knowing the damage limits more precisely). I don't really know what you are trying to say with your last sentence. Some people (e.g. me) expect Lithium demand to greatly increase because of increased demand for battery production. That is because of renewable energies and their related technologies: electric cars and battery storage systems to compensate for the fluctuating power generation of wind-turbines and photovoltaic-plants. But that expectation is not influenced by a research team looking into the microscopic details of a battery but based purely on environmental, technical and economic expectations. The biggest potential influence of fundamental research onto technology that I currently expect is new types of Lithium batteries (namely Lithium-Sulfur). These do indeed promise higher energy densities. Especially for electric cars, which are often considered as having too little battery capacity, that could have a real impact (but still result in an increased demand in Lithium).

They said they will not publish your manuscript.

I just saw you wrote phonon, not photon - I first misread that. It that case I replace my previous "from experiments" with "they are completely different by concept". Neutrinos are particles that can exist in vacuum. Phonons are a concept to describe the state of a crystal.

From experiments.

Write a cheat for Pokemon Go. Technically legal. Lots of potential customers. Caveat: The idea is not the prime example of a unique idea that no one else will think of, and you may be too late to jump on the bandwagon. Seriously: If anyone with good coding skills had the idea what the next Facebook is they would probably pull it off themselves instead of posting it in a forum.

Particle physics was one of the problems I encountered with ordering your list (which in the end I simply did not do). I agree that the physics part in current particle physics research is extremely unlikely to have an impact on technology, soon. On the other hand, the technology used in and developed for particle physics experiments is extremely cutting edge. The only one of your choices that really stood out for me was your two examples for quantum theory, which I do not expect to have an impact in the foreseeable future (and even that is making a bet against the advent of quantum computers that some people envision).

I find that comment a bit aggressive, given that B. John Jones hasn't actually said much. But the OP indeed begs the question what other methods there could be. Just because anecdotal evidence is an alternative method, adding it as a second source of verification of ideas does not really offer much hope of improving the output. Or to stay in the picture: Putting all eggs in one basket seems like a better idea than putting half of them in the basket and throwing the other half of them down a cliff.

I don't know anything about creating leather-like materials. But I like reading a post about an idea that sounds original to me. If the process you want to use is not well-described in literature testing it out and writing down a protocol of the process and the results already sounds like a cool project. If you need more depth then from what you wrote I see two more or less obvious routes to go (assuming the results are not well-known already): 1) Perform some standard tests on the materials and compare them with leather. Elasticity, robustness and water resistance could be examples. Being a fashion designer you will probably have a better idea than me about what properties are relevant. 2) Go a more theoretical way and make a comparison of the material's "sustainability" compared to other materials (like leather, maybe also others). I expect there are a variety of sustainability measures that could be considered: Total energy use or total use of drinking water for the fabrication are examples that come to my mind spontaneously. Or maybe just total cost of production (not in the greeny sustainable category but still a very relevant parameter).