There are two expressions regarding relativistic mass of photon; namely relativistic approach:  $$m = \frac {m_0} {({1 - \frac {v^2 } {c^2 }) } ^\frac {1 } {2} }. $$  And, energy-mass equivalence formula:  $$ E =  m {c}^2. $$     There common uses in physics books:   First formula is used to prove that rest mass of photon is zero.   Second formula is used to find out what is called kinetic mass of photon in motion.      MY QUESTION:   first formula suggests that photon must have infinite mass in motion, and second gives finite mass (kinetic), why is this disperacy?
I've read a number of the helpful Q&amp;As on photons that mention the mass/mass-less issue. Do I understand correctly that the idea of mass-less (a rest mass of 0) may be just a convention to make the equations work?  From a layperson's view, it's difficult to understand how a particle of light (photon) can be mass-less. A physical object (everyday world-large or quantum-small) must have a mass. Yet, if my understanding is correct, the mass of a moving object/particle increases in proportion to its speed/velocity...so that at the speed of light, its mass would be infinite. A photon travels at the speed of light, but it obviously doesn't have infinite mass, right? Can someone formulate a practical explanation that can be understood by middle-school to high school kids? Much thanks for the help.    Wow--your answers to my original Q below clear up much of my confusion. I now have the daunting task of going over these nuggets and working up an equation-less (hopefully) explanation of the mass-less photon for non-physicist types.  Yes, from a layperson's view, it does seem remarkable that an existing piece of matter-- which has to be made of physical substance--could have zero mass at rest (though a photon is never at rest). It would be almost understandable if a piece of matter made of nothing had zero mass, but that  seems to be an oxymoron, and "nothing" would equate to nonexistent, right?  In case you might find it interesting: I'm working on a writing project that posits we inhabit a universe that consists of matter (physical stuff) only, and that the NON-physical (aka supernatural) does not (and cannot) exist. For instance, if a purported supernatural phenomenon is found to actually exist, then by definition, its existence is proof that it is mundane/natural. All it would take to disprove this premise is reliable proof that ONE supernatural event has occurred. Despite thousands of such claims, that's never yet happened.  Who else better than physicists to confirm my premise? However, I do wish the TV physicists would explain the terms they throw about, some of which mislead/confuse their lay viewers. Case in point: "The universe is made up of matter and energy" (without properly defining the term "energy" as a property of matter).  The result is that laypersons are left with the impression that energy must therefore be something apart from or independent of matter (ie, nonphysical). Their use of the term "pure energy" without specifying exactly what that means adds to the confusion. (Thanks to your replies on this forum, I now understand that "pure energy" refers to photon particles.) However, "psychics" and other charlatans take advantage of such confusion by hijacking terms like energy (as in "psychic energy"), frequencies, vibrations, etc to give perceived scientific legitimacy to their claims that a supernatural spirit world, etc., exists. As you may realize, the majority of people in the US (per 2009 Harris Poll) and around the world believe in the existence of nonphysical/supernatural stuff such as ghosts and spirits.  My purpose is to give laypersons the information they need to distinguish what's real from what's not.  Thanks so much for help...And, PLEASE, add any further comments you think might be helpful/insightful to better inform laypersons.
Does the Sun produce audible sound? Theoretically if I were able to build some sort of device that let me sit 1 foot away from the surface of the Sun (or any star for that matter) without being vaporized, would a star produce any sort of audible sound at that distance?   From my understanding, sound waves need a medium to propagate through (air, water, etc).   Does this mean that all stars are completely silent (in the audible spectrum of frequencies at least) as they fuse  hydrogen into helium?   I know stars emit radio, xray, infrared, ultraviolet electromagnetic waves, but how about audible (20 Hz to 20Khz) frequencies?   For some reason it seems like this process would produce some sort of sound. jQuery .delay does not delay Adding a Method to an Existing Object Instance I've read that it is possible to add a method to an existing object (i.e., not in the class definition) in Python.   I understand that it's not always good to do so. But how might one do this? Why can't I suggest edits on SE meta sites? Why didn't (or did) I or some other user get a hat although the requirements were (or weren't) fulfilled? During Winter Bash, users can earn hats. But sometimes it seems that a hat was awarded even though its requirements weren't (yet) met, or vice versa.  What could be the reason for this? breaking of output into new lines Flow chart using Tikz- spanning multiple pages I am trying to create a flowchart with Tikz. Since it is a long one, it spans three pages. So after creating a node to stop, I am continuing to the next page using \newpage command. Unfortunately some elements in page 1 are connected to page 2, 3 and vice versa. So when I try to create the arrow connection, it is not possible since the \newpage command comes in between. I am sharing the code with you for info. Could  anyone help me to improve the flowchart so that I could direct the arrows among multiple pages. My sample code is below:  \begin{tikzpicture} \node 1 \node 2 ........ \draw[arrow] (node1)--(node2) \draw[arrow] (node2)--(node3) ---- \end tikzpicture} \newpage \begin{tikzpicture} \node 1 \node 2 ........ \draw[arrow] (node1)--(node2) \draw[arrow] (node2)--(node3) ---- \end tikzpicture} \newpage  \begin{tikzpicture} \node 1 \node 2 ........ \draw[arrow] (node1)--(node2) \draw[arrow] (node2)--(node3) ---- \end tikzpicture} Find the asymptotic tight bound in  $$ T(n) = 4T\left(\frac{n}{2}\right) + n^{2}\log n. $$  where $ \log n= \log _{2}n $ and $T(1) = 1$.  I should solve this using all three common methods: iteration, master theorem and substitution.  It is highly likely that this kind of recurrence equation will be in my test in two days. Thank you very much in advance! If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication) Is an increasing union of subspaces a subspace? How do I audit my reputation? If I am concerned that my reputation score is incorrect, how can I audit it, or get a report of a detailed breakdown of my reputation? JavaScript private methods To make a JavaScript class with a public method I'd do something like:  function Restaurant() {}  Restaurant.prototype.buy_food = function(){    // something here }  Restaurant.prototype.use_restroom = function(){    // something here }   That way users of my class can:  var restaurant = new Restaurant(); restaurant.buy_food(); restaurant.use_restroom();   How do I create a private method that can be called by the buy_food and use_restroom methods but not externally by users of the class?  In other words, I want my method implementation to be able to do:  Restaurant.prototype.use_restroom = function() {    this.private_stuff(); }   But this shouldn't work:  var r = new Restaurant(); r.private_stuff();   How do I define private_stuff as a private method so both of these hold true?  I've read  a few times but it doesn't seem like "private" methods can be called by public methods and "privileged" methods can be called externally. If the sum of $n$ cubes is zero, then the sum must be no larger than $\frac n3$. Assume that $a_1,...a_n$ are real numbers and $-1 \leq a_i\leq 1$ for $1\leq i\leq  n$. If $$a_1^3+\ldots +a_n^3=0$$ Then show that $$a_1+a_2+\ldots+a_n\le n/3$$   I just came cross this problem the other day. I totally have no idea how to prove it. Are there any hints about which theorem, principle or method to apply? Given a 4-vector $p^\mu$ the Lorentz group acts on it in the vector representation: $$ \tag{1} p^\mu \longrightarrow (J_V[\Lambda])^\mu_{\,\,\nu} p^\nu\equiv \Lambda^\mu_{\,\,\nu} p^\nu. $$ However, I can always represent a 4-vector $p^\mu$ using left and right handed spinor indices, writing $$ \tag{2} p_{\alpha \dot{\alpha}} \equiv \sigma^\mu_{\alpha \dot{\alpha}} p_\mu.$$ So the question is: in what representation does the Lorentz group act on $p_{\alpha \dot{\alpha}}$?    There are a lot of questions about this and related topics around physics.se, with a lot of excellent answers, so let me clear up more specifically what I am asking for.  I already know that the answer to this question is that the transformation law is  $$ \tag{3} p_{\alpha \dot{\alpha}} \rightarrow (A p A^\dagger)_{\alpha\dot{\alpha}}$$ with $A \in SL(2,\mathbb{C})$ (how is mentioned for example in ). I also understand that $$ \tag{4} \mathfrak{so}(1,3) \cong \mathfrak{sl}(2,\mathbb{C}),$$ (which is explained for example  by Edward Hughes,  by joshphysics,  by Qmechanic).  So what is missing? Not much really. Two things:   How do I obtain (3) and what is the specific form of $A$, i.e. its relation with the vector representation $\Lambda^\mu_{\,\,\nu}$? Defining the following $$ (\tilde p) \equiv p^\mu, \qquad \Lambda \equiv \Lambda^\mu_{\,\,\nu},$$ $$ \sigma \equiv  \sigma_{\alpha \dot \alpha}, \qquad \hat p \equiv p_{\alpha \dot \alpha},$$ we can rewrite (1) and (2) in matrix form as $$ \tag{5} \hat p \equiv \sigma \tilde p \rightarrow \sigma \Lambda \tilde p  = ( \sigma \Lambda \sigma^{-1}) \hat p,$$ however, this disagrees with (3) which I know to be right, so what is wrong with my reasoning? Why does the transformation law (3) has a form $$\tag{6} A \rightarrow U^{-1} A U,$$ while the usual vector transformation (1) has a form $V \rightarrow \Lambda V$? I suspect this comes from a similar reason to that explained  by Prahar, but I would appreciate a confirmation about this. I upgraded my Nexus 4 to Lollipop a few days ago but I don't like it. I'll leave out my reasons because they're not relevant here. I wiped my phone and installed a clean stock 4.2.2 version instead. I'm happy with this.  Not long after, Android automatically downloaded the 4.3 upgrade and notifies me with the choices "Later" and "Install". I don't want to do this upgrade.  How do I:   get rid of the notification, and  remove the downloaded update (to free up precious storage space).     I have already tried choosing "Later" but the same notification immediately reappears.    Based on Google search results, I also tried going to Settings &gt; Apps &gt; All &gt; Google Services Framework and unticked "show notifications" but it still appears. Force stop or disable also doesn't seem to help, so I've re-enabled the service including notifications. I didn't see any other apps in this list that sounded relevant - did I just not see it? Optimizing logical sector size for physical sector size 4096 HDD Why is Earth's gravity stronger at the poles? Many sources state that the Earth's gravity is stronger at the poles than the equator for two reasons:   The centrifugal "force" cancels out the gravitational force minimally, more so at the equator than at the poles. The poles are closer to the center due to the equatorial bulge, and thus have a stronger gravitational field.   I understood the first point, but not the second one. Shouldn't the gravitational force at the equator be greater as there is more mass pulling the body perpendicular to the tangent (since there is more mass aligned along this axis)? How to check if jQuery.ajax() request header Status is "304 Not Modified"? SQL - Order by with alphanumeric characters Why did Superman & Supergirl start to suffocate instantly when Luthor made our yellow Sun red? Spoiler Alert: If you haven't read all comics series &amp; story arc of New Krypton Saga viz. New Krypton, World of New Krypton, Last Stand of New Krypton, Superman: War of Supermen etc, drop this question right away!  While battling the evil alien Brainiac, Superman &amp; Supergirl discovered the long-lost bottled city of Kandor which was stolen from Krypton prior to its destruction. Superman re-enlarged the city on Earth, but it wasn't welcomed by Humans. Humans assaulted the city in which Kryptonian's leader Zor-El (Supergirl's father) was killed. Using highly evolved science, Alura (Zor-El's wife) created a new planet "New Krypton". Plus, she, as a new leader, freed General Zod from Phantom Zone to command new super military of New Krypton (every kryptonians had super powers due to yellow sun).  While New Krypton &amp; Earth were at cold war, Zod ordered his military to attack Earth. When military was in space, Sam Lane (Lois Lane's father) destroyed New Krypton by a trick making their race extinct again. Kryptonian military successfully crushed Earth's Mars defense facility &amp; they headed towards Earth.  When they were about to enter atmosphere of Earth:      Many Kryptonians died under the red sun because they couldn't survive in empty space. Its somewhat plausible because they weren't under yellow sun for long. But, what about Superman &amp; Supergirl? They did survive because they were under yellow sun for very long. But, why did they become very weak instantly? If the power draining rate by radiation of red sun was that high, how did Superman &amp; Supergirl survive?  Is this a plot hole? Or, am I missing something?