I'm no physicist so it might be a stupid question but is there a maximum energy a single photon can have?  My idea was, that there might be restriction for the minimum wavelength and I thought about the Planck length: $1.616 · 10^{−35}$ m  So my hypothetical photons energy would be:  $$E=hf=\frac{hc}{\lambda}$$  So I put the values inside: $$E=\frac{6.62607015 \cdot 10^{−34}\cdot 299792458}{1.616 \cdot 10^{−35}} \frac{\text {J s m}}{\text{s m}}$$  which gives me the value: $1.23*10^{10}$ J  Is this the maximum amount of energy that a single photon can have, or is the concept of using the planck length as minimal possible wavelength not correct?   And are photons with that much energy even existing in the universe?
Is there any lower or upper limit on the energy of a photon? i.e. does the mathematical framework we currently use to study photons blow up when a photon surpasses a certain upper limit of energy? (or the same on the opposite side?)  My thoughts: If I let the energy of a photon tend to infinity, its wavelength would be tending to zero, and since it is thought that we cannot really distinguish things when they are on the scale of a Planck Length, would the photon have its maximum energy when its wavelength is equal to the Planck length? (Feel free to correct me, I feel I might not be.) and for the opposite end of the spectrum a photon with the least energy would have zero wavelength, implying no photon, which is a trivial case.
Undefined control sequence error on \fancy@reset, \f@ncyolh and \f@ncyorh when using newlfm class I updated to TeXLive 2017 and couldn't get newlfm.cls to work without errors.  Here is a minimal example:  \documentclass{newlfm} \begin{document} \begin{newlfm} \end{newlfm} \end{document}   LaTex is throwing undefined control sequence errors on \fancy@reset, \f@ncyolh, and \f@ncyorh.  What causes the errors?  What am I missing? Best practice: card expiry date on checkout As made clear in update 3 on , this notation: var hash = {}; hash[X]  does not actually hash the object X; it actually just converts X to a string (via .toString() if it's an object, or some other built-in conversions for various primitive types) and then looks that string up, without hashing it, in &quot;hash&quot;. Object equality is also not checked - if two different objects have the same string conversion, they will just overwrite each other. Given this - are there any efficient implementations of hashmaps in JavaScript? (For example, the second Google result of  yields an implementation which is O(n) for any operation. Various other results ignore the fact that different objects with equivalent string representations overwrite each other. Norm is sup of inner products (proof). Let $V$ be a vector space with an inner product $\langle.,. \rangle$ and associated norm $|| . ||$ Then:    Could I have a proof of this fact? How do I get rid of eggs? Need Basic Viewer template for ArcGIS JSAPI 3.2/3.3 I am looking for basic viewer for ArcGIS JSAPI  but not  getting  proper sample/example.  I am going through  also but looks like its not working.  Going through  question also.  Checking out  example and getting confused that what is difference between Viewer template and layout?  So any help regarding this will be great! so i change my MAC address with macchanger -A wlp68s0b1 at boot with crontab, here is what happens when i disconnect and reconnect :  while connecting after boot :  rahman@debian:~$ macchanger -s wlp68s0b1 Current MAC:   00:22:31:c6:38:45 (SMT&amp;C Co., Ltd.) Permanent MAC: 00:00:00:00:00:00 (FAKE CORPORATION)   after disconnecting :  rahman@debian:~$ macchanger -s wlp68s0b1 Current MAC:   16:7b:e7:3c:d3:cd (unknown) Permanent MAC: 00:00:00:00:00:00 (FAKE CORPORATION)   after reconnecting :  rahman@debian:~$ macchanger -s wlp68s0b1 Current MAC:   00:00:00:00:00:00 (FAKE CORPORATION) Permanent MAC: 00:00:00:00:00:00 (FAKE CORPORATION)   and so on, and with every disconnect i get a different random MAC address which fades on reconnecting giving me my real MAC address , what causes that and how to stop it ?  some outputs :  rahman@debian:~$ lspci -nn |grep 14e4 44:00.0 Network controller [0280]: Broadcom Limited BCM4313 802.11bgn Wireless Network Adapter [14e4:4727] (rev 01) rahman@debian:~$ uname -a Linux debian 4.9.0-3-amd64 #1 SMP Debian 4.9.30-2+deb9u5 (2017-09-19) x86_64 GNU/Linux rahman@debian:~$ sudo ifconfig  enp0s25: flags=4099&lt;UP,BROADCAST,MULTICAST&gt;  mtu 1500         ether 00:24:c0:7b:a8:8b  txqueuelen 1000  (Ethernet)         RX packets 0  bytes 0 (0.0 B)         RX errors 0  dropped 0  overruns 0  frame 0         TX packets 0  bytes 0 (0.0 B)         TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0         device interrupt 20  memory 0xd4800000-d4820000    enp0s25:avahi: flags=4099&lt;UP,BROADCAST,MULTICAST&gt;  mtu 1500         inet 169.254.9.109  netmask 255.255.0.0  broadcast 169.254.255.255         ether 00:24:c0:7b:a8:8b  txqueuelen 1000  (Ethernet)         device interrupt 20  memory 0xd4800000-d4820000    lo: flags=73&lt;UP,LOOPBACK,RUNNING&gt;  mtu 65536         inet 127.0.0.1  netmask 255.0.0.0         inet6 ::1  prefixlen 128  scopeid 0x10&lt;host&gt;         loop  txqueuelen 1  (Local Loopback)         RX packets 9436  bytes 6584515 (6.2 MiB)         RX errors 0  dropped 0  overruns 0  frame 0         TX packets 9436  bytes 6584515 (6.2 MiB)         TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0  wlp68s0b1: flags=4163&lt;UP,BROADCAST,RUNNING,MULTICAST&gt;  mtu 1500         inet 192.168.1.5  netmask 255.255.255.0  broadcast 192.168.1.255         inet6 fe80::6711:9875:eb78:24fc  prefixlen 64  scopeid 0x20&lt;link&gt;         inet6 fd9c:c172:b03b:ce00:f1e0:695e:7da0:91a  prefixlen 64  scopeid 0x0&lt;global&gt;         ether 00:00:00:00:00:00  txqueuelen 1000  (Ethernet)         RX packets 484346  bytes 641850809 (612.1 MiB)         RX errors 0  dropped 0  overruns 0  frame 0         TX packets 368394  bytes 44259668 (42.2 MiB)         TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0  rahman@debian:~$ sudo iwconfig  lo        no wireless extensions.  enp0s25   no wireless extensions.  wlp68s0b1  IEEE 802.11  ESSID:"3bdo"             Mode:Managed  Frequency:2.447 GHz  Access Point: 9C:C1:72:B0:3B:D4              Bit Rate=65 Mb/s   Tx-Power=30 dBm              Retry short limit:7   RTS thr:off   Fragment thr:off           Encryption key:off           Power Management:off           Link Quality=54/70  Signal level=-56 dBm             Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0           Tx excessive retries:4  Invalid misc:183   Missed beacon:0 Electrical potential energy stored in vacumm for a single point charge? I have come to know the electrostatic potential energy in vacuum is given by $${\frac{1}{2}} \epsilon_0\int d^3x {E^2} $$ and this energy  is due to the mutual electrostatic coulomb potential energy. So only a single point charge in space also contributes to some electrostatic potential energy according to $${\frac{1}{2}} \epsilon_0 \int d^3x {E^2} $$  as due to a single point charge also we have an electric field at every point in space. Now I am not getting it physically, why should there be any Coulomb energy in this case as there is no other charge to provide the electrostatic coulomb potential energy? I was browsing flight price at Singapore Airlines website, and a one-way flight from SIN to SFO cost this much:    That's quite expensive. I tried browsing around and found that a return flight from SFO to SIN and back to SFO cost much cheaper:    It's really weird because the second ticket includes the exact same flight that cost 1900+, but it's almost half the price. The reason for this counter-intuitive situation is explained in the answers this question   If I am located in Singapore and my intention is to fly one-way to SFO, is it safe to book the flight in the second picture and only board SFO-SIN leg? Will they deny me because I miss the SIN-SFO flight? I want to have an index entry typeset as $a_\text{T}$, so I issue the command \index{at@$a_\text{T}$}. Each use of this index command creates a separate line in the index. How can I get \makeindex to recognize they all reference the same topic?  My index entries look like this: I have put a bounty on , however I don't see it appear in the  (also not when I'm not logged in).  Why is this. Aren't all bounty questions supposed to be visible there? When I measure a 9V DC wall adapter power supply with a multimeter it shows 11.8V. When connected to my board this voltage lowers to 10V. Is this normal? Should I be afraid of toasting my  supplied board when using this adapter?  Edit: This regulator accepts up to 12V inputs. So that will be no problem. A second "9V" adapter yields 15V to the multimeter. Will this one burn my circuit? Applied boolean modifier leaving shading artifacts with flat shading I tried to manipulate a cube with the Boolean modifier. I tried to cut out an edge of the cube with a cylinder. Also, the shading result looks awful in FLAT SHADING mode, so I turned on SMOOTH SHADING.   Has anyone an idea how to achieve a better result. (I also cut out a Sphere first, this made the result less awful).   I used Blender Internal and rendered with smooth shading for smoothness.  Using flat shading looks okay, except the "round" cutouts :/  Face normals are okay.  First image is smooth shading.    EDIT: User Pisurquatre suggested the EdgeSplit modifier, works perfect to me (Maybe a little tweaking here and there): Show that given seven real numbers, it is always possible take two of them, such that $\left\vert\frac{a-b}{1+ab}\right\vert<\frac{1}{\sqrt{3}}$ Show that given seven real numbers, it is always possible take two of them, such that $$\left\vert\frac{a-b}{1+ab}\right\vert&lt;\frac{1}{\sqrt{3}}$$   The "Pigeonhole principle" states that if $n$ items are put into $m$ containers, with $n &gt; m$, then at least one container must contain more than one item, but how I an define my "container" such that meets the condition of the problem? I have this string  'john smith~123 Street~Apt 4~New York~NY~12345'   Using JavaScript, what is the fastest way to parse this into  var name = "john smith"; var street= "123 Street"; //etc... What does a program do when it's sent SIGKILL signal? When I used killall -9 name to kill a program, the state become zombie. Some minutes later, it stopped really. So, what's happening during those minutes? In Iron Man 3,      When the real villain kidnapped the President of the United States,   it is never explained why none of the other Avengers came to help, or why Tony didn't call them. The only explanation so far is: "it was an Iron Man movie...", but an in universe answer would be good. How does deleting work? What can cause a post to be deleted, and what does that actually mean? What are the criteria for deletion? What circumstances can cause a question or answer to be deleted, and what does that actually mean?    How can a post be deleted? When can't I delete my own post? Can I still see my post even after it's deleted? Can I see a list of my deleted posts? How can I undelete one of my posts? What does deletion mean for a post? How do votes to delete work? What are the criteria for deletion? What else should I know about deleted posts? If I flag my question with a request to delete it, what will happen?       For more information, see the articles about  and  in the . gedit "cannot open display" , on remote computer , using ssh - Ubuntu 12.04 Riemann integrabilty of an indicator function Consider the following function on $[0,1]$:   $$f(x)=\begin{cases}1&amp;x\in\{a_1,a_2,\dots,a_n\}\\0 &amp;\text{otherwise}\end{cases}$$   The $a_i$ are fixed and all in $[0,1]$. Determine whether $f$ is Riemintegrable or not.   By the Riemann&ndash;Lebesgue criterion $f$ is Riemann integrable. How to prove directly?