According to Einstein's mass energy equivalence equation, $$ E = mc^2$$ where $m$ is the rest mass and $c$ is speed of light. According to Planck's equation, $$ E=hv$$ If Planck's equation suggests that energy can only come in discrete packets, and if mass is equivalent to energy, then wouldn't this mean mass only comes in discrete packets? I saw this  and I found one answer discussing my question, however it was downvoted with no explanation on why it's wrong. The accepted answer's give evidence for why it should be the case that mass is continuous, however, there are a few 'downvoted' answers which suggest the idea I said before and have been downvoted. So, I'm trying to understand why exactly those answers are wrong. Edit: The answer where I saw it in , see answer by user &quot;howyoudoin&quot; and by user &quot;hhh&quot;,
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I learned today in class that photons and light are quantized.  I also remember that electric charge is quantized as well.  I was thinking about these implications, and I was wondering if (rest) mass was similarly quantized.  That is, if we describe certain finite irreducible masses $x$, $y$, $z$, etc., then all masses are integer multiples of these irreducible masses.  Or do masses exist along a continuum, as charge and light were thought to exist on before the discovery of photons and electrons?  (I'm only referring to invariant/rest mass.)
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Why can't photons have a mass? Could you explain this to me in a short and mathematical way?
66996
Do x-rays and gamma rays also contain photons like visible light does? If so, then what makes photons of visible light and other waves different?  The rest mass of a photon is zero, but as it moves at the speed of light, its mass is infinite. By $E=mc^2$, its energy is infinite, but using formula $ E=h\nu$, we get finite energy. How is this happening?
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At a very basic level I know that gravity isn't generated by mass but rather the  and when I wave my hands a lot it seems like that implies that energy in $E^2 = (pc)^2 + (mc^2)^2$ is the source of gravity.  If the total energy of a particle contributes to the generation of a gravitational field, that seems to imply some strange things.  For example, you could accelerate a particle like an electron to such a high velocity that it has enough momentum / kinetic energy to collapse into a black hole.  An observer traveling with the electron would see an electron and stationary observers would see an arbitrarily massive black hole flying by.  These observations seem to be contradictory.  The same would be true of an extremely high energy photon.  Another consequence is that a stationary particle could appear to have so much mass that it could attract / deflect the trajectory of a rapidly moving observer.  It seems odd that at low velocities you wouldn't even notice a stationary electron as you pass it by but at high velocities the gravitational field you observe could be significant enough to alter your path.  Am I correct that non-mass-energy generates a gravitational field?  If it does, how are these strange observations like a particle looking like a black hole in one reference frame but not another reconciled?
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Some time ago I asked my quantum physics lecturer the question:     How did Planck derive his formula, the    $$E=hf$$    with constant of proportionality $h$, the .   I was motivated by the fact that every lecturer talks about the history of this formula (black body, birth of quantum mechanics etc) but I've never encountered an explanation of how Planck derived it.   My lecturer told me that he had researched it and found only old articles in German. Moreover he said that he couldn't find a derivation in professional physics books. This is something that every author assumes needs no derivation.  So how did Planck derive this formula?
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Consider the  of Bennett et. al. How does one prove that this protocol would never violate the conservation of energy? At the face of it, it doesn't seem to be something obvious, as the various measurements, communications, rotations etc. don't seem to be able to account for the differences in the Hamiltonians of Alice's and Bob's labs. The state $\psi$ might have an expected energy $E_1$ in Alice's lab and a completely different expected energy $E_2$ in Bob's. Where does the difference come from?
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In non-relativistic QM, on one hand we have the following relations:  $$\langle x | P | \psi \rangle ~=~ -i \hbar \frac{\partial}{\partial x} \psi(x),$$  $$\langle p | X | \psi \rangle ~=~ i \hbar \frac{\partial}{\partial p} \psi(p).$$  On the other hand, despite the similarities, the relations cannot be directly applied to energy and time:  $$\langle t | H | \psi \rangle ~=~ i \hbar \frac{\partial}{\partial t} \psi(t),$$  $$\langle E | T | \psi \rangle ~=~ -i \hbar \frac{\partial}{\partial E} \psi(E).$$  Just wondering, how can one mathematically prove that the "classical time" (which means no QFT or relativity involved), unlike its close relative "position", is not a Hermitian operator?  I ask your pardon if you feel the question clumsy or scattered. But to be honest, if I can clearly point out where the core issue of the problem is, I may have already answered it by myself :/
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is the famous mass-energy equation of Albert Einstein. I know that it tells that mass can be converted to energy and vice versa. I know that $E$ is energy, $m$ is mass of a matter and $c$ is speed of light in vacuum.   What I didn't understood is how we will introduce speed of light?  Atom bomb is made using this principle which converts mass into energy; in that the mass is provided by uranium but where did speed of light comes into play? How can speed of light can be introduced in atom bomb?
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Consider a free theory with one real scalar field: $$ \mathcal{L}:=-\frac{1}{2}\partial _\mu \phi \partial ^\mu \phi -\frac{1}{2}m^2\phi ^2. $$ We write this positive coefficient in front of $\phi ^2$ as $\frac{1}{2}m^2$, and then start calling $m$ the mass (of who knows what at this point) and even interpret it as such.  But pretend for a moment that you've never seen any sort of field theory before:  if someone were to just write this Lagrangian down, it's not immediately apparent why this should be the mass of anything.  So then, first of all, what is it precisely that we mean when we say the word "mass", and how is our constant related to this physical notion in a way that justifies the interpretation of $m$ as mass?  If it helps to clarify, this is how I think about it. There are two notions of mass involved: the mathematical one that is part of our model, and the physical one which we are trying to model. The physical mass needs to be defined by an idealized thought experiment, and then, if our model is to be any good, we should be able to come up with a 'proof' that our mathematical definition agrees with the physical one.  (Of course, none of this at all has anything to do with this particular field theory; it was just the simplest Lagrangian to write down.)
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We've all heard of the inverse square law, but apparently that refers to the flux or intensity or number of photons hitting an imaginary surface area. This is not exactly what I want to ask about.  I'm asking about the energy level of an individual photon, or individual ray of light. The light could be any frequency or wavelength.  If I'm not mistaken, the amplitude of the light ray is directly related to its energy.  Consider a ray of light travelling through a vacuum. Does its energy decrease over time according to inverse square law? Maybe inverse linear? Or not at all?  This question comes from . If it's true that the energy doesn't diminish at all, then that would mean a laser beam shot into space (and never hits anything) would never lose any energy and arrive at the other side of the Universe with the same energy it started with. That's kinda hard to believe.  EDIT: It appears "energy" and "amplitude" are not synonyms for light rays. Apparently the concept of waves is tricky for light, since after all, a vacuum has no medium to propagate through in the normal wave sense. So let the question be, "Does an individual photon lose energy solely from the act of traveling through a vacuum?"
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My understanding of Quantum physics and String Theory is very basic and I don't yet have a grasp on the maths, but in my research I have come up with a question.  Does a decrease in temperature also signify/create a decrease in mass?  I am quite willing to believe the concepts I think I am beginning to understand are totally misconceptions on my part.  But, as I see it mass is a product/mark of disruption to the Higgs field as a particle moves.  If these particles are ultimately composed of vibrating Strings, their mass is given by the rate at which they vibrate and how it interacts with the Higgs field.  I don't have any idea if, as the temperature (as we know it) approaches 0k, the string/quark/sparticle would change its state in any way or if the changing of the state of the String would change what type of particle it represents.  It seems I'm more full of questions than answers, but that's why I love these topics!  I know what I'm learning is new if the best and brightest are still working on the 'basics' to just make their systems work :).
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I'm curious where the  $p=\frac{h}{\lambda}$ comes from?   I know that for light (which has no rest mass), the following is true:  $E=pc$ and $E=hf$  so,  $$pc=hf \Rightarrow p=\frac{hf}{c}=\frac{h}{\lambda}$$  But how is the expression $p=\frac{h}{\lambda}$ obtained for a massive particle where $E\neq pc$? I've read some people claim that the expression can be derived, and others saying it's an experimentally verified relationship.
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In physics there is quanta and energy occurs per this unit. Is it it then reasonable that probability also is quantized since energy is?
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I know that there's a difference between relativistic and rest mass. Relativistic mass is "acquired" when an object is moving at speeds comparable to the speed of light. Rest mass is the inherent mass that something has regardless of the speed its moving at.  When fusion happens, a certain percentage of the rest mass of two hydrogen atoms is converted into energy. I understand that $E = m_{rest}c^2$.   How does the rest mass of an object turn into energy? Does this involve particle physics? Doesn't this suggest that rest mass can be viewed as some sort of potential energy? It seems to me that it's a sort of locked energy that has to undergo a certain process to expel its energy to surrounding particles.  Also, Why does only a small percentage of rest mass turn into energy? Why not all of it. What dictates how much rest mass gets converted into energy?
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As a student in a highschool physics class, my teacher has repeatedly told me that photons are massless. Yet, I have also heard from other sources that photons have momentum. If photons were to have momementum, that would mean that they have mass as according to p = mv.  Do photons really have mass?  Also, how would this mass be calculated?
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Let us suppose a particle with so much energy $ E= h \frac{c}{\lambda} $ so $ \lambda $ is smaller than Planck's length ?  Would it be possible? I mean if the particle has so much energy then its mass would be very huge and would itself collapse into a black hole  This means that we could not 'see' what is beyond the Planck's length because a very energetic particle would turn into a micro black hole before reaching 'Planck's lenght' am i right?  Is this fact supported by SR and GR? what would be then the Einstein equations ? $ R _{a,b} =0 $?
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Meaning, why is it the exact number that it is? Why not 2x10^8 m/s instead of 3? Does it have something to do with the mass, size or behavior of a photon? To be clear, I'm not asking "how we determined the speed of light". I know there isn't a clear answer, I'm really looking for the prevailing theories.