As per the Einstein equation , the energy of the particle is depends on the mass of the particle. Or else in other terms the energy is proportional to the mass. If the photons are having zero (rest) mass, then how the photons are having energy? Can we say the massless particles are also having energy?
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Photons are massless, but if $m = 0$ and , then $E = 0c^2 = 0$. This would say that photons have no energy, which is not true.  However, given the formula $E = ℎf$, a photon does have energy as $ℎ$ is a non-zero constant and photons with a zero frequency do not exist.  What am I missing here, or does the famous formula not apply to photons?
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I will try to be as explanatory as possible with my question. Please also note that I have done my share of googling and I am looking for simple language preferable with some example so that I can get some insight in this subject.  My question is what is so special about $c$? Why only $c$. Its like chicken and egg puzzle for me. Does Einstein reached to $c$ observing light or does he got to light using some number which turned out equal to $c$.   Why is $c$ not relative. If something has zero rest mass like a photon why they only travel at $c$ in vacuum and not with $c+1$ or $c-1$?
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Are there any massless (zero invariant mass) particles carrying electric charge?  If not, why not? Do we expect to see any or are they a theoretical impossibility?
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Due to the mass-energy equivalence, both matter and EM radiation bend spacetime, and both are capable of forming singularities (black hole, white hole/kugelblitz). In light of this, why do photons traveling from the most distant reaches of the observable universe not lose energy due to the gravitational radiation they must emit? Furthermore, mustn't cosmic rays (e.g. protons) slow down or stop as they lose energy through the same mechanism?
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I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force holding a subatomic particle together? What keeps mass in it's state? I hope this is not a silly question but I am clueless. Thanks
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Is charge of something for (e.g.) an electron related to electromagnetic space if it exists due to energy, due to which it may have mass? I don't know about quantum mechanics or advanced particle models. Can anyone just simply give an intuitive idea?   EDIT I want to mean what actually gives electron charge if it is not assumed fundamental but result of some other physical phenomenon or it is  just the quantity defined to explain physical interactions?I think now it is clear
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I'm trying to find out if black holes could be created by focusing enough light into a small enough volume.  So far I have found (any or all may be incorrect):   Maxwell's equations are linear, dictating no interaction of radiation. The Kerr effect and self-focusing has been observed in mediums, but not vacuums. Masses bending light have been observed per general relativity. Photons are said to have no rest mass, just energy and momentum (???). General relativity seems to provide for energy to energy interaction.   This leads to a more specific question:  Does electromagnetic radiation or energy curve space like mass curves space?
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I used to read the term "pure energy" in the context of matter-antimatter annihilation.  Is the "pure energy" spoken of photons? Is it some form of heat?  Some kind of particles with mass?   Basically, what does "pure energy" in the context of matter-antimatter annihilation refer to?
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I don't understand why it is said that the (rest) mass of a system is not conserved in relativity. I mean, the momentum of a system is conserved (i.e.: it remains constant in a frame of reference without any external influence). Also the energy of a system is conserved in relativity: it doesn't change without any external agency  and the (rest) mass of a system is just  $$m^2=E^2-p^2$$  $E$ is constant, $p$ is constant, how can $m$ change?  For example, entropy is not conserved in a system, that means that the entropy of the system will increase spontaneously with time, which is really the case. But, is this true for mass?   here is the problem from Griffiths and exact solution as given in the Griffiths,  Two lumps of clay, each of rest mass $m$, collide head-on at $3c/5$ and they stick together. Question: what is the rest mass $M$ of the composite lump?  Solution: In this case conservation of momentum is trivial it is zero before and zero after. The energy of each lump prior to the collision is $$mc^2/\sqrt{1-v^2/c^2} =5mc^2/4.$$ The energy of the composite lump after the collision is $Mc^2$ (since its at rest). so the conservation of energy says: $5mc^2/4 + 5mc^2/4 =Mc^2$ and hence $M=5m/2$.  Notice that this is greater than the sum of the initial masses! Mass was not conserved in this collision; kinetic energy was converted into rest energy, so the rest mass increased.
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Does light have mass? If yes, will it exert force? If no, then how are light particles are travelling at light speed? If light doesn't have mass how is it attracted by gravitational force (black holes)? And what actually is light?
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In the famous equation , the variables stand for:     $E$ is energy, $m$ is mass, and $c$ is the speed of light (in vacuum).   And I understand the equation fairly but limited in knowing in its effects/outputs in reality, honestly.   Some example? Could anybody please give me some sort of examples in real world which are done by this equation?
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Regarding this thread:    Why is the idea that the total energy in the universe "zero" so popular (re: Laurence Krauss) and why is the flatness of the universe used to back this up when, according to that post, an open universe would not conserve energy so the total energy of the universe cannot be "zero", can it? What's the energy being defined as zero and why is that energy used to predict things about the universe when "the" energy (as the term is used in that post) is not zero?  Additionally, I found one very good explanation here for this,    This seems to indicate that in flat space (the sort of space used in these zero energy universe theories) the mass can NOT be positive thus contradicting the notion that mass is positive and gravity negative and the whole thing winds up being zero. Did I interpret that correctly?  The MO question is cross-posted to Physics.SE here,
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Why don’t photons interact with the Higgs field and hence remain massless?
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In popular science books and articles, I keep running into the claim that the total energy of the Universe is zero, "because the positive energy of matter is cancelled out by the negative energy of the gravitational field".  But I can't find anything concrete to substantiate this claim. As a first check, I did a calculation to compute the gravitational potential energy of a sphere of uniform density of radius $R$ using Newton's Laws and threw in $E=mc^2$ for energy of the sphere, and it was by no means obvious that the answer is zero!  So, my questions:   What is the basis for the claim &ndash; does one require General Relativity, or can one get it from Newtonian gravity? What conditions do you require in the model, in order for this to work? Could someone please refer me to a good paper about this?
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Do massless particles have a meaning in Newtonian mechanics? Do they have a physical interpretation? Because we don't have an equation of motion for massless particles, we don't have a gravitational potential. We could have electric potential but then we lack the equation of motion. I don't see how they can be a physical object, but I would love to hear from you about this.
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A charged particle undergoing an acceleration radiates photons.  Let's consider a charge in a freely falling frame of reference.  In such a frame, the local gravitational field is necessarily zero, and the particle does not accelerate or experience any force. Thus, this charge is free in such a frame. But, a free charge does not emit any photons. There seems to be a paradox. Does a freely falling charge in a gravitational field radiate?
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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?"