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You can get an exact solution for $t(p)$, although it involves a rather nasty integral that I'm not sure can be written in closed form. Here's how: The equations of motion are $$\frac{dp}{dt} = -kx \qquad \frac{dx}{dt} = \frac{1}{m} \frac{p}{\sqrt{1 + p^2/m^2 c^2}}.$$ This second equation can be obtained by taking the equation $p = m v /\sqrt{1 - ... 3 There's no one-to-one relationship. With zero rest mass, a particle must always be observed to move at$c$. A particle with nonzero rest mass, on the other hand, can move at any speed in$[0,\,c)$(note the closed-open interval). At the risk of putting words in your mouth, I think I can recall the exact same question in my mind and it went something like ... 2 People are addressing the speed question, but just to be clear: a photon can be very low energy. For instance, radio waves are much lower energy than gamma rays, even though both are made of photons (and, in vacuum, both travel at the speed$c$). What determines the energy of a photon is the frequency of the excitation (frequency of the corresponding light ... 2 Special relativity and general relativity have different views about inertial frames, but in some ways the general relativity take on them is (perhaps surprisingly) easier to explain. So I'll start with GR then extend the description to SR. In general relativity there are usually no global inertial frames i.e. it is impossible to construct a frame that ... 2 SECTION A : Non-relativistic conservation of energy The work done by the non-relativistic force$\:\mathbf{f}\:$per time unit, that is the power produced or consumed, on a particle moving with velocity$\:\mathbf{v}=d\mathbf{r}/dt\:is \begin{align} \dfrac{dW}{dt}=\mathbf{f}\circ \mathbf{v}=&\dfrac{d\mathbf{p}}{dt}\circ \mathbf{v}=\\ ... 2 Light has a frequency of approx. 1e15Hz. Can light be transmitted in a hollow copper tube? Yes. No need to go relativistic. Can objects move at near the speed of light in a coax cable with inner conductor? No. They can't move in there, at all, not even at walking speed. Does any of this has anything to do with photons? No. Your experiment does have a ... 1 Refractive Index is when light travels more slowly in a medium. Here is an example of light being slowed down to 38 miles per hour. The speed of a photon does not affect its energy. It has zero mass, therefore zero kinetic energy. The energy it has is due to its frequency (color), and nothing else. (However, it does have momentum!) 1 There is a subtle difference between saying(2,2)$and$2\otimes 2$. In the latter case we are thinking of both reps as transforming under the same element of the group$SU(2)$. In the former case we are thinking of$(2,2)$as transforming under the Lorentz group, which contains two distinct copies of$SU(2)$. Call one copy the$L$copy and the other the ... 1 Although it has been said in other comments and answers, it bears repeating succinctly: photons (as far as any experiment can tell) are massless and therefore always move at the universal, invariant speed of light. There is NO non-relativistic description of the photon. Even the "classical" description of light - Maxwell's equations - can be interpreted as ... 1 I will reply to this because the checked answer is not answering the question.The question is about photons, the answer is about light. It is as if the question were about atoms and the answer is about density of material. The question is asked about photons, the quantum mechanical framework is relevant to it. The checked answer is about light which is in ... 1$E = pc$is only true for massless particles. For massive particles you have the mass-shell relation:$E^2 = m^2c^4+p^2c^2$After you use$E=T+mc^2$and you can find$p\$