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In physics, it always takes some time for a particle to move from rest to some speed.

However, photons (light particles) accelerate instantly from zero to c. How? (A visualization would be helpful.)

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    $\begingroup$ A photon is never at any other speed than c. If you look at it from the photons perspective, in it's frame of reference it is a continuous spear going from creation to annihilation. It is merely a bridge between two events that are separated by spacetime. $\endgroup$ Aug 17 at 5:19
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    $\begingroup$ @StianYttervik Correct me if I'm wrong, but I thought photons didn't have a frame of reference? $\endgroup$
    – gardenhead
    Aug 17 at 14:05
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    $\begingroup$ I’m voting to close this question because there doesn't seem to be an astronomy angle to this question. It is about the properties of light, not the properties of astronomical objects. It's not a bad question for Physics, so I've upvoted. $\endgroup$
    – James K
    Aug 17 at 15:10
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    $\begingroup$ Who told you no other phenomenon do it? Gravitational waves and gluons also travel at c. As would any other particle or wave we might discover that doesn't have a rest mass. $\endgroup$ Aug 17 at 21:08
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"Accelerate instantly" would imply that a photon takes many different velocities at the same point in time. In fact, it would imply that a photon takes on every velocity between $0$ and $c$ simultaneously, but that clearly makes no sense at all - a particle cannot have many instantaneous velocities simultaneously.

When a photon is created, it is traveling at $c$. A photon is always traveling at $c$, there is no such thing as a stationary photon which is then accelerated. As an imperfect analogy, consider a pressure wave like sound traveling through air - the pressure wave itself is the movement of energy, you can't have a sound wave that remains stationary and does not move. Similarly, a stationary photon does not exist - if it exists, the electromagnetic wave (which is the photon) must be moving at $c$.

As another analogy, consider what happens when you throw a rock into a pond - ripples expand from the point of contact. How fast were the ripples moving before you threw the rock? That's unanswerable, since the ripples did not exist before you threw the rock. The ripples are simply the movement of water, so the ripples require movement - the ripples come into existence already moving.

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    $\begingroup$ The point is; how can we visualise a particle which simply starts at c?Say you were a lecturer at a high school,how would you describe it to students?(Somebody who was in this situation consulted me ,so I wish to post it here) $\endgroup$ Aug 16 at 16:48
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    $\begingroup$ @AnnexRemotelearn I suppose you could consider the wave-like transfer of energy. It's not a perfect analogy, but consider a sound wave as it travels through a medium - the pressure wave exists because it's moving, you can't have a pressure wave that remains stationary. The phenomenon itself requires velocity. Either it doesn't exist at all, or it comes into existence with some velocity. $\endgroup$ Aug 16 at 17:00
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    $\begingroup$ @nick012000 Good point, but a standing wave is actually two waves moving in opposite directions. A standing pressure wave still requires movement of molecules - the air inside a pipe resonating with a standing wave is not stationary (en.wikipedia.org/wiki/File:Molecule2.gif). $\endgroup$ Aug 17 at 13:17
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    $\begingroup$ @AnnexRemotelearn I think the trick is to get past the concept that "at rest" is somehow privileged. (That is, that when you create something, "of course" it would start at rest.) When you actually get into special relativity (which is where "light always travels at c" comes from), "rest" isn't anything special. What's at rest for one person/particle is 90% the speed of light for another. There's reasons massive particles tend to be created at rest with respect to certain specific reference frames (Conservation of Energy & Momentum), but they don't apply to photons the same way. $\endgroup$
    – R.M.
    Aug 17 at 19:07
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    $\begingroup$ You may want to address this: Photons in matter travel at a different velocity than photons in vacuum. Does that mean it gets accelerated when it changes from one medium to another? $\endgroup$
    – gerrit
    Aug 17 at 19:13
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I am not sure this is a problem of visual communication. My incling would be to think this is a problem of language communication. The equations of relativity tell us that anything with zero rest-mass can only ever exist at the speed of light.
So photons don't really accelerate, it is more a fundamental property of their existence to travel at c.

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    $\begingroup$ This is my intuition as well. Everything in the universe moves at c because that is simply the natural speed of things. But once a thing has mass then it interacts with the Higgs field and thus move at speeds other than c (slower). $\endgroup$
    – slebetman
    Aug 18 at 9:17
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You are looking for a way to visualize the fact that a photon is created traveling at the speed of light.

Remember that a photon is actually a perturbation of the electromagnetic field. That field is everywhere at once. It is part of the fundamental construct of the Universe and it has, essentially, always been so.

An approximation of photon propagation might be to consider a mallet hitting a gong. The force waves (sound waves in the case of the gong) induced by the mallet striking the gong travel with an instantaneous speed; they do not accelerate, they simply propagate. The velocity at which they propagate is determined by the physical characteristics of the gong itself; it's the speed of sound.

The electromagnetic field has the property that all of its waves propagate at the speed of light, c, no matter what else is happening. because of this the gong comparison has its limits.

The key thing to remember is that the photon is not a particle; it is a perturbation. It is the field which determines the velocity of that perturbation and, in our Universe, that velocity is c.

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    $\begingroup$ I'm not downvoting, but I don't think an explanation on the level of quantum field theory and quantum electrodynamics is appropriate for someone who wants a high school level explanation. $\endgroup$ Aug 16 at 17:22
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    $\begingroup$ Yes I can understand waves are disturbances/pertubations,but what is difficult is ;if you were watching the disturbance start,why do you see it instantaenously start at c?Say I had a photon detector,I would have to see some physical effect to measure c,and no physical effect's rate of occurrence can equal c.,as the pyhsics textbooks say? $\endgroup$ Aug 16 at 17:28
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    $\begingroup$ @DavidHammen High school teaches about electric fields and magnetic fields and the only part that's beyond reach is how a wave in a field can also be a particle, but that's typically pointed out and handwaved in high school anyway. $\endgroup$
    – user253751
    Aug 17 at 14:28
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    $\begingroup$ P@David Hammen; Popular science programs on television cover this much, and I didn't think it would be too deep. I thought this about the level given to "Why can't objects travel at the speed of light?" type questions. $\endgroup$
    – JohnHunt
    Aug 18 at 6:51
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    $\begingroup$ @AnnexRemotelearn; If you strike a stretched bit of wire, say a piano string, with a mallet, the wave that is produced does not "speed up". The energy from the mallet is simply transferred to the string and it continues on its merry way. Light works the same way. The photon is a packet of energy which is transferred to the EM field in the same sense that the energy from the mallet transferred to the string. In neither case does that energy wave accelerate. It moves through the medium (String/EM) at the medium's speed of sound. The "speed of sound" for the EM field is C. $\endgroup$
    – JohnHunt
    Aug 18 at 7:05
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Take a look at this diagram from Feynman's lectures at Caltech on angular momentum. Here, an atom with angular momentum $m=1$ starts out in an excited state on the left hand side of the diagram. Then it moves to a ground state as it emits a photon, traveling at $c$. Angular momentum is conserved, so the photon now has an angular momentum of 1.

enter image description here

As an analogy, suppose you are on the edge of a merry-go-around, which is spinning very fast. If you let go, you won't speed up, instead you will continue moving in a straight line with linear momentum. The merry-go-around system will lose a corresponding amount of angular momentum so that momentum is conserved. No acceleration is necessary around the time you let go! This analogy, of course has its limitations, since a photon may be emitted off the rotational plane.

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I think your core misunderstanding is this :

In physics, it always takes some time for a particle to move from rest to some speed.

If a particle breaks up into two other particles, then the moment those two particles are created they have whatever velocities are required to conserve momentum (i.e. momentum before the break up must equal total momentum after). There's no acceleration required - they get that velocity the instant they are created.

Now photons have another property - they absolutely always travel at the speed of light. For photons their momentum and energy are dependent on their frequency (or wavelenght if you prefer), so momentum/energy is not dependent on velocity for a photon. This means there is no problem at all with the photon starting out at the speed of light.

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    $\begingroup$ "Photons... always travel at the speed of light" in a vacuum. But when they travel through matter - the glass of a lens, for instance - they slow down, and speed up when they leave the glass. But AFAIK (I'm no expert) there's no force applied to slow them down, or speed them up again, and the photons always have the same energy coming out as they did going in. Seemingly another case where photons don't act like ordinary matter. $\endgroup$
    – jamesqf
    Aug 17 at 6:38
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    $\begingroup$ @jamesqf Photons don't act like ordinary matter because they are not matter. You are looking for a simple, classical explanation for a complex, quantum phenomenon. If it helps, consider that photons are massless - so can undergo instantaneous acceleration. $\endgroup$ Aug 17 at 7:50
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    $\begingroup$ @OscarBravo The point I'm making is that they never travel at any other velocity than the speed of light (traveling in a medium is a complex case). They never accelerate because they always start at the speed of light. $\endgroup$
    – StephenG
    Aug 17 at 13:05
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    $\begingroup$ @jamesqf If you are interested in the reason why light in a medium apparently travels slower than the speed of light in a vacuum then I'd suggest starting with this Q&A on Physics SE. $\endgroup$
    – StephenG
    Aug 17 at 16:41
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    $\begingroup$ @jamesqf There is no "your" definition of matter. It's not a question of linguistics; it's physics, which is not a matter of opinion. In the Standard Model, photons, along with all other gauge bosons, are not matter particles. $\endgroup$ Aug 18 at 12:52
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In physics,some time is always need for a particle to move from rest to some speed.

This is not true in quantum mechanics. Particles created during a quantum interaction can be born with non-zero linear momentum with respect to the rest frame of the particles that generate the new particle. There is no acceleration. For example, there is no acceleration when a pair of photons are created via a electron-positron collision. The two photons are moving at the speed of light from the instant the collision created them.

Regarding a visualization,

Feynman diagram depicting an electron-positron annihilation

This is a Feynman diagram that depicts an electron-positron annihilation. Starting at the bottom of the diagram, the diagram shows an electron and a positron moving toward one another. At some point in time, the two particles get close enough together that their fields interact. This is the horizontal line in the middle of the diagram. At that point in time, a pair of photons are created that conserve the energy and momentum of the incoming particles. The created photons are born moving at the speed of light.

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    $\begingroup$ How is such a thin visualisable? $\endgroup$ Aug 16 at 16:28
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    $\begingroup$ Thanks for the visual and URL;shall read through it $\endgroup$ Aug 16 at 17:30
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    $\begingroup$ I don't think that Feynman diagrams are appropriate to educate somebody with little to no background in physics, $\endgroup$
    – Thomas
    Aug 16 at 18:15
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    $\begingroup$ @Thomas I respectfully disagree. Feynman diagrams are extremely easy to understand, even for children. "This straight line is a particle, which is something you can hold. This wiggly line is a wave, just like the waves in the ocean. We can't hold them, but we can feel them push us." It doesn't have to be 100% accurate, it just has to be accurate enough for the layman to grasp. $\endgroup$
    – dotancohen
    Aug 19 at 6:56

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