# What is the difference between “accelerating a particle to light speed” and “turning on a flashlight”?

According to how we understand the universe it would take an infinite amount of energy to accelerate the ambiguous "particle" to light speed. Yet there are all kinds of reactions that cause light, seemingly without providing the infinite amount of energy needed to accelerate particles to light speed. Burning wood in a campfire or heating tungsten in a vacuum both cause particles that were not traveling at light speed to somehow become traveling at light speed, otherwise both would be totally useless. What am I doing when I light my cigarette that the guys at CERN can't figure out?

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The guys at CERN can light a cigarette easily, like you. But you should try to accelerate a proton beam to 3 TeV to see what issues they had to resolve. There is a big difference between accelerating massive particles (that cannot move at the speed of light) and sending out photons (that are born moving at the speed of light and actually are unable to move with any other speed). – mpv Jul 15 '14 at 12:28

Yet there are all kinds of reactions that cause light, seemingly without providing the infinite amount of energy needed to accelerate particles to light speed.

If you're imagining that there are photons at rest within the flashlight when it's off and the flashlight accelerates photons to light speed when it's turned on, then I can see why you're asking this question.

But that's not the case. A photon is created when it is emitted by some process, e.g., an electron dropping from a higher energy orbital to a lower energy orbital.

The photon is created at light speed and, in fact, this must be the case for any massless particle.

A massive particle cannot be accelerated to light speed but a massless particle must travel at light speed.

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It takes an infinite amount of energy to accelerate a particle with mass to the speed of light. A photon does not have mass, thus can move at the speed of light. Note that a photon does not accelerate; the moment it is created it moves at the speed of light.

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Photons have no mass, they always travel at the speed of light. Not so for massive particles. You could try building a collider with massless particles, but you would fail for several reasons: The only freely propagating massless particle is the photon, but it does not have a charge, so you cannot bend it to follow a circular collider. You could still build a linear accelerator, though. But then, it is not interacting with itself, since it couples to electric charge only, so there's no point in shooting photons on photons. You could propose to build a fixed target experiment, where you shoot photons on resting particles. This can be done, and is generally called Compton scattering or Photoelectric effect. But your experiment would still be not very interesting, because it's not the speed of the particles, that makes these collision events creating new physics, but the energy they carry. If you want to create new particles, you need to have the energy equivalent to do so:

$$E^2 = m^2c^4 + \lvert \vec{p} \rvert^2c^2$$

There is no velocity in here, the velocity does hardly change anyway for highly energetic massive particles. Last but not least, the photons couple only via electromagnetic interaction, while the hadrons that are used in the LHC for example, couple via strong, weak and electromagnetic interaction, so you will have a much richer spectrum using hadrons. There are many more technical reasons why to not use photons (lower cross-section for example).

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Good question. $E=mc^2$ is not the full energy relation. I updated my answer. For a photon, it is simply $E= \lvert \vec{p} \rvert c$. – pfnuesel Jul 15 '14 at 13:07
I wasn't sure how to ask that question and deleted it so I'm glad you caught it while it was up, thanks. – Derek Roberts Jul 15 '14 at 13:08
There are plenty of points of shooting photons to photons. Of course they need to carry quite a lot of energy. Have a quick google search for "gamma gamma collider" ;) – DarioP Sep 17 at 7:12