# Speed of light and lorentzian factors [duplicate]

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How can a photon have no mass and still travel at the speed of light?

If light travels at the speed of light, and anything with rest mass will experience relativistic effects based on the Lorentzian equations, why doesn't light experience these kinds of effects?

For example, relativistic mass and rest mass are related via

$$m = \frac{m_0}{\sqrt{1-\dfrac{v^2}{c^2}}}$$

Shouldn't light therefore have no rest mass (since the Lorentzian is $0$)?

## marked as duplicate by Qmechanic♦Jan 23 '13 at 9:52

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## 1 Answer

You are quite correct, light has zero invarient mass.

Light does experience relativistic effects, but because $\gamma$ goes to infinity at $c$ you'll get confused using the Lorentz transformation to try and understand what is going on. The best way to understand the effect of relativity on light is to note that light travels on null geodesic. We can use the heavy machinery of general relativity to calculate the null geodesics for any spacetime and hence work out what happens to light. For example this allows us to calculate the bending of light in a gravitational field and also the fact light can't escape from a black hole.

• Why would it go to infinity at c? Shouldn't that be 0? – PixelArtDragon Jan 23 '13 at 9:01
• $\gamma$ is $1/(1 - v^2/c^2)$ so it goes to $\infty$ as $v$ goes to $c$. However $1/\gamma$ does indeed go to zero. – John Rennie Jan 23 '13 at 9:11
• Ah. So according to what I said, light would not have mass (or at least incalculable mass), but with what you have said, it has a mass that can be used in calculations? – PixelArtDragon Jan 23 '13 at 9:22
• No, light has zero mass. It has energy and it carries momentum, and these are important when calculating it's behaviour, but the mass is always zero. – John Rennie Jan 23 '13 at 9:34