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Old Jan 3rd 2013, 06:29 PM   #1
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Lightbulb How come photons travel at the speed of light?

Sounds like a silly question but hear me out.

A photon has energy, right? And isn't energy equivalent to mass? An object with mass cannot travel at the speed of light. However a photon (being a quanta of light) can travel at the speed of light. How is this possible due to mass-energy equivalence?

Also, if gravity is an attraction between two massive objects, how come light is affected by gravity (such as with a black hole)? Most scientists would say this is because mass is equivalent to energy right? So in reality gravity is an attraction between two objects with energy right?

To summarize, mass is equivalent to energy, and objects with mass cannot travel at the speed of light. How come Photons can travel at the speed of light despite having energy?

Last edited by urooj177; Jan 3rd 2013 at 07:24 PM.
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Old Jan 4th 2013, 12:23 PM   #2
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It is assumed (though actually not yet proved) that the "rest mass" of a photon is 0. In special relativity the total energy of a particle is given by:

E^2 = p^2c^2 + m(rest)^2c^4

For a tyical particle with mass, if its momentun is 0 (ie if p = 0) then this becomes the familiar (though a bit misunderstood) equation E=mc^2. But for a photon, which is assumed to have rest mass = 0, it becomes E=pc. Hence photons can have momentum and energy, even though they don't have rest mass. And since they don't have rest mass they travel at the speed of light.

As for why photons are effected by gravity if they don't have mass - it's due to the effects of the curvature of space-time by an object with mass. When a photon travels from point A to point B it takes the shortest path, which in our normal everyday experience is a straight line. But when a massive star or black hole causes significant curvature of space-time that shortest path is not a straight line, and we see that the light path is bent.

It's also a consequence of Einstein's principle of the equivalence of gravity and acceleration. He maintained that if you are in a closed room (like an elevator car) and you feel a force pushing you downward it's impossible to tell whether that force is due to gravity (ie your weight) or due to an upward acceleration. So when you feel your weight pressing through your feet onto the floor it's impossible to say whether the elevator car is stationary on earth or is in space and accelerating at 9.8m/s^2. Now suppose you are on an elevator accelerating upwards and consider what happens to a light beam that enters the car horizontally (perpendicular to your acceleration) through a small window in the side of the car - you would perceive that the light beam comes through the car and appears to curve downward slightly before hitting the opposite wall, due to the increase in the car's velocity during the time it takes the photon to traverse the car. If you believe Einstein's equivalence principe, this means that if the car is stationary but in a gravity field a beam of light entering through the window would also appear to curve downward. Hence light beams curve in gravitational fields. Note that this has nothing to do with classical physics, objects with mass, or the arc that a thrown object takes due to forces as defined by Newton's law of gravity (i.e. F = GMm/d^2).

Last edited by ChipB; Jan 4th 2013 at 12:26 PM.
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Old Jan 4th 2013, 07:07 PM   #3
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Oh ok thank you I get it now
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Old Jan 5th 2013, 12:58 AM   #4
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Originally Posted by urooj177 View Post
Sounds like a silly question but hear me out.

A photon has energy, right? And isn't energy equivalent to mass? An object with mass cannot travel at the speed of light. However a photon (being a quanta of light) can travel at the speed of light. How is this possible due to mass-energy equivalence?

Also, if gravity is an attraction between two massive objects, how come light is affected by gravity (such as with a black hole)? Most scientists would say this is because mass is equivalent to energy right? So in reality gravity is an attraction between two objects with energy right?

To summarize, mass is equivalent to energy, and objects with mass cannot travel at the speed of light. How come Photons can travel at the speed of light despite having energy?
a photon has no mass. photons can be converted to energy.
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Old Jan 5th 2013, 06:28 PM   #5
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Originally Posted by urooj
Sounds like a silly question but hear me out.

A photon has energy, right? And isn't energy equivalent to mass? An object with mass cannot travel at the speed of light.
However a photon (being a quanta of light) can travel at the speed of light. How is this possible due to mass-energy equivalence?
This is a very common mistake - Yes, a photon has energy E and the energy of a photon has inertial mass m (aka relativistic mass) which is related to E as E = mc[sup]2[/sup]. However it's only true to say that a particle which has a non-zero proper mass m[sub]0[/sub] (aka rest mass) cannot travel at the speed of light.

Originally Posted by urooj
Also, if gravity is an attraction between two massive objects, how come light is affected by gravity (such as with a black hole)?
Because light has non-zero passive gravitational mass.

This problem arises so often because physicists disagree on the definition of mass when used unqualified.
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Old Jan 5th 2013, 06:30 PM   #6
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Originally Posted by dennisfl8 View Post
a photon has no mass. photons can be converted to energy.
Photons do have mass, they have relativistic mass defined by m = p/v = p/c. But its meaningless to say that anything can be converted into energy. Objects have energy in the first place due to their mass.
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