This is actually not too difficult and we can do it just by a few basic principles of relativity and some simple algebra. These are explained in much more detail in my article on special relativity , which is aimed for beginners in the topic. A spacetime interval is simply a path through both space and time, which is the same for all observers i. Lorentz invariant.
The spacetime interval denoted by dS connects both space and time in the following way analogous to the Pythagorean theorem :. Okay, then we need the definition for a proper time interval. A proper time interval is connected to the spacetime interval by a factor of the speed of light squared:. Just know that these are some of the most central concepts in special relativity. Anyway, from these quantities, it is possible to derive a formula for momentum that works for photons as well.
If you know about special relativity already, you might see something here. In fact, they are just derivatives with respect to proper time. Now, what is this sum of the squares of these time derivatives? They are simply velocities! Together these three terms are simply just the total velocity v and we get:. So, we end up with:. This is explained in more detail in my introductory article to SR. The idea of four-velocity is not really anything difficult. It is simply a velocity with four spacetime components t,x,y,z as opposed to the normal three space components x,y,z.
The normal three velocity is defined as the derivative of the spacial components with respect to time. Similarly, four-velocity is defined as the derivative of the spacetime components with respect to proper time. So, four-velocity is simply the relativistic analogue of the regular velocity. Momentum can be thought of as an object's ability to push another object due to its motion.
Since light has no mass, you may be tempted to say that light has no momentum. Additionally, everyday experiences may seem to confirm that light has no momentum sunlight does not knock over soda bottles like baseballs do. However, light does indeed carry momentum in the form of energy. The momentum that light carries is so small that we don't notice it in everyday life.
We do not get knocked over when we turn on light bulbs, and the light from candles does not make the curtains sway. But the momentum of light is large enough to be measurable, and can in fact be used in certain applications.
For instance, laser cooling machines shoot a sample from all directions with laser light in order to use the laser light's momentum to slow down the atoms in the sample, thereby cooling it. In optical traps, also called optical tweezers, the momentum of the light is used to trap and manipulate small objects. I think it was Einstine who proved that no mass can travel at the speed of light.
As any object of any arbitrary mass when approximates the speed of light increases in mass. When it reaches the vecinity of speed of light its mass is so enormous that it requires infinite amount of energy to propel it.
Am I correct? Since photons have zero rest mass they can move with the speed of light. Light has mass. Generally,Mass is defined as the amount of substance or matter contained in the body. Also , according to the Newton's gravitational law mass can be defined as a quantity which has gravitational property that is it can apply gravitational force to other body and also it can be influenced.
When light passes through the gravitational field of any heavenly body it deviates toward the heavenly body. So light has mass on the basis of Newton's gravitational law.
You're on the right track in important ways, but it turns out life isn't quite so simple. Yes, if we define the source of gravitational effects to be mass, we can see that light has mass in that sense. However, if you tried to use that force equation you gave, you'd calculate some bending of light in a gravitational field, but it would only be half the observed amount.
General Relativity, which describes the distortion of space-time by mass and momentum, is needed to get the right answer. Your other definition, "Mass is defined as the amount of substance or matter contained in the body. It just substitutes some words for others, and doesn't tell us what to expect to see in the world.
Light sails use the momentum of photons to provide propulsion for space flights. If a photon is reflected and hence loses momentum to the sail what effect is there on the reflected photon. Does its wavelength change? If so why dont we see a change in colour if we view things in a mirrow single reflection and why do LASERS work in spite of multiple reflections in the laser tube stimulating a single frequency of output light?
Bill- I'm very sorry that this question somehow slipped between the cracks long ago. When light bounces off an object it does impart momentum to it. In the simplest case, light bouncing off a very massive stationary object, the light imparts no energy to the object. The momentum imparted is twice that of the incoming light, since it just changes directions and thus changes the sign of its momentum.
A more interesting case looks at this from the point of view of somebody who says the big object is moving, for example away from the light source.
From the new point of view, the light transferred energy to the object, since the momentum transfer times the velocity of the object isn't zero. Thus the reflected light has less energy and lower absolute value of momentum than the incoming light. You do in fact see a tiny change in color if you bounce light off moving objects. The effect is called laser Doppler velocimetry, or quasi-elastic light scattering. I used to do experiments of exactly that type. The broadening of the frequency spectrum of the light emitted by atoms due to the Doppler shifts associated with their motions in the mirror frame is a real effect in laser technology.
See Mike W. How can a particle have momentum when it does not have mass?
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