# Question on speed on light

Acc to einstein mass of a body increases when its speed approaches to the speed of light or tends to approach because the energy of the body adds to its mass but my question is that light also has particles called photons then why its mass doesnot approaches to infinity and light slow down ?

Note by Vivek Bhal
5 years, 2 months ago

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One needs to be specific when talking about relativity, mass, etc. I find that students often get confused when they talk about energy, mass, etc. in relativity so let me try and lay it out. In Newtonian physics, the energy of a particle is given by $$E=1/2 m v^2$$. In special relativity the total energy of a particle as observed by someone in a laboratory is determined by the relation $$E^2=p^2c^2 + m^2 c^4$$, where E is the energy, p is the momentum, c is the speed of light, and m is the rest mass. The rest mass and the speed of light are measured, fixed quantities, while the energy and momentum obviously depend on how fast the particle travels. If you plot the energy vs. momentum you will find that it is a hyperbola that goes through $$(0,mc^2)$$ and asymptotes to the line E=pc.

How fast does a particle travel in terms of its momentum and energy? Although you are likely used to using the group velocity for the speed of waves, one can use the same technique to get the speed of a particle. Again, consider Newtonian physics. The energy is $$E=1/2 m v^2= p^2/2m$$. The group velocity is $$v=dE/dp=p/m$$ which is just the standard notion of speed in Newtonian mechanics! In relativity it's easy to see from the graph of the E vs. p hyperbola that the group velocity, which is after all just the slope of the graph, only approaches the speed of light as $$p,E\rightarrow \infty$$. Hence it takes an infinite energy to make something that has a non-zero rest mass travel at the speed of light

Now consider photons. Photons have zero rest mass, so the relationship between E and p is $$E^2=p^2 c^2$$ and $$v=dE/dp=c$$. In other words photons always travel at the speed of light by definition - they cannot speed up or slow down. As well, their energy does not affect their speed. Photons are very different beasts than other massive particles.

Staff - 5 years, 2 months ago

everything we see is matter. and every matter possesses energy. There are no energy type which can exist independently matter and energy exist together.

- 5 years ago

Wait, the speed of light is calculated in vacuum is 299792458 m/s. OK but the speed of light is not tested in other areas which has a gravitational potential. at that time it might travel slower. Also, when I worked out the particle energy equation, it shows that it is travelling at the speed of light even if it had mass.

OK, that's no problem. But Gravitational redshift and radiation pressure requires light to have mass. 'Massless particles are always impossible' Also look at another thing.. 'matter tells spacetime how to curve, and spacetime tells matter how to move' so, if light is massless, it would go straight. again, light requires to be massive. its mass is ~4.4*10-44 kg.

- 5 years ago

i think it is the thing with tachyonss..

- 5 years, 2 months ago

the thing is all the massless particles need 2 travel at the speed of light to exist

- 5 years, 2 months ago

You're missing a point when you say light is "Made up" of particle. You cannot argue whether light is made of something. What you CAN argue is what nature it is showing at particular coordinate in space-time. When light is travelling in space, its nature is explained by it's wave nature. And this nature has a speed limit. You cannot assume light to be travelling as a stream of tiny particles called photons, no. Photons materializes when you try to detect or observe them. In all other situations, light is believed to be wave, hence it can't slow down according to Einstein's theory. I once read a beautifully written line in my physics book: Light originate from its source as Photon, travels as wave and meets destination as photon.

- 5 years, 2 months ago

Photon is energy barrier, which is fundamentally different from common particles like electrons, protons and neutrons. Thus photon has zero mass/

- 5 years, 2 months ago

as photon slows down and itsmass comes to zero...if its speed comes to zero

- 5 years, 2 months ago

Rest mass of photon is zero. As the photon speed increases its mass increases according to Einstein's relativestic mass formula..

- 5 years, 2 months ago

pls refer Aurthor Beiser's Basics of modern physics

- 5 years, 2 months ago