Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: hamza on 16/10/2007 14:37:34
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I have a question regarding the fact that light waves or any others, transfer energy without transferring matter. These waves are known to posess momentum too. I am not getting the momentum thing.. I mean that momentum is a product of velocity and mass. I accept that waves have velocity but howcame they have mass.. Light waves are composed of photons and if they dont transfer matter of what mass is a component of, than how do they have momentum. i hope u guys get what i say.if there is s no matter that there should not be any mass and waves should not posess momentum.. Right??
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This is an old chestnut.
Momentum is momentum. It is a property of things which obeys a 'conservation law'.
Waves and masses can exchange momentum; photons can push dust particles away from the Sun, for instance. The wavelength of the photon will change, as a consequence. Momentum is conserved in situations where mass is not; there's not a momentum equivalent to E = mcsquared which allows mass not to be conserved in interactions.
If momentum had been 'invented' before mass, by scientists, there wouldn't have been this confusion.
The momentum of something with mass is mass X velocity.
For a photon it is wavelength / the planck constant. It is measured in kg m per second - we don't give it its own unit.
There is a parallel with Energy; energy can be transformed from heat to electricity to sound etc. but we still call it energy and its measured in Joules.
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If you like math, you can see this from Einstein's famous equation E=mc2. This version of the equation actually assumes the object has no momentum. The full equation is:
E2-p2c2=m2c4.
For something with no mass (like an electromagnetic wave), set m=0, and the equation is
E2=p2c2.
Rearranging things and taking square roots
p=E/c.
Since waves carry energy, and c is just a number, waves must have momentum.
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Sorry! but i did not get it..you just said that m=0 in the case of electro magnetic waves than p should also be equal to zero in p=E/c.. Could u please explain it in a more easy manner. Can something with zero mass still have momentum??
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There is only a problem if you insist that the only formula is mass times velocity.
AS jpetruccelli says, you can use p=E/c and you don't need mass for that.
He does NOT say that p should be zero; he says m = 0.
Just think of momentum as something on its own and not just a 'derived' quantity.
If you have to insist that momentum is just mass times velocity then you will never get it.
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The confusion is from the fact that everyone learns that P = mv when in fact that is a very specific definition. It is only valid for objects with mass. Momentum can also be refered to as inertia. For objects with mass, inertia is directly proportional with the mass and the velocity of the object...it is harder to change its state of motion as the object is more massive or moves faster. For massless objects (which are always waves and move at the speed of light, a wave itself) inertia (momentum) is directly proportional to the energy of the object and does not depend on its velocity (which is constant).
For those who want to see math for this, Newton originally stated his second law as
F = dP/dt
or the rate of change of momentum with respect to time. Work (which is a change in energy) is ∫F•dx. Solving that for force you get F = dE/dx where dE is work. Setting the two equations equal gives:
dE/dx = dP/dt
dE(dt/dx) = dP --> dv = dx/dt
dE/dv = ∫dP = P
For an object with mass this yields P = mv but for a massless object, v = c and is constant so P = E/c = hν/c = h/λ. Thus, energy of a light wave does not depend on anything except its wavelength. In fact, for anything, momentum only depends on its kinetic energy (dE in the above equations). The only difference practically speaking between energy and momentum is that energy is a scalar and momentum is a vector. The use of one or the other is only to make any one problem easier to solve.
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The only difference practically speaking between energy and momentum is that energy is a scalar and momentum is a vector.
Plus the fact that one is conserved and the other isn't?
I just wish we had started it all with momentum - then no one would be having this difficulty..
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Thanx Mr Andrew.. I got what u said.. This means that in the case of waves, momentum is a property of energy which a wave possesses while travelling with the speed of light and for matter it depends on the mass.. In waves that mass is analogue to the energy.. Tell me if i am wrong??
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This means that in the case of waves, momentum is a property of energy which a wave possesses while travelling with the speed of light...
Yes, momentum is related to the energy of waves, since waves have no mass. Waves still carry momentum even if they're traveling slower than light speed. Light traveling through glass is significantly slower than "light speed", but it still carries momentum.
...and for matter it depends on the mass.. In waves that mass is analogue to the energy.. Tell me if i am wrong??
You're basically right. Classical mass isn't a wave, and doesn't have wave-momentum (which is based on the energy of the wave). Classical mass gets momentum from mass times velocity.
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Momentum, no matter what kind, is dE/dv, or the rate of change of energy with velocity. This is true for waves, classical matter, what have you. The only difference is what properties of the thing with momentum are used in the equation for E. For matter it is mass and velocity but for waves it is wavelength.
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For massive bodies, momentum is not m*v but m*v*γ; the first is only valid at very low speeds.
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Another wave that can be regarded as having momentum is the 'phonon'. Phonons are an idea which is used to explain / analyse the vibrations in crystal structures. They obey the rules for momentum conservation - but they're not 'really there' - they are just a way of looking at things - just like magnetic and gravitational field lines.