EM waves have no mass but they do have momentum?

[BranRubaba]

I was studying radiation and came across an article:

https://www.wtamu.edu/~cbaird/sq/2014/04/01/light-has-no-mass-so-it-also-has-no-energy-according-to-einstein-but-how-can-sunlight-warm-the-earth-without-energy/#:~:text=In summary, all objects with,not the only massless object.

Which said that waves have no mass but they do have momentum. Now, this boggled my mind a bit and messed with my understanding of the term Momentum.
Now here's what I want to know... Is it appropriate for me to define momentum as the amount of influence that existence A will have on existence B's motion?

Here I am using the term "existence" instead of "object" because I don't consider waves as an object... please also let me know if a wave can be considered an object in the strict sense of the physics definition of an object.
I also want to know if momentum only affects the motion of an object or there's something else that it affects.

 

[anorlunda]

Start your research here
https://en.wikipedia.org/wiki/Solar_sail

 

[PeroK]

Now here's what I want to know... Is it appropriate for me to define momentum as the amount of influence that existence A will have on existence B's motion?

No, it's not valid. In fact, I can make no sense of that definition.

 

[Drakkith]

Now here's what I want to know... Is it appropriate for me to define momentum as the amount of influence that existence A will have on existence B's motion?

Not really, as it's too vague to be useful. One could say something similar about kinetic energy or force. Momentum has a very specific meaning in physics and I suggest you stick to its meaning there.

please also let me know if a wave can be considered an object in the strict sense of the physics definition of an object.

Physics doesn't have a strict definition for 'object'. It's more of a general use term in English. And for good reason, as many things in nature blend together in ways that make a strict definition problematic. Is the solar system an object? Or just a collection of widely spaced, relatively weakly interacting objects? How about a city? Do objects need to be made of tightly bound atoms? If so, does that mean the ocean isn't an object? What about a person, who's made of solids, liquids, and gasses. Whatever definition you come up with will have to be broad enough to cover pretty much any conceivable situation, which means that the definition cannot be strict.

 

[Drakkith]

As for what momentum is in physics, the answer is that it depends on the context. Newtonian physics, electromagnetism, and quantum physics all have different descriptions of momentum since the math used in each on is different. They all match with each other, in the sense that the more accurate and complex theories 'reduce' to the less accurate and less complex theories at appropriate scales.

For the motions of particles and other physical objects, as opposed to EM radiation and fields, momentum is the product of the objects mass and velocity. In electromagnetism a charged particle has momentum in the form of its mass-velocity product AND in the form of a magnetic vector potential that accounts for the additional momentum it has from its interaction with the EM field. Quantum physics takes the EM description and gets even more complex.

 

[Ibix]

It's true that one way of quantifying momentum is to look at the effect a thing with momentum has on the motion of some standard mass, but there's a lot missing in the OP. You need to make sure the object (or whatever) interacts with your standard mass at all, then that all the momentum is absorbed by the standard mass, and you need to worry about the energy as well.

 

[BranRubaba]

Start your research here
https://en.wikipedia.org/wiki/Solar_sail

Wow, so there was such a thing as solar pressure or rather radiation pressure... thanks I learned something new

 

[BranRubaba]

As for what momentum is in physics, the answer is that it depends on the context. Newtonian physics, electromagnetism, and quantum physics all have different descriptions of momentum since the math used in each on is different. They all match with each other, in the sense that the more accurate and complex theories 'reduce' to the less accurate and less complex theories at appropriate scales.

For the motions of particles and other physical objects, as opposed to EM radiation and fields, momentum is the product of the objects mass and velocity. In electromagnetism a charged particle has momentum in the form of its mass-velocity product AND in the form of a magnetic vector potential that accounts for the additional momentum it has from its interaction with the EM field. Quantum physics takes the EM description and gets even more complex.

Thanks, Drakkith, so what I can surmise is that when it comes to definitions and terms, I should pay attention to the discipline that I am reading over and look for the definition that applies to the context right?

 

[BranRubaba]

Not really, as it's too vague to be useful. One could say something similar about kinetic energy or force. Momentum has a very specific meaning in physics and I suggest you stick to its meaning there.Physics doesn't have a strict definition for 'object'. It's more of a general use term in English. And for good reason, as many things in nature blend together in ways that make a strict definition problematic. Is the solar system an object? Or just a collection of widely spaced, relatively weakly interacting objects? How about a city? Do objects need to be made of tightly bound atoms? If so, does that mean the ocean isn't an object? What about a person, who's made of solids, liquids, and gasses. Whatever definition you come up with will have to be broad enough to cover pretty much any conceivable situation, which means that the definition cannot be strict.

I see... thanks

 

[phinds]

Thanks, Drakkith, so what I can surmise is that when it comes to definitions and terms, I should pay attention to the discipline that I am reading over and look for the definition that applies to the context right?

Yes, and most importantly, never believe that English words mean in science what they mean in standard conversational English usage (or that they necessarily have any meaning at all in science, such as is the case here).

 

[BranRubaba]

No, it's not valid. In fact, I can make no sense of that definition.

I'm having a difficult time understanding how a wave, which is massless can have momentum... which is defined as the product of the force and mass of an object.

 

[PeroK]

I'm having a difficult time understanding how a wave, which is massless can have momentum... which is defined as the product of the force and mass of an object.

Well, a wave has energy, yet one definition of energy is $\frac 1 2 mv^2$. How can something massless have energy?

 

[phinds]

I'm having a difficult time understanding how a wave, which is massless can have momentum... which is defined as the product of the force and mass of an object.

Definitions do not always transfer from one level of physics to another. You are using a Newtonian definition in an area where it does not apply. Go back and read post #5 again.

 

[BranRubaba]

Definitions do not always transfer from one level of physics to another. You are using a Newtonian definition in an area where it does not apply. Go back and read post #5 again.

Okay, so the momentum of an EM wave is the energy carried by the wave divided by the speed of light. in this sense, a wave doesn't need mass to have momentum. I think that I'm starting to understand now.

 

[anorlunda]

Wow, so there was such a thing as solar pressure or rather radiation pressure... thanks I learned something new

No. The light sail works from the radiation pressure of the light.

For a more dramatic example of radiation pressure, consider a thermonuclear warhead.

https://en.wikipedia.org/wiki/Thermonuclear_weapon#Radiation_pressure

The radiation pressure exerted by the large quantity of X-ray photons inside the closed casing might be enough to compress the secondary. Electromagnetic radiation such as X-rays or light carries momentum and exerts a force on any surface it strikes. The pressure of radiation at the intensities seen in everyday life, such as sunlight striking a surface, is usually imperceptible, but at the extreme intensities found in a thermonuclear bomb the pressure is enormous.

For two thermonuclear bombs for which the general size and primary characteristics are well understood, the Ivy Mike test bomb and the modern W-80 cruise missile warhead variant of the W-61 design, the radiation pressure was calculated to be 73×106 bar (7.3 TPa) for the Ivy Mike design and 1,400×106 bar (140 TPa) for the W-80.

 

[PeroK]

Okay, so the momentum of an EM wave is the energy carried by the wave divided by the speed of light. in this sense, a wave doesn't need mass to have momentum. I think that I'm starting to understand now.

If we start with classical physics, then the fundamental things are mass, length and time, which leads to mass and velocity as fundamental things in some sense. But, there are two niggling things.

1) Light has energy (and, as it turms out, momentum) but no mass.

2) Kinetic energy and momentum are similar but not the same: $\vec p = m\vec v$ and $E = \frac 1 2 mv^2$. That means we actually have three conservation laws: mass, energy and momentum.

If we look instead at Special Relativity (SR), we find first that mass is associated with energy. In the most famous equation in physics: $E = mc^2$. This is actually a special case of a more general equation:$$E^2 = |\vec p|^2 c^2 + m^2c^4$$This second equation remains valid for something with mass $m = 0$: namely, $E = |\vec p|$.

This allows us to unify the three conservation laws into a single law for conservation of the energy-momentum vector:$$\mathbf p = (E, \vec p)$$And we see that, for example, two particles with non-zero mass may annihilate into two massless photons, while the energy-momentum of the system is conserved.

To associate massless particles with the electromagnetic field requires another large step into the world of quantum mechanics and quantum field theory. Nevertheless, SR shows us that energy and momentum do not require particles to have a rest mass.

 

[bob012345]

Start your research here
https://en.wikipedia.org/wiki/Solar_sail

Wow, so there was such a thing as solar pressure or rather radiation pressure... thanks I learned something new

No. The light sail works from the radiation pressure of the light.

I think that is what @BranRubaba is saying here.

 

[ergospherical]

Matter has mechanical momentum with density $\mathbf{p} = \rho \mathbf{v}$. Associated with the electromagnetic field is a so-called electromagnetic momentum with density $\mathbf{g} = \varepsilon_0 \mathbf{E} \times \mathbf{B}$. These guys are not separately conserved in the general case but their sum, with density $\boldsymbol{\pi} = \mathbf{g} + \mathbf{p}$, is conserved. Its derivative $\partial \boldsymbol{\pi} / \partial t$ equals the divergence of the Maxwell stress tensor. In other words, the rate of change of mechanical plus electromagnetic momentum contained inside some region is equal to the momentum flux carried into that region, through its surface, by the field.

 

[Klystron]

Beyond the scope of classical physics but for your information,

In computer science an object can be a variable, function, method, data structure, or member or partition of the aforementioned sets. Once identified, objects form the basis of object-oriented programming, database design and other useful methodologies.

 

[phinds]

Beyond the scope of classical physics but for your information,

In computer science an object can be a variable, function, method, data structure, or member or partition of the aforementioned sets. Once identified, objects form the basis of object-oriented programming, database design and other useful methodologies.

Yet another example of how "object" is VERY loosely defined to encompass LOTS of things that sometimes have nothing to do with each other.

 

[Drakkith]

I'm having a difficult time understanding how a wave, which is massless can have momentum... which is defined as the product of the force and mass of an object.

What type of wave? A gravity wave (a wave on the surface of the water, not a gravitational wave) certainly has momentum since water molecules are moving up and down and thus must have momentum from their motion. Other types of waves in physical media, such as seismic waves associated with earthquakes, also share this property.

As for EM waves, consider the following. A charged particle stationary in space is hit by an EM wave. An EM wave, in very simplified terms, is nothing more than a propagation of alternating electric and magnetic forces. When the wave passes by a charged particle these forces act on the charged particle, accelerating it. Since the particle was accelerated, and thus is now moving, it has momentum and so it must have had momentum transferred to it by the wave in order to satisfy the conservation of momentum.

The reverse is true for the charged particle(s) that created the wave in the first place. They were moving and the creation of the wave slowed them down*, causing them to lose momentum. So some of their momentum must have been transferred to the EM wave, again because of the conservation of momentum.

*A simplification. You can create EM waves using charged particles without slowing them down, but we're sticking to a very simple example here.

So we can either say that the conservation of momentum is broken temporarily in between the creation of the wave and its interaction with another charged particle, or we can extend our definition of momentum. We choose to do the latter.

For a more in depth explanation, see this link.

 

[vanhees71]

Matter has mechanical momentum with density $\mathbf{p} = \rho \mathbf{v}$. Associated with the electromagnetic field is a so-called electromagnetic momentum with density $\mathbf{g} = \varepsilon_0 \mathbf{E} \times \mathbf{B}$. These guys are not separately conserved in the general case but their sum, with density $\boldsymbol{\pi} = \mathbf{g} + \mathbf{p}$, is conserved. Its derivative $\partial \boldsymbol{\pi} / \partial t$ equals the divergence of the Maxwell stress tensor. In other words, the rate of change of mechanical plus electromagnetic momentum contained inside some region is equal to the momentum flux carried into that region, through its surface, by the field.

For a derivation of this most simple "dust model" for the charged medium in terms of the action principle, see Sect. 4.7 in

https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf