If light has momentum then wouldn't it have force?

[zeromodz]

We know that light has momentum, but doesn't have mass. So if light reflects of say a mirror. The change in momentum is zero. If it is zero then we have a problem.

ΔP = ΔFT
ΔT = ΔP / F
ΔT = 0 / F
ΔT = 0

This shows that light is instantaneous because the time it takes for light to bounce of something is zero. Is there something I am doing wrong here? And if I am wrong and there is a change in momentum then wouldn't light create a force when it reflects?

 

[AJ Bentley]

And if I am wrong and there is a change in momentum then wouldn't light create a force when it reflects?

You are, there is and it does. Look up 'solar sails' in Google.

 

[LostConjugate]

We know that light has momentum, but doesn't have mass. So if light reflects of say a mirror. The change in momentum is zero. If it is zero then we have a problem.

ΔP = ΔFT
ΔT = ΔP / F
ΔT = 0 / F
ΔT = 0

This shows that light is instantaneous because the time it takes for light to bounce of something is zero. Is there something I am doing wrong here? And if I am wrong and there is a change in momentum then wouldn't light create a force when it reflects?

I see your error. Light has relativistic mass, otherwise known as kinetic mass, or kinetic energy, or just mass. You may have heard that light is like an object that has 0 rest mass, or no mass in it's rest frame, that does not mean that light doesn't have mass. Light in many ways is the most fundamental way to understand what it means to have mass.

This is all well explained in a Special Relativity course.

 

[diazona]

I see your error. Light has relativistic mass, otherwise known as kinetic mass, or kinetic energy, or just mass. You may have heard that light is like an object that has 0 rest mass, or no mass in it's rest frame, that does not mean that light doesn't have mass. Light in many ways is the most fundamental way to understand what it means to have mass.

Energy, not mass. Most modern physicists would say that light has energy, not mass, and that the term "relativistic mass" is potentially misleading and discouraged.

But other than the choice of terminology, you're right, of course

 

[Andy Resnick]

Is there something I am doing wrong here? And if I am wrong and there is a change in momentum then wouldn't light create a force when it reflects?

You are on the right track. It's more appropriate to consider the *pressure* (force/area) that light can exert on ponderable matter; pressure is a more appropriate concept because the field is distributed over space, not concentrated at a point.

 

[zeromodz]

So light itself exerts a pressure on you. That is really interesting.

 

[threadmark]

My understanding is light can exert pressure to mass through coupling. Kinetics does not apply because Photons have zero mass. I think that the transfer is mediated by the W and Z bosons. The kinetics can however be applied when the momentum is transferred from the W and Z bosons to mass because they both have mass.
TM

 

[Dr Lots-o'watts]

So light itself exerts a pressure on you. That is really interesting.

A metal having been hit by a high energy laser pulse can sound as though it's been hit by some sort of small hammer.

 

[LostConjugate]

Energy, not mass. Most modern physicists would say that light has energy, not mass, and that the term "relativistic mass" is potentially misleading and discouraged.

But other than the choice of terminology, you're right, of course

Since when is there a difference between energy and mass? Perhaps before 1905.

 

[Dr Lots-o'watts]

Not a difference, but a factor of c^2, when momentum is 0.

Saying mass and energy are the same because of e=mc^2 is like saying energy and height are the same because e=mgh. Don't get things mixed up. Interchangeable does not mean the same.

 

[diazona]

Since when is there a difference between energy and mass? Perhaps before 1905.

Um... since probably around the 1950s or '60s? I think :shy: Actually Dr. Lots-o-watts is completely correct, there is a factor of c², but I'm talking about more than that...

It's most clear to talk about it in mathematical terms. The formula that relates the two is
$$E^2 = m^2c^4 + p^2c^2$$
(direct from SR) In modern terminology, E is the energy and m is the mass. In older terminology, m was "rest mass", and there was this thing called "relativistic mass" (which is what you are calling "mass") that was defined as E/c².

 

[LostConjugate]

Um... since probably around the 1950s or '60s? I think :shy: Actually Dr. Lots-o-watts is completely correct, there is a factor of c², but I'm talking about more than that...

It's most clear to talk about it in mathematical terms. The formula that relates the two is
$$E^2 = m^2c^4 + p^2c^2$$
(direct from SR) In modern terminology, E is the energy and m is the mass. In older terminology, m was "rest mass", and there was this thing called "relativistic mass" (which is what you are calling "mass") that was defined as E/c².

Ok, first of all the factor c^2 should not be there, unless you are working in different units of time and space, but that's like working with meters and inches. In SR you should always work with c = 1 unless your working on a special project that involves meters or feet or whatever.

So we have $$E^2 = m^2 + (mv)^2$$

But $$m$$ and $$E$$ are equivalent, so $$(mv)$$ is just $$E_2v$$ (where $$E_2$$ is some energy in the object)

and $$v$$ is just d/dt which is another form of $$E$$, let's say $$E_3$$. So we have $$E - (E_2E_3)^2 = m$$

So $$E_t = m$$ where $$E_t$$ is the total energy of the object.Mass is the result of field permutations, objects that was see and feel as tangible solid objects are just persistent illusions.

 

[ZapperZ]

Ok, first of all the factor c^2 should not be there, unless you are working in different units of time and space, but that's like working with meters and inches. In SR you should always work with c = 1 unless your working on a special project that involves meters or feet or whatever.

You should not confuse "short-formed notations" with actual physics. In physics, we use MANY shortcuts. We often set h=c=k=1. This means nothing physically other than an easy form of notation. Simply looking at the dimensions alone is sufficient to indicated that they are not identical.

There IS a difference between mass and energy. An electron isn't JUST made up of mass that can be converted into energy. It's spin must also be taken into consideration, and here, a one-to-one conversion of energy into mass cannot occur without other external factors coming into play. The same with a photon being converted into mass. You can't just take a photon and completely turn it into just one particle.

Zz.

 

[LostConjugate]

You should not confuse "short-formed notations" with actual physics. In physics, we use MANY shortcuts. We often set h=c=k=1. This means nothing physically other than an easy form of notation. Simply looking at the dimensions alone is sufficient to indicated that they are not identical.

There IS a difference between mass and energy. An electron isn't JUST made up of mass that can be converted into energy. It's spin must also be taken into consideration, and here, a one-to-one conversion of energy into mass cannot occur without other external factors coming into play. The same with a photon being converted into mass. You can't just take a photon and completely turn it into just one particle.

Zz.

Well I wasn't trying to say that we as humans have the technology to make these conversions, just that we first defined mass, then we defined energy, then we found that they are one and the same. Mass is just a word we use, but it means no more than internal energy of the object.

I don't think we set c=1 just for convenience, that is much more natural unit to work with, meters is just a random length we made up to measure things on earth. c was found empirically.

 

[ZapperZ]

Well I wasn't trying to say that we as humans have the technology to make these conversions, just that we first defined mass, then we defined energy, then we found that they are one and the same. Mass is just a word we use, but it means no more than internal energy of the object.

I don't think we set c=1 just for convenience, that is much more natural unit to work with, meters is just a random length we made up to measure things on earth. c was found empirically.

Yes, it is found empirically, and it's number isn't 1, and it has a dimension.

I work with stuff a lot by setting h or h-bar=1. Look in any photoemission papers and you'll see that "energy" has a symbol of omega, which is angular frequency. This isn't physics. It is short-hand notation.

Mass also is not a word. In the Standard Model, mass can interact with the Higgs field, while photons do not! So already here, the physics is different!

Zz.

 

[LostConjugate]

Mass also is not a word. In the Standard Model, mass can interact with the Higgs field, while photons do not! So already here, the physics is different!

Zz.

I didn't know about that. I thought the Higgs field was still just theory. I will look into that, a photon should be effected by it just as it is by the gravitational field. I don't know anything about the Higgs field though other than LHC has not been able to prove its existence.

-- I was trying to say because it was found empirically it should be normalized.

 

[Dead Boss]

So we have $$E^2 = m^2 + (mv)^2$$

But $$m$$ and $$E$$ are equivalent, so $$(mv)$$ is just $$E_2v$$ (where $$E_2$$ is some energy in the object)

and $$v$$ is just d/dt which is another form of $$E$$, let's say $$E_3$$. So we have $$E - (E_2E_3)^2 = m$$

So $$E_t = m$$ where $$E_t$$ is the total energy of the object.

First, you're missing $$\gamma$$ factor in momentum. Second, you're mixing rest mass (first equation) and relativistic mass (last equation). Third, that mumbo jumbo in the middle is just wrong. (How did you come to conclusion that velocity is energy?) The dimensions are completely off, which is why you should keep the c factors in the equations, unless you know what you're doing (hint: E - E^4).

 

[LostConjugate]

First, you're missing $$\gamma$$ factor in momentum. Second, you're mixing rest mass (first equation) and relativistic mass (last equation). Third, that mumbo jumbo in the middle is just wrong. (How did you come to conclusion that velocity is energy?) The dimensions are completely off, which is why you should keep the c factors in the equations, unless you know what you're doing (hint: E - E^4).

All I did was remove c^2 from their equation.

velocity is just another form of energy, the exact amount may be 1/2v^2 per unit mass but that is irrelevant.

Either way, I am not sure if your trying to say that mass is something more than just energy or not.

 

[Dead Boss]

All I did was remove c^2 from their equation.

I understand very well what you did.

velocity is just another form of energy

Saying that velocity is just another form of energy is one thing (philosophy), and making equivalence between E and v is another (bad maths).

the exact amount may be 1/2v^2 per unit mass but that is irrelevant.

That's hardly irrelevant. The square there is very important as well as that 'per unit mass'.

Either way, I am not sure if your trying to say that mass is something more than just energy or not.

I consider questions like this to be too philosophical for my tase. I am just pointing what I think are errors in your derivation.

I understand what your point is, but why are you trying to make it more rigorous by showing horrible mathematical skills?

 

[LostConjugate]

I understand what your point is, but why are you trying to make it more rigorous by showing horrible mathematical skills?

I was trying to show that the equation provided instead of E = Mc^2 is really just the same thing, it still shows that energy and mass are equivalent.

 

[Dead Boss]

That depends on whether you use rest mass or relativistic mass. And you mixed them up in your derivation.
$$E^2 = m^2 + p^2$$
Where m is rest mass. You set
$$p = mv$$
which is true only for relativistic mass. For rest mass you have
$$p = \gamma{}mv$$
Then you did something awful and arrived at surprising conclusion that
$$E = m$$
which is true
a) for relativistic mass in general
b) for rest mass in the rest frame of particle

I think this debate is pointless. You seem to understand the difference between rest and relativistic mass. You just made some esoteric calculations in which you messed it up (pun intended).

 

[LostConjugate]

But the gamma doesn't change any of my argument. It is just another form of energy again, in fact its the same, its just the inverse of v^2 with some constants. So you just added more v's to the equation.

I do not disagree that my math was quick and dirty, my math skills are rusty at best, but why introduce another symbol with the point I was trying to prove?

I understand your plight from a mathematician's point of view, but not from the physics standpoint.

 

[ZapperZ]

I didn't know about that. I thought the Higgs field was still just theory. I will look into that, a photon should be effected by it just as it is by the gravitational field. I don't know anything about the Higgs field though other than LHC has not been able to prove its existence.

It doesn't matter. The physics of both of them are still different based on what we already know. Whether the Higgs is found or not, we have to figure out why particles with mass couple to some "thing" that caused them (i) to have mass (ii) to not travel at c; why photons only interact based on QED description, but other particles have additional interaction via weak, strong, etc. This is a profound and fundamental difference!

-- I was trying to say because it was found empirically it should be normalized.

By whom? You? The rest of the community from what I've seen only "normalized" h, c, and k simply as a shorthand notation. You are saying this is something physically significant. There's a difference.

You still haven't address the fact that E and m are different simply via dimensional analysis.

Zz.

 

[Dr Lots-o'watts]

I don't need any equations to prove that I am not light! Therefore, mass is not the same as light!

 

[LostConjugate]

I don't need any equations to prove that I am not light! Therefore, mass is not the same as light!

A lot of light is involved in what makes you you. Perhaps there are other fields involved, but they also travel at speed c and are considered zero rest mass.

 

[LostConjugate]

It doesn't matter. The physics of both of them are still different based on what we already know. Whether the Higgs is found or not, we have to figure out why particles with mass couple to some "thing" that caused them (i) to have mass (ii) to not travel at c; why photons only interact based on QED description, but other particles have additional interaction via weak, strong, etc. This is a profound and fundamental difference!
Zz.

Sure,

Photons are not the only type of energy out there, there are particles of other fields as well, such as the weak and strong fields. I am only saying that I think Mass and energy (energy being permutations in any of these fields) are one and the same and as far as I knew I thought that was the general understanding.

So yes I am not saying that all Mass is made up of photons, just that all Mass is made up of energy.

 

[diazona]

(energy being permutations in any of these fields)

I'm not exactly sure what you mean by that but it doesn't seem to make much sense.

You can certainly say that anything that has mass must also have energy. But that doesn't mean that mass is made of energy.

I'm fairly sure that the general understanding, to the extent that there is one, is that mass and energy are not the same thing.

 

[ZapperZ]

Sure,

Photons are not the only type of energy out there, there are particles of other fields as well, such as the weak and strong fields. I am only saying that I think Mass and energy (energy being permutations in any of these fields) are one and the same and as far as I knew I thought that was the general understanding.

So yes I am not saying that all Mass is made up of photons, just that all Mass is made up of energy.

This doesn't make any sense.

1. Being made up of energy ISN'T THE SAME as being equal to energy.

2. The energy equivalent of a mass is NOT the complete property of that mass. For example, while an electron has an energy equivalent, it also has CHARGE and SPIN, which are NOT accounted for by the energy content!

You are simply accounting for ONE particular quality. That's like saying a cow is equal to a watermellon, because they are both edible! You take only ONE characteristics and use that as the basis to argue that they are one of the same thing. Using your logic, a positron and a proton are equal to one another, because they have the same charge. End of story. Does this makes any sense to you?

And no, that is NOT the general understanding. Again, do a dimensional analysis of E and m, and tell me why you think they are "the same".

Zz.

 

[LostConjugate]

This doesn't make any sense.

1. Being made up of energy ISN'T THE SAME as being equal to energy.

2. The energy equivalent of a mass is NOT the complete property of that mass. For example, while an electron has an energy equivalent, it also has CHARGE and SPIN, which are NOT accounted for by the energy content!

You are simply accounting for ONE particular quality. That's like saying a cow is equal to a watermellon, because they are both edible! You take only ONE characteristics and use that as the basis to argue that they are one of the same thing. Using your logic, a positron and a proton are equal to one another, because they have the same charge. End of story. Does this makes any sense to you?

And no, that is NOT the general understanding. Again, do a dimensional analysis of E and m, and tell me why you think they are "the same".

Zz.

As you gain energy you gain mass. So why is it unreasonable to say that mass is just energy? Why would I even think it is something else? What else is there in this universe other than the fundamental fields and the energy in the permutation of these fields?

 

[diazona]

As you gain energy you gain mass.

No you don't.

Besides, to rehash an example I think I saw earlier in this thread, on the Earth's surface, as you gain height, you gain energy. So why is it unreasonable to say that height is energy?

 

[ZapperZ]

As you gain energy you gain mass. So why is it unreasonable to say that mass is just energy? Why would I even think it is something else? What else is there in this universe other than the fundamental fields and the energy in the permutation of these fields?

Because of ALL the reasons that I've told you already!

Besides the fact that there are already tons of threads discussing the fact that "relativistic mass" is really a misleading concept[1] that even Einstein abandoned it[2], there is already an issue on why you refuse to address the points that I already brought up. Your arguments now has nothing to do with physics, but rather based on TASTES. The FACT that dimensionally, E and NOT the same as m should end this whole discussion. The FACT that "energy" cannot produce charge and the spin required, should also end this whole discussion.

You only focused on one conservation issue while ignoring others. In other words, a cow is a watermelon.

Zz.

[1] L.B. Okun Am. J. Phys. v.77, p.430 (2009).
[2] E. Hecht, Am. J. Phys. v.77, p.799 (2009).

 

[brainstorm]

How could light have force unless it accelerates? F=MA. Doesn't light always travel full speed according to the limits of its medium? It never accelerates within the same medium, correct?

 

[diazona]

A couple things: first of all, acceleration does not come from a change in speed, it comes from a change in velocity, which has both a magnitude and a direction. So if an object's speed of motion changes, it accelerates, but if its direction of motion changes, that's also acceleration.

Besides, ΣF=ma is actually a special case of Newton's second law that only applies to objects of constant, nonzero mass. The more general equation is
$$\vec{F} = \frac{\mathrm{d}\vec{p}}{\mathrm{d}t}$$
in other words, force = rate of change of momentum. And like acceleration, momentum is a vector quantity, so it changes when either its magnitude or direction changes. (Or both, of course)

 

[brainstorm]

A couple things: first of all, acceleration does not come from a change in speed, it comes from a change in velocity, which has both a magnitude and a direction. So if an object's speed of motion changes, it accelerates, but if its direction of motion changes, that's also acceleration.

Besides, ΣF=ma is actually a special case of Newton's second law that only applies to objects of constant, nonzero mass. The more general equation is
$$\vec{F} = \frac{\mathrm{d}\vec{p}}{\mathrm{d}t}$$
in other words, force = rate of change of momentum. And like acceleration, momentum is a vector quantity, so it changes when either its magnitude or direction changes. (Or both, of course)

Doesn't this suggest that light only has force when it is interacting with matter, either to change direction or get absorbed and re-emitted? Light seems to translocate momentum more so than it actually carrying momentum the way matter does. An object acted upon by force can accelerate and increase its kinetic energy but can light's energy ever increase because it is acted upon by an external force (gravity, for example)? It seems to me that this would violate the conservation of energy whereas matter accelerating/decelerating can't because it can store and release energy in terms of its position and direction within a gravity field. Am I grasping straws here?

edit: radiation seems more like a form of energy storage between matter than a thing that is itself energized. I don't see how it could change momentum when it just seems to deliver momentum from emitting particles to others.

 

[diazona]

Doesn't this suggest that light only has force when it is interacting with matter, either to change direction or get absorbed and re-emitted?

Light doesn't have force, it exerts and experiences force when it interacts with matter. Same applies to matter, by the way, it doesn't have a force, it exerts and experiences force when it interacts with anything else.

Light carries momentum, just like moving matter does. No idea what you're getting at with this "translocation" idea, but that's a totally unnecessary concept.

The energy of a light wave can certainly increase or decrease when it interacts with something else. You might consider gravitational redshift to be an example of this: gravitational potential energy is converted into electromagnetic energy (or vice-versa). The total energy is conserved.

edit: radiation seems more like a form of energy storage between matter than a thing that is itself energized. I don't see how it could change momentum when it just seems to deliver momentum from emitting particles to others.

Well then you have the wrong idea about what radiation is. It has momentum and energy, just like matter does; and that momentum (and energy) can change.