Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Ben on 08/06/2010 09:30:04
-
Ben asked the Naked Scientists:
Hi, how light can travel at c, have energy but no mass even though E=mc^2 ?
how does this work?Â
Cheers
What do you think?
-
Photons, if you think of light as particles, have zero rest mass. This is another way of saying they can't exist unless they are travelling at lightspeed (in a vacuum). The "m" in E=mc^2 is the mass at the velocity that the object has. According to Special Relativity this mass increases with velocity relative to an observer. At the speed of light this mass would go to infinity and it would take infinite energy to get it to that speed (so it can't happen). The equation is not violated because you could think of the zero rest mass being multiplied by infinity and ending up with a finite number! However it is probably more correct to say that photons are exceptions. The energy of a photon is proportional to its frequency so that
Energy = Plancks constant x Frequency
-
Hi, how light can travel at c, have energy but no mass even though E=mc^2 ?
Because that equation is wrong...
A lot of times popular books write that (in)famous equation believing to know the real meaning or making the reader believe to have understood it.
The fact is that the equation E = mc2 is valid only if the body is not moving. Have you ever seen a not-moving photon? So, how can that equation be valid in this case?
The correct equation is:
E2 = (mc2)2 + (cp)2
where p is the body's momentum. In the case of a photon, E = cp (this last relation comes from classical electrodynamics, that is Maxwell's equations, that is from XIX century), so m = 0.
-
Lightarrow is correct, but for many of us, in the past, it was taught that E=mc^2 was correct if you took the view that the mass increases with velocity
m*=m•[1/√(1-v²/c²)]
If you expand this for v<<c you get the more classical
E = mc² + ½mv²
It has become the convention today to have m as just the rest mass and to not consider the mass as increasing with velocity. It is a technicality which makes little difference in special relativity but is a more important distinction in General Relativity and in Electrodynamics.
In teaching many subjects, especially Physics, it can be hard to get off the ground if you are too rigorous though.
-
Ben
You have to conserve energy not matter. Light energy is electromagnetic and like electricity in a conductor it does not increase in mass with more kWs inside.
Think of electromagnetic light energy as a loop of flux current helixing forward through space. OR like lightning plasma in a vacuum.
Electromagnetic energy is magnoflux energy and can exist without matter.
CliveS
-
Because that equation is wrong...
The equation is not wrong. People simply need to know the correct interpretation and definitions of the terms in that equation. IF E is the total inertial energy of the particle then the m is the relativistic mass of the particle. If E is the proper energy of the particle then the m is the proper mass of the particle.
-
Because that equation is wrong...
The equation is not wrong. People simply need to know the correct interpretation and definitions of the terms in that equation. IF E is the total inertial energy of the particle then the m is the relativistic mass of the particle. If E is the proper energy of the particle then the m is the proper mass of the particle.
Yes, but since the OP interpreted it in the correct way, that is:
1. E = total energy
2. m = mass (invariant mass, as most physicists intend now and as the OP intended since he stated: "how light can travel at c, have energy but no mass"),
then the formula is wrong for photons, so is wrong in general. The other one I wrote has the advantage to be always correct, so I personally prefer it.
-
virtual photons are not particles, anti particles or massless beta rays. In my view they are made up of a tiny volume of magnetic flux a sort of magnoflux energy bubble.
Light is just a vibrating volume of electromagnetic loop current energy only.
CliveS
-
It all depends on how you interpret the word mass I think :)
We say that instead of 'invariant mass' (aka matter) a photon have a momentum.
That momentum it gathers due to its intrinsic energy and its motion, as I understands it.
Matter on the other hand is something you can hold and feel, it doesn't need to move to gather its intrinsic energy, not macroscopically at least :) There are different types of mass, we speak of relativistic mass f.ex. that type of mass is created by invariant mass and/or motion, when it's only motion without invariant mass we like to define that as momentum instead nowadays. Light can push things due to that momentum even though it misses out on all invariant proper mass.
What energy 'really' consists of is a very tough question, that I don't think anyone can answer, not as I've seen at least. But both photons and invariant mass you can 'break down' to energy, and with high enough energies you find it 'spontaneously' creating particles that we deem to be of 'invariant mass' aka matter. So the formula is correct, even though we find an enormous difference between light and, let's say an apple :)
-
What energy 'really' consists of is a very tough question, that I don't think anyone can answer, not as I've seen at least. But both photons and invariant mass you can 'break down' to energy, and with high enough energies you find it 'spontaneously' creating particles that we deem to be of 'invariant mass' aka matter. So the formula is correct, even though we find an enormous difference between light and, let's say an apple :)
Yoron - My understanding is very limited, but I think that is the really big question.
-
Yes, it is a really big question and needs to be answered as researchers who are looking into squeezing more digital information into a fibre optic cable now know that lazer light can be quadrature amplitude modulated. This to me proves that light is a volume helix beam of magnoflux energy and has nothing to do with classical matter at all. There is an article in theiet.org 20 February 2010 magazine which will enlighten you on ths subject
CliveS
-
Clive - thats a little bit of a leap. QAM is an encoding method which utilises π/2 out-of-phase waves (quadrature waves) to encode more information than simple amplitude modulation. I do not understand how the existence of a encoding method (which could, technically if not practically, be used with sound waves as carriers, or even more extremely use waves on a piece of string) can 'prove' an esoteric theory relating to the fundamental qualities of electromagnetic radiation. Matthew
-
Yes, but since the OP interpreted it in the correct way, that is:
The OP didn't understand what the m and E are in that equation. Every time people ask this question it's always the same misunderstanding. But its always best to ask the OP what/how he thinks something is defined then merely assume we know. If a person is asking a question such as this then it's safe to say that there is something they are misinterpreting. The fact that he needs to ask this question demonstrates that he is mistaking the definition of a term in that equation.
-
Imatfaal
If a single light photon is able to be not only polarized; but be quadrature modulated means that it is more than a two dimensional wave and must therefore contain a 3D volume of magnetic magnoflux energy.
CliveS
-
I don't think anyone knows whether a photon has mass or not, off-hand I don't think it's ever been experimentally established one way or another.
-
I don't think anyone knows whether a photon has mass or not, off-hand I don't think it's ever been experimentally established one way or another.
I have proved it has no mass in my first post... [:)]
-
I have proved it has no mass in my first post... [:)]
That is not a proof. You started with a relationship which assumes that the m that it starts with is proper mass which is zero for photons. It is not a proof at all.
To be more precise; you basically said E = mc^2 was wrong but offered no clarification or justification for such a claim. You then pulled the expression E^2 - (pc)^2 = (mc^2)^2 out of thin air without a defining those terms. It follows that m = 0 for a photon. However one can just as easily say that E = Mc^2 holds at all times and then pull (Mc^2)^2 - (pc)^2 = (mc^2)^2 out of thin air and then state that m = proper mass and M = "mass" (what you refer to as relativistic mass). There would not be any error in doing so and in fact many physicists/physicst text authors do just that. Most often when they do so they use the notation m = M and m_0 = m
-
Is a photon's mass zero or not?
Please answer just this question, then we can keep discussing.
-
Is a photon's mass zero or not?
Please answer just this question, then we can keep discussing.
As you know, whether a photon has mass depends on what you mean by "mass." I.e. it depends on how the term "mass" is defined. The following relationships are true
Let m = proper mass and M = inertial mass (aka relativistic mass aka mass)
For particles or closed systems we have
m is the magnitude of 4-momentum
M = |p/v| = m/sqrt(1 - v^2/c^2)
Proper mass of photon = 0
Relativistic mass of photon is not zero but has the value M = p/c. E = pc for photon so p = E/c. Therefore M = (p/c)/c = E/c^2
You can find this defined and explained in many relativistic texts such as the following (the following texts use m as inertial mass and not proper mass)
Special Relativity, A. P. French, MIT Press, page 20
Let us now try to put together some of the results we have discussed. For photons we have
E = cp
and
m = E/c^2
(the first experimental, the second based on Einstein's box). Combining these, we have
m = p/c
Relativity: Special, General and Cosmological, Wolfgang, Oxford Univ., Press, (2001), page 120
According to Einstein, a photon with frequency f has energy hf /c^2, and thus (as he only came to realize several years later) a finite mass and a finite momentum hf/c.
Introducing Einstein's Relativity, Ray D'Inverno, Oxford Univ. Press, (1992), page 50
Finally, using the energy-mass relationship E = mc^2, we find that the relativistic mass of a photon is non-zero and given by m = p/c.
Combining these results with Planck's hypothesis, we obtain the following formulae for the energy E, relativistic mass m, and linear momentum p of the photons:
E = hf m = hf/c^2 p = hf/c
Also found in Concepts of Mass In Contemporary Physics and Philosophy, Max Jammer, Princeton University Press
The same thing is found in Alan Guth's lecture notes from his course at MIT, the Early Universe.
Were you aware of the fact that some physicists define M in this way in recently published relativity texts?
-
PMB
A photon has no mass; it is made from magnetic energy only. If you look up wikipedia "Eulers formlua" you will see a diagram that shows the inphase and quadrature modulation of magnoflux energy. Laser light is 3D magnetic energy and forms a helix [ magnoflux tunnel] as the photons move through a magnetized volume of space. Any physics model of a photon or light that is not 3D is therefore highly suspect in my view
CliveS
-
Is a photon's mass zero or not?
Please answer just this question, then we can keep discussing.
As you know, whether a photon has mass depends on what you mean by "mass." I.e. it depends on how the term "mass" is defined. The following relationships are true
Let m = proper mass and M = inertial mass (aka relativistic mass aka mass)
For particles or closed systems we have
m is the magnitude of 4-momentum
M = |p/v| = m/sqrt(1 - v^2/c^2)
Proper mass of photon = 0
Relativistic mass of photon is not zero but has the value M = p/c. E = pc for photon so p = E/c. Therefore M = (p/c)/c = E/c^2
[cut]
Were you aware of the fact that some physicists define M in this way in recently published relativity texts?
Then, why the Particle Data Group says that photon's mass is zero? :
http://www.google.com/url?sa=t&source=web&cd=1&ved=0CBQQFjAA&url=http%3A%2F%2Fpdg.lbl.gov%2F2009%2Flistings%2Frpp2009-list-photon.pdf&ei=qN80TPO5KIffOLOE-ekG&usg=AFQjCNHfpSKjWRlYcvFaVItpK1UAfEeSWg&sig2=_t7tTE581BuWCcxl_A9YWg
-
There does seem to be something slightly paradoxical going on here.
As I understand it, it takes an infinite amount of energy to accelerate any mass to the speed of light.
But photons are accelerated to the speed of light, apparently without consuming an infinite amount of energy, so how can they have mass?
-
PMB
A photon has no mass;..
You failed to get my point, which is when people refer to a photon as having zero mass they mean that the proper mass of a photon is zero. Not that it's inertial mass (aka relativistic mass) is zero. I never said that the proper mass of a photon wasn't zero. That'd be silly.
-
Then, why the Particle Data Group says that photon's mass is zero?
Because you're supposed to know that by mass they mean proper mass, not inertial mass. If you also look at the site you might see that the lifetime of a free neutron you'll see that it says 15 minutes. You're also supposed to know that they mean proper lifetime. We all know that the life time of a particle increases with speed. But that isn't evident in the lifetime that they give of 15 minutes.
Those things are read and used by professional physicists and whoever reads them knows what those terms mean. I know that it refers to proper mass (aka rest mass). Nobody has to tell me that. But that's particle physics. If you expect to go to other branches of physics and expect the term to mean what you think it does then you'll be sorely mistake. E.g. Misner, Thorne and Wheeler's text "Gravitation" uses mass in one key derivation where it means "inertial mass" (what you'd call relativistic mass) but merely says "mass." Other texts are the same.
Show me where you think I made a mistake. And please don't tell me that one definition is "right" and the other is "wrong" because that's not a valid arguement when the relativity literature uses the same term both ways. Mostly as a matter of taste. Some people get tired or writing "rest" and others get tired of writing "inertial" in front of the term "mass". That's the only real difference.
Please recall that I was answering Ben's questioi
Hi, how light can travel at c, have energy but no mass even though E=mc^2 ?
how does this work?
And it is this question that I'm responding to. As such I was basically explaining what the "m" in that expression stands for and my answer is that it refers to the inertial mass of a body, not its proper mass. The proper mass of a photon is zero while the inertial mass is not. There are other kinds of mass too,i,e, passive gravitational mass, active gravitational mass.
-
There does seem to be something slightly paradoxical going on here.
As I understand it, it takes an infinite amount of energy to accelerate any mass to the speed of light.
But photons are accelerated to the speed of light, apparently without consuming an infinite amount of energy, so how can they have mass?
You're thinking of Euler's definition of mass, not Newton's. Newton defined inertial mass as that which determines momentum, not that which determines acceleration. And thats how its used in modern physics.
-
Then, why the Particle Data Group says that photon's mass is zero?
Because you're supposed to know that by mass they mean proper mass, not inertial mass.
Yes, of course. The point is not that I intended to say that you misunderstood the term proper mass, but that in particle physics the concept of relativistic mass is not used, at least because you wouldn't know what value to write...
If you also look at the site you might see that the lifetime of a free neutron you'll see that it says 15 minutes. You're also supposed to know that they mean proper lifetime. We all know that the life time of a particle increases with speed. But that isn't evident in the lifetime that they give of 15 minutes.
Those things are read and used by professional physicists and whoever reads them knows what those terms mean. I know that it refers to proper mass (aka rest mass). Nobody has to tell me that. But that's particle physics. If you expect to go to other branches of physics and expect the term to mean what you think it does then you'll be sorely mistake. E.g. Misner, Thorne and Wheeler's text "Gravitation" uses mass in one key derivation where it means "inertial mass" (what you'd call relativistic mass) but merely says "mass." Other texts are the same.
Show me where you think I made a mistake.
And what if I would say it's the Sun to orbit around the Earth and not the other way...around? [:)] Can you show me I'm wrong? You probably can't (at least I think so) but we find it more convenient to say it's the Earth to orbit around the Sun. In a similar way, most physicists find it more convenient to consider mass as invariant and not speed dependent; I mean, nothing forbids that tomorrow most physicists will change theyr mind, of course.
And please don't tell me that one definition is "right" and the other is "wrong" because that's not a valid arguement when the relativity literature uses the same term both ways. Mostly as a matter of taste. Some people get tired or writing "rest" and others get tired of writing "inertial" in front of the term "mass". That's the only real difference.
Please recall that I was answering Ben's questioi
Hi, how light can travel at c, have energy but no mass even though E=mc^2 ?
how does this work?
And it is this question that I'm responding to. As such I was basically explaining what the "m" in that expression stands for and my answer is that it refers to the inertial mass of a body, not its proper mass. The proper mass of a photon is zero while the inertial mass is not. There are other kinds of mass too,i,e, passive gravitational mass, active gravitational mass.
Since you talked about inertial mass, I have a question for you, I know that you know more than me about it (I speak seriously). Spacetime curvature near an object with proper mass = M is independent of the frame of reference from which you measure ithe curvature, isnt'it? And what about near a zero mass object as a photon?
-
how do the lightmills, spinning mills inside a glass enclosure, spin faster when placed in direct sunlight & effect a spin & not just heat up if photons have no mass?
-
how do the lightmills, spinning mills inside a glass enclosure, spin faster when placed in direct sunlight & effect a spin & not just heat up if photons have no mass?
1. In those devices the effect is actually given by the (spare) air molecules heated from the black part of the blades (infact it rotates in the opposite sense respect to the one it should).
2. Even if it would work correctly and the force were given by the light reflecting back from the polished part of the blade, the effect would be simply described by classic electrodynamics: light has momentum even if it has no mass.
Hope you don't ask why does light have momentum without having mass, we have discussed this subject hundreds of times... [:)]
-
There does seem to be something slightly paradoxical going on here.
As I understand it, it takes an infinite amount of energy to accelerate any mass to the speed of light.
But photons are accelerated to the speed of light, apparently without consuming an infinite amount of energy, so how can they have mass?
You're thinking of Euler's definition of mass, not Newton's. Newton defined inertial mass as that which determines momentum, not that which determines acceleration. And thats how its used in modern physics.
Ah! So that means I could travel at the speed of light then.
-
how do the lightmills, spinning mills inside a glass enclosure, spin faster when placed in direct sunlight & effect a spin & not just heat up if photons have no mass?
1. In those devices the effect is actually given by the (spare) air molecules heated from the black part of the blades (infact it rotates in the opposite sense respect to the one it should).
2. Even if it would work correctly and the force were given by the light reflecting back from the polished part of the blade, the effect would be simply described by classic electrodynamics: light has momentum even if it has no mass.
Hope you don't ask why does light have momentum without having mass, we have discussed this subject hundreds of times... [:)]
long time since ive seen the lightmill. whats its proper name? i wanna research it.....thanx
-
how do the lightmills, spinning mills inside a glass enclosure, spin faster when placed in direct sunlight & effect a spin & not just heat up if photons have no mass?
1. In those devices the effect is actually given by the (spare) air molecules heated from the black part of the blades (infact it rotates in the opposite sense respect to the one it should).
2. Even if it would work correctly and the force were given by the light reflecting back from the polished part of the blade, the effect would be simply described by classic electrodynamics: light has momentum even if it has no mass.
Hope you don't ask why does light have momentum without having mass, we have discussed this subject hundreds of times... [:)]
long time since ive seen the lightmill. whats its proper name? i wanna research it.....thanx
http://en.wikipedia.org/wiki/Crookes_radiometer
-
Yes, of course. The point is not that I intended to say that you misunderstood the term proper mass, but that in particle physics the concept of relativistic mass is not used, at least because you wouldn't know what value to write...
That's because particle physicists concern themselves with intrinsic properties. I didn't know that you were focused on particle physics.
And what if I would say it's the Sun to orbit around the Earth and not the other way...around? [:)]
Actually that's a very valid view in general relativity where preferred reference frames are not singled out.
Can you show me I'm wrong?
I'd say that you'd be justified in doing so if you were to say that you're speaking from a GR point of view and then made it clear that you're referring to the Earth frame of reference.
You probably can't (at least I think so) but we find it more convenient to say it's the Earth to orbit around the Sun.
I agree that its convenient. But physics deals with the laws of nature, regardless if something is convenient for humans to work with. :)
In a similar way, most physicists find it more convenient to consider mass as invariant and not speed dependent; I mean, nothing forbids that tomorrow most physicists will change their mind, of course.
I find that to be a bit misleading. It is certainly true that particle physicists tend to do that, if for no other reason than brevity of writing. A friend of mine used to teach particle physics at Tufts University and when we speak about this he keeps reminding me to "choose what you mean and then stick with it." and leaves it at that. He doesn't make a big point out of it. However for someone whose field is relativity then that's not the most useful notion. Especially since its not one that can be given a general meaning.
Since you talked about inertial mass, I have a question for you, I know that you know more than me about it (I speak seriously). Spacetime curvature near an object with proper mass = M is independent of the frame of reference from which you measure the curvature, isn't it?
It depends on what you mean by "curvature". Spacetime curvature is a tensor quantity and as such the components are frame dependant. However the tensor itself is a geometric object whose absolute meaning is in dependant of the frame. But when you measure things you must choose a frame of reference, or to be more precise, an observer. There are some interesting exercises in MTW regarding this.
And what about near a zero mass object as a photon?
It still has zero proper mass. :)
-
how do the lightmills, spinning mills inside a glass enclosure, spin faster when placed in direct sunlight & effect a spin & not just heat up if photons have no mass?
As mentioned above, those devices don''t work by photons impacting on the vains. However photons do exert a force on the vains merely because they carry momentum.
-
Ah! So that means I could travel at the speed of light then.
Nope. Anything with non-zero proper mass can not travel at the speed of light. Your proper mass is non-zero.
-
Einstein predicted a shifting of the stars, planetary alignment & increased gravity affect, to prove that light has matter?
-
Ah! So that means I could travel at the speed of light then.
Nope. Anything with non-zero proper mass can not travel at the speed of light. Your proper mass is non-zero.
Oh. So photons only have improper mass then? Yes! Yes! That must be it, I'm sure.
(I'm beginning to think there's a "word-trick" going on here [;D])
-
Oh. So photons only have improper mass then? Yes! Yes! That must be it, I'm sure.
:) The term "proper" here does not mean "correct". It means "characteristic".
-
Einstein predicted a shifting of the stars, planetary alignment & increased gravity affect, to prove that light has matter?
Actually in Einstein's 1916 GR paper he defined the word "matter" so as to include EM fields and thus EM radiation.
-
Oh. So photons only have improper mass then? Yes! Yes! That must be it, I'm sure.
:) The term "proper" here does not mean "correct". It means "characteristic".
I knew it! A word trick!
-
Oh. So photons only have improper mass then? Yes! Yes! That must be it, I'm sure.
:) The term "proper" here does not mean "correct". It means "characteristic".
I knew it! A word trick!
Not really. It's more about the various meanings of a given term. Sometimes I find it quite usefull to look up even simple words in a dictionary. For example; suppose you really wanted a new set of golf clubs and you told your wife "I need a new set of golf clubs." Your wife might respond "Since you're health and well being doesn't depend on you getting a new set of clubs then you don't really need them." Sounds reasonable, right? Now let's check the dictionary
http://www.merriam-webster.com/dictionary/need
need - 1a - a lack of something requisite, desirable, or useful
You show your wife the dictionary and you get your way. LOL!
Same with the term "proper." I was a bit confused as why that word was chosen. It was merely a matter of checking the dictionary. So its not really a word trick. Its just something most people don't know and need to look up.
-
Oh. So photons only have improper mass then? Yes! Yes! That must be it, I'm sure.
:) The term "proper" here does not mean "correct". It means "characteristic".
I knew it! A word trick!
Not really. It's more about the various meanings of a given term. Sometimes I find it quite usefull to look up even simple words in a dictionary. For example; suppose you really wanted a new set of golf clubs and you told your wife "I need a new set of golf clubs." Your wife might respond "Since you're health and well being doesn't depend on you getting a new set of clubs then you don't really need them." Sounds reasonable, right? Now let's check the dictionary
http://www.merriam-webster.com/dictionary/need
need - 1a - a lack of something requisite, desirable, or useful
You show your wife the dictionary and you get your way. LOL!
Same with the term "proper." I was a bit confused as why that word was chosen. It was merely a matter of checking the dictionary. So its not really a word trick. Its just something most people don't know and need to look up.
You'll be trying to tell me "normal" means perpendicular next.
-
You'll be trying to tell me "normal" means perpendicular next.
Well, as you knnow, context is everything, right? :)
-
You probably can't (at least I think so) but we find it more convenient to say it's the Earth to orbit around the Sun.
I agree that its convenient. But physics deals with the laws of nature, regardless if something is convenient for humans to work with. :)
And which law of nature justifies to call "mass" the quantity E/c2 ?
-
And which law of nature justifies to call "mass" the quantity E/c2 ?
The question, as stated, is not considered to be a meaningful question. It's like asking me "What law of physics justifies calling you Pete?" No law of physics can justify any definition of any of the basic quantities of nature. Thus nothing we see in nature can justify what we call "time" for the same reason. Same with "length/distance".
Since this seems to be taking a turn to opinions on how mass "should be" defined I'd rather merely post a link to an article I wrote on this subject and then you can read it and comment on that instead of me repeating what I already wrote in that paper. I wrote the paper just for conversations like this. There are a great deal of reasons that physicists chose to define the term "mass" to mean m = |p/v. Let me know what you think of the articles and the arguements it outlines. Thanks!
Note: Let me note that it was Einstein himself who assigned mass to EM radiation. He did this in one of his earliest E = mc^2 papers and is one of the reasons he referred to EM fields has having "matter." Would you like to read that paper? I have it in PDF format and can e-mail it to anyone who wishes to read it.
-
There does seem to be something slightly paradoxical going on here.
As I understand it, it takes an infinite amount of energy to accelerate any mass to the speed of light.
But photons are accelerated to the speed of light, apparently without consuming an infinite amount of energy, so how can they have mass?
Ahh Geezer, welcome to the land of no return :)
You have just defined a photon as needing acceleration, even if only a 'instant' one, (just as I've done too at times, but don't tell anyone about that. It will ruin me reputation, what little i have left, and now after all, we're only considering yours. Yes geezer, the Nobel-Committee are assembled here, all beards and wrinkled brows.. :)
So0ooooo me lad, accelerating photons indeed, huh :)
=
But in a way you truly hit the head of the nail with that one. I'm flabbergasted too, every time I think of how a photon moves from a 'standing position' to 'c' without any acceleration involved?
On the other hand we can't observe that moment, can we? We only observe it dying.
Magic I say ..
And slippery too.
===
Or can we?
Bose Einstein condensates?
Freezing the light, but that are 'already made' photons, isn't it?
But perhaps we could observe the 'birth' of a photon in such a one?