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A Follow Up On Neutrinos
- Thread starter Photonic
- Start date
PolyHedral
Superabacus Mystic
Ah...no proof is backed better than oppinions. Math is just another oppinion.
2+2=4 is not an opinion.
shawn001
Well-Known Member
What is the mass of a photon?
This question falls into two parts:
Does the photon have mass? After all, it has energy and energy is equivalent to mass.
Photons are traditionally said to be massless. This is a figure of speech that physicists use to describe something about how a photon's particle-like properties are described by the language of special relativity.
The logic can be constructed in many ways, and the following is one such. Take an isolated system (called a "particle") and accelerate it to some velocity v (a vector). Newton defined the "momentum" p of this particle (also a vector), such that p behaves in a simple way when the particle is accelerated, or when it's involved in a collision. For this simple behaviour to hold, it turns out that p must be proportional to v. The proportionality constant is called the particle's "mass" m, so that p = mv.
In special relativity, it turns out that we are still able to define a particle's momentum p such that it behaves in well-defined ways that are an extension of the newtonian case. Although p and v still point in the same direction, it turns out that they are no longer proportional; the best we can do is relate them via the particle's "relativistic mass" mrel. Thus
p = mrelv .
When the particle is at rest, its relativistic mass has a minimum value called the "rest mass" mrest. The rest mass is always the same for the same type of particle. For example, all protons, electrons, and neutrons have the same rest mass; it's something that can be looked up in a table. As the particle is accelerated to ever higher speeds, its relativistic mass increases without limit.
It also turns out that in special relativity, we are able to define the concept of "energy" E, such that E has simple and well-defined properties just like those it has in newtonian mechanics. When a particle has been accelerated so that it has some momentum p (the length of the vector p) and relativistic mass mrel, then its energy E turns out to be given by
E = mrelc2 , and also E2 = p2c2 + m2restc4 . (1)
There are two interesting cases of this last equation:
Is there any experimental evidence that the photon has zero rest mass?
Alternative theories of the photon include a term that behaves like a mass, and this gives rise to the very advanced idea of a "massive photon". If the rest mass of the photon were non-zero, the theory of quantum electrodynamics would be "in trouble" primarily through loss of gauge invariance, which would make it non-renormalisable; also, charge conservation would no longer be absolutely guaranteed, as it is if photons have zero rest mass. But regardless of what any theory might predict, it is still necessary to check this prediction by doing an experiment.
It is almost certainly impossible to do any experiment that would establish the photon rest mass to be exactly zero. The best we can hope to do is place limits on it. A non-zero rest mass would introduce a small damping factor in the inverse square Coulomb law of electrostatic forces. That means the electrostatic force would be weaker over very large distances.
Likewise, the behavior of static magnetic fields would be modified. An upper limit to the photon mass can be inferred through satellite measurements of planetary magnetic fields. The Charge Composition Explorer spacecraft was used to derive an upper limit of 6 × 10−16 eV with high certainty. This was slightly improved in 1998 by Roderic Lakes in a laboratory experiment that looked for anomalous forces on a Cavendish balance. The new limit is 7 × 10−17 eV. Studies of galactic magnetic fields suggest a much better limit of less than 3 × 10−27 eV, but there is some doubt about the validity of this method.
References:
E. Fischbach et al., Physical Review Letters 73, 514—517 25 July 1994.
Chibisov et al., Sov. Ph. Usp. 19, 624 (1976).
See also the Review of Particle Properties at http://pdg.lbl.gov
This question falls into two parts:
Does the photon have mass? After all, it has energy and energy is equivalent to mass.
Photons are traditionally said to be massless. This is a figure of speech that physicists use to describe something about how a photon's particle-like properties are described by the language of special relativity.
The logic can be constructed in many ways, and the following is one such. Take an isolated system (called a "particle") and accelerate it to some velocity v (a vector). Newton defined the "momentum" p of this particle (also a vector), such that p behaves in a simple way when the particle is accelerated, or when it's involved in a collision. For this simple behaviour to hold, it turns out that p must be proportional to v. The proportionality constant is called the particle's "mass" m, so that p = mv.
In special relativity, it turns out that we are still able to define a particle's momentum p such that it behaves in well-defined ways that are an extension of the newtonian case. Although p and v still point in the same direction, it turns out that they are no longer proportional; the best we can do is relate them via the particle's "relativistic mass" mrel. Thus
p = mrelv .
When the particle is at rest, its relativistic mass has a minimum value called the "rest mass" mrest. The rest mass is always the same for the same type of particle. For example, all protons, electrons, and neutrons have the same rest mass; it's something that can be looked up in a table. As the particle is accelerated to ever higher speeds, its relativistic mass increases without limit.
It also turns out that in special relativity, we are able to define the concept of "energy" E, such that E has simple and well-defined properties just like those it has in newtonian mechanics. When a particle has been accelerated so that it has some momentum p (the length of the vector p) and relativistic mass mrel, then its energy E turns out to be given by
E = mrelc2 , and also E2 = p2c2 + m2restc4 . (1)
There are two interesting cases of this last equation:
- If the particle is at rest, then p = 0, and E = mrestc2.
- If we set the rest mass equal to zero (regardless of whether or not that's a reasonable thing to do), then E = pc.
Is there any experimental evidence that the photon has zero rest mass?
Alternative theories of the photon include a term that behaves like a mass, and this gives rise to the very advanced idea of a "massive photon". If the rest mass of the photon were non-zero, the theory of quantum electrodynamics would be "in trouble" primarily through loss of gauge invariance, which would make it non-renormalisable; also, charge conservation would no longer be absolutely guaranteed, as it is if photons have zero rest mass. But regardless of what any theory might predict, it is still necessary to check this prediction by doing an experiment.
It is almost certainly impossible to do any experiment that would establish the photon rest mass to be exactly zero. The best we can hope to do is place limits on it. A non-zero rest mass would introduce a small damping factor in the inverse square Coulomb law of electrostatic forces. That means the electrostatic force would be weaker over very large distances.
Likewise, the behavior of static magnetic fields would be modified. An upper limit to the photon mass can be inferred through satellite measurements of planetary magnetic fields. The Charge Composition Explorer spacecraft was used to derive an upper limit of 6 × 10−16 eV with high certainty. This was slightly improved in 1998 by Roderic Lakes in a laboratory experiment that looked for anomalous forces on a Cavendish balance. The new limit is 7 × 10−17 eV. Studies of galactic magnetic fields suggest a much better limit of less than 3 × 10−27 eV, but there is some doubt about the validity of this method.
References:
E. Fischbach et al., Physical Review Letters 73, 514—517 25 July 1994.
Chibisov et al., Sov. Ph. Usp. 19, 624 (1976).
See also the Review of Particle Properties at http://pdg.lbl.gov
Gjallarhorn
N'yog-Sothep
One could argue that the chosen symbols are subjective, yet that does not devalue the objectivity of math, just its representation in communication.
2+2=4 is not an opinion.
Photonic
Ad astra!
That is a trapping of language, the concept is static though.
Unless you want to argue that nothing can ever be subject to quantities.
So a plane moving twice the speed of another plane experiences twice the aerodynamic drag, even if its the same kind of plane?
What you stated is not an expression of physics nor do u understand the difference between theory and physical proof.
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Photonic
Ad astra!
So a plane moving twice the speed of another plane experiences twice the aerodynamic drag?
What you stated is not an expression of physics nor do u understand the difference between theory and physical proof.
He's not wrong.
Yea so it's a little different than 2+2=4, but imputing the values yields essentially the same result.
And the amount of power required to overcome the drag:
Is hardly an opinion.
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He's not wrong.
Yea so it's a little different than 2+2=4, but imputing the values yields essentially the same result.
Lot of letters mind putting some definitions in?
Photonic
Ad astra!
FD is the force of drag, which is by definition the force component in the direction of the flow velocity,[1]
ρ is the mass density of the fluid, [2]
v is the velocity of the object relative to the fluid,
A is the reference area, and
CD is the drag coefficient a dimensionless constant related to the object's geometry and taking into account both skin friction and form drag.
ρ is the mass density of the fluid, [2]
v is the velocity of the object relative to the fluid,
A is the reference area, and
CD is the drag coefficient a dimensionless constant related to the object's geometry and taking into account both skin friction and form drag.
You failed to consider Parasitic drag and what is known as the Power curve:
Filerag Curve 2.jpg - Wikipedia, the free encyclopedia
Hardly linear...but then again those that think 2 + 2 can describe the universe are pretty linear thinking types...
Gjallarhorn
N'yog-Sothep
Not fully understanding what you suppose you have proven by bringing more math to the table as an argument about math being the foundation of the universe.
Photonic
Ad astra!
I gave you what I deemed necessary to make my point, or are you going to base your already weak argument on the even weaker premise of technicalities?
I never said that mathematics wasn't a valid means of describing the universe. But without physical proof a mathematical expression is JUST AN OPINION!
outhouse
Atheistically
Yes, but it is, so there.
speaking of time.
Had the weirdest dream last night and I came up with the new engine for space travel.
Looks like this threads played out so ill deviate a hair LOL
A time generator, the trottle works as as a normal engine does but full thottle is "now" in and around the craft.
Basically put in the coordinates and as you only accelerate slowly as not to destroy the occupants LOL
probably thought of already but flying it was a blast :areyoucra
Photonic
Ad astra!
speaking of time.
Had the weirdest dream last night and I came up with the new engine for space travel.
Looks like this threads played out so ill deviate a hair LOL
A time generator, the trottle works as as a normal engine does but full thottle is "now" in and around the craft.
Basically put in the coordinates and as you only accelerate slowly as not to destroy the occupants LOL
probably thought of already but flying it was a blast :areyoucra
I prefer the "Heart of Gold" myself.
outhouse
Atheistically
Photonic
Ad astra!
I suggest reading the books if you have not already done so!