I need help understanding light.

[panzerschiffer]

Astrophysicists are pretty smart guys...

From the "Ask a High Energy Astronomer" maintained by NASA...

"The Question
(Submitted July 31, 1996)

Do photons have mass? Because the equations E=mc2, and E=hf, imply that m=hf/c2 . Is it so?


The Answer

No, photons do not have mass, but they do have momentum. The proper, general equation to use is E2 = m2c4 + p2c2 So in the case of a photon, m=0 so E = pc or p = E/c. On the other hand, for a particle with mass m at rest (i.e., p = 0), you get back the famous E = mc2.
This equation often enters theoretical work in X-ray and Gamma-ray astrophysics, for example in Compton scattering where photons are treated as particles colliding with electrons.

Andy Ptak"

photon-The smallest (quantum) unit of light/electromagnetic energy. Photons are generally regarded as particles with zero mass and no electric charge.

"The Question
(Submitted November 02, 1996)

This questions has been bugging me and my chemistry class. Does light have mass? Most people would think not but here's why I argue against it. Even though light does not effect anything it its path like a solid object, it is affected by gravity. Anything that has mass is affected by gravity. Why do I say that light has mass? Well, If a black holes gravity field is so strong that light cannot escape itself, light must have mass? Am I right? Everyone argues against it.


The Answer
These are interesting issues that you bring up. Whether or not light( or more accurately photons, the indivisible units in which light can be emitted or absorbed) has mass, and how it is affected by gravity, puzzled scientists for many, many years. Figuring it all out is what made Albert Einstein famous. Bear with me and I'll try to explain both the theory and the observation.
Back in the 1700s, scientists were still struggling to understand which theory of light was correct: was it composed of particles or was it made of waves? Under the theory that light is waves, it was not clear how it would respond to gravity. But if light was composed of particles, it would be expected that they would be affected by gravity in the same way apples and planets are. This expectation grew when it was discovered that light did not travel infinitely fast, but with a finite measurable velocity.

Armed with these facts, a paper was published in 1783 by John Michell, in which he pointed out that a sufficiently massive compact star would possess a strong enough gravitational field that light could not escape --- any light emitted from the star's surface would be dragged back by the star's gravity before it could get very far. The French scientist Laplace came to a similar conclusion at roughly the same time.

Not much was done over the next hundred years or so with the ideas of Michell and Laplace. This was mostly true because during that time, the wave theory of light became the more accepted one. And no one understood how light, as a wave, could be affected by gravity.

Enter Albert Einstein. In 1915 he proposed the theory of general relativity. General relativity explained, in a consistent way, how gravity affects light. We now knew that while photons have no mass, they do possess momentum (so your statement about light not affecting matter is incorrect). We also knew that photons are affected by gravitational fields not because photons have mass, but because gravitational fields (in particular, strong gravitational fields) change the shape of space-time. The photons are responding to the curvature in space-time, not directly to the gravitational field. Space-time is the four-dimensional "space" we live in -- there are 3 spatial dimensions (think of X,Y, and Z) and one time dimension.

Let us relate this to light traveling near a star. The strong gravitational field of the star changes the paths of light rays in space-time from what they would have been had the star not been present. Specifically, the path of the light is bent slightly inward toward the surface of the star. We see this effect all the time when we observe distant stars in our Universe. As a star contracts, the gravitational field at its surface gets stronger, thus bending the light more. This makes it more and more difficult for light from the star to escape, thus it appears to us that the star is dimmer. Eventually, if the star shrinks to a certain critical radius, the gravitational field at the surface becomes so strong that the path of the light is bent so severely inward so that it returns to the star itself. The light can no longer escape. According to the theory of relativity, nothing can travel faster than light. Thus, if light cannot escape, neither can anything else. Everything is dragged back by the gravitational field. We call the region of space for which this condition is true a "black hole" (a term first coined by American scientist John Wheeler in 1969).

Now, being scientists, we do not just accept theories like general relativity or conclusions like photons have no mass. We constantly test them, trying to definitively prove or disprove. So far, general relativity has withstood every test. And try as we might, we can measure no mass for the photon. We can just put upper limits on what mass it can have. These upper limits are determined by the sensitivity of the experiment we are using to try to "weigh the photon". The last number I saw was that a photon, if it has any mass at all, must be less than 4 x 10-48 grams. For comparison, the electron has a mass of 9 x 10-28 grams.

Hope this answers the questions that you and your Chemistry class have.

Good luck,
Laura Whitlock."

 

[rimshaker]

Depends how you look at light since it has both wave and particle properties. In the macro sense (waves), it has no mass but does have energy since it's just an EM wave. In the micro sense (particles), it does have some hint of mass by quantum and academic standards. Obvisouly a photon at rest doesn't exist..... can be slowed down as recent technology has shown.... but not at rest.

 

[Shalmanese]

Originally posted by: trak0rr0kart
Nobody has proved that light has mass conclusively or inconclusively. Here is an interesting quote though..

(( "We have, however, put an upper limit on the photon mass. In 1994, the Charge Composition Explorer spacecraft measured the Earth's magnetic field and physicists used this data to define an upper limit of 0.0000000000000006 electron volts for the mass of photons, with a high certainty in the results.

This number is close to zero; it is equivalent to 0.00000000000000000000039 times the mass of an electron (the lightest particle), says Turner. "

-Answered by April Holladay, science correspondent, November 22, 2000 ))

Oh, Momentum=mass*velocity is correct.

Just personally, I dont trust any article that doesnt even do Scientific Notation for their numbers. And momentum = mass*velocity is a CLASSICAL equation just like F=ma. It doesnt apply to relativistic situations.

 

[panzerschiffer]

"Does light have mass?
The short answer is "no", but it is a qualified "no" because there are odd ways of interpreting the question which could justify the answer "yes".

Light is composed of photons so we could ask if the photon has mass. The answer is then definitely "no": The photon is a massless particle. According to theory it has energy and momentum but no mass and this is confirmed by experiment to within strict limits. Even before it was known that light is composed of photons it was known that light carries momentum and will exert a pressure on a surface. This is not evidence that it has mass since momentum can exist without mass.

Sometimes people like to say that the photon does have mass because a photon has energy E = hf where h is Planck's constant and f is the frequency of the photon. Energy, they say, is equivalent to mass according to Einstein's famous formula E = mc2. They also say that a photon has momentum and momentum is related to mass p = mv. What they are talking about is "relativistic mass", an outdated concept which is best avoided. Relativistic mass is a measure of the energy E of a particle which changes with velocity. By convention relativistic mass is not usually called the mass of a particle in contemporary physics so it is wrong to say the photon has mass in this way. But you can say that the photon has relativistic mass if you really want to. In modern terminology the mass of an object is its invariant mass which is zero for a photon.

If we now return to the question "Does light have mass?" this can be taken to mean different things if the light is moving freely or trapped in a container. The definition of the invariant mass of an object is m = sqrt{E2/c4 - p2/c2}. By this definition a beam of light, is massless like the photons it is composed of. However, if light is trapped in a box with perfect mirrors so the photons are continually reflected back and forth in the box, then the total momentum is zero in the boxes frame of reference but the energy is not. Therefore the light adds a small contribution to the mass of the box. This could be measured - in principle at least - either by an increase in inertia when the box is slowly accelerated or by an increase in its gravitational pull. You might say that the light in the box has mass but it would be more correct to say that the light contributes to the total mass of the box of light. You should not use this to justify the statement that light has mass in general.

It might be thought that it would be better to regard the relativistic mass as the actual mass of photons and light, instead of invariant mass. We could then consistently talk about the light having mass independently of whether or not it is contained. If relativistic mass is used for all objects then mass is conserved and the mass of an object is the sum of the masses of its part. However, modern usage defines mass as the invariant mass of an object mainly because the invariant mass is more useful when doing any kind of calculation. In this case mass is not conserved and the mass of an object is not the sum of the masses of its parts. For example the mass of a box of light is more than the mass of the box and the sum of the masses of the photons (the latter being zero). Relativistic mass is equivalent to energy so it is a redundant concept. In the modern view mass is not equivalent to energy. It is just that part of the energy of a body which is not kinetic energy. Mass is independent of velocity whereas energy is not.

Let's try to phrase this another way. What is the meaning of the equation E=mc2? You can interpret it to mean that energy is the same thing as mass except for a conversion factor equal to the square of the speed of light. Then wherever there is mass there is energy and wherever there is energy there is mass. In that case photons have mass but we call it relativistic mass. Another way to use Einstein's equation would be to keep mass and energy as separate and use it as an equation which applies when mass is converted in energy or energy is converted to mass as in nuclear reactions. The mass is then independent of velocity and is closer to the old Newtonian concept. In that case only total of energy and mass would be conserved but it seems better to try to keep conservation of energy. The interpretation most widely used is a compromise in which mass is invariant and always has energy so that total energy is conserved but kinetic energy and radiation does not have mass. The distinction is purely a matter of semantic convention.

Sometimes people ask "If light has no mass how can it be deflected by the gravity of a star?" One answer is that any particles such as photons of light, move along geodesics in general relativity and the path they follow is independent of their mass. The deflection of star-light by the sun was first measured by Arthur Eddington in 1919. The result was consistent with the predictions of general relativity and inconsistent with the Newtonian theory. Another answer is that the light has energy and momentum which couples to gravity. The energy-momentum 4-vector of a particle, rather than its mass, is the gravitational analogue of electric charge. The corresponding analogue of electric current is the energy-momentum stress tensor which appears in the gravitational field equations of general relativity. A massless particle can have energy E and momentum p because mass is related to these by the equation m2 = E2/c4 - p2/c2 which is zero for a photon because E = pc for massless radiation. The energy and momentum of light also generates curvature of space-time so according to theory it can attract objects gravitationally. This effect is far too weak to have been measured. The gravitational effect of photons does not have any cosmological effects either (except perhaps in the first instant after the big bang). There are far too few with too little energy to make up any noticeable proportion of dark matter."

-Phillip Gibbs, 1997

"Does the photon have mass, after all it has energy and energy is equivalent to mass?
This question comes up in the context of wondering whether photons are really "massless," since, after all, they have nonzero energy and energy is equivalent to mass according to Einstein's equation E=mc2. The problem is simply that people are using two different definitions of mass. The overwhelming consensus among physicists today is to say that photons are massless. However, it is possible to assign a "relativistic mass" to a photon which depends upon its wavelength. This is based upon an old usage of the word "mass" which, though not strictly wrong, is not used much today. See also the Faq article Does mass change with velocity?.

The old definition of mass, called "relativistic mass," assigns a mass to a particle proportional to its total energy E, and involved the speed of light, c, in the proportionality constant:

m = E / c2. (1)

This definition gives every object a velocity-dependent mass.

The modern definition assigns every object just one mass, an invariant quantity that does not depend on velocity. This is given by

m = E0 / c2, (2)

where E0 is the total energy of that object at rest.

The first definition is often used in popularizations, and in some elementary textbooks. It was once used by practicing physicists, but for the last few decades, the vast majority of physicists have instead used the second definition. Sometimes people will use the phrase "rest mass," or "invariant mass," but this is just for emphasis: mass is mass. The "relativistic mass" is never used at all. (If you see "relativistic mass" in your first-year physics textbook, complain! There is no reason for books to teach obsolete terminology.)

Note, by the way, that using the standard definition of mass, the one given by eqn (2), the equation "E = m c2" is not correct. Using the standard definition, the relation between the mass and energy of an object can be written as

E = m c2 / sqrt(1 - v2/c2), (3)

or as
E2 = m2 c4 + p2 c2, (4)

where v is the object's velocity, and p is its momentum.

In one sense, any definition is just a matter of convention. In practice, though, physicists now use this definition because it is much more convenient. The "relativistic mass" of an object is really just the same as its energy, and there isn't any reason to have another word for energy: "energy" is a perfectly good word. The mass of an object, though, is a fundamental and invariant property, and one for which we do need a word.

The "relativistic mass" is also sometimes confusing because it mistakenly leads people to think that they can just use it in the Newtonian relations

F = m a (5)

and
F = G m1 m2 / r2. (6)

In fact, though, there is no definition of mass for which these equations are true relativistically: they must be generalized. The generalizations are more straightforward using the standard definition of mass than using "relativistic mass."

Oh, and back to photons: people sometimes wonder whether it makes sense to talk about the "rest mass" of a particle that can never be at rest. The answer, again, is that "rest mass" is really a misnomer, and it is not necessary for a particle to be at rest for the concept of mass to make sense. Technically, it is the invariant length of the particle's four-momentum. (You can see this from eqn (4).) For all photons this is zero. On the other hand, the "relativistic mass" of photons is frequency dependent. UV photons are more energetic than visible photons, and so are more "massive" in this sense, a statement which obscures more than it elucidates.

Reference: Lev Okun wrote a nice article on this subject in the June 1989 issue of Physics Today, which includes a historical discussion of the concept of mass in relativistic physics.

Is there any experimental evidence that the photon has zero rest mass?
If the rest mass of the photon was non-zero, the theory of quantum electrodynamics would be "in trouble" primarily through loss of gauge invariance, which would make it non-renormalizable; also, charge-conservation would no longer be absolutely guaranteed, as it is if photons have vanishing rest-mass. However, whatever theory says, it is still necessary to check theory against experiment.

It is almost certainly impossible to do any experiment which would establish that the photon rest mass is exactly zero. The best we can hope to do is place limits on it. A non-zero rest mass would lead to a change in the inverse square Coulomb law of electrostatic forces. There would be a small damping factor making it weaker over very large distances.

The behavior of static magnetic fields is likewise modified. A limit on the photon mass can be obtained through satellite measurements of planetary magnetic fields. The Charge Composition Explorer spacecraft was used to derive a limit of 6x10-16 eV with high certainty. This was slightly improved in 1998 by Roderic Lakes in a laborartory experiment which looked for anomalous forces on a Cavendish balance. The new limit is 7x10-17 eV. Studies of galactic magnetic fields suggest a much better limit of less than 3x10-27 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 (1976) 624."

 

[panzerschiffer]

Some more cut and paste:

"Does mass change with velocity?

There is sometimes confusion surrounding the subject of mass in relativity. This is because there are two separate uses of the term. Sometimes people say "mass" when they mean "relativistic mass", mr but at other times they say "mass" when they mean "invariant mass", m0. These two meanings are not the same. The invariant mass of a particle is independent of its velocity v, whereas relativistic mass increases with velocity and tends to infinity as the velocity approaches the speed of light c. They can be defined as follows:

mr = E/c2
m0 = sqrt(E2/c4 - p2/c2)

where E is energy, p is momentum and c is the speed of light in a vacuum. The velocity dependent relation between the two is

mr = m0 /sqrt(1 - v2/c2)

Of the two, the definition of invariant mass is much preferred over the definition of relativistic mass. These days, when physicists talk about mass in their research, they always mean invariant mass. The symbol m for invariant mass is used without the subscript 0. Although the idea of relativistic mass is not wrong, it often leads to confusion, and is less useful in advanced applications such as quantum field theory and general relativity. Using the word "mass" unqualified to mean relativistic mass is wrong because the word on its own will usually be taken to mean invariant mass. For example, when physicists quote a value for "the mass of the electron" they mean its invariant mass.

At zero speed, the relativistic mass is equal to the invariant mass. The invariant mass is therefore often called the "rest mass". This latter terminology reflects the fact that historically it was relativistic mass which was often regarded as the correct concept of mass in the early years of relativity. In 1905 Einstein wrote a paper entitled Does the inertia of a body depend upon its energy content?, to which his answer was "yes". The first record of the relationship of mass and energy explicitly in the form E = mc2 was written by Einstein in a review of relativity in 1907. If this formula is taken to include kinetic energy, then it is only valid for relativistic mass, but it can also be taken as valid in the rest frame for invariant mass. Einstein's conventions and interpretations were sometimes ambivalent and varied a little over the years; however an examination of his papers and books on relativity shows that he almost never used relativistic mass himself. Whenever the symbol m for mass appears in his equations it is always invariant mass. He did not introduce the notion that the mass of a body increases with velocity--just that it increases with energy content. The equation E = mc2 was only meant to be applied in the rest frame of the particle. Perhaps Einstein's only definite reference to mass increasing with kinetic energy is in his "autobiographical notes".

To find the real origin of the concept of relativistic mass, you have to look back to the earlier papers of Lorentz. In 1904 Lorentz wrote a paper Electromagnetic Phenomena in a System Moving With Any Velocity Less Than That of Light. There he introduced the "longitudinal" and "transverse" electromagnetic masses of the electron. With these he could write the equations of motion for an electron in an electromagnetic field in the Newtonian form F = ma where m increases with mass. Between 1905 and 1909 Planck, Lewis and Tolman developed the relativistic theory of force, momentum and energy. A single mass dependence could be used for any acceleration if F = d/dt(mv) is used instead of F = ma. This introduced the concept of relativistic mass which can be used in the equation E = mc2 even for moving objects. It seems to have been Lewis who introduced the appropriate velocity dependence of mass in 1908, but the term "relativistic mass" appeared later. [Gilbert Lewis was a chemist whose other claim to fame in physics was naming the photon in 1926.]

Relativistic mass came into common usage in the relativity text books of the early 1920s written by Pauli, Eddington and Born. As particle physics became more important to physicists in the 1950s, the invariant mass of particles became more significant, and inevitably people started to use the term "mass" to mean invariant mass. Gradually this took over as the normal convention, and the concept of relativistic mass increasing with velocity was played down.

The case of photons and other particles that move at the speed of light is special. From the formula relating relativistic mass to invariant mass, it follows that the invariant mass of a photon must be zero, but its relativistic mass need not be. The phrase "The rest mass of a photon is zero" might sound nonsensical because the photon can never be at rest; but this is just a side effect of the terminology, since by making this statement, we can bring photons into the same mathematical formalism as the everyday particles that do have rest mass. In modern physics texts, the term mass when unqualified means invariant mass, and photons are said to be "massless" (see Physics FAQ What is the mass of the photon?). Teaching experience shows that this avoids most sources of confusion.

Despite the general usage of invariant mass in the scientific literature, the use of the word mass to mean relativistic mass is still found in many popular science books. For example, Stephen Hawking in A Brief History of Time writes "Because of the equivalence of energy and mass, the energy which an object has due to its motion will add to its mass." and Richard Feynman in The Character of Physical Law wrote "The energy associated with motion appears as an extra mass, so things get heavier when they move." Evidently, Hawking and Feynman and many others use this terminology because it is intuitive and useful when you want to explain things without using too much mathematics. The standard convention followed by some physicists seems to be: use invariant mass when doing research and writing papers for other physicists but use relativistic mass when writing for non-physicists. It is a curious dichotomy of terminology which inevitably leads to confusion. A common example is the mistaken belief that a fast moving particle must form a black hole because of its increase in mass (see relativity FAQ article If you go too fast do you become a black hole?).

Looking more deeply into what is going on, we find that there are two equivalent ways of formulating special relativity. Einstein's original mechanical formalism is described in terms of inertial reference frames, velocities, forces, length contraction and time dilation. Relativistic mass fits naturally into this mechanical framework, but it is not essential. If relativistic mass is used, it is easier to form a correspondence with Newtonian mechanics, since some Newtonian equations remain valid:

F = dp / dt

p = mr v

Also, in this picture mass is conserved along with energy.

The second formulation is the more mathematical one introduced a year later by Minkowski. It is described in terms of spacetime, energy-momentum four vectors, world lines, light cones, proper time and invariant mass. This version is harder to relate to ordinary intuition because force and velocity are less useful in their four-vector forms. On the other hand, it is much easier to generalise this formalism to the curved spacetime of general relativity where global inertial frames do not usually exist.

It may seem that Einstein's original mechanical formalism should be easier to learn, because it retains many equations from the familiar Newtonian mechanics. In Minkowski's geometric formalism, simple concepts such as velocity and force are replaced with world lines and four vectors. Yet the mechanical formalism often proves harder to swallow, and is at the root of many people's failure to get over the paradoxes that are so often discussed. Once students have been taught about Minkowski space, they invariably see things more clearly. The paradoxes are revealed for what they are and calculations also become simpler. But it is debatable whether or not the relativistic mechanical formalism should be avoided altogether. It can still provide the correspondence between the new physics and the old, which is important to grasp at the early stages. The step from the mechanical formalism to the geometric can then be easier. An alternative modern teaching method is to translate Newtonian mechanics into a geometric formalism, using Galileian relativity in four dimensional spacetime, and then modify the geometric picture to Minkowski space.

The preference for invariant mass is stressed and justified in the classic relativity textbook Spacetime Physics by Taylor and Wheeler who write

"Ouch! The concept of `relativistic mass' is subject to misunderstanding. That's why we don't use it. First, it applies the name mass--belonging to the magnitude of a four-vector--to a very different concept, the time component of a four-vector. Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of space-time itself."

In the final analysis the issue is a debate over whether or not relativistic mass should be used, and is a matter of semantics and teaching methods. The concept of relativistic mass is not wrong: it can have its uses in special relativity at an elementary level. This debate surfaced in Physics Today in 1989 when Lev Okun wrote an article urging that relativistic mass should no longer be taught (42 #6, June 1989, pg 31). Wolfgang Rindler responded with a letter to the editors to defend its continued use. (43 #5, May 1990, pg 13).

The experience of answering confused questions in the news groups suggests that the use of relativistic mass in popular books and elementary texts is not helpful. The fact that relativistic mass is virtually never used in contemporary scientific research literature is a strong argument against teaching it to students who will go on to more advanced levels. Invariant mass proves to be more fundamental in Minkowski's geometric approach to special relativity, and relativistic mass is of no use at all in general relativity. It is possible to avoid relativistic mass from the outset by talking of energy instead. Judging by usage in modern text books, the consensus is that relativistic mass is an outdated concept which is best avoided. There are people who still want to use relativistic mass, and it is not easy to settle an argument over semantic issues because there is no absolute right or wrong; just conventions of terminology. There will always be those who post questions using terms in which mass increases with velocity. It is unhelpful to just tell them that what they read or heard on cable TV is wrong, but it might reduce confusion for them in the longer term if they can be persuaded to think in terms of invariant mass instead of relativistic mass.

In a 1948 letter to Lincoln Barnett, Einstein wrote

"It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than `the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."

The viewpoint above, emphasising the distinction between mass, momentum, and energy, is certainly the modern view. Fifty years later, can relativistic mass be laid to rest?





Addendum: What is the relativistic version of F = ma ?
For this last section, we'll write down the relativistic version of Newton's second law, F = ma. In Newton's mechanics, this equation relates vectors F and a (hence the bold script) via the mass m of the object being accelerated, which is invariant in Newton's theory. Because m is just a number, in Newton's theory the force on a mass is always parallel to the resulting acceleration.

The corresponding equation in special relativity is a little more complicated. It turns out that the force F is not always parallel to the acceleration a! To express this fact, we need to use matrix notation. Letting m be the invariant mass, v be the velocity as a column vector, and 1 be the 3 x 3 identity matrix, the actual result turns out to be

F = gamma m (1 + gamma2 v vt) a

and

a = (1 - v vt) F / (gamma m)

(As an aside, there's a nice correspondence to the one dimensional case here. Just as gamma2 can be written as 1 + gamma2 v2, and its inverse (i.e. reciprocal) is 1 - v2, so the matrix 1 + gamma2 v vt has inverse 1 - v vt, as well as determinant gamma2.)

Looking at this relativistic version of F = ma, we might say that when the (invariant) mass m appears, it's accompanied by a factor of gamma, so that really it is the relativistic mass that's appearing. Isn't this then, a good reason why we might want to give the notion of relativistic mass more credence? Not really. Notice that now the acceleration is not necessarily parallel to the force that produced it. It's not hard to see from the above equations that it's easier to accelerate a mass sideways to its motion, than it is to accelerate it in the direction of its motion. So now, if we still want to maintain some meaning for relativistic mass, then we'll have to realise that it has a directional dependence--as if the object somehow has more mass in the direction of its motion, than it has sideways. Evidently the idea of relativistic mass is becoming a little more complicated than at first we might have hoped! And this is another reason why, in the end, it's so much easier to just take the mass to be the invariant quantity m, and to put any directional information into a separate, matrix, factor.





References:
Arguments against the term "relativistic mass" are given in the classic relativity text book Space-Time Physics by Taylor and Wheeler, 2nd edition, Freeman Press (1992).

The article Does mass really depend on velocity, dad? by Carl Adler, American Journal of Physics 55, 739 (1987) also discusses this subject and includes the above quote from Einstein against the use of relativistic mass.

Einstein's original papers can be found in English translation in The Principle of Relativity by Einstein and others, Dover Press.

Some other historical details can be found in Concepts of mass by Max Jammer and Einstein's Revolution by Elie Zahar."

Hope this clears up some misconceptions people might have about the whole thing. It doesn't seem so cut and dry as it may appear at first glance.

 

[trak0rr0kart]

"Just personally, I dont trust any article that doesnt even do Scientific Notation for their numbers. And momentum = mass*velocity is a CLASSICAL equation just like F=ma. It doesnt apply to relativistic situations."[/quote]


To graciously correct you, when I was replying that "No, momentum=mass*velocity is correct", i was replying to something someone had said earlier in the thread. I wasn't using it in any answer I replied with for realitivistic math.

I have seen you on a lot of forums stirring up trouble. Please stop or take it elsewhere because this place is for openminded and professionals people. This isn't a kiddie place as the forum implies in its description.

As far as your comments on the article is concerned.. I don't think they put the numbers in non-scientific form just because they didn't know what they were talking about.. I think they did it to impress upon people without much scientific background the magnitude of the the answer.

Now that that is out of the way.. we can move onto better things.

 

[Spacehead]

Originally posted by: trak0rr0kart

AS far as light escaping a black hole is concerned I would say this. According to Stephen Hawking.. black holes have a thing called an event horizon. What this means is that at a certain radius from the center of the black hole (extremely massive body) there is a point where light can escape. Below this it will not, and above it.. it will escape at exactly C. So light that is bent at just above the critical angle for the space-time warp will escape then just above the surface. Because the black holes do not emit visable light does not mean that it dosen't emit any of the EMS (electro magnet spectrum) radiation. According to him and other scientists in the field (his coworkers), Higher level energy.. in the order of gamma rays etc.. are able to escape the black hole. The reason why you don't see any light at all.. is because none of the visible light is escaping from it.. but you can see it through gamma ray detection etc (all this is just theory as of yet and when it comes to extremely LARGe black holes then I think that even the gamma radiation might be extremely hard to detect as well).

Aren't the X-rays detected at potential black holes the result of matter "falling into" the black hole/event horizon, not so much the X-rays escaping from it?

 

[f95toli]

Originally posted by: Spacehead
[Aren't the X-rays detected at potential black holes the result of matter "falling into" the black hole/event horizon, not so much the X-rays escaping from it?

Yes, that is correct. The X-ray radiation is generated by the enormous "heat" which generated when matter is torn apart falling into the hole. There is another form of radiation called "Hawking radiation" which is "emitted" by the black hole itself but that is low energy radiation, not X-rays.

 

[Voidboy]

Well, I think we've just about covered my intro to modern physics class. I'm going to ask for my money back.

 

[trak0rr0kart]

Originally posted by: f95toli

Originally posted by: Spacehead
[Aren't the X-rays detected at potential black holes the result of matter "falling into" the black hole/event horizon, not so much the X-rays escaping from it?

Yes, that is correct. The X-ray radiation is generated by the enormous "heat" which generated when matter is torn apart falling into the hole. There is another form of radiation called "Hawking radiation" which is "emitted" by the black hole itself but that is low energy radiation, not X-rays.

I thought that his radiation was gamma rays and it was high energy.. just made sense that it would be able to escape because it was high energy. I could be wrong, it has been a while since I read his books.

 

[f95toli]

No, the fact that the radiation "escapes" has nothing to do with the energy. As far as I remember it works in the following way:
A pair of virtual particles are created just at the event horizon. Since the particles are virtual the sum of their energies must be zero (E(A)+E(B)=0). However, imagine that they were created in such a way that their positions are as follows

x
A x B
x

The "x" indicate the position of the event horizon, the left particle (A) will fall into the black hole but B will be able to escape. B will now be a real particle, this is possible since A had a negative energy ; hence the total energy is conserved:

"Energy of black hole"+E(A)+E(B)=constant

This means that some energy was "stolen" from the black hole in the process.
"B" is what we call Hawking radiation.

An interesting consequence of this is that a black hole can shrink by radiating Hawking radiation.

 

[sgtroyer]

Good explanation f95. I believe you're correct. Nothing actually escapes the black hole, that is, nothing that was inside the event horizon can ever make it back out. Gamma rays are very energetic, but the velocity is still c. They can't escape a black hole any more than any other wavelength of radiation.

 

[trak0rr0kart]

Ok, that makes sense.. I was just confused on that part. Thanks for clearing that up!

 

[Fencer128]

Hi,

Just a suggestion mind - but this thread has become over complicated by cases of unsound reasoning and too many questions. To get the qualified answers I think you were originally looking for I would possibly start another thread and address this on a point by point basis.

Cheers,

Andy

 

[trak0rr0kart]

Unsound reasoning? Which parts? Care to help us out here?

Edited -> Show us the unsound reasoning Dr, we would really like to know what it is all about. Duh, that is why this thread was started. He just wanted to understand light and so far we have tried. If you can add something that is worth more then two cents and helps clear things up.. then be our guest.

 

[Mday]

Originally posted by: syberscott
I'll get right to it. Do photons have mass or not?
If so then how do they travel as fast as they do? (I'm assuming that anything with mass cannot travel at a velocity of c, but I'm not too familiar with particles so I may be off track here.)
And if photons don't have mass, then how do they carry momentum and energy?

thing is, not everyone understands light. and those that do cant predict what light will do given every scenario. light is still a mystery. we only have clues (and lots of them)

 

[prometheusxls]

Originally posted by: syberscott
I'll get right to it. Do photons have mass or not?
If so then how do they travel as fast as they do? (I'm assuming that anything with mass cannot travel at a velocity of c, but I'm not too familiar with particles so I may be off track here.)
And if photons don't have mass, then how do they carry momentum and energy?

At the level I understand it, college level physics (most advanced course was physical chemistry), light and other radient energy displays both wave and particle properties. Neither model is fully correct. In certain cases it will be more convenient or correct to use either of these models. The choice is up to you and depends mostly on the scale you are interested in.

I think that in a subject such as this it is important to remeber that models are conceptualizations and do not represent the thing in its self. I think you are mixing the particle and wave models and this is a big no no. Terms like momentum, and mass probabbly refer to the particle model and terms like energy, frequency, etc... are more related to the wave model. Mixing terms is very sloppy, confusing, and probabbly incorrect.

 

[Fencer128]

Originally posted by: trak0rr0kart
Unsound reasoning? Which parts? Care to help us out here?

Edited -> Show us the unsound reasoning Dr, we would really like to know what it is all about. Duh, that is why this thread was started. He just wanted to understand light and so far we have tried. If you can add something that is worth more then two cents and helps clear things up.. then be our guest.

Well, I was trying to be helpful as I have some knowledge in this area - not act conceited or derrogatory. The unsound reasoning was in relation to comments regarding classical theory. i.e. momentum as a mass x velocity etc. as well as comments such as:

"I was taught that Light at rest has no mass, but a moving beam of light does have mass". That not only confuses with classical theory, but also presents the opposite result from that predicted by the "the photon possibly does have a small rest mass" camp.

I'm not trying to blame anyone for making these comments - I just suggested that now the debate has realised that you're better off abandoning classical theory - it'd be clearer to everyone if a new thread was started, containing all of the valid (ie technically correct) comments from this one.

If I were writing it, I'd do it this way. You would really want to start with the De Broglie wavelength definition and work from there. Trying to understand wave particle duality has been a struggle for every physicist - and I've not yet met one who can reconcile it rigorously. If we except the wave-particle nature of light, work off of the de broglie wavelength and try and understand momentum from this perspective we can gain a couple of things:

1. An understanding of the momentum of waves without involving mass.

2. Eventually if you wish you can push this to looking at space-time, general relativity and the fact that light "bends" not because of the influence of gravity on the mass of a photon, but due to the localised curvature of space-time being effected by the presence of a large object and it's associated gravity.

I have been deliberately vague on the de broglie wavelength and curvature of space-time because there are many pages (easily accessable on google) to deal with this.

By trying to tackle the problem in this way I think it will be easier to see the fundamental points and to get near to the (let's face it - the nature of light cannot be completely, and especially non-mathematically, reconciled due to wave-particle duality) "meaning" that the poster is looking for.

Thanks ,

Andy

 

[trak0rr0kart]

Thank you for taking responsibilty for your comments. It is cool that you would make a response like that instead of the first; even if it we were wrong. I just assumed you were being arrogant, My opologies.

So I get that it is following the curvature... but why? if not gravity... if not for the mass of photons.. then what would cause the particles to even change position? Do they just like space-time curvature and want to follow it?

Thanks in advance.
.

 

[Fencer128]

Originally posted by: trak0rr0kart
Thank you for taking responsibilty for your comments. It is cool that you would make a response like that instead of the first; even if it we were wrong. I just assumed you were being arrogant, My apologies.

No problem. I just wanted to try to make the correct arguments easier to "see".

So I get that it is following the curvature... but why? if not gravity... if not for the mass of photons.. then what would cause the particles to even change position? Do they just like space-time curvature and want to follow it?

Thanks in advance.

That's a good point. They change position because the portion of space-time through which they are moving is shaped. It is shaped by the gravity of nearby objects (such as the sun). So, it is not the hypothetically extremely small "gravity of the photon" that causes it to move from one path to another, but the changing curvature of space-time through which it travels.

As to why particles/waves follow space-time - if you think of it as the fabric of the universe, it's pretty difficult not to "follow" it. There's no where else to go!

There are other (mainly visual) and better ways of describing this - but unfortunately since we're dealing with a very conceptually abstract out-of-everyday experience that is only ultimately comprehensible through mathematics - it's difficult to think on these points!

Cheers,

Andy

 

[trak0rr0kart]

I understand that they follow the Gravitized space-time, the thing that is hard not to follow, but why. If it is gravity that makes the warped space-time, then it would only make sense to me that things affected by gravity would follow the path. I see the bowling ball sitting on the bed, and the golf ball swirling around it, but I just don't see how these massless particles follow a mass created space-time. Are the gravitrons (if exist, not sure) follow the idea of a stream in guiding these massless photons along its path?

I realize that everyone says that light follows space time and I agree, however, if a moon was to pass by the sun its deflection would be very large, but if it speed up, then it would be very small.. so take light that passes the sun, it is only deflected very slightly, but if it where to slow down, like increasing the frequency of the light so as to have a slower overall wave velocity (like in recent expirements through certain medians), then it would bend at a larger angle?

I know that it follows space-time, I just want to know why. What causes it to bend around the sun besides just following a mass created warped space-time?

Sorry if this is seems redundant :S

 

[Fencer128]

Originally posted by: trak0rr0kart
I understand that they follow the Gravitized space-time, the thing that is hard not to follow, but why. If it is gravity that makes the warped space-time, then it would only make sense to me that things affected by gravity would follow the path.

That's where I think you are confused. This is not the case. You have to remember that although the "bowling ball on the bed" analogy is nice and easy to conceptualise - it's a 2-D model that uses forces to move the masses. Space-time is 4-D. If space-time were flat (you imagine painting a line on a flat surface) then that line would appear straight. Now, if that were the surface of a deflated baloon that we then inflated - the line would appear curved. Does that mean that the line has "moved"? No, it means that, in the case of space-time, the space-time has distorted. As I tried (rather unsuccessfully!) to explain in my last post - you have to imagine space-time as "the fabric" of the universe. When the fabric changes shape straight lines become curved not becuase there is some "force" acting on them as in your "bowling ball" example (that would then only apply to something with mass or charge), but because the universe has altered shape locally.

I see the bowling ball sitting on the bed, and the golf ball swirling around it, but I just don't see how these massless particles follow a mass created space-time. Are the gravitrons (if exist, not sure) follow the idea of a stream in guiding these massless photons along its path?

I think I covered this in my first paragraph. The bowling ball is using gravity so force to achieve movement. This is different to distorting space-time.

I realize that everyone says that light follows space time and I agree, however, if a moon was to pass by the sun its deflection would be very large, but if it speed up, then it would be very small.. so take light that passes the sun, it is only deflected very slightly, but if it where to slow down, like increasing the frequency of the light so as to have a slower overall wave velocity (like in recent expirements through certain medians), then it would bend at a larger angle?

Firstly, the "recent experiments" you mention I believe to be refraction experiments. ie put white light through a medium (ie a glass prism) and note that different wavelengths are refracted by different amounts. The media is higher index than the surrounding air, which with a bit of maths shows that light moves "more slowly" through it (though the speed of light is still constant! - without going into the details I believe it is the phase velocity of the beam of light that is changing, not the group velocity) and so this is proportional to the bending.

Secondly, with respect to the moon moving past the sun. If the move speeds up then it moves more quickly through the sun's gravitational field. This means it moves more quickly to a greater distance from the sun and thus to weaker gravitational attraction. So overall its motion is effected by the gravity of the sun less than it would be if it was travelling slower. If the moon was moving at a large percentage of the speed of light then its effective/reletavistic mass would lower and this would also cause the gravitaional forces between the moon and sun to be less than if it were travelling more slowly. Keep in mind that these are 2 seperate effects.

Thirdly, the speed of light is constant (and this is particularly easy to see in a vacuum). I'm having to double check this with a colleague - but I think that because the relativistic momentum of the light is inversely proportional to its wavelength via de broglie's equation, a lower frequency light beam (larger wavelength) will have a lower momentum than an analogous beam with a higher frequency. I'm *guessing* (will check this) that the lower relativistic momentum means that the light beam is effected more greatly by the sun's space-time distortion and so bends more than a beam with a higher momentum (the lower momentum beam will I think fall more deeply into the sun's gravity well). Remember though, no matter what the momentum - the beam will still bend to some degree because space-time is curved in the region.

I know that it follows space-time, I just want to know why. What causes it to bend around the sun besides just following a mass created warped space-time?

Nothing. It can only follow the "shape" of the universe/space-time. No force is involved as there is no mass or charge for it to act on! This follows on as the conclusion from my first paragraph.

Sorry if this is seems redundant :S

It not that it is redundant - it's just that space-time and it's effects are incredibly difficult to conceptualise. Show me someone who can conceptualise 4-D and I'll show you a liar!

Cheers,

Andy

 

[trak0rr0kart]

when I was refering to light slowing down for an expirement I was refering to the expirements where they slowed light down to a 30 mph.. even though the photons were still travelling at the speed of light, the phase change for time was greater.. hence increased frequency. What I was trying to get at.. is having more photons in the same length of ray as opposed to a lower frequency ray that would have less. But I guess that was off in left field because I keep thinking gravity and we are talking about space-time. Space-time is like a cone for me.. the small end of the cone was like the beginning of the universe and the big end is now, like in stephen hawkings books.

Would'nt it make sense, thinking in space-time, that the light, travelling at realitivistic speeds would'nt be effected by the very small passing of even the sun? I mean, in the time that it took to pass the sun, the sun would'nt have made too much of an effect on space-time would it because it hadn't moved much?

If it isn't gravity, and the movement of the sun in space-time to create a warped space-time, then why is there a warped place for the light to be warped at? I mean if I replace the sun with one that is 1000 times more massive, but same dia, instantly, then shot light passed it.. the bent light would be at a greater angle then the one made when passing our current sun right? So if thats the case and the new sun has only moved as much as our current sun realitive to the universe or whatever, then it would only make as much of a space-time warp as our current sun. So then why does the light bend more?

Maybe I'm just stupid or something, but this isn't adding up for me. I can't see how light passing by a star is less effected then light passing by a black hole, when the star is many times greater in dia,,... if it is just a space-time warp that is causing it to not bend as much... Why isn't it just gravity that does it -> That makes sense :S

You don't need to reply to this message if you don't want.. I know your just going to say that it is space-time and it is the fabric of the universe etc.. To me it is like saying that there is just dark matter out there because we cannot explain the reason for all the extra mass in the universe. I don't need an answer like that.. it isn't helping.

thanks for your help in trying. I think I just need a different approach to understanding this.

 

[Fencer128]

Originally posted by: trak0rr0kart
when I was refering to light slowing down for an expirement I was refering to the expirements where they slowed light down to a 30 mph.. even though the photons were still travelling at the speed of light, the phase change for time was greater.. hence increased frequency. What I was trying to get at.. is having more photons in the same length of ray as opposed to a lower frequency ray that would have less. But I guess that was off in left field because I keep thinking gravity and we are talking about space-time. Space-time is like a cone for me.. the small end of the cone was like the beginning of the universe and the big end is now, like in stephen hawkings books.

I think we best leave the seperate issue of "slowing light" alone until we understand space-time! Also, for the purposes of this argument, leave the "light cone" (Minkowski) diagram you describe, where every event traces a (world) line somewhere through the cone, well alone for now.

Would'nt it make sense, thinking in space-time, that the light, travelling at realitivistic speeds would'nt be effected by the very small passing of even the sun? I mean, in the time that it took to pass the sun, the sun would'nt have made too much of an effect on space-time would it because it hadn't moved much?

This sounds a little confused to me:

"in the time that it took to pass the sun, the sun would'nt have made too much of an effect on space-time would it because it hadn't moved much"

Forgive me if I misunderstand you, and I'm telling you what you already know, but let me elaborate. The sun has "made its effect" in space-time. If we assume it's mass is constant (which it almost nearly is) then there is no change in "the effect on space-time" due to the sun as the light moves through that portion of space. The sun's mass has gravity associated with it. This distorts space-time into a gravity "well" with the sun in the middle. As light passes through the well, the shape of the well's sides will cause it's "straight" velocity to become "curved" - in effect bending it. Let me reiterate. There is no change to the shape of the space-time whilst the beam of light is passing through.

If it isn't gravity, and the movement of the sun in space-time to create a warped space-time, then why is there a warped place for the light to be warped at? I mean if I replace the sun with one that is 1000 times more massive, but same dia, instantly, then shot light passed it.. the bent light would be at a greater angle then the one made when passing our current sun right? So if thats the case and the new sun has only moved as much as our current sun realitive to the universe or whatever, then it would only make as much of a space-time warp as our current sun. So then why does the light bend more?

You're right, for what you describe - the movement of the sun has very little to do with it. All that matters is it's mass. The mass has associated gravity. The gravity distorts space-time. A light beam passing through the distorted space-time is bent due to the localised curvature of space-time. Gravity causes space-time to bend - its does not act directly on the light (hence light does not require mass).

Remembering that motion of the sun is not pertinent to this arguement - a more massive star (ie a black hole) will have an associated larger gravity, which implies a larger distortion of localised space-time. This will mean a greater curvature of the space-time and so a greater bend in the path of a light beam passing through.

Maybe I'm just stupid or something, but this isn't adding up for me. I can't see how light passing by a star is less effected then light passing by a black hole, when the star is many times greater in dia,,... if it is just a space-time warp that is causing it to not bend as much... Why isn't it just gravity that does it -> That makes sense :S

You're not stupid - this is tricky stuff! The light is less bent by a less massive star (as compared to a black hole) because the star has less mass than a black hole. Less mass means less distortion to space-time, which means less steep sides of the associated gravity well. This means light moving near to this gravity well is less bent. Mass is the key parameter in this. Diameter, volume, surface area, etc. are not at all important. Any clearer?

You don't need to reply to this message if you don't want.. I know your just going to say that it is space-time and it is the fabric of the universe etc.. To me it is like saying that there is just dark matter out there because we cannot explain the reason for all the extra mass in the universe. I don't need an answer like that.. it isn't helping.

thanks for your help in trying. I think I just need a different approach to understanding this.

Don't try too hard to conceptualise 4-D. It won't work! You just have to take it on trust that the maths of general relativity show that gravity affects space-time. The universe is space-time and that every experiment to verify/test general relativity that has been performed vindicates the theory.

I think it's not that you can't understand the mechanism by which the light is bent, but more that you don't understand the nature of space-time - i.e. it "consists" of 3-D of space and 1-D of time - and the two are linked. By looking at it that way does it seem any clearer why we refer to "space-time" and why it is "the fabric of the universe" (ie we can't escape living in a 3-D world that moves forward (ie 1-D) in time)?

Cheers,

Andy

 

[trak0rr0kart]

I think I will take your advice and study up more on space-time because my view of it isn't correct and has led me to believe certain things about light and gravity that don't add up. Like you described.. space-time creating a gravity well and the light following it makes sense.. but not because of gravity that causes the light to follow it.. but something else. I am starting to get real curious about space-time now!

Thank you again for the clarification, I must be hard to deal with