Exploring the Paradox: Light's Mass and its Inability to Escape a Black Hole

[sclancy]

if light doesn't have mass, how come it can't escape from a black hole?

 

[DaveC426913]

Gravity causes EM radiation to redshift. Light attempting to escape from a black hole gets infinitely red-shifted.

 

[Upisoft]

$$m=E/c^2$$

The light is energy and energy has mass.

 

[DaveC426913]

$$m=E/c^2$$

The light is energy and energy has mass.

Um no. That is not what the formula means.

 

[franznietzsche]

if light doesn't have mass, how come it can't escape from a black hole?

1) Black holes can only be treated with GR. Do not try to treat one with Newtownian Gravity. Just don't. It doesn't work.

2) Gravity is not a force in GR. Objects that are moving under the "force" of gravity move in straight 4-dimensional lines (geodesics), just as in Newtonian mechanics an object with no net force on it will move in a straight 3-dimensional line. However, in GR, spacetime gets bent, So a geodesic is not a straight line in the euclidean sense, it is simply the shortest path between two points (in 4-dimensions. This is the key part, 4 dimensions). Inside the event horizon of a black hole, spacetime is so greatly bent that all geodesics go towards the singularity. Light is not acted on by a force, space is bent such that the only path it can take is towards the singularity.

 

[Oxymoron]

I don't have anything to add, but I'd like to say that I really liked franznietzsche's post:

Posted by franznietzsche:

2) Gravity is not a force in GR. Objects that are moving under the "force" of gravity move in straight 4-dimensional lines (geodesics), just as in Newtonian mechanics an object with no net force on it will move in a straight 3-dimensional line. However, in GR, spacetime gets bent, So a geodesic is not a straight line in the euclidean sense, it is simply the shortest path between two points (in 4-dimensions. This is the key part, 4 dimensions). Inside the event horizon of a black hole, spacetime is so greatly bent that all geodesics go towards the singularity. Light is not acted on by a force, space is bent such that the only path it can take is towards the singularity.

 

[rbj]

Um no. That is not what the formula means.

Um, yes. that is what the formulae mean.

$$E = m c^2 = h \nu = \hbar \omega$$

means that the a photon of radian frequency of $\omega$ has a mass:

$$m = \frac{\hbar}{c^2} \omega$$

and since

$$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$

the rest mass is

$$m_0 = m \sqrt{1 - \frac{v^2}{c^2}}$$

and since $v = c$ for the photon, its rest mass is zero.

Light has mass (but no rest mass).

 

[DaveC426913]

Ok, well I'm just trying not to confuse the OP. The reason light can't escape from a black hole is NOT because gravity pulls on its mass.

 

[rbj]

Ok, well I'm just trying not to confuse the OP. The reason light can't escape from a black hole is NOT because gravity pulls on its mass.

true from the perspective of GR (the light is going in a straight line, just as it would be in Eistein's thought experiment of light traveling in an accelerting rocket). in that case, gravity doesn't pull on anything, it "just" distrorts space.

but if the OP is thinking about this in a more classical physics POV, then it would be accurate to say that gravity is pulling on of the photons, just as it pulls on us.

 

[franznietzsche]

true from the perspective of GR (the light is going in a straight line, just as it would be in Eistein's thought experiment of light traveling in an accelerting rocket). in that case, gravity doesn't pull on anything, it "just" distrorts space.

but if the OP is thinking about this in a more classical physics POV, then it would be accurate to say that gravity is pulling on of the photons, just as it pulls on us.

No, that would be wrong. If the OP is thinking about this in a more classical physics POV, then he/she is thinking about it the wrong way.

Stop trying to explain GR with Newtonian ideas. It doesn't work. Gravity is not a force in GR. It doesn't pull on matter or on photons.

 

[franznietzsche]

Um, yes. that is what the formulae mean.

$$E = m c^2 = h \nu = \hbar \omega$$

means that the a photon of radian frequency of $\omega$ has a mass:

$$m = \frac{\hbar}{c^2} \omega$$

and since

$$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$

the rest mass is

$$m_0 = m \sqrt{1 - \frac{v^2}{c^2}}$$

and since $v = c$ for the photon, its rest mass is zero.

Light has mass (but no rest mass).

This is wrong.

Light does not have mass. It has energy, and momentum. No mass.

 

[rbj]

No, that would be wrong. If the OP is thinking about this in a more classical physics POV, then he/she is thinking about it the wrong way.

Stop trying to explain GR with Newtonian ideas. It doesn't work. Gravity is not a force in GR. It doesn't pull on matter or on photons.

that is true, but the concept of photons and the mass (or "momentum" if you prefer) thereof comes before that of GR.

you see, even though Newtonian gravitation and mechanics is "wrong", we still seem to use these concepts daily to design and build bridges and rockets. when thinking in that conceptual frame, rather than that, standing on the Earth's surface, i am accelerating "upward" in this curved space (due to the force exerted on my feet by the ground), we like to say that the force pushing up on my feet is equal to and opposite of the force of gravity pulling me toward the center of mass of the earth. it's not correct, but we treat it as if it were.

we know from the EP that if i was instead standing in a spaceship accelerating at 9.8 m/s², i would experience an environment indistinguishable from standing on the earth. and we know that a truly straight beam of light would appear to me curved downward because of my acceleration and if, instead, i was standing on the surface of the earth, i would experience the same thing, including the bending of the beam of light. if, in the second (earthbound) case, i would say "gravity is pulling down on me" and you find that acceptable, then you would have to also accept the same reason for the ostensible diversion of the beam of light.

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This is wrong.

Light does not have mass. It has energy, and momentum. No mass.

so, how does a photon have momentum without mass? what is the definition of momentum of any particle?

evidently i have a lot of company in being "wrong".

e.g. http://musr.physics.ubc.ca/~jess/p200/emc2/node11.html :

... Thus, even though light has no REST MASS (because it can never be at rest!), it does have an effective mass which (it turns out) has all the properties one expects from MASS - in particular, it has weight in a gravitational field [photons can "fall''] and exerts a gravitational attraction of its own on other masses. The classic Gedankenexperiment on this topic is one in which the net mass of a closed box with mirrored sides increases if it is filled with light bouncing back and forth off the mirrors!

or just google "mass of light" and ignore the music/worship hits.

my 30 year old physics text says "Although a photon has no rest mass, it nevertheless behaves as though it possesses inertial mass

$$m = \frac{h \nu}{c^2}$$ "

and later goes on to equate the inertial mass to gravitational mass and obtains a result for gravitational red shift. it did not use GR nor is it as accurate as if it had used GR (the gravitational radius for creating a black hole is shown to be half of the Schwarzschild radius, so it is physics that is farther down the slope of revelation of truth than where GR is) but there is a physical concept of red shift without GR, and that requires a concept of the mass of a photon. but, of course, it's not rest mass (which must be zero for a photon).

i don't know what physics prof told you light has no mass, but either he/she screwed up or between the two of you the terms "rest mass" and "mass" in general got a little bit confused. because $p = m v$ anything with a non-zero momentum must have a non-zero mass.

 

[robphy]

As a postscript to franznietzsche's first post in this thread...

In my opinion, this spacetime diagram of the region near a black hole https://www.physicsforums.com/showpost.php?p=546921&postcount=12
is very useful in partly explaining what is going on near a black hole. (One may have to follow up with words of explanation and maybe a calculation... but the diagram does "say" a lot.)

The key is the "tipping over of the light cones".

 

[diracbracket]

Does a photon have a mass? Yes it does.

Energy and mass are the same thing, which is the reason physicists coined the term mass-energy. Historically "mass" has been the name given to an amount of mass-energy when it is in the form of matter, i.e. atoms. In this case it is measured in kg. "Energy" has been the name given to mass-energy in forms other than matter. In this case it is measured in Joules.

The formula

$$E = m c^2$$

can be regarded as the formula for converting between the two types of units.

Mass-energy in Joules = mass-energy in kg x [an arbitrary constant]

It is really no more mysterious than the formula for converting between inches and centimeters. The constant of proportionality connecting E and m is arbitrary because it depends the definitions of the meter and the second, which are historical accidents having nothing to do with each other, just as it is in the case of inches and centimeters.

What this means is that, if you think a photon has energy, then logically you must concede that a photon can rightly be described as having mass.

 

[franznietzsche]

that is true, but the concept of photons and the mass (or "momentum" if you prefer) thereof comes before that of GR.

you see, even though Newtonian gravitation and mechanics is "wrong", we still seem to use these concepts daily to design and build bridges and rockets. when thinking in that conceptual frame, rather than that, standing on the Earth's surface, i am accelerating "upward" in this curved space (due to the force exerted on my feet by the ground), we like to say that the force pushing up on my feet is equal to and opposite of the force of gravity pulling me toward the center of mass of the earth. it's not correct, but we treat it as if it were.

we know from the EP that if i was instead standing in a spaceship accelerating at 9.8 m/s², i would experience an environment indistinguishable from standing on the earth. and we know that a truly straight beam of light would appear to me curved downward because of my acceleration and if, instead, i was standing on the surface of the earth, i would experience the same thing, including the bending of the beam of light. if, in the second (earthbound) case, i would say "gravity is pulling down on me" and you find that acceptable, then you would have to also accept the same reason for the ostensible diversion of the beam of light

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so, how does a photon have momentum without mass? what is the definition of momentum of any particle?

evidently i have a lot of company in being "wrong".

e.g. http://musr.physics.ubc.ca/~jess/p200/emc2/node11.html :



or just google "mass of light" and ignore the music/worship hits.

my 30 year old physics text says "Although a photon has no rest mass, it nevertheless behaves as though it possesses inertial mass

$$m = \frac{h \nu}{c^2}$$ "

and later goes on to equate the inertial mass to gravitational mass and obtains a result for gravitational red shift. it did not use GR nor is it as accurate as if it had used GR (the gravitational radius for creating a black hole is shown to be half of the Schwarzschild radius, so it is physics that is farther down the slope of revelation of truth than where GR is) but there is a physical concept of red shift without GR, and that requires a concept of the mass of a photon. but, of course, it's not rest mass (which must be zero for a photon).

i don't know what physics prof told you light has no mass, but either he/she screwed up or between the two of you the terms "rest mass" and "mass" in general got a little bit confused. because $p = m v$ anything with a non-zero momentum must have a non-zero mass.

No, no no.

You CAN treat light as having an effective mass. You will get the same numerical results. That does not make it right. I'm talking about the nature of light. What light is. It does not have mass.

Your link does not support your case, and your comment about having lots of people agree with you is inane. Reality is non democractic.

Light does NOT have mass. You can treat it as if it had an effective mass, and get the same answers, but that is not the same as if it were matter with mass.

If you insist on using an incorrect conceptual view as an equivalent mathematical one, fine. It doesn't really matter. What does matter is you using incorrect conceptual explanations of why light gets trapped in a black hole.

No, you cannot use Newtonian mechanics here. PERIOD. The phenomenon of a black hole are very relatvistic. Explaining gravity as a force in this case is wrong. Explaining it as light having a mass to be acted on is wrong, because there is no force to act on any mass.

No, non-zero momentum does not mean non-zero mass. This has nothing to do with 'rest mass' versus 'mass'.

Your 30-year old text says 'light behaves as if it posses an inertial mass' that is not the same thing as having one. Light also sometimes behaves like wave. Othertimes it behaves like a particle. But it isn't really either of those.

You are unable to separate the model of pretending an 'equivalent mass' is real, and the actual reality. Light has no mass. You can pretend it has a mass dependent on its energy, but that is not the same thing as having mass.

 

[pervect]

This is a somewhat boring but frequently posted topic, well covered in the sci.physics.faq http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html

We see here a few posters who maintain contrary views to those accepted by the scientific community, they get corrected (mostly gently, sometimes with a little bit of non-gentlness) by those posters who have studied the subject, but the posters with contrary views don't listen.

You can tell this is happening (and that any controversy is a few isolated individuals vs everyone else) because all the science advisors as well as the offical FAQ have basically the same viewpoint.

If someone learns something, the thread might be moderatly worthwhile, but generally speaking the people with the contrary views don't listen, (you'd think they'd learn - no such chance) while the people who have done some reading on the topic always knew better.

 

[rbj]

You can tell this is happening (and that any controversy is a few isolated individuals vs everyone else) because all the science advisors as well as the offical FAQ have basically the same viewpoint.

i don't know if you include me as one of the "science advisors". i do basically agree with the FAQ, but i have semantic differences which might come from the fact that I'm just now starting my 6th decade on this planet. back in my day, we were taught to differentiate "rest mass" from the term "mass". nowadays that doesn't seem to be the case. from the FAQ:

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.

i like the semantics we learned about this 30 years ago.

 

[pervect]

i don't know if you include me as one of the "science advisors".

Sure you are -- look right under "recognitions".

i do basically agree with the FAQ, but i have semantic differences which might come from the fact that I'm just now starting my 6th decade on this planet. back in my day, we were taught to differentiate "rest mass" from the term "mass". nowadays that doesn't seem to be the case. from the FAQ:

i like the semantics we learned about this 30 years ago.

I think the single most important point to be made is that there *are* two different defintions of mass, and that one has to be careful when reading and writing as to the difference.

The typical "stupid" statement I see, time and time again is "light has mass". There are no qualfiiers here, no discussions of different sorts of mass, no references to the literature, just a sort of dumb repetivenes, as if a person can say it 1,000,000 times and make it true by sheer repitition.

Frankly I'm a bit tired of it, in large part because I really do think the majority of people making these statements ("light has mass") are not making them in ignorance, but they actually know better.

 

[rbj]

Sure you are -- look right under "recognitions".

yeah, but I'm the one saying "light has mass" (but i had been careful to qualify it, from the beginning).

I think the single most important point to be made is that there *are* two different defintions of mass, and that one has to be careful when reading and writing as to the difference.

The typical "stupid" statement I see, time and time again is "light has mass". There are no qualfiiers here, no discussions of different sorts of mass, no references to the literature, just a sort of dumb repetivenes, as if a person can say it 1,000,000 times and make it true by sheer repitition.

Frankly I'm a bit tired of it, in large part because I really do think the majority of people making these statements ("light has mass") are not making them in ignorance, but they actually know better.

is it not equally "stupid" to make the contrary statement "light has no mass" without qualification and to just repeat it time and again with no support?

Your link does not support your case, and your comment about having lots of people agree with you is inane. Reality is non democractic.

oh, i see. reality is whatever you say it is.

Light does NOT have mass. You can treat it as if it had an effective mass, and get the same answers, but that is not the same as if it were matter with mass.

where did i say that light was matter? matter has nonzero rest mass.

If you insist on using an incorrect conceptual view as an equivalent mathematical one, fine. It doesn't really matter. What does matter is you using incorrect conceptual explanations of why light gets trapped in a black hole.

it's not the most accurate conceptual model, but it puts it in the ball park (and you can find it in some college physics books - there's a lot of physics before someone gets to GR).

No, you cannot use Newtonian mechanics here. PERIOD.

such a persuasive argument!

The phenomenon of a black hole are very relatvistic. Explaining gravity as a force in this case is wrong. Explaining it as light having a mass to be acted on is wrong, because there is no force to act on any mass.

listen, Newtonian gravitation & mechanics are blurry revelations of nature that approximates the truth in conditions of reasonably flat spacetime (which a black hole is not) and slow speeds but you can still get a result that is in the ballpark with it and the concept of conservation of energy. but the result is off by a factor of two (which is why GR is a necessary refinement). so the Newtonian theory does not fully explain it, but there is a concept there that is useful. nonetheless, i was not pushing it so much for the case of the black hole, but more for the general case of the diverting of a beam of light (as we see it in Euclidian 3-space) for someone standing on a planet.

No, non-zero momentum does not mean non-zero mass. This has nothing to do with 'rest mass' versus 'mass'.

and this, my obstinant 18 year old, is the smoking pistol. this is the proof that you really do not know what you are talking about. you are merely repeating by rote what you have read or think you have read.

You are unable to separate the model of pretending an 'equivalent mass' is real, and the actual reality. Light has no mass. You can pretend it has a mass dependent on its energy, but that is not the same thing as having mass.

you need to learn the difference between rest mass and mass in general. you can repeat time and again that light has no mass, even though it is quite well established that light is affected by gravitation and can even generate its own gravitational field (but it's very weak). one last thing, you might want to look up what NIST is going to do real soon in redefining the kilogram (which is a measure of what?):
http://www.wired.com/news/technology/0,1282,66727,00.html
http://www.physorg.com/news3178.html
http://www.nist.gov/public_affairs/newsfromnist_redef_kilogram.htm
http://www.extra.rdg.ac.uk/news/details.asp?ID=479
http://www.iop.org/EJ/article/0026-1394/36/1/11/me9111.pdf

The kilogram is the mass of a body at rest whose equivalent energy equals the energy of a collection of photons whose frequencies sum to 135639274 x 10⁴² Hz.

this redefinition of the kg will have the effect of defining Planck's Constant in a similar manner that the redefinition of the meter in 1983 had in defining the speed of light.

now what would happen if you put that collection of photons in a hypothetical mirrored box of negligible mass, and put that box on a scale? would the scale read zero?

 

[pervect]

yeah, but I'm the one saying "light has mass" (but i had been careful to qualify it, from the beginning).

That's really all that's necessary, some indication of what sort of mass one is taliking about, and a bit of care.

Though I will put in a good word for coordinate independence now and then, and hope it doesn't fall on deaf ears.

is it not equally "stupid" to make the contrary statement "light has no mass" without qualification and to just repeat it time and again with no support?

Sure, that's why I always post a link to the FAQ. Which goes into all the details about relativistic mass, and invariant mass, and modern usage, etc. etc. etc.

After only 20-30 postings of said link for the 20-30 times this "question" comes up, though, I get just a tiny bit tired of the "question".

Which is (as I have pointed out) generally NOT even phrased as a question (just someone making a statement - and the sort of sloppy statement that could potentially mislead people, taking the most charitable view of such statements).

You don't seem to have any serious argument with the FAQ, so I'm not quite sure what you are arguing about.