Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Craftybutterfly on 31/03/2015 03:25:11
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I've been reading "the edge of space" and I am having some trouble wrapping my brain around the details of the event horizon.
1. how fast does it grow? Is that growth based on the mass already inside the black hole or does it only grow when new matter gets sucked in.
2. By what means is light unable to escape a black hole? Does light have mass and if so then does it have mass as a particle, a wave, or both? does time/space continue to warp and stretch inside the black hole growing at a rate faster that light travels?
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1. https://en.wikipedia.org/wiki/Schwarzschild_radius ...That's what defines it basically.
2. light doesn't have a mass, but it has a energy that you mathematically (and experimentally) can convert into mass, just as we can convert mass into energy. Actually it's about geodesics when it comes to light, which are the paths taken by everything I know of, from light to matter, except possibly SpaceTime itself (when thinking of gravitational waves). Because, as I see it at least, those 'gravity waves' should be a property of SpaceTime itself, if found.
you can try this one too.
http://www.askamathematician.com/2014/05/q-if-nothing-can-escape-a-black-holes-gravity-then-how-does-the-gravity-itself-escape/
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And yes, as it keeps its gravity constant even as a black hole, as long as you're not too close to that event horizon, meaning that the Earths gravity would still be the same if it was 'compressed' into a black hole, and our moon should be in the same orbit as always. then to 'grow' you would need matter passing that event horizon for it to grow even more. Everything passing that event horizon will be gone to us outside it but we should notice a gravitational change.
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1. how fast does [a black hole] grow?
The radius of a black hole is proportional to its mass.
If the mass stays the same, the radius stays the same (no growth).
If matter and/or energy falls into a black hole, it's mass grows, and its radius grows.
2. By what means is light unable to escape a black hole?
Similar to the Doppler shift (imagine a fire engine siren passing you on the street), there is a gravitational red shift (http://=http://en.wikipedia.org/wiki/Gravitational_redshift) in the vicinity of any mass, as predicted by Einstein.
A photon released outside the event horizon of a black hole can escape from the black hole, but after escape, it's frequency is lower (red-shifted), and its energy is lower (the energy of a photon is proportional to frequency).
The closer to the event horizon you release a photon, the more the energy is red-shifted. If this trend continued, a photon released at the event horizon would have its energy red-shifted away to nothing.
does time/space continue to warp and stretch inside the black hole?
There are various theories about what goes on inside a black hole. But current theories are pretty unanimous in saying that observers outside the black hole can only find out a very limited amount about what is inside the event horizon. For example, the black hole's Mass, Electric Charge, and Angular Momentum (http://en.wikipedia.org/wiki/No-hair_theorem) (how fast it spins).
The best of our current theories break down at the event horizon - all we can say is what we expect as we approach the event horizon.
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I've been reading "the edge of space" and I am having some trouble wrapping my brain around the details of the event horizon.
Welcome to our little forum, CB! :)
Let's see what we can do to help answer your questions.
1. how fast does it grow? Is that growth based on the mass already inside the black hole or does it only grow when new matter gets sucked in.
That depends on how fast matter enters the event horizon. Anything that has mass/energy will add to the mass of the black hole and thus to the size of the event horizon.
2. By what means is light unable to escape a black hole?
Light has mass and since anything that has mass is attracted to a gravitating body it follows that light also is attracted and thus falls in.
Does light have mass ...
There are various kinds of mass. They're defined as follows:
1) Inertial mass - The quantity that gives matter momentum. See definition on one of my web pages at
http://home.comcast.net/~peter.m.brown/sr/inertial_mass.htm
2) Passive gravitational mass - The quantity on which gravity acts.
3) Active gravitational mass - The quantity that generates a gravitational field.
The 3-momentum p of a point object whose inertial mass is m is p = mv where v is the particles 3-velocity.
There are also different uses of the term mass besides that above. They are
1) "mass" = Inertial Mass aka Relativistic Mass
2) "mass" = Proper Mass aka Invariant mass - Magnitude of the particle's 4-momentum.
For more on invariant mass please see my web page at: http://home.comcast.net/~peter.m.brown/sr/invariant_mass.htm
A photon has zero proper mass but non-zero inertial mass.
...and if so then does it have mass as a particle, a wave, or both?
It's not one or the other. A particle and a wave can both have mass. For example: an electromagnetic wave has momentum and as such it has mass by virtue of its momentum.
.. does time/space continue to warp and stretch inside the black hole growing at a rate faster that light travels?
No.
2. light doesn't have a mass, but it has a energy that you mathematically (and experimentally) can convert into mass, just as we can convert mass into energy.
That is incorrect. Please see The statement "Light has mass" by Alan Guth at
http://www.newenglandphysics.org/Science_Literature/Journal_Articles/DSC_0003.MOV
but it has a energy that you mathematically (and experimentally) can convert into mass, just as we can convert mass into energy.
That, too, is incorrect. It's a misconception to assert that mass can be converted into energy. See
Does nature convert mass into energy? by Ralph Baierlein, Am. J. Phys. 75(4), April 2007
http://home.comcast.net/~peter.m.brown/ref/baierlein.pdf
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1. how fast does [a black hole] grow?
The radius of a black hole is proportional to its mass.
If the mass stays the same, the radius stays the same (no growth).
If matter and/or energy falls into a black hole, it's mass grows, and its radius grows.
2. By what means is light unable to escape a black hole?
Similar to the Doppler shift (imagine a fire engine siren passing you on the street), there is a gravitational red shift (http://=http://en.wikipedia.org/wiki/Gravitational_redshift) in the vicinity of any mass, as predicted by Einstein.
A photon released outside the event horizon of a black hole can escape from the black hole, but after escape, it's frequency is lower (red-shifted), and its energy is lower (the energy of a photon is proportional to frequency).
The closer to the event horizon you release a photon, the more the energy is red-shifted. If this trend continued, a photon released at the event horizon would have its energy red-shifted away to nothing.
does time/space continue to warp and stretch inside the black hole?
There are various theories about what goes on inside a black hole. But current theories are pretty unanimous in saying that observers outside the black hole can only find out a very limited amount about what is inside the event horizon. For example, the black hole's Mass, Electric Charge, and Angular Momentum (http://en.wikipedia.org/wiki/No-hair_theorem) (how fast it spins).
The best of our current theories break down at the event horizon - all we can say is what we expect as we approach the event horizon.
Hmmm.... reminds me of a thread .... "Would the photon lose all its energy at infinity"
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I don't think it's wrong Pete? As far as I know you won't find a (proper, or rest) mass for light, unless you use a equivalence to mass. Then again, tried to download your link but it was somewhat too big for my taste? Thought it would be normal size there.
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Ok, 'mov' format is it? You wouldn't happen to have a *.pdf discussing it?
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As far as I know you won't find a (proper, or rest) mass for light, unless you use a equivalence to mass.
If you're referring to E = mc2 then while you can use that, and Alan actually did, you don't really need to. All radiation has momentum. E.g. a beam of radiation directed/collimated entirely in the +x-direction then the momentum, p, and is related to the energy in the light wave by E = ps. For proof please see:
http://home.comcast.net/~peter.m.brown/em/poyntings_theorem.htm
http://home.comcast.net/~peter.m.brown/em/momentum_of_radiation.htm
Since momentum is defined as p = mv and for light v = c we have p = mc or m = p/c. That is the mass of an amount of light whose momentum is p. You can actually find this defined in many relativity texts such as the ones listed in this page: http://home.comcast.net/~peter.m.brown/ref/relativistic_mass.htm
Notice that if m = p/c and E = pc then p = E/c and therefore m = (E/c)/c = E/mc2. Does that look familiar to you? :)
Einstein himself derived an expression for the mass density of light in the following article:
The Principle of Conservation of the Center of Gravity and the Inertia of Energy, Albert Einstein, Annalen der Physik, 20 (1906): 626-633.
I placed a clean version of the derivation with a nice set of diagrams at:
http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm
Ok, 'mov' format is it? You wouldn't happen to have a *.pdf discussing it?
Just let me know what you want to know about it and I'll explain it to you. Or read the pages above
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Thanks for the clarifications everyone, I like this website a lot. [:D]
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Have no problem with light having a momentum Pete, neither with having a energy. It's the idea of rest mass I'm wondering about there. Seems we might mean the same thing though, which is why I asked if you happened to have a pdf presenting Alan Guth's definition of a mass.
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when it comes to the definition of energy able to generate stuff defined as having a rest mass though? Seen other definitions there, not mine solely. https://en.wikipedia.org/wiki/Matter_creation What I was thinking of there was particle accelerators as the LHC.
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Have no problem with light having a momentum Pete, neither with having a energy. It's the idea of rest mass I'm wondering about there.
When someone speaks of the rest mass m0 of light they have something very specific in mind. Suppose you have a particle which is moving in the inertial frame of reference S. Let E represent the total energy and K the kinetic energy of the particle, m0 represent the rest mass and E0 = m0c2 the rest energy. Then
E = K + E0
If the particle is a photon then its energy is entirely kinetic energy. Therefore E = K and which implies that E0 = 0. For this to be true m0 = 0. That is one meaning of "the rest mass of a photon is zer0." There's another one having to do with the magnitude of the 4-momentum's but it's quite similar and there's nothing to be gained by describing it. However we recognize that it's not logical to call something rest mass when it can never be at rest. The better name for this is proper mass. That's the one I use.
Seems we might mean the same thing though, which is why I asked if you happened to have a pdf presenting Alan Guth's definition of a mass.
No. Alan mostly teaches more advanced courses which means that in whatever he's writing he is assuming that the reader knows what mass is. Typically when an author uses the term its clear from the context what is meant by "mass."
When it comes to the definition of mass he, and others in the physics community, mean the ratio m = p/v. To see examples of relativists who use mass this way please see the following: http://home.comcast.net/~peter.m.brown/ref/relativistic_mass.htm
The relativists in that page are quite famous. They include
Wolfgang Rindler
Ray D'Inverno
A. P. French
Misner, Thorne and Wheeler (MTW)
John A. Peacock
Bernard F. Schutz
Foster & Nightingale
..when it comes to the definition of energy able to generate stuff defined as having a rest mass though?...
I'm sorry but that sentence makes no sense to me. Please restate it but this time make it clearer for me. Okay? Thanks buddy! :)
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Let E represent the total energy and K the kinetic energy of the particle, m0 represent the rest energy E0. Then E0 = m0c2. Then E = K + E0
The whole quote makes sense, but I’m not clear about the bit I underlined.
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Let E represent the total energy and K the kinetic energy of the particle, m0 represent the rest energy E0. Then E0 = m0c2. Then E = K + E0
The whole quote makes sense, but I’m not clear about the bit I underlined.
mo represents the rest energy by the equation E0 = m0c2 unless Pete corrects me on that.
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Thanks Jeffrey, That makes sense. I think I was thrown by the punctuation.
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Let E represent the total energy and K the kinetic energy of the particle, m0 represent the rest energy E0. Then E0 = m0c2. Then E = K + E0
The whole quote makes sense, but I’m not clear about the bit I underlined.
I fixed it. Now it reads
Let E represent the total energy and K the kinetic energy of the particle, m0 represent the rest mass and E0 = m0c2 the rest energy.
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I don't know, still get stuck on your definition. "Rest mass is a somewhat obsolete term for what is referred to more commonly today as the invariant mass, proper mass or simply just mass in relativistic physics. http://physics.stackexchange.com/questions/8610/whats-the-difference-between-the-five-masses-inertial-mass-gravitational-mass
Your definition is "If the particle is a photon then its energy is entirely kinetic energy. Therefore E = K and which implies that E0 = 0. For this to be true m0 = 0. That is one meaning of "the rest mass of a photon is zer0." There's another one having to do with the magnitude of the 4-momentum's but it's quite similar and there's nothing to be gained by describing it.
However we recognize that it's not logical to call something rest mass when it can never be at rest. The better name for this is proper mass. That's the one I use."
I think I can see the point you want to make though, that everything is (and has) a 'mass', according to the definition you use, if I now got your definition right. That doesn't mean that light has a rest mass though, and your definition of a proper mass is new to me.