[College - Space-Time Physics] Can't solve this paradox

[Ratchetlombax]

Oh, crud.
I got slammed with a huge homework assignment and can't do half of it.
I have to solve a scientific paradox related to black holes.
In a nutshell:
Photons are massless gauge bosons that convey electromagnetism, or light. Inside a hypothetical black hole's event horizon is a realm where the escape velocity is greater than the speed of light.
Light that travels within one will be pulled in, because it travels slower than the escape velocity. But light is massless; it is not affected by gravity. Why, then, do black holes suck in light?

Calling all theoretical physicists!
I'm not used to this kind of workload, because most (except my friend Ben) eighth graders don't take STP. Help, please!

[igotrhythm]

Re: [Master's Degree Level--Space-Time Physics] Can't solve this paradox

As much as I find it doubtful that a teenager is gunning for a master's degree, I'm going to give this a shot. *deep breath*

I think e=mc^2 might have something to do with it. Photons have energy, and thus, they have a rest mass equivalent, or the amount of mass their energy equates to under the theory of relativity. Basically, it's what the scale would register as the mass of a photon if only you could get one to stay still long enough. Thus, light (or more correctly, the photons that make up light) may not be as massless as you may assume.

Hope that helps. And if it turns out I'm full of BS, hey, it's 3 in the morning here right now, and it's been a while since I've had a physics class. -_-

[dag12]

Re: [Master's Degree Level--Space-Time Physics] Can't solve this paradox

Uh. If you're going for a master's degree, shouldn't a problem like this be incredibly simple for you?

I'm not even specialized in the field, and I (think I) can answer it... unless I'm missing something huge; if I am wrong, same reason as igotrhythm haha.

As far as my limited understanding goes, electromagnetic waves don't have any mass, so they do travel in a straight line.
The bending of light towards a black hole is because of the curvature of space-time, so light *technically* travels in a straight line in that particular geometry. [General Relativity (?)]

Someone correct me if I'm wrong, but that's what I think... note that I'm no specialist in this field. (sorry if I'm no help)

[Reach]

Re: [Master's Degree Level--Space-Time Physics] Can't solve this paradox

Well, you have to understand General Relativity to answer this question. It is a mistake to think that light is not affected by gravity because it lacks any real mass. It is simply not the case.

Mathematically, in General Relativity, a Black hole is a point in space that is incredibly curved (E.g: http://www.sfgate.com/blogs/images/s...ngularity1.jpg). Under all normal circumstances, light will take the shortest path between two points during travel. In flat, normal space, this is simply a straight line, but in highly curved space things become slightly more complicated. Light will still take the same path, but that path has become bent and distorted.

You see, space-time is normally flat, but can be disturbed by what we describe as the 'stress-energy tensor'. Basically, any concentration of energy in space causes some degree of distortion relative to flat space, and this distortion is proportional to the concentration of energy. In the case of a black hole, to make it as simple as possible to understand, the concentration at some point, which we call the singularity, has reached infinity, causing an infinitely large distortion in space.

In essence, a black hole really isn't 'sucking in' light - but rather, space within the event horizon can be described as every point in space being bent such that a straight line in any direction leads back into the black hole.

In summary, space is curving back in onto itself within a black hole.

[Ratchetlombax]

Re: [Master's Degree Level--Space-Time Physics] Can't solve this paradox

I just realized something...photons actually have a little mass, or a lot, depending on the energy they have. It's all relative to E=MC^2, and the huge amount of energy in a gamma ray would give a photon a respectable amount of "mass" and thus cause it to be affected by gravity.
Otherwise, like you say, it could just be traveling through bent space, causing an apparently straight line to look curved and vice versa. TY, all.
Edit: BTW, thanks, rhythm.

[makdaddy]

Re: [Master's Degree Level--Space-Time Physics] Can't solve this paradox

Interesting stuff, I've never wondered why light gets sucked into black holes, I just always took it as is, but I can see that it is quite fun to try to explain these things.

[Reach]

Re: [Master's Degree Level--Space-Time Physics] Can't solve this paradox

I just realized something...photons actually have a little mass, or a lot, depending on the energy they have. It's all relative to E=MC^2, and the huge amount of energy in a gamma ray would give a photon a respectable amount of "mass" and thus cause it to be affected by gravity.
Otherwise, like you say, it could just be traveling through bent space, causing an apparently straight line to look curved and vice versa. TY, all.
Edit: BTW, thanks, rhythm.

We have to be careful here though. Photons do NOT have any real mass. Mass and energy are different manifestations of the same thing, but they are not the same thing.

Photons just about always carry momentum though, so you want to describe them using E^2 = m^2c^4 + p^2c^2, not E=mc^2 (only applies to photons at rest), where m= 0.

It is quite crucial, at least with respect to General Relativity, that you recognize that photons are not effected by gravity because of their energy-mass equivalents, but because of gravitational fields themselves and how they distort the space-time fabric.

General Relativity is a theory that has withstood much testing, and as far as I know, no test has ever shown a photon to have mass.

[lord_carbo]

Re: [Master's Degree Level--Space-Time Physics] Can't solve this paradox

Photons don't have any mass.

Otherwise, like you say, it could just be traveling through bent space, causing an apparently straight line to look curved and vice versa. TY, all.

That's somewhat it. But I get the impression that you're still thinking in three-dimensional, Euclidean terms, and it simply "is," not "could just be."

[devonin]

Re: [University--Space-Time Physics] Can't solve this paradox

Okay, after some consultation, I'm downgrading your schooling level on that thread. Neither physicist I spoke to puts that question at being past a 2nd or 3rd year sort of level.

They also offered some insight into your issue:

This is the thing about that...

That sort of explanation about escape velocity is something that was cooked up so that people not completely familiar with relativity can understand it.

In actually, gravity distorts space and so in a black hole's event horizon, the gravity is so strong that every path one can take in that space leads back into the black hole
there isn't a path that leads out of the event horizon because of the warping of space itself in that region

[tha Guardians]

Re: [Master's Degree Level--Space-Time Physics] Can't solve this paradox

Mathematically, in General Relativity, a Black hole is a point in space that is incredibly curved (E.g: http://www.sfgate.com/blogs/images/s...ngularity1.jpg). Under all normal circumstances, light will take the shortest path between two points during travel. In flat, normal space, this is simply a straight line, but in highly curved space things become slightly more complicated. Light will still take the same path, but that path has become bent and distorted.

You see, space-time is normally flat, but can be disturbed by what we describe as the 'stress-energy tensor'. Basically, any concentration of energy in space causes some degree of distortion relative to flat space, and this distortion is proportional to the concentration of energy. In the case of a black hole, to make it as simple as possible to understand, the concentration at some point, which we call the singularity, has reached infinity, causing an infinitely large distortion in space.

You seem to know your stuff. Random question: is there any conclusive evidence that "black holes" exist on Earth? In the Bermuda Triangle, in a drop of water, or in your backyard? I know there have been many hypotheses including black holes on Earth, but to my knowledge there is no proof.

Also, do you believe that a black hole around Earth, or our solar system, distorts our perception of time and distance? (now don't get all philosophical :P)

[Reach]

Re: [Master's Degree Level--Space-Time Physics] Can't solve this paradox

You seem to know your stuff. Random question: is there any conclusive evidence that "black holes" exist on Earth? In the Bermuda Triangle, in a drop of water, or in your backyard? I know there have been many hypotheses including black holes on Earth, but to my knowledge there is no proof.

Also, do you believe that a black hole around Earth, or our solar system, distorts our perception of time and distance? (now don't get all philosophical :P)

Q1: Certainly not regular blacks holes. Black holes just don't spontaneously appear - they require incredibly large amounts of energy to form. From here, whether or not you would see any on Earth is going to depend on what model of physics you're looking at, but from a standard perspective, even Ultra High Energy Cosmic Radiation do not generate enough energy upon impact to create a black hole. It's simply not possible for them to exist here. However, assuming they could form, under non standard conditions, it would necessitate the existence of 'Hawking Radiation', which would mean these tiny black holes would evaporate instantaneously.

As such, the answer is no, not only is there no conclusive evidence, but it isn't possible.

#2: No

Highly distorted space-time caused by a black hole only really becomes a problem for objects around the black hole when you get very close to it (i.e. near the event horizon). Realistically, you would probably die upon approaching a black hole due to gamma radiation long before time and distance became seriously distorted for you.

It is important to note though, that if the black hole is large enough, it can generate astronomically large gravitational fields. We know that, for example, our galaxy is spinning around a super massive black hole.

[tha Guardians]

Re: [Master's Degree Level--Space-Time Physics] Can't solve this paradox

Q1: Certainly not regular blacks holes. Black holes just don't spontaneously appear - they require incredibly large amounts of energy to form. From here, whether or not you would see any on Earth is going to depend on what model of physics you're looking at, but from a standard perspective, even Ultra High Energy Cosmic Radiation do not generate enough energy upon impact to create a black hole. It's simply not possible for them to exist here. However, assuming they could form, under non standard conditions, it would necessitate the existence of 'Hawking Radiation', which would mean these tiny black holes would evaporate instantaneously.

As such, the answer is no, not only is there no conclusive evidence, but it isn't possible.

#2: No

Highly distorted space-time caused by a black hole only really becomes a problem for objects around the black hole when you get very close to it (i.e. near the event horizon). Realistically, you would probably die upon approaching a black hole due to gamma radiation long before time and distance became seriously distorted for you.

It is important to note though, that if the black hole is large enough, it can generate astronomically large gravitational fields. We know that, for example, our galaxy is spinning around a super massive black hole.

Well I've seen more people trying to disprove micro black holes on Earth than proving them, and the theory that they'd evaporate is usually the counter.

The reason I asked the second question is because some scientists have hypothesized that maybe the universe isn't infinitely expanding, it just seems that way because of minor distortion caused by a black hole near us.

Thanks for the clarity.

[Ratchetlombax]

Re: [College - Space-Time Physics] Can't solve this paradox

Er...I turned in my homework a while ago, and I got an AAA (jk, just an A-).

Now I have a slightly harder problem to deal with, relative to the black hole singularity theory I presented to my class yesterday.

If the infinitesimal singularity at the beginning of our universe was in fact a black hole, how would one rephrase/paraphrase the Information Paradox as to explain the spontaneous symmetry-breaking, between Gravity and the Electronuclear force, at one Planck-time or so after the Big Bang?
Now I'm stuck for sure. Even Ben can't help me on this one, he says it's impossible to tell.
My theory has anomalies, and my theory's dead till I resolve them.
Edit: BTW, devonin, I know the question itself is in fact college level. However, the class I'm in is actually one in which my middle-school science teacher is enrolled to obtain his Master's. This is the lightest part of my workload; don't get me started on Differential Equations.

[Reach]

Re: [College - Space-Time Physics] Can't solve this paradox

If the infinitesimal singularity at the beginning of our universe was in fact a black hole, how would one rephrase/paraphrase the Information Paradox as to explain the spontaneous symmetry-breaking, between Gravity and the Electronuclear force, at one Planck-time or so after the Big Bang?

I'm not sure you can answer this, as the Information Paradox could be unrelated to symmetry breaking in the early universe.

You can solve the Information Paradox with respect to black holes as a non paradox by having information leave our universe and enter some other space beyond our horizon.

From there, if you assume the newest data on Inflation Theory is correct, Inflation in a Multiverse of 'bubble' universes explains symmetry breaking nicely.

[Sol_Solis]

Re: [College - Space-Time Physics] Can't solve this paradox

Oh, crud.
I got slammed with a huge homework assignment and can't do half of it.
I have to solve a scientific paradox related to black holes.
In a nutshell:
Photons are massless gauge bosons that convey electromagnetism, or light. Inside a hypothetical black hole's event horizon is a realm where the escape velocity is greater than the speed of light.
Light that travels within one will be pulled in, because it travels slower than the escape velocity. But light is massless; it is not affected by gravity. Why, then, do black holes suck in light?

Calling all theoretical physicists!
I'm not used to this kind of workload, because most (except my friend Ben) eighth graders don't take STP. Help, please!

Hey! Actually,

http://hubblesite.org/explore_astronomy/black_holes/

What I learned: the gravity of a black hole's pull becomes so strong that it collapses on itself from the prior stage of the star itself. The light curves into it because of the gravitational pull, so the black hole becomes more dynamic in that they do more things with matter around them instead of blazing and fading away.