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Can we test for a singularity of a black hole using Hawking Radiation?(Speculation)


Raider5678

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Hawking radiation derives energy from the black hole(to put it simply).

Would we be able to test for the existence of a singularity inside of a black hole by looking at How powerful the Hawking Radiation is at the Event Horizon?

I was curious because if a one-dimensional point of infinite density emits Hawking Radiation differently then a given amount of mass at the center of a black hole that has volume due to the distance required for Hawking radiation to "travel?" from the "surface" of the mass to the event horizon.

If I'm right about what I just said above(I'm probably not. Someone correct me), then this would be how we could test it:

Larger black holes compared to smaller black holes, if they had a singularity, the Hawking radiation would in part be due to the distance from the singularity to the event horizon.

Larger black holes compared to smaller black holes, if they didn't have a singularity, the Hawking radiation would in part be due to the distance to the event horizon from the surface of the mass in the middle.

 

This could, in turn, be measured by the energy of the Hawking Radiation, which would be more powerful for large black holes and weaker for smaller black holes because of the distance required to travel. The energy of Hawking radiation for black holes with a singularity in comparison with size would be linear as the distance would increase solely between the distance of the event horizon and the singularity.

If there wasn't a singularity, the graph would be curved because the distance between the black hole and the surface area of the mass in the middle would not be linear, as the amount of mass required to increase the volume of a sphere doesn't linearly correspond with the surface area. Surface area to volume of a sphere:

image.png.66ac83e1fc146237102837f6c100dd16.png

 

 

I'm pretty certain I just have a flawed understanding of how Hawking Radiation works, so just let me know.

Edited by Raider5678
I said "where the hawking radiation Originates" and I meant to say "How powerful the hawking radiation is"
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17 minutes ago, Raider5678 said:

Would we be able to test for the existence of a singularity inside of a black hole by looking at where the Hawking Radiation originates at the Event Horizon?

No, because everything we know about a black hole is "available" at the horizon. We can't know anything about the internal structure or mass distribution.

And in the case of Hawking radiation that arises is an effect of the existence of the event horizon, not the singularity. It is created immediately outside the event horizon, which is why it can escape the black hole.

20 minutes ago, Raider5678 said:

This could, in turn, be measured by the energy of the Hawking Radiation, which would be more powerful for large black holes and weaker for smaller black holes because of the distance required to travel.

Perhaps surprisingly, the radiated power and temperature of Hawking radiation is inversely proportional to mass (temperature goes as 1/M and radiated power as 1/M2).

If you want to play around with the properties of different sized black holes, there is a neat interactive calculator here: http://xaonon.dyndns.org/hawking/ You can plug in any parameter (mass, radius, temperature, etc) and it will calculate all the others for you.

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3 minutes ago, Strange said:

It is created immediately outside the event horizon, which is why it can escape the black hole.

Wait, doesn't Hawking radiation escape a black hole though? I thought that's how they lost energy over time?

3 minutes ago, Strange said:

If you want to play around with the properties of different sized black holes, there is a neat interactive calculator here: http://xaonon.dyndns.org/hawking/ You can plug in any parameter (mass, radius, temperature, etc) and it will calculate all the others for you.

Alright, thank you for your answer.

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3 minutes ago, Raider5678 said:

Wait, doesn't Hawking radiation escape a black hole though? I thought that's how they lost energy over time?

The usual analogy (*) is that there is a sea of virtual particles in the space outside the event horizon (as there is everywhere). Occasionally, one of the pair will be pulled into the event horizon and the other will escape. Normally, virtual parties appear and disappear immediately so there is zero net energy. In the case of Hawking radiation, there needs to be a source of energy to convert the two virtual particles into "real" particles so they can be separated. This requires energy equivalent to the total mass of the two particles. This energy comes from the gravitational field of the black hole (when it pulls the particles apart). One of the particles falls into the black hole, returning half the energy. The other one escapes. So the black hole loses the energy of one particle. This happens more if space-time around the event horizon is more extremely curved and so the amount of radiation produced is greater.

 

(*) The analogy is from Hawking himself. But I have seen others dispute how well it matches what the mathematics describes (the math is way over my head) - the trouble is they end up with a non-mathematical explanation that is pretty incomprehensible! 

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I think it would be better to try to test for what is in a black hole by just using antimatter and making it lose enough mass in order to show a naked singularity.  I still haven't gotten anyone to tell me why it is always the negative particle that ends up going into the black hole, but I think Hawking retracted his theory before he died anyways.  Then the amount of particle pairs is only about one pair per cubic meter, so they would have trouble interacting with the black hole to even begin with.  Then Hawking did claim the theory became more inaccurate at smaller scales, but he never seemed to mention that.  It seems like it would be a good idea for the LHC to keep a canister of antimatter to shoot at a black hole, just in case someone decides to really crank it one day anyways rather they are testing for them or not.  

Edited by Conjurer
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2 hours ago, Conjurer said:

I think it would be better to try to test for what is in a black hole by just using antimatter and making it lose enough mass in order to show a naked singularity. 

Why do you think it would cause it to lose mass? Anything that falls into the black hole adds to its mass. 

2 hours ago, Conjurer said:

I still haven't gotten anyone to tell me why it is always the negative particle that ends up going into the black hole

It doesn’t matter which particle falls in. In either case, the black hole has provided the energy to create a pair of particles and then gets half the energy back and loses half of it. 

2 hours ago, Conjurer said:

I think Hawking retracted his theory before he died

That would have been big news. So I am assuming it didn’t happen. 

 

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4 hours ago, Conjurer said:

 I still haven't gotten anyone to tell me why it is always the negative particle that ends up going into the black hole, but I think Hawking retracted his theory before he died anyways.  

It needn't be......The particle that escapes becomes real, and to conserve the law of conservation of energy and matter, the particle falling in assumes negative status and subtracts from the BH's mass. I am open to correction on that interpretation, but it was explained to me that way.

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3 minutes ago, beecee said:

It needn't be......The particle that escapes becomes real, and to conserve the law of conservation of energy and matter, the particle falling in assumes negative status and subtracts from the BH's mass. I am open to correction on that interpretation, but it was explained to me that way.

I would say it is the other way round. :) 

But remember this is just an analogy. One way we can see this is not a very accurate analogy is the fact that someone free falling into a black hole would not observe any Hawking radiation. A more accurate description involves the division of the vacuum energy into positive and negative components and how these differ for an observer near the black hole compared to one at an infinite distance. (Or something like that.)

I have seen another interpretation of Hawking radiation (and I'm not sure if this is generally accepted or not) where it is radiation released when the black hole formed and escapes later (and cooler) because of the time dilation near the event horizon.

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10 hours ago, Strange said:

Why do you think it would cause it to lose mass? Anything that falls into the black hole adds to its mass.

 

I think it would lose mass, because the collision of matter and antimatter would convert whatever mass there is inside into energy.  Then energy has little to no mass.  That is why the theory says that black holes would evaporate to begin with.

 

10 hours ago, Strange said:

It doesn’t matter which particle falls in. In either case, the black hole has provided the energy to create a pair of particles and then gets half the energy back and loses half of it. 

The particle pairs are not generated from the energy of the black hole.  The are freely created particle pairs that are created and annihilated with each other everywhere in space.  The event horizon just creates the possibility for the situation where they do not annihilate each other which is a different situation for when the particles are created elsewhere.  These particle pairs have been discovered with the absence of black holes, since one has been created in the lab.  

 

10 hours ago, Strange said:

That would have been big news. So I am assuming it didn’t happen. 

 

I think Leonard Susskind finally conned him out of it with his theory from the idea of the holographic universe where he said that all the information would be stored on the surface of a black hole, so there was no need for theory since information wouldn't be lost from going inside of a black hole to begin with. 

Edited by Conjurer
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10 minutes ago, Conjurer said:

I think it would lose mass, because the collision of matter and antimatter would convert whatever mass there is inside into energy.  Then energy has little to no mass.  That is why the theory says that black holes would evaporate to begin with.

 

Energy  contributes just as much to the Black hole's gravity as matter.  The amount of Energy generated by the matter-antimatter collision has a mass equivalent equal to the mass of the matter-antimatter combination that created it, and is responsible for the same amount of gravity. 

Black hole evaporation has nothing to do with the mass to energy ratio.  I think you might be confusing this with the fact that in order to evaporate, loss to Hawking radiation must exceed mass gain from other sources.  So for example, even in a near perfect vacuum, energy in the form of the CMBR is bombarding the BH, this energy, in the form of photons, is taken in and adds to the mass of the BH( another example of energy adding to the effective mass of the BH).  If the Black hole is large enough, its own Hawking temp is lower than the CMBR temp, you have a net gain of energy and the BH grows.  In order to evaporate, the BH must be a least small enough for its Hawking temp to exceed the background temp of the universe.

10 minutes ago, Conjurer said:

The particle pairs are not generated from the energy of the black hole.  The are freely created particle pairs that are created and annihilated with each other everywhere in space.  The event horizon just creates the possibility for the situation where they do not annihilate each other which is a different situation for when the particles are created elsewhere.  These particle pairs have been discovered with the absence of black holes, since one has been created in the lab.  

I didn't say that the black hole causes the original particle pair creation.  But once the pair is separated by the event horizon, something has to make up for the sudden occurrence of a real particle outside of the event horizon. The BH is the available energy source to do this.

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8 hours ago, Strange said:

I would say it is the other way round. :) 

But remember this is just an analogy. One way we can see this is not a very accurate analogy is the fact that someone free falling into a black hole would not observe any Hawking radiation. A more accurate description involves the division of the vacuum energy into positive and negative components and how these differ for an observer near the black hole compared to one at an infinite distance. (Or something like that.)

I have seen another interpretation of Hawking radiation (and I'm not sure if this is generally accepted or not) where it is radiation released when the black hole formed and escapes later (and cooler) because of the time dilation near the event horizon.

 

On 11/3/2018 at 2:38 AM, Strange said:

(*) The analogy is from Hawking himself. But I have seen others dispute how well it matches what the mathematics describes (the math is way over my head) - the trouble is they end up with a non-mathematical explanation that is pretty incomprehensible! 

Interesting what you say....I actually found Hawking Radiation a difficult scenario to contemplate many years ago. But gradually realised that while even today, we have yet to actually validate any Hawking Radiation, it is logically  mathematically consistent and makes sense.

here is a simplified explanation and other consequences of Hawking Radiation.

https://www.vox.com/science-and-health/2018/3/14/17119320/stephen-hawking-hawking-radiation-explained

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19 hours ago, beecee said:

It needn't be......The particle that escapes becomes real, and to conserve the law of conservation of energy and matter, the particle falling in assumes negative status and subtracts from the BH's mass. I am open to correction on that interpretation, but it was explained to me that way.

It kind of makes the law of conservation sound like some type of mechanism for an additional force of nature.  Sometimes, I wonder if Hawking was too big of a fan of conservation laws.

11 hours ago, Janus said:

Energy  contributes just as much to the Black hole's gravity as matter.  The amount of Energy generated by the matter-antimatter collision has a mass equivalent equal to the mass of the matter-antimatter combination that created it, and is responsible for the same amount of gravity. 

A matter antimatter collision result into pure energy or only photons.  Photons have no mass, so I have no idea where all of this is coming from.  It all seems like news to me; even though, Einstein did show that energy can exert a gravitational pull.  

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3 hours ago, Conjurer said:

A matter antimatter collision result into pure energy or only photons.  Photons have no mass, so I have no idea where all of this is coming from.  It all seems like news to me; even though, Einstein did show that energy can exert a gravitational pull.  

Mass and energy are equivalent, they both have a gravitational effect (in fact, the mass doesn't even appear in the equations of GR, just the energy). So when particles are converted to photons the energy of those photons has exactly the same gravitational effect as the mass of the particles.

14 hours ago, beecee said:

here is a simplified explanation and other consequences of Hawking Radiation.

https://www.vox.com/science-and-health/2018/3/14/17119320/stephen-hawking-hawking-radiation-explained

That's a very good explanation. It takes a slightly different view of the "energy bookkeeping" than the version I gave: because the net energy of the two new particles must be zero (because they arise from a quantum fluctuation) and the energy of the particle that escapes is positive (because it is a real particle), then the other particle must have negative energy to balance. That way of describing it also sounds like it could be closer to what the math says.

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9 hours ago, Conjurer said:

A matter antimatter collision result into pure energy or only photons.  Photons have no mass, so I have no idea where all of this is coming from.  It all seems like news to me; even though, Einstein did show that energy can exert a gravitational pull.  

Photons have zero rest mass.  But gravity doesn't rely on on rest mass alone but comes form the stress momentum tensor, of which rest mass is only one component.  Light has both energy and momentum and so also produces gravity.   When you convert matter to photons, you are removing the rest matter component, but increases in other components increase to compensate.  1 gram of matter could be converted into ~9e13 joules of photons, and those photons will have the same gravitational effect as the 1g of matter that created them.

If this is news to you, then it means you haven't studied the subject deeply enough.

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3 hours ago, Janus said:

If this is news to you, then it means you haven't studied the subject deeply enough.

It sounds like an argument against Hawking Radiation even working at all.  How could a black hole evaporate if the anti particle adds to the mass of a black hole?  According to what you are saying, the black hole should increase in mass due to Hawking Radiation.  I don't think Hawking radiation even considers the mass of the energy in a black hole.  

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5 minutes ago, Conjurer said:

It sounds like an argument against Hawking Radiation even working at all.  How could a black hole evaporate if the anti particle adds to the mass of a black hole?  According to what you are saying, the black hole should increase in mass due to Hawking Radiation.  

Because there are two particles created: one falls in and one escapes. The pair takes an amount of energy from the black hole and half of it is returned. Or read the explanation linked to by beech, which describes how you can treat the particle that falls in as having negative energy (which is matched by the positive energy of the escaping particle, so energy is conserved).

But note that these are just analogies; ie simplified descriptions of what happens. You cannot really use these as a way of properly understanding what happens. If you want to understand the detailed mechanism, you would need to have a solid grounding of QM, GR and how to apply Bogoliubov transformation (an isomorphism of either the canonical commutation relation algebra or canonical anticommutation relation algebra. This induces an autoequivalence on the respective representations).

Quote

I don't think Hawking radiation even considers the mass of the energy in a black hole. 

The power and temperature of Hawking radiation is inversely proportional to the mass of the black hole. And it reduces the mass of the black hole. Which results in higher temperature and radiated power, which reduces the mass further. 

 

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14 minutes ago, Strange said:

Because there are two particles created: one falls in and one escapes. The pair takes an amount of energy from the black hole and half of it is returned. Or read the explanation linked to by beech, which describes how you can treat the particle that falls in as having negative energy (which is matched by the positive energy of the escaping particle, so energy is conserved).

But note that these are just analogies; ie simplified descriptions of what happens. You cannot really use these as a way of properly understanding what happens. If you want to understand the detailed mechanism, you would need to have a solid grounding of QM, GR and how to apply Bogoliubov transformation (an isomorphism of either the canonical commutation relation algebra or canonical anticommutation relation algebra. This induces an autoequivalence on the respective representations).

I am theoretical physics buff, and I like to read books from professors in theoretical physics targeted to laymen.  I have a degree in electronics, and I am currently a math major.  (Didn't have enough money to go to an expensive school to learn about much of anything else)

The description of this effect in every one of those books describes the particle pairs as being the same particle pairs that randomly appear and annihilate each other all throughout space.  There is no explanation as to where they come from, and they seem to violate conservation of energy due to popping into existence out of nothing.  These particles would be no different than any other particle and anti particle, so basically it is like you are saying that antiparticles just have negative energy, now, but they can add to the total mass, which makes zero sense.

Hawking Radiation was intended to use this aspect of quantum mechanics, which seems to violate conservation of energy, and black holes, which violate conservation of energy, in order to show that there is still conservation of energy.  It is a law of nature that it used to develop physics theories, because it acts like a balance that can't be broken.

I am sorry to say, but you guys seemed to be misinformed about things from the internet.

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8 minutes ago, Conjurer said:

The description of this effect in every one of those books describes the particle pairs as being the same particle pairs that randomly appear and annihilate each other all throughout space.  There is no explanation as to where they come from, and they seem to violate conservation of energy due to popping into existence out of nothing.  These particles would be no different than any other particle and anti particle, so basically it is like you are saying that antiparticles just have negative energy, now, but they can add to the total mass, which makes zero sense.

They arise because of quantum effects. The lowest energy state of a vacuum is greater than zero. Because of the uncertainty principle, there are a range of possible values of energy possible for a short period of time: larger energy fluctuations exist for shorter time, smaller ones for longer. If the energy fluctuation is large enough this can temporarily create a particle-antiparticle pair. The pair will immediately annihilate returning the "borrowed" energy.

Unlike "real" particles, these virtual particles can only exist for a short time.

https://en.wikipedia.org/wiki/Quantum_fluctuation

Quote

Hawking Radiation was intended to use this aspect of quantum mechanics, which seems to violate conservation of energy, and black holes, which violate conservation of energy, in order to show that there is still conservation of energy.

Quantum mechanics doesn't violate conservation of energy. Neither do black holes.

The reason Hawking came up with Hawking radiation is because he was trying to understand how quantum information could be preserved if things fall into black holes.

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8 minutes ago, Strange said:

Quantum mechanics doesn't violate conservation of energy. Neither do black holes.

The reason Hawking came up with Hawking radiation is because he was trying to understand how quantum information could be preserved if things fall into black holes.

Ya, it doesn't violate conservation laws, because Stephan Hawking developed his theory about Hawking Radiation to prove that both of these instances actually don't violate it when combined together.  The loss of information was considered to be a violation of the conservation laws in of itself.

Edited by Conjurer
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19 minutes ago, Strange said:

I don't know what you mane by that. "One" what? The density of a black hole decreases with mass. (Not that density really means anything in this context.)

"First, the average density of a SMBH (defined as the mass of the black hole divided by the volume within its Schwarzschild radius) can be less than the density of water in the case of some SMBHs.[6] "

Bloody excellent point, and speaks volumes as to who is confused and has his wires crossed re some claims in this thread. Speaking of a BH density is near absurd,  based on what GR tells us re the compulsory collapse of mass, once the Schwarzchild radius is reached/breached. In essence, a BH that is dormant, can be reasonably thought to be no more then a volume containing critically curved spacetime, with nothing else, until we arrive at a point where GR fails us  and we can assume exists the mass, with a finite surface of sorts, at or just below the quantum/Planck level...ignoring the now generally invalid concept of a mathematical singularity with infinite density and spacetime curvature.

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10 hours ago, Conjurer said:

 

It is believed that space is a scaler, and it has a low energy level.  Then particle pairs were never confirmed to lower this energy level in the lab, since they result in a photon after the collision (which is how they are detected).  I never heard any news of this discovery being changed at some point in time. 

To me, it just sounds like that you guys have just gone out on your own to determine that certain aspect of the theory is incorrect and needs to be changed.  Then your viewpoint of the original theory has become distorted by the concept of energy having the potential to generate the same amount of mass. 

You can't just assume that one aspect of the theory is wrong and adapt every other aspect of the theory to fit it so that everything about it fits into your viewpoint of the laws of physics, unless you write a paper or something to prove it to science.  I don't know of any papers written that have changed all these aspects of the theory. 

I would have to ask if you had any proof in any of this, because for a couple of mods, you guys seem way off track in all of this stuff.  It is like you guys have been making into a completely different theory, since; 

1) you don't accept particle pairs violating conservation laws,

2) you don't accept that antiparticles will lower the mass of the black hole by converting the matter in it to energy.    

I don't even really accept the Theory of Hawking Radiation, but I do accept the Holographic Principle.  These two theories are in conflict with each other, so you cannot accept them both.  But, I do accept both the number 1 and 2 things I just mentioned, and those are not the reasons why I don't prefer Hawking Radiation instead. 

It does make think that it could be possible that Hawking Radiation is false, because the energy would most likely be converted into electrons where the mass would actually remain the same since the average density of a supper-massive black hole is one, and maybe it is wrong because of that.  A sea of electrons would have that approximate density.

No one here is trying to rewrite the theory of Hawking radiation here except for you.   You are the only one claiming that antiparticles will lower the mass of a black hole,  presently accepted physics does not.    If you don't want to believe in the accepted physics, that's up to you, but don't try to pass your own ideas off as accepted physics. 

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2 minutes ago, Conjurer said:

Then how does the mathematics say that there is conservation with photons with no source that didn't exist before popping up?  How does any type of reasoning say this? 

You have been given several explanations before. The one provided by beecee is good:

On 03/11/2018 at 7:53 PM, beecee said:

here is a simplified explanation and other consequences of Hawking Radiation.

https://www.vox.com/science-and-health/2018/3/14/17119320/stephen-hawking-hawking-radiation-explained

Or here is Wikipedia: https://en.wikipedia.org/wiki/Hawking_radiation

Energy conservation is not violated because the mass lost by the black holes is the same as the energy radiated away.

You say the book you checked (Hidden Reality) also says energy is conserved. Do you now concede you were mistaken?

 

And here is the article I posted earlier on the source of quantum fluctuations:

14 hours ago, Strange said:

Anyway, here is a good article on quantum fluctuations (by a physicist at CERN): https://profmattstrassler.com/articles-and-posts/particle-physics-basics/quantum-fluctuations-and-their-energy/

Or: https://en.wikipedia.org/wiki/Quantum_fluctuation

Energy conservation is not violated because the particles only exist for a short time.

 

7 minutes ago, Conjurer said:

I am really not clear on how/why you believe there is\has to be conservation here.  I don't know the official reason why it should. 

Because conservation of energy is a fundamental aspect of the universe. Basically it means that things behave the same way at different times. (Noether's theorem shows that conservation laws are equivalent to symmetries. In the case of energy, it is equivalent to time translation.)

We have found no examples of energy not being conserved.

 

You clearly have some gaps in your knowledge and some serious misunderstandings. That is OK, as long as you are willing to learn (we all have to learn - that is why a lot of us are on this forum). Perhaps spend a bit more time asking questions, and less making assertions. If you can't easily find a source that confirms what you think, then maybe consider that you could be mistaken.

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4 minutes ago, Strange said:

Energy conservation is not violated because the mass lost by the black holes is the same as the energy radiated away.

That is just saying that it is conserved, because Hawking discovered that conservation could exist in this instance by combining these two principals.  Then there are not any black holes at the LHC!  Then this is not even saying that there is conservation in the lab with the absence of black holes.  Random particle pairs were discovered in particle accelerators, not black holes.

11 minutes ago, Strange said:

You say the book you checked (Hidden Reality) also says energy is conserved. Do you now concede you were mistaken?

  It sounded a lot like what swonsont said, and I was surprised actuall surprised to read that.  That is a newer book, and apparently viewpoints have changed on this topic.  Random particle pairs use to be one of the leading candidates for the start of the Big Bang.  

Then it didn't explain how they account for the energy that would be created from the newly generated photon which allowed them to detect it in the first place in the lab.  Then I still don't understand that part, as to why there is conservation without black holes or Hawking Radiation.

 

14 minutes ago, Strange said:

We have found no examples of energy not being conserved.

Right, because people like Stephen Hawking develop theories to show how it is always conserved, and it allows a mathematical framework to relate different principals from it being a part of the same value.  Then Hawking retracted his theory to the Holographic Principal, and the Holographic Principal doesn't even involve random particle pairs.  Then conservation was found for black holes in a different way, but that doesn't explain how conservation with random particle pairs is made anymore.

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On 11/5/2018 at 7:12 PM, Conjurer said:

 Right, because people like Stephen Hawking develop theories to show how it is always conserved, and it allows a mathematical framework to relate different principals from it being a part of the same value.  Then Hawking retracted his theory to the Holographic Principal, and the Holographic Principal doesn't even involve random particle pairs.  Then conservation was found for black holes in a different way, but that doesn't explain how conservation with random particle pairs is made anymore.

!

Moderator Note

If you are going to keep claiming this, you need to cite references. Black holes don't violate conservation of energy, and neither do virtual particle pairs. AFAIK Hawking never retracted the evaporation model. What he retracted were his views on information.

 
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A good explanation of Hawking radiation here: 

Quote

Yes, it’s true that Hawking’s original picture of particle-antiparticle pairs produced outside of the event horizon, with one escaping and carrying energy away while the other falls in and causes the black hole to lose mass, is oversimplified to the point of being totally wrong. Instead, radiation is formed outside the black hole owing to the fact that different observers cannot agree on what is happening in the strongly-curved space outside a black hole, and that someone who’s stationary a far distance away will see a steady stream of thermal, blackbody, low-energy radiation emanating from it.

https://medium.com/starts-with-a-bang/ask-ethan-how-do-black-holes-actually-evaporate-1f195c289aa1

There is a link in there to a blog by Sabine Hossenfelder which explains a bit more: http://backreaction.blogspot.com/2015/12/hawking-radiation-is-not-produced-at.html

 

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