# Escape Velocity of virtual particles

• RuroumiKenshin
So you can take a system of non-interacting fields and say that there are "virtual" interactions going on that you are ignoring for the moment. This can be done in a well-defined way (you use perturbation theory) and you can compute the results of ignoring the interactions, and that is what we call "virtual particles."Note that in the standard model, which is a QFT, there are lots of fields and lots of interactions. In some cases, like when you are calculating a simple scattering, you can ignore some of the fields and interactions for the moment, and pretend that there are virtual particles around, doing virtual interactions. In other words, they're a useful mathematical tool
RuroumiKenshin
I know that the escape velocity for virtual particles being emitted from black holes is c2+ (in the black hole entropy formula, there is an escape velocity of c3). I also know that Hawking radiation and for that matter*(I don't mean matter in physics terms), any radiation being emitted from a black hole supposedly escapes the gravitational pull of the black hole. But how does this happen? Does this imply superluminal travel?

the way i understand hawking radiation it is not radiation that is emitted by black holes but the result of a pair of virtual particles being created near the black hole, ie outside the event horizon, with one of the particles entering the black hole and the other flying off into space

Originally posted by MajinVegeta
I know that the escape velocity for virtual particles being emitted from black holes is c2+ (in the black hole entropy formula, there is an escape velocity of c3). I also know that Hawking radiation and for that matter*(I don't mean matter in physics terms), any radiation being emitted from a black hole supposedly escapes the gravitational pull of the black hole. But how does this happen? Does this imply superluminal travel?

It is only at the event horizon itself that the escape velocity is c. Get a little above the horizon and the escape velocity is some value less than c. And it is a little above the horizon that the Hawking radiation arises, so the escaping particle does not have to move faster than light.

Greetings MajinVegeta !

To make it clearer, gravity is not really the
point here. The point is a VERY strong field -
it could be an electric field (for particles
that have electric charge) too for example.
If it is strong enough then it can "split"
the virtual pairs of particles created as
a result of zero-point-field quantum fluctuations.
But, like I said, it has to be VERY strong.
So, when it comes to a gravity field it is only
strong enough near(OUTSIDE !) a BH's EH to be able
to split the ZPF particles.

Live long and prosper.

What's a EH and a ZPF?

It is only at the event horizon itself that the escape velocity is c. Get a little above the horizon and the escape velocity is some value less than c. And it is a little above the horizon that the Hawking radiation arises, so the escaping particle does not have to move faster than light.

Why do virtual particles do behave like so?
Can you give me an approximate escape velocity of a particle NEAR the event horizon?

Virtual particles behave more-or-less like real particles, which would do the same thing.

As for escape velocity near the black hole... hmmm. That's a GR question, and I'm not sure how to do it -- or even how to frame it coherently right now. The problem is that around the event horizon (drag's 'EH') which frame you measure the energy in is tremendously important.

One thing to remember is that the whole virtual-particles thing is just kind of a heuristic approximation: it almost always vaguely works, but the actualy theory is a field theory, of interacting fields, not particles. The actual derivation of Hawking radiation comes from looking at the ground state of the field near the black hole from two different reference frames (moving relative to each other), not from invoking virtual particles at all.

aren't interacting fields composed of particles?

Originally posted by MajinVegeta
What's a EH and a ZPF?
Shorts for Event Horizon and Zero Point Field(which
I wrote in the body of the message too ).
ZPF quantum fluctuations are the virtual particles
that are momentarily created in a relativly (for
you as an observer) "empty" part of space with no
strong fields passing through it - not fluctuations
that are directly due to a "real" energy source.

Live long and prosper.

Originally posted by MajinVegeta
aren't interacting fields composed of particles?
According to QM - yes. What happens is that due to
the HUP the value of these fields (or virtual
particles if you wish) also fluctuates, which means
that it could "jump" high enough in some places
to allow other virtual particles to be created
momentarily.

Live long and prosper.

I am unsure about what a ZPF is (this is, its definition, not what it stands for).

"Ground state", "zero point energy", and "vacuum state/energy" are more common terms AFAIK. In a quantum system, the lowest energy state -- this is the unexcited state in quantum mecahnics, or the empty state (no particles) in a field theory -- actually has nonzero energy. This lowest state is the vacuum/ground/zero point state.

Whats the difference between zero point fluctuations and zero point quantum fluctuations?

are virtual particles, from the way I understand them, particles, although they themselves cannot be detected exactly, but are detected to their indirect (virtual=indirect) influence in space?

>>Whats the difference between zero point fluctuations and zero point quantum fluctuations?

Same thing.

Technically, virtual particles actually arise when you consider the perturbation-series approximation to a quantum field interaction.

They are sort of "temporary" or short-lived particles... kinda. Real particles the long-time or long-distance limits of virtual particles.

so they're not real particles? (i'm getting a bit confused here...)

Originally posted by MajinVegeta
so they're not real particles? (i'm getting a bit confused here...)
Not really, they're the result of mathematical
abstractions. In QM you can't have any
continuos interaction/field/whatever because
everything is made of qauntums - individual
pieces.

Live long and prosper.

What do you mean by mathematical abstractions? What is their relation to their surroundings?

I'm getting a notion this has to do with dark matter?

Nothing to do with dark matter -- dark matter is just anything not currently undergoing nuclear fusion and glowing like the sun. You are dark matter, I am dark matter, the Earth is all dark matter...

No, virtual particles are not real particles. Hmmm... okay, they arise in the context of quantum field theory; in QFT everything consists of interacting fields. However, symmetries and conservation laws make it so that non-interacting fields always are of a form that can be described by some number of particles. That's why the idea of a particle is so useful: on a large enough scale, we can ignore the field-like nature of what's going on and talk about discrete particles.

Now, when you get to interacting fields -- take two particles and shoot them really close together for instance -- the picture of these discrete particles breaks down, and you have to look at the underlying fields. However, much of the time, it turns out you can approximate the field picture very closely and in a very intuitive (if you know some QFT) way by introducing virtual or 'temporary' particles. They appear like regular particles, but can have any mass, velocity, etc (they need not "be on their mass shell") and only exist for short periods of time/distance.

why do they exist for short periods of time?

Dark matter is involved in the brane theory. Dark matter accounts for the weird velocity of stars for instance. Their calculated velocities don't correspond with their current velocity. Their velocity relative to their placement in their galaxy (in the outskirts of a galaxy, this is a common occurance) doesn't make sense. For example, a star in the outskirts of a galaxy wouldn't be traveling at c+, right? That sort of thing happens. That's when dark matter comes in. Oh dear..I have to go to bed, but I'm pretty sure you know what I'm talking about, damgo.

BTW, I'm only 13, in pre-algebra so if my questions involve some seriously complex math, can you try and simpliyfy it for me or just tell me what I need to know or something?

maybe since the singularity is a source of untapped energy,outside the event horizon or in it spacetimes interaction with energy is what makes particles or matter just like in the begining.the amount of energy in spacetime somehow converts this excess energy into particles.so next to the black hole spacetime is highly charged with energy from the gravity,so what if every now and then spacetime steals energy from the black holes gravity and creates particles from it!then when the two virtual particles come into existence,the normal one is then attracted by the black holes gravity and is pulled back,then the anti particle then leaves traveling at light speed because of it's repulsion to spacetime,like photons just pure anti energy repelling against the positive energy background of spacetime.and all that's leaving the black hole is anti matter.

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The Heisenberg uncertainty principle allows for h>2mc2t=2mc(ct), where m is the mass of one of the virtual pair which escapes the event horizon, mc2 its rest energy, and ct=h/2mc the maximum distance of the pair production from the horizon.

I'm trying to boil it down as much as possible, Majin, but it's just not a simple topic. It's impressive that you understand it at all if you're only 13. :)

Simple answer 1) Virtual particles do not really exist. They are just a mathematical trick that gives a good approximation of what's really going on, which is a bunch of quantum fields.

The more complicated answer -- which is why virtual particles are such a good approximation, and why all particles are to some degree 'virtual', and when we can use them -- probably has to wait a while. I barely understand it myself! :)

Branes are part of string theory and not really connected with dark matter. You're right about galaxies velocities! That's the evidence for dark matter: galaxies aren't spinning at the right speed for the amount of matter we can see in them; so we conclude they must have more matter we can't see. This could be just planets, burnt-out stars, etc; but AFAIK recent evidence is that it's probably something more obscure.

dark matter giving a system of mass more energy for faster orbits at greater distances from the center than should be,can be explained by a different means than using dark matter.gravity is produced by matter as a property of energy itself.since spacetime was charged by matter itself when the universe was created when a star collapsed into a black hole both matter and spacetime have the same properties.so gravity attracts energy from spacetime like a super energy sucker.as gravity pulls energy toward it it curves spacetime because magnets do to iron dust.the curvature of spacetime is like how the lines of force interact between gravity and spacetime.so spacetime energy is being pulled in toward a mass at light or faster.thus spacetime energy is at a high rate of motion.gravity is not a attraction between two masses but a masses attraction to the flow of spacetime energy.on the Earth you have the same gravity field as the whole earth,so when you jump up.as the Earth suck energy toward it you are attracted to the flow to the Earth and follow the current and are pulled back down.so at great distances away from a galaxies center that is spinning causing energy to move in a spiral motion.toward the center as it moves around in a circle.the motion of the spacetime energy caused by the ratating center is attracted by the stars around it and start moving around the center from the motion of the energy.so the dark matter effect is because the largewr the mass of a star versus the distance from the center will cause a mass to move a different speed based on motion of spacetime energy and the gravity field of the star,so all the stars at the outer rim are just super massive stars.

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Originally posted by damgo
I'm trying to boil it down as much as possible, Majin, but it's just not a simple topic. It's impressive that you understand it at all if you're only 13. :)

Simple answer 1) Virtual particles do not really exist. They are just a mathematical trick that gives a good approximation of what's really going on, which is a bunch of quantum fields.

The more complicated answer -- which is why virtual particles are such a good approximation, and why all particles are to some degree 'virtual', and when we can use them -- probably has to wait a while. I barely understand it myself! :)

Branes are part of string theory and not really connected with dark matter. You're right about galaxies velocities! That's the evidence for dark matter: galaxies aren't spinning at the right speed for the amount of matter we can see in them; so we conclude they must have more matter we can't see. This could be just planets, burnt-out stars, etc; but AFAIK recent evidence is that it's probably something more obscure.

Damgo, in Stephen Hawking's The Universe In A Nutshell, Hawking distinctly, coherently specifies dark matter, and further associates it with branes. Maybe you could look it up or something.

Tell me if I have this right:

Hmm... I don't have the book, and honestly I can't think of any real connection. There was a proposal that really huge 'cosmic strings' might make up some of the dark matter, but AFAIK this is generally considered a long shot. Maybe someone else can clue me in?

OK -- The Schwarzschild radius is defined to be the radius of the event horizon for a simple (non-spinning, 'Schwarzschild') black hole. The idea is that a pair of virtual particles appear near the event horizon, one headed away from the black hole at high speed, one headed in. Normally, they would attract each other and annihilate; however, sometimes the gravitational field of the black hole will pull one in quickly enough that the other can escape.

A similar sort of thing can happen with a really strong electric or magnetic field... this is believed to happen around some neutron stars.

Hawking (not Schwarzschild) radiation is pure theory -- it's so small that it's impossible for us to actually observe it. Hawking came up with it in 1975; Schwarzschild did his stuff back in the 30s I think. He got the radius by discovering black holes could exist and solving for where the event horizon was.

Greetings !

Majin,
Schwarzschild was making calculations a few years
after the 1915 publication of GR and came up
at which the curvature of space-time is
so extreme that the escape velocity is larger
than c (and since nothing can go faster than
c - nothing escapes). He sent his solution to
Einstein and thus it was published.

About 40 - 50 years ago as indirect observations
of the cores of galaxies and stars apparently
emmissions became considrable, the BHs finally
seemed "real". In the years before that
Schwarzschild's solution just seemed to be a
"weird" result of GR.

if BHs are real then they appear to violate the
second law of Thermodynamics that states that
entropy must always increase. It seemed, at the
time, as though BHs just absorb energy and never
"give it up". Then he considered what will
happen near a BH from the perspective of QM.

QM states that space is not "empty". It is full
of particles of all kind that appear and then
anihilate each other on the microscopic space-time
scales.

However, like damgo and I said before - if you can
create a strong enough field you can prevent these
particles from anhilitaing with each other. So,
Hawking calculated that the amount of energy that
will be "released" to the rest of the Universe
from near the EH accounts precisely(I believe) for
the "requirement" of the second law of Thermodynamics.

Live long and prosper.

Damgo:
Because light doesn't propagate into the shadowing brane, the darkness/unknown matter (aka dark matter) we see is due to this effect. Since only gravitational forces can propagate through the shadowing brane, the abnormal velocities of galaxies is caused by the gravity which influences the galaxies through the other brane. If there's a book store around where you live, you could probably read about it there(if you do, it's in the last chapter).

Drag:
I thought Hawking radiation was the result of quantum fluctuations. I read photons where emitted from the black hole. This is wierd, right? If it is perfectly tenable, then I am induced to conclude that virtual particles are a classification for a variable characteristic for particles (I have yet to discover this variable).

Greetings MajinVegeta !

First of all I'd like to suggest something if
I may - all this discussion of theories currently
in the process of development should be separated
from this discussion. Further more, I think it's a
good idea to have such a separation in general
between accepted theories and incomplete theories
that are possibly wrong or misguiding. The greatest
minds on the planet are working to develop these
theories, so I believe it would be most sensible
not to question them too closely unless/until they
establish themselves as really accepted theories.
(Though prof. Hawking's popular science books can
really spark an amateur's imagination. )

Now to the subject at hand: Hawking Radiation
particles are NOT virtual particles ! They are
real. The virtual particles we discussed earlier
are quantified fields/interactions. QM does
not have "fields" it quantifies everything including
fields - separates them into individual quanta -
wave-particles.

The particles that are momentarily created near and
outside the EH (and everywhere else in the Universe too)
are real. The difference is that near an EH the
gravitational fields are so powerful that the
"reunion" may be prevented and one of the particles
(or both) is absorbed by the BH.

Hawking radiation particles are not just photons
(EM waves), they can be any particles or anti-particles.

I do not know the likeliness of the creation of
massless particles and photons in particular as
compared to that of particles that do have rest
mass(and thus travel at less than c - light speed),
but clearly the first are sure to escape from the
vecinity of a BH if their counterpart is destroyed
while particles with rest mass will require a lot of
energy to do so. So, photons are the more important
"candidates".

Is it clearer now ?

Live long and prosper.

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YES, much clearer. But I still don't comprehend the "existence" of non-real particles.

Can you differentiate the incomplete theories between the complete theories for me?

Greetings !
Originally posted by MajinVegeta
But I still don't comprehend the "existence"
of non-real particles.
Try these links (they're not that great really
but unfortunately they're not easy to find, maybe
someone can post better ones):
http://www.boogieonline.com/seeking/destruction/empty.html
http://www.wikipedia.org/wiki/Virtual_particle
http://www.wikipedia.org/wiki/Quantum_physics
http://shop.store.yahoo.com/scibook/nothingness.html
http://users.senet.com.au/~wiblin/science/quantum/question6.html
http://www.calphysics.org/zpe.html
http://members.optushome.com.au/aussff/quantumphysics.html
Originally posted by MajinVegeta
Can you differentiate the incomplete theories
between the complete theories for me?
QM and GR are mostly complete and accepted theories.
Strings, branes, quantum gravity and others are not, yet.

Live long and prosper.

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## 1. What is the escape velocity of virtual particles?

The escape velocity of virtual particles refers to the minimum velocity required for a virtual particle to escape the gravitational pull of a massive object, such as a black hole. This velocity is dependent on the mass and radius of the object.

## 2. How is the escape velocity of virtual particles calculated?

The escape velocity of virtual particles can be calculated using the formula: v = √(2GM/r), where G is the gravitational constant, M is the mass of the object, and r is the distance from the center of the object.

## 3. Can the escape velocity of virtual particles be greater than the speed of light?

No, according to the theory of relativity, the speed of light is the maximum speed at which any object can travel. Therefore, the escape velocity of virtual particles cannot exceed the speed of light.

## 4. How does the escape velocity of virtual particles differ from that of physical particles?

The escape velocity of virtual particles differs from that of physical particles because virtual particles do not have a physical form and are subject to the laws of quantum mechanics. This means that they can potentially escape the gravitational pull of an object even if their velocity is less than the escape velocity calculated using classical mechanics.

## 5. What is the significance of the escape velocity of virtual particles?

The escape velocity of virtual particles is significant in understanding the behavior of particles near massive objects and in predicting the formation of black holes. It also plays a role in theories of quantum gravity and the study of the early universe.

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