2 Q's - hawking radiation and inflationary universe

[jnorman]

Q1 - hawking radiation hinges around spontaneous particle pair creation near the EH of a BH. the spontaneous pair can only exist for less than the Planck time. how can either of the particle pair travel a far enough distance in that ridiculously small amount of time to actually cross the EH before recombining back into nothingness? it seems like they don't exist for a long enough time to do anything but pop into and out of existence. (notwithstanding that i STILL have no understanding of why ONLY the negative energy particle is "allowed" to fall into the BH, while the "positive energy particle is somehow excluded from being able to fall into the BH). (also notwithsthanding that after (trying)reading hawking's essays in "the nature of space and time" with roger penrose, i find penrose's writing to be accessible and reasonably understandable, while hawking's writings are COMPLETELY obtuse and not even close to understandable, which reminds me of feynman's comment about "if you are not able to convey a concept to a laymen, it means you do not understand it well enough yourself"...)

Q2 - in alan guth's wonderful book, the inflationary universe, i think he is inferring that for at least some small period of time, the universe expanded at a speed greater than the spped of light. is that correct? and if so, how could any material of the early universe have moved faster than the speed of light without violating the rule of matter being unable to reach or exceed C? thanks.

 

[Chalnoth]

Q1 - hawking radiation hinges around spontaneous particle pair creation near the EH of a BH.

Not really. The effect can be independently derived using a wide variety of methods.

 

[MeJennifer]

Q2 - in alan guth's wonderful book, the inflationary universe, i think he is inferring that for at least some small period of time, the universe expanded at a speed greater than the spped of light. is that correct? and if so, how could any material of the early universe have moved faster than the speed of light without violating the rule of matter being unable to reach or exceed C? thanks.

The distance between two objects is partly determined by the curvature of space between them. A change in such curvature can cause a change in distance that gives the appearance the objects move away from each other faster than the speed of light.

 

[Chalnoth]

The distance between two objects is partly determined by the curvature of space between them. A change in such curvature can cause a change in distance that gives the appearance the objects move away from each other faster than the speed of light.

This is a bit of nitpicking, but I thought I'd mention that nothing actually appears to be moving away faster than the speed of light. It is true that the distances to many objects, by some specific measures of distance, appears to be increasing faster than the speed of light, but there is another way to look at the recession velocity: the redshift.

And as far as the redshift is concerned, if we were to interpret said redshift as due to a velocity, nothing "appears" to be receding at faster than light.

 

[jnorman]

chalnoth - thanks for your response, but as far as everything i have read, i think i stated that correctly. please feel free to elucidate, and/or perhaps try to actually answer my question.

me jennifer - what you stated is rather in conflict with guth's premise. i was inquiring as to guth's explanation of how the universe accomplished the short term extremely rapid expansion without violating one of the most fundamental principles of SR/GR.

 

[benk99nenm312]

Q1 - hawking radiation hinges around spontaneous particle pair creation near the EH of a BH. the spontaneous pair can only exist for less than the Planck time.

I actually thought that te extreme curvature of spacetime near a black hole put enough energy to "make the pair real" for an extended period of time. In other words, I thought the extreme curvature let's the pair exist longer than the Planck time. If so, then you wouldn't have a problem. If not, then please someone let me know.

 

[Chalnoth]

me jennifer - what you stated is rather in conflict with guth's premise. i was inquiring as to guth's explanation of how the universe accomplished the short term extremely rapid expansion without violating one of the most fundamental principles of SR/GR.

Er, because there's no such thing as expansion greater than light. It's a bad description, as it doesn't even make sense: expansion has units of inverse time (or velocity per unit distance). You can't compare something with units of inverse time to a speed, so it makes no sense to say it's faster (or slower) than the speed of light.

As for violating SR/GR, well, it obviously violates SR because space-time is curved in an expanding universe: we have to use GR. And the expansion of the universe (whether during inflation or at any other time) doesn't violate GR because GR is used as one of its fundamental assumptions!

 

[mjacobsca]

Q2 - in alan guth's wonderful book, the inflationary universe, i think he is inferring that for at least some small period of time, the universe expanded at a speed greater than the spped of light. is that correct? and if so, how could any material of the early universe have moved faster than the speed of light without violating the rule of matter being unable to reach or exceed C? thanks.

Spacetime itself can expand faster than light. However, nothing can move THROUGH spacetime faster than light. Therefore, the bounds of the universe can expand exponentially faster than the speed of light during inflation, and matter that is pulled apart because of the increase of spacetime between particles can move apart from each other faster than the speed of light.

 

[MeJennifer]

Spacetime itself can expand faster than light. However, nothing can move THROUGH spacetime faster than light. Therefore, the bounds of the universe can expand exponentially faster than the speed of light during inflation, and matter that is pulled apart because of the increase of spacetime between particles can move apart from each other faster than the speed of light.

For the good order space can expand, however spacetime is fixed. A possible universe is an instance of spacetime and encompasses the universe's whole life cycle.

 

[Chronos]

See the paper by Davis and Lineweaver:
http://arxiv.org/abs/astro-ph/0310808

Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe
Authors: Tamara M. Davis, Charles H. Lineweaver
(Submitted on 28 Oct 2003 (v1), last revised 13 Nov 2003 (this version, v2))
Abstract: We use standard general relativity to illustrate and clarify several common misconceptions about the expansion of the Universe. To show the abundance of these misconceptions we cite numerous misleading, or easily misinterpreted, statements in the literature. In the context of the new standard Lambda-CDM cosmology we point out confusions regarding the particle horizon, the event horizon, the ``observable universe'' and the Hubble sphere (distance at which recession velocity = c). We show that we can observe galaxies that have, and always have had, recession velocities greater than the speed of light. We explain why this does not violate special relativity and we link these concepts to observational tests. Attempts to restrict recession velocities to less than the speed of light require a special relativistic interpretation of cosmological redshifts. We analyze apparent magnitudes of supernovae and observationally rule out the special relativistic Doppler interpretation of cosmological redshifts at a confidence level of 23 sigma.