Great work Aron!
Paradox (I think):
Imagine a star that is just on the verge (a few atoms shy) of imploding into a black hole.
Imagine two stationary observers (A and B), relative to the star, who are very far away.
Imagine that observer A starts accelerating towards the star. By relativity, the observer is justified in claiming that the star is accelerating towards him (observer A).
At some velocity, the star's apparent mass will exceed the threshold of collapsing into a black hole.
Therefore, observer A can rightly claim that the star is collapsing..
Observer B, at the original observation point (who remains stationary relative to the star) claims that the star has not reached a mass level that initiates a collapse and therefore the star is not collapsing.
Given that a collapse to a black hole is not reversible, we have a paradox.
One observer seeing a collapse, the other does not.
Worse yet, once the collapse is initiated (for observer A), that same observer A can decelerate to a relative velocity of zero (relative to the star). At this relative velocity of zero, a mass measurement reveals that the start is not massive enough to collapse and, in fact, has not done so.
This must mean that as observer A is decelerating the collapse to a black hole is somehow reversed.
This seeming paradox has been bugging me for years and I have not been able to reverse it.
Is there any indication that quantum gravity can explain this?
Your problem can be resolved within the scope of GR, so there's no need to bring in quantum gravity. There are a couple things you are assuming that came from people's attempts to explain GR, but unfortunately they often use some sloppy explanations which can be misunderstood.
The first issue is with this statement:
This is not really a correct statement of the principle of relativity. The correct statement is that the laws of physics are invariant under a change of coordinates. But this change of coordinates will affect the spacetime metric as well as the star and the observer, so you can't account for it in the way you say.
Given the metric of spacetime, you can determine in an absolute way whether or not an object is accelerating. An accelerating object does not behave in the same way as an unaccelearted object! This is similar to the mistake some people make with the twin paradox, where they think that relativity allows them to symmetrically interchange the life histories of the two twins. It doesn't. One of them is accelerates and the other doesn't. This is an objective physical fact.
The second issue is with this statement:
You have been told that:
1) objects that are moving faster have a greater energy relative to the frame of reference of a stationary observer, and
2) when enough mass/energy is concentrated into a small enough space, a black hole forms.
so you have deduced that an object moving fast enough must collapse into a black hole. But this interpretation of #2 is false. In order for a star to collapse into a black hole, it needs to have a certain amount of mass as measured in the frame of reference of the star itself. Giving the star a velocity, no matter how large, does not make it collapse into a black hole.
Thank you for your posts on the Beginning of Time and on The Name. I am grateful.
I have invested the day reading through your posts on a Beginning. Under what assumptions, if any, does the Standard Model of the Big Bang and Special Relativity possibly imply a Beginning from "absolutely Nothing"--- no matter, no energy, no space, no time ? Do most non-theistic adherents to the Standard Model hold to an eternally pre-existing field in which the physical laws exist eternally? If there is no singularity at the Beginning of our universe, do all physical laws break down as Hawking appears to suggest, in the absence of the No Boundary Proposal? Finally, Is the No Boundary Proposal falsifiable? Has it resulted in any testable predictions? I am going to read through your posts on the Beginning several times, and I apologize if I, as a non-physicist, am asking ignorant questions. I teach an introductory apologetics course to high school seniors and I want to serve them well by not making blanket statements that amount to "cardstacking" on the side of a personal infinite Creator, by over-reaching. The Second Law, the existence of rationality woven into the universe which makes science and math possible, and the wonders of personality/consciousness/choices/ethics and beauty seem to be a fruitful place to begin. In the area of cosmology, it is difficult to know in what directions to look for evidence of a Beginning, and so start to prepare my students for the wonders and pitfalls of the philosophy of science in the science classes in their future, when the mathematics and the conceptual physics is so challenging...but an amazing universe, with mind expanding questions and possibilities, is just what I would expect from a personal infinite Creator-- both the expected and the unexpected and awe-inspiring. I appreciate your honesty and patience in handling the deep stuff and the complex. An encouraging thought for your day: "I will show you what he is like who comes to Me and hears My words and puts them into practice. He is like a man building....... a house, who dug down DEEP and laid the foundation on rock. WHEN a flood came, the turrent struck that house, but it was not shaken, for it was well built." Luke 6:47-48... Thanks again for your hard work.... keep digging deep and keep on building on that which lasts for the Lord Jesus' honor. Isn't He so kind to forgive you and I and to reason with us so patiently? Your hard work in Him is not in vain. You and I, and precious people all around us, ARE the work--and so valuable ! God bless you as you trust Him. Grateful, Daniel Frederiks Hawthorne Christian Academy NJ
Thanks for your comment, Daniel.
Under what assumptions, if any, does the Standard Model of the Big Bang and Special Relativity possibly imply a Beginning from "absolutely Nothing"--- no matter, no energy, no space, no time?
That is the subject of the singularity theorems, which I described here. However, there is the question of to what extent these theorems apply in quantum gravity, which would have been important at the beginning of the universe, and which we do not understand. As for beginning from "Absolutely nothing", we have to be careful what we mean by this. Nothing is not itself a thing, but the absence of things. At least in the standard classical (i.e. nonquantum) Big Bang model, there was no time before the Big Bang, so there can't have been anything else "before" it in a temporal sense, although God is still logically prior since he exists timelessly.
Do most non-theistic adherents to the Standard Model hold to an eternally pre-existing field in which the physical laws exist eternally?
You don't want to say "field" here, since that's a technical term and it isn't what you mean. Just say, do the physical laws exist eternally? Most nontheistic physicists would probably say yes to that, although some might say that the laws of physics don't really exist, they just describe other things which do exist. Some might even think that there's no such thing as the final theory of everything. I'm not sure how to answer, since non-theism isn't a homogeneous worldview, and most physicists don't talk much about this type of philosophical issue.
If there is no singularity at the Beginning of our universe, do all physical laws break down as Hawking appears to suggest, in the absence of the No Boundary Proposal?
Not sure what quotation of Hawking you're referring to; certainly Hawking's No Boundary Proposal isn't the only idea for dealing with the beginning of time. If there is no singularity, then it might just be that there is a "bounce" or some other type of transition to a previous time, such that the laws of physics are valid the whole time. If there is a singularity, then the laws break down if you try to extend them past the singularity, but that seems like just another way of saying that the laws say you can't extend past the singularity. A separate issue is that we don't understand quantum gravity, so the known laws of physics would break down near a singularity. This makes it a bit hard to answer the other questions...
Finally, Is the No Boundary Proposal falsifiable? Has it resulted in any testable predictions?
Yes, it appears to make a wrong prediction for the initial size of the universe. Perhaps this is fixable with further thought, perhaps not.
I teach an introductory apologetics course to high school seniors and I want to serve them well by not making blanket statements that amount to "cardstacking" on the side of a personal infinite Creator, by over-reaching.
Good! I appreciate the fact that you resist that temptation and thus remain intellectually honest. As you can see, philosophy of cosmology raises lots of questions and so it is difficult to make a completely watertight argument. Personally I consider the cosmological stuff to be some evidence, but that miracles, especially the Resurrection of Jesus, are even better evidence. I hope you spend more time on that topic...?
At the end of the day, the most important thing is not what you teach specifically, but that your students see you as an example of a rational person with faith who thinks things through to the best of your ability. That type of good example is generally more persuasive than any particular argument. Keep up the good work!
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