Re: "Shape" of the universe
On Tuesday, May 19, 2020 at 6:26:08 PM UTC-6, Lawrence Crowell wrote:
>
> You cannot of course circumnavigate the spatial manifold of the universe.
> Anything beyond the cosmological horizon moves away faster than you can
> ever catch up. It is a bit like the part in the movie The Shining with Jack
> Nicholson where the hotel hallway expanded faster than he could run. If we
> could though observe this, say analogous to Jack Nicholson in the film,
> there would be optical effects. The spatial manifold could be a k = 1
> closed or k = -1 hyperbolic or the dodecahedral tessellated universe of
> Poincaré. Yet so far data is not forthcoming.
>
> A Planck energy of quanta, say a UV graviton, could have causal influence
> on us is it expands to the cosmological horizon or near so. The B-modes of
> inflation, which are still being pursued, represent Planck units redshifted
> to some appreciable scale comparable to the cosmological horizon. This is a
> z factor z = 10^{10}ly/ℓ_p = 6.3×10^{60}, where taking the nat-log of this
> and multiplying by the horizon scale 1.3×10^{10}ly we get 1.8×10^{12}ly.
> The furthest out anything can have traversed at the speed of light to reach
> is from that distance and from the earliest near Planck time in the
> universe. What this means is the source or emitter of this graviton was
> early on close to our region and the source is not that incredible distance
> away.
>
> LC
>
Is this estimate reasonable, also from
https://www.forbes.com/sites/startswithabang/2020/05/19/would-a-long-journey-through-the-universe-bring-us-back-to-our-starting-point/#fe376fef6c50
The appearance of different angular sized of fluctuations in the CMB
results in different spatial curvature scenarios. Presently, the Universe
appears to be flat, but we have only measured down to about the 0.4% level.
At a more precise level, we may discover some level of intrinsic curvature,
after all, but what we've observed is enough to tell us that if the
Universe is curved, it's only curved on scales that are ~(250)^3 times (or
more than 15 million times) larger than our presently-observable Universe
is.
AG
>
>
> On Tuesday, May 19, 2020 at 1:41:45 AM UTC-5, Philip Thrift wrote:
>
>>
>>
>> *Would traveling out in a "straight" line bring you back to where you
>> started?*
>>
>>
>> https://www.forbes.com/sites/startswithabang/2020/05/19/would-a-long-journey-through-the-universe-bring-us-back-to-our-starting-point/#1781c2ccf6c5
>>
>> In the writer's (Ethan Siegel's) *opinion*:
>>
>>
>> On a cosmic scale, there is no indication that the Universe is anything
>> other than infinite and flat. There is no evidence that features in one
>> region of space also appear in any other well-separated region, nor is
>> there evidence of a repeating pattern in the Universe's large-scale
>> structure or the Big Bang's leftover glow. The only way we know of to turn
>> a freely moving object around is via gravitation slingshot, not from cosmic
>> curvature.
>>
>> And yet, it's a legitimate possibility that the Universe may, in fact, be
>> finite in extent, but larger than our observations can currently take us.
>> As the Universe unfolds over the coming billions of years, more and more of
>> it (about 135% more, by volume) will become visible to us. If there's any
>> hint that a long-distance journey would bring us back to our starting
>> point, that's the only place we'll ever find it. Our only hope for
>> discovering a finite but traversible Universe lies, quite ironically, in
>> our far distant future.
>>
>> @philipthrift
>>
>
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Re: "Shape" of the universe
You cannot of course circumnavigate the spatial manifold of the universe.
Anything beyond the cosmological horizon moves away faster than you can
ever catch up. It is a bit like the part in the movie The Shining with Jack
Nicholson where the hotel hallway expanded faster than he could run. If we
could though observe this, say analogous to Jack Nicholson in the film,
there would be optical effects. The spatial manifold could be a k = 1
closed or k = -1 hyperbolic or the dodecahedral tessellated universe of
Poincaré. Yet so far data is not forthcoming.
A Planck energy of quanta, say a UV graviton, could have causal influence
on us is it expands to the cosmological horizon or near so. The B-modes of
inflation, which are still being pursued, represent Planck units redshifted
to some appreciable scale comparable to the cosmological horizon. This is a
z factor z = 10^{10}ly/ℓ_p = 6.3×10^{60}, where taking the nat-log of this
and multiplying by the horizon scale 1.3×10^{10}ly we get 1.8×10^{12}ly.
The furthest out anything can have traversed at the speed of light to reach
is from that distance and from the earliest near Planck time in the
universe. What this means is the source or emitter of this graviton was
early on close to our region and the source is not that incredible distance
away.
LC
On Tuesday, May 19, 2020 at 1:41:45 AM UTC-5, Philip Thrift wrote:
>
>
> *Would traveling out in a "straight" line bring you back to where you
> started?*
>
>
> https://www.forbes.com/sites/startswithabang/2020/05/19/would-a-long-journey-through-the-universe-bring-us-back-to-our-starting-point/#1781c2ccf6c5
>
> In the writer's (Ethan Siegel's) *opinion*:
>
>
> On a cosmic scale, there is no indication that the Universe is anything
> other than infinite and flat. There is no evidence that features in one
> region of space also appear in any other well-separated region, nor is
> there evidence of a repeating pattern in the Universe's large-scale
> structure or the Big Bang's leftover glow. The only way we know of to turn
> a freely moving object around is via gravitation slingshot, not from cosmic
> curvature.
>
> And yet, it's a legitimate possibility that the Universe may, in fact, be
> finite in extent, but larger than our observations can currently take us.
> As the Universe unfolds over the coming billions of years, more and more of
> it (about 135% more, by volume) will become visible to us. If there's any
> hint that a long-distance journey would bring us back to our starting
> point, that's the only place we'll ever find it. Our only hope for
> discovering a finite but traversible Universe lies, quite ironically, in
> our far distant future.
>
> @philipthrift
>
--
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Re: Deriving the Born Rule
On Monday, May 18, 2020 at 6:29:04 PM UTC-5, Bruce wrote:
>
> On Mon, May 18, 2020 at 10:57 PM Lawrence Crowell <
> goldenfield...@gmail.com > wrote:
>
>> On Monday, May 18, 2020 at 12:12:28 AM UTC-5, Brent wrote:
>>>
>>>
>>>
>>> On 5/17/2020 6:20 PM, Lawrence Crowell wrote:
>>>
>>> On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote:
On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell <
goldenfield...@gmail.com> wrote:
> There is nothing wrong formally with what you argue. I would though
> say this is not entirely the Born rule. The Born rule connects
> eigenvalues
> with the probabilities of a wave function. For quantum state amplitudes
> a_i
> in a superposition ψ = sum_ia_iφ_i with φ*_jφ_i = δ_{ij} the spectrum of
> an
> observable O obeys
>
> ⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.
>
> Your argument has a tight fit with this for O_i = ρ_{ii}.
>
> The difficulty in part stems from the fact we keep using standard
> ideas of probability to understand quantum physics, which is more
> fundamentally about amplitudes which give probabilities, but are not
> probabilities. Your argument is very frequentist.
>
I can see why you might think this, but it is actually not the case. My
main point is to reject subjectivist notions of probability:
probabilities
in QM are clearly objective -- there is an objective decay rate (or
half-life) for any radioactive nucleus; there is a clearly objective
probability for that spin to be measured up rather than down in a
Stern-Gerlach magnet; and so on.
>>> Objective probabilities are frequentism.
>>>
>>>
>>> No necessarily. Objective probabilities may be based on symmetries and
>>> the principle of insufficient reason. I agree with Bruce; just because you
>>> measure a probability with frequency, that doesn't imply it must be based
>>> on frequentism.
>>>
>>
>> That is not what I meant. Bruce does sound as if he is appealing to an
>> objective basis for probability based on the frequency of occurrences of
>> events. I am not arguing this isy wrong, but rather that this is an
>> interpretation of probability.
>>
>
>
> I am sorry if I have given the impression that I thought that objective
> probabilities were possible only with frequentism. I thought I had made it
> clear that frequentism fails as a basis for the meaning of probability.
> There are many places where this is argued, and the consensus is that
> long-run relative frequencies cannot be used as a definition of
> probability.
>
> I was appealing to the propensity interpretation, which says that
> probabilities are intrinsic properties of some things.; such as decay
> rates; i.e., that probability is an intrinsic property of radio-active
> nuclei. But I agree with Brent, probabilities can be taken to be anything
> that satisfies the basic axioms of probability theory -- such as
> non-negative, normalisable, and additive. So subjective degrees of belief
> can form the basis for probabilities, as can certain symmetry properties,
> relative frequencies, and so on.
>
> The point is that while these things can be understood as probabilities in
> ordinary usage, they don't actually define what probability is. One can use
> frequency counts to estimate many of these probabilities, and one can use
> Bayes's theorem to update estimates of probability based on new evidence.
> But Bayes's theorem is merely an updating method -- it is not a definition
> of probability. People who consider themselves to be Bayesians usually have
> a basically subjective idea about probability, considering it essentially
> quantifies personal degrees of belief. But that understanding is not
> inherent in Bayes' theorem itself.
>
> As Brent says, these different approaches to probability have their uses
> in everyday life, but most of them are not suitable for fundamental
> physics. I consider objective probabilities based on intrinsic properties,
> or propensities, to be essential for a proper understanding of radio-active
> decay, and the probability of getting spin-up on a spin measurement, and so
> on. These things are properties of the way the world is, not matters of
> personal belief, or nothing more than relative frequencies. Probabilities
> may well be built into the fabric of the quantum wave-function via the
> amplitudes, but the probabilistic interpretation of these amplitudes has to
> be imposed via the Born rule: Just as with any mathematical theory -- one
> needs correspondence rules to say how the mathematical elements relate to
> physical observables. From that point of view, attempts to derive the Born
> rule from within the theory are doomed to failure -- contrary to the
> many-worlders' dream, the theory does not contain its own interpretation.
>
> Bruce
>
I will not say that this is wrong, but it strikes me as more
Re: Deriving the Born Rule
On Tue, May 19, 2020 at 4:47 PM smitra wrote: > On 19-05-2020 03:51, Bruce Kellett wrote: > > On Tue, May 19, 2020 at 11:16 AM 'Brent Meeker' via Everything List > > wrote: > >> > >> But even if you're right (and I think you are) does that affect the > >> MWI. In an Everett+Born theory there will still be other worlds and > >> the interpretation will still avoid the question, "When and where is > >> a measurement?"...answer "Whenever decoherence has made one state > >> orthogonal to all other states." Of course we could then as the > >> question, "When and where has the wave function collapsed?" and give > >> the same answer. Which would be CI+Zurek. > > > > Does this analysis affect the MWI? I think it does, because if > > probabilities are intrinsic, and the Born rule is merely a rule that > > connects the theory with experiment; not something that can be > > derived from within the theory, then we are left with the tension that > > I mentioned a while ago between many-worlds and the probability > > interpretation. Everett says that every outcome happens, but separate > > outcomes are in separate "relative states", or separate, orthogonal, > > branches. This can only mean that the probability is given by branch > > counting, and the probabilities are necessarily 50/50 for the > > two-state case. Then the probability for each branch on repeated > > measurements of an ensemble of N similarly prepared states is 1/2^N, > > and those probabilities are independent of the amplitudes. This is > > inconsistent with the analysis that gives the probability for each > > branch of the repeated trials by the normal binomial probability, with > > p equal to the mod-squared amplitude. (This is the analysis with which > > I began this thread.) The binomial probabilities are experimentally > > observed, so MWI is, on this account, inconsistent with experiment > > (even if not actually incoherent). > > > > The question of the preferred basis and the nature of measurement is > > answered by decoherence, and the collapse of the wave function is > > another interpretative move. On this view, the wave function is > > epistemic rather that ontological. The ontology is the particles or > > fields that the wave function describes, and these live on ordinary > > 3-space. This is not necessarily CI+Zurek, because Zurek still thinks > > he can derive probabilities from within the theory, and CI does not > > encompass decoherence and the quantum nature of everything. Nor is it > > Qbism, since that idea does not really encompass objective > > probabilities. > > > > Bruce > > It's implausible that a fundamental theory can have a macroscopic > concepts like "environment", "experiment" etc. in it build in. Where are these concepts "built in" to the theory as I have outlined it? One mentions things like experiments and the environment because the theory has, after all, to explain things like that. There is no question that experiments, apparatuses, observers, and the environment are all ultimately quantum, and must be encompassed within the quantum theory; that is something that Everett's approach taught us. But that insight has not been violated by anything that I have said. As Bell stressed, the fundamental theory should not refer to "measurement" or "observers". But we have to relate the theory to observation, or else the theory is useless. That's what motivated the MWI in the first place. Now, the MWI may not be > exactly correct as QM may itself only be an approximation to a more > fundamental theory. But the approach of trying to address > interpretational problems by relying on macroscopic concepts is a priori > doomed to fail > Not necessarily doomed to fail -- such an approach may not be entirely useless. The Copenhagen Interpretation did work well for nearly 100 years, and it still works in practise. The CI may not satisfy ones fundamentalist realist leanings, but that is another matter. Bruce -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQaWMF2dF2dnLYxavQ2cMQiFVLPhf3jfHaGfAZmBHAKoA%40mail.gmail.com.
Re: Deriving the Born Rule
On Monday, May 18, 2020 at 7:02:58 PM UTC-6, Bruce wrote: > > On Tue, May 19, 2020 at 9:59 AM Alan Grayson > wrote: > >> On Monday, May 18, 2020 at 5:29:04 PM UTC-6, Bruce wrote: >>> >>> >>> I am sorry if I have given the impression that I thought that objective >>> probabilities were possible only with frequentism. I thought I had made it >>> clear that frequentism fails as a basis for the meaning of probability. >>> There are many places where this is argued, and the consensus is that >>> long-run relative frequencies cannot be used as a definition of >>> probability. >>> >>> I was appealing to the propensity interpretation, which says that >>> probabilities are intrinsic properties of some things.; such as decay >>> rates; i.e., that probability is an intrinsic property of radio-active >>> nuclei. But I agree with Brent, probabilities can be taken to be anything >>> that satisfies the basic axioms of probability theory -- such as >>> non-negative, normalisable, and additive. So subjective degrees of belief >>> can form the basis for probabilities, as can certain symmetry properties, >>> relative frequencies, and so on. >>> >>> The point is that while these things can be understood as probabilities >>> in ordinary usage, they don't actually define what probability is. One can >>> use frequency counts to estimate many of these probabilities, and one can >>> use Bayes's theorem to update estimates of probability based on new >>> evidence. But Bayes's theorem is merely an updating method -- it is not a >>> definition of probability. People who consider themselves to be Bayesians >>> usually have a basically subjective idea about probability, considering it >>> essentially quantifies personal degrees of belief. But that understanding >>> is not inherent in Bayes' theorem itself. >>> >>> As Brent says, these different approaches to probability have their uses >>> in everyday life, but most of them are not suitable for fundamental >>> physics. I consider objective probabilities based on intrinsic properties, >>> or propensities, to be essential for a proper understanding of radio-active >>> decay, and the probability of getting spin-up on a spin measurement, and so >>> on. These things are properties of the way the world is, not matters of >>> personal belief, or nothing more than relative frequencies. Probabilities >>> may well be built into the fabric of the quantum wave-function via the >>> amplitudes, but the probabilistic interpretation of these amplitudes has to >>> be imposed via the Born rule: Just as with any mathematical theory -- one >>> needs correspondence rules to say how the mathematical elements relate to >>> physical observables. From that point of view, attempts to derive the Born >>> rule from within the theory are doomed to failure -- contrary to the >>> many-worlders' dream, the theory does not contain its own interpretation. >>> >>> Bruce >>> >> >> "Propensity" seems pretty vague. Hard to imagine finding an objective >> principle underlying probabilities. What precisely does Born's rule mean? >> AG >> > > > "Propensity" is just a word, the usage originates with Karl Popper, who > used it to convey the idea that probability may be a primitive concept, > like mass or charge, that is not analysable in terms of anything more > fundamental. So you cannot expect to explain the concept in terms of > anything else. > > The Born rule is really just the statement that quantum mechanics is a > theory that predicts probabilities, and those probabilities are given by > the mod-squared amplitudes. In other words, it is an interpretative rule, > connecting the theory with observation. Seen in this light, it does not > make sense to attempt to derive Born's rule from within the theory itself. > I think the analysis that I gave at the beginning of this thread is > probably the best that one can do -- one shows that the mod-squared > amplitudes play the role of probabilities, and that those are the > probabilities needed to connect the theory to experiment. The probabilities > are objective in that they are already part of the theory: the amplitudes > are objective aspects of the theory. > > Bruce > I haven't followed every detail of this discussion, but enough to get this important point; now I have no idea what the Born's rule means. Whereas it affirms something about "probabilities", it doesn't tell us what this means! To quote our Chief Asshole (DJT), Sad! AG -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/9248f071-6bef-4952-b991-fa237f8510b8%40googlegroups.com.
Re: Deriving the Born Rule
On 19-05-2020 03:51, Bruce Kellett wrote: On Tue, May 19, 2020 at 11:16 AM 'Brent Meeker' via Everything List wrote: On 5/18/2020 4:28 PM, Bruce Kellett wrote: I am sorry if I have given the impression that I thought that objective probabilities were possible only with frequentism. I thought I had made it clear that frequentism fails as a basis for the meaning of probability. There are many places where this is argued, and the consensus is that long-run relative frequencies cannot be used as a definition of probability. I was appealing to the propensity interpretation, which says that probabilities are intrinsic properties of some things.; such as decay rates; i.e., that probability is an intrinsic property of radio-active nuclei. But I agree with Brent, probabilities can be taken to be anything that satisfies the basic axioms of probability theory -- such as non-negative, normalisable, and additive. So subjective degrees of belief can form the basis for probabilities, as can certain symmetry properties, relative frequencies, and so on. The point is that while these things can be understood as probabilities in ordinary usage, they don't actually define what probability is. One can use frequency counts to estimate many of these probabilities, and one can use Bayes's theorem to update estimates of probability based on new evidence. But Bayes's theorem is merely an updating method -- it is not a definition of probability. People who consider themselves to be Bayesians usually have a basically subjective idea about probability, considering it essentially quantifies personal degrees of belief. But that understanding is not inherent in Bayes' theorem itself. As Brent says, these different approaches to probability have their uses in everyday life, but most of them are not suitable for fundamental physics. I consider objective probabilities based on intrinsic properties, or propensities, to be essential for a proper understanding of radio-active decay, and the probability of getting spin-up on a spin measurement, and so on. These things are properties of the way the world is, not matters of personal belief, or nothing more than relative frequencies. Probabilities may well be built into the fabric of the quantum wave-function via the amplitudes, but the probabilistic interpretation of these amplitudes has to be imposed via the Born rule: Just as with any mathematical theory -- one needs correspondence rules to say how the mathematical elements relate to physical observables. From that point of view, attempts to derive the Born rule from within the theory are doomed to failure -- contrary to the many-worlders' dream, the theory does not contain its own interpretation. But even if you're right (and I think you are) does that affect the MWI. In an Everett+Born theory there will still be other worlds and the interpretation will still avoid the question, "When and where is a measurement?"...answer "Whenever decoherence has made one state orthogonal to all other states." Of course we could then as the question, "When and where has the wave function collapsed?" and give the same answer. Which would be CI+Zurek. Does this analysis affect the MWI? I think it does, because if probabilities are intrinsic, and the Born rule is merely a rule that connects the theory with experiment; not something that can be derived from within the theory, then we are left with the tension that I mentioned a while ago between many-worlds and the probability interpretation. Everett says that every outcome happens, but separate outcomes are in separate "relative states", or separate, orthogonal, branches. This can only mean that the probability is given by branch counting, and the probabilities are necessarily 50/50 for the two-state case. Then the probability for each branch on repeated measurements of an ensemble of N similarly prepared states is 1/2^N, and those probabilities are independent of the amplitudes. This is inconsistent with the analysis that gives the probability for each branch of the repeated trials by the normal binomial probability, with p equal to the mod-squared amplitude. (This is the analysis with which I began this thread.) The binomial probabilities are experimentally observed, so MWI is, on this account, inconsistent with experiment (even if not actually incoherent). The question of the preferred basis and the nature of measurement is answered by decoherence, and the collapse of the wave function is another interpretative move. On this view, the wave function is epistemic rather that ontological. The ontology is the particles or fields that the wave function describes, and these live on ordinary 3-space. This is not necessarily CI+Zurek, because Zurek still thinks he can derive probabilities from within the theory, and CI does not encompass decoherence and the quantum nature of everything. Nor is it Qbism, since that idea does not really encompass objective probabilities. Bruce It's implausible
"Shape" of the universe
*Would traveling out in a "straight" line bring you back to where you started?* https://www.forbes.com/sites/startswithabang/2020/05/19/would-a-long-journey-through-the-universe-bring-us-back-to-our-starting-point/#1781c2ccf6c5 In the writer's (Ethan Siegel's) *opinion*: On a cosmic scale, there is no indication that the Universe is anything other than infinite and flat. There is no evidence that features in one region of space also appear in any other well-separated region, nor is there evidence of a repeating pattern in the Universe's large-scale structure or the Big Bang's leftover glow. The only way we know of to turn a freely moving object around is via gravitation slingshot, not from cosmic curvature. And yet, it's a legitimate possibility that the Universe may, in fact, be finite in extent, but larger than our observations can currently take us. As the Universe unfolds over the coming billions of years, more and more of it (about 135% more, by volume) will become visible to us. If there's any hint that a long-distance journey would bring us back to our starting point, that's the only place we'll ever find it. Our only hope for discovering a finite but traversible Universe lies, quite ironically, in our far distant future. @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/30d645b0-cbdd-4caf-a640-63d538e6ddb2%40googlegroups.com.
