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Showing posts with label Tegmark. Show all posts
Showing posts with label Tegmark. Show all posts
Monday, June 4, 2012
Saturday, September 4, 2010
Born in an infinite universe: a cosmological interpretation of quantum mechanics
This paper argues the Born rule is actually rendered redundant in an infinite universe in which all outcomes are realized.
this paper takes the conclusions of Page from the paper linked in the August 27 post immediately below a step further.
Page argued that Born's Rule would be insufficient in an extremely large universe due to the lack of definite projection operators.
this paper takes the conclusions of Page from the paper linked in the August 27 post immediately below a step further.
Page argued that Born's Rule would be insufficient in an extremely large universe due to the lack of definite projection operators.
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inlfation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantummeasurement in different regions, with relative frequencies given by the square of the wave function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. Replacing the standard hypothetical ensemble of measurements repeated ad inifnitum by a concrete decohered spatial collection of experiments carried out in different distant regions of space provides a natural context for a statistical interpretation of quantum mechanics. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics.
We also argue that after discarding a zero-norm part of the wavefunction, the remainder consists of a superposition of indistinguishable terms, so that arguably “collapse” of the wavefunction is irrelevant, and the “many worlds” of Everett’s interpretation are uniifed into one. Finally, the analysis suggests a “cosmological interpretation” of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer’s inability to self-locate in this collection.
Wednesday, May 13, 2009
Tegmark's Parallel Universes article
This article on parallel universes is linked on a few sites I have previously listed, however I believe it is worthy of a direct link. Tegmark provides a good, uncomplicated overview of the different types, or levels, of possible parallel universes. Some or all of them may actually exist.
The first three levels of parallel universe are completely distinct from our universe, and get progressively strange (for lack of a better description) comparison to the universe we are in. For instance, level one is essentially just regions of our present universe that are beyond our light horizon. It is estimated that the region of our universe we can actually see is only a very small portion of the whole, however the actual size and shape of our universe is not established. Level two parallel universes represent other post-inflation bubbles; in other words other universes that may have resulted from the big bang and subsequent inflation. In these universes the fundamental physics would be the same but the constants would be different. Finally, the level three universes would have different fundamental physics.
Level four universes can be considered somewhat distinct from the first three, in that if the parallel universes of quantum mechanics exist they overlap and interact in a way the other levels do not. These universes would all share the laws of quantum mechanics.
Thursday, February 5, 2009
Monday, July 28, 2008
Friday, May 23, 2008
Many lives in many worlds
Article by Max Tegmark in July, 2007 Nature on Many Worlds theory (as posted on 12 Degrees of Freedom).
Friday, October 5, 2007
Friday, September 28, 2007
New Scientist article on new work by Deutsch
Parallel universes make quantum sense
19 September 2007 NewScientist.com
by Zeeya Merali -- If you think of yourself as unique, think again.
The days when physicists could ignore the concept of parallel
universes may have come to an end. If that doesn't send a shudder down
your spine, think of it this way: our world is just one of many. You
are just one version of many.
David Deutsch at the University of Oxford and colleagues have shown
that key equations of quantum mechanics arise from the mathematics of
parallel universes. "This work will go down as one of the most
important developments in the history of science," says Andy Albrecht,
a physicist at the University of California at Davis. In one parallel
universe, at least, it will - whether it does in our one remains to be
seen.
The "many worlds" interpretation of quantum mechanics was proposed 50
years ago by Hugh Everett, a graduate student at Princeton University.
Rather than apply one set of rules to the subatomic quantum world and
another to the larger-scale everyday world, as physicists tend to do,
Everett wanted to apply quantum mechanical equations to everything.
This had some startling consequences.
According to quantum mechanics, particles do not have set properties
before they are observed. Instead, particles are described by "wave
functions" representing many mutually contradictory properties. It is
only when an observer measures a property that the particle somehow
settles into one of these multiple options. The paradox is exemplified
by Schrodinger's cat - the famous thought experiment in which a cat in
a box can be said to be both alive and dead. It is traditionally
thought that the act of observation, opening the box to check the cat,
is what forces it to settle into a state, living or dead.
If, as Everett argued, quantum mechanics is applied to the whole
universe, then it too should exist in a multitude of separate states.
There would be a "multiverse" of parallel universes - one for every
physical possibility. So when you open the box holding Schrodinger's
cat, the universe splits, forming two new "yous" - one whose future
involves viewing the live cat and the other who sees the dead cat.
Dismissed by the scientific establishment as ridiculous for decades,
the many-worlds scenario may at last come in from the cold thanks to
Deutsch's work.
The biggest criticism leveled at many worlds was that it seemed to
make a puzzle about the outcomes of quantum experiments even worse.
Physicists can predict the probability of getting a certain outcome
from a quantum experiment from the square of its wave function,
according to the Born rule. Nobody can explain why this rule works, it
simply fits with experimental observations. The problem was there
seemed to be no place for the Born rule in the multiverse. In fact,
there didn't seem to be any space for any probabilities at all, says
Deutsch.
"You toss a coin, but what does it mean to say that the probability of
it coming up heads is 50 per cent?" Deutsch asks. "According to
Everett, both outcomes must happen."
In the mid-1990s, Deutsch set out to put the uncertainty we see in
quantum mechanical experiments back into the many-worlds scenario.
Now, with additional work by Simon Saunders and David Wallace, also at
Oxford, he believes they have succeeded. The trick is to examine a
quantum experiment while excluding probability theory and accepting
the many-worlds interpretation.
The multiverse has a branching structure, created as the universe
splits into parallel versions of itself. The thickness of the branches
can be calculated solely using deterministic equations, getting around
the uncertainties usually associated with quantum physics. What the
Oxford gang found is that the branching structure exactly reproduces
the peculiar probabilities predicted by the Born rule. The branching
also gives the illusion of probabilistic outcomes to measurements.
Deutsch believes this solves the problem of the origin of quantum
probability once and for all. "Probabilities used to be regarded as
the biggest problem for Everett, but ironically, they are now its most
powerful success," he says.
"We've cleared up the obscurities and come up with a pretty clear
verdict that Everett works," says Saunders, who is presenting the work
with Wallace at the Many Worlds at 50 conference at the Perimeter
Institute for Theoretical Physics in Waterloo, Canada, this week.
"It's a dramatic turnaround and it means that people now have to
discuss Everett seriously."
Albrecht agrees that the work will shake up physicists' worlds. "Many
people are uncomfortable about the probabilities at the heart of
quantum mechanics and attempt to get rid of quantum mechanics because
of it," he says. "But this greatly amplifies the fundamental place of
quantum mechanics in our understanding of the physical world."
David Papineau, a philosopher of physics at King's College London,
says that he has been converted from scepticism about many worlds to
belief, based on its potential to one day solve this puzzle of quantum
probabilities. He adds, though, that the work by Deutsch, Wallace and
Saunders must now be scrutinised. "It's an ambitious claim and so we
have to be careful," he says. For Papineau, the problem is whether a
belief in parallel universes should affect the way we live our
everyday lives .
Max Tegmark at the Massachusetts Institute of Technology has long been
a fan of the many-worlds scenario. But while he believes the new work
on probability should help convince physicists of its reality, it will
never be enough to win over die-hard sceptics. "The critique of many
worlds is shifting from 'it makes no sense and I hate it' to simply 'I
hate it'," he says.
David Albert, a philosopher of physics at Columbia University, New
York, is sceptical. He argues there is good reason to be wary because
the Oxford group may be guilty of sleight of hand. "When you first
hear about this you feel euphoric," he says. "But then you think,
maybe this is too good to be true." He believes that it is irrelevant
that Deutsch and his colleagues can show that branching universes give
the illusion of probabilistic outcomes to measurements. What we really
want to know, says Albert, is why this branching happens in the first
place. "They have answered a question, but I think it's the wrong
question," he says.
Wojciech Zurek at the Los Alamos National Laboratory in New Mexico
believes that the Born rule is exactly the right question to tackle.
However, he believes that it can be answered without resorting to
parallel universes. Zurek points out that Everett never used the term
"many worlds" in his papers, and says that his work can be interpreted
in less controversial ways.
Zurek is also inspired by Everett's ideas, particularly his insight
that quantum mechanics must be applied to the entire universe rather
than a limited quantum realm. He interprets this to mean that quantum
entanglement - the process in which quantum particles can become
inextricably linked and act in unison no matter how far apart they are
- is a fundamental ingredient of quantum physics. Zurek has already
used this property to explain why we see a single objective reality
when we make a measurement of a quantum state (New Scientist, 30 June,
p 18). Zurek says that entanglement can also be used to derive the
Born rule (www.arxiv.org/abs/0707.2832). "I could not have derived
probability without using Everett," says Zurek, who is also presenting
his work at the conference. "But at no point am I forced to assign
equal reality to all other versions of the universe in the many-worlds
scenario."
For Tegmark, the fact that many worlds is sparking such debate, 50
years after its conception, is a triumph in itself. He believes that
physicists interested in quantum computing and cosmology are now
warming to it. Will the majority be won over? "That depends on what
parallel universe you live in," he says.
>From issue 2622 of New Scientist magazine, 19 September 2007, page 6-7
[Just another universe]
Like Schrodinger's cat, you're locked in a box with a vial of poison
gas. If a radioactive atom decays before someone opens the box to
observe you, the gas will be released. According to the multiverse
picture, in one future "you" will live, because the atom has not
decayed, and in another "you" will die. So, should you be worried?
The issue of how we should feel and act when faced with a constantly
splitting identity will be addressed by David Papineau of King's
College London at a conference on the many-worlds scenario in
Waterloo, Canada this week.
To start with, Papineau considers feelings of guilt and hope in the
multiverse. Suppose that you are driving recklessly and narrowly avoid
crashing into another car. "You might think 'lucky escape', but you
should be feeling guilty about the passengers your other self has
killed," says Papineau.
He also questions the use of hope. "You hope your football team will
win a match, but that's meaningless - they both win and lose," he says.
Although each of our descendant selves is equally real, thankfully
Papineau argues that their fates shouldn't affect our choices before
we make them. We should be just as reluctant, or excited, about
climbing into Schr?dinger's box in the many-worlds picture, as we
would be if we believed that only one outcome is actually realised.
Simon Saunders at the University of Oxford doesn't think that Papineau
is wrong, but does think he is asking too much of us. "The multiverse
will drive you crazy if you really think about how it affects your
life, and I can't live like that," he says. His solution? "I'll just
accept Everett and then think about something else, to save my
sanity."
19 September 2007 NewScientist.com
by Zeeya Merali -- If you think of yourself as unique, think again.
The days when physicists could ignore the concept of parallel
universes may have come to an end. If that doesn't send a shudder down
your spine, think of it this way: our world is just one of many. You
are just one version of many.
David Deutsch at the University of Oxford and colleagues have shown
that key equations of quantum mechanics arise from the mathematics of
parallel universes. "This work will go down as one of the most
important developments in the history of science," says Andy Albrecht,
a physicist at the University of California at Davis. In one parallel
universe, at least, it will - whether it does in our one remains to be
seen.
The "many worlds" interpretation of quantum mechanics was proposed 50
years ago by Hugh Everett, a graduate student at Princeton University.
Rather than apply one set of rules to the subatomic quantum world and
another to the larger-scale everyday world, as physicists tend to do,
Everett wanted to apply quantum mechanical equations to everything.
This had some startling consequences.
According to quantum mechanics, particles do not have set properties
before they are observed. Instead, particles are described by "wave
functions" representing many mutually contradictory properties. It is
only when an observer measures a property that the particle somehow
settles into one of these multiple options. The paradox is exemplified
by Schrodinger's cat - the famous thought experiment in which a cat in
a box can be said to be both alive and dead. It is traditionally
thought that the act of observation, opening the box to check the cat,
is what forces it to settle into a state, living or dead.
If, as Everett argued, quantum mechanics is applied to the whole
universe, then it too should exist in a multitude of separate states.
There would be a "multiverse" of parallel universes - one for every
physical possibility. So when you open the box holding Schrodinger's
cat, the universe splits, forming two new "yous" - one whose future
involves viewing the live cat and the other who sees the dead cat.
Dismissed by the scientific establishment as ridiculous for decades,
the many-worlds scenario may at last come in from the cold thanks to
Deutsch's work.
The biggest criticism leveled at many worlds was that it seemed to
make a puzzle about the outcomes of quantum experiments even worse.
Physicists can predict the probability of getting a certain outcome
from a quantum experiment from the square of its wave function,
according to the Born rule. Nobody can explain why this rule works, it
simply fits with experimental observations. The problem was there
seemed to be no place for the Born rule in the multiverse. In fact,
there didn't seem to be any space for any probabilities at all, says
Deutsch.
"You toss a coin, but what does it mean to say that the probability of
it coming up heads is 50 per cent?" Deutsch asks. "According to
Everett, both outcomes must happen."
In the mid-1990s, Deutsch set out to put the uncertainty we see in
quantum mechanical experiments back into the many-worlds scenario.
Now, with additional work by Simon Saunders and David Wallace, also at
Oxford, he believes they have succeeded. The trick is to examine a
quantum experiment while excluding probability theory and accepting
the many-worlds interpretation.
The multiverse has a branching structure, created as the universe
splits into parallel versions of itself. The thickness of the branches
can be calculated solely using deterministic equations, getting around
the uncertainties usually associated with quantum physics. What the
Oxford gang found is that the branching structure exactly reproduces
the peculiar probabilities predicted by the Born rule. The branching
also gives the illusion of probabilistic outcomes to measurements.
Deutsch believes this solves the problem of the origin of quantum
probability once and for all. "Probabilities used to be regarded as
the biggest problem for Everett, but ironically, they are now its most
powerful success," he says.
"We've cleared up the obscurities and come up with a pretty clear
verdict that Everett works," says Saunders, who is presenting the work
with Wallace at the Many Worlds at 50 conference at the Perimeter
Institute for Theoretical Physics in Waterloo, Canada, this week.
"It's a dramatic turnaround and it means that people now have to
discuss Everett seriously."
Albrecht agrees that the work will shake up physicists' worlds. "Many
people are uncomfortable about the probabilities at the heart of
quantum mechanics and attempt to get rid of quantum mechanics because
of it," he says. "But this greatly amplifies the fundamental place of
quantum mechanics in our understanding of the physical world."
David Papineau, a philosopher of physics at King's College London,
says that he has been converted from scepticism about many worlds to
belief, based on its potential to one day solve this puzzle of quantum
probabilities. He adds, though, that the work by Deutsch, Wallace and
Saunders must now be scrutinised. "It's an ambitious claim and so we
have to be careful," he says. For Papineau, the problem is whether a
belief in parallel universes should affect the way we live our
everyday lives .
Max Tegmark at the Massachusetts Institute of Technology has long been
a fan of the many-worlds scenario. But while he believes the new work
on probability should help convince physicists of its reality, it will
never be enough to win over die-hard sceptics. "The critique of many
worlds is shifting from 'it makes no sense and I hate it' to simply 'I
hate it'," he says.
David Albert, a philosopher of physics at Columbia University, New
York, is sceptical. He argues there is good reason to be wary because
the Oxford group may be guilty of sleight of hand. "When you first
hear about this you feel euphoric," he says. "But then you think,
maybe this is too good to be true." He believes that it is irrelevant
that Deutsch and his colleagues can show that branching universes give
the illusion of probabilistic outcomes to measurements. What we really
want to know, says Albert, is why this branching happens in the first
place. "They have answered a question, but I think it's the wrong
question," he says.
Wojciech Zurek at the Los Alamos National Laboratory in New Mexico
believes that the Born rule is exactly the right question to tackle.
However, he believes that it can be answered without resorting to
parallel universes. Zurek points out that Everett never used the term
"many worlds" in his papers, and says that his work can be interpreted
in less controversial ways.
Zurek is also inspired by Everett's ideas, particularly his insight
that quantum mechanics must be applied to the entire universe rather
than a limited quantum realm. He interprets this to mean that quantum
entanglement - the process in which quantum particles can become
inextricably linked and act in unison no matter how far apart they are
- is a fundamental ingredient of quantum physics. Zurek has already
used this property to explain why we see a single objective reality
when we make a measurement of a quantum state (New Scientist, 30 June,
p 18). Zurek says that entanglement can also be used to derive the
Born rule (www.arxiv.org/abs/0707.2832). "I could not have derived
probability without using Everett," says Zurek, who is also presenting
his work at the conference. "But at no point am I forced to assign
equal reality to all other versions of the universe in the many-worlds
scenario."
For Tegmark, the fact that many worlds is sparking such debate, 50
years after its conception, is a triumph in itself. He believes that
physicists interested in quantum computing and cosmology are now
warming to it. Will the majority be won over? "That depends on what
parallel universe you live in," he says.
>From issue 2622 of New Scientist magazine, 19 September 2007, page 6-7
[Just another universe]
Like Schrodinger's cat, you're locked in a box with a vial of poison
gas. If a radioactive atom decays before someone opens the box to
observe you, the gas will be released. According to the multiverse
picture, in one future "you" will live, because the atom has not
decayed, and in another "you" will die. So, should you be worried?
The issue of how we should feel and act when faced with a constantly
splitting identity will be addressed by David Papineau of King's
College London at a conference on the many-worlds scenario in
Waterloo, Canada this week.
To start with, Papineau considers feelings of guilt and hope in the
multiverse. Suppose that you are driving recklessly and narrowly avoid
crashing into another car. "You might think 'lucky escape', but you
should be feeling guilty about the passengers your other self has
killed," says Papineau.
He also questions the use of hope. "You hope your football team will
win a match, but that's meaningless - they both win and lose," he says.
Although each of our descendant selves is equally real, thankfully
Papineau argues that their fates shouldn't affect our choices before
we make them. We should be just as reluctant, or excited, about
climbing into Schr?dinger's box in the many-worlds picture, as we
would be if we believed that only one outcome is actually realised.
Simon Saunders at the University of Oxford doesn't think that Papineau
is wrong, but does think he is asking too much of us. "The multiverse
will drive you crazy if you really think about how it affects your
life, and I can't live like that," he says. His solution? "I'll just
accept Everett and then think about something else, to save my
sanity."
Saturday, April 28, 2007
Max Tegmark's new paper "The Mathematical Universe"
http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.0646v1.pdf
Interesting paper that is a follow up on the 1996 article that asked "Is the theory of everything merely the ultimate ensemble theory?" The technical parts of this one are going to be difficult reading for even many with scientific backgrounds.
Interesting paper that is a follow up on the 1996 article that asked "Is the theory of everything merely the ultimate ensemble theory?" The technical parts of this one are going to be difficult reading for even many with scientific backgrounds.
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