#37
Oct1206, 04:21 AM

P: n/a

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbigremove CLOTHES to reply) wrote: > > The question in my mind is where does this energy come from and it would > > seem that more and more of it is needed in order to increase the expansion > > rate. > > It doesn't have to come from anywhere. The FriedmannLemaître equations > allow for such a term, and apparently it has been observed. Note that > there is not a problem with energy conservation, since energy isn't > conserved in general relativity anyway. (Imagine a universe consisting > only of radiation. It expands. The number of photons remains the same, > but the energy of each decreases due to the redshift. No, this lost > energy does not do the work of expanding the universe.) > What, if any, conserved quantities are there in General Relativity? I recall there is an EnergyMomentum tensor, but I know little beyond that. Is that conserved or involved in a conservation law? If so, what does it mean? thanks.  Lou Pecora (my views are my own) REMOVE THIS to email me. 


#38
Oct1206, 04:21 AM

P: n/a

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbigremove CLOTHES to reply) wrote: > > The question in my mind is where does this energy come from and it would > > seem that more and more of it is needed in order to increase the expansion > > rate. > > It doesn't have to come from anywhere. The FriedmannLemaître equations > allow for such a term, and apparently it has been observed. Note that > there is not a problem with energy conservation, since energy isn't > conserved in general relativity anyway. (Imagine a universe consisting > only of radiation. It expands. The number of photons remains the same, > but the energy of each decreases due to the redshift. No, this lost > energy does not do the work of expanding the universe.) > What, if any, conserved quantities are there in General Relativity? I recall there is an EnergyMomentum tensor, but I know little beyond that. Is that conserved or involved in a conservation law? If so, what does it mean? thanks.  Lou Pecora (my views are my own) REMOVE THIS to email me. 


#39
Oct1206, 04:21 AM

P: n/a

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbigremove CLOTHES to reply) wrote: > > The question in my mind is where does this energy come from and it would > > seem that more and more of it is needed in order to increase the expansion > > rate. > > It doesn't have to come from anywhere. The FriedmannLemaître equations > allow for such a term, and apparently it has been observed. Note that > there is not a problem with energy conservation, since energy isn't > conserved in general relativity anyway. (Imagine a universe consisting > only of radiation. It expands. The number of photons remains the same, > but the energy of each decreases due to the redshift. No, this lost > energy does not do the work of expanding the universe.) > What, if any, conserved quantities are there in General Relativity? I recall there is an EnergyMomentum tensor, but I know little beyond that. Is that conserved or involved in a conservation law? If so, what does it mean? thanks.  Lou Pecora (my views are my own) REMOVE THIS to email me. 


#40
Oct1206, 04:21 AM

P: n/a

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbigremove CLOTHES to reply) wrote: > > The question in my mind is where does this energy come from and it would > > seem that more and more of it is needed in order to increase the expansion > > rate. > > It doesn't have to come from anywhere. The FriedmannLemaître equations > allow for such a term, and apparently it has been observed. Note that > there is not a problem with energy conservation, since energy isn't > conserved in general relativity anyway. (Imagine a universe consisting > only of radiation. It expands. The number of photons remains the same, > but the energy of each decreases due to the redshift. No, this lost > energy does not do the work of expanding the universe.) > What, if any, conserved quantities are there in General Relativity? I recall there is an EnergyMomentum tensor, but I know little beyond that. Is that conserved or involved in a conservation law? If so, what does it mean? thanks.  Lou Pecora (my views are my own) REMOVE THIS to email me. 


#41
Oct1206, 04:21 AM

P: n/a

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbigremove CLOTHES to reply) wrote: > > The question in my mind is where does this energy come from and it would > > seem that more and more of it is needed in order to increase the expansion > > rate. > > It doesn't have to come from anywhere. The FriedmannLemaître equations > allow for such a term, and apparently it has been observed. Note that > there is not a problem with energy conservation, since energy isn't > conserved in general relativity anyway. (Imagine a universe consisting > only of radiation. It expands. The number of photons remains the same, > but the energy of each decreases due to the redshift. No, this lost > energy does not do the work of expanding the universe.) > What, if any, conserved quantities are there in General Relativity? I recall there is an EnergyMomentum tensor, but I know little beyond that. Is that conserved or involved in a conservation law? If so, what does it mean? thanks.  Lou Pecora (my views are my own) REMOVE THIS to email me. 


#42
Oct1206, 04:21 AM

P: n/a

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbigremove CLOTHES to reply) wrote: > > The question in my mind is where does this energy come from and it would > > seem that more and more of it is needed in order to increase the expansion > > rate. > > It doesn't have to come from anywhere. The FriedmannLemaître equations > allow for such a term, and apparently it has been observed. Note that > there is not a problem with energy conservation, since energy isn't > conserved in general relativity anyway. (Imagine a universe consisting > only of radiation. It expands. The number of photons remains the same, > but the energy of each decreases due to the redshift. No, this lost > energy does not do the work of expanding the universe.) > What, if any, conserved quantities are there in General Relativity? I recall there is an EnergyMomentum tensor, but I know little beyond that. Is that conserved or involved in a conservation law? If so, what does it mean? thanks.  Lou Pecora (my views are my own) REMOVE THIS to email me. 


#43
Oct1206, 04:21 AM

P: n/a

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbigremove CLOTHES to reply) wrote: > > The question in my mind is where does this energy come from and it would > > seem that more and more of it is needed in order to increase the expansion > > rate. > > It doesn't have to come from anywhere. The FriedmannLemaître equations > allow for such a term, and apparently it has been observed. Note that > there is not a problem with energy conservation, since energy isn't > conserved in general relativity anyway. (Imagine a universe consisting > only of radiation. It expands. The number of photons remains the same, > but the energy of each decreases due to the redshift. No, this lost > energy does not do the work of expanding the universe.) > What, if any, conserved quantities are there in General Relativity? I recall there is an EnergyMomentum tensor, but I know little beyond that. Is that conserved or involved in a conservation law? If so, what does it mean? thanks.  Lou Pecora (my views are my own) REMOVE THIS to email me. 


#44
Oct1206, 04:21 AM

P: n/a

In article <dg0qo6$hmt$1@online.de>,
helbig@astro.multiCLOTHESvax.de (Phillip Helbigremove CLOTHES to reply) wrote: > > The question in my mind is where does this energy come from and it would > > seem that more and more of it is needed in order to increase the expansion > > rate. > > It doesn't have to come from anywhere. The FriedmannLemaître equations > allow for such a term, and apparently it has been observed. Note that > there is not a problem with energy conservation, since energy isn't > conserved in general relativity anyway. (Imagine a universe consisting > only of radiation. It expands. The number of photons remains the same, > but the energy of each decreases due to the redshift. No, this lost > energy does not do the work of expanding the universe.) > What, if any, conserved quantities are there in General Relativity? I recall there is an EnergyMomentum tensor, but I know little beyond that. Is that conserved or involved in a conservation law? If so, what does it mean? thanks.  Lou Pecora (my views are my own) REMOVE THIS to email me. 


#45
Oct1206, 05:06 AM

P: n/a

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion >> rate increase that is working against the force of gravity? >> >> The answer seems to be Dark Energy. Correct. > Whatever that is! Dark energy may be modelled by adding a constant to Einstein's equations; hence the term "cosmological constant". >> The question in my mind is where does this energy come from >> and it would seem that more and more of it is needed in order >> to increase the expansion rate. Correct. The energy comes from the expansion (a form of gravitational or geometric energy) which is negative. As the universe expands the positive energy locked as dark energy increases (density is constant, but volume increases); this is offset by the negative energy in the Hubble expansion which decreases (becomes more negative). In the case of dark energy this process can continue for ever; it's a slow form of inflation. > > It doesn't have to come from anywhere. The FriedmannLemaître > equations allow for such a term, and apparently it has been observed. > Note that there is not a problem with energy conservation, since > energy isn't conserved in general relativity anyway. That is not true. Energy is conserved in GR, with the obvious caveat that we have to adopt a sensible definition of energy. http://www.physics.adelaide.edu.au/~...energy_gr.html > (Imagine a universe consisting only of radiation. It expands. > The number of photons remains the same, but the energy of each > decreases due to the redshift. No, this lost energy does not do > the work of expanding the universe.) Then why does a radiantfilled universe decelerate faster than a matterfilled universe? Because the energy lost in the redshift cancels some of the negative energy tied up in the Hubble expansion. Cheers, Michael C Price  http://mcp.longevityreport.com http://www.hedweb.com/manworld.htm 


#46
Oct1206, 05:06 AM

P: n/a

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion >> rate increase that is working against the force of gravity? >> >> The answer seems to be Dark Energy. Correct. > Whatever that is! Dark energy may be modelled by adding a constant to Einstein's equations; hence the term "cosmological constant". >> The question in my mind is where does this energy come from >> and it would seem that more and more of it is needed in order >> to increase the expansion rate. Correct. The energy comes from the expansion (a form of gravitational or geometric energy) which is negative. As the universe expands the positive energy locked as dark energy increases (density is constant, but volume increases); this is offset by the negative energy in the Hubble expansion which decreases (becomes more negative). In the case of dark energy this process can continue for ever; it's a slow form of inflation. > > It doesn't have to come from anywhere. The FriedmannLemaître > equations allow for such a term, and apparently it has been observed. > Note that there is not a problem with energy conservation, since > energy isn't conserved in general relativity anyway. That is not true. Energy is conserved in GR, with the obvious caveat that we have to adopt a sensible definition of energy. http://www.physics.adelaide.edu.au/~...energy_gr.html > (Imagine a universe consisting only of radiation. It expands. > The number of photons remains the same, but the energy of each > decreases due to the redshift. No, this lost energy does not do > the work of expanding the universe.) Then why does a radiantfilled universe decelerate faster than a matterfilled universe? Because the energy lost in the redshift cancels some of the negative energy tied up in the Hubble expansion. Cheers, Michael C Price  http://mcp.longevityreport.com http://www.hedweb.com/manworld.htm 


#47
Oct1206, 05:06 AM

P: n/a

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion >> rate increase that is working against the force of gravity? >> >> The answer seems to be Dark Energy. Correct. > Whatever that is! Dark energy may be modelled by adding a constant to Einstein's equations; hence the term "cosmological constant". >> The question in my mind is where does this energy come from >> and it would seem that more and more of it is needed in order >> to increase the expansion rate. Correct. The energy comes from the expansion (a form of gravitational or geometric energy) which is negative. As the universe expands the positive energy locked as dark energy increases (density is constant, but volume increases); this is offset by the negative energy in the Hubble expansion which decreases (becomes more negative). In the case of dark energy this process can continue for ever; it's a slow form of inflation. > > It doesn't have to come from anywhere. The FriedmannLemaître > equations allow for such a term, and apparently it has been observed. > Note that there is not a problem with energy conservation, since > energy isn't conserved in general relativity anyway. That is not true. Energy is conserved in GR, with the obvious caveat that we have to adopt a sensible definition of energy. http://www.physics.adelaide.edu.au/~...energy_gr.html > (Imagine a universe consisting only of radiation. It expands. > The number of photons remains the same, but the energy of each > decreases due to the redshift. No, this lost energy does not do > the work of expanding the universe.) Then why does a radiantfilled universe decelerate faster than a matterfilled universe? Because the energy lost in the redshift cancels some of the negative energy tied up in the Hubble expansion. Cheers, Michael C Price  http://mcp.longevityreport.com http://www.hedweb.com/manworld.htm 


#48
Oct1206, 05:06 AM

P: n/a

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion >> rate increase that is working against the force of gravity? >> >> The answer seems to be Dark Energy. Correct. > Whatever that is! Dark energy may be modelled by adding a constant to Einstein's equations; hence the term "cosmological constant". >> The question in my mind is where does this energy come from >> and it would seem that more and more of it is needed in order >> to increase the expansion rate. Correct. The energy comes from the expansion (a form of gravitational or geometric energy) which is negative. As the universe expands the positive energy locked as dark energy increases (density is constant, but volume increases); this is offset by the negative energy in the Hubble expansion which decreases (becomes more negative). In the case of dark energy this process can continue for ever; it's a slow form of inflation. > > It doesn't have to come from anywhere. The FriedmannLemaître > equations allow for such a term, and apparently it has been observed. > Note that there is not a problem with energy conservation, since > energy isn't conserved in general relativity anyway. That is not true. Energy is conserved in GR, with the obvious caveat that we have to adopt a sensible definition of energy. http://www.physics.adelaide.edu.au/~...energy_gr.html > (Imagine a universe consisting only of radiation. It expands. > The number of photons remains the same, but the energy of each > decreases due to the redshift. No, this lost energy does not do > the work of expanding the universe.) Then why does a radiantfilled universe decelerate faster than a matterfilled universe? Because the energy lost in the redshift cancels some of the negative energy tied up in the Hubble expansion. Cheers, Michael C Price  http://mcp.longevityreport.com http://www.hedweb.com/manworld.htm 


#49
Oct1206, 05:06 AM

P: n/a

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion >> rate increase that is working against the force of gravity? >> >> The answer seems to be Dark Energy. Correct. > Whatever that is! Dark energy may be modelled by adding a constant to Einstein's equations; hence the term "cosmological constant". >> The question in my mind is where does this energy come from >> and it would seem that more and more of it is needed in order >> to increase the expansion rate. Correct. The energy comes from the expansion (a form of gravitational or geometric energy) which is negative. As the universe expands the positive energy locked as dark energy increases (density is constant, but volume increases); this is offset by the negative energy in the Hubble expansion which decreases (becomes more negative). In the case of dark energy this process can continue for ever; it's a slow form of inflation. > > It doesn't have to come from anywhere. The FriedmannLemaître > equations allow for such a term, and apparently it has been observed. > Note that there is not a problem with energy conservation, since > energy isn't conserved in general relativity anyway. That is not true. Energy is conserved in GR, with the obvious caveat that we have to adopt a sensible definition of energy. http://www.physics.adelaide.edu.au/~...energy_gr.html > (Imagine a universe consisting only of radiation. It expands. > The number of photons remains the same, but the energy of each > decreases due to the redshift. No, this lost energy does not do > the work of expanding the universe.) Then why does a radiantfilled universe decelerate faster than a matterfilled universe? Because the energy lost in the redshift cancels some of the negative energy tied up in the Hubble expansion. Cheers, Michael C Price  http://mcp.longevityreport.com http://www.hedweb.com/manworld.htm 


#50
Oct1206, 05:06 AM

P: n/a

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion >> rate increase that is working against the force of gravity? >> >> The answer seems to be Dark Energy. Correct. > Whatever that is! Dark energy may be modelled by adding a constant to Einstein's equations; hence the term "cosmological constant". >> The question in my mind is where does this energy come from >> and it would seem that more and more of it is needed in order >> to increase the expansion rate. Correct. The energy comes from the expansion (a form of gravitational or geometric energy) which is negative. As the universe expands the positive energy locked as dark energy increases (density is constant, but volume increases); this is offset by the negative energy in the Hubble expansion which decreases (becomes more negative). In the case of dark energy this process can continue for ever; it's a slow form of inflation. > > It doesn't have to come from anywhere. The FriedmannLemaître > equations allow for such a term, and apparently it has been observed. > Note that there is not a problem with energy conservation, since > energy isn't conserved in general relativity anyway. That is not true. Energy is conserved in GR, with the obvious caveat that we have to adopt a sensible definition of energy. http://www.physics.adelaide.edu.au/~...energy_gr.html > (Imagine a universe consisting only of radiation. It expands. > The number of photons remains the same, but the energy of each > decreases due to the redshift. No, this lost energy does not do > the work of expanding the universe.) Then why does a radiantfilled universe decelerate faster than a matterfilled universe? Because the energy lost in the redshift cancels some of the negative energy tied up in the Hubble expansion. Cheers, Michael C Price  http://mcp.longevityreport.com http://www.hedweb.com/manworld.htm 


#51
Oct1206, 05:06 AM

P: n/a

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion >> rate increase that is working against the force of gravity? >> >> The answer seems to be Dark Energy. Correct. > Whatever that is! Dark energy may be modelled by adding a constant to Einstein's equations; hence the term "cosmological constant". >> The question in my mind is where does this energy come from >> and it would seem that more and more of it is needed in order >> to increase the expansion rate. Correct. The energy comes from the expansion (a form of gravitational or geometric energy) which is negative. As the universe expands the positive energy locked as dark energy increases (density is constant, but volume increases); this is offset by the negative energy in the Hubble expansion which decreases (becomes more negative). In the case of dark energy this process can continue for ever; it's a slow form of inflation. > > It doesn't have to come from anywhere. The FriedmannLemaître > equations allow for such a term, and apparently it has been observed. > Note that there is not a problem with energy conservation, since > energy isn't conserved in general relativity anyway. That is not true. Energy is conserved in GR, with the obvious caveat that we have to adopt a sensible definition of energy. http://www.physics.adelaide.edu.au/~...energy_gr.html > (Imagine a universe consisting only of radiation. It expands. > The number of photons remains the same, but the energy of each > decreases due to the redshift. No, this lost energy does not do > the work of expanding the universe.) Then why does a radiantfilled universe decelerate faster than a matterfilled universe? Because the energy lost in the redshift cancels some of the negative energy tied up in the Hubble expansion. Cheers, Michael C Price  http://mcp.longevityreport.com http://www.hedweb.com/manworld.htm 


#52
Oct1206, 05:06 AM

P: n/a

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion >> rate increase that is working against the force of gravity? >> >> The answer seems to be Dark Energy. Correct. > Whatever that is! Dark energy may be modelled by adding a constant to Einstein's equations; hence the term "cosmological constant". >> The question in my mind is where does this energy come from >> and it would seem that more and more of it is needed in order >> to increase the expansion rate. Correct. The energy comes from the expansion (a form of gravitational or geometric energy) which is negative. As the universe expands the positive energy locked as dark energy increases (density is constant, but volume increases); this is offset by the negative energy in the Hubble expansion which decreases (becomes more negative). In the case of dark energy this process can continue for ever; it's a slow form of inflation. > > It doesn't have to come from anywhere. The FriedmannLemaître > equations allow for such a term, and apparently it has been observed. > Note that there is not a problem with energy conservation, since > energy isn't conserved in general relativity anyway. That is not true. Energy is conserved in GR, with the obvious caveat that we have to adopt a sensible definition of energy. http://www.physics.adelaide.edu.au/~...energy_gr.html > (Imagine a universe consisting only of radiation. It expands. > The number of photons remains the same, but the energy of each > decreases due to the redshift. No, this lost energy does not do > the work of expanding the universe.) Then why does a radiantfilled universe decelerate faster than a matterfilled universe? Because the energy lost in the redshift cancels some of the negative energy tied up in the Hubble expansion. Cheers, Michael C Price  http://mcp.longevityreport.com http://www.hedweb.com/manworld.htm 


#53
Oct1206, 05:06 AM

P: n/a

>> My understanding is that the Universe is expanding and that
>> this expansion is speeding up. What is fuelling this expansion >> rate increase that is working against the force of gravity? >> >> The answer seems to be Dark Energy. Correct. > Whatever that is! Dark energy may be modelled by adding a constant to Einstein's equations; hence the term "cosmological constant". >> The question in my mind is where does this energy come from >> and it would seem that more and more of it is needed in order >> to increase the expansion rate. Correct. The energy comes from the expansion (a form of gravitational or geometric energy) which is negative. As the universe expands the positive energy locked as dark energy increases (density is constant, but volume increases); this is offset by the negative energy in the Hubble expansion which decreases (becomes more negative). In the case of dark energy this process can continue for ever; it's a slow form of inflation. > > It doesn't have to come from anywhere. The FriedmannLemaître > equations allow for such a term, and apparently it has been observed. > Note that there is not a problem with energy conservation, since > energy isn't conserved in general relativity anyway. That is not true. Energy is conserved in GR, with the obvious caveat that we have to adopt a sensible definition of energy. http://www.physics.adelaide.edu.au/~...energy_gr.html > (Imagine a universe consisting only of radiation. It expands. > The number of photons remains the same, but the energy of each > decreases due to the redshift. No, this lost energy does not do > the work of expanding the universe.) Then why does a radiantfilled universe decelerate faster than a matterfilled universe? Because the energy lost in the redshift cancels some of the negative energy tied up in the Hubble expansion. Cheers, Michael C Price  http://mcp.longevityreport.com http://www.hedweb.com/manworld.htm 


#54
Oct1206, 05:06 AM

P: n/a

In article <3%Q3f.1089$WI4.1078@newsfe4gui.ntli.net>, "Michael C Price"
<michaelEXCISESPAMprice917@tesco.net> writes: > >> My understanding is that the Universe is expanding and that > >> this expansion is speeding up. What is fuelling this expansion > >> rate increase that is working against the force of gravity? > >> > >> The answer seems to be Dark Energy. > > Correct. > > > Whatever that is! > > Dark energy may be modelled by adding a constant to Einstein's > equations; hence the term "cosmological constant". > > >> The question in my mind is where does this energy come from > >> and it would seem that more and more of it is needed in order > >> to increase the expansion rate. > > Correct. The energy comes from the expansion (a form of > gravitational or geometric energy) which is negative. As the > universe expands the positive energy locked as dark energy > increases (density is constant, but volume increases); this is > offset by the negative energy in the Hubble expansion which > decreases (becomes more negative). Where did you get this idea from? Explain how the energy of the cosmological constant "comes from" the expansion. The stuff about "dark energy" is OK, but the claim that it is "offset by the negative energy in the Hubble expansion" is completely bogus. Actually, gravitational energy is such that the closer two gravitating objects are, the more negative the energy, thus with expansion it would become more positive, not become more negative. Also, imagine a universe with NO cosmological constant. There would thus be no "offset". Are you claiming that such a universe is impossible? > > It doesn't have to come from anywhere. The FriedmannLemaître > > equations allow for such a term, and apparently it has been observed. > > Note that there is not a problem with energy conservation, since > > energy isn't conserved in general relativity anyway. > > That is not true. Energy is conserved in GR, with the obvious > caveat that we have to adopt a sensible definition of energy. > http://www.physics.adelaide.edu.au/~...energy_gr.html Quoting from this: The Cosmic Background Radiation (CBR) has redshifted over billions of years. Each photon gets redder and redder. What happens to this energy? Cosmologists model the expanding universe with FriedmannRobertsonWalker (FRW) spacetimes. (The familiar "expanding balloon speckled with galaxies" belongs to this class of models.) The FRW spacetimes are neither static nor asymptotically flat. Those who harbor no qualms about pseudo tensors will say that radiant energy becomes gravitational energy. Others will say that the energy is simply lost. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^ The issue is much more complicated than the "this link proves that energy is conserved" you claim. > > (Imagine a universe consisting only of radiation. It expands. > > The number of photons remains the same, but the energy of each > > decreases due to the redshift. No, this lost energy does not do > > the work of expanding the universe.) Give a "sensible definition of energy", which is not adhoc, which is conserved in this case. > Then why does a radiantfilled universe decelerate faster than > a matterfilled universe? Because the energy lost in the redshift > cancels some of the negative energy tied up in the Hubble > expansion. I think you need to spell out exactly what you mean by "decelerate faster". Presumably, two universes which are otherwise equivalent decelerate differently. What does "otherwise equivalent" mean here? The expansion histories are obviously different; WHEN does it "decelerate faster"? 


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