Jump to content

About "Forget time" by Carlo Rovelli


Recommended Posts

If someone read Carlo Rovelli "Forget time"

http://fqxi.org/community/forum/"Forget time"topic/237

...

 

Your link doesn't seem to work, the link I have is this:

http://www.fqxi.org/community/forum/topic/237

 

and there you click on download PDF to get the text of the essay:

 

http://www.fqxi.org/data/essay-contest-files/Rovelli_Time.pdf

=============================

 

It is an exceptional essay. Clear. Not hard to read. Eminently reasonable. It resolves several apparent confusions about time that have puzzled people---and so simply that one wonders why this hasn't been seen by everybody years ago.

 

The only technical element that may not be familiar is in the section on QFT where he refers to the Tomita flow. But that is only a small part of the whole essay and you can skip that part if you like.

 

Here are the conclusions:

==quote==

I have presented a certain number of ideas and results:

 

1. It is possible to formulate classical mechanics in a way in which the time variable is treated on equal footings

with the other physical variables, and not singled out as the special independent variable. I have argued that

this is the natural formalism for describing general relativistic systems.

 

2. It is possible to formulate quantum mechanics in the same manner. I think that this may be the effective

formalism for quantum gravity.

 

3. The peculiar properties of the time variable are of thermodynamical origin, and can be captured by the thermal

time hypothesis. Within quantum field theory, “time” is the Tomita flow of the statistical state in which the

world happens to be, when described in terms of the macroscopic parameters we have chosen.

 

4. In order to build a quantum theory of gravity the most effective strategy is therefore to forget the notion of

time all together, and to define a quantum theory capable of predicting the possible correlations between partial

observables.

==endquote==

Edited by Martin
Link to comment
Share on other sites

4. In order to build a quantum theory of gravity the most effective strategy is therefore to forget the notion of

time all together, and to define a quantum theory capable of predicting the possible correlations between partial

observables.

==endquote==

 

I am probably taking it out of context, but time is such a slippery eel, isn't it.

The phrase ....."forget the notion of time altogether....." leads me to wonder whether time as we are taught it is in fact an analogy whose usefulness can be in doubt. Analogies are wonderful things to aid everyday understanding, yet failing to recognise when their veracity ends can be an obstacle to deeper understanding.

Link to comment
Share on other sites

In parts III and IV he seems to be saying that you can represent time as the phase of a pendulum and restate other variables in terms of that. But this does not forget time, it merely renames it. Time is the phase of an oscillation.

 

I'm not sure his objection "How do we know that a clock measures time, if we can only check it against another clock?" means anything. Isn't the same thing true of mass? Can you measure mass without using forces? A clock measures time because that's how we define it.

Edited by swansont
corrected: III vs II
Link to comment
Share on other sites

http://fqxi.org/community/forum/category/10

 

There have revealed leaders of the posts number. Carlo Rovelli among them.

 

Here is a list where it is easier to see how the contest essays stand

http://fqxi.org/community/vote

because the list is ranked by the number of votes received, most votes first.

Rovelli's essay has received the most popular votes so far, so it is at the top of the list. The one that comes closest, in the number two spot, has an odd title: A Mystic Dream of Four.

 

The voting will close and the winner will be announced on 15 December.

 

There are two categories of votes---FQXi members and contest entrants votes are counted separately.

 

I'm not sure his objection "How do we know that a clock measures time, if we can only check it against another clock?" means anything.

 

Help me out. Where in the essay are you quoting from?

 

Isn't the same thing true of mass? Can you measure mass without using forces? A clock measures time because that's how we define it.

 

 

The main thing he wants to do is reformulate to get rid of the assumed Newtonian time. There is no imagined King of Clocks. All clocks are just ordinary fallible devices, more or less reliable, basically all created equal.

 

Any particular clock is a quantum mechanical system and what it says is an observable. We can't confuse what an observer's real, necessarily imperfect and uncertain clock says with the observer's true perfect time (if it even makes sense to talk about an observer's true perfect time---maybe such a thing does not exist in nature.)

 

It sounds like you would propose something like "let's take a particular real clock and for this particular experiment let's define time to be what this clock says----and we agree to correlate the readings of the experiment with this clock, as we record them." I think Rovelli would like that, so he would agree with you!

 

In both Newtonian mechanics and conventional Quantum Mechanics, there is, in the formalism, a true perfect time. What we observe, or the wave function we believe in, evolves according to this time, which is a fundamental part of nature. This also carries over to special relativity where each observer can refer to a perfectly accurate clock, and we can transform with perfect accuracy between them. There is still an absolute time for each observer. There is an ideal time variable built into the formalism. This, I take it, is something Rovelli would dispense with. It does not exist in nature, so in a fundamental theory the formalism should not pretend that it does (I think he would say.)

 

There is more to say about this----the motivation is interesting. Why should one want to reformulate QFT for example, so that the ideal time parameter disappears---so that time is no longer something fundamental in nature but something that emerges in systems with a large number of degrees of freedom. What understanding does the thermodynamic emergence of time give us about the nature of time? And so on... I will stop here, but just want to suggest that there are interesting further questions that the essay brings up.

 

Oh, about mass! I forgot to respond directly to your question! In conventional particle physics, there is assumed to be a perfect ideal mass---even though every real laboratory measurment involves uncertainty and imprecision. Even though we realize that we can only measuire approximately, we believe that the electron does have a true absolute rest mass, and this is built into the formalism.

 

You ask isn't the same thing true of time! Isn't there really in nature a true time just like there is a true electron mass---and we just have limited accuracy measuring? I think a major point of Rovelli's essay is he says NO. He has no quarrel with the rest mass of the electron---it is not analogous to time. We keep particle rest masses, he says, but we can and should get rid of the perfect time element in our equations---and he gives motivation.

Edited by Martin
multiple post merged
Link to comment
Share on other sites

Help me out. Where in the essay are you quoting from?

 

My be here?

http://www.scienceforums.net/forum/showthread.php?t=34689

http://www.scienceforums.net/forum/showthread.php?t=34831

 

I remember quote from Lubos Motl:

 

"And yes, I am convinced that the best, most universal description of the degrees of freedom in quantum gravity will have no space - and probably no time - to start with. But because space - and especially time - is so essential to design any system of physics that qualitatively resembles what we know, we will learn some rules that allow you to define what you mean by space and especially time in the pre-geometric structure.

 

There is no guarantee that such a structure exists or will be found in five years or fifty years. But people simply have to keep on trying because such a setup would become an extremely robust pillar of any research of quantum gravity in particular and theoretical physics in general".

Edited by Yuri Danoyan
multiple post merged
Link to comment
Share on other sites

Help me out. Where in the essay are you quoting from?

Rovelli's;

III A. Back to Galileo and Newton, end of first paragraph. He appears to be complaining that a clock measures time and presenting it as a circular argument, rather than it being by definition.

Link to comment
Share on other sites

Rovelli's;

III A. Back to Galileo and Newton, end of first paragraph. He appears to be complaining that a clock measures time and presenting it as a circular argument, rather than it being by definition.

 

Thanks, I looked at section IIIA Back to Galileo and Newton, and found the sentence that you quoted earlier.

 

If you put that quote back into context with the rest of that short section, you may see it differently. I don't see him as either complaining or as countering an argument by calling it circular. What he is trying to do is clear from the final three sentences, I think:

==quote==

Thus, it is true also in non-relativistic mechanics that what we measure is only relative evolution between variables.

 

But it turns out to be convenient to assume, with Newton, that there exist a background variable t, such that all observables quantities evolve with respect to it, and equations are simple when written with respect to it.

 

What I propose to do in the following is simply to drop this assumption.

==endquote==

 

The whole section IIIA is only a dozen or so sentences, we could quote them all, but I don't think it makes much difference, the gist is in the last three.

 

There is no argument presented that he calls circular AFAICS. What he is proposing in this section is to drop an assumption. Am I missing something?

 

Here's how I personally would paraphrase those 15-or-so sentences. Rovelli points out a simple well-known fact about nature, about reality. He points out that we never measure the ideal time of Newton (or a Minkowskian observer). In the real world we only just compare various real devices undergoing various real processes. I think that much is almost obvious, I doubt there is any argument about it. Then he says that in Newtonian formalism (as well as others) there is a convenient assumption of a perfect time parameter, imagined to be told by a King Clock :).

 

Having made two observations that I think nobody will object to, he then says the first nontrivial thing: that he proposes to drop that convenient assumption.

 

Remember that we are still on page 5! He is just introducing the issues. The bulk of the paper is in the last half: pages 5-10.

The interesting part is

1 how he motivates dropping that assumption.

2 how he accomplishes it (to reformulate physics without imagining a King Clock) and

3 how he thinks that the passage or experience of time can be recovered (pages 7 and 8) as an emergent feature from complicated systems (systems with a large number of degrees of freedom).

 

Anyway, that's my off-the-cuff paraphrase. Maybe somebody else would like to read pages 5-10 and take a stab at summarizing.

Edited by Martin
Link to comment
Share on other sites

Thanks, I looked at section IIIA Back to Galileo and Newton, and found the sentence that you quoted earlier.

 

If you put that quote back into context with the rest of that short section, you may see it differently. I don't see him as either complaining or as countering an argument by calling it circular. What he is trying to do is clear from the final three sentences, I think:

==quote==

Thus, it is true also in non-relativistic mechanics that what we measure is only relative evolution between variables.

 

But it turns out to be convenient to assume, with Newton, that there exist a background variable t, such that all observables quantities evolve with respect to it, and equations are simple when written with respect to it.

 

What I propose to do in the following is simply to drop this assumption.

==endquote==

 

The whole section IIIA is only a dozen or so sentences, we could quote them all, but I don't think it makes much difference, the gist is in the last three.

 

There is no argument presented that he calls circular AFAICS. What he is proposing in this section is to drop an assumption. Am I missing something?

 

Here's how I personally would paraphrase those 15-or-so sentences. Rovelli points out a simple well-known fact about nature, about reality. He points out that we never measure the ideal time of Newton (or a Minkowskian observer). In the real world we only just compare various real devices undergoing various real processes. I think that much is almost obvious, I doubt there is any argument about it. Then he says that in Newtonian formalism (as well as others) there is a convenient assumption of a perfect time parameter, imagined to be told by a King Clock :).

 

Having made two observations that I think nobody will object to, he then says the first nontrivial thing: that he proposes to drop that convenient assumption.

 

Remember that we are still on page 5! He is just introducing the issues. The bulk of the paper is in the last half: pages 5-10.

The interesting part is

1 how he motivates dropping that assumption.

2 how he accomplishes it (to reformulate physics without imagining a King Clock) and

3 how he thinks that the passage or experience of time can be recovered (pages 7 and 8) as an emergent feature from complicated systems (systems with a large number of degrees of freedom).

 

Anyway, that's my off-the-cuff paraphrase. Maybe somebody else would like to read pages 5-10 and take a stab at summarizing.

 

 

Right, he's saying that we never measure time at all, since we're measuring some physical process.

 

[math] \omega = \frac{d\phi}{dt}[/math]

 

(I blogged about this today, though the motivation for doing so was unrelated to this thread)

 

We attempt to measure the phase in order to tell us the time, t. So Rovelli is right — we never actually measure t. But when you find the mass of an object, are you measuring the mass, or are you measuring a force that indirectly measures the mass? His objection is an artificial one. All he appears to be doing is saying "get rid of t and use [math]\phi[/math] " But that's just semantics. You haven't really removed time from the problem, you've just renamed it.

 

The whole field of metrology is trying to measure constants and realize standards. None of them can be done perfectly, so I fail to see why time should be singled out on the basis of imperfect clocks. There's no Galilean master length, either, because of relativity, so that can't be the criterion for tossing the idea of time.

Link to comment
Share on other sites

... so I fail to see why time should be singled out on the basis of imperfect clocks. There's no Galilean master length, either, because of relativity, so that can't be the criterion for tossing the idea of time.

 

I will try to help us be clear about what Rovelli is actually saying. Let's look at what he says right on page 1 in the introductory section.

==quote==

The spacetime of general relativity, indeed, (a 4d pseudo-riemannian space) is likely to be just a classical approximation that loses its meaning in the quantum theory, for the same reason the trajectory of a particle does (see

for instance [1]). How should we then think about time in the future quantum theory of gravity?

 

Here I argue for a possible answer to this question. The answer I defend is that we must forget the notion of time altogether, and build a quantum theory of gravity where this notion does not appear at all. The notion of time familiar to us may then be reconstructed in special physical situations, or within an approximation, as is the case for a number of familiar physical quantities that disappear when moving to a deeper level of description (for instance: the “surface of a liquid” disappears when going to the atomic level, or “temperature” is a notion that makes sense only in certain physical situations and when there are enough degrees of freedom.)

==endquote==

 

The first thing to notice is that he proposes to eliminate time only in the quantum gravity context. In a more general context, like experimental physics, metrology, or daily life, he is NOT proposing to eliminate time. In fact three of the 10 pages of the essay (pages 7-9) are devoted to reconstructing time---getting it to emerge from a more fundamental description of nature at a microscopic level.

 

To understand the necessity (as he sees it) of constructing QG in a timeless format, we have to understand something about the problems of quantizing general relativity. Fortunately nothing especially technical is required. I will take a shot at it. Don't have a lot of time myself right at the moment :) so will proceed gradually.

===========================

 

first thing to note, I guess, is that he doesn't propose tossing out time from the whole of physics (! :) )

he proposes doing that only in a particular area of theoretical physics, where this concept doesn't fit in (the problem in GR context has been known for years and studied by a lot of people before Rovelli came along)

 

Next, he doesn't propose tossing out time simply because clocks are imperfect approximations of a perfect clock.

We are all familiar with the difficulties of measuring physical quantities, like mass.

I think we'd both agree that it would be silly to propose discarding the idea of the mass of a particle simply because we know we can't measure it with total accuracy.

That is not what Rovelli is doing by any stretch of the imagination :D The guy is smart. He's not talking about something trivial.

 

Next, he doesn't propose tossing out time merely because SPECIAL relativity tells us that there is no Galilean length or Galilean time interval

because moving observers measure differently. That would be ridiculous, wouldn't you say? If we just had to cope with special relativity we could pick a reference frame and make that our standard and transform to other frames as needed.

=======================

 

I'm not sure how best to explain this. Maybe we should take a look at the analogy he offers of "the surface of a liquid".

 

That concept is valid at a macroscopic level, it is a good concept and you can do physics with it. But at a micro level the surface of a liquid does not even exist.

It is not part of a fundamental description of nature. It is something you can recover statistically from information about a large number of degrees of freedom.

 

I'll try to think of more things to say about this as I get time later on today.

Edited by Martin
Link to comment
Share on other sites

I saw that the context was QG. I think there's little need for all of the preamble. He could just explain why quantum gravity would best be served without a time variable, but the context of this is "the nature of time" so one has to wonder how much of this is localized to the QG framework.

Link to comment
Share on other sites

I saw that the context was QG. I think there's little need for all of the preamble. He could just explain why quantum gravity would best be served without a time variable, but the context of this is "the nature of time" so one has to wonder how much of this is localized to the QG framework.

 

That's a good point! And it leads to our asking the question of how QG relates to the rest. I'll try to respond.

 

What I have to say first is just in case anybody else might be reading---I'm sure you know this. General Relativity gives us our model of spacetime. It is a theory of geometry. Dynamically evolving spatial geometry, is one way to look at it (maybe not the best or most general, but one way.)

 

Gravitational waves, for example, are waves that propagate in geometry, in the process of which lengths, areas, angles etc momentarily change slightly. The gravitational field is the metric (the distance function) that describes the geometry. Ripples in the metric are ripples in geometry.

 

Minkowski space (the geometry of special relativity) is just one particular solution to the Einstein equation, a particular metric which is a solution in the absence of matter. So far standard QFT is typically constructed on Minkowski space. Basically assuming flat zero gravity, zero curvature. This is an excellent approximation for most applications, but nevertheless unrealistic. Usual QFT is relativistic only in the weak sense of special relativity. But we know that, in the real world, space has a dynamic changing geometry, to make things more realistic fields should be defined on the space of general relativity.

 

However from the quantum gravitist's standpoint even that is not yet realistic enough. The QGist wants a quantized general relativity*. This means a quantum picture of geometry and its interaction with matter at the most fundamental microscopic level. In a sense the QGist is looking for a theoretic model of the most fundamental degrees of freedom, what space or spacetime are really made of, how matter connects to geometry.

 

So he wants a quantum GR. And if there is some basic obstacle to having time be a fundamental part of the picture (I will talk about that later), then time is an emergent phenomenon. It is not part of the picture at the most fundamental level, but rather something like temperature, that arises in a nice reliable way in macroscopic systems.

 

Let me see if I have clarified or muddied things so far, in this post. I am trying to respond to the question you raised about:

In what way basic to the rest of physics? Or, on the other hand...

To what extent confined to the specialty field of quantum general relativity?

 

============================

OK your post raises the question of what Rovelli might say about that, what you asked. To what extent is QG formalism confined to the QG context? Well here's a wildass guess as to what he might say. In one sense whatever QGists do is completely confined to their QG specialty.

But in another sense it logically underlies the rest of physics. Because the QG people are trying to construct the most realistic microscopic picture of the geometry within which everything happens.

 

They are developing a new model of the continuum. And if the program is successful then one can imagine that QFT, the theory of matter fields, may eventually be based on this new continuum rather than on the flat Minkowski space it's based on at present. Of course that is idle speculation for the moment, but it's something to visualize as a goal.

 

So then whatever the QG people find out about the true nature of space and time---about the geometry that physics happens in---that could be seen to underlie the rest. So in that sense QG ideas of space and time potentially have more general relevance outside the specialty.

=========================

 

Now let me think if I've responded adequately. In your post you say "one has to wonder" about this issue. And I guess essentially what I've done is AGREE. Indeed it is an interesting question. In some sense the conclusions are confined to a narrow specialty, and in another sense they might not be. If QGists find a successful quantum dynamics of geometry and time is not represented at the fundamental level, but rather emerges---then most of the rest of physics would go on business as usual with the emergent time.

 

The example of temperature illustrates how a quantity that is emergent can nevertheless be perfectly valid and even indispensible.

=========================

 

There's more to say. I'll get back to this as time permits. Meanwhile, I'd really like to hear any reactions you might have.

 

*because classical GR breaks down in certain situations, and is not expected to give the correct geometry at very small scale.

Edited by Martin
Link to comment
Share on other sites

The essential fuzziness of time may be the limiting factor for a gravitational-wave detector in Germany

 

http://www.nature.com/news/2008/081110/full/news.2008.1217.html#B1

 

I have to say I am very skeptical of Hogan's conjecture. But it is good to know about it, so thanks for pointing out the article. Also I think you "hit pay dirt" when you brought us the link to Rovelli's article. So thanks for that too.

 

One point to make about Rovelli's ten-page FQXi essay is that it is a popularization and simplification of the discussion in his book Quantum Gravity (2004, Cambridge University Press).

 

If you are at all interested, you should get this book out at the University of Utah physics library (I would assume they have a copy.) It is a remarkable book, combining brilliant insight, a sense of the history of science, originality, and explanatory skill.

 

Passages relevant to the FQXi essay are on pages

28-31

82-87

140-144

204-206

 

Time in Quantum Gravity---and the issue what is space what is time fundamentally---is a theme running through this book and the discussion is spread out, as I indicate.

 

There is a 2003 draft of the book online at Rovelli's website, or there used to be. If the library does not have it one can try reading this draft version, but it is not the final version and the page numbering could be different. It is free though. You just google the name Rovelli. That is, if you are interested.

Link to comment
Share on other sites

Thank you.

I left two jokes post on Rovelly in"Forget time".

 

"For best understanding how the Universe working need some time switch of the Time.TIME OUT FOR TIME."

 

"Time- anesthesia help better understanding anatomy of the Universe.I think it is right time and right place forget about time."

Link to comment
Share on other sites

  • 2 weeks later...

IMPORTANT DATES

 

Monday, August 4, 2008 – Essay Contest Launched!

 

Monday, August 4, 2008 – Monday, December 1, 2008 – Essays, Restricted Votes and Public Votes may be submitted online

 

Monday, December 1, 2008 – Last opportunity to submit Essays.

 

Monday, December 15, 2008 – Essay Contest Closes – Last opportunity to submit Restricted or Public Votes

 

Monday, January 19, 2008 – Essay Contest Winners Announced!

Link to comment
Share on other sites

  • 2 months later...

February 2009 – Essay Contest Winners Announced!

 

Yes, the FAQ confirms that the winners will be announced in February:

http://www.fqxi.org/community/essay/faq

 

apparently the deadline for voting was extended and so the whole schedule was stretched out some. Thanks for noting this! I am interested to see which essays get picked.

Link to comment
Share on other sites

A brief comment on Carlo Rovelli's view of "time". A couple of the posts suggest that Carlo does not want to eliminate "Time" in all cases - just QG Time. This is not really what he says. Carlo distinguishes between [T]ime which is a fundamental variable, and [t]ime which is a variable that is essentially derived from relative motion. In fact he argues that Time does not exist in the universe - period. General relativity does not require a fundamental T, nor does Quantum Mechanics as formulated by the more general, atemporal, Heisenberg equations rather than the Schrodinger, Time dependent, equations. Carlo's views are far more radical, and promising, than the posts suggest. You might find our explanation and links at http://www.ws5.com/spacetime interesting if you want to look deeper into his amazing atemporal view of the universe. Carlo has expressed his general approval of the interpretation of his ideas that we present there.

Link to comment
Share on other sites

Well it's coming up on February, when FQXi says they will pick the winner of the essay contest on the topic What Is Time?

 

I have no hunch as to whose the winning essay might be.

 

Here at SFN we happen to have discussed Carlo Rovelli's entry in the context.

I found that essay extremely interesting and I'd be delighted if it won, but there are others that we might have discussed as well, which make good points about time. George Ellis and Julian Barbour are world-famous experts on spacetime geometry and the problem of time---and they both submitted essays, to mention just two.

 

FQXi is a new foundation that was started just about 3 years ago, they give research grants, some 50 large grants every 2 years, and smaller grants as well. Lee Smolin and Frank Wilczek are on their scientific advisory board. This essay contest is what they call their inaugural essay contest. I guess they plan to have more in future.

 

The contest is a way of celebrating their getting the new foundation rolling.

 

So anyway, let's keep an eye out for any news about the contest. Unless there is a delay for some reason, winners should be announced some time in the next 4 weeks or so. Possibly as early as next week.

 

Here's the HTML page for Rovelli's essay:

http://www.fqxi.org/community/forum/topic/237

Here's the PDF of the full essay:

http://www.fqxi.org/data/essay-contest-files/Rovelli_Time.pdf

Here's the FAQ page that says down at the bottom when the winners will be announced:

http://www.fqxi.org/community/essay/faq

Here's the list of essays:

http://fqxi.org/community/vote

 

The essays are ordered latest first

so the Ellis and Barbour essays which were submitted 1 December 2008 are at the top of the list.

The Rovelli essay was one of the earliest, among the first 3 or 4 submitted back in August 2008, so it is at the bottom of the list.

Scanning thru I find essays by many other well-known people, plus others less widely known whose work in cosmology or quantum gravity I am familiar with.

Edited by Martin
Link to comment
Share on other sites

  • 1 month later...

http://fqxi.org/community/forum/topic/426

 

First Juried Prize: Julian Barbour on "The Nature of Time" (download essay)

 

The jury panel admired this essay for its crystal-clear and engaging presentation of a problem in classical dynamics, namely to find a measure for duration or the size of a time interval. The paper argues lucidly, and in a historically well-informed manner, that an appropriate choice for such a measure is not to be found in Newton's pre-existing absolute notion of time, but rather emerges, in the form of ephemeris time, from the observable motions and the assumption of energy conservation. The paper also suggests how this emergence of duration might be relevant to problems in quantum gravity.

Link to comment
Share on other sites

There were two first prizes, a Juried prize and a Community prize.

In one case it was a select panel of judges, in the other it was a larger group of people who have been made FQXi community members.

 

One essay could not be awarded both first prizes, and Rovelli's was a clear choice for the Community first prize. He got by far the largest number of votes in the open voting.

 

The two essays form an interesting pair, because they have the same message, but Rovelli pushes it farther, writes more, and includes more technical detail.

 

The basic message is that you don't need a designated time-variable to do physics, and at the fundamental level a preferred time variable just gets in the way.

It's a hard message to assimilate. Probably the best is to read both firstprize essays. Here's Rovelli's

http://www.fqxi.org/data/essay-contest-files/Rovelli_Time.pdf

Here's Barbour's

http://www.fqxi.org/data/essay-contest-files/Barbour_The_Nature_of_Time.pdf

Edited by Martin
Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.