Special relativity prohibits faster than light travel unless you don't care about causality.
Given that it's hard to do science at all without causality that's going to be a hard sell. So the alternative is to throw out (tweak) special relativity.
Maxwell's equations imply special relativity imply nothing can travel faster than light.
There's a lot of very established physics that is going to need rethinking if this result is real.
"Which is why it must be all wrong - causality becomes inconsistent"
Or special relativity is wrong. Which seems more likely assuming that this is a real result. And I think that if special relativity is wrong then Maxwell's equations must be wrong too.
There's also the possibility of something akin to the alcubierre drive. Somehow, via physics we're getting our first glimpses at now, very high speed massive particles warp space in a way outside of general relativity.
These results are 60 ns in about 2 ms, or a factor of 0.00003. The LMC (home of SN1987A) is 160,000 light years away, so this would have the neutrino signal arriving several years ahead of the optical signal.
Page 3 of the paper in the introduction.
At much lower energy, in the 10 MeV range, a stringent limit of |v-c|/c < 2Ã--10-9 was set by the observation of (anti) neutrinos emitted by the SN1987A supernova [7].
The problem is that you stop being social with those who need it the most - those you won't find on Facebook.
While I'm sure there are lonely people who are not on Facebook, them going on facebook is not going to stop them being lonely.
I have very recently joined facebook but that's not to make new friends but because my friends were organizing things on facebook and I couldn't access the details.
I've just gone and looked at who my "friends" are. All of them are either relatives (about 20%) or people I've had recent (less than 6 months ago) face to face encounters with (with one exception). It's also almost exactly 50/50 male/female.
There are a couple of my "friends" who have moved abroad very recently. It will be interesting to see whether facebook means that I do keep in touch with them - something that historically I've been extremely bad about or whether in twelve months time, assuming I'm still using facebook, I'll be deleting them from my friends list.
"The climate" is not, nor has it ever been, a static system. We have only begun to study it in earnest. Let's let the science and data develop, before we go pumping CO2 into the atmosphere to cause tropospheric warming, and other such possibly world-changing problems. Let's employ rationality and healthy skepticism to further our understanding, before we go trying to change what may well prove to be a critical part of the environment we live in.
I wonder if eventually we will have objects which resemble paper books, but the individual pages will be easily rewritable?
This would be fantastic and could, potentially, obviate the need for a power supply or buttons at all. You'd "dock" the book and rewrite the pages and then carry it around and use it just like an ordinary book.
I haven't read TFA but I don't think that's the idea here.
You have spare computer processing going that I'm prepared to pay for.
I have a dataset 'x' and an algorithm 'A' I want to run on it. I want A(x) but I don't want to give you x.
What I can do (in theory) is encrypt the data to give me E(x), then give that to you where you run A'(E(x)). I then run D(A'(E(x))) and I get back to A(x) that I wanted all along.
The problems are finding secure E such that A' and D can easily be derived from A and, usually, you want E and D to be cheap calculations in comparison with A' or A.
I can try. But as someone else has replied what I wrote is not actually correct.
Because there are three different neutrinos, we need three different numbers to describe how they can oscillate (change) between flavours.
What oscillate means is that if you start with a beam of pure electron neutrinos and then, at some later time measure the type of the neutrinos you will find that some of them are now muon or tau neutrinos.
Two of those numbers were known to be non-zero. This result suggests that the third number is also non-zero.
I had thought that all three numbers being non-zero was sufficient to show that neutrinos violate CP - but that is incorrect.
CP violation is when you replace every particle with its antiparticle (C) and look at the resulting system in a mirror (P). CP violation means that you can tell the difference between the two systems
CP has been observed and is important because it's conjectured that the fact that the universe has more matter than anti-matter is a feature of CP violation.
Yup. Thanks. I put P85 which I don't think exists. Not sure if I was thinking P45 (employment ends in the tax year) or P60 when I wrote that (or even R85 mentioned earlier.)
I would also point out that PAYE doesn't always work well. Changing jobs and the previous employer failing to provide a P45 (or the employee losing it) is the most common problem.
Another is being paid on a Week1/Month1 instead of cumulative basis when income is very variable. IIRC this is also a feature of your taxcode (final X?).
And once upon a time (although I believe this is now fixed) if you had several jobs, none of which individually paid enough to use up your tax free allowance then your tax code could only be applied to one of them so you would end up not using your entire tax free allowance and would have to reclaim the overpaid tax at the end of the year (IMO this was particularly egregious as it tended to be the low paid that were caught by this - it's all well and good getting 120GBP back eventually but these are the sorts of people where a 10GBP/month cashflow change can make all the difference between being able to balance the books and having to borrow - often at punitive rates)
Actually, it doesn't really matter. If they think you're an ebay trader then they might ask you to submit a tax return. If you're not an ebay trader then you just don't mention it. They will probably then decide to do an audit (because they think you have undeclared income) and ask to see things like bank account statements. And that will be it.
It could be a bit complicated if you've just been selling off some old junk on ebay and then you'll have to justify the payments coming in. But selling a mobile phone will be easy to explain as "just an old phone that I no longer used", selling 100 mobile phones starts looking like a trade and will be harder to justify.
At least in the UK I would think the majority of people already pay 'every last penny they're "supposed" to owe.'
We have something called PAYE which every employer uses to (hopefully) correctly take income tax at source.
Interest and dividends are also taxed at source and for basic rate taxpayers there will be no additional tax to pay. People who don't reach the income tax threshold can submit a form R85 to their bank/building society to receive their interest without tax deducted. Dividend tax cannot be reclaimed any more - this was "Gordon Brown's great pension heist" that is oft talked about.
Higher rate tax payers do have some extra tax to pay but HMRC applies a "fudge factor" (tax coding) to the PAYE system to balance it out. For example my tax code consists of a component for the tax free allowance, a component for tax relief on pension contributions, a component for tax relief on charitable giving and a component for the tax due on health insurance benefits. You get a letter from the tax office explaining how your tax code was calculated and you can ask to have the calculation redone if you think the numbers aren't correct.
At the end of the year, for most people, this is so close to being right that nobody, neither HMRC, nor the taxpayer, wants the hassle of "fixing" the errors of a few pounds here and there.
For some people HMRC requires them to submit a tax return at the end of the year. For these people there will be a balancing payment made or received and the tax will be exactly correct.
Additionally, anybody is allowed to submit a tax return if they want. I would estimate that for a standard employee (maybe with multiple jobs) this amounts to about 1-2 hours of work total - your employer is required by law to give you certain forms, P11D, P85, and you just have to copy these numbers into your tax return. Then it's just finding all those bank accounts and totting up all the interest (again, the bank should give you a certificate of interest paid and tax deducted but with modern online banking you tend to have to remember what accounts you've got rather than receive something through the post to remind you.) Ditto dividends.
Do it online and you get the tax calculation instantly. If you owe tax then you'll have to pay it by 31st Jan of the following year. if you're overpaid tax then, IME, you'll get the money paid into your bank within a month of submitting the tax return.
It's only when you have other sources of income that fall outside the PAYE system that there is even the opportunity for tax evasion (short of outright lying - for example you could claim to make 10K of charitable donations but not make them which would only be caught if/when the taxman does an audit)
In the UK if you run a "trade" then you are required to submit accounts to HMRC and, if necessary, pay tax on any profit.
For ebayers, this would be people who buy stuff with the intention of reselling it. It does not apply to people who are just having a clearing out.
For small traders the "accounts" can comprise of basically a few lines - income, expenditure, profit. HMRC can ask for a more detailed breakdown (which is why you're required to keep records for seven years - might be three for small traders) but by default you don't need to.
Once your turnover exceeds 75K (I think) you're also required to register for VAT. This means that you have to charge VAT on your sales but can reclaim it on your purchases. VAT is much more onerous than the P&L accounting and I could see it being prohibitive for a low margin high volume ebay business. But reading between the lines in TFA I think HMRC are looking for income tax cheats rather than VAT issues.
There are stars with predictable brightnesses that are close enough to exhibit parallax.
Those same stars in other galaxies then give us a distance to other galaxies.
There are other events, supernovas etc that are known to have an upper limit in brightness. From that we can estimate distances to far away galaxies.
Or we can use redshift to estimate the same distances.
Of course there are wide error bars. But it's not just a random guess.
And what is this "mathematical models without observational support". The whole point of a mathematical model is that it explains observations. There are two types of model - empirical, where the model agrees with the observations but we don't understand why the model should agree (the early atomic emission spectroscopy results fell into this category) and physical, where the model is based around our understanding of the underlying physics, those same atomic spectroscopy models are now physical models given that we now understand emission spectra based on the ideas of atomic number, electron shells etc
It won't work for the very simple reason that the rich are much more able to optimize their tax paying to take advantage of what is in the tax code.
For example, in the UK the rich pay 50% tax on income (42.5% tax on dividends) but only 28% tax on capital gains (might even be 18% if they can get their taxable income low enough - I'm not absolutely sure what happens at this extreme)
So it currently makes sense for the rich to buy shares that tend to generate capital gains in favour of shares that tend to generate income - especially if there intention would have been to reinvest the dividends anyway.
Change that around and the rich will shift their investment strategies around to get the best deal they can. The poor (and in this case I mean almost everybody) will typically only have a single source of income (their job) and no opportunity to optimize their tax rates because they'll be "trapped" in a single taxation regime.
So if you try and optimize it so that nobody ends up better or worse off, what will actually happen is that the rich will then optimize their tax rates and end up paying less. The only way to recover the missing tax will be to put up rates so that, for at least some people, they will end up worse off.
I agree with your point "the value of information is not [necessarily] the same as the cost of copying it."
But I do not accept that pictures by Van Gogh are a good example of this. A van Gogh original might be worth 50M. A copy that can only be recognised as a copy by experts might be worth as much as 1% of that.
There are pictures where the original painter isn't known but there's a chance it is one of the "greats". Painted by the great master it's worth millions. Painted by one of his students it's hundreds of thousands at most. The same picture.
And photographic forgery is even more bizarre. An "original" can be worth a small fortune. A "copy" - same negative, same photographic paper, same developing process, just done by someone else can be worthless.
Much of the data on the laserdisc is analogue. The images definitely are.
Even the digital data is stored in an audio track - not sure if it was played through the cassette port of the BBC micro to decode or whether the laserdisc hardware did the decoding.
I don't understand the point you are trying to make.
I can buy a copy of van Gogh sunflowers for 3.99 (GBP)
The "Essential extras" frame comes in at 19.99
I suspect, in real terms, the frame plus poster costs less than the paint that van Gogh used.
You could value a copy of sunflowers at 50M but then nobody would buy it.
OTOH, I went to see the Zubaran paintings at Bishop Auckland a week or so ago. The thirteenth picture of the set is, in fact, a copy but it cost Bishop Trevor 21GBP - one of the most expensive to acquire because the owner of the original would not sell. The collection is described as "priceless". I've no idea what the value of the copy alone would be but it's certainly not going to be 3.99.
I've no idea what it would cost to have a modern painted copy of the sunflowers made but I would imagine prices ranging from 10K upwards depending on the skill and reputation of the person doing the copy.
But this all shows that, in out of copyright art, the cost of a copy is proportional to the cost of producing that copy. Art is unusual in that there are people who are prepared to pay a huge premium to own the original.
It's counter-intuitive, but to catch up with something ahead of you but in the same orbit as you, you need to fire your retrorockets. You will then fall into a lower orbit, exchanging gravitational potential energy for kinetic energy and end up going faster.
The maximum speed of information cannot be exceeded - by definition.
So now we're left asking what the maximum speed of information is. There are only two possible answers, finite, or infinite.
If the speed of information is infinite then there must be a definition of absolute time. I set up a clock and then transmit the time to everywhere in the universe instantaneously. Everyone uses this "UTC" to assign times to events and an absolute ordering of everything is defined and everyone, everywhere agrees on what the time is.
Now it is experimentally observed that time stops (actually it's asymptotic - time slowing is observed) when a clock moves at the speed of light. (subatomic particle decay rates are the classic demonstration of time slowing)
I now have have a second clock identical to the first one. They start together in space and are synchronized at t=0. (Because they start at the same point there's no problem about making sure they have the same time regardless of whether the speed of information is finite or infinite). I send one of them off across the galaxy at the speed of light. After 100000 years my second clock arrives at point B displaying time t=0.
What is the time at B? One of my clocks says t=0, the other (whose time is transmitted infinitely fast to B) says t=100000 years. Both clocks are identical.
The only thing that makes sense is to assume that the maximum speed of information is the same as the speed of light.
Slashdot Mirror
Special relativity prohibits faster than light travel unless you don't care about causality.
Given that it's hard to do science at all without causality that's going to be a hard sell. So the alternative is to throw out (tweak) special relativity.
Maxwell's equations imply special relativity imply nothing can travel faster than light.
There's a lot of very established physics that is going to need rethinking if this result is real.
Tim.
"Which is why it must be all wrong - causality becomes inconsistent"
Or special relativity is wrong. Which seems more likely assuming that this is a real result. And I think that if special relativity is wrong then Maxwell's equations must be wrong too.
There's also the possibility of something akin to the alcubierre drive. Somehow, via physics we're getting our first glimpses at now, very high speed massive particles warp space in a way outside of general relativity.
Exciting times.
Tim.
These results are 60 ns in about 2 ms, or a factor of 0.00003. The LMC (home of SN1987A) is 160,000 light years away, so this would have the neutrino signal arriving several years ahead of the optical signal.
Page 3 of the paper in the introduction.
At much lower energy, in the
10 MeV range, a stringent limit of |v-c|/c < 2Ã--10-9 was set by the observation of (anti) neutrinos
emitted by the SN1987A supernova [7].
Tim.
The problem is that you stop being social with those who need it the most - those you won't find on Facebook.
While I'm sure there are lonely people who are not on Facebook, them going on facebook is not going to stop them being lonely.
I have very recently joined facebook but that's not to make new friends but because my friends were organizing things on facebook and I couldn't access the details.
I've just gone and looked at who my "friends" are. All of them are either relatives (about 20%) or people I've had recent (less than 6 months ago) face to face encounters with (with one exception). It's also almost exactly 50/50 male/female.
There are a couple of my "friends" who have moved abroad very recently. It will be interesting to see whether facebook means that I do keep in touch with them - something that historically I've been extremely bad about or whether in twelve months time, assuming I'm still using facebook, I'll be deleting them from my friends list.
Tim.
"The climate" is not, nor has it ever been, a static system. We have only begun to study it in earnest. Let's let the science and data develop, before we go pumping CO2 into the atmosphere to cause tropospheric warming, and other such possibly world-changing problems. Let's employ rationality and healthy skepticism to further our understanding, before we go trying to change what may well prove to be a critical part of the environment we live in.
What does Philip do, drive a cab?
+1 genius. British humour at its best.
I wonder if eventually we will have objects which resemble paper books, but the individual pages will be easily rewritable?
This would be fantastic and could, potentially, obviate the need for a power supply or buttons at all. You'd "dock" the book and rewrite the pages and then carry it around and use it just like an ordinary book.
Tim.
I haven't read TFA but I don't think that's the idea here.
You have spare computer processing going that I'm prepared to pay for.
I have a dataset 'x' and an algorithm 'A' I want to run on it. I want A(x) but I don't want to give you x.
What I can do (in theory) is encrypt the data to give me E(x), then give that to you where you run A'(E(x)). I then run D(A'(E(x))) and I get back to A(x) that I wanted all along.
The problems are finding secure E such that A' and D can easily be derived from A and, usually, you want E and D to be cheap calculations in comparison with A' or A.
Tim.
I can try. But as someone else has replied what I wrote is not actually correct.
Because there are three different neutrinos, we need three different numbers to describe how they can oscillate (change) between flavours.
What oscillate means is that if you start with a beam of pure electron neutrinos and then, at some later time measure the type of the neutrinos you will find that some of them are now muon or tau neutrinos.
Two of those numbers were known to be non-zero. This result suggests that the third number is also non-zero.
I had thought that all three numbers being non-zero was sufficient to show that neutrinos violate CP - but that is incorrect.
CP violation is when you replace every particle with its antiparticle (C) and look at the resulting system in a mirror (P). CP violation means that you can tell the difference between the two systems
CP has been observed and is important because it's conjectured that the fact that the universe has more matter than anti-matter is a feature of CP violation.
Tim.
Yes, you're right. I had thought that non-zero theta13 was sufficient.
It's a particular oscillation that they've observed for the first time.
Assuming this result is correct then this result implies that there is a CP symmetry violation between the neutrino and anti-neutrino.
Previously to this result this particular mixing term could have been zero and if it was zero then CP symmetry would have been preserved.
Tim.
Yup. Thanks. I put P85 which I don't think exists. Not sure if I was thinking P45 (employment ends in the tax year) or P60 when I wrote that (or even R85 mentioned earlier.)
I would also point out that PAYE doesn't always work well. Changing jobs and the previous employer failing to provide a P45 (or the employee losing it) is the most common problem.
Another is being paid on a Week1/Month1 instead of cumulative basis when income is very variable. IIRC this is also a feature of your taxcode (final X?).
And once upon a time (although I believe this is now fixed) if you had several jobs, none of which individually paid enough to use up your tax free allowance then your tax code could only be applied to one of them so you would end up not using your entire tax free allowance and would have to reclaim the overpaid tax at the end of the year (IMO this was particularly egregious as it tended to be the low paid that were caught by this - it's all well and good getting 120GBP back eventually but these are the sorts of people where a 10GBP/month cashflow change can make all the difference between being able to balance the books and having to borrow - often at punitive rates)
Tim.
Actually, it doesn't really matter. If they think you're an ebay trader then they might ask you to submit a tax return. If you're not an ebay trader then you just don't mention it. They will probably then decide to do an audit (because they think you have undeclared income) and ask to see things like bank account statements. And that will be it.
It could be a bit complicated if you've just been selling off some old junk on ebay and then you'll have to justify the payments coming in. But selling a mobile phone will be easy to explain as "just an old phone that I no longer used", selling 100 mobile phones starts looking like a trade and will be harder to justify.
Tim.
At least in the UK I would think the majority of people already pay 'every last penny they're "supposed" to owe.'
We have something called PAYE which every employer uses to (hopefully) correctly take income tax at source.
Interest and dividends are also taxed at source and for basic rate taxpayers there will be no additional tax to pay. People who don't reach the income tax threshold can submit a form R85 to their bank/building society to receive their interest without tax deducted. Dividend tax cannot be reclaimed any more - this was "Gordon Brown's great pension heist" that is oft talked about.
Higher rate tax payers do have some extra tax to pay but HMRC applies a "fudge factor" (tax coding) to the PAYE system to balance it out. For example my tax code consists of a component for the tax free allowance, a component for tax relief on pension contributions, a component for tax relief on charitable giving and a component for the tax due on health insurance benefits. You get a letter from the tax office explaining how your tax code was calculated and you can ask to have the calculation redone if you think the numbers aren't correct.
At the end of the year, for most people, this is so close to being right that nobody, neither HMRC, nor the taxpayer, wants the hassle of "fixing" the errors of a few pounds here and there.
For some people HMRC requires them to submit a tax return at the end of the year. For these people there will be a balancing payment made or received and the tax will be exactly correct.
Additionally, anybody is allowed to submit a tax return if they want. I would estimate that for a standard employee (maybe with multiple jobs) this amounts to about 1-2 hours of work total - your employer is required by law to give you certain forms, P11D, P85, and you just have to copy these numbers into your tax return. Then it's just finding all those bank accounts and totting up all the interest (again, the bank should give you a certificate of interest paid and tax deducted but with modern online banking you tend to have to remember what accounts you've got rather than receive something through the post to remind you.) Ditto dividends.
Do it online and you get the tax calculation instantly. If you owe tax then you'll have to pay it by 31st Jan of the following year. if you're overpaid tax then, IME, you'll get the money paid into your bank within a month of submitting the tax return.
It's only when you have other sources of income that fall outside the PAYE system that there is even the opportunity for tax evasion (short of outright lying - for example you could claim to make 10K of charitable donations but not make them which would only be caught if/when the taxman does an audit)
Tim.
In the UK if you run a "trade" then you are required to submit accounts to HMRC and, if necessary, pay tax on any profit.
For ebayers, this would be people who buy stuff with the intention of reselling it. It does not apply to people who are just having a clearing out.
For small traders the "accounts" can comprise of basically a few lines - income, expenditure, profit. HMRC can ask for a more detailed breakdown (which is why you're required to keep records for seven years - might be three for small traders) but by default you don't need to.
Once your turnover exceeds 75K (I think) you're also required to register for VAT. This means that you have to charge VAT on your sales but can reclaim it on your purchases. VAT is much more onerous than the P&L accounting and I could see it being prohibitive for a low margin high volume ebay business. But reading between the lines in TFA I think HMRC are looking for income tax cheats rather than VAT issues.
Tim.
The BBC news website really went downhill when it was no longer possible to tell it where you were.
When I'm at work it's now convinced I live in the US. Even on the UK specific page it now tells me when the page was last updated in ET time.
I also get a "US view" of the world on the front page which is less than ideal.
Tim.
It's a multifaceted calibration.
There are stars with predictable brightnesses that are close enough to exhibit parallax.
Those same stars in other galaxies then give us a distance to other galaxies.
There are other events, supernovas etc that are known to have an upper limit in brightness. From that we can estimate distances to far away galaxies.
Or we can use redshift to estimate the same distances.
Of course there are wide error bars. But it's not just a random guess.
And what is this "mathematical models without observational support". The whole point of a mathematical model is that it explains observations. There are two types of model - empirical, where the model agrees with the observations but we don't understand why the model should agree (the early atomic emission spectroscopy results fell into this category) and physical, where the model is based around our understanding of the underlying physics, those same atomic spectroscopy models are now physical models given that we now understand emission spectra based on the ideas of atomic number, electron shells etc
Tim.
It won't work for the very simple reason that the rich are much more able to optimize their tax paying to take advantage of what is in the tax code.
For example, in the UK the rich pay 50% tax on income (42.5% tax on dividends) but only 28% tax on capital gains (might even be 18% if they can get their taxable income low enough - I'm not absolutely sure what happens at this extreme)
So it currently makes sense for the rich to buy shares that tend to generate capital gains in favour of shares that tend to generate income - especially if there intention would have been to reinvest the dividends anyway.
Change that around and the rich will shift their investment strategies around to get the best deal they can. The poor (and in this case I mean almost everybody) will typically only have a single source of income (their job) and no opportunity to optimize their tax rates because they'll be "trapped" in a single taxation regime.
So if you try and optimize it so that nobody ends up better or worse off, what will actually happen is that the rich will then optimize their tax rates and end up paying less. The only way to recover the missing tax will be to put up rates so that, for at least some people, they will end up worse off.
Tim.
Does my employer buy my services and pay 10% sales tax on my wages?
If I buy Treasuries do I pay 10%?
What about equities? Or buying and selling gold?
Or I sell my house and buy another one somewhere else in the country. Do I lose 10%?
Tim.
I agree with your point "the value of information is not [necessarily] the same as the cost of copying it."
But I do not accept that pictures by Van Gogh are a good example of this. A van Gogh original might be worth 50M. A copy that can only be recognised as a copy by experts might be worth as much as 1% of that.
There are pictures where the original painter isn't known but there's a chance it is one of the "greats". Painted by the great master it's worth millions. Painted by one of his students it's hundreds of thousands at most. The same picture.
http://tom-flynn.blogspot.com/2010/05/christies-face-lawsuit-over.html
And photographic forgery is even more bizarre. An "original" can be worth a small fortune. A "copy" - same negative, same photographic paper, same developing process, just done by someone else can be worthless.
Tim.
All I want is a copy of the laserdisc etc.
Much of the data on the laserdisc is analogue. The images definitely are.
Even the digital data is stored in an audio track - not sure if it was played through the cassette port of the BBC micro to decode or whether the laserdisc hardware did the decoding.
Tim.
I don't understand the point you are trying to make.
I can buy a copy of van Gogh sunflowers for 3.99 (GBP)
The "Essential extras" frame comes in at 19.99
I suspect, in real terms, the frame plus poster costs less than the paint that van Gogh used.
You could value a copy of sunflowers at 50M but then nobody would buy it.
OTOH, I went to see the Zubaran paintings at Bishop Auckland a week or so ago. The thirteenth picture of the set is, in fact, a copy but it cost Bishop Trevor 21GBP - one of the most expensive to acquire because the owner of the original would not sell. The collection is described as "priceless". I've no idea what the value of the copy alone would be but it's certainly not going to be 3.99.
I've no idea what it would cost to have a modern painted copy of the sunflowers made but I would imagine prices ranging from 10K upwards depending on the skill and reputation of the person doing the copy.
(Quick google gives: http://globalwholesaleart.com/Van-Gogh-Paintings-ar-57.html?gclid=CL7R-Y7S4qgCFcbc4AodtllDEg so it's actually a lot cheaper than I'd expected)
But this all shows that, in out of copyright art, the cost of a copy is proportional to the cost of producing that copy. Art is unusual in that there are people who are prepared to pay a huge premium to own the original.
Tim.
The lower the orbit the faster the orbital speed.
It's counter-intuitive, but to catch up with something ahead of you but in the same orbit as you, you need to fire your retrorockets. You will then fall into a lower orbit, exchanging gravitational potential energy for kinetic energy and end up going faster.
Tim.
no such algorithm exists to solve an NP complete problem rather than NP hard problem.
NP hard problems are at least as hard as everything in NP but might be harder than anything in NP. For example, the halting problem is NP hard.
NP complete problems are at least as hard as everything in NP and, additionally, are in NP, thus they are the hardest possible problems in NP.
Tim.
The maximum speed of information cannot be exceeded - by definition.
So now we're left asking what the maximum speed of information is. There are only two possible answers, finite, or infinite.
If the speed of information is infinite then there must be a definition of absolute time. I set up a clock and then transmit the time to everywhere in the universe instantaneously. Everyone uses this "UTC" to assign times to events and an absolute ordering of everything is defined and everyone, everywhere agrees on what the time is.
Now it is experimentally observed that time stops (actually it's asymptotic - time slowing is observed) when a clock moves at the speed of light. (subatomic particle decay rates are the classic demonstration of time slowing)
I now have have a second clock identical to the first one. They start together in space and are synchronized at t=0. (Because they start at the same point there's no problem about making sure they have the same time regardless of whether the speed of information is finite or infinite). I send one of them off across the galaxy at the speed of light. After 100000 years my second clock arrives at point B displaying time t=0.
What is the time at B? One of my clocks says t=0, the other (whose time is transmitted infinitely fast to B) says t=100000 years. Both clocks are identical.
The only thing that makes sense is to assume that the maximum speed of information is the same as the speed of light.
Tim.