The future is impossible
-
Phase velocity can exceed the speed of light - it may be exploitable, but for sending information and not any physical objects. It all comes down to the relativistic mass of any object with mass. As it approaches the speed of light its mass approached infinity - so acceleration becomes impossible. An interesting caveat to that could be that as anything with any mass approaches c, they all approach the same mass. Which causes all sorts of conflicts, logically - and one might as well accelerate an entire planet as accelerate a grain of sand as they'll take the same effort in the end. Special relativity does bend the brain, a bit.
"The difference between genius and stupidity is that genius has its limits." - Albert Einstein
"If you are searching for perfection in others, then you seek disappointment. If you are seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010
W∴ Balboos wrote:
as anything with any mass approaches c, they all approach the same mass
The problem here is that you are treating infinity as a quantity, which leads to all sorts of paradoxical things. Infinity is a concept not a number, it has no quantity that can be compared to some other quantity. This is why mathematicians talk about approaching infinity rather than infinity itself as a number. Besides, before the object approached "infinite" mass, the universe would collapse around it and destroy everything anyway, because gravity. You would destroy the universe before you approached the speed of light, even leaving aside the fact that you used up most of the energy in the universe in the process.
-
W∴ Balboos wrote:
as anything with any mass approaches c, they all approach the same mass
The problem here is that you are treating infinity as a quantity, which leads to all sorts of paradoxical things. Infinity is a concept not a number, it has no quantity that can be compared to some other quantity. This is why mathematicians talk about approaching infinity rather than infinity itself as a number. Besides, before the object approached "infinite" mass, the universe would collapse around it and destroy everything anyway, because gravity. You would destroy the universe before you approached the speed of light, even leaving aside the fact that you used up most of the energy in the universe in the process.
I did say approach, and besides that, these are both approaching the same order of infinities (Alephs). The universe wouldn't collapse around it - if for no other reason than that the information about it's mass would still be constrained to traveling at c. Anything else moving at 'c', therefore, may never know of the event unless it's heading more-or-less towards it. Or - if I were politically motivated I'd say: you've no experimental proof - but one doesn't present politics in the Lounge.
"The difference between genius and stupidity is that genius has its limits." - Albert Einstein
"If you are searching for perfection in others, then you seek disappointment. If you are seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010
-
I did say approach, and besides that, these are both approaching the same order of infinities (Alephs). The universe wouldn't collapse around it - if for no other reason than that the information about it's mass would still be constrained to traveling at c. Anything else moving at 'c', therefore, may never know of the event unless it's heading more-or-less towards it. Or - if I were politically motivated I'd say: you've no experimental proof - but one doesn't present politics in the Lounge.
"The difference between genius and stupidity is that genius has its limits." - Albert Einstein
"If you are searching for perfection in others, then you seek disappointment. If you are seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010
I'm not clear on how bringing set theory into it changes things. The initial energy required for acceleration would be much greater for the planet than for the grain of sand, so that is still going to carry forward as you approach infinity, right? It would amount to the same energy in both cases if you actually reached infinity, but of course you never would. Also, I'm not clear about how that mass is going to effect (or not) the rest of the universe. Are you saying that there would be no gravitational force exerted on the surrounding universe as a near-infinite bit of mass passed by? Is the gravity somehow localized? Let me guess, relative to the object travelling at c? So would the spaceship crush itself then? I'm sure I'm missing something, but I can't help but see near-infinite mass as near-infinite gravity, and gravity on that scale seems like it would have an effect on something. And, experimental proof of what? We're talking about thought experiments.
-
I'm not clear on how bringing set theory into it changes things. The initial energy required for acceleration would be much greater for the planet than for the grain of sand, so that is still going to carry forward as you approach infinity, right? It would amount to the same energy in both cases if you actually reached infinity, but of course you never would. Also, I'm not clear about how that mass is going to effect (or not) the rest of the universe. Are you saying that there would be no gravitational force exerted on the surrounding universe as a near-infinite bit of mass passed by? Is the gravity somehow localized? Let me guess, relative to the object travelling at c? So would the spaceship crush itself then? I'm sure I'm missing something, but I can't help but see near-infinite mass as near-infinite gravity, and gravity on that scale seems like it would have an effect on something. And, experimental proof of what? We're talking about thought experiments.
The set theory view is to narrow – they infinities are of the same order of magnitude (infinity-wise). Now, be they a grain of sand or a planet, they rapidly converge, asymptotically in mass as the sand would accelerate much faster (at first) until it’s mass was the same as the planet. Catch-up. The energy required for acceleration of either is "within experimental error", the same. (You know - infinit vs. infinity+1) And I didn’t say “space ship” or any other specific object traveling at ‘c’. Take, for example, any light in the universe – which is part of the universe – and would always be out of reach of the gravitational waves (if they travel at ‘c’). Unless you consider a universe containing just light is not a universe. The ‘experimental proof’ was a jab at those saying there’s no ‘experimental proof’ for climate change – but what experiment would the propose? So that’s why I said it had a political scent to it. Now, I’ve had to spell it out – which is what I tried to avoid, before – I brought a ray of darkness into the Lounge.
"The difference between genius and stupidity is that genius has its limits." - Albert Einstein
"If you are searching for perfection in others, then you seek disappointment. If you are seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010
-
Mike Marynowski wrote:
Pick the further thing in the universe you can think of. If you get your ship up to 99.99999% the speed of light, you will literally get there in a second.
So, if you go slower than light, you travel further than light itself travels in a second? I'm going to re-read this thread later on again, I must have missed some things :thumbsup:
Bastard Programmer from Hell :suss: If you can't read my code, try converting it here[^][](X-Clacks-Overhead: GNU Terry Pratchett)
Haha...the closer to the speed of light you go, the slower time becomes in your frame of reference. Very close to speed of light travel will get you anywhere in the universe instantly from your perspective because of time dilation. The faster you go from Earth to say Planet X, the more "slow motion" you look to someone observing you from Earth or Planet X, and the more sped up everything on Earth and Planet X looks to you. When you move at the speed of light relative to something, from your perspective you get there instantly, and that thing ages the amount of light-time away it is.
-
The set theory view is to narrow – they infinities are of the same order of magnitude (infinity-wise). Now, be they a grain of sand or a planet, they rapidly converge, asymptotically in mass as the sand would accelerate much faster (at first) until it’s mass was the same as the planet. Catch-up. The energy required for acceleration of either is "within experimental error", the same. (You know - infinit vs. infinity+1) And I didn’t say “space ship” or any other specific object traveling at ‘c’. Take, for example, any light in the universe – which is part of the universe – and would always be out of reach of the gravitational waves (if they travel at ‘c’). Unless you consider a universe containing just light is not a universe. The ‘experimental proof’ was a jab at those saying there’s no ‘experimental proof’ for climate change – but what experiment would the propose? So that’s why I said it had a political scent to it. Now, I’ve had to spell it out – which is what I tried to avoid, before – I brought a ray of darkness into the Lounge.
"The difference between genius and stupidity is that genius has its limits." - Albert Einstein
"If you are searching for perfection in others, then you seek disappointment. If you are seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010
W∴ Balboos wrote:
You know - infinit vs. infinity+1
This kind of arithmetic with infinity is exactly what bugs me, that's treating it as a quantity, the problem being that you have to actually reach infinity before you can add 1 to it. But never mind, that's a small point and it's purely academic. I get what you mean that at some point it would take almost exactly the same amount of energy to get both objects up to the same velocity.
W∴ Balboos wrote:
Take, for example, any light in the universe – which is part of the universe – and would always be out of reach of the gravitational waves
Well, photons don't have mass right? Gravity can affect light but light can't produce gravity AFAIK. I thought we were taking about accelerating matter. Obviously light doesn't take on infinite mass at the speed of light, we don't need an experiment to know that, we'd be able to tell :) Anyway, it's interesting to think about, but we are obviously never going to do interstellar travel by accelerating mass through space. It seems we would have to manipulate space somehow.
-
Haha...the closer to the speed of light you go, the slower time becomes in your frame of reference. Very close to speed of light travel will get you anywhere in the universe instantly from your perspective because of time dilation. The faster you go from Earth to say Planet X, the more "slow motion" you look to someone observing you from Earth or Planet X, and the more sped up everything on Earth and Planet X looks to you. When you move at the speed of light relative to something, from your perspective you get there instantly, and that thing ages the amount of light-time away it is.
I get how time may appear relative, but not how that means you move instantly.
Mike Marynowski wrote:
When you move at the speed of light relative to something, from your perspective you get there instantly, and that thing ages the amount of light-time away it is.
So, accelerating to lightspeed means time stands still from your own point of view? I kinda doubt that :)
Bastard Programmer from Hell :suss: If you can't read my code, try converting it here[^][](X-Clacks-Overhead: GNU Terry Pratchett)
-
I get how time may appear relative, but not how that means you move instantly.
Mike Marynowski wrote:
When you move at the speed of light relative to something, from your perspective you get there instantly, and that thing ages the amount of light-time away it is.
So, accelerating to lightspeed means time stands still from your own point of view? I kinda doubt that :)
Bastard Programmer from Hell :suss: If you can't read my code, try converting it here[^][](X-Clacks-Overhead: GNU Terry Pratchett)
Yes. Read the last section here for an explanation: Time Dilation[^] Some more reading if you are interested: Time Dilation[^] Q: If time slows down when you travel at high speeds, then couldn’t you travel across the galaxy within your lifetime by just accelerating continuously? | Ask a Mathematician / Ask a Physicist[^]
-
I get how time may appear relative, but not how that means you move instantly.
Mike Marynowski wrote:
When you move at the speed of light relative to something, from your perspective you get there instantly, and that thing ages the amount of light-time away it is.
So, accelerating to lightspeed means time stands still from your own point of view? I kinda doubt that :)
Bastard Programmer from Hell :suss: If you can't read my code, try converting it here[^][](X-Clacks-Overhead: GNU Terry Pratchett)
This is what most people that complain about the speed of light as a limit don't fully comprehend. It's not a speed limit, so much as it is the universe's infinity. It takes infinite energy to get there for a massful object because IT IS infinity from the perspective of that object. An outside observer watching their friend fly off in a spaceship at close to the speed of light will see a completely frozen person moving at 300,000km/s. The person in the space ship will see everything around them aging millions of years in an instant. From their perspective, they can travel millions of light years in an instant at that speed and no laws regarding faster-than-light information travel are being broken because of relativity - the object they are moving towards is aging fast enough that the information technically still took millions of years to get there. So the good news is that it could be possible for us to reach the furthest stars if we want to, as long as we are willing to leave behind an earth that will age millions of years when we arrive there.
-
Yes. Read the last section here for an explanation: Time Dilation[^] Some more reading if you are interested: Time Dilation[^] Q: If time slows down when you travel at high speeds, then couldn’t you travel across the galaxy within your lifetime by just accelerating continuously? | Ask a Mathematician / Ask a Physicist[^]
Thanks - but the explanation isn't for me; I'd refute it, where most people seem to agree that it is correct :) "So, when we move, at whatever speed, time slows down relative to a stationary observer." ..means it doesn't slow down for you if you move at that speed. So, again, I do not see how a photon travels instantly; not even from it's own perspective.
Bastard Programmer from Hell :suss: If you can't read my code, try converting it here[^][](X-Clacks-Overhead: GNU Terry Pratchett)
-
Thanks - but the explanation isn't for me; I'd refute it, where most people seem to agree that it is correct :) "So, when we move, at whatever speed, time slows down relative to a stationary observer." ..means it doesn't slow down for you if you move at that speed. So, again, I do not see how a photon travels instantly; not even from it's own perspective.
Bastard Programmer from Hell :suss: If you can't read my code, try converting it here[^][](X-Clacks-Overhead: GNU Terry Pratchett)
I don't know what you mean by your first line. When they say "it doesn't slow down for you" they are clarifying that it means that it's not like your spaceship will be moving in slow motion around you, it slows down from the reference frame of someone looking at you from where you left. That said, it does *appear* to you like you are travelling faster than 300,000km/s if you accelerated close to the speed of light towards an object because time will be moving very slow for you. If you take the trip distance as measured from a stationary point, divided by the time measured on a time taking device on your ship, it will certainly work out to considerably faster than the speed of light. Relativity is fascinating and kind of awesome. You need to rethink how you look at everything for it to make sense.
-
Thanks - but the explanation isn't for me; I'd refute it, where most people seem to agree that it is correct :) "So, when we move, at whatever speed, time slows down relative to a stationary observer." ..means it doesn't slow down for you if you move at that speed. So, again, I do not see how a photon travels instantly; not even from it's own perspective.
Bastard Programmer from Hell :suss: If you can't read my code, try converting it here[^][](X-Clacks-Overhead: GNU Terry Pratchett)
Remember that there is also length contraction at close to the speed of light...so time slows, and length contracts to close to 0 as well. So the distance you have to cover when you are moving that fast, relative to your frame of reference, has now decreased to almost 0 as well. Perhaps that's an easier way of thinking about it from the perspective of the traveler.
-
Remember that there is also length contraction at close to the speed of light...so time slows, and length contracts to close to 0 as well. So the distance you have to cover when you are moving that fast, relative to your frame of reference, has now decreased to almost 0 as well. Perhaps that's an easier way of thinking about it from the perspective of the traveler.