But Why?
You might as well ask why energy increases with the square of velocity in classical mechanics?
We don’t (yet) have any way to test this, but University of Adelaide applied mathematicians are suggesting that an extended version of Einstein’s Theory of Special Relativity also holds true for velocities beyond lightspeed. One of the main predictions of Special Relativity is that the speed of light is treated as an absolute …
You might as well ask why energy increases with the square of velocity in classical mechanics?
"You might as well ask why energy increases with the square of velocity in classical mechanics?"
Well isn't that just e=mc^2 ?
Given that we're not getting very much further than "because that's what the theoretical maths predicts" on the question of light speed, maybe you're right, and the answer is intrinsic to why energy increases with the velocity squared. I accept it does, but why?
If my speed doubles, why doesn't my energy level merely double?
"You might as well ask why energy increases with the square of velocity in classical mechanics?"
It doesn't - the classical equation for kinetic energy is 0.5mv^2
The equation for relativistic kinetic energy is :-
E=(mc2/sqrt(1-((v/c)2)))-mc2
Apologies - I didn't read the original post accurately - let's say classical kinetic energy is proportional to the velocity squared.
Given that we're not getting very much further than "because that's what the theoretical maths predicts" on the question of light speed,
I'm not sure what the antecedent of your "we" is here. If you mean "people commenting in this forum", then perhaps that's an accurate statement; but if you mean "human beings in general", you're hugely underestimating the vast array of experimental results confirming relativity, and the very nuanced understanding of it that researchers have.
maybe you're right, and the answer is intrinsic to why energy increases with the velocity squared.
No, the special status of c as the upper (asymptotic) limit on the speed of a mass doesn't derive from the relationship of velocity and kinetic energy in classical mechanics. I think you misunderstood JDX's point, which was that asking "why?" in some cases is rather difficult to explain. One problem is that the domain of the desired answer isn't clear. I can explain "why" E=1/2 mv^2 in classical mechanics in terms of calculus (ie, derive it mathematically from other observations about mechanics) - that's a formalist why. I can explain "why" in terms of experimental observations - that's an empiricist why. I can offer an explanation that appeals to the well-formedness of the universe (metaphysical) or the goodness of God (theological) or what have you. "Why?" by itself is an underdetermined problem.
I accept it does, but why?
Well, you could try starting with this: https://en.wikipedia.org/wiki/Lorentz_transformations#Visualizing_the_transformations_in_Minkowski_space. That visualizes what's happening between the two frames of reference (stationary observer and moving particle or whatever). If you understand those diagrams - and I admit they are not the sort of thing most people deal with on an everyday basis - then you'll see that there has to be a transformation to map the coordinates of one frame to the other frame.
Lorentz (with many refinements by Poincare, but he gave Lorentz credit, as he was wont to do) mucked about with Maxwell's equations, trying to understand the velocity of light and the symmetries of electromagnetism, and figured out the transformation in question. The key to it is that the speed of light is the same for all observers, which means that, as the Wikipedia article puts it, "the Lorentz transformation must preserve the spacetime interval between any two events in Minkowski space".
That there preservation of your spacetime intervals is what gives you yer c speed limit.
If my speed doubles, why doesn't my energy level merely double?
Because then mechanics would be inconsistent. Many of the basic equations of mechanics are just the derivatives and integrals of one another. Velocity is the derivative of position - it's how position is changing at any given moment - and the integral of acceleration, the overall result of whatever acceleration has been doing in a given interval. If kinetic energy were proportional to velocity (rather than to its square), and you derived energy from momentum (which is proportional to velocity) and then derived momentum back from energy, you'd have a different equation than the one you started with - and so two inconsistent equations for momentum. And so on.
In particular, if E was, say, 1/2 mv, then its derivative (holding m constant) would just be 1/2 m, and momentum wouldn't be affected by velocity. Well, that's a problem. The derivative of 1/2 mv^2, on the other hand, is mv, which is just what we want.
If you get an introductory physics text and spend some time deriving one linear-mechanical quality from the others, you'll find that the v^2 has to be what it is, for mechanics to be consistent.
Cubert J. Farnsworth: That's impossible. You can't go faster than the speed of light.
Professor Hubert Farnsworth: Of course not. That's why scientists increased the speed of light in 2208.
"It's one of the "difficult" bits of relativity: even if you and I are travelling in opposite directions at 55 percent of the speed of light, the sum is 100 percent, not 110 percent"
actually, .55c +.55c = .84c
see here: http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_theory_of_relativity
That's very interesting and a worthwhile comment to make, however, that Wikipedia reference just fused my brains so thanks very much.
The implications of special relativity are quite simple - lightspeed is a barrier to going faster than light as transition requires infinite energy. On top of that you might also consider that it can be viewed as a theory about simultaneous events and anything going faster than light maps onto a reversed time line. That is, to an observer, anything moving relative to them faster than light will appear to be moving in time. The end result is that transluminal travel creates time travel causality problems.
Bottom line tends to be that there aren't any rules saying you can't travel faster than light, just rules that say you can't get there. The natural 'speculation' is to imagine quantum tunnelling through the light speed barrier but since it is infinitely high this doesn't make sense either. The whole area has been done to death many years ago.
Not necessarily. If we assume faster than light is possible (only getting there from our side of v= c requires infinite energy so is not possible to attain from our side of the light barrier) then you may have to accept that imaginary time exists.
That is, if you travel at velocity 2c then your mass would be restMass/i , or -i*restMass, whatever that means. If it means anything then it follows that velocity can take values on the entire complex plane. Special relativity equations for mass and energy simply have a pole at v = c. But that doesn't stop us side-stepping the pole and heading into complex velocities and then back onto the real line after meandering past the pole. Again, this assumes complex velocities means something. i.e. travelling through an extra space dimension.
For the last footnote, the sum is actually something like 84%, not 100%.
Using the info from wikipedia linked below, here's your answer:
0.8445297504798464491362763915547
Anon in case I'm wrong ;)
"The surprising outcome: with just two assumptions"
I stopped reading then.
I don't think much of the assumptions made. I can make two assumptions and give a whole different graph (although, I'll admit, I only play part-time with neutrinos as I design particle accelerators in my spare time) but this article smacks of 'having an interview and needing to get some use of it'
"We made two assumptions. 1) Cheese makes great bicycles 2) FTL is possible.
We sent these assumptions through a grinder, and wow, FTL is possible!"
And your comment smacks of sourpussing, and I need no assumptions for that at all.
[laughs] Attack ships on fire off the shoulder of Orion. I watched c-beams glitter in the dark near the Tannhäuser Gate. All those moments will be lost in time, like [coughs] tears in rain. Time to make some really cool quilts.
Hybrid? Can you show me how to download?
photons travel at their natural speed without any extra input.. We can break the sound barrier... beating photons in a race shouldnt be that hard... be interesting to see what happens when you approach the FTL barrier.. does everything get blurry and then blackout?
Just remove the bosons and add energy?
...sucks.
Who made it 2141.38M linguini/s anyway? Can't the noodly appendage count any higher?
I say put the Germans or Clarkson in charge and we'll have free speed in some parts, so we can visit the neighbours in a reasonable amount of time.
"Australian" and "Mathematician" fits like "American" and "Sensible" anyway. So there.
There's also the small problem of causality: if FTL is consistent with relativity, relativity is still true, and FTL is possible, suddenly our concept of causality is thrown out of the window.
As far as I can understand, that does not change with this paper.
Do we really hope to live in an universe where retro-causality is true?
Bravo, sir, for being the first commentard to point out the what-should-be-obvious, and rather showing up said commentards (and reporter) above.
Unless there is a way to arrange FTL travel such that causality paradoxes are avoided, it cannot be possible.
These sorts of articles strike me as having got things backward, because it is a resolution to this issue that is required first before it's even worth bothering to think about how to go about doing it.
Having said that...
>>> Do we really hope to live...
A few commentards above talked wistfully about hope and dreams of a more positive sort. I'm down with that, but hard reality is a better guide. I'm afraid the same goes with the negative - if causality paradoxes are somehow sustainable, well then I suppose we're all fuct if we ever work out how to exploit the fact. The universe does not give a two penny shag what your little monkey brain has dreamed up as "hope".
It depends if time and speed really are linked as we currantly think. To our currant knowledge causality breaks if we acheve FTL, what happens if our currant knowledge is wrong?
So yes your right, but hopefully your also wrong. But you might be right and wrong at the same time...or yesterday.
The part about hoping to live was directed to those that when you speak about FTL suddenly start jumping around all happy like puppies... if causality is not assured, our very existence become very precarious.
Said that, I agree with you that what it is, it is: when exploring nature belief have to remain out of the window.
If timeand speed are not really linked as we think, relativity is not true, and so my statement remains: causality and FTL remains, and relativity goes out of the window.
Said that, relativity have been verified at quite an impressive range of conditions, so to throw it out of the window is not a small task.
if causality paradoxes are somehow sustainable, well then I suppose we're all fuct if we ever work out how to exploit the fact
Some hard-SF authors have played with this idea. I'm currently reading Charles Stross' Singularity Sky (among too many other books). One of his theses is that FTL travel is possible, but it's policed by a future civilization which uses its technology to maintain a monopoly on causality weapons. Anyone else tries to get clever with causality and they slap 'em hard - and they can do so before their opponents even develop a causality weapon, because they can change the past.
So we can go ahead and screw up causality in the hope that someone else already got there and will bail us out retroactively. Problem solved! Before it even became a problem, in fact.
Of course, the simplest fix is for the first civilization that develops causality weapons to prevent anyone else from ever inventing FTL tech.[1] So there's another reason why it won't happen. Sorry, FTL-travel fans.
[1] Because they can do this retroactively, they don't have to be the first first civilization to develop FTL. The first civilization to develop FTL and get the idea to stop everyone else will retroactively prevent any earlier civilizations from developing FTL, and thereby become the first to develop it. Simples.
about dreams:
I sure hope you don't think anyone with dreams is a "tard" (how am I supposed to take that "commen<i>tard</i>" remark, anyway?<i>!</i>). Remember, with that kind of attitude, we'd still be in caves.
But yes, one does need "hard reality" to tell one <i>which dreams can be made to come true and which ones can't<i>. But that doesn't mean one shouldn't have dreams. A knowledge of "hard reality" tells you where you can go, can't go, how hard it is to get there, and, of course, <i>how</i> to get there if you can get there. But the <i>desire</i> to go and the <i>direction</i> in which to go requires, at some level, dreams. The two work together.
What I don't get is the obsession with going faster than light in the first place.
Yes, it would be better if we could get to very far away star systems in months or even a lifetime but if you are talking about the expansion of the species then why does that even matter? Even if it takes centuries to "system hop" there will be pioneers willing to be part of that either through stasis pods, generational ships or whatever. Yes it'd be a 1 way trip but so was emigrating to another country thousands of years ago.
Because!
If there's a limit, there's been a talking ape that tried to figure out how to get past it. If there's a horizon, there's always someone who's going to look what's beyond it. If "everybody knows" [something], there's someone figuring out how everybody has been wrong all along.
As soon as humanity loses this trait, we're truly doomed.
If we are concentrating on travelling faster than light, surely we can come up with some inventive ways to massively slow down the light? So much so that we can perform an experiment where someone gets to the destination quicker than light. Thus, claiming the prize and the adoration of all
Alright, they subjects would be travelling through different mediums, but this is all about making spurious claims, not about fair tests.
Advice on how we can achieve this please science intellectuals?
x
so your plan is to slow down the universe, and then simply walk to alpha centarui? Basicaly a cheats version of FTL? Its inventive, but i suspect horribly flawed.
The current record, if I recall correctly, is something like walking pace. (I'm sure it's been reported here if you care to look.) C on the other hand is a fundamental physical constant. Unless you happen to be a member of the Q continuum you don't get to change it. It's simply a part of how the world works.
Now that doesn't mean there might not be workarounds but those workarounds need to be compatible with relativity in much the way relativity is compatible with Newtonian physics.
I know exactly how to slow down light. All you need is a flask of water.
Unless you are talking about speed of light in a vacuum. Which is really the maximum speed information can be sent. i.e. the maximum possible velocity for sending information. Ever. Even quantum entanglement experiments don't truly break this limit (that is, entangled particles separated by a great distance acting as an entangled pair). Since the observers of either particle would not be able to get information about the other particle faster than c.
...which states that any question in a headline can be answered "no".
I think I first read about this in A Brief History of Time: physics doesn't ban FTL particles, but c is a barrier which cannot be crossed (so how do FTL particles get created in the first place?).
The light speed limit only applies to things moving - e.g. quantum entanglement effects are, as far as we know at the moment, instantaneous. Similarly the (very) early cosmos is thought to have expanded faster than its local speed of light.
Or, consider looking at a spoon in a glass of water; it appears bent due to the effect of refraction at the air/water boundary, which is an effect of the different speeds at which light travels through air and water. If you now move the spoon around, the "bend" changes in a predictable way which can be calculated by assuming the light travel time is minimised (by trading off speed vs distance in air vs water). Which begs the question of how do the photons involved know which combination of paths in air and water will produce this minimum time - perhaps something is working it out for them in advance, implying a faster than light effect. Or not.
Shortest path provides a very handy way of calculating for us, but it doesn't mean that the universe does some calculating ahead of time.
Here's an analogy; when you drop something, it falls in such a way as to preserve various truths/values about its energy (and there is a way of calculating this that provides some very elegant maths). How does it know in advance which way to move to do this? Does it calculate all possible options? However, apply Newtonian mechanics to the exact same situation, and it falls in the direction that weight (i.e. the force due to gravity) applies. This explanation does not "require" any pre-calculation about which way to fall to do the same thing to its energy - that is a by-product of obeying the Newtonian mechanics.
Which is "correct"? Both methods give the same answer, verified by experiment. They are two different mathematical ways of describing the same phenomenon and the fact that one of them involves "knowing" which path is the path that meets requirements on its energy doesn't mean that something somewhere is calculating all the options.
Here's an analogy; when you drop something, it falls in such a way as to preserve various truths/values about its energy (and there is a way of calculating this that provides some very elegant maths). How does it know in advance which way to move to do this? Does it calculate all possible options? However, apply Newtonian mechanics to the exact same situation, and it falls in the direction that weight (i.e. the force due to gravity) applies. This explanation does not "require" any pre-calculation about which way to fall to do the same thing to its energy - that is a by-product of obeying the Newtonian mechanics.
Agreed. To put it another way: if the dropped object didn't follow the path of least effort, it would be moving away from a lower potential energy state. That means you could in principle take the difference between the state it did move to, and the actual lowest state, and extract energy from it for free. You'd be violating thermodynamics (and the authorities take a dim view of that), you could build a perpetual motion machine, you'd be inflating the universe, etc.
1) Check out Feynman's books on QED (there is one for the lay public and one called "Feynman Path Integrals" or something). The idea:
You "just" need to add the complex amplitudes (at the target) of EVERY POSSIBLE PATH that a photon might take from source to the target. Square the value, which gives you a classical probability density function. A photon will be detected according to this PDF.
Everything (shortest path through spacetime, diffraction, refraction, Heisenberg uncertainty, interference, the works) can be explained by this simple principle - use EVERY POSSIBLE PATH (also the fractal ones - especially the fractal ones, though Feynman didn't know about that adjective, I think - and even the ones going faster-than-light, to the edge of the universe and back) AND SUM OVER THEM. For every photon. There are exponentially more paths in case you have more particles. Tremendous computational capability in this universe, wouldn't you think (but sadly NP-hard problems stay unsolvable even so)
2) In classical mechanics, you have the "Lagrangian formalism" which gives you the path an object takes through (flat) spacetime by requiring that INTEGRATION OVER TIME OF THE DIFFERENCE BETWEEN KINETIC ENERGY AND POTENTIAL ENERGY SHALL YIELD AN EXTREMUM. Simple as that. And it works bombers. Time disappears and the classical trajectories are simple solutions of a minimization procedure. Great stuff! (not so great that it would allow you do NP-hard problems efficiently though)
What does it all mean? Nobody knows.
What is the difference between travelling just under the speed of light and just over it?
My point being, if we could devise some "ship" that would take a human to a speed just under the speed of light, why would we not be able to devise a "ship" that travels just a bit faster than that?
as suggested above .... if I can build a car that travels at 40mph why can't I create a car that travels at 60mph if light travels at 50mph ?
How does light somehow prevent us going any further?
Surely it just prevents us "perceiving" going any faster than actually moving any faster?
Or is that just too simplistic a view?
"can't I create a car that travels at 60mph if light travels at 50mph "
The normal, simple model for this is as the speed of light is approached the mass of the vehicle actual increases in a non-linear manner so that more and more energy is required to accelerate it. The mass becoming infinite at c unless the original rest mass was zero.
This might sound like madness but in particle accelerators that is precisely what is seen, furthermore time itself alters so that short-lived particles have a vastly increased lifetime. This all predicted by SR.
Reality is pretty weird