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Science and Astronomy Questions
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| DoctorOfSpace | Date: Sunday, 16.10.2016, 16:01 | Message # 856 |
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| Watsisname, great post and very informative, about what I was looking for. Not that Destructor1701 wasn't helpful but that much I had down 
Quote Watsisname (  ) and according to relativity they can't exist.
Do you mean simply because nothing can go faster than light or have I missed something that specifically says tachyons can't exist?
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| Watsisname | Date: Monday, 17.10.2016, 06:52 | Message # 857 |
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| Short answer is that they violate causality. But I'll take some time to explain, as best as I can anyway, what that means and why that is. Much of this I'm sure you and others already know, but let's run through it anyway. This will be a 'Why is the speed of light the cosmic speed limit?' post.
Let's start from the statement "nothing can go faster than light" specifically. It is an assertion, and an observation, but where does it come from? What is it that makes it impossible to go faster than c?
The first thing we might try is a 'brute force' method of accelerating a particle to faster and faster speeds. Surely, if we just accelerate it enough, it would break the speed of light. But it doesn't. What we find is that it takes infinite energy to accelerate any massive particle to c. Massless particles move at (and only at) c.
So it is hopeless to get anything which was sub-light up to the speed of light, let alone past it (unless we suppose warping the space-time like with an Alcubierre drive). But what if something was already faster than light, and was always that way? There is no problem with passing the infinite energy requirements if it never had to be accelerated past c. That's where the idea of tachyons comes in.
But there is another problem. This one is causality, and it's a bit more subtle and more fundamental to the laws of the universe. To understand it, we'll need to look at some space-time diagrams. Here's one (shamelessly taken from lecture notes from University of Toronto).
Time runs vertically up the graph and has units ct (speed of light times time to give a distance). Position in space is the horizontal. An 'event' is a point in space-time. It says 'something happens here and now'. A world line shows the history of an object through space and time. If an object is not moving through space, then it makes a vertical line. If it does move through space, then its line becomes tilted -- more tilted the faster it moves. The speed of light is a line tilted 45° (we usually make it be that angle out of convenience, by choosing units where the speed of light is 1 unit of distance for 1 unit of time, like one light year per year). Things moving faster than light are then closer to horizontal than that 45°.
Finally, something moving backward in time traces a path downward rather than upward.
It is often said that tachyons move backward in time. But that's not quite right. For instance, a 60° angle to the vertical is faster than light, but still going forwards in time. So why would that violate causality?
The answer lies in the way which intervals of space and intervals of time transform from one frame of reference to another. Space and time are relative, and they are relative in a specific way which is described by the Lorentz transformation. This transformation ultimately arises because the speed of light must be the same for everyone. For the speed of light to be a constant, space and time must be relative in a way which preserves that constant. This is Einstein's great discovery.
Here is a bit goofy-looking animation showing how the Lorentz transformation works:
It shows the location of events (the small white dots) in space and time, according to an observer who changes their speed (they follow the curved world line). The big white dots along the world line represent equal intervals of proper time, which is the time the observer measures. There's some math behind this which we won't worry about here, but the basic idea is that the transformation is hyperbolic. The more important point is to visually understand what is happening:
Notice that the distance between any two points changes when the observer's speed changes. And even more than that, their sequence can change. Two events which were on the same horizontal line don't necessarily stay on that line. This is one of the startling implications of relativity: two events which are simultaneous in one frame are not simultaneous in other frames! And the relative order of two events can even be different, if they are separated more in space than in time. This means they are not causally related, since information can't propagate from one event to the other. In the space-time diagram, the future light cone starting from one event does not include the other event. The other event is "elsewhere" from it, which we also describe as being a "space-like" separation.
For an event which is contained in the other event's light cone (a "time-like" separation), there is no question about which event happens first. The two are in causal contact -- information from one event reaches the other event. All observers will agree on which event happened first, even if they disagree on how much time elapsed between them, or how far apart they are in space. And we see this in the transformation -- no event ever crosses that 45° line from another event.
This potential for flipping the sequence of events separated by space-like intervals is the heart of the problem of tachyons. The reason is because tachyons allow the transfer of information from one event to another event in elsewhere. Since the relative sequence of those two events depends on frame of reference, there will exist frames of reference where a faster-than-light particle would arrive at the destination at an earlier time. This leads to situations with logical paradox, like a signal returning to its origin before it was sent.
Suppose it's the future. Humans have colonized Mars. But a twisted Bond villain wants to undo it all. He has placed planet-busting bombs on both Earth and Mars, and will set them off simultaneously unless his demands are met. To make sure they go off at the same time, the bombs are detonated when they receive a radio signal, which he will send from a point equidistant from the two planets.
Such is his plan, anyway. The people of Earth and Mars know about the bombs, but not that he intends to detonate them simultaneously. So as soon as one explodes, a tachyon signal will be sent to the other planet to warn them to disable the bomb there.
Of course, this plan would fail. Both planets blow up simultaneously. There's no hope for saving either of them.
Or is there?
You are Bond. You are currently flying from Earth to the midway point to confront the villain. Too late -- the signal has been sent. It sweeps past you. What do you see?
Remember you see the same speed of light as everyone else. You can say you are staying still but it is the Earth flying away behind you and Mars coming towards you. And since you see the same speed of the detonation signal coming towards you as away from you, Mars is rushing into the signal, while Earth is moving away from it. Mars hits the signal and blows up first.
Simultaneity is relative.
That seems preposterous. But it's true and it's not a problem (for physics -- morality of destroying two planets and everyone on them notwithstanding). The two events (Earth and Mars blowing up) are not causally related to one another. They are more separated in space than in time. Instead, they are causally related to the event which is the signal sent from half-way in between. No observer will disagree that Mars and Earth blew up after the signal was sent.
Now let's throw in the tachyons.
You see Mars blow up first. The moment the bomb-detonating signal arrived there, the Martians frantically sent their faster-than-light signal to Earth to warn them to disable the bomb. In your frame of reference, this signal reaches Earth before the detonating signal does. Earth is saved.
Paradox. Are both planets destroyed, or is Earth saved? Or is Mars saved? You could have been flying from Mars to Earth, and you'd see Earth blow up first.
Relativity tells us that separation of events in space and in time is relative, but events themselves are physical. So we can't have a planet either destroyed or not destroyed depending on your reference. That's an event. It can't both happen and not happen. Furthermore, relativity says that there is no 'special' frame of reference. We must treat them all as being equally valid. So this paradox tells us that this situation cannot occur. Information cannot be sent faster than light, therefore there cannot be tachyons. If they exist, then they can't interact with anything, which is equivalent to not existing.
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| steeljaw354 | Date: Monday, 17.10.2016, 10:01 | Message # 858 |
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| Watsisname, So speed of light isn't the limit?
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| Watsisname | Date: Monday, 17.10.2016, 13:22 | Message # 859 |
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| No, I'm showing that it is. Unless wormholes or Alcubierre drives are possible (and they probably aren't), then this is what relativity tells us. You cannot accelerate something to faster than the speed of light, nor can there be any particle moving faster than the speed of light to begin with. If we supposed that such a thing could exist, it would lead to paradoxes.
This limit also has less to do with light, and more to do with causality. There is a limit to how fast information can travel between events, and it happens to be the speed of light. It's a property of space-time.
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| spacer | Date: Monday, 17.10.2016, 16:01 | Message # 860 |
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| Watsisname, how will you define teleportation? will teleportation work like worm hole?
"we began as wanderers, and we are wanderers still"
-carl sagan
-space engine photographer
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| DoctorOfSpace | Date: Monday, 17.10.2016, 16:33 | Message # 861 |
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| Watsisname, even when it is a subject I am fairly well versed in your posts are always a treat to read.
I still do not see how this invalidates tachyons completely. What about the reinterpretation principle where by trying to detect a tachyon generates that tachyon, it is perceived as traveling forward in time, and observers can't distinguish between the emission and absorption?
Secondly isn't there still the possibility that tachyons are either minimally interacting or non interacting and completely causally disconnected? (This is getting into Russell's teapot scenario)
Regarding light cones, what about scenarios where no FTL is required for paths that are on tilted trajectories?
I would be interested to see your view on this page here
http://www.bibliotecapleyades.net/ciencia....l01.htm
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| Aerospacefag | Date: Monday, 17.10.2016, 21:32 | Message # 862 |
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| Quote DoctorOfSpace ( ) I would be interested to see your view on this page here
Quote In a curved space-time it is possible to "tilt" or "tip over" light cones. With a sufficient amount of space-time curvature a particle or person could continue to move into their own local future at sub-light speed but actually travel along a world line that loops back on itself as shown in the illustration.
Impossible, actually. The "cone" is not a fixed figure and is in fact a result of series of equations, interpreted in a certain way. From my knowledge of physics, I suppose the cone will change it's shape according to the difference of equations, but without having actual equations on hand, I would need to work on that to prove it. And it is pretty hard analytical problem at that.
Thus, the cone will never "tilt over", like an actual goddamn coffee cup and there's no violation of causality at all, as well as speed of light violation and reversed flow in time.
Quote DoctorOfSpace ( ) Secondly isn't there still the possibility that tachyons are either minimally interacting or non interacting and completely causally disconnected? (This is getting into Russell's teapot scenario)
I have the faint idea that further study in the direction of "dark matter/energy" theory can prove that, but the problem with them is pretty much the same as with tachyons - they don't like to interact with normal matter too.
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| steeljaw354 | Date: Monday, 17.10.2016, 21:38 | Message # 863 |
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| Watsisname, Maybe other civilizations found ways to circumvent the time dilations, let's say we have a ship that leaves it's home planet. It takes 1 year to go it's destination and 1 year passes at it's destination for example. But we haven't found those circumventions yet.
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| Watsisname | Date: Tuesday, 18.10.2016, 01:04 | Message # 864 |
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| Quote DoctorOfSpace ( ) even when it is a subject I am fairly well versed in your posts are always a treat to read.
Thanks! I can never be quite sure if I'm going into too much detail or just ranting pointlessly.  But I love discussing these things and I'm glad you enjoy it too.
Quote I still do not see how this invalidates tachyons completely. What about the reinterpretation principle where by trying to detect a tachyon generates that tachyon, it is perceived as traveling forward in time, and observers can't distinguish between the emission and absorption?
Right, I should make a disclaimer: it is specifically looking at faster-than-light particles which carry information (or can be used to transfer information), and in flat space-time (though curved space-time is also locally flat).
But if we imagine a tachyon which is impossible to distinguish between its absorption and emission, then this might work. Like an analogy to the delayed-choice quantum eraser experiment, where we literally are sending a signal back in time, but the receiver cannot extract any information from it. It's like the universe conspires to prevent us from sending information faster than light. This is ultimately the nature of causality more so than the nature of light itself.
Quote DoctorOfSpace ( ) Secondly isn't there still the possibility that tachyons are either minimally interacting or non interacting and completely causally disconnected? (This is getting into Russell's teapot scenario)
Precisely. We might suppose that a thing exists which does not interact in any way whatsoever. This would then be okay for tachyons. But it is also the ultimate Teapot. It cannot ever be detected, by definition, so we cannot know of its existence. The thing which does nothing is indistinguishable from nothing. It could be interesting for the philosopher, but for the physicist it is exactly equivalent to not existing.
Quote DoctorOfSpace ( ) Regarding light cones, what about scenarios where no FTL is required for paths that are on tilted trajectories?
In general relativity we can consider a space-time geometry with closed timelike curves (CTCs) and time travel to the past by going slower than light. There are many space-time geometries which do this, such as the Kerr metric for a rotating black hole, Godel's metric for a rotating universe, and the scenarios discussed in David Anderson's page that you linked.
However, I disagree with the language there. I would not say that these are examples of how time travel is possible or could be achieved. Instead I would say that these are solutions to general relativity which are unphysical. They may satisfy the field equations, but they don't exist in nature. Like the Kerr metric for the rotating black hole, where we know the solution is valid outside the horizon, but not correct for the interior where the CTCs occur. The appearance of CTCs (among other reasons) signals that the metric is unphysical there. What really happens must be different.
So I think the study of such a metric is more a study of the properties of space-time. It is fascinating in and of itself to examine the things that can come out of the field equations, and further useful for testing our assumptions which built those metrics to begin with. Kerr's metric tells us that the details of the collapse to singularity in a rotating black hole is important, whereas it was not important if the matter was not rotating to begin with (Schwarzschild solution). Godel's metric tells us that the whole universe cannot be rotating (actually it's a bit more subtle than that, but close enough). CTCs around an infinite rotating cylinder tells us that we can't build such a cylinder. Similar things for wormholes used as time machines -- presumably Hawking radiation destroys the holes the moment it is attempted.
Quote spacer ( ) how will you define teleportation? will teleportation work like worm hole?
I think there are a few ways we could define teleportation. We could imagine literally transferring all of your particles to a new location in space, faster than light or instantaneously. Or we could imagine not sending the particles themselves, but only the information about them, to reconstruct your body on the other end. We could imagine teleportation by wormhole. Or teleportation of the consciousness. These have varying degree of plausibility or basis in physics.
In my opinion, teleportation of your self by copying the information seems the least implausible.
Quote Aerospacefag ( ) Impossible, actually. The "cone" is not a fixed figure and is in fact a result of series of equations, interpreted in a certain way. From my knowledge of physics, I suppose the cone will change it's shape according to the difference of equations, but without having actual equations on hand, I would need to work on that to prove it. And it is pretty hard analytical problem at that.
Orientation of light cones depends on the geometry. Even in a non-rotating Schwarzschild black hole, the light cones tip to the side. Or rather, inward.
This is actually the reason the event horizon exists and has the properties it does (or we can say it is a different, mathematical description of the same physical fact.) The tipping over of the light cone prevents the ability of a light-like or time-like curve (any allowed particle or observer) from escaping the inside of the horizon. To escape, you would need to go faster than light -- to travel to your own light cone's "elsewhere". Which I think is my new favorite way of describing why you can't escape a black hole. Once inside, the outside is not merely "outside". It is literally removed from your potential futures -- your future light cone. It is as elsewhere as elsewhere could possibly be.
Quote steeljaw354 ( ) Maybe other civilizations found ways to circumvent the time dilations, let's say we have a ship that leaves it's home planet. It takes 1 year to go it's destination and 1 year passes at it's destination for example. But we haven't found those circumventions yet.
There may be ways of circumventing the speed of light with suitable distortions of the space-time, but we're not sure if it's really possible. The Alcubierre drive is in my opinion the neatest example.
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| DoctorOfSpace | Date: Tuesday, 18.10.2016, 02:41 | Message # 865 |
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| Quote Watsisname ( ) I can never be quite sure if I'm going into too much detail or just ranting pointlessly.
You have a great way of putting complex ideas into understandable explanations.
Quote Watsisname ( ) It is literally removed from your potential futures -- your future light cone. It is as elsewhere as elsewhere could possibly be.
If one crossed the event horizon and then used something like an Alcubierre drive to escape it what would the results be? Would you emerge far in the future?
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| Watsisname | Date: Tuesday, 18.10.2016, 05:42 | Message # 866 |
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| Quote DoctorOfSpace ( ) If one crossed the event horizon and then used something like an Alcubierre drive to escape it what would the results be? Would you emerge far in the future?
It's a great question. I wish I had a good answer. I've thought about it, but I honestly have no idea what would happen besides guessing. I don't know how to work the math for it, and the only answers I've been able to find are 'gut feeling' assertions, and for that reason I don't trust them.
To solve it, we would have to combine the Alcubierre metric with the black hole metric, producing some smooth timelike curve that goes into the horizon, generates a warp bubble, and then comes back out again. But coming up with a metric that does this is... challenging, and possibly not unambiguous.
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| midtskogen | Date: Tuesday, 18.10.2016, 05:47 | Message # 867 |
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| Quote Watsisname ( ) There may be ways of circumventing the speed of light with suitable distortions of the space-time, but we're not sure if it's really possible. The Alcubierre drive is in my opinion the neatest example.
To me, to say that we can do f-t-l space travel by manipulating space-time in such ways is about as neat as saying that f-t-l space travel is possible because we can simply manipulate the laws of physics. It must first be demonstrated a way by which space-time actually can be manipulated as described. The same goes for wormholes. Create a wormhole to the other end of the universe by folding the entire universe over? It's like saying that in the future intercontinental travel will be as convenient as a local bus trip because we can "neatly" move the continent to the traveller. Only much more absurd.
Quote DoctorOfSpace ( ) If one crossed the event horizon and then used something like an Alcubierre drive to escape it what would the results be?
Something absurd.
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| DoctorOfSpace | Date: Tuesday, 18.10.2016, 07:01 | Message # 868 |
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| Quote Watsisname ( ) I don't know how to work the math for it
I think that covers most people.
Quote midtskogen ( ) It must first be demonstrated a way by which space-time actually can be manipulated as described.
I think that was the point of the basic experiment Harold White had proposed with the interferometer. Focus lasers to a point and record the data and see if the distance the light traveled was shorter. As far as I know, every experiment was inconclusive and well within the margin of error.
Eric W. Davis has some interesting papers and presentations on the subject of casimir like forces, negative energy/pressure, which hypothetically should allow some form of space time manipulation. Haven't seen any experimental evidence for any of that yet.
There are enough unknowns where such things might be possible through clever engineering, but from what is known it would seem such technologies will forever be out of reach.
Quote midtskogen ( ) Something absurd. smile
https://youtu.be/65nSJrF-zgw?t=1m29s
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| midtskogen | Date: Tuesday, 18.10.2016, 07:54 | Message # 869 |
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| Quote DoctorOfSpace ( ) I think that was the point of the basic experiment Harold White had proposed with the interferometer.
Having a way of testing warp is a start, but it's a huge leap from creating detectable warp to the warp required for an Alcubierre drive to work. Still, I think Alcubierre drives seem more feasible than wormholes, but I suspect that the gap from detectable to usable spans over ridiculously many orders of magnitude even for an Alcubierre drive.
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| DoctorOfSpace | Date: Tuesday, 18.10.2016, 17:49 | Message # 870 |
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| Quote midtskogen ( ) Having a way of testing warp is a start, but it's a huge leap from creating detectable warp to the warp required for an Alcubierre drive to work.
Thats the distinction that news articles loved to ignore.
Quote midtskogen ( ) Still, I think Alcubierre drives seem more feasible than wormholes
At least with warp drives there is a basic structure for how it would work, all we need is that magic ring around the craft. Where would one even start on forming a wormhole?
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