The Universe itself can exceed it though because after the big bang the universe's expansion would have been faster than light (it had to have been and still is?).
The Speed of Light is the same for all observers.
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The Universe itself can exceed it though because after the big bang the universe's expansion would have been faster than light (it had to have been and still is?).
as i understand it light travels between atoms at the same speed as in a vacuum - it is only the interaction with atoms (the electron clouds in particular) that 'slow' it down.
it depends how you think about light really - if you think in waves it would be the difference between phase velocity and group velocity.
i have never seen a satisfactory explanation as to what is going on - probably because we don't know.
why does it have to have been? And in any case, 'the universe itself''s expansion speed doesn't really make any sense. Speed relative to what? And what information is it carrying?
photon hits atom, atom excites electron into unstable state. electron drops into a more stable orbit and (re)emits a photon. Obviously the more times this happens, the longer it will take for 'a photon' to get from A to B.
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Ok couple of things here:
1) Spacetime itself is expanding as the Universe expands... so while light appears to be travelling faster than the speed of light, it's actually travelling through expanding spacetime which gives this effect
2) But actually, Faster Than Light travel is possible... however what is absolutely and completely impossible in ANY WAY as transmitting "Information" at Faster Than Light speeds... information can be ANYTHING (mass, a singal, atoms, anything) that allows you to tell something about the signal's source. So when something moves Faster than Light (mass cannot do this) then all information is lost about that something...
But if measured from the speeding object, the speed of light never exceeds c as that would be impossible
Sort of, but it isn't that the universe is an exception to SR, it's just there is a common misconception with one of the postulates of special relativity.
The more 'correct' way of defining the first postulate of special relativity is that information cannot be sent faster than the speed of light in a vacuum*. That is, Alice and Bob can talk to each other, flash a torch at each other or throw a rock at each other and regardless of the method employed they cannot communicate faster than the speed of light. It is said that the two points in space and time that Alice and Bob occupy are causally connected.
However, consider two points in a vacuum. They do not send information between each other, so they can travel faster than the speed of light relative to each other. Now if Alice and Bob were separated from each other with such a vacuum inbetween them then they are no longer causally connected. There is no method they could ever use which would allow each other to communicate (forever alone
).This effect has been observed countless times. The expansion of the vacuum is accelerating, and as a result galaxies on the edge of our observable universe have been seen to just disappear. Furthermore, we are at the centre of the our universe.
*Exceptions do exist in QM. However, classically speaking this is always correct.
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Given that our observable Universe and our Universe are not the same thing, how can we know that?
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Saying that the speed of light changes is a little misleading. The photons are absorbed and re-emitted at different rates in different materials, but when travelling between atoms / molecules in those materials it still travels at c. The net time it takes to traverse a material may change, but light itself still travels at c.
Semantics really, I probably should have thrown in the word observable but it's pretty meaningless. Once we are no longer causally connected to an object for all we care it's gone forever. Whether it still exists is more the realm of philosophy which I'm not so good at.
Of course if someone could sort out the theory of the Alcubierre drive and successfully implement it I'll happily eat my shoes and accept that there is a difference between the observable universe and our universe.
edit: I should also add as a further aside that even when the entire universe was causally connected then there is still no 'centre' point of expansion beyond where we are today. Imagine the universe as lying on the surface of a balloon. The point of expansion is actually in the centre of the balloon, but to observers on the surface of the balloon can't see this. To them it looks like all objects are expanding away from them, i.e. they are the centre of their own universe and all other places are moving away from them.
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Take out a smooth edged coin such as a two pence piece, spin it and wait for it to start to fall.
Note the speed of the fall decreasing constantly, whilst the sound gets higher and higher in pitch as the part of the edge of the coin in contact with the table changes more and more rapidly.
If you were measure "speed" as how long it takes for the full circumference of the coin to make contact with the table, and you had a sufficiently big table and coin, this "speed" can be faster than the speed of light in a vacuum.
This is just one example of how we can percieve something to have a speed faster than light without breaking physics (no information is transmitted)
Note the speed of the fall decreasing constantly, whilst the sound gets higher and higher in pitch as the part of the edge of the coin in contact with the table changes more and more rapidly.
If you were measure "speed" as how long it takes for the full circumference of the coin to make contact with the table, and you had a sufficiently big table and coin, this "speed" can be faster than the speed of light in a vacuum.
This is just one example of how we can percieve something to have a speed faster than light without breaking physics (no information is transmitted)
Actually this is not true at all. Information is being transmitted and therefore the motion you describe cannot exceed the speed of light.
What would actually happen is the rigidity of the coin would fail. I.e. the angular velocity of all points would not be the same. It would either break well before the edge of it reaches the speed of light or would not be rigid. Either way, the edge cannot exceed the speed of light.
No, no information is being transmitted. Its the same principle as if you were to spin around on the spot with a laser pen, the speed at which the illuminated part of the wall is very great, but no information is being transmitted, if your surrounding walls are sufficeintly far away then the speed at which the point of illumination travels can exceed c too.
As to my previous example, it seems that the only the only way the contact edge could exceed c would be in a perfect vacuum with no friction, and a much stronger gravitational field.
http://www.nature.com/nature/journal/v404/n6780/full/404833a0.html
My apologies, I didn't quite understand your initial post. After reading that paper it makes sense now.
However, information is still being transferred using your definition of speed. You say that:
Then this would be the equivalent of marking a point on the coin at time t = 0 when it is at contact with point P (as from the article). You then measure the time interval taken for the marked point to return to point P, and determine the speed of rotation from that. Is this what you mean, or am I getting the wrong end of the stick?
If that is the case, then clearly this speed cannot exceed c. I can measure that point's position as a function of time, its momentum etc. All of this is information and would violate SR if it was travelling faster than c.
The paper you quote uses non-relativistic mechanics, and rightly so. There might be a singularity but as they say various resistive forces prevent it ever becoming a relativistic problem. If you were able to magically create a system without the resistive forces in question then you would still not be able to exceed c, unfortunately I do not have the time to mathematically prove it to you.
As for your example with the laser pen, this is a very different problem which boils down to the fact that you're in an non-inertial frame of reference. One cannot employ special relativity to say anything about a rotating frame. With that in mind, and I know nothing about general relativity, I will leave it to more knowledgeable people to reply
.Take a coin and spin it yourself, you can see that although the pitch increases (indicating that the point of contact is moving faster and faster) the actual rotation of her majesty's portrait slows.
So unless I'm reading your explaination wrong (which is entirely possible) I don't believe the location of the point of contact represents "information"
As for your example with the laser pen, this is a very different problem which boils down to the fact that you're in an non-inertial frame of reference. One cannot employ special relativity to say anything about a rotating frame. With that in mind, and I know nothing about general relativity, I will leave it to more knowledgeable people to reply
You could spin the laser pen at 1000 or 10,000hz without having special relativity coming into the picture, so if you spin the pen at 10,000Hz, and stand in a 50Km radius circular enclosure, the point of illumination would be travelling faster than the speed of light to someone standing in the middle. The only thing actually moving is the laser pen, but the illumination point looks like its travelling faster than light.
I know next to nothing about general relativity myself, but I don't think it applies in this case
I was referring to marking a location on the disk, not point P in the paper. Yes P can travel faster than c, and I totally understand what you mean now.
Yeah I was just being retarded on both accounts, my apologies. I blame reading too many papers
.I'll go back to particle physics now...
I was referring to marking a location on the disk, not point P in the paper. Yes P can travel faster than c, and I totally understand what you mean now.
Yeah I was just being retarded on both accounts, my apologies. I blame reading too many papers
I'll go back to particle physics now...
How are you finding particle physics? I only ask because my Bsc project next year is on designing a neutron scattering experiment, which wasn't my first choice, so I don't really know what to expect apart from a lot of programming
I'm not sure how helpful my advice would be. My project next year is more on extensions of the standard model rather than nuclei. Plus I'm a theorist, I haven't touched an experiment since second year
.A friend of mine did a similar sort of experiment. He seemed to like it, I think the data in these sort of experiments are usually pretty good.
It's the same principle as above
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