Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Murchie85 on 16/09/2010 22:37:19
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I was wondering if, in special relativity there is a connection to mass in lorrenz contraciton.
As if I understand it correctly, things approaching the speed of light will appear shorter to stationary observers. For any non zero mass to approach the speed of light, a force is required, and energy must be put into the system, and as energy and mass are one in the same and it approaches infinity reaching light speed. My point is this, if this truly is the case then would the huge mass create its own bending of space similar to that of a black hole and thus be the reason for the dialation effect?
I am of course wrong as my lecturer in Uni has told me so and is an active member of cern, but he didn't really have the time to explain to me why? Or where my reasoning has gone wrong. So if someone can enlighten me further and see where im tripping up then I would be grateful.
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I was wondering if, in special relativity there is a connection to mass in lorrenz contraciton.
As if I understand it correctly, things approaching the speed of light will appear shorter to stationary observers. For any non zero mass to approach the speed of light, a force is required, and energy must be put into the system, and as energy and mass are one in the same and it approaches infinity reaching light speed. My point is this, if this truly is the case then would the huge mass create its own bending of space similar to that of a black hole and thus be the reason for the dialation effect?
I am of course wrong as my lecturer in Uni has told me so and is an active member of cern, but he didn't really have the time to explain to me why? Or where my reasoning has gone wrong. So if someone can enlighten me further and see where im tripping up then I would be grateful.
Relativistic time dilation is a consequence of space-time and how our rate of movement through one is reflected in our rate of movement through the other such that the summed vector of our spatial speed and our temporal speed is always equal to the speed of light 'c'. Thus, as our spatial speed increases, our temporal speed must decrease (and visa-versa) to maintain that same summed vector.
Imagine you are driving directly North in a car, at its highest possible speed. While you are doing this your East/West speed is zero. If you then drive directly East, still at top speed, your North/South speed becomes zero. Finally, you decide to drive on a heading of NE i.e. 45 degrees, still at the top speed of the car, but now you're travelling at less than top speed in both the North/South and the East/West directions. What we've done here is to represent our spatial and temporal speeds with the N/S & E/W directions and the speed of light 'c' with the top speed of the car.
The Lorentz formula for relativistic time dilation is essentially a transposition of Pythagoras's right-angled triangle formula to find the length of one of the sides, where the lengths of the hypotenuse and the other side are known. In relativistic time dilation the length of the hypotenuse is always 'c' and the side we know is our spatial speed. From this then, we can work out our temporal speed.
One of the things I really like about relativistic time dilation is that it shows that space and time are essentially the same, even though it may not be apparent from our point of view, for if they were different we would not be able to sum their vectors in this way.
Interestingly, if you take into account relativistic mass increase, and combine this with relativistic length contraction (which will effectively reduce volume and therefore increase density), then objects that are approaching 'c' should appear to become Black Holes. Now this is a curious thought because if the object were to subsequently slow down again we would effectively have seen something that has escaped, or perhaps a better term might be 'recovered', from a BH.
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The problem here is that the idea that "if you cram enough mass into a small enough space, you get a black hole" isn't exactly correct. Mass (or energy) alone isn't enough to tell you how space-time gets curved. You need to know the energy, momentum and how they flow in space and time. If the object is stationary, then its momentum is zero, nothing is flowing, and so the curving of space-time only depends on mass/energy. Cramming enough mass into a small enough volume will form a black hole. If the object starts moving, it now has momentum and energy which are moving in space and time. This means forming a black hole depends on all of these quantities and you can't simply say that putting enough energy into a small enough space forms a black hole.
There's a fairly simple argument that makes this seem plausible. First you have to make the assumption that a black hole, being a singularity, will have to appear to be a black hole to all inertial reference frames, i.e. you'll see a black hole regardless of whether you're moving or not. Then, just imagine that in any case of a moving mass, you can fly alongside it in a spaceship. It will appear to be stationary to you, and therefore not a black hole. Since it isn't a black hole to you, it won't be a black hole to anyone else.
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There's a fairly simple argument that makes this seem plausible. First you have to make the assumption that a black hole, being a singularity, will have to appear to be a black hole to all inertial reference frames, i.e. you'll see a black hole regardless of whether you're moving or not. Then, just imagine that in any case of a moving mass, you can fly alongside it in a spaceship. It will appear to be stationary to you, and therefore not a black hole. Since it isn't a black hole to you, it won't be a black hole to anyone else.
Wait a minute! I sense a "word trick" here. Either that, or it's the old Three Card Monte routine again.
Is this a polite way of saying there's not likely to be such a thing as a singularity, or that the stuff of black holes always has some dimensions?
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I'm just talking about singularities in the mathematical sense, and that they're a signature in this case of a black hole. When you create a black hole, you end up with a singularity in the space-time of general relativity that exists in all coordinate systems, which means that the black hole exists in all coordinate systems. There's usually a proof done when discussing Schwarzschild (non-rotating, static) black holes, that while there appear to be two singularities, one at the center and one at the event horizon, only the one at the center appears to exist in all coordinate frames:
http://en.wikipedia.org/wiki/Schwarzschild_metric
Even if the singularities at the centers of black holes aren't infinitely small, the fact that they appear in general relativity is still a signature that a black hole exists, and the fact that according to GR, black holes are black holes in all reference frames should still hold.
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I'm just talking about singularities in the mathematical sense, and that they're a signature in this case of a black hole. When you create a black hole, you end up with a singularity in the space-time of general relativity that exists in all coordinate systems, which means that the black hole exists in all coordinate systems. There's usually a proof done when discussing Schwarzschild (non-rotating, static) black holes, that while there appear to be two singularities, one at the center and one at the event horizon, only the one at the center appears to exist in all coordinate frames:
http://en.wikipedia.org/wiki/Schwarzschild_metric
Even if the singularities at the centers of black holes aren't infinitely small, the fact that they appear in general relativity is still a signature that a black hole exists, and the fact that according to GR, black holes are black holes in all reference frames should still hold.
Dang! If I wasn't so confused I might be sorry that I even asked [;D]
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Yeah that one is classical JP, Baez takes it up too. If I move a mass close to the speed of light, why wouldn't it form a black hole? (http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/BlackHoles/black_fast.html)
If that was what you meant Murchie?
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Special relativity is just a matter of perception because it is reciprocal. Unless you try to push and object at relativistic speed you will not no it has a relativistic mass. This is solved by general relativity which says that acceleration is the same as gravity... It doesn't mean that special relativity equations are useless though, it just means that you need general relativity to understand what is really happening...
I just found that the Doppler effect of light has a transverse component that is always a redshift, so it means that its angular momentum is always smaller than its proper angular momentum because its frequency and thus its energy appear lower. Many people wonder why light bend more than what they expect...In quantum mechanics, particles have a wave model. By analogy, it could explain relativistic gravity!!!
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Well kind of guys, thanks for the input. Although I see that it may not be possible for a black hole to form as it doesn't take into account momentum and angular momentum, I am still left wondering if the dilation effect from a black hole and the relativistic effects of near light speed non zero masses are connected? I mean a black hole isn't the only thing that can bend space. I mean the one thing they both have in common is huge mass is required for both. Is it just a coincidence that both phenomena act in a similar way or is there a deeper connection?
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Oh yes, I'm sure they're connected too Murchie. But the whole idea of motion and frames of reference is murky to me. We have no defined zero motion in the universe f.ex, so either you go on what you assume to be the red / blue-shift as an indicator of your 'speed/velocity' relative something else, remembering that it only give you the combined result of your frame relative someones else's frame, or you trust in acceleration as a true definition. But then you have accelerations equivalence to gravity, in that gravity also can be seen as an accelerating frame like our Earth, even though 'uniformly moving'.
Never the less, defining a motion to Earth is always relative something else as I see it. As far as I understand we can't define any 'uniform motion' as being faster or slower, other than by 'qualified guess work' like using those stars of what we expect to be a 'uniform luminosity' or as we deem it, laying sufficiently 'far away' from us to become 'fixed' relative us, unmoving on the firmament. Eh, we can always define it relative another frame of course, but I was thinking of 'absolute universal sort of objectively true motion' here, kind'a :) The one not needed to be defined as 'relative any other frame you choose", just existing :)
What really confuses me is thinking of black holes, spinning close to lights speed in a vacuum :) How the he* do they do it, and what happens there, with the frame dragging? Also considering that if they exist they would be an example of your idea in a way, as you there will have a mass near light speed, as defined by its geodesics. Ah well, the mass is more or less infinite at its center, but maybe one could use the event horizon as a measure, possibly?
A Merry-go-Round at Near Warp Speed (http://www.nasa.gov/vision/universe/starsgalaxies/spinning_blackhole.html)
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Well kind of guys, thanks for the input. Although I see that it may not be possible for a black hole to form as it doesn't take into account momentum and angular momentum, I am still left wondering if the dilation effect from a black hole and the relativistic effects of near light speed non zero masses are connected? I mean a black hole isn't the only thing that can bend space. I mean the one thing they both have in common is huge mass is required for both. Is it just a coincidence that both phenomena act in a similar way or is there a deeper connection?
They're connected, but different effects. The way you experience space and time in general relativity includes effects from moving fast as well as from curved space-time. Motion alone is sufficient to cause these effects, even if space-time is flat.
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the idea of relativistic mass seems to be losing popularity.
For one thing transverse mass is different from longitudinal mass.
Instead of speaking or 'relativistic mass' it might be better to speak of 'relativistic velocity'.
http://en.wikipedia.org/wiki/Rapidity
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That one was weird, but interesting granpa :)
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Had to look that one up some more.
Reading the wiki didn't bring me any intuitive understanding but How Do You Add Velocities in Special Relativity (http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html) did :)
In a limited sense, that is :)
As I understands it you use 'rapidity' as a way of 'transforming' the relativistic math treating different frames motion, relative any frame defined, be it yours or not. It's not a new theory of motion, more an alternative way of describing it, simplifying the mathematics involved, well, as I understands it?
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As for "transverse mass is different from longitudinal mass."?
That one refers to the fact that electrostatic energy behaves as having some sort of electromagnetic mass, which can increase the normal mechanical mass of the bodies, right? Now, that one is quite confusing as it suddenly discuss electromagnetic 'forces', that depending on if they are 'transverse, at an right angle to the motion induced, or 'longitudinal', that is following the induced motion then presents us with different mass. Intuitively it seems true that a force acting transverse, at a right angle to the induced motion, will introduce a higher resistance than a 'force' applied in the direction of the motion 'longitudinally'. But now we are discussing 'forces' and different types of 'resistance' it seems to me, and then wonder what effects they might have on a 'rest mass' motion?
"Since a lot of relativistic effects are keyed off of speed, you can imagine then that applying forces along the direction of motion (which change speed) would have significantly different effects than forces perpendicular to motion (which don't change speed)."
For a clearer understanding of how I like to see it you might look at MATTER, MASS AND ELECTROMAGNETIC MASS (http://www.relativityoflight.com/Chapter17.pdf) And to get to how Einstein saw it I believe Transverse Mass in Einstein’s Electrodynamics (http://www.mathpages.com/home/kmath674/kmath674.htm) to express it nicely. One can get quite a clear impression of the ideas from those two without needing to dive too deep in the math. Have to admit that the wiki Mass in special relativity (http://en.wikipedia.org/wiki/Mass_in_special_relativity#The_relativistic_mass_concept) fail to make the distinctions between them clear to me. But reading those others I refer to I find me begetting a succinct description of the difference between the concepts rest mass and electromagnetic mass.
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Got to admit though that the concept of 'rest mass' is more ambiguous than it seems at a first look, well, to me it is. It's pretty simple to see that electromagnetic forces are involved in all descriptions of matter that I know of, I can't really see how to exclude it to get to some state of matter not involving those? But it's still quite simple to differ between radiation and matter, just take a look at your telly. If you read "MATTER, MASS AND ELECTROMAGNETIC MASS" you can see that the author brings out some thoughts of his own at the end, wherein he questions Einsteins ideas, or maybe how they are interpreted? Those ones I'll leave to the author to defend :)
( Although it seems that some suggest that there is a difference between 'energy' and 'mass' making the equivalence slightly misaligned according to The Equivalence of Mass and Energy (http://plato.stanford.edu/archives/sum2010/entries/equivME/). And The Inertia of Energy (http://www.mathpages.com/rr/s2-03/2-03.htm) have this to say about the Mass/Energy-equivalence.
"The exact proportionality between the extra inertia and the extra energy of a moving particle naturally suggests that the energy itself has contributed the inertia, and this in turn suggests that all of the particle’s inertia (including its rest inertia m0) corresponds to some form of energy. This leads to the hypothesis of a very general and important relation, E = mc2, which signifies a fundamental equivalence between energy and inertial mass. From this we might imagine that all inertial mass is potentially convertible to energy, although it's worth noting that this does not follow rigorously from the principles of special relativity. It is just a hypothesis suggested by special relativity (as it is also suggested by Maxwell's equations)." )
It all seems to fall down to if there would be any matter if those different 'forces' were taken away, and looked at it that way, I don't expect it to be. But not all of them are electromagnetic, right :) So wanting to justify matter from that point of view you will need to find a way of transforming all those 'forces' into some electromagnetic equivalences it seems to me? Don't expect that to be do-able myself. We define electromagnetism to the 'electrons' orbitals and interaction with 'photons', virtual or not, am I right? And what they do seems to be bringing in are some 'kinetic energy' into the atoms 'equilibrium' that then gets transformed?
Awhh :)
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Had to look that one up some more.
Reading the wiki didn't bring me any intuitive understanding but How Do You Add Velocities in Special Relativity (http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html) did :)
In a limited sense, that is :)
As I understands it you use 'rapidity' as a way of 'transforming' the relativistic math treating different frames motion, relative any frame defined, be it yours or not. It's not a new theory of motion, more an alternative way of describing it, simplifying the mathematics involved, well, as I understands it?
Adding velocities requires doing a Lorentz boosts, which aren't too hard to do, but it's a pain to do a bunch of them in a row. Also, they aren't terribly intuitive--to me at least. Rapidity makes it much easier, since increasing velocity is essentially a rotation in the funny geometry of space-time.
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the idea of relativistic mass seems to be losing popularity.
For one thing transverse mass is different from longitudinal mass.
Instead of speaking or 'relativistic mass' it might be better to speak of 'relativistic velocity'.
http://en.wikipedia.org/wiki/Rapidity
I'm a fan of rapidity too.
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I was wondering if, in special relativity there is a connection to mass in lorrenz contraciton.
As if I understand it correctly, things approaching the speed of light will appear shorter to stationary observers. For any non zero mass to approach the speed of light, a force is required, and energy must be put into the system, and as energy and mass are one in the same and it approaches infinity reaching light speed. My point is this, if this truly is the case then would the huge mass create its own bending of space similar to that of a black hole and thus be the reason for the dialation effect?
I am of course wrong as my lecturer in Uni has told me so and is an active member of cern, but he didn't really have the time to explain to me why? Or where my reasoning has gone wrong. So if someone can enlighten me further and see where im tripping up then I would be grateful.
I wrote an article about this subject. Please see it at http://arxiv.org/abs/0709.0687
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Cool.