To throw a bit of a kink into the works, there has been recent indications that although matter moving through space time cannot exceed the speed of light, that space time itself can.

For example of this there have been recent detections of a few galaxies, one of which estimated as moving at 2.34c and another at 5.8c.

What this means yet is anyones guess, but as they appear to be supermassive galaxies, either they have enough gravity that thier portion of space time is isolated, or enough dark/exotic matter for the same.

It's one of the reasons some are starting to call Galaxies, 'Island Universes' as each Galaxy might actually be in it's own pocket of space time.

What is intresting though is somehow light can make the transition out of the superluminal space time, and into sub-luminal space time.

__________________
There is no problem that cannot be solved by a suitable application of high explosives - US Army Demolitions School

I just saw Hayley's comet, she waved, Said "why you always running in place? Even the man in the moon disappeared, Somewhere in the stratosphere" - Shinedown

http://worldsofothersuns.home.comcast.net/

Yup, accelerating expansion of the universe. Takes you right out of special relativity. The speed limit still applies to local mass/energy.

References? The dark energy/accelerating expansion concept suggests that other galaxies may eventually disappear from view or possible access, but I haven't heard anything about multi-c galaxies, and would wonder how they could be detected.

I'll see if I can find some actuall writeup's on this.

My source for it was a recent show (about 1 month ago) on SCICH with william shattner doing the voice over. It was either the Around the Galaxy, or the Understanding show on SCICH.

__________________
There is no problem that cannot be solved by a suitable application of high explosives - US Army Demolitions School

I just saw Hayley's comet, she waved, Said "why you always running in place? Even the man in the moon disappeared, Somewhere in the stratosphere" - Shinedown

http://worldsofothersuns.home.comcast.net/

Ravana,

You asked for a reference to a good book on Relativity. If I may, I would suggest Relativity by Albert Einstein, may as well go straight to the source no?I have a copy I picked up that was published by three rivers press. I found it was a great read, the equations are mostly appendixed in the back and the reasoning is in chapter style writings.
Good luck
Brandon

Thanks--I'm actually in the middle of it right now. That's where much of my comprehension of how the theory works is coming from (that, plus some helpful discussion here). And I agree, it's a good book, better than most I have seen (and I second the recommendation, if anyone else is looking for a good basic explanation of the theory). But I have found some points I question, or quibble with. Going to wait to the end, though, before I get serious about them; I want to give the old fellow a chance to explain first. No reason to jump the gun; I've got plenty of time.

Glancing ahead, however, I don't *think* he answers the underlying question that I posed. Even if it's 100% accurate--even if it's "truly" the way things work, and not just an accurate explanatory system--I'd still like to know, in physical, not mathematical, terms, what prevents a body from reaching the speed of light. (Maybe he does get to it; like I said, I'll wait to the end. Meanwhile, anyone have any ideas about someone who does answer that question--in case Al doesn't?)

I think it may be in part that all reference frames are equivalent. I may not be stating this well but I'll try to illustrate, and to the more knowledgeable readers, if I am wrong set me straight in whatever tones seem neccesary. If c was not held to be a constant, then we would always have an indication of what direction we are travelling. For instance, on a moving train, with a constant velocity, through careful measurement of light hitting two sensors, one at the back of a train and one at the front, we would be able to tell which direction that train is moving by the time it takes light travelling from the bulb to reach the 2 sensors and measuring the difference between the two. That would violate the principle of equivalence, we wouldn't be able to say that our train was a stationary platform, and likewise, applying the same logic to the earth, we would be able to determine its direction of motion in reference to what would have to be the single meaningful frame of reference by the difference in light hitting it at the "front" of its motion to the "back." I think that gets to part of the point of why the equations say c is constant.
Brandon

Well, I don't know if John Dlugosz or anyone else still cares, but I've been double checking my answers to the questions above and trying to come up with an easily comprehensible answer to his last question. Unfortunately, I haven't been able to come up with good heuristic explanations; my final answer is basically, "That's what the mathematics of GR says", which I will admit is probably unsatisfying.

Everything I said before is accurate. (I even withdrew a disclaimer I had inserted in an intermediate post above, as it was unnecessary.) In GR, the curvature of space is determined by the stress-energy tensor. When you work out the case of relativistic speed but non-relativistic masses, the only term in the stress-energy tensor of importance is T^{00}, which is the total energy density. In this case, to first order, the potential Phi due to an object moving relativistically with total energy E is the Newtonian potential, Phi = -Gm/r', where m = E/c^2. If the total energy arises only from kinetic energy and rest mass-energy, then m = gamma m_0, where m_0 is the rest mass of the object. (The prime on the r is meant to convey that it must be evaluated at the retarded time, i.e., you must take into account that the changes in potential only propagate at c.) So the relativistic mass increase does increase an object's gravitational effect (even to first order).

I came up with several nice and simple explanations for this, but they all suffered the serious flaw of being wrong. The only thing I can say is that special relativity doesn't apply when the mass-energy densities get too high, so when the relativistic mass becomes large, you can't use special relativity anymore and must apply the full apparatus of general relativity. (More specifically, you can only use special relativity when the size r of a mass M obeys r >> GM/c^2, i.e., well away from the Schwarschild criteria for a black hole.)

So I'm back to referring to the Einstein equation of GR (relating curvature to the stress-energy tensor). In the reference frame of a black hole at rest, the only non-zero term in the stress-energy tensor is T^{00}, the total energy density. When looking at the stress-energy tensor of an object moving relativistically, it is possible for T^{00} to exceed the Schwarschild density, but the object doesn't look like a black hole because other components of the stress-energy tensor (which correspond to momentum densities and momentum flux densities) are non-zero. The commonly stated form of the Schwarschild criteria only applies in the rest frame of the object; the more general form would have to be written as some complex relationship between the components of the stress-tensor. And that general form would be invariant to changes in reference frame; an object would either satisfy it and be a black hole, or not satisfy it and not be a black hole, regardless of reference frame.

Again, this may not be a particularly satisfying answer to someone not acquainted with the mathematics of GR, but I couldn't come up with anything simpler other than simply appealing to the principle of equivalence (which states that the inertial mass and the gravitational mass must be the same). If anyone wants to get into the details, I can recommend the textbooks I used: at the advanced undergraduate level, "Gravitation and Spacetime" by Ohanian, and at the graduate level, the classic "Gravitation" by Misner, Thorne, and Wheeler (all 1300 pages!).

I would note that there are a few sites I've found on the web that also get this wrong, also incorrectly saying that the relativistic mass increase is only an increase in inertia but not gravitational effect. (They don't actually state it quite that simply, or they would immediately realize that that is in contradiction to the principle of equivalence.) I may e-mail them, but several of the sites Google turned up are newsgroup archives that can't be fixed.

Possibilities for FTL Drives

The following are my pet theories on how it might be accomplished, as using gravity to alter space time to accomplish it would require far too much energy then practical for a self contained ship.

1. Space Time Pocket Drive
In this theory instead of moving the ship, or altering gravity to move the ship, some mechanism is used to isolate space time around the ship, and accelerate the space time itself instead of the ship. Time/movement within the pocket would obey all known SR and GR theories. This would however require some discovery of an energy or quantum particle that could be used to accomplish both the isolation, and then the acceleration/deceleration of the space time pocket. Personally I think this is really the only semi-realistic method to accomplish superluminal travel, but someone would need to find the mechanism’s to do this, and don’t think anyone is researching space time pocket isolation at this time. It is technically possible though, as it’s been proven (I think) that space time itself can move at superluminal speeds.

2. Quantum Signature Drive
This works by changing the entire Quantum State of matter of the ship and contents, so that it periodically has negative (anti) mass and therefore can exceed the know speed limits of mass less photons. The problems would be the side affects of such a change of quantum state. Would Negative mass have Negative gravity, any just fly apart? Is Negative Mass even possible with some combinations of the known quantum particles?

3. Sub Dimensional Drive (Sub Space)
This functions by changing the state around the ship, such that it drops from fourth dimensional Space/Time, into third Dimensional Space only. As Time no longer is a constraint, movement through just Space can exceed GR and SR velocities there. Issues with this are that Space Time will cast shadows into third dimensional space (so to speak); this could cause disruptions or other even nastier effects. As time becomes just a shadow per say, it may be that computer and mental activity isn’t possible at all, and thus, once you drop down into third dimensional space, you are in effect dead, and nothing functions, and the ship can’t get itself back. Subspace if possible at all, would probably be only useful for communication and not travel.

4. Extra Dimensional Drive
This functions by changing the state around the ship, such that it moves up from fourth dimensional Space/Time, into fifth Dimensional Space/Time/?. As this would in effect make the ship a shadow in the fifth dimension, the shadow would have to obey that dimensions movement limits. Additionally the shadows of fifth dimensional constructs would total interfere with ships movement, possibly even obliterate said ship as two shadows probably could not exist at the same time/space/?.


5. Alter Reality Drive (my somewhat humorous theory)
This functions by changing all the known laws of the universe so that your ship, or self, can do whatever it needs to do to get where it wants to at almost instantaneous speeds. A theory highly favored amongst Dungeons and Dragons fans, but unless you believe in magic, this will never get off the ground. A ‘Blink’ drive if you will or better known as a ‘Wish’ spell to some.


Basically I think our only chance at FTL drives, is something involving moving space/time itself, and not the ships. Yet the mechanism behind accomplishing that may not exist or if it does could be more dangerous then useful.

__________________
There is no problem that cannot be solved by a suitable application of high explosives - US Army Demolitions School

I just saw Hayley's comet, she waved, Said "why you always running in place? Even the man in the moon disappeared, Somewhere in the stratosphere" - Shinedown

http://worldsofothersuns.home.comcast.net/

Hey, chiaroscuro25, thanks for this answer. Although my level of physics understanding is at the level of an amateur, I've been always intruiged by the particular question answered above. Now, if I understand your answer correctly, electromagnets which keep, say, electron beams afloat in an accelerator will have to increase the upward component of the force they generate in order to keep the electrons afloat as these speed up to high relativistic speeds. I guess the upward component, being proportional to m g is much less than the steering (transverse) component proportional to m v^2 , but the effect should still be noticeable. Is this indeed what happens?

Thanks for your time.

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"Its full of stars!"

[What motivated my question is this: *why* is the speed of light priveleged? All the Lorenz transformations in the world can only show *that* it is, not *why* it is. Why, for that matter, is it the speed it is? Why not, say, 187,000 mps, instead of 186,000? (No, that's not quite like asking "Why is water wet?"--though that deserves a complex, well-reasoned and well-grounded answer as well... and one that I can come at least slightly closer to giving. At least there *is* an answer.) And why can't anything else ever reach that speed? I know, I know: energy requirement increases to infinity... but *why does it?*

[/quote]

In Einstein's 1905 paper, first and second pages, he says that,"...the same laws of electrodynamics and optics will be valid for all frames of reference where the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereby be called the Principle of Relativity) to the status of a postulate, and introduce another postulate, which is only apparently irreconcible with the former, that light is always propagated in an empty space c which is independent of the state of motion of the emitting body."

Actually, even contrary to what Einsein said, the first postulate implies the second postulate because the speed of light is one of the laws of electrodynamics and optics. If the speed of light weren't constant, in the sense of an ether wind, all electrical devices would stop working at some high speed because the speed of light changed.

All electrical devices including us stop working. So a changing speed of light implies that you would drop dead if you get moved near the speed of light. Your nerve cells transmit electricity with a certain capacitance between dendrites. Capacitance depends on the speed of light in a vacuum. If it changes, goodbye.

So the speed of light is part of the law of electrodynamics, which have already been postulated to be constant. So this would seem to make electrodyanamics In fact, it is constant and independent of speed in all possible force laws.

Traveling FTL might indeed be possible if conditions equivalent of being "inside" the event horizon of a black hole can be created.
In principle this can be done with focused high frequency gravitational waves. This is standard general relativity literature plus the ability of generating those waves. In any case it is for "theoretically certain" that matter is not required to create a gravitational field.
More information here:
http://arxiv.org/find/grp_physics/1/...,2003,2004/0/1

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Giorgio

Yet in a dielectric medium the speed of light changes.
And all the lenses (my glasses included) work fine and in agreement with the laws of optics.

There is a reason why Einstein talks about "speed of light in empty space".

Why would my speed affect the speed of light in vacuum?


The laws of electrodynamics do not require a constant speed of light (as a matter of fact, if it was, there would be no refraction, hence no lenses, hence no astronomy).

__________________
papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

I've actually written a story which uses this as a method of FTL travel, actually it was As Fast As Light travel or AFAL, it’s a comedy and I’m not sure exactly why I wrote it but I like it. The comedy element is that he managed it by STL travel and became the slowest man in the universe (story name), oh and he turned the whole of NASA into a retirement home

One thing I would like to add is:

6. The Hyperdrive

It works out side of gravity wells where they have no effect. The downside is that you go anywhere near a singularity (gravity) your screwed. Say been in a car and hitting a solid brick wall at 10mph you probably wouldn't get whiplash now try it 1/3 of a light year a minute hitting that brick wall. 8-[

7. Slip Stream (Andromeda)

It works inside gravity wells that are (possibly) anchor points for strings (M-Theory ones) that connect the gravity wells together. The downside is that you have no autopilot (in the show sense) as it requires a human navigator, as AI's tend to blow themselves and the ships and the crews up.

I have to say i like slip stream a lot better then star treks warp drive, granted it breaks as often though

Chaim Weizmann was once on a ship with Einstein and said: "He explained his theory to me every day, and on my arrival I was fully convinced that he understood it."

__________________
When I die I want to go peacefully in my sleep, like my grandfather. Not screaming in terror, like his passengers.

I might add thaat slipstream in Andromeda is a lot faster than warp drive. Intergalactic travell in less than days compared to trek warp drive which takes 70 years to traverse the milky way.

__________________
NCC 2000 - USS Excelsior. Commanded by captain Hikaru Sulu.

John Cramer has written one of the best essays on the Alcubierre drive
http://www.npl.washington.edu/AV/altvw81.html
and on the modification by Van Den Broeck
http://www.npl.washington.edu/AV/altvw99.html

basically Alcubierre's drive needs more energy than can be found in the entire universe, but if you put your spaceship inside a baby universe warp which is connected to the rest of the universe by a bottleneck smaller than an atom, it can be done.

Problems with the Van Den Broeck drive include- getting into this baby universe through a bottleneck smaller than an atom; getting out again at the other end; and seeing where you are going en route. Additionally all the spacetime paradoxes mentioned on this page
http://www.physicsguy.com/ftl/html/F...ec:warppicture
will come into play; especially if there are any traversible wormholes around, any kind of FTL travel will quickly lead to time travel and the collapse of causality.

So it is not recommended.

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New Orion's Arm Site . The Starlark . Against a Diamond Sky (OA Novella Collection) . OA Flickr set

Those two links are from the NASA Breakthrough Propulsion Physics (BPP) Project Page, I read it a couple of years ago and liked it quite a bit, the original author is an Aerospace Engineer at Nasa's Glenn Research Center called Marc G. Mills who also has some interest in Scf-Fi. In his bibliography he actually mentions a couple of short Sci-Fi stories he wrote.

__________________
Sic Transit Gloria Mundi

Why would my speed affect the speed of light in vacuum?
[/quote]

The speed of light is part of a formula for dielectric constant of the insulator used to make a capacitor, which determines the capacitance.

As an approximation, in some systems of units (which I forgot, look them up) the square root of the dielectric constant of a material is the index of refraction of a material. There are some exceptions where one has to use a more complex formula for index of refraction, especially with materials where the molecule forms a dipole (e.g., water). Such materials have an extremely high dielectric constant.

The index of refraction for low frequency radio waves in materials often fit the approximation, even with dipole molecules. The square root formula works in the limit of small frequencies. The dipole molecules need time to turn around, which high frequency (e.g., visible light) doesn't give them.

The square root formula works really well, even with visible light, for the alkanes and other materials where the dipole moment of the molecules is small.



The laws of electrodynamics do not require a constant speed of light (as a matter of fact, if it was, there would be no refraction, hence no lenses, hence no astronomy).[/quote]

Well, yes they do. The microscopic (or submicroscopic) version of Maxwell's equations are written with the speed of light in a vacuum, with no index of refraction correction. In the microscopic version, the role of molecules are that of electric charges, which impact the calculation as either electric charges and electric currents. The motion of these electric charges are controlled by dynamics outside of Maxwell's equatiions. Although the mathematics of this type of representation is far too difficult to be practical, one doesn't fundamentally need an "index of refraction" to understand "refraction" effects.

The index of refraction being inversely proportional to the speed of light is only a macroscopic approximation, the results of averaging the impact of different molecules.

My point is that:
The speed of light in a vacuum is fundamental to the properties of materials, although it is often "hidden" in approximations and averages. So if Einstein said that the physical laws are unchanged in different inertial frames, and the properties of a material (e.g., index of refraction) iare part of the physical laws, then the speed of light in a vacuum must be unchanged.[/img]

In the frame of reference where the capacitor is at rest, the speed of light in its dielectric and in empty space does not change.
Why would the capacitor stop working as observed in another frame of reference, moving at high speed with repect to it?

And your reply does not say that the laws of electromagnetism and optics require the speed of light in empty space to be a constant independent of the speed of the source.

The square root of the real part of the dielectric function is the refraction index.
It does not depend on the units used.

Consider that Einstein was referring to the macroscopic laws, which is indicated by his mention of the laws of optics.
Optics is macroscopic. It becomes electromagnetism microscopically.

Or simply in the fine-structure constant which gives the strength of the EM interaction.

You do not think that changing frame of reference might "scale" the parameters that characterize the interactions in way that keeps the laws unchanged?

If the second postulate of SR could be derived from the first, there would not be a second postulate.

__________________
papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)