FTL == Time Travel, or not ???

bonkey

Obviously my brain is growing soft these days...

I've read quite a lot about relativity, quantum mech and all those various areas, but there's one thing I cant wrap my head around...

Every so often, someone comes out with the statement that Faster Than Light travel must be impossible, because FTL would equate to time-travel, and time-travel doesnt exist by virtue of the fact that we have never met any time travellers!

Now, igfnoring the possibility/impossibility aspect, WHY does FTL travel equate to time-travel. I can understand the concept that you could witness something, and arrive at another location with information of what you witnessed before they were aware of the event, but this is not time travel.

For example, if our sun were simply to stop, they tell us that it would take 7 minutes for us to find that out. If I was stationed right beside the sun (somehow), I could arrive at earth, and tell people that the sun had disappeared, but this is not time travel...

So where is the problem? What bit of the puzzle am I missing?

On a related note, (for bonus points) ghravitational effects are supposed to be instantaneous. If the sun were to disappear right now, it would take 7 minutes for us to run out of light, but we would feel the gravitational difference immediately.

Therefore, gravitational attraction is "transmitted" at FTL (bearing in mind the concept of gravitons, as opposed to the bending of space-time) speeds - instantaneous speeds in fact. Is this not a direct "breach" of the absolute speed of light?

jc

satchmo

As far as I know (which isn't much as far as this stuff goes), it's something like the faster you go, the slower time goes. So as you approach the speed of light time slows down, and as you pass the speed of light you get that funky psychodelic sequence from 2001, and time reverses. Or something.

As far as I remember, they've tested this by getting two synchronized clocks and flying one in a jet at supersonic speeds around the world. When the flight finished and the clocks were put back together, the jet's clock was behind the clock on the ground.

I'm sure someone more scientific can give you a proper answer.

bonkey

Originally posted by Jazz
As far as I remember, they've tested this by getting two synchronized clocks and flying one in a jet at supersonic speeds around the world. When the flight finished and the clocks were put back together, the jet's clock was behind the clock on the ground.

Actually, I believe that was an experiment which was supposed to show that gravity influenced time, which backs up the concept of a 4+ dimensional time-space universe, where gfravity distorts or bends the various dimensions.

It showed that there is a difference in the rate of passage of time (miniscule) based on gravitational effects....something which I am actually not convinced is a valid argument, but which is not quite relevant to this current thread.

Thanks for the thoughts anyway. The other half of your post has me looking at something, and I might get back on it...

jc

satchmo

Originally posted by bonkey
Actually, I believe that was an experiment which was supposed to show that gravity influenced time, which backs up the concept of a 4+ dimensional time-space universe, where gfravity distorts or bends the various dimensions.

Uh yeah, that's what I meant to say... :rolleyes:

Well I stand corrected. In the light of this new information I'd like to retract any and all above statements. Still, I like reading about this sort of stuff so if you gain and new insights let us know!

nesf

Well on a related subject, tachyons are theoretically possible, I'm not sure if they are experementally found yet tho. These are particles that are always moving FTL.

The theories are that you have to stay on either side of the speed of light.


The slowing of time is necessarily a gravitational effect but an effect of the conservation of the speed of light. For example if you did move FTL, then you would be moving in time reverse with respect to us, but you'd still measure the speed of light as c. Just your perspective would have changed.

SHAMAN

There r so many theories on time travel we wont actually how to do it til its done.Also, nothing can go faster than the speed of light.But u r right in saying that the closer u get to FTL,the more time slows down.If we were going very close to FTL and we were travelling to a close star,It might take an hour.BUT when u get back,TEN years will have passed.The universe is so confusing,how r we 2 know?

satchmo

Originally posted by SHAMAN
...Also, nothing can go faster than the speed of light...

They said nothing could go faster than the speed of sound, until somebody did. Do you have proof?

bonkey

Originally posted by SHAMAN
There r so many theories on time travel we wont actually how to do it til its done.Also, nothing can go faster than the speed of light.But u r right in saying that the closer u get to FTL,the more time slows down.If we were going very close to FTL and we were travelling to a close star,It might take an hour.BUT when u get back,TEN years will have passed.The universe is so confusing,how r we 2 know?

Well, see, this is where the problems come in.

1) We cannot say that nothing can go FTL. We *believe* that nothing can go FTL - but given that our models are nto complete and known to have incorrectness in them, we cannot state this for a fact

2) Does time slow down the closer you get to c? If you take two highly accurate clocks, synchromise them, and then leave on standing still while the other is travelled through a fixed circuit a number of times at very high speeds....will they disagree afterwards? This cannot be done in a plane, as the measurement there is influenced by altitude as much as speed.

3) The information you are presenting is the extrapolated conclusions of the theory I am questioning. It has not been proven.

Come to think of it - here's an interesting thought...

Lets go back to the fact that clocks in satellites (e.g. GPS systems) need to account for the "different speed of time passing" between the satellite and the earth. But, here's the thing...time is measured locally on a satellite, and locally on earth. We theorise that the differences in measurement are caused by time passing at different rates for whatever reason.

BUT, if both satellite and earth were to base their measurements of time passing on (say) a pulsar, then they woul dboth agree, wouldnt they?

See - part of me dislikes the methods we use for measuring time. We look at oscillations in crystals, decay in radioactivity, and what have you. When using these techniques for measuring time, are we not saying that we trust these techniques because they are constant and that if they differ in two locations, then this must be time passing at a different rate. But they cant be constant - by definition, only the speed of light in a vacuum is constant. So, unless we are using "optical" clocks, which use a beam of light travelling a known distance in a vacuum as our measurement, we are not measuring by a constant.

And even if we did that, surely our own models of gravity warping space-time would mean that the distance could be warped by gravity, which would mean that it wasnt travelling the same distance.

So - now we come to an even thornier problem....

What is time, and how do we measure it

Damn - what a confusing way to start the week.

And to make it worse....

If time slows down as you approach the speed of light, and goes into reverse when you exceed the speed of light, it is logical to conclude that time *stops* at the speed of light. This leads to even more confusing things. Arrgghh
jc

nesf

Originally posted by bonkey


What is time, and how do we measure it

Time is officially measured as the second being a fraction of the movement of the earth spinning on it's axis. IOW one second is officially 1/200ish i think of a single rotation of the earth. OR we can take one complete rotation as 24 hours. That work for you?


Things can move faster than light! Theoretically at least, I belive but i'm not definite that a type of muon which exhibits tachyon properties has been tracked. It gains mass the further into earth's athmosphere it travels. The easiest explanation for this is that it is a particle decelerating to light speed from FTL speed.

bonkey

Originally posted by nesf

Time is officially measured as the second being a fraction of the movement of the earth spinning on it's axis. IOW one second is officially 1/200ish i think of a single rotation of the earth. OR we can take one complete rotation as 24 hours. That work for you?

Fraid not. Given that the earth is rotating about the sun, the entire solar system is rocketing through the galaxy, and so on, how do you define the rotational speed of the earth. Plus, that isnt a constant value - you can be pretty sure that the earth has (tiny) variations in its spin over time. So, the measurement of 1 second is varying constantly, albeint in very small ways, if that is how it is measured.

And, taking it one step further, in all these experiments which "show" that time is not constant, how do they measure time? not through the earth's rotation, but by using some completely unrelated techniques which *in certain conditions* have been calibrated to match our definition of time. If those conditions change, we cannot assume that the technique is still valid - and when it isnt, we sometimes decide that it is time which has varied in value....not the behaviour of our time-measuring instrument.

Simply put, our definition of the dimensions of the universe *requires* that time be variable, because the speed light isnt variable. In other words, we appear to have chosen an arbitrary constant value, which sometimes doesnt appear to be constant. In order to maintain that constant, the other factors must change.

Of course, this then ends up in a discussion of "absolute" vs. "imaginary" vs. "relative" time....which is where my brain starts melting again...

jc

Bob the Unlucky Octopus

If I remember my AP chemistry right, time is measured by the half-life fluctuations of a xenon atom. It was found (by almost sheer coincidence) to precisely and consistently be the exact division of a four year cycle (inclusive of leap year corrections) into equivalent parts. Pretty precise stuff.

As for gravity- I'm by no means an expert on the subject...but what I've read tends to agree that gravity is a special case in terms of universal forces. The other forces (strong/weak nuclear, electrical, magnetic) are all split into attractive and repulsive forces based on charge and other subatomic factors...gravity is only an attractive force. This is one of the major issues some physicists have with Total Unification...that a defining Universal force is so odd.

Occy

nesf

I was giving the most basic definition of time bonkey I think it's the caesium atom than is used or another radioactive atom, for definig time to a high level of accuracy.

But my basic example works as the spinning earth is an inertial frame of reference. Time is relative, if we measured earth's spin from space we would get a different value due to being in a different reference frame. Time IS relative, but what matters is what value it has in your reference frame only! It's only when 2 events in different refernce frames or a single one observed in 2 refence frames that we have time dialation and thus an ambiguity of time intervals.


The point of the relative movement of the solar system and the earth is not needed when one is only concerned with measuring earth's rotation from the earth's surface. The earth itself acts as an inertial refence frame. I agree with what you said with slight fluctuations, but the problem is, unless you are taking measurements from space, then the effect is not measureable! We only have time dialation when we have 2 measurement instruments in 2 different frames of reference.

bonkey

Originally posted by nesf
The point of the relative movement of the solar system and the earth is not needed when one is only concerned with measuring earth's rotation from the earth's surface. The earth itself acts as an inertial refence frame. I agree with what you said with slight fluctuations, but the problem is, unless you are taking measurements from space, then the effect is not measureable! We only have time dialation when we have 2 measurement instruments in 2 different frames of reference.

Err, no. I dont think so.

You cannot measure the earth's rotation from the surface - you can *indirectly* measure it by observing the motion of a fixed point, or by calculating it from inertial factors, which involves knowing exactly how far from the exact centre of the earth you are, which is never constant.

As to the effect not being measureable - I can pretty much guarantee it is, just very small. Which brings us back to the original point...

Time measurements have shown to differ by *tiny* amounts, and this is usually put down to the effect of gravity, or speed, or whatever, distorting/slowing time. My question is whether or not it is changing the rate of time, or simply changing the rate at which something occurs - which is not the same thing.

Put it like this...is the halflife of an atom proveably indendant of gravitational effects, speed/acceleration effects, energy (heating, freezing) effects ??? Is it completely independant of all outside interference, so that the only way in which we can affect the half-life is by altering the rate of time's passing?

In order to be able to prove this, we need to show that all methods of measuring time behave in a similar manner when subjected to these conditions, and even then it depends on what youre talking about when you say "time".

Here's an example. Lets imagine that we could create a computer program which was self-aware. This program would be self-aware, no matter how quickly or slowly the computers on which it was based were running. It would not be the rate of change which made it self aware, but the nature of that change.

So...if we take said self-aware program, and run it on a machine of some arbitrary speed (x), and then run it on a machine of speed 2x, what has happened? To us, the observer, the program runs twice as quickly. To the self aware-program, the outside world runs at half the speed it used to. This is the essence of relativity. However, any method which the two parties could previously agree on for measuring time is now obsolete, as the original frame of reference has been changed. We cannot say that for the computer program time has slowed to half its speed, simply because it runs at twice its original speed. Perhaps *subjective* time has, but is that all time is?

Is time simply our perception of change? Is there truly no such thing as "absolute time" ????

The notion of "subjective time" is where it all stems from. Hawking et al will argue that the question of "what came before the big bang" is meaningless, as time did not exist before the BB. Time did not exist, simply because there was no frame of reference.

Is this a valid argument, or not?

jc

OSiriS

I have read alot of crap about FTL, and here is where a mis-conception "seems" to be.

Say u were travelling away from the earth at high speed, and viewing light (reflected for the picky) from the earth. As you approachthe speed of light, time would appear to slow down as your speed begins to match the speed of the light from earth to the point where time "freezes" at light speed. Now if you excede light speed you are over taking light, and so you perceve events to be going in reverse, hence "time travel". You are not actually travelling through time, it is just at extremely high speeds,your perception of time is altered.

This is of course only my opinion ... *runs off to study Einsteins Theory of Reletivity more closely*


Also ... Nesf: The earth doesnt take 24hrs to rotate, it takes slightly less, which combined with the fact that it takes slightly more than 365 days for the earth to orbit the sun mens we must have a leap year every 4 years ... and that every century is it, there is no leap year all to maintain the calander as we know it relative to the earths univeral position. Bonkey is right though, conventional time measuring devices are inaccurate as they are not measuring time relkative to a constant.

DeadBankClerk

Originally posted by bonkey
But they cant be constant - by definition, only the speed of light in a vacuum is constant. So, unless we are using "optical" clocks, which use a beam of light travelling a known distance in a vacuum as our measurement, we are not measuring by a constant.

what happens if the light-in-a-vacuum clock is moving? if the clock was moving at velocity C (with the same direction), would the light inside the clock be static, as the quantum of light is moving at C. Would the quantum of light move at velocity C relative to the vacuum-box, and thus be moving at 2C relative to a stationary observer?



on a slight tangent, i was watching the discovery channel a few onths ago, and they had a documentary on time travel. one oriental/american scientist had a theory on how to travel through time. You take 2 (i cant remember was it 2 sets of) metal plates and place them parrallel like a capacitor, and charge them up (with more energy then there is on earth) and then the plates (or was it 2 sets of parrallel plates) are seperated. One plate is kept stationary, and the other is taken to a distand location. a worm hole is created in space between the two, and you can travel instantly between the two plates.

DiscoStu

All this talk of ftl speeds are fine but doesnt the lorentz transformation show that along with time length is also contracted. so if you hit c you become the most dense partical in the universe as you have no length, width or depth. this infinitly dense thingy could cause problems for the rest of the universe such as a "big bang"?
i dunno

bonkey

Originally posted by DeadBankClerk



what happens if the light-in-a-vacuum clock is moving? if the clock was moving at velocity C (with the same direction), would the light inside the clock be static, as the quantum of light is moving at C. Would the quantum of light move at velocity C relative to the vacuum-box, and thus be moving at 2C relative to a stationary observer?

Apparently, and I have no idea how this has been shown, but the speed of light is always a constant. The wavelength of light gets red- or blue -shifted if the source of light is moving towards/away from you, but the actual velocity with which the individual photons arrive is still c. Which I find very confusing

So, if I am travelling away from you at .5c, and carrying a light-source, whcih I shine backwards, the light receeds from me at c. The light reaches you at c. What differs is the wavelength which we each perceive the light to be! This is closely related to the "dual nature" of light, being considered both a waveform and a particle.

Osiris - I would tend to agree with your definition of seeing events "run backwards" as you overtake the light from an event source at >c. However, apparently you can also show that you can arrive back at a location before you left as well, which is where it all gets silly.

As for the concept that a particle travelling at c would have no length, width, depth....I've seen this before, but somehow it completely ignores the fact that photons have a wavelength. So, it only (perhaps) applies to things which have mass. But, mass is just an expression of energy...so why is it any different to a photon, which is also an expression of energy?

Bah. I'm confused again.

jc

popinfresh

How I see it, we are never going to be able to go faster than the speed of light, so there's no way of proving it. Now I'm no scientist:rolleyes: , but wouldn't you like die or something if you went that fast?? Or would matter be able to stay together at that speed?

Bob the Unlucky Octopus

Because of time dilation, and relative mass expansion, you would approach an infinte mass as you approached c and would therefore require approaching infinite amounts of energy to accelerate to that point...which would needless to say, be impossible. At least as far as we know...

Occy

nesf

Originally posted by OSiriS
Also ... Nesf: The earth doesnt take 24hrs to rotate, it takes slightly less, which combined with the fact that it takes slightly more than 365 days for the earth to orbit the sun mens we must have a leap year every 4 years ... and that every century is it, there is no leap year all to maintain the calander as we know it relative to the earths univeral position. Bonkey is right though, conventional time measuring devices are inaccurate as they are not measuring time relkative to a constant.

The basic point is that time isn't constant. Even without relativistic conditions you get this. But if you use Gallelian transformations, it makes no difference. There is no definite time, theres just one particular variant, that we all adhere to. My example of the spinning earth wasn't meant to be perfect, I'm just pointing out, for all intents and purposes it works for everyday.

DiscoStu

maybe the speed of light is the origin of a 4 dimensional universe. it seems to make sense if tachyons have negative mass as has been suggested and time goes in reverse past c etc.. its just like going past the the origin in a cartesian plane eveything is negative.

maybe our inability to percive in 4 dimensions has led us to reduce the 4 dimensional origin into a single quatifiable value which actually means somthing and fits into our perception of the universe?

OSiriS

Originally posted by Bob the Unlucky Octopus
Because of time dilation, and relative mass expansion, you would approach an infinte mass as you approached c and would therefore require approaching infinite amounts of energy to accelerate to that point...which would needless to say, be impossible. At least as far as we know...

Occy

Hence the reason why it is still just a theory, and not a law. It doesn't hold for extremeties.

][cEMAN**

yes DBC that is pretty much correct.

What the energy is there fore is to create a gravitational field which in turn creates the wormhole.
When you part the two plates (afaik) it will hold the same gravitational connection between them therefore creating the wormhole......

Not too clear on this next part though as I think it also involves another 2 sets of plates set at the same frequency that actually relate to the part of space the first two are occupying. That is not only to do with time travel though but general travel such as the infamous "transporter" in star trek.

One thing to remember is Einsteins equation E=mC^2 which in turn means that E is directly proportional to m therefore....to increase speed you must increase energy. Though as energy increases so does mass therfore never really reaching the speed of light. That is one point. That is why WE can't.

Another note is that (I think it's these) quarks travel so close to the speed of light (or AT the speed of light) that they have been known to instantaniously travel back in time.

One theory as to how we can travel back in time is THROUGH that wormhole DBC mentioned or more likely "A black hole" but....in a gravitational field so powerful as to refract time there would be an immense amount of radiation which an unshielded human would never hope to survive. They are trying to find some way to ovecome this along with the mind shatteringly large field of gravity which would create it in the firstplace.

Along with this the reason why we would not have come across time travelers is because they would create a paradox, which as we all know according to "Back to the future" would "Destroy the galaxy".

What would be more likely here is the theory on dimensions where there are more dimensions than the 3 that we currently adhere to. I also personaly believe that in at least one of these dimensions time itself is not linear but possibly one of the other non-linear dimensions would be.

Eg. Simpsons - we remove the third dimension of their being to incorporate the time shifts within the program back and forth (hehe)

All food for thought though. Notice how mostly all of the above are theories?

Well I hope some day that they become fact but this is going my articles I have read years ago and if I am wrong in any point please correct me. If any of this has gone past theory as well then please also update me.

bonkey

Originally posted by ][cEMAN**
Another note is that (I think it's these) quarks travel so close to the speed of light (or AT the speed of light) that they have been known to instantaniously travel back in time.

I'd be really interested in links on this, but it sounds suspect to me.

How can you identify that an object is moving backwards in time?

If at time X it is at position Y, then at X1 its at position Y1, X2 puts it at Y2.

If it then "travels back in time", it reaches Y3 at some point *before* X2 rather than after it.

SO, to the observer, we would effectively see a particle in the following locaations at the follosing times...

Time Position
X0 Y0
X1 Y1 Y3
X2 Y2
X3 --

So, to the observer, it would look like a quark arbitrarily appeared at position Y3 at time X1, travelled to Y2 at the same time as our "original" quark travelled to Y2, and then BOTH of those quarks would completely disappear!!!

I'm not saying its impossible, but its bloody weird. You sure you're not thinking of quantum tunelling and getting it mixed up?

Also screws the theory of energy remaining a constant, because thats "over time" !!!

Like I said....I'd appreciate any links.

jc
[/B][/QUOTE]

][cEMAN**

Sorry Double post......

][cEMAN**

Sorry no links - all from books and televsion science studies - OPEN UNIVERSITY and such.

btw you're wrong there.....

you would see going by your theory....

x0 y0
x1 y1 y3
x2 y2 y4
x3 -- y5

You're forgetting that if traveling at the same speed even though at point 3 it would travel back in time it would still be ahead of point 1 and because it will still travel in a linear direction the quark which has traveled back at point y3 will be ahead of the other and therefore will not touch or meet.

TIME | POSITION 1 | POSITION 2 | POSITION 3 | POSITION 4 | POSITION 5

X0............Y0

X1...................................Y1..................Y3

X2.........................................................Y2..................Y4

X3..........................................................................................................Y5


This means a paradox would not happen and IF the energy is related it would also (I'm guessing this part) mean if the 2 quarks sharing the same time were linked it would account for the extra energy without mass needed to get it TO the speed of light.

OSiriS

[QUOTE
One thing to remember is Einsteins equation E=mC^2 which in turn means that E is directly proportional to m therefore....to increase speed you must increase energy. Though as energy increases so does mass therfore never really reaching the speed of light. That is one point. That is why WE can't.[/QUOTE]

I believe that there is a wide misconception where people have used this equation to prove that faster than light travel is impossible. It has been show that the equation does not hold for larger values of E. Think of it as a square function. For the shallow part of the curve (close to zero) results are within an acceptable tolerance to be considered true, but as the curve steepens results become more and more inaccurate.

bonkey

Originally posted by ][cEMAN**
btw you're wrong there.....

You're forgetting that if traveling at the same speed even though at point 3 it would travel back in time it would still be ahead of point 1 and because it will still travel in a linear direction the quark which has traveled back at point y3 will be ahead of the other and therefore will not touch or meet.

Actually, they must meet.

Consider the non-time-travelling particle. It goes from position Y1 to Y2 to Y3 to Y4, and so on, in a straight line (for simplicity sake.

Now, lets assign the following :

Starting position : Y1
arbitrary position while travelling : Y2
position *at the instant it begins timetravelling* : Y3
arbitrary position during time-travel : Y4.

We can ignore the case where it stops time travelling and begins to move forward in time again, as it will, in fact, be the exact same model (or a mirror image). So, for simplicity, lets assume that we are analysing a one-off change here...

Now... If time travelling were not happening at all, these 4 points would be reached at time X1 thru X4, and everyone would be happy.

Now, remember that time-travel doesnt "jump" the particle backwards in time, where it then begins travelling forward again (a la science fiction) but rather time travel is where the object is travelling backwards thru time at a particular rate - much like we travel forwards through time. Therfore, to an outside observer, it appears to be going backwards. The only sci-fi I ever saw which discussed this was Dan Simmons' Hyperion series.

Therefore, to the observer, at time t, where t = X2. we see the particle moving forwards in time travelling towards Y3, but we also see the particle travelling backwards in time coming from Y3. To us, it will appear to be coming from Y4 and heading towards Y3.

As our observed time clicks forward, our particle reaches Y3. If it now starts travelling backwards in time, it no longer exists in our visible timeline, but only in our past, therefore it disappears.

So, we see two particles heading to Y3, where they appear to annihilate each other. In actual fact, what has happened is that one particle came to Y3 and continued travelling on, but continued on by travelling back thru time.

Now....if this is possible, then we can also get the situation where the particle stops time-travelling and starts moving forwards thru time.

So consider...At time Z1 we see no particle. At time Z2 we see the particle "spring into being" as it reverses from "time-travel" to "normal travel". In fact, you will also see the particle which came back in time....so you will see two particles spring from nothing!

I'm not saying that this is impossible, but it doesnt sound like anything which experimentation has ever shown.

jc

Bob the Unlucky Octopus

Let's not forget that EVERYTHING we now know about the universe depends on the assumption that nothing, nothing, nothing travels faster than the speed of light. If there is evidence to the contrary, we would be forced to scrap everything we thought we knew about physics. There is no such thing as "time travel" for the simple reason that time doesn't travel, it flows in a relation to speed. Time is inseperable from the speed at which it is measured. Exceeding c is not accounted for in any current widely-accepted theory. These concepts are a little difficult to understand- even beginning with so simple an idea, that a photon hasn't aged since the beginning of the universe. Time has no meaning for photon energy, so "time travel" isn't an issue really.

There is no way to make a convincing argument for FTL- simply because it is impossible- that is a fundamental truth of the universe. Just as fundamental as the idea that energy cannot be created or destroyed.

Occy

][cEMAN**

OK say for arguments sake that the particle when it begins to travel (visably) forward through time again it is parallel to the original - well as you mentioned before you would see (and remember science is NOT about what we can see but of what IS) 2 particles but when we see (at the Z time frame which I assume you meant runs parallel to the time BEFORE the particle looks to reach Y3) the original coment of the 2 particles colliding and seemingly dissappearing you would still actaully be left with 1 particle continuing onwards.

It would be difficult to see but then I don't think they saw it more either theorised or studied from data....possible in some lab.

I know this is true but I just can't remember where to quote it from.

][cEMAN**

Originally posted by OSiriS


I believe that there is a wide misconception where people have used this equation to prove that faster than light travel is impossible. It has been show that the equation does not hold for larger values of E. Think of it as a square function. For the shallow part of the curve (close to zero) results are within an acceptable tolerance to be considered true, but as the curve steepens results become more and more inaccurate.

Actually I think you would be better looking the other way......

I actually said WE can't travel faster than light but I also mentioned that quarks can and spontaniously do at times. Thes are reaching the end where mass is almost infintessable....yet still has energy.

At this point (I haven't CLOSELY studied the equation and would love to see it some day) but it may be that the theory does not hold and would be WHY it IS possible for quarks to do this.

It would ALSO explain why the equation is E=mC^2 and not E (add symbol of 3 parallel lines here) mC^2 ie. E is ALWAYS equal to rather than E IS equal to.

That is part of the mathematical statement which allows for it otherwise I think he would have added the extra horizontal line