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"Light Barrier" bothers me

Originally posted by Space Cadet:
Tachyons are a form of matter that always travel faster than the speed of light, the slower they travel the higher their kinetic energy.
snip
I interpret this to mean that there are two velocities 100c, one where the gamma factor is positive and another where the gamma factor is negative. tachyons can range in speed from just above the speed of light to infinite to just above the speed of light but travelling backwards in time.
Tachyons are a hypothetical form of matter. They have never been observed, so there is no proof of their existence. General relativity allows them, but does not require them.

Tachyons traveling backwards in time would have negative energy, so would be interpreted as positive-energy tachyons moving forward in time. (If any were ever observed).
 
The gamma factor describe above applies to the relative mass of the moving body, and the relative energy required to move it. What the author does not mention (he actually skips over it) is that the gamma equation he states shows that an infinite amount of energy is required to achieve light speed; this is because the relative mass of the moving object is also infinite! Thus, the moving object will never go faster than c because it would acquire the relative mass of the entire universe and require all of the available energy in the entire universe!

Also, his gamma-squared formula is incorrect, due to a first-year algebraic error. Here is the correct progression:

gamma = 1 / SQR(1 - (V^2/c^2))

(Note: When V and c are of equal value, 1 -(1^2/1^2) becomes zero, its square root becomes zero, and its reciprocal (and thus "gamma") becomes infinite, which is an undefinable value.)

1/gamma = SQR(1 - (V^2/c^2))

(1/gamma)^2 = 1 - (V^2/c^2)

1 - (1/gamma)^2 = V^2/c^2

QED: By review of the correct gamma formulae and their meanings, one can easily determine that in the real world, there is no velocity equal to or greater than the speed of light. Thus, trans-light velocities cannot be achieved.

Also, a tachyon is merely a mathematical artifice that lends itself well to explaining certain vague physical concepts, and fills in for as-yet-undefined principles. Nor have Tachyons been observed in the laboratory or in nature, thus there is indeed no real proof for their existance. They are only hypothetical constructs used in higher mathematics to balance certain equations.

Three key scientific principles:

Extraordinary claims demand extraordinary proof.

Never posit an hypothesis beyond the available evidence.

The burden of proof rests solely on the claimant.

Now, if you are trying to develop a technobabble explanation for Marc Miller's Jump Drive, the less "proof" you offer, the more "believable" it becomes for purposes of the game.
 
Originally posted by flykiller:
</font><blockquote>quote:</font><hr />there is no velocity equal to or greater than the speed of light
so how does light go as fast as light? </font>[/QUOTE]Photon is massless. The energy-mass-momentum relation means that a massless particle can only move at c.
 
The energy-mass-momentum relation means that a massless particle can only move at c.
looking on wikipedia (for what it's worth) I see this relation described as

e^2 = m^2 c^4 + p^2 c^2

and that for a massless body this reduces to

e = pc

which makes no sense to me because I thought p = mv.

(reading - how interesting. I never knew henri poincare published "e=mc^2" five years before einstein did. least that's what wiki says.)
 
Originally posted by Heretic Keklas Rekobah:
The gamma factor describe above applies to the relative mass of the moving body, and the relative energy required to move it. What the author does not mention (he actually skips over it) is that the gamma equation he states shows that an infinite amount of energy is required to achieve light speed; this is because the relative mass of the moving object is also infinite! Thus, the moving object will never go faster than c because it would acquire the relative mass of the entire universe and require all of the available energy in the entire universe!

Also, his gamma-squared formula is incorrect, due to a first-year algebraic error. Here is the correct progression:

gamma = 1 / SQR(1 - (V^2/c^2))

(Note: When V and c are of equal value, 1 -(1^2/1^2) becomes zero, its square root becomes zero, and its reciprocal (and thus "gamma") becomes infinite, which is an undefinable value.)

1/gamma = SQR(1 - (V^2/c^2))

(1/gamma)^2 = 1 - (V^2/c^2)

1 - (1/gamma)^2 = V^2/c^2

QED: By review of the correct gamma formulae and their meanings, one can easily determine that in the real world, there is no velocity equal to or greater than the speed of light. Thus, trans-light velocities cannot be achieved.
Did you happen to notice that the gamma factors I arrived at for faster than light velocities are imaginary?
When I took algebra, there was a chapter on imaginary numbers, that is what the gamma values I give for superluminal objects end with the letter i.

The rules for dealing with imaginary mumbers are rather simply the most important one being

i * i = -1
i * i * i = -i
i * i * i * i = 1
-i * i = 1
1 * i = i

When you multiply two complex numbers, you multiply their real components and their imaginary components together, for example:

4i * 3i = -12

The is multiply to make -1 and you multiply the 4 and the 3 to make 12 and then you multiply 12 by -1 to make -12

These are the rules of imaginary multiplication, I'm surprised you haven't heard of them.

Now just because numbers are imaginary doesn't mean that they don't represent real phenomina.

The slope of a verticle line is infinite, that doesn't mean that verticle lines do not exist, it just means that you cannot express a verticle line using the formula
y = ax + b
as a would have to be infinite
instead the proper way to express a verticle line would be x = b.

To prove whether tachyon's exist, one has to either find them or make them. Absence of evidence isn't evidence of absence. There is no way to mathematically prove or disprove the existance of tachyons. There are just two states, proven and unproven. It doesn't matter to me whether tachyons exist, I'm only saying that if they do exist, the would follow the above formula and have imaginary gamma factors. In mathematics, imaginary doesn't mean "don't exist", it is simply another type of number, and if you use a restricted mathematics that doesn't include imaginary numbers and tachyons do in fact exist, then all your proving is that the mathematics you are using is insufficient to describe the physical phenomina of faster than light travel.

Also the fact that you need infinite energy to accelerate up to light speed is irrelevant as tachyons always travel faster than the speed of light, they don't need to start as slower than light particles, just as electrons and protons don't need to slow down from FTL velocities through the speed of light to attain their slower than light velocity.

Light travels at the speed of light, to make a slower than light particle you simply convert the energy of the photon into mass using E=mc^2.

To make a tachyon, you do the same. You don't take an electron and try to accelerate it past the speed of light.

Originally posted by Heretic Keklas Rekobah:
Also, a tachyon is merely a mathematical artifice that lends itself well to explaining certain vague physical concepts, and fills in for as-yet-undefined principles. Nor have Tachyons been observed in the laboratory or in nature, thus there is indeed no real proof for their existance. They are only hypothetical constructs used in higher mathematics to balance certain equations.
The same could be said for String Theory, yet physicists use string theory to explain all sorts of things, but it hasn't been proven.

In science fiction we are assuming faster than light travel, failure to prove that faster than light travel exists in the Universe has not stopped its use in science fiction or Traveller, and if we are going to have faster than light travel, we might as well use the same equations we use to describe slower than light travel and apply those results as it makes more sense to be mathematically consistant. If people mention using a hypothetical particle, the Tachyon in science fiction, then I supplied the rules for how a tachyon may behave if they exist, I haven't said they did exist, I only applied the conditional if the exist. By the rules of logic, if the first part of the conditional isn't satisfied, the conditional can't be proven false if the second part isn't upheld. What you need is to have the first part of the conditional satisfied, in other words tachyons are found to exist, and then observe tachyons to behave diffferently from my equation above to prove it false. If you can't find a real tachyon to satisfy my conditional, you can't prove it false.

You can't prove the statement, "If bunnies had wings, they'd all be pink." false because no one has every found a bunny with wings that wasn't pink because no one has ever found a bunny with wings.

Originally posted by Heretic Keklas Rekobah:
Three key scientific principles:

Extraordinary claims demand extraordinary proof.

Never posit an hypothesis beyond the available evidence.

The burden of proof rests solely on the claimant.

Now, if you are trying to develop a technobabble explanation for Marc Miller's Jump Drive, the less "proof" you offer, the more "believable" it becomes for purposes of the game.
Not necessarily so, things must behave consistently if you want them to be believeable and for someone to believe that it could be true.

What if the GM used the Jump Drive inconsistantly?

For instance, what if the GM described the stars whizzing past the view screen after the ship jumps?

What if next time the ship jumps he describes a screen that is black and empty.

What if he insists that the ship must move to 100 diameters to jump one time and then says its 100 radii another?

What if the next time the characters simply make the jump while the ship is on the ground and the time after that the GM does not allow it?

What if one time the ship makes a jump he describes the crew growing long beards and their hair turning gray and skin getting wrinkled, but he then says the jump only takes 2 days? and the next time the ship makes a jump, it takes 25 days, and the ship emerges from the jump in the hangar bay of some gigantic fleet carrier, the crew rescues the princess from the detention cell, but the GM says they can't leave the ship until they blast open the hangar bay doors so the ship can make good its escape?

These inconsistencies make the game less believable and annoys the players to no end.
 
Photons have relative mass, they just don't have a rest mass as photons are never at rest.

Electrons do have a rest mass, and they have a variable velocity unlike a photon and as the electron's velocity changes, so does its relative mass. electrons can't accelerate to the speed of light as its relative mass would approach infinity.

photons have nothing but relative mass and you can't slow them down or speed them up, their mass depends on their wavelength and the shorter their wavelength the greater the energy and through E=mc^2 the greater the mass.
 
Originally by Space Cadet:
photons have nothing but relative mass and you can't slow them down or speed them up
Actually you can speed and slow photons quite significantly. The proof of this I will leave for a google search
 
Originally posted by veltyen:
http://en.wikipedia.org/wiki/Cerenkov_radiation

photons do have mass (kind of) it is just very very small. Hence it is possible to make something go faster then light (see above about Cerenkov radiation).
It is current assumption of physicists that photons are massless.

It is not helpful to say that they have "kind of" mass, which you perhaps might wish to relate to their momentum? They have no mass as defined in the E=mc^2 sense of mass which is what is important here.

Empirically, there have been experiments to try to measure the mass of photons. These, in effect, place an upper limit on the mass the photon has if it has one. The experiments always hit a noise floor and the photon mass is in the signal buried in the noise if there is one. So, the noise floor gives an upper limit on the mass.

I have a colleague currently preparing a grant application to measure the electomagnetic resonances between the Earth and the upper atmosphere which are excited by lightning strikes. This requires an antenna array in the Arctic btw as it's far from normal EM interference. The resonances are at very low frequencies and so would show a divergence from normal EM theory if the photon has a mass at some level.

The assumption, of course, is that this new, better experiment will lower the upper limit on the photon mass.
 
Originally posted by veltyen:
</font><blockquote>quote:</font><hr />Originally by Space Cadet:
photons have nothing but relative mass and you can't slow them down or speed them up
Actually you can speed and slow photons quite significantly. The proof of this I will leave for a google search
</font>[/QUOTE]Well, you can slow a light wave quite significantly but that's a bit different to doing much to an individual photon.

Work on this (slow light) depends on a careful analysis of phase velocity, group velocity and the effects of absorption on pulse profiles.

The current interpretation of the speed of light limit appears t0 be that a shock-wave of light (i.e. a sudden on-off step-change) can't propagate faster than c.
 
Hi !

Well, I know that it is possible to alter the effective velocity of light propagation thru different media, because of slowed down absorbtion and re-emmission.
Velocity of light in vaccum is pretty fixed. A contradicting verified experiment outcome would surely be a sensation


Regards,

TE
 
Originally posted by Baphomet69:
</font><blockquote>quote:</font><hr />Originally posted by SGB - Steve B:
One physicist I've read about (forgot his name unfortunately)accepted most of Einstein's equations but had a very different view of what was driving the equations. The alternate theory dealt with either and has met understandable skepticism. However the alternate theory addressed the histroical results of either (and other) experiments effectively and appeared to be as internally consistent as relativity. The consequences of the different views were tremendous. If Einstein had the right explanation, then the "light limit" is real - if the other guy was right, then the "light limit" does not exist. If I had to bet who was right, I'd go with Einstein - but if I'm speculating potential future developments for a story line I see no problem with looking at the implications of the alternative theory.
Oh, man! Don't do this to me! ;) That sounds intriguing and now I want to read this guy's theory. Argh! I need his name!

file_21.gif
</font>[/QUOTE]Black Cat responded with
Dutch theoretical Physicist Hendrick Lorentz -clip-
The one I read about is a current physicist basing his research on some of Lorentz' work. I did some more digging but did not find the exact article again.

What I did find is that there are a number of current physicists who admit that ether (or aether) theory explains much if not all of what SR and GR do without fudge factors - provided you assume the "ether" density is tied to the locally dominate gravitational field. If you insist (as most proponents of "ether" theory did in the 19th and early 20th centuries) that the "ether" has a uniform density and that it's moving relative to the locally dominate gravity field, then the theory is falisfied by experiments conducted at that time. However, if the ether is relatively motionless compared to the locally dominate gravity field and is of varied density depending on the strength of the gravity field, then the experimental results are easily explained. The arguments presented for this modified "ether" theory sound logical and it appears that there are some high powered physicists on both sides - at least for now the majority of physicist are in the Einsteinian camp.

As an engineer, I find the implications staggering. If "ether" is the real explaination then not only is the "light barrier" not necessarily accurate, but manuever drives without reaction mass may be possible as well (just have to figure out how to push or pull on the "ether".)

Shouldn't this alternative to Einstein be considered fair game for SciFi? It may turn out to be as off the wall as some of the late 19th century SciFi such as Verne's "Journey to the Center of the Earth" or it may be as prophetic as the nuclear submarine in "20,000 Leagues Under the Sea."
 
Originally posted by Paul Snow:
</font><blockquote>quote:</font><hr />Originally posted by veltyen:
http://en.wikipedia.org/wiki/Cerenkov_radiation

photons do have mass (kind of) it is just very very small. Hence it is possible to make something go faster then light (see above about Cerenkov radiation).
It is current assumption of physicists that photons are massless.

It is not helpful to say that they have "kind of" mass, which you perhaps might wish to relate to their momentum? They have no mass as defined in the E=mc^2 sense of mass which is what is important here.

Empirically, there have been experiments to try to measure the mass of photons. These, in effect, place an upper limit on the mass the photon has if it has one. The experiments always hit a noise floor and the photon mass is in the signal buried in the noise if there is one. So, the noise floor gives an upper limit on the mass.

I have a colleague currently preparing a grant application to measure the electomagnetic resonances between the Earth and the upper atmosphere which are excited by lightning strikes. This requires an antenna array in the Arctic btw as it's far from normal EM interference. The resonances are at very low frequencies and so would show a divergence from normal EM theory if the photon has a mass at some level.

The assumption, of course, is that this new, better experiment will lower the upper limit on the photon mass.
</font>[/QUOTE]Didn't Einstein write the equation E=mc^2?
And isn't a photon a form of energy, the 'E' in the equation?

It would seem to me that if energy and mass are equivalent and a photon is a form of energy, then photons must have mass, it was also mentioned that photons can be slowed down. I believe that photons can be made into a particle such as an electron or a proton. All nuclear reactions are reversible, so if you can get an electron and a positron together to make high energy photons, you can also to the opposite and put high energy photons together to make an electron and a positron. Perhaps a form of imaginary energy photons could be brought together to make a tachyon/antitachyon pair. If such a thing were possible, then that would be how tachyions would be made. The first most obvious use of a tachyion emitter would be as a form of communication.

Also if you could convert energy into tachyions, then another application would be a tachyon drive. A tachyion drive couldn't push a rocket past light speed, but it would give a very high specific impulse, higher in fact that a rocket that emmited pure photons in a coherent beam with 100 percent efficiency in matter/energy conversion. Also if you had a Star Trek style matter transmitter, you could use a tachyion version of that for faster than light travel, it would basically be another kind of stargate not too different from a wormhole in results.

the lowest energy tachyions are by the way the fastest, they travel with infinite speed and have zero mass due to the gamma factor of zero that I have calculated.
 
Err, sorry, but we don't really want to talk about aether in its classical meaning ?

Einstein als used the term "aether" for his interpretation of the space/time matrix, so do QM people sometimes do, if they talk about the somehow strange origin and destiny of virtual particles...

Anyway, about what physicist is it about here ?
 
Originally posted by Space Cadet:
Did you happen to notice that the gamma factors I arrived at for faster than light velocities are imaginary?
No. I noticed that the gamma function is a real-number scalar value with no imaginary component whatsoever. The rest of your explanation is therefore irrelevant.

What you are doing is equivocating the two distinct meanings of "imaginary":

1) In or of the mind: existing only in the mind, not in reality, a fantasy.

2) Relating to imaginary numbers: relating to or containing imaginary numbers, or being the coefficient of the imaginary part in a complex number.


Your imaginative hypothesis notwithstanding, complex numbers are expressed in the form:

x ± iy

Where "x" is the real-number component, "i" is a multiplier equal to the square root of negative 1, and "y" is another real-number value that is modified by "i" to represent the imaginary component. The values of "x" and "y" can be plotted out on graph paper, with values of "x" on the horizontal axis, and values of "y" on the vertical axis, with point {0,0} at the center (or origin) of the graph. This is called the Cartesian Co-Ordinate system.

Another system is called the "Polar Co-Ordinate System." It also uses two values; "r" for range or distance, and "Θ" ("Theta") for angle. Thus, a position can be expressed as "r ± Θ°"

The interesting thing is that it's possible to convert from one system to the other.

r = SQR(x² + y²)

Θ° = ArcTan(y ÷ x)

And:

x = r · Cos(Θ°)

y = r · Sin(Θ°)

Nowhere in your "tutorial" or in any previous postings do you list the imaginary component of gamma, nor is there any mention of an angular component in the polar conversion that you have made. This is understandable, since there are none. Any "imaginary" or angular component of gamma is canceled out in converting to it from V and c.

Top this off with the facts the neither tachyons or wormholes have ever been discovered, observed, or otherwise proven to exist, and it should be easy to see why your thesis is both debunked and rejected.

Again, if you are just trying to explain events IYTU, the old adage "less is more" is appropriate. But if, instead, you are trying to prove a real-world hypothesis, then I suggest that you read up on the following subjects:

- Algebra (especially Complex and Matrix math).
- Trigonometry.
- Geometry (Planar, solid, and extra-dimensional).
- Calculus (all forms).
- Classical Physics.
- Orbital Mechanics.
- Quantum Physics.
- Relativity (Special and general).
- String Theory.

And pay close attention to:

- Tensor Transforms.
- Hilbert Space.
- Phase Space.
- Eigen Values.

Good Luck.
 
Originally posted by Heretic Keklas Rekobah:
</font><blockquote>quote:</font><hr />Originally posted by Space Cadet:
Did you happen to notice that the gamma factors I arrived at for faster than light velocities are imaginary?
No. I noticed that the gamma function is a real-number scalar value with no imaginary component whatsoever. The rest of your explanation is therefore irrelevant.</font>[/QUOTE]Here is my gamma values again. Notice the i at the end of the gamma values to FTL velocities, this indicates that they are imaginary numbers.

V/c = gamma^2 --------> gamma
0.0001 = 1.00000001 -->1.000000005
0.001 = 1.000001 ----->1.0000005
0.01 = 1.00010001 ---->1.000050004
0.1 = 1.01010101 ----->1.005037815
0.2 = 1.041666667 ---->1.020620726
0.3 = 1.098901099 ---->1.048284837
0.4 = 1.19047619 ----->1.091089451
0.5 = 1.333333333 ---->1.154700538
0.6 = 1.5625 --------->1.25
0.7 = 1.960784314 ---->1.400280084
0.8 = 2.777777778 ---->1.666666667
0.9 = 5.263157895 ---->2.294157339
0.95 = 10.25641026 --->3.202563077
0.98 = 25.25252525 --->5.025189076
0.99 = 50.25125628 --->7.08881205
0.999 = 500.2501251 -->22.36627204
0.9999 = 5,000.250013 ->70.71244596
0.99999 = 50,000.25 -->223.6073568
0.999999 = 500,000 --> 707.1067812
1.000001 = -500,000 -> 707.1067812i
1.00001 = -49,999.75 -> 223.6062387i
1.0001 = -4,999.750013 > 70.70891042i
1.001 = -499.7501249 -> 22.3550917i
1.01 = -49.75124378 --> 7.053456159i
1.1 = -4.761904762 ---> 2.182178902i
1.2 = -2.272727273 ---> 1.507556723i
1.3 = -1.449275362 ---> 1.203858531i
1.4 = -1.041666667 ---> 1.020620726i
1.5 = -0.8 -----------> 0.894427191i
1.6 = -0.641025641 ---> 0.800640769i
1.7 = -0.529100529 ---> 0.727392967i
1.8 = -0.446428571 ---> 0.668153104i
1.9 = -0.383141762 ---> 0.61898446i
2.0 = -0.333333333 ---> 0.577350268i
3.0 = -0.125 ---------> 0.35355339i
10 = -0.01010101 -----> 0.100503781i
100 = -0.00010001 ----> 0.010000499i
infinite = 0.00000 ---> 0.00000

The formula I used to plot out these numbers is

gamma = 1 / square_root( 1 - (V^2/c^2) )

This is the exact same formula I obtained from The Starflight Handbook by Eugene Mallove and Gregory Matloff. I checked the values obtained against the values presented in the book for sublight speeds and they match, so I'm sure this is the correct formula

As you see, I've also indicated the values of gamma squared in the middle collumn, as you can see, the values for gamma squared are negative whenever V is greater than c. When you take the square root of a negative number the result is imaginary, but that's just fine and dandy, because role playing games are imaginary too.

One can plot out world lines in cartesian coordinates too, the vertical axis is time we can label it t, and the horizontal axis is one dimension in space, it could be either x, y, or z, it doesn't really matter. When an object is traveling a certain velocity relative to a certain frame of reference, the slope of the objects world line is its velocity. That is how much x the object moves for a given amount of t. In this coordinate system a distance or a light year along the x axis is equated with a duration of a year along the y axis, in this diagram, a beam of light moving away from the origin to the right describes a 45 degree angle with a positive slope of 1, a beam of light moving to the left from the origin has a negative slope of -1, everything in this universe that begins at the origin is bound between these two 45 degree lines. The slopes of slower than light objects moving to the right are greater than 1, the slopes of slower than light objects moving to the left are less than -1 and an object that is stationary relative to the frame of reference has an infinite slope where x has a constant value of 0. To go faster than light in this diagram means having a slope of less that 1 if moving to the right and a slope of greater than -1 if moving to the left. What this diagram demonstrates is that there is always a slower than light object whose reference point is such that a specific faster than light object appears to be moving backwards in time. A faster than light object can move freely to the right and left of the 45 degree slopes of a beam of light eminating from the origin, it can move forwards and backwards in time as a slower than light object may move in space.

Whether this is possible is up to the GM, with a tachyon beam, you can send messages backwards in time, but I imagine that assuming freedom of choice, all possible futures would be broadcasting their tachyons, and their combined emmisions would drown out any particular message sent from any particular future. You can say FTL is impossible, but then you can just go home and not play Traveller. Whether tachyons exist, I don't know, and I don't think you can find out just by manipulating numbers, but applying an equation for slower than light particles to faster than light particles seems to make logical sense.
 
I personally don't care whether tachyons are possible or not, my purpose here is to make them sound believably possible in the context of the game So I added all these gamma values for FTL objects. What it seems to indicate, that the faster an object goes, the smaller the gamma until it diminishes right down to zero for an object travelling at infinite speed.

You can just ignore the i if you like.

What seems to be happening is the faster tachyons have smaller gammas, as their gammas drop below 1, these objects tend to stretch in the direction of their motion as opposed to being compressed, their mass diminishes and their clocks tick ever faster. An object with infinite speed would have an infinite length, a zero mass and an infitesmal second. Probably their length isn't actually infinite but only stretches for that length of space that it crosses until it changes its velocity to non-infinite. To get a tachyon to go backwards in time, you need to start out with negative energy and convert that into tachyons using E=mc^2. Negative energy is rather hard to obtain, so usually tachyons emitted travel in a positive direction in time.

Now what does this mean for Traveller?
If someone succeeds in producing a tachyon emitter, the most detectable tachyons would be the slowest ones that travel just above the speed of light, these can be used for communitations, but the faster tachyons are harder to detect as they contain less energy. You would need larger and more sensitive equipment to detect the faster tachyons. To communicate across many parsecs of space in real time would require a really massive tachyon detector. The tachyon beams would be very weak, and hard to tell from absolutely nothing at all.

Tachyons in the OTU would be a form of radio, it would allow for real time communications between distant parts of the Imperium. The Imperium would probably set about placing really huge tachyon relay satellites so that it can keep in touch with the fleet and give orders in real time and react to threats more quickly placing ships to where they are needed.
 
Originally posted by Space Cadet:
I personally don't care whether tachyons are possible or not, my purpose here is to make them sound believably possible in the context of the game,
Why don't you call then Byrons* then?

Tachyon is a general class of all particles moving faster than c. If you want to invent some new physics then invent some believable psuedo-science and a new specific tachyon.

It doesn't seem helpful to instead try to achieve believability by choosing to use words and ideas that are not congruent with current scientific understanding and usage. (i.e. photons must have mass.. NO. No No ...)

Paul Snow (real physicist)

*They have a Scottish accent, walk with a limp and are mad, bad and dangerous to know
 
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