Would Tachyons have negative real mass?

[iantresman]

Hypothetical particles must have hypothetical properties, which is pretty much anything you want. The concept of "negative real mass" is surely meaningless. We might as well designate that they have intrinsic humour measured in giggles.

[csmyth3025]

Hypothetical particles must have hypothetical properties, which is pretty much anything you want. The concept of "negative real mass" is surely meaningless. We might as well designate that they have intrinsic humour measured in giggles.

I don't want to mix this thread with another on the subject of Hawking radiation. Leaving aside the question of exactly what is the mechanism of Hawking radiation, as far as I know it's postulated that a black hole will lose mass by means of Hawking radiation provided that the "temperature" of the black hole is greater than the region of space surrounding it (and assuming that it's not absorbing matter).

I may have this wrong, but since nothing can cross the event horizon of a black hole from the inside going out, the energy/mass loss of the black hole is attributed to negative energy (or negative mass, perhaps) crossing the event horizon from the outside going in. This may be in the form of hypothetical particles or virtual particles or just nameless mathematical constructs, but the effect is that the mass of the black hole is reduced.

If mass loss by a black hole is considered plausible, then the concept of "negative real mass" surely cannot be meaningless.

Chris

[WayneFrancis]

Hypothetical particles must have hypothetical properties, which is pretty much anything you want. The concept of "negative real mass" is surely meaningless. We might as well designate that they have intrinsic humour measured in giggles.

I wouldn't agree to that as a blanket statement. The Higgs Boson is a "hypothetical particle" but its properties are not willy nilly picked. We expect the Higgs Boson to have certain properties and those properties are model Dependant and fairly constrained. For example we don't think the Higgs will have and energy over 185 GeV

[iantresman]

I would argue that the Higgs Boson is part of a family of existing particles, whereas tachyons "break" physicals laws by their vary existence: (a) Faster than the speed of light (b) negative mass.

As Alice in Wonderland said "I've believed as many as six impossible things before breakfast", and since we're a third of the way there, who knows how many impossible properties and impossible particle may have. But I agree with you, such properties are not picked willy-nilly.

Note to physics students: do not quote Charles Dodgson in your exams.

[csmyth3025]

Hypothetical particles must have hypothetical properties, which is pretty much anything you want. The concept of "negative real mass" is surely meaningless. We might as well designate that they have intrinsic humour measured in giggles.

I wouldn't agree to that as a blanket statement. The Higgs Boson is a "hypothetical particle" but its properties are not willy nilly picked. We expect the Higgs Boson to have certain properties and those properties are model Dependant and fairly constrained. For example we don't think the Higgs will have and energy over 185 GeV

There is a Wikipedia article on "negative mass" which states, in part:

...Although no particles are known to have negative mass, physicists (primarily Hermann Bondi and Robert L. Forward) have been able to describe some of the anticipated properties such particles may have...
-----and----
...Forward extended Bondi's analysis to additional cases, and showed that even if the two masses m(-) and m(+) are not the same, the conservation laws remain unbroken...

(ref. http://en.wikipedia.org/wiki/Negativ...d.27s_analysis )

Like the hypothetical (and as yet unobserved) Higgs boson, hypothetical "negative mass" is expected to have certain properties which (to an untrained eye) seem to have been analyzed by Bondi and Forward in a scientific manner.

Since Bondi first presented this concept in 1957 and apparently very little has been done since to develop it - should it be considered "fringe science"?

Chris

[tommac]

whereas tachyons "break" physicals laws by their vary existence: (a) Faster than the speed of light (b) negative mass.
.

What law does that break????? There is no law that says that particles cant travel faster than the speed of light. If there is please tell me which one.

What law says that negative mass cant exist? Please quote the exact laws you are referring to.

[tommac]

Since Bondi first presented this concept in 1957 and apparently very little has been done since to develop it - should it be considered "fringe science"?

I guess so ... I know that usually any mention of negative mass will usually get thread closed or moved to ATM.

[iantresman]

What law does that break????? There is no law that says that particles cant travel faster than the speed of light. If there is please tell me which one.
What law says that negative mass cant exist? Please quote the exact laws you are referring to.

The law of nature :-) Provide me with physical measurements of any particle that travels faster than light, or has negative mass.

[tommac]

OK .... fair enough ... so you are just saying that they dont exist. You are not saying that there are any real laws prohibiting them from existing. I can agree with that.

The law of nature :-) Provide me with physical measurements of any particle that travels faster than light, or has negative mass.

[iantresman]

You are not saying that there are any real laws prohibiting them from existing. I can agree with that.

I don't know any laws prohibiting them from existing, but we don't know all the laws :-)

[WayneFrancis]

The law of nature :-) Provide me with physical measurements of any particle that travels faster than light, or has negative mass.

There is a big difference in not being able to make a measurement of a phenomena and a model not allowing the phenomena. We have yet to provide any measurements of the Higgs boson. We have not found any monopoles. Yet the current models don't preclude them. So while I agree the tachyon is hypothetical it does not violate anything within GR or SR.

[WayneFrancis]

I don't know any laws prohibiting them from existing, but we don't know all the laws :-)

Correct! But according to your logic their might be a physical law that we have not discovered that says they must exist.
Again I get your point and agree that in most cases we can just ignore them because they don't seem to have an effect on the universe as we currently know it.

[BattleMage]

Not to mention that FEYNMAN wasn't the biggest fan of the diagrams that adopted his name. He used them as a teaching aid and to the best of my knowledge, never intended them to be used to extrapolate physical meaning.

We can definitely view a positron as an electron in reverse time, but even reverse time doesn't make sense to me. I can't nake a coherent picture of it.

Back to tachyons. Make note the formula we've been using here is the special relativity view of rest mass. We're ignoring momentum.

E= mc²/sqrt(1-v²/c²)

1 : sqrt(1-v²/c²) when v > c gives an imaginary number. There's only one i because we take a single sqrt of a single negative number.

2 : if the mass is negative, then the energy is imaginary. I'd love to work with negative mass myself, but the imaginary energy might slow me down.

3 : assume the mass is imaginary, now we are dividing one imaginary number by another. This is very easy to do. Multiply the numerator and denominator by the conjugate of the denominator. Life is even easier when we realize we are dividing imaginary numbers with no real parts. The answer is a positive number.

Also, I find it quite rude to answer "uggg" to someone. If you don't like what someone has to say, ignore it or say why you don't agree. A post which simply reads "disgust" will rarely be taken well.

Following your suggestion here, if you start with a normal mass and assume it moves faster than light (say, c²), you end up with something that looks like a tachyon with negative energy. Taking the limit as v approaches c²:

lim_v→cē mc²/√(1-v²/c²)

= mc²/√(lim_v→cē[1-v²/c²])

= mc²/√(1-c⁴/c²)

= mc²/√(1-c²)

= mc²/√[i²(c²-1)]

= mc²/i√(c²-1)

= i⁴mc²/i√(c²-1)

= i³mc²/√(c²-1)

= -imc²/√(c²-1)

So in this case, E = -imc²/√(c²-1), which is both negative and imaginary. Does that mean that normal objects moving faster than the speed of light would actually be tachyons with negative energy? Or would they be objects with negative mass that have an imaginary energy? Of course, this seems to be an epic contradiction, since the starting assumption was that the object had normal mass. Hmmm...

[Shaula]

You are not looking at its total energy there though. You are looking at its rest mass energy equivalent. E^2 = (pc)^" + (mc^2)^2 is the correct form. Plus the mass you are looking at there is a relativistic mass, a concept people try to avoid these days thanks to the confusion it causes. The relativistic mass is observer dependent and tells you how a particle acts, not what its mass actually is. The rest mass is there for that.

[ShinAce]

The way I see it, it doesn't matter all that much. Special relativity clearly shows that it is impossible to take a normal particle(say a ball bearing) and accelerate it beyond the speed of light. If you have a particle going less than c, it will always go less than c.

Now, if you imagine that tachyons already exist, that's fine. But then special relativity again shows that the tachyon will never be able to travel less than c. I know of no way to detect a particle which travels faster than c(in vacuo). So if they exist, they can't be detected. Like the human soul. You can argue for it or against it, but it won't make any difference.

Shaula:
I think you've both done the same thing. Battlemage use (gamma*rest mass) which is in fact the total energy content of a particle. Your approach separates the invariant rest mass and the momentum. The only difference I can see is that your form (E² = p²c² + ...) makes me think of a right angle triangle with rest mass and momentum as the two sides. The hypotenuse is the total energy. Which is in fact, gamma*mc².

Note that we don't even need to get into the energy-momentum four vector. Although I must admit, learning the invariant form of displacement(was it the Lorentz transform matrix?) and energy-momentum helped me a lot. Before that, I truly felt that an inertial frame change would destroy the concept of speed, momentum, and displacement.

[Shaula]

My point was that the rest mass remains the rest mass. In the post the question was "Or would they be objects with negative mass that have an imaginary energy? Of course, this seems to be an epic contradiction, since the starting assumption was that the object had normal mass." - I am pointing out that an object's relativistic mass can be whatever. Its actual rest mass does not change so there is no epic contradiction. People need to be very careful as to whether they are considering apparent masses or invariant masses when they get into this.

[Markus Hanke]

My point was that the rest mass remains the rest mass. In the post the question was "Or would they be objects with negative mass that have an imaginary energy? Of course, this seems to be an epic contradiction, since the starting assumption was that the object had normal mass." - I am pointing out that an object's relativistic mass can be whatever. Its actual rest mass does not change so there is no epic contradiction. People need to be very careful as to whether they are considering apparent masses or invariant masses when they get into this.

Very true.
Now, the interesting question is - how do you define "at rest" for a tachyon ? Technically, its state of lowest kinetic energy is reached when it moves at infinite speed, so that would be its "rest" state. One would have to give it energy in order to slow it down, and the limit is once again the speed of light ( albeit approached from "the other side" ), which it can never reach since it is spin-0 with non-vanishing mass.