For real physical objects, what is Vmax?

Question

If E=mc^2: algebraically, Vmax should = c^2, yes? Therefore, at any point for real physical objects, if c=299,792,458 m/s; c^2 = 89,875,517,873,681,800 m/s = Vmax(local), yes? ["(local)" is to acct for variable time]

Assuming a device could be constructed to produce a relatively stable gravitational distortion disproportional to (and much greater than indicated by) its actual mass (thus artificially slowing time locally for it), could that object and its artificial gravitational distortion be accelerated to or beyond c^2 relative to the faster time outside the artificial gravitational distortion?

Understanding that realization of the gravitational effect would include some delay, it seems at least superficially plausible foreign-body gravitational influence would be negligible.

For years, people thought the displacement hull was the only form for waterborne vessels; that's no longer true. The analogy is to accelerating a mass significantly beyond our perception of c.

David J: so the faster i go, the more mass i have? how has this been verified experimentally? it seems quite specious.

Many assume the truth of what David J said; however, for that to be true, E=mc^2 cannot be true if algebraic principles remain valid. He seems to be saying that Ec=mc, which is not at all the same as E=mcc. If you divide the RH side of the equation by c, you have to DIVIDE the LH side of the equation by c: E/c=mc (the practical value of which is as meaningless as the equally valid E/m=cc and E/cc=m).

uusuzanne: your answer is fascinating; however, I have to wonder if what we're dealing with is akin to the old arguments the sound barrier couldn't be broken.

Yes, it's a different phenomenon, but old formulae "proved" it couldn't be done; even so, a bunch of "fruitcakes" decided to challenge those beliefs -- and found scientists to help them.

Early supersonic cannon projectiles disintegrated before they went very far; slower projectiles went farther (basically, the projectiles were disintegrating like meteors). Improvements in metallurgy and aerodynamics has resulted in long-range hypersonic projectiles that until very recently were mere subjects of science fiction.

Is is plausible that gamma is a tool of convenience, that reasonably approximates sub-c observations but that may not be accurate for speeds exceeding c? Or do the analogs of history not apply because the limits we now imagine are the real limits?

Curly -- in part I ask if those physicists base their work on a valid premise: maybe their approach is why they don't get the desired result.

In the early-mid 1980s, a US DoD contractor claimed it accelerated electrons to 1.15c in a tiny, low-mass airborne device that was operationally deployed, but I can't say anything more about that.

If the statement was inaccurate, it was HUGELY inaccurate -- and it calls into question the veracity of claims that matter has been artificially produced, and that artificial gravitational fields have been produced (etc., ad nauseum).

A wall of infinite thickness is impenetrable, unless a passage is found through it. Making the analogy less extreme, I can unsuccessfully bash (expend E) against a wall (barrier); if I open a door (change the conditions/assumptions), I can pass through the wall. I still expend E, but nothing close to what emperical research & formulae based on a solid wall suggested was required.

Answer 1

Let's look at E = mc^2.

E is energy. It is measured in joules.
m is mass. It is measured in kilograms.
c is the speed of light. It is measured in meters per second.

Kilograms multiplied by (meters per second)squared are joules. If you don't have a mass multiplied by the square of a velocity (or something with equivalent units), you don't have energy.

The maximum speed any mass can have is infinitesimally less than the speed of light. c^2 would be the square of that speed.

Now, let's consider the practicalities. Experimentally, we find that, as we accelerate something very close to the speed of light (which is done every day in particle accelerators, for example), it becomes harder and harder to accelerate the closer it gets to the speed of light. E = mc^2 is the energy of a mass at rest; this is where the energy of nuclear weapons and nuclear power plants comes from. As an object moves, its energy is multiplied by a factor usually abbreviated with the Greek letter gamma; its value is:

gamma = 1/[1 - (v/c)^2]^1/2

So it's 1 over the square root of [1 minus (v/c)squared].

As v becomes closer and closer to the speed of light, v/c becomes closer and closer to 1, the denominator of the fraction becomes closer and closer to zero, and gamma becomes larger and larger. If v were to equal c, gamma would be infinite. This is why you can't accelerate any massive object to the speed of light - it would take an infinite amount of energy.

So, you may ask, what about photons? They go at the speed of light, don't they? Indeed they do. They manage this because their mass is zero, and they can never travel at any speed other than the speed of light.

Incidentally, it is indeed true that m = E/c^2; this is often useful in physics calculations.

Answer 2

The mass dialation due to high speed is empirically validated in particle accelerators, as is time dialation. Its very specific and very accurate. Thats why physicists had the huge push for larger and larger supercolliders, to get much higher speeds, and much more accurate numbers.

Physicists want to go faster than the speed of light too. Breaking the speed of light barrier is to physicists what Riemanns hypothesis is to mathematicians: the graveyard of great minds. They bash themselves against the wall and never break it.

Answer 3

E=mc^2 is not the whole picuture and only applies to objects not in motion (m=rest mass). V max is < c.

As an object approaches c, it's mass goes to infinity, and energy required to accelerate it through space goes to infinity, therefore it is immposible to accelerate an object to c.

As far as gravity, one thing to remember is, gravity warps space, so even if it appears to be breaking relativity theory, it is because it is not traveling "through" space above c, but mearly stretching space. This is why it is possible for the universe to theoretically be expanding faster then c. It only appears to be.

Answer 4

V is velocity, but assuming that V^2 is velocity too, is not TRUE.