Haug has recently introduced a new maximum velocity for subatomic particles (anything with rest mass) that is just below the speed of light. This is combined with the relativistic rocket equation in order to assess how much fuel would be needed to accelerate an ideal particle rocket to its maximum velocity.

Planck masses of fuel 4.35302 × 10^{−08} kg.

Max speed for an electron 99.9999999999999999999999999999999999999999999124% of the speed of light

Max speed for a proton 99.999999999999999999999999999999999999705 of the speed of light

The maximum amount of fuel needed for any fully-efficient particle rocket is equal to two Planck masses. This amount of fuel will bring any subatomic particle up to its maximum velocity. At this maximum velocity the subatomic particle will itself turn into a Planck mass particle and likely will explode into energy. Interestingly, we need no fuel to accelerate a fundamental particle that has a rest-mass equal to Planck mass up to its maximum velocity. This is because the maximum velocity of a Planck mass particle is zero as observed from any reference frame. However, the Planck mass particle can only be at rest for an instant. The Planck mass particle can be seen as the very turning point of two light particles; it exists when two light particles collide. Haug’s newly-introduced maximum mass velocity equation seems to be fully consistent with application to the relativistic rocket equation and it gives an important new insight into the ultimate limit of fully-efficient particle rockets.

Arxiv – The Ultimate Limits of the Relativistic Rocket Equation The Planck Photon Rocket

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Would the law of conservation of energy even apply if they create an photonic energy generator to power the craft, the internal functions, and the artificial electromagnetic fields used to manipulate the mass of the craft? You would also not have to worry about exit velocity or thrust because a craft of this magnitude and powered by an photogenic generator should be able to generate enough energy to pull itself and occupants across frictionless space at and possibly faster than the speed of light.

I don’t really understand why anyone would want to go anywhere close it the speed of light … sure it’ll get you to the edge of the visible universe in fifty years of YOUR time … but billions of years of time in the rest of the universe … a huge WASTE of time IMO. Plenty of matter an energy to be had if we move out from Sol at a slow rate <0.1c - even if we are growing exponentially.

> the fine art of intercepting it, staying “on course”, dealing with very small orbital deviations of the transmitter resulting in rather large deviations of point-of-focus,

The operational scenario I envision is when the vehicle is starting out, you aim the laser directly at it. When it gets too far away to focus, you switch to using the star as a lens to improve your visibility. If you plan ahead, you don’t have to have short-response communications. For example, your laser can always be aimed directly at the destination star. That’s easy to do, because the gravitational lens works the other way too. The star will be in focus at the transmitter to serve as a reference.

Then the vehicle will have the responsibility of keeping itself along the known beam path (i.e. an exact line between the sun and destination star). To do this it will need some small maneuvering capability. I would expect by the time we attempt something like this, we will have solved fusion, and that will supply some fraction of a percent of c capability. The laser is used for the major acceleration, supplying multiple percent of c, or tens of percent of c.

Note that slowing down means pointing your particle accelerator forward while keeping the beam collector pointed aft.

And, of course, all of this is speculative engineering. We have much more work to do to even find what solar system objects exist in the “scattered disk”. This is beyond the Kuiper belt out to 2000 AU, after which you are in the Oort Cloud region. We have found a few dozen objects, but there are expected to be thousands more, and maybe a Neptune-sized planet. After finding what’s there comes exploring the region, then maybe building stuff. By the time we are ready to do interstellar missions, the future engineers will probably laugh at our naive assumptions.

Unbelievable. The physics is flawed and violates the law of conservation of energy.

Using the beta for the top speeds in Haug’s analysis kind of obscures things. I much prefer the Lorentz factor. As the Planck mass is ~10^19 GeV, that means a Lorentz factor of about 10^19 for a proton (mass ~ 0.938 GeV) and about 2 x 10^22 for electrons (0.000511 GeV).

Several problems arise long before you get to such a high Lorentz factor. For starters, at 1 gee acceleration, it’d take an acceleration distance of ~10^19 light-years for a proton, etc. Of course accelerators manage much higher accelerations. Say we can manage about 1 GV/m accelerating voltage – therefore a path length of 10^19 metres is required – about 1,000 light-years.

For photon pushed vehicles, the acceleration fails long before a Lorentz factor of 10^19. The relativistic aberration and concentration of the CMB will balance the push from the red-shifted photons coming from behind at a top Lorentz factor of about ~100 or so.

For a perfect rocket that magics fresh reaction mass to its co-moving instantaneous reference frame, a Lorentz factor of a few thousand will mean the CMB will be aberrated into a source concentrated almost directly ahead at a temperature hot enough to melt any known material.

If that can be avoided, eventually the flux of relic neutrinos from the Big Bang will become energetic and concentrated enough to start slamming into nucleii and dissipating energy that way. Quark matter shielding might attenuate that flux, but eventually the flux will cause significant drag…

So ultimate speed-limits… meh.

However, for reference sake, if we could manage 1 gee for arbitrary amounts of time, the maximum speed will be reached after 43 years ship-time.

That’s not a relativistic mass/energy relation (ironically) for dealing with relativistic point masses. You want to use E^2 – (pc)^2 = m^2 c^4

That’s going to depend on the engine size and architecture because it’s proportional to mass flow rate. Maximum exit velocity in the relativistic rocket equation is agnostic to mass flow rate but not to mass fraction or specific impulse. Thrust is relevant to how quickly you reach max velocity and what sort of orbital trajectories you can get on, but this is a purely mathematical analysis that doesn’t speak to thrust.

Hey, you’ve got a point. But remember I was invoking magic. That beats the pants off of reality every time!

The “original rocket equation” (Tsiolkovsky’s, of course) still applies for reaction-mass exhausting rockerty, whether the energy to thrust the reaction mass comes from chemical potential (as in conventional rocketry), nuclear potential (“nuclear rockets”) or beamed-and-intercepted energies. Doesn’t matter which system, Tsiolkovsky’s rules.

In the depressingly “real” world (depressing from an interstellar transport perspective), the use of particle beams or anything else is undermined by TIME and DISTANCE. Sure we can use the Einsteinian gravitational lensing effect of “our star” (or any others we choose to harness) to focus a powerful beam of energy (be it matter or light!) onto some invisibly small dot some great distance away, with fairly decent conservation-of-stuff too … but the fine art of intercepting it, staying “on course”, dealing with very small orbital deviations of the transmitter resulting in rather large deviations of point-of-focus, and the near-impossibility of telegraphing to the transmitter the INTENTION to change course slightly (say: avoidance of collisions with little hard rocks) with enough lead time to have the transmitter track the receiver … yields an (again) depressingly impractical use-case.

The least distance from Sun to Transmitter isn’t roughly 500 AU, but for a convergent focussed beam, approximately 1,000 AU. Sucks. Because each AU is about 150,000,000 km, which at the speed of light (300,000 km/s) is 500 seconds. Not only would one’s interstellar power transmitter need to be 1,000+ AU away from the Sun, but the receiver would also too need to be that far, and receding. 2,000 AU minimum total distance.

2,000 AU × 500 seconds per AU → 1,000,000 sec → 278 hours → 11.6 days. ONE direction. If you’re trying to telegraph from the interstellar craft to the humungous transmitter course changes, the round-trip is twice that! 23 days. … … … “Move!” … 23 days later … “OK!”

Just saying,

[b]Goat[/b]Guy

V = 2/k … with k = newtons per watt of reactionless-thruster input energy.

The physics is so simple that one can literally do it on the back of a napkin. In pen. Without crossing out mistakes. Actually, at V = 1/k, is when the kinetic energy of a stand-alone reactionless thrusted machine is acquiring exactly as much kinetic energy as input energy.

At all speeds above that, it acquires more kinetic than input energy.

At v = 2/k, the total kinetic energy of the device equals the total input energy.

At all speeds above that, its total Ek is greater than input energy.

Pull out a napkin, work with F = kP (force equals ‘k’ times power), Ek = ½mv², v = at, a = F/m, and absolutely no calculus … just high school algebra and plenty of substitution, and you can derive for yourself exactly these 2 points. The 1/k and 2/k points.

GoatGuy

> and an equally fantastical antimatter power supply to juice it

The highest vehicle performance isn’t reached with any antimatter power supply, because that is limited by the mass-energy of the matter + antimatter being consumed. The highest performance is reached with an external beamed energy source, such as a laser focused by a stellar gravitational lens. This allows you to focus over interstellar distances.

The beamed energy isn’t limited by the energy sources within the vehicle. It can be an arbitrary multiple of it. If used to power a particle accelerator, you are also not limited by the usual rocket equation. Relativistic particles gain mass. Therefore you can expel more total mass than you started with in your propellant tank. The mass gain is only limited by how many GeV the accelerator can provide to the particles.

In the somewhat more real world where we consider engineering problems, *storing* antimatter is likely to have a higher overhead ratio than 150:1 kg equipment/kg antimatter stored. In that case, a tank of fusion fuel would have a higher energy content, since propellant tanks generally have low overhead mass.

So, what amount of thrust might one expect after having accelerated some matter to this speed out the back of a motor?

The bane of any and all propellantless (reactionless) drives.

Anything with an efficiency of Newtons per watt above a perfectly collimated photon rocket, will become an over-unity (perpetuum mobile) at a certain speed smaller than c. And an infinite energy generator above it.

OK… but I kind of thought that the ‘ultimate’ was not to use particles with mass, but massless particles … called photons … to do the thrusting.

If for instance one has a truly gargantuan laser (which with my best magic … weighs almost nothing, fits in your pocket and sold the Dollar store), and an equally fantastical antimatter power supply to juice it … at 100% numerical efficiency … then it’ll happily produce 3.33 newtons for every gigawatt of power chowder pushed into it.

And using (m = E/c²) the inverse of (E = mc²), we show that the same ultimate magical photon rocket loses 11 milligrams of mass per second. Well, spitting out that energy takes its Einsteinian toll. Dâhmn the troll under the energy bridge!

Just saying.

GoatGuy