Understanding Relativity: How Moving Objects Experience Near Light Speed Travel

[PeterDonis]

This is what I actually said

You said pair production "arbitrarily close to c". But it's quite possible to make interstellar trips without getting "arbitrarily close to c". So even if pair production is physically possible "arbitrarily close to c", that doesn't mean it's actually relevant for interstellar trips. Which is what other people have been pointing out, but you don't seem to be agreeing with them.

Other than pair production, you have mentioned inverse Compton effect and vague handwaving about "viscosity". But Lesch isn't saying either of those things.

In other words, people are pushing back against the Lesch reference because you appear to be claiming that Lesch said something that was relevant to interstellar trips, which, as above, does not appear to be the case.

 

[fresh_42]

Which is what other people have been pointing out, but you don't seem to be agreeing with them.

See Lesch's paper in post # 70 on extragalactic jets.

 

[PeterDonis]

there are no scientific papers of rockets at near c speed

Plenty of posters here are perfectly capable of making reasonable estimates--several of them have done just that in this thread. But you have not. You have simply thrown around names of possible effects--pair production, inverse Compton effect, "viscosity"--without making any attempt that I can see to estimate how relevant they are for the gamma factors expected for interstellar trips. And the references you have pointed to, to the extent they give numbers, give numbers that appear to make the claimed effects irrelevant for interstellar trips.

For example:

See Lesch's paper in post # 70 on extra gallactic jets.

The energy per particle in these jets, from what I can see, is in the range $10^{18}$ to $10^{21}$ eV (p. 6). Which, given a proton rest mass of about $10^9$ eV, gives gamma factors of $10^9$ to $10^{12}$--again, irrelevant to interstellar trips.

So, again, you are getting pushback because none of the references you give seem to be saying anything that is relevant to interstellar trips.

 

[fresh_42]

So, again, you are getting pushback because none of the references you give seem to be saying anything that is relevant to interstellar trips.

I can only assume that Lesch generalized the results of this paper to rockets near the speed of light. This makes a barrier of 0.99995c according to Wikipedia. So it is higher than I thought, but it is an upper bound below c.

 

[PeroK]

I've battled my way through the video (he speaks German so clearly that I can actually follow what he's saying). He does claim that you can't get to Andromeda in 28 years proper time. He talks about the increasing radiation pressure, but then a secondary effect kicks in: the high-energy-cosmic ray "speedlimit", which he described as a "wall" where pair production takes place.

The main issue with this is that by the above calculations, the pair production kicks in at speeds far in excess of what is needed to get to Andromeda in approximately 28 years.

We could do a calculation for a proton at this threshold energy, which is $5 \times 10^{19}eV$, a gamma factor of $5 \times 10^{10}$. Such a proton would travel the $2.5 \times 10^6$ light years to Andromeda in a proper time of a fraction of a year.

To be fair to @fresh_42, I think Professor Lesch ought to check the numbers for the trip to Andromeda.

PS I think the 28 years is an acceleration and deceleration trip to Andromeda. If you have a proper acceleration of $g$, then you may reach the pair production gamma factor after 28 years. I haven't got time to check the calculation now.

That might explain the confusion and where the 28 years comes from and how a trip to Andromeda got mixed up in this.

 

[PeterDonis]

This makes a barrier of 0.99995c according to Wikipedia.

What Wikipedia reference are you talking about here? The only Wikipedia references I see in this thread are to the article on UHECRs, which gives energies like $10^{18}$ eV and above, which correspond (for protons) to gamma factors of $10^9$ and above, which correspond to relative velocities much closer to 1 than 0.99995c.

 

[fresh_42]

What Wikipedia reference are you talking about here? The only Wikipedia references I see in this thread are to the article on UHECRs, which gives energies like $10^{18}$ eV and above, which correspond (for protons) to gamma factors of $10^9$ and above, which correspond to relative velocities much closer to 1 than 0.99995c.

That was a quick search for the speed of extragalactis jets. It is probably too high. The paper says

The hadronic jet constituents can efficiently be accelerated in such fields all along the jets. To estimate the maximum energy the accelerated jet hadrons can achieve we consider energy loss processes as photon-pion and pair production as well as synchrotron and inverse Compton radiation.

So I looked up whether those jets are comparably fast to that of an hadronic spacecraft .

 

[PeterDonis]

It is probably too high.

I would say more like "definitely too high"; a trip anywhere in our galaxy, or even to the Andromeda galaxy, as @PeroK has pointed out, won't get you anywhere near the gamma factor involved with those jets.

 

[DrStupid]

PS I think the 28 years is an acceleration and deceleration trip to Andromeda. If you have a proper acceleration of $g$, then you may reach the pair production gamma factor after 28 years. I haven't got time to check the calculation now.

I just checked it and it is indeed 28 years with 1 g proper acceleration. In a Newtonian universe I would get 3100 years (Lesch says it would be 2800 years). That's pretty much the message of the first part: The cosmic speed limit is our friend and not the problem.

Than he switches to the blue-shifted CMB radiation and pair production at very high speeds (with high-energy-cosmic rays as a real-world example for particles with sufficient speed). But he doesn’t say that it happens in case of the 28 year trip to Andromeda. In this special case I get a gamma factor of 1,300,000 and the maximum of the CMB radiation would be blue-shifted to "just" 3.3 keV. That is well below the limit of 1.022 MeV for pair production.

Thus, the video is correct, but it might be misleading because Lesch doesn’t say that it takes much longer trips for the effect to become a problem. He also didn't mention temperature and radiation pressure as a problem. In case of the trip to Andromeda it would be up to 7 million K and 500 GPa. That means there is no material that could survive and it would take 150 EW/m² just to keep the speed constant.

The resistance starts long before paar production becomes relevant. I'm not even sure if something special happens when it starts. Maybe it is just another way to waste energy.

 

[PeroK]

I think this is the root of the confusion.

If we take a proper acceleration of $g$ for 14 years proper time, then we travel about $1.2$ million light years (half way to Andromeda), reach a speed of about $(1 - \epsilon)c$, where $\epsilon = 3 \times 10^{-13}$, with a gamma factor of about $1.2 \times 10^6$, boosting the CMB to X-rays at about $4 \times 10^{17}Hz$

A trip to Andromeda, where the second half was a deceleration at $g$ would then take 28 years, and the maximum CMB would be X-Rays

If, instead, we keep accelerating at $g$ then we reach Andromeda in less than 15 years proper time and still have no more than CMB X-rays.

But, if we keep accelerating at $g$ for 23 years, then we reach a gamma factor of about $5 \times 10^{10}$, which boosts the CMB to gamma rays, and the pion pair production problem, associated with the GZK limit for cosmic ray protons. The distance traveled in this case is about $1.5 \times 10^{10}$ light years, i.e. more than the diameter of the observable universe.

As far as I can see from these calculations, the GZK limit is not a problem for getting to Andromeda in 28 years, but it becomes a problem to overcome if you want to accelerate at $g$ for 20+ years.

 

[JerryF]

Hi, thanks hugely for all posts. Great reading and they’ve given me much to think about and investigate.

2 things I don’t understand (amongst many others) are;

a) why we need an increasing amount of energy input when accelerating?, and,

b) Deep space viscosity at at nearly c. I interpret the comments like this:
blue shift will accelerate approaching photons real* energy to such high levels as to obliterate the ship.
If so, would there be a real corresponding depletion of energy density behind the ship?

*I use real in the sense that these effects could interact with the ship

Thanks again

 

[PeroK]

Hi, thanks hugely for all posts. Great reading and they’ve given me much to think about and investigate.

2 things I don’t understand (amongst many others) are;

a) why we need an increasing amount of energy input when accelerating?, and,

b) Deep space viscosity at at nearly c. I interpret the comments like this:
blue shift will accelerate approaching photons real* energy to such high levels as to obliterate the ship.
If so, would there be a real corresponding depletion of energy density behind the ship?

*I use real in the sense that these effects could interact with the ship

Thanks again

a) In SR, as opposed to Newtonian physics, total energy of a particle in a given frame of reference is $$E = \gamma mc^2$$ where $$\gamma = \frac 1 {\sqrt{1 - v^2/c^2}}$$ And, if you draw the graph of energy as a function of speed ($v$), then you'll find a vertical asymptote at $v = c$.

That means that no matter how much kinetic energy you add to the particle, it never reaches a speed of $c$ relative to the original (or any) reference frame.

b) The CMB radiation is a major practical problem to relativistic space travel, as the energy of the CMB relative to the spaceship increases without limit (in the same way that the energy of the spaceship increases without limit in the original reference frame). As the ship gets faster relative to the original frame, so the CMB photons in front of the ship get more and more energetic, through UV to X-rays and eventually to gamma rays.

And, yes, the CMB coming from behind the ship will redshift to lower and lower energies relative to the ship.

 

[PeterDonis]

why we need an increasing amount of energy input when accelerating?

Because you have to overcome an increasing force pushing back against the ship. Just considering the CMB alone (and, as has been mentioned, the CMB is not the only thing that can cause a force pushing back against the ship--the interstellar medium contains other things as well), the possible sources of a force pushing back against the ship, which include radiation pressure, inverse Compton scattering, and pair production (just to name those that have been mentioned in this thread), all increase in magnitude as the ship's velocity relative to the CMB rest frame increases. (The relative magnitudes of these effects also change as the ship's velocity increases--much of the discussion in this thread has been focused on how high a gamma factor you have to achieve for pair production to become significant.) So as the ship's velocity increases, the force pushing back on it due to the CMB also increases, which means the ship's engines would have to burn more energy and produce more thrust to keep it accelerating at the same proper acceleration.

 

[JerryF]

thank you :)