You can’t “get to” light speed, that’s one of the big punchlines in relativity.
If you pick an acceleration equal to the acceleration we experience on Earth (aka 1g, aka ~9.8m/s^2), you hit relativistic speeds (speeds at which you need to take into account the effects of relativity to do anything) surprisingly fast. On the order of hundreds of days. So, it is not really a matter of safe acceleration on a long space trip. Instead you have to worry about the actual speed you are traveling at—even though space is very empty, there are still atoms floating around out there, and you’ll be moving at very high speeds relative to them, leading to interesting collisions.
It's kind of funny that the actual big punchline is that light speed matters at all. There would be no meme of "reaching lightspeed" without relativity, despite that meme originating from relativity specifically mentioning lightspeed as something you can't reach.
> Instead you have to worry about the actual speed you are traveling at
That's the other big punchline in relativity: There's no one "actual speed" because that implies that there is a single "important" frame of reference wherein those atoms are floating around waiting to be hit by a spaceship.
> A comoving observer is the only observer who will perceive the universe, including the cosmic microwave background radiation, to be isotropic. Non-comoving observers will see regions of the sky systematically blue-shifted or red-shifted. Thus isotropy, particularly isotropy of the cosmic microwave background radiation, defines a special local frame of reference called the comoving frame. The velocity of an observer relative to the local comoving frame is called the peculiar velocity of the observer.
What if you define the "important" reference frame as the speed of light's (in the same direction you are going). Since c is universally constant, it seems like a reasonable privileged reference.
Doesn't really work this way. A lot of the wonkiness in SR is tied to the fact that the speed of light is the same, measured in _any_ reference frame.
So, say you're on earth and you measure the speed of light... you find that it's c (~3x10^8 m/s).
Now you get on a spaceship and accelerate to 0.5c with respect to earth, and you measure the speed of light relative to your spaceship... still c!
In this way, you can't really define a reference frame with a speed "the same as the speed of light". And if you try, you'll run into nasty infinities in all your equations that will cause them to blow up and stop being useful.
So depending on how you measure, you’re always stationary or moving near light speed, or somewhere in between, depending on your measurement reference (the thing you’re moving relative to)?
How is there a speed limit at all, if that’s the case? You can accelerate to 0.5c and then toss an apple out the window and say you’re moving at the speed of an apple tossed out of the window, relative to the apple. You have all of c available as headroom again? You can accelerate up to 0.5c again, relative to the apple you tossed out the window?
I am imagining you will say that it will seem like this is what is happening to folks in the spaceship, but what’s really happening is that time is slowing for the spaceship and it’s passengers, and that they still can’t reach c. Fine. But c relative to what? There is no absolute c because there are no truly fixed points, so c relative to what?
There is no underlying reference frame. All motion is relative. Everyone, no matter how fast they are already going, will measure the speed of light as c. Accelerate to .99c and shine a flashlight in front of you. That light is moving ahead of you at the speed of c. Because to you, you are not moving.
That's true for the laws of physics, yes, but our universe does have a 'natural' frame of reference.
> A comoving observer is the only observer who will perceive the universe, including the cosmic microwave background radiation, to be isotropic. Non-comoving observers will see regions of the sky systematically blue-shifted or red-shifted. Thus isotropy, particularly isotropy of the cosmic microwave background radiation, defines a special local frame of reference called the comoving frame. The velocity of an observer relative to the local comoving frame is called the peculiar velocity of the observer.
> You can accelerate to 0.5c and then toss an apple out the window and say you’re moving at the speed of an apple tossed out of the window, relative to the apple. You have all of c available as headroom again? You can accelerate up to 0.5c again, relative to the apple you tossed out the window?
Yes you can. You can even do it with 0.6c for both those speeds.
it's either "relative to any observer." or "relative to any inertial reference frame". no matter where you go (on the ship, on a planet you pass by, on another ship) you will never see the apple travel as fast as the photons coming out of your flashlight. Depending on where the observer is, they will see the apple accelerate to 0.5c (if they are aboard the ship) or they will see it gain mass (or rather, see you throw it more slowly as if it had gained mass), contract in the direction it's thrown, and slow down (due to time dilation...relative to the moving frame).
The case I don't know how to answer is two apples thrown at each other, each with a speed greater than 0.5c.
Suppose there is a starting point A from which your ship is moving away from. At the same time, a photon is shot out from A. You can take the distance traversed between A and the ship as D1, and the distance traversed by the photon as D2. Then your "percentage of C" is D1/D2.
How can you get the distance D2? I'm not sure. I guess we have to pretend it's also a ship that is traveling at C that can emit information to us (also at C :p )
Not a physicist, but my impression is that you're always going 0 percent of the speed of light (in all directions) from your own frame of reference. All you notice is that our solar system is moving away, faster.
I guess you'd notice a change in light frequency based on the light in front/behind. Redder behind, bluer in front.
> I guess you'd notice a change in light frequency based on the light in front/behind. Redder behind, bluer in front.
The light in question is not uniform like white noise; the spectral power distribution has relatively light and dark lines in them as a result of the physics of the bright sources and intervening gas and dust. Those features also get redshifted.
If one is moving relative to the sun, one would pay attention to the sun's Fraunhofer lines <https://physics.weber.edu/palen/clearinghouse/labs/Solarspec...>, which would be Doppler shifted to different wavelengths. These lines also appear in reflected light from bodies in the solar system; if you were flying towards Pluto you would see a corresponding blueshift of the reflected Fraunhofer lines (plus some additional structure related to the chemistry of Pluto; it has some luminescence, as does our moon, as do the leaves of plants, and luminescence tends to impinge on the narrower Fraunhofer lines).
Indeed, measuring the Doppler shifts of multiple known-chemistry light sources is a useful technique in navigation of spacecraft within our solar system; it can in principle do better than precision measurement of angles to multiple light sources.
The spectral distortions of the CMB are certainly interesting, but it's hard to imagine their utility for spacecraft navigation within the Milky Way, rather than helping to physical cosmologists understand why there even is a Milky Way.
In the solar system we have kind-of the opposite problem: in order to get reliable anisotropy data of the Milky Way, probes like WMAP need excellent almanac data for the ephemeris of Jupiter (it's a bright reflector of sunlight and its cloud-tops at ~70 kPa are ~22 GHz microwave-bright; I gather other outer planets are used too, but the details are beyond me) to check its 22-GHz-band detection of the CMB Doppler shift in the directions it looks.
In short, a reference frame moving at c is pretty much a logical absurdity, because by definition it would mean having massive objects move at c as well.
The tl;dr is that often one wants to know about an event on the past or future light cone of an initial event, like connecting the detection of a soft X-ray with an inverse Compton scattering at some astrophysical source like a black hole's corona or high-energy galaxy cluster electrons (the Sunyaev-Zel'dovich effect), where one wants to trace out the evolution of the scattered photon's momentum across cosmological distances. Coordinate systems along the photon's path from the thermal emission source (the black hole accretion disc or the surface of last scattering) can facilitate this. These coordinate systems are reference frames moving at c.
As long as one is working with covariant descriptions of matter, taking a notion like a photon's "affine time" or similar for a classical electromagnetic wave into (signed) momentum imparted to some object on a timelike path (such an object will have rest mass) is straightforward. The justifications mainly originate with Newman & Penrose in the early 1960s.
Here's a nice (and very fresh -- it's an incomplete draft) technical note that details one use of the Newman-Penrose formalism in the flat spacetime of Special Relativity. Note the extract from Chandrasekhar's 1983 textbook in section 7.3 (the author sources from a 1998 reprinted edition). <https://astromontgeron.fr/SR-Penrose.pdf> (PDF). The observations in §7.7 and §7.9 would be enough for me, if I hadn't already internalized the ideas further below.
I'll raise a couple of important and noncontroversial points from Jacques Fric's note: a photon -- whose frequency is proportional to its momentum -- oscillates some number of times along its null path lending a useful affine parametrization of the geodesic (photon motion is for all practical purposes always geodesic) that takes into account the spacetime curvature along the geodesic. Deploying the NP formalism in such a situation gives a nice analogy between motion through curved spacetime and motion through a refractive medium. And finally, covariant results in the NP coordinate system are readily interconvertible with covariant results in Minkowski coordinates.
Coordinate systems built along null geodesics -- typically lightlike Fermi-normal coordinates (FNC) -- also find applications in generalizations of the Jacobi equation, geodesic deviation, conjugate points, and so forth.
Now a step back to your comment. Null-basis FNC approaches let one calculate the momentum of a massless force carrier at any point along its evolution from p_{emited} to p_{observed}, and find cosmological applications (redshift of an astrophysical megamaser, the Lyman-alpha forest, etc) and microscopic ones (for the latter see ref [1] at <https://physics.stackexchange.com/questions/62488/local-iner...>).
In reading that stack exchange answer you'll want to know that 'Penrose showed that any [Einsteinian] spacetime [...] has a limit which is a plane wave, which can be thought of as a "first order approximation" to the spacetime along a null geodesic.' (from <https://link.springer.com/referenceworkentry/10.1007/1-4020-...>).
Pointing to references rooted in string theory and supersymmetry are not endorsements of those families of microscopic theories; they're just the most accessible examples of the practical use of lightlike FNCs for small locally relativistic systems.
So, not a logical absurdity, not useless, and not even especially uncommon.
Relativity (the fact that the laws of motion are the same in all inertial frames of reference) is itself a crucial part of Newtonian mechanics, except that Einstein's theories of relativity were such a big deal that we now tend to reserve the word "relativity" for his stuff, and call the old thing "Galilean invariance" or similar.
dumb question - why does going faster make it more likely you encounter fast protons? couldn’t protons in any reference frame be going quite fast relative to you?
Nah, most of the random atoms floating around in space are going to be travelling very roughly as fast as the things (stars, planets, etc..) around them -- because anything travelling much faster is likely to eventually bump into something and lose some of its momentum.
no a proton is a hydrogen nucleus (or at least can be seen as one) and has a charge. travelling near lightspeed you would have to worry most about uncharged atoms/molecules (because of their mass) and neutrons, neither of which can be deflected.
