As an object accelerates, its length along the direction of movements becomes smaller. (Right?)
I take this to mean that the distance between points in space is relative to observer frameworks. (Right?)
And if I understand correctly, if I am in a rocket travelling at high speed, the length of my rocket will be normal as measured by myself, but the length of things outside my rocket will be shortned as measured by myself. (Right?)
My question, then, is how far does this shortening of external objects go? If I’m really close to the speed of light, does the entire universe measure (in my framework) as very short along the direction I’m travelling? Does this length approach zero? If I’m going really really close to the speed of light, do I seem to myself to be traversing a very short distance extremely slowly?
Pretty much. As long as by “things outside my rocket” you mean “things moving relative to me”.
Length contraction can indeed go to zero as relative velocity goes to c. So if you were zipping across the Milky Way at 0.9999999999999999999999999999999999999999 times the speed of light, you would see the Milky Way (120,000 light-years across, in its own rest frame) contracted down to be about 10 metres across in the direction of your travel, zipping by you at the above velocity. It would take only a fraction of a second (about 30 nanoseconds, to be precise) for the entire Galaxy to zoom by.
Of course, you would “observe” yourself not to be moving at all; it’s not really correct to say that “you observe yourself to be travelling such-and-such distance” in relativity. The whole point of relativity is that nobody “seems to themselves” to be moving in some well-defined sense; all reference frames with constant velocity are equally valid. Rather, in your example you would observe the Milky Way moving relative to you.
:smack: Of course. I was thinking of time dilation backwards, but I usually know better than that.
Of course, you would “observe” yourself not to be moving at all; it’s not really correct to say that “you observe yourself to be travelling such-and-such distance” in relativity. Rather, it’s the Milky Way that’s moving relative to you.
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I didn’t use the kind of language you’re critiquing here.
Here’s a related question. An object moving relative to me has its length smaller than it would if it were at rest relative to me. Generally, when I watch things becoming compactified, they undergo stress. And I imagine if an atom were squeezed hard enough, you’d get some kind of nuclear reaction or something. My question is, will a fast-moving object in my framework undergo any kind of stress or anything like this as a result of its length shortening?
I’d have a hard time understanding how this is possible (if its a person, then from my framework the person is crushed to death but from hers she’s fine?) but the physics people are always saying the craziest shit and they always turn out to be right.
I didn’t use the kind of language you’re critiquing here.
Here’s a related question. An object moving relative to me has its length smaller than it would if it were at rest relative to me. Generally, when I watch things becoming compactified, they undergo stress. And I imagine if an atom were squeezed hard enough, you’d get some kind of nuclear reaction or something. My question is, will a fast-moving object in my framework undergo any kind of stress or anything like this as a result of its length shortening?
I’d have a hard time understanding how this is possible (if its a person, then from my framework the person is crushed to death but from hers she’s fine?) but the physics people are always saying the craziest shit and they always turn out to be right.
-FrL-
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They wouldn’t feel any stress because all their atoms, electrons etc would be contracting too, so nothing would be pushing against anything else more they would do if you were at rest.
They wouldn’t feel any stress because all their atoms, electrons etc would be contracting too, so nothing would be pushing against anything else more they would do if you were at rest.
Okay, that’s what I was kind of thinking, but it still seems like you’ve got higher density–greater density, I guess, since IIRC mass increases with speed as well–which should have gravitational effects, right?
But I must be wrong, because then it seems like you could have a situation where in one framework, a ship carrying a person accelerates to a high speed, then decelerates and the person walks out of the ship, while from another framework, the ship accelerates to a very high speed, and collapses into a black hole.
As I’ve said before, but it can’t be repeated too often, the most important concept that is crucial to any understanding of relativity is that whatever frame you are in, whatever speed you’re traveling, everything always looks normal to you. Time passes at one second per second. Length is always the same number of feet. Mass is always the same number of pounds.* Nothing ever changes. The secret of relativity is that inside a framework all is invariant. You can’t tell any difference in what you are doing. Ever.
Proof. To a distant quasar, we are the ones traveling at .999C.
*Note to nitpickers. Go away.
Everything attached to your inertial reference frame. Things outside tend to get squished.
Note that objects outside your frame of reference tend to be contracted, but only along axes normal to your vector of momentum. So the spaceship you fly past at .9c is going to appear compressed, but the one you are headed straight in a collision course toward is going to be kind of stretched across your forward horizon. The distance to your target appears less corresponding to the amount of personal time it takes you to reach it (witnessed by an external observer as a contraction of time on your clock).
Non-inertial frames (i.e. those under acceleration) have somewhat different rules where the history of the reference frame does matter, hence why the twin on the rocket ship ages less than the one who remains on Earth. As a practical matter, attempting to accelerate to “0.9999999999999999999999999999999999999999 times the speed of light” in any reasonable personal timeframe will result in your being little more than a squishy pool of goo on the aft deck of your spaceship.
You asked, “Do I seem to myself to be travelling a very short distance?”, which was why I made the comment. My apologies if I saw confusion where there wasn’t any, but given that it’s really one of the fundamental points of relativity, I figured I would better be safe than sorry.
That they will. If you’re talking about a mass distribution with some finite extent, you can describe it by a stress-energy tensor, whose various components can be interpreted as the mass density, momentum, pressures, and shears inside the object. When we move to another frame, these components all mix together, not unlike the way in which time intervals mix with space intervals when we boost frames.
For example, suppose I have a rod of matter with negligible internal pressures at rest in my frame. In such a circumstance, the only non-vanishing component of the stress-energy tensor is T[sub]tt[/sub], which is interpreted as the mass density. If you zoom by me in your frame (travelling in the x-direction, say) then you’ll observe three independent components of the stress-energy tensor to be non-zero: T[sub]tt[/sub], since you observe there to be mass/energy density in the rod; T[sub]tx[/sub], which corresponds to the density of the momentum in the rod (you observe the rod to have some momentum, after all); and T[sub]xx[/sub], which you would interpret as a pressure density in the rod.
To reiterate Exapno Mapcase’s point, though: in my frame, the rod is not undergoing any stress and is not experiencing any pressure in its own rest frame. It appears so to you since you’re moving relative to the rod, but not to me.
Perhaps, but what you really would want to think about in such a case would be the pressures present in the atom’s own rest frame, not those in some other frame where the atom is moving. I can make the pressures in a carbon nucleus appear to be arbitrarily large in my frame by accelerating it up to the speed of light, but that doesn’t mean it will undergo spontaneous fission in my or any other frame.
That’s something I’m having trouble with. It has been my understanding that how things “appear” from a particular frame is just how they are from that frame. In other words, it has been my understanding that “appearances”, from any frame, will always be consistent with the laws of physics, and will always give rise to exactly the same causal effects in that frame that they would if they were “real”–because they are real. Hence my confusion over things like what I’ve been describing. If there’s a frame in which an object’s acceleration causes such a high density that it should collapse into a black hole, then in that frame, it collapses into a black hole, and yet, it is possible for there to be other frames in which that very same object does not get dense enough to collapse into a black hole (for example, the frame centered on the world-line of the object itself could be one of these frames) and so, in these frames, it doesn’t collapse into a black hole. But this seems impossible, since now from some frames, light can not escape from the object in any finite time, yet in other frames, there is a finite time in which light can escape from the object. In my head (always a mistake to try that though ) I can not figure out how to “reconcile” these two frames as part of a single consistent reality.
For a story once I put together a spreadsheet for 1G acceleration so that I could input any time, distance, or speed and get the other values. (Of course, today there are websites that will do this for you.)
At 1G you get to .99C in a little over 2.5 years of ship time. That translates to 6.8 years on earth. Three nines takes about 4 years, four nines takes 5 years. So very roughly each additional nine takes an additional year of ship’s time. That gets you places in a very reasonable lifetime. Seven years of ship’s time will bring you 665 light years. Fourteen years is 915690 light years.
Your gas bills will be beyond the limit on your credit card, though.
In principle, all true “laws of physics” are supposed to be “covariant”, meaning that all observations are phenomena are defined in an observer-independent fashion. For example, the so-called singularity theorems (governing when stress-energy configurations will collapse into black holes) don’t refer to the “mass density” of an object; rather, they refer to certain combinations of the components of the stress-energy tensor that happen to be the same for everyone. (I’m playing a little fast and loose here, but this is basically correct.)
Now, in practice, only a few fields of physics (general relativity and particle physics, mainly) regularly deal with objects that are moving relative to each other at high velocities, and for which there isn’t necessarily a “natural” frame to work in. In many other fields (solid state physics, nuclear physics, acoustics, plasma physics, biophysics, etc.) there quite frequently is a “natural” frame to work in — namely, the rest frame of the crystal/nucleus/air mass/etc. that you’re working with. In principle, though, the laws of physics in these situations could be derived from the the laws of GR and/or particle physics (well, most likely just particle physics) in some limit, and so we could in principle derive these laws in the same limit but in a different frame. Usually, though, nobody bothers to do this, since how often do you have crystals moving near the speed of light?
See, here I am worried about the nature of reality and all excited about apparent paradoxes with implications for ontology, and you have to go and turn it into an engineering problem.
