About how close can an object that has mass get to C before the laws of physics start to rear their ugly heads? .1C? .(lots of zeroes)C?
The subject line question is VERY different than the actual post.
For the subject line: Let’s take something with a really tiny amount of mass, like a single proton. It can get really close to C if you push it hard enough. Like in the course of 100 years, it might have traveled 100 lightyears minus one Planck length. Umm… wait… Actually, even very massive objects can go that fast, if you push hard enough. The only real limiting factor is how much energy you put into it.
For the actual post: Relativistic effects can be noticed even at surprisingly slow speeds. Clocks brought into earth orbit go measurably slower than their earthbound twins, though the difference is so tiny that it has little or no practical significance. On the other hand, the GPS system works by measuring the distance from your device to the various satellites in orbit, and those distances are calculated by measuring the time it takes for a signal to go from the satellite to your device. Those times would be VERY inaccurate if they didn’t compensate for the time dilation caused by the velocity at which those satellites are moving.
If you are an electron the answer is really really slowly.
Watch this: That is relativity at work.
0.1c is still very slow from a relativistic POV. This particle traveled at 0.9999999999999999999999951c.
For the limit, you would need to keep adding 9s.
According to the comments there, that’s magnetism, not relativity.
The GZK limit for cosmic ray protons is about 99.99999999999999999998% of the speed of light; beyond that, interactions with the cosmic photon background will slow them down.
Sure, but where did the magnetism come from? That is why I made the comment about electrons moving.
It really is relativity under the covers.
While it is possible to derive Maxwell’s equations using special relativity, the demonstration is only an example of speed of light considerations in the same way that light from a light bulb is an example of quantum mechanics.
It’s true that electrons in solids move slower than in free space, but the fact is they don’t move very far, either. There isn’t a river of electrons moving through the copper unmolested. There are collisions (the lattice, grain boundaries, other electrons, etc.) that prevent this.
For the record, it has great practical significance. If they didn’t correct for the fact that clocks in orbit run slower than those on the ground, the GPS coordinates would drift by something like 8 miles per day.
Sure, but doesn’t change the basic fact. No relativity, this demonstration would not work. Electrons moving at the drift velocity in a conductor results in clear effects that are due to relativity.
Although it is not obvious to anyone who hasn’t studied special relativity, to four-velocity (vector of movement through spacetime) is c for all objects. When you are viewing things with little apparent motion relative to your reference frame, most of that magnitude is in the time component of the four vector, which means that the experience of time for that object is essentially the same as it is in your reference frame. For something moving in some spatial direction at a speed close to c (again, relative to your reference frame), the magnitude in the time direction is much smaller, which is why you experience time dilation (e.g. a clock on the object is moving slower than your watch). Of course, as far as a non-accelerating ‘moving’ object is concerned, it is in a stationary reference frame and the rest of the universe is stationary relative to it, with all of the observed effects. It does not perceive any change in the local flow of time, or additional mass, et cetera.
Stranger
If you did (forever), wouldnt it equal 1?
[g,d,rlh]
The idea is right but the direction is wrong. Clocks run slower deeper in a gravity well than further out. The GPS satellite clocks go a bit faster.
Right, the effect from being in orbit is larger than the effect from their speed, and in the opposite direction.
The Oh-My-God Particle is (probably) the fastest-moving massive object ever observed, but it’s probably not the fastest ever (how wild would that be, if we just happened to observe the fastest object ever?). There’s no known bound less than c: You can get as close to c as you’d like, with enough energy.
Incidentally, that “(probably)” there is because of neutrinos. We don’t know how fast they go. The difficulty is that we don’t generally measure speeds of subatomic particles like neutrinos or the OMG directly: If you try, you just get an answer of “it’s really, really close to c, too close to tell the difference”. What we measure is the energy, and then we can calculate the speed from the energy and their mass. And we don’t know the mass of neutrinos. Heck, even the speed quoted for the OMG particle is based on the assumption that it was a proton: That’s a very sound assumption, with plenty of reason to believe it’s probably correct, but it’s still only an assumption.