If I understand basic physics correctly (pretty big “if”), velocity, and indeed speed, are dependent on a reference frame, that is, you are inertial in your frame, but to someone moving 12 km/hr relative to you, you are moving 12 km/hr relative to them. Is this correct?
If so, I recall reading something about how the speed of light does not depend on a reference frame, and is therefore absolute. Is this also true? And if so, does this mean that something traveling at, let’s say, c-1 m/s does not perceive a photon of light as travelling at 1 m/s, but rather at c? if so, how is that possible (if it can be easily explained).
At any velocity less than c an observer will measure the speed of light as c. I don’t think there is any reason known. Actually the speed of light being the same for all observers is one of the postulates on which Einstein based his theory. I have to admit that it puzzles me as to what happens when the speed of the observer approaches c as a limit.
Einstein’s Theory of Special Relativity explains exactly this, that your understanding is correct. The mechanisms are called “dilation” (of time) and “contraction” (of length). An observer traveling at a high speed relative to you will appear “shrunk” along the axis of travel, and will appear to experience time more slowly.
It might help to remember that each observer measures things relative to his frame of reference in which he is always standing still. In that case why shouldn’t both of them measure light as having c as its velocity?
Can you expound on that, Nametag? Will he experience time more slowly compared to me? and if so, that has to be determined by someone in another frame, right? How can I determine how he experiences time?
Thanks!
You make a good point there. However, if I’m travelling at 10 km/hr compared to inertial Earth reference frame and someone is travelling in the same direction at 11 km/hr, I will perceive them as going 1 km/hr. Why would the same not happen travelling at c-1 m/s (compared to the same inertial reference frame) behind a photon of light (travelling at c in the same intertial reference frame, but also travelling at c in all reference frames). I hope that makes sense?
Imagine you’re in a rocket travelling at 99% of C relative to someone on Earth. You fire a laser beam out ahead of you. What do you see? And what does the observer on on Earth see?
You see the laser beam moving away from you at 100% of the speed of light.
The Earth observer sees the laser beam creeping away from you at 1% of the speed of light.
There is no contradiction, because the Earth observer also sees time flowing more slowly for you, and sees the length of your rocket compressed.
The one thing that nobody else has mentioned is that this formula you state has to be modified.
Okay, so let’s say I see a dart fly by me at a velocity v. Meanwhile, I’m moving past you at the velocity u (in the same direction as the dart is flying by me). Now I can actually tell how fast you’ll oberve the dart to be travelling, and it’s not u+v. Instead, the answer turns out to be (u+v)/(1-uv/c[sup]2[/sup]), where c is the speed of light.
So what happens when our speeds are low? Well, if both u and v are very small compared to c, then the denominator here is pretty darn close to 1, so we get an answer so close to u+v that we can’t tell the difference. In the “limit of low velocities”, the Einsteinian formula for adding velocities becomes the old Galilean formula.
I am not Einstein, I am not “an Einstein”, and I don’t even grok math very well. But I think his insights are best understood as equation-solutions. Albert Einstein cannot tell us what the actual experience of traveling 0.999 c would be like; what he was able to do was reconcile a set of equations by picking what aspects made most elegant sense as constants. I think there’s a mathematician’s delight in seeing what happens within the relationships if we posit the speed of light as a universal constant.
Meanwhile, as a person who is neither a physicist nor a mathematician, I too have mental problems with the notion that “everything w/regards to motion is relative, except oopsie light is different”. Especially given red-shifts. Dammit, astronomers and physicists always make me feel stoopid! I want them to 'splain it all so I can get it. Either I haven’t found the right astrophysicist/teacher or the real answer really is “we just like the way the equations play out if we assume that”.
Basically, it was discovered, through experiments in the laboratory, that light simply DOES travel at the same speed in every inertial frame. Einstein proved that the only way that’s possible is if certain extremely counterintuitive things, including time dilation, length contraction, non-simultaneity of events (if I say two things happened at the same instant, you might say they don’t), a universal speed limit (no object can travel at the speed of light, except light itself, and maybe some other massless particles), and non-Newtonian velocity addition (as Mathochist described). There are some fun thought experiments you can do, involving, for example, a fast-moving rocketship that is contained completely inside a long tunnel, for observers inside the rocket, but is far too big to fit inside the tunnel for observers standing against the tunnel walls.
I know it’s all really hard to believe, but it’s the only way to explain the results that scientists were finding in Einstein’s time. And, some of these effects can actually be measured. They’ve actually done the famous “twin paradox,” not with a real set of twins, but with ultra-accurate atomic clocks in airplanes and the results are exactly predicted by Einstein’s equations.
That’s a great explanation, thanks! - It’s not that light is different, it’s just that the factors that make light appear different are insignificant at ordinary everyday velocities.
I think I’m right in saying that these factors do have to be taken into consideration when they’re designing space probes that will be sent off at 20 times the speed of a rifle bullet, or whatever - even though this is still slow compared to c.
Apparently not. In fact I think it’s true that individual electrons in the wire travel extraordinarily slowly. The propagation of electricity through a conductor (which could be thought of as one marble popping out of the opposite end of a packed tube when you push one in at this end) is quite fast, but still not the speed of light.
There is one rather finicky nitpick to be made here. The value of “C” at 186,282 MPS is the same regardless of frame of reference.
But that is “the speed of light in a vacuum” as well as a universal constant. Note that the speed of light through, e.g., translucent quartz may be some fraction of C. In fact, the famous blue glow called Cherenkov Radiation is produced by particles travelling slower than C but faster than the speed of light in the medium through which they are moving.
People in this thread are acting as if it’s not an unexpected and remarkable thing that the speed of light (in vacuum) should be the same in all reference frames. It is, I think, which is why no one came up with relativity earlier. Einstein’s brilliance was to ask what a beam of light would look like if you were travelling along at the same speed, and following that through to its logical conclusion. Before that, velocities added vectorially. Einstein came cup with an internally consistent theory that let the speed of light be the same in all reference frames, and it’s consistent with experiment, so it wins the prize.
Einstein himself wrote a popular book (meaning one for a non-scientific audience) that is very well-done, and worth reading. It’s titled relativity.
When you make a measurement it’s always made relative to you. You can make a measurement of two objects A and B relative to you. You can then compute what velocity for B you would measure if you were on A. There again, you have put yourself in a different frame of reference in which your velocity is still zero relative to yourself.
The thing is we have no idea what would be the absolute velocity of A and B because there isn’t any such thing. The velocities we know are measurements that we make and they are relative to us.
And, by the way, you would not measure the other person traveling at precisely 1 m/s but rather at a velocity determined by the same geometry that is used in relativity. It’s just that at velocities that are low compared to the speed of light the difference is so small we can neglect it without causing us difficulties.
