Posted by
michael
on from the close-only-counts-in-horseshoes dept.
DrBlake writes "New York Times has an article about a study of Einsteins theory of relativity that I found very interesting. Not only might the speed of light be relative under certain circumstances, the famous equation E=mc2 might not be entirely correct."
Re:can someone explain to me
by
rossifer
·
· Score: 5, Interesting
c is relative to the observer, no matter which observer we're talking about. Anything that can measure the speed of a photon will always measure it going at the speed of light through that substance. Through a perfect vacuum, it's c. Through space it's c - epsilon (epsilon is an infintesimally small number). Through water it's about c/1.335.
If you are zooming past me at half the speed of light and both of us measure the speed of a particular photon at the same time, we'll both measure it's speed as c. What will be different about our two measurements is that you'll see a higher energy photon (bluer) than me if the photon is moving opposite to your motion relative to me and a lower energy photon (redder) if the photon is moving in the same direction as your motion relative to me.
No particular point in space is special. Once you identify where the observer is located, you can call that point in space an "origin" or "zero" and make all of your measurements from that point in space. The rest of the universe relative to that origin is called an "inertial reference frame", but it's just the same as any other reference frame. There's another trick. Behavior of things in inertial reference frames is time dependent because gravity pulls your frame around and changes everything around it slightly every moment. Besides that, two inertial reference frames may have a relative velocity but for a moment share the same point in space (the example above).
That's when tensor math starts to come in handy. Don't worry, I won't torture you with that.
Relativity, once you grok it, will bend your mind. From a metaphysical perspective, it emphasizes the reality that most of what we call facts are actually just high probability observations.
Remember, there is no spoon.
Regards, Ross
Re:FTL == Time Travel ?
by
Soft
·
· Score: 5, Interesting
I have been told that theory forbids any travel faster than light, no matter what the means ("warp drive", "hyperspace", "teleporter", whatever). My understanding is that if you could, some observers would see you traveling back in time, and this is forbidden.
Yes. One of the hypotheses of relativity is causality, that is, one event can possibly cause another only if the latter occurs at a later time than the former, and this must hold true for all possible observers whatever their frame of reference.
Now, as you know, the passing of time for an observer varies with his frame of reference (his speed, to put it simply). Hence, given two events, the interval of time from one to the other will not be the same for all observers. But if one is to cause another, it must always remain in its past; the sign of the time difference "t2-t1" must not change whatever the observer.
Unfortunately, my memories of relativity are too scarce to put this into equations, but if you could travel faster than light, you could, say, watch an asteroid smash into the Earth and warn your friend on the Centauri stock market to sell shares of all Terran businesses before anyone could "see" the flash of the impact.
And in a given frame of reference (maybe that of a traveler aboard a STL ship in-between), it would look as if you knew about it before it happened; stretching it further, it would be possible for the traveler (maybe through another FTL "jump") to warn Earth before the impact. Bye-bye causality.
If these situations are not to happen, information must not travel FTL.
Examine your assumptions
by
naasking
·
· Score: 4, Interesting
What makes you think there even was a beginning? Keep in mind that we have never actually seen the beginning of an event and the end; those boundaries are imposed by us. Reality is really a continuous cascade of effects which themselves become causes. How do we know there even is a beginning to the universe?
E=mc^2 is actually a simplified form of the real equation, E=mc^2/sqrt(1-v^2/c^2).
Please don't forget your subscripts! As everyone learns in basic special relativity, total energy, which is kinetic + potential, is
E = m0 * c^2 * gamma,
where gamma = 1 / sqrt( 1-v^2/c^2 ) and m0 is the rest mass.
At v = 0, gamma = 1 and E = m0 c^2, Einstein's famous formula for rest energy. Kinetic energy is given by KE = E - m0 c^2, or
KE = m0 c^2 ( gamma - 1 ).
To see any appreciable effect of velocity, consider the situation where you are going fast enough to double your effective mass (gamma = 2). Solving for velocity gives v = c sqrt(3/4) = 86.6% of the speed of light. Not gonna happen with current technology (outside of atom smashers).
As v -> c, gamma -> infinity and this is Einstein's rationale for saying it's impossible to accelerate any matter up to the speed of light, since doing so would require an infinite amount of kinetic energy. On the other hand, the formula for photons is
E = p c = h c / lambda = h nu,
where p is momentum, h is Planck's constant, lambda is wavelength, and c / lambda = nu is the frequency. Since photons are never at rest (remember the constant speed of light?), you won't see any m's make an appearance here. And just for the record, this last formula explains the photoelectric effect, which is what won Einstein his Nobel, not E = m c^2.
-- This post expresses my opinion, not that of my employer. And yes, IAAL.
Slashdot Mirror
c is relative to the observer, no matter which observer we're talking about. Anything that can measure the speed of a photon will always measure it going at the speed of light through that substance. Through a perfect vacuum, it's c. Through space it's c - epsilon (epsilon is an infintesimally small number). Through water it's about c/1.335.
If you are zooming past me at half the speed of light and both of us measure the speed of a particular photon at the same time, we'll both measure it's speed as c. What will be different about our two measurements is that you'll see a higher energy photon (bluer) than me if the photon is moving opposite to your motion relative to me and a lower energy photon (redder) if the photon is moving in the same direction as your motion relative to me.
No particular point in space is special. Once you identify where the observer is located, you can call that point in space an "origin" or "zero" and make all of your measurements from that point in space. The rest of the universe relative to that origin is called an "inertial reference frame", but it's just the same as any other reference frame. There's another trick. Behavior of things in inertial reference frames is time dependent because gravity pulls your frame around and changes everything around it slightly every moment. Besides that, two inertial reference frames may have a relative velocity but for a moment share the same point in space (the example above).
That's when tensor math starts to come in handy. Don't worry, I won't torture you with that.
Relativity, once you grok it, will bend your mind. From a metaphysical perspective, it emphasizes the reality that most of what we call facts are actually just high probability observations.
Remember, there is no spoon.
Regards,
Ross
Yes. One of the hypotheses of relativity is causality, that is, one event can possibly cause another only if the latter occurs at a later time than the former, and this must hold true for all possible observers whatever their frame of reference.
Now, as you know, the passing of time for an observer varies with his frame of reference (his speed, to put it simply). Hence, given two events, the interval of time from one to the other will not be the same for all observers. But if one is to cause another, it must always remain in its past; the sign of the time difference "t2-t1" must not change whatever the observer.
Unfortunately, my memories of relativity are too scarce to put this into equations, but if you could travel faster than light, you could, say, watch an asteroid smash into the Earth and warn your friend on the Centauri stock market to sell shares of all Terran businesses before anyone could "see" the flash of the impact.
And in a given frame of reference (maybe that of a traveler aboard a STL ship in-between), it would look as if you knew about it before it happened; stretching it further, it would be possible for the traveler (maybe through another FTL "jump") to warn Earth before the impact. Bye-bye causality.
If these situations are not to happen, information must not travel FTL.
What makes you think there even was a beginning? Keep in mind that we have never actually seen the beginning of an event and the end; those boundaries are imposed by us. Reality is really a continuous cascade of effects which themselves become causes. How do we know there even is a beginning to the universe?
Higher Logics: where programming meets science.
Please don't forget your subscripts! As everyone learns in basic special relativity, total energy, which is kinetic + potential, is
where gamma = 1 / sqrt( 1-v^2/c^2 ) and m0 is the rest mass.At v = 0, gamma = 1 and E = m0 c^2, Einstein's famous formula for rest energy. Kinetic energy is given by KE = E - m0 c^2, or
To see any appreciable effect of velocity, consider the situation where you are going fast enough to double your effective mass (gamma = 2). Solving for velocity gives v = c sqrt(3/4) = 86.6% of the speed of light. Not gonna happen with current technology (outside of atom smashers).As v -> c, gamma -> infinity and this is Einstein's rationale for saying it's impossible to accelerate any matter up to the speed of light, since doing so would require an infinite amount of kinetic energy. On the other hand, the formula for photons is
where p is momentum, h is Planck's constant, lambda is wavelength, and c / lambda = nu is the frequency. Since photons are never at rest (remember the constant speed of light?), you won't see any m's make an appearance here. And just for the record, this last formula explains the photoelectric effect, which is what won Einstein his Nobel, not E = m c^2.This post expresses my opinion, not that of my employer. And yes, IAAL.