Posted on 11/21/2008 6:38:36 PM PST by camerakid400
Yes, the bug would see the laser light moving at the speed of light.
read later
Actually, Einstein's Special Theory of Relativity deals with that exact problem and the key requirement is that EVERY observer of a beam of light in a vacuum will measure the velocity of the beam as c, the speed of light.
So, the bug riding on the laser pointer sees the light emitted from the pointer and leaving his location at the speed of light. The contribution of Einstein's theory is that this "impossible" result is made possible by changes to other observables to accomplish this.
One such change is that observers of the beam who are moving relative to each other will disagree about what the frequency of the light being emitted is. Another consequence is that observers moving relative to each other will disagree about WHEN things happened. Things that are simultaneous in one frame of reference can appear to happen at different times to a different observer, depending upon how that observer is moving.
A clock moving toward you at relativistic speeds will appear to you as running more slowly than to an observer moving with the clock.
All sorts of nuclear interactions prove it. The kinetic energy plus rest energy is conserved when particles collide and interact to create new particles.
The idea here is that the calculations account for the rest mass of neutrons and protons in terms of the interaction energy of quarks and gluons. This is more a validation of quark theory than a proof of E = mc2, IMHO. The latter is amply demonstrated by the annihilation of a proton with an antiproton.
What is the formula to calculate the energy required to accelerate a mass to some speed just shy of the speed of light?
Einstein ping!
And the proof of the existence of an antiproton is found where?
The famous example is the half-life of secondary particles created by cosmic rays striking the atmosphere. Some of them are detected at the ground even though they "should" decay before they have traveled a fraction of the necessary distance. The paradox is resolved by time dilation.
The formulas of special relativity are the work-a-day tools of the "ultrarelativistic regime" created in high energy particle accelerators. It's just the opposite of the "classical regime" where the kinetic energy is much less than the rest energy. In the ultrarelativistic regime, all particles behave approximately as massless particles, like gamma rays.
Here is the famous picture of the first antiparticle discovered, the positron, which is an anti-electron. Of course, the positron is used in PET scans ( Positron Emission Tomography ) . It's every bit as weird and exotic as the antiproton, but a lot easier to produce since it has 1/2000 of the rest energy.
Well, I don't have the capability to format algebraic expressions, but I will attempt to do this.
First let's recognize that the calculation is going to be such that the energy must approach an infinite value as the velocity approaches the speed of light.
The total energy of the particle consists of the rest energy, which is the familiar E=mc2, plus the kinetic energy.
The formula for the total of these two terms is E=gamma*(rest mass), where gamma = 1/sqrt(1-v2/c2).
To calculate the energy required to accelerate to a given velocity v, calculate the total energy at that velocity and then subtract the rest energy.
One can also calculate the energy required to accelerate from velocity v1 to velocity v2 by calculating the total energy at each velocity and then subtracting.
The statement:
The formula for the total of these two terms is E=gamma*(rest mass), where gamma = 1/sqrt(1-v2/c2).
Should be:
"The formula for the total of these two terms is E=gamma*(rest energy), where gamma = 1/sqrt(1-v2/c2)."
The statement:
"The formula for the total of these two terms is E=gamma*(rest mass), where gamma = 1/sqrt(1-v2/c2). "
Should be:
"The formula for the total of these two terms is E=gamma*(rest energy), where gamma = 1/sqrt(1-v2/c2). "
A very disappointing outcome. I had come to believe, over the years, that e might actually be equal to something, anything, else. My life is now without meaning.
Seems possible!
http://en.wikipedia.org/wiki/Superluminal_communication
http://query.nytimes.com/gst/fullpage.html?res=940DE5DE123BF931A15754C0A961958260
Apparent movement is not real movement so there is nothing to carry information. Just like you can’t send an apparent letter to carry a message.
Briane Greene had a great book, that if you expland space enough, time also changes.
IE, if you could see someone across the universe 13b light years away, you’d be able to fast forward and rewind by moving towards and away from them. Basically, if you’re far enough, motion towards and away causes time to contact/expand.
Amazing stuff, and very important to understanding of the universe.
Actually, with is the opposite of without. Nice try, but you learn that in high school.
P.S. It’s Saturday.
From the Photon's point of view, there is no journey. And that's where it gets WEIRD for most people, but it explains a lot from a quantum mechanical point of view (think: 2 slits).
So if M is fixed and the other two move around - -well that is just a mind blowing thing.
Wow, that article is written so badly it’s almost like babelfish.
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