I might sadly add that, as a CMU student, this our third professor who we have lost in the past year. The other two professors, both in the biology department of CMU, were Dr. William Brown (http://www.cmu.edu/bio/news/2007/brown_tribute.html) and Dr. Elizabeth Jones (http://www.cmu.edu/bio/faculty/jones.shtml). All will be sorely missed, with Dr. Pausch being the most recent and visible.
Sorry, you are correct. What the proof I mentioned shows is that observers with a clock at a lower gravitational potential (deeper in a gravitational well) receive pulses from an emitter with a clock at a higher gravitational potential faster than the rate at which they were emitted. That is, if somebody counts the natural numbers at a rate of 1 number/sec, then somebody at a lower gravitational potential will say they are counting >1 number/sec (interval between each number is less than 1 second), and thus say that higher gravitational potential person's clock runs faster.
So yes, clocks do appear to run slower at lower gravitational potentials, that is, deeper in gravitational wells. My bad, I misinterpreted the text. (I'm glad I didn't claim to be an expert (-yet)!)
Actually, clocks "run" faster in gravitational wells. For proof, just think of the equivalence principle
, and clocks as sources of periodic light, or at least just think of light as a series of wavefronts (helps in understanding gravitational redshift too!). A good source on this is "Gravity: An Introduction to Einstein's General Relativity" by James Hartle.
It is also important to remember the principle of proper time
when considering the formation of these stars. Ignoring special relativity concerns for a second, clocks only run at relative different rates if they are at different gravitational potentials (the only way to measure gravitational potential anyway). So if the entire early universe were all at nearly the same gravitational potential, then all matter would be experiencing the same "proper" time, and things such as star formation rates would still be comparable; so this case examined here is still, probably, exceptional.
For further reading and a great intro to the formation of the universe and gravity and such, check out the book I mentioned above and "Introduction to Cosmology" by Barbara Ryden. I am not an expert-yet (grad school in a bit!)- but the cosmo. book is a great read for anyone interested and the gravity book is great for anyone with a little background in general and special relativity and some advanced linear algebra. Hope this helps!
Incorrect. I LIVE in Oakland. It is not "right next" to "Da Hood" (though boundary-wise it technically is "next to" Oakland). Unfortunately the route to downtown goes through the Bluff (a.k.a the Hill District), but Oakland itself is rarely affected by the blight that sits there. Oakland's problem is more bike theft than anything else, and while certain areas of Pittsburgh city are exposed to high violent crime (like the Hill District, or less and less East Liberty), if you went to Pitt you certainly know that the universities are excellent at keeping their campuses safe. Additionally (reading on), the Pittsburgh metro area has the "lowest crime among the 25 largest metro [areas]."
I attend a university in Pittsburgh and it is a fine city dealing with an overshadowing past. For proof of its green "transformation", check out some of the initiatives:
Slashdot Mirror
I might sadly add that, as a CMU student, this our third professor who we have lost in the past year. The other two professors, both in the biology department of CMU, were Dr. William Brown (http://www.cmu.edu/bio/news/2007/brown_tribute.html) and Dr. Elizabeth Jones (http://www.cmu.edu/bio/faculty/jones.shtml). All will be sorely missed, with Dr. Pausch being the most recent and visible.
Sorry, you are correct. What the proof I mentioned shows is that observers with a clock at a lower gravitational potential (deeper in a gravitational well) receive pulses from an emitter with a clock at a higher gravitational potential faster than the rate at which they were emitted. That is, if somebody counts the natural numbers at a rate of 1 number/sec, then somebody at a lower gravitational potential will say they are counting >1 number/sec (interval between each number is less than 1 second), and thus say that higher gravitational potential person's clock runs faster.
So yes, clocks do appear to run slower at lower gravitational potentials, that is, deeper in gravitational wells. My bad, I misinterpreted the text. (I'm glad I didn't claim to be an expert (-yet)!)
Actually, clocks "run" faster in gravitational wells. For proof, just think of the equivalence principle , and clocks as sources of periodic light, or at least just think of light as a series of wavefronts (helps in understanding gravitational redshift too!). A good source on this is "Gravity: An Introduction to Einstein's General Relativity" by James Hartle.
It is also important to remember the principle of proper time when considering the formation of these stars. Ignoring special relativity concerns for a second, clocks only run at relative different rates if they are at different gravitational potentials (the only way to measure gravitational potential anyway). So if the entire early universe were all at nearly the same gravitational potential, then all matter would be experiencing the same "proper" time, and things such as star formation rates would still be comparable; so this case examined here is still, probably, exceptional.
For further reading and a great intro to the formation of the universe and gravity and such, check out the book I mentioned above and "Introduction to Cosmology" by Barbara Ryden. I am not an expert-yet (grad school in a bit!)- but the cosmo. book is a great read for anyone interested and the gravity book is great for anyone with a little background in general and special relativity and some advanced linear algebra. Hope this helps!
Incorrect. I LIVE in Oakland. It is not "right next" to "Da Hood" (though boundary-wise it technically is "next to" Oakland). Unfortunately the route to downtown goes through the Bluff (a.k.a the Hill District), but Oakland itself is rarely affected by the blight that sits there. Oakland's problem is more bike theft than anything else, and while certain areas of Pittsburgh city are exposed to high violent crime (like the Hill District, or less and less East Liberty), if you went to Pitt you certainly know that the universities are excellent at keeping their campuses safe. Additionally (reading on), the Pittsburgh metro area has the "lowest crime among the 25 largest metro [areas]."
I attend a university in Pittsburgh and it is a fine city dealing with an overshadowing past. For proof of its green "transformation", check out some of the initiatives:
http://www.pittsburghgreenstory.org/html/index.html
http://www.popcitymedia.com/inthenews/solarcity0926.aspx
http://www.city.pittsburgh.pa.us/mayor/assets/08_green_up_app.pdf
(unfortunately, Pittsburgh's typical weather doesn't allow for strikingly efficient solar power use)