Is it possible to stop time completely?

[RisingSun361]

When I was in school, I learned only Newtonian physics. Recently I have discovered that what they taught me was wrong, that gravity is not a force, it doesn't occur simultaneously, blah, blah, blah

Anyway, based on my study of Einstein's relativity, I was wondering if it's possible to slow time all the way to zero. For example, would a clock on a neutron star or at the center of a black hole completely stop? Does time stop at the speed of light?

 

[PeterDonis]

would a clock on a neutron star or at the center of a black hole completely stop?

First of all, there is no "center of a black hole". The singularity at $r = 0$ in a black hole spacetime is a moment in time, not a place in space--once you fall inside the hole's horizon, the singularity is in your future. A black hole is not the same as an ordinary spherical object like a planet or a star.

Second, a clock anywhere in spacetime ticks normally as far as the clock itself is concerned; if you were on the surface of a neutron star (assuming you were made of a substance that could withstand the large acceleration), or falling into a black hole, everything in your vicinity would seem normal, and your clock would seem to you to be ticking at one second per second, just like it always does. The only sense in which your clock might be said to be "running slow" is in comparison to other clocks following different paths through spacetime; for example, if you travel down to the surface of a neutron star, stay there for a while, and then return back up to your mother ship, while your friend stays on the mother ship, your clock will show less elapsed time when you return than your friend's clock does. But there is no way to set up a scenario like this in which your clock shows zero elapsed time; so in that sense the answer to your question is "no".

Does time stop at the speed of light?

No. First, an ordinary object like you or me can't go at the speed of light, so it's meaningless to ask what would happen if we did. Second, for an object like a light ray that can go at the speed of light, the concept of "elapsed time" does not make sense; the math we use to represent "elapsed time" for you and me breaks down for light. Pop science presentations often say "time stops" for light, but that's not correct; what they should say is that "time" is undefined.

 

[Nugatory]

When I was in school, I learned only Newtonian physics. Recently I have discovered that what they taught me was wrong, that gravity is not a force, it doesn't occur simultaneously, blah, blah, blah

The Newtonian physics they taught you is not wrong. It's just not the whole story, and we teach physics that way because it is impossible to learn relativity and quantum mechanics if you do not already have an absolute rock-solid understanding of Newtonian physics. You might find this essay by Isaac Asimov (who was a highly regarded scientist - biochemistry - even though we remember him for his science fiction) interesting: http://chem.tufts.edu/AnswersInScience/RelativityofWrong.htm

Anyway, based on my study of Einstein's relativity, I was wondering if it's possible to slow time all the way to zero. For example, would a clock on a neutron star or at the center of a black hole completely stop? Does time stop at the speed of light?

It is not possible to slow time all the way to zero. The most you can ever do is arrange for one clock to run very slow relative to another clock.

 

[harrylin]

When I was in school, I learned only Newtonian physics. Recently I have discovered that what they taught me was wrong, that gravity is not a force, it doesn't occur simultaneously, blah, blah, blah

Anyway, based on my study of Einstein's relativity, I was wondering if it's possible to slow time all the way to zero. For example, would a clock on a neutron star or at the center of a black hole completely stop? Does time stop at the speed of light?

If gravity is a force or not is a matter of definition. And a black hole is more like a bubble; what happens at the boundary is interpreted differently by different people, but a clock will not completely stop although it may look so.

For less exotic cases, this is how Einstein phrased it (apparently some people consider that "pop science"!):

"Physical Meaning [..]
For v=c all moving objects—viewed from the “stationary” system—shrivel up into plane figures.
[..] the velocity of light in our theory plays the part, physically, of an infinitely great velocity. [..]
[the elapsed moving clock time] tau = t √(1-v²/c²)"
- http://fourmilab.ch/etexts/einstein/specrel/www/

However, obviously no clock can reach v=c.

 

[stedwards]

[...]And a black hole is more like a bubble; what happens at the boundary is interpreted differently by different people, but a clock will not completely stop although it may look so.

Have you done the calculations?

 

[phinds]

Have you done the calculations?

What calculations?

 

[Nugatory]

Have you done the calculations?

The calculations for what happens to a clock falling through the event horizon of a black hole?
They've been done many times, as this is a standard exercise on GR textbooks - google for "proper time falling into black hole".