Did Newton Predict Black Holes?
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- čas přidán 7. 12. 2020
- In physics, there exists two main theories of gravity: general relativity and Newtonian gravity. While Newton's theory works wonders in most cases, we know that it must break down at some point and should be replaced with general relativity.
General relativity predicts the existence of black holes: objects with such a strong gravitational pull that nothing can escape them once they pass the event horizon. But does Newton's theory secretly predict that black holes should exist?
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John Michell predicted black holes (he called them 'dark stars') in 1783, way before Einstein was born, and even pondered how to find them. He also designed the machine Cavendish used to weigh the world. That guy was a genius.
Was really interesting to see
I enjoyed the show..Well done.
Can you do a video on Total Internal Reflection explained by QM
Something I've noticed about the classical velocity term at 2:05 is that if you plug it into the lorrentz factor of special relativity, you get the general relativity term for gravitational time dilation.
I assume this also isn't a coincidence?
This is an excellent observation! Yes, again, this is a reflection of the fact that certain constants in the Schwarzschild solution are fixed to give the results of Newtonian gravity far from the black hole.
(Though I think it is closer to a coincidence that the gravitational time dilation looks so much like the time dilation one sees in special relativity, but I would bet that there is a relationship there as well)
@@zapphysics I think this is actually by design because the free falling observer can see this time dilation, but sees spacetime as flat. So it is what they would see if they dropped a bunch of clocks in a classical gravitational field. But I'm currently having a very hard time wrapping my head around spacetime curvature from an inertial observers perspective...
@@narfwhals7843 @WWLinkMasterX I've given this some more thought and I think I have a more satisfactory answer here. The TL;DR answer is that Narf is pretty much correct, but there are some subtleties that I want to address.
The first thing to talk about is what the Schwarzschild solution actually describes. These coordinates describe the experience of an observer at a fixed radius infinitely far away from the black hole. So, as Narf suggested, consider this observer dropping a clock which then free-falls toward the black hole. We care about how much time goes by on this clock.
Again, as Narf talked about, the equivalence principle tells us that a freefalling observer in a small enough (in space *and* time) reference frame has the same experience as an observer in flat spacetime. Specifically, we want the change in the clock's time at some radius R. Since it is freefalling, the clock will only sit at this radius for some infinitesimal time, dt, so if the clock is very small spatially, then it will feel like it is in flat spacetime at this radius, so the time dilation should be given by the time dilation from special relativity. So, what we have to do is figure out how fast the clock is moving at this radius.
But this is just the inverse of the question asked in the video: instead of finding the speed we need to shoot an object at radius R for it to just make it to infinity, we want to find the speed of the object dropped at infinity with zero initial velocity once it reaches a radius R. The two calculations are equivalent, just the direction of the velocity is flipped. So, in the Newtonian case, one finds of course that the clock will be travelling at the escape velocity associated with that radius. It turns out that if you do the same calculation in GR, you get exactly the same result. This would not be the case if we didn't fix the constant in the Schwarzschild solution so that the relativistic results reduce to the Newtonian results, so here we see the connection.
So, by this argument, one can find the gravitational time dilation for a clock at radius R by just plugging in the escape velocity into the Lorentz factor (there is a much easier way to find the same result by just using the metric, but this argument is much more intuitive if you are more familiar with special relativity). Note that this will change if we give the clock some not-insignificant angular momentum (like in the case that we want to find the time dilation of an observer who is orbiting near the black hole), but as long as the tangential velocity of the orbit is small compared to the speed of light, we can neglect this contribution.
Sorry for the huge wall of text, but I hope that clears things up!
The connection between the Lorentz factor and the escape velocity equation is just noticing that the time dilation of a point in a gravitational field can be calculated from the escape velocity at that point. So, you can just plug the escape velocity of a point into the Lorentz transform and you will get the time dilation experienced at that point due to the gravitational field. One might view this as space-time in a gravitational field 'falling over' the point at the escape velocity, and thereby creating a time dilation that is equivalent to the object travelling through space-time at that same speed. This is the waterfall model of space-time. Another way to view it is as 'pressure' where the escape velocity determines the pressure experienced by an object, and that moving through space also creates a pressure that slows down time relative to an object that is not experiencing that pressure. Keep in mind that the gravitational acceleration (e.g. 10 m/s2 at earth's surface) at a certain point does not determine time dilation - only the escape velocity. Two objects experiencing the same gravitational acceleration can experience very different time dilations. An interesting question is what are the properties of space-time that make traveling through space-time equivalent to being in a gravitational field with the same gravitational potential. Is it a flow, a pressure, or something else? The antithesis towards and 'ether' makes asking this question highly controversial, but there is clearly a medium of some sort and looking into its properties (including how time varies in relation to the ether) seems like something that needs to be done.
@@zapphysics Newtonian mechanics does not predict black hole because you can escape Newtonian black hole without escape velocity by applying opposite force more than what force black hole applies to you but you can never escape event horizon of general relativistic black hole no matter how much opposite force you apply because in general relativity gravity is not a force it is either curvature of spacetime or flow of spacetime towards centre of mass and inside black hole your future points towards singularity therefore you can't escape general relativistic black hole
Great video
6:31 also that's such a great fan art
3:29
Light is affected by gravity this is guaranteed by both newtons law of gravity and Einstein‘s general theory of relativity,
In fact in all rigorous theories of gravity the bending of the passage of starlight is unavoidable
the gravitational acceleration from gravity is GMm/r^2, if m=0 like for light, theres no acceleration.
@@lih3391Yes, but light also has no mass, meaning that any finite force would cause infinite acceleration, meaning that no other result would make sense.
In a sense, Newton’s laws predict an acceleration of all objects independent of their mass, which could include light.
It’s not that Newton’s laws either predict that light is or is not affected by gravity. It can’t do either. Light is almost this limiting “indeterminate form” that Newton’s laws cannot resolve, but GR can.
Will you stream again
Yes! I am hoping to do a stream either next week or the week after!
Big fan of green planets.
I take a non-realist stance that assigns less hope of any manmade theory of physics be close to ontologically true laws of nature. Even if one is hopeful, your definition of effective theory is quite broad.
In 5:50, I note c jumps from being speed of light to being a constant of distance on one slide. Something else if you're interested: There's no sounds of "child" in Schwarzschild. The "Schwarz" means "black" and "Schild" means "shield". Your Profs might not know better either, but the sound of it is quite different.
It is definitely a very valid philosophical viewpoint that the only theories we can ever hope to have are effective theories in that there is always something deeper that can be described and our mathematical theories always break down on some level.
The point about 5:50 can be marked up to bad notation on my part (whoops!). In reality, the constant appearing in the Schwarzschild solution ends up being the Schwarschild radius itself!
pog