1

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 09/01/2019 21:28:34 »

Einstein did not posit a train moving at light speed.

Wrong. Einstein noted that if his train moved faster, he would see the clock tower clock move more slowly and if it went at the speed of light, the clock would appear to slow to a halt.

Which is why I said 'even in principle'.  One can communicate faster than light with such a rope.  I can build an infinite energy engine with such material.

Wrong. If you learn how to set up relativistic thought experiments you'll learn that the only physical traits you are allowed to idealize are those that do not alter the outcome of the experiment. As I explained, the rope and mirror are metaphors to show the point of reflection of the light beam.

The answer is very dependent on how the light is observed down there, but you're not observing it at all.

Wrong. There needn't be an observer at the mirror. If you want to set up a different experiment and place an observer at the mirror, that's fine. I didn't do that because this setup is simpler and reveals the result I was trying to find.

It isn't infinite anything if the light doesn't reach the event horizon.  If it does, nothing is reflected, so there is no light observed at all coming back, shifted or not.

This thought experiment uses what is called "reductio ad absurdum". I begin by assuming that a Schwarzschild black hole is possible and that it is possible for matter to travel to the event horizon. Then I show that this is impossible because it would require infinite time. Because anything that cannot happen in finite time is impossible, I conclude Einstein was correct that black hole event horizons are impossible.

You say the mirror motion is fixed and finite, and you measure it by counting winch revolutions of your hypothetical unstretchable rope.  I can allow that I think, but I don't think you ever reach the black hole using such coordinates.

Correct. Nothing moving at a finite speed can travel to an event horizon in finite time. Not light and certainly not anything moving slower than light.

You have no observer specified, so I cannot accept this.  Our observer is on the platform and any relativistic shift is undone by the return trip.

I don't really care if you understand it or can accept it. It is a fact of causality that the light beam cannot have an infinite sequence of light waves until after the source has generated the light waves. If you aren't able to apply conservation of energy (gravitational blueshift/redshift) and causality to solve a physics problem, I can't help you.

2

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 09/01/2019 19:41:04 »

And yet gravity waves from objects falling in cease abruptly as the event horizon is crossed.  Sounds like it falls in to me.

No, they don't. In fact, the ringdown of merging black holes lasts longer than predicted and does not show an abrupt termination. It fades but does not present an abrupt cutoff.

3

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 09/01/2019 18:12:39 »

Yes, in the experiment the light goes to the mirror and back. But, if the event horizon is a finite distance from the platform then, if the mirror is lowered into the event horizon, the light beam will cease to be reflected when the mirror reaches and passes into the event horizon.

Agree with all that.

The length of rope would be finite.

That depends how it is measured.  Using Schwarzschild coordinates, yes, it would be finite.
The rope is stretched due to tension and also contracted due to dilation, so using the rope as a measurement isn't the best tool.

But, as the experiment makes clear, an infinite length of rope must be paid out for the mirror to reach the event horizon.

That's using different coordinates than Schwarzschild coordinates then.

I don't use the Schwarzschild coordinates because the Schwarzschild Radius, Rs, is not a unit of distance through space. Rs is the apparent radius at which an event horizon would form if viewed from an infinite distance. The fact that it takes longer for light to travel from 3 Rs to 2 Rs than it takes to go from 4 Rs to 3Rs shows that it's not a measure of distance in space.

The fact that it takes light infinite time to travel from 2Rs to 1Rs means nothing can ever fall to an event horizon. This is because the Shapiro Delay is infinite.

4

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 09/01/2019 18:08:46 »

I did this diagram to help make the thought experiment easier to visualize:
https://photos.app.goo.gl/2BqU6nZW85oToXw77

All sorts of invalid conclusions can be drawn from invalid premises.
The picture shows an infinite strength rope which can be shown to violate special relativity.  You cannot lower a mirror to an event horizon even in principle.

Anyway, the mirror is depicted as having not yet arrived there, so the rope has finite tension on it, and it works.  So long as the winch is not moving the mirror, the scenario pretty much is what I'm talking about.  The picture says the winch is moving at some constant rate, and that means the mirror is not stationary, so a redshift will be observed at the platform because the path is getting longer.  Relativity has something to say about exacty how redshifted that light will be, since it will not be a constant redshift like you would get for a mirror moving away but not into a gravity well.

This is a correctly structured thought experiment. If you study Relativity you'll learn about Einstein's train that travels near and even at the speed of light. The physical constraints of normal matter are not relevant in thought experiments. The mirror is just a metaphor to identify a point in space where the light beam is imagined to reverse direction. The entire experiment is set up to make conceptually clear how a light beam behaves in a gravity well.

The Doppler redshift due to the motion of the mirror is fixed and finite. Because its finite it is insignificant compared to the infinite blueshift/redshift due to gravity.

If you accept that the blueshift of the light beam down to the event horizon will be infinite then you must accept that infinite time must pass at the light source before the front of the light beam can reach the event horizon.

5

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 09/01/2019 17:44:33 »

If I put a mirror stationary (relative to the platform) near a black hole

How do you define, "near a black hole"?

Outside the event horizon somewhere, but deeper in the gravity well than is the light source.

As the experiment shows, and the Shapiro Delay confirms, light cannot travel from any point in space to an event horizon in finite time. How are you defining two points, stationary WRT each other, to be "near" each other when light cannot travel from one to the other in finite time?

The light is not traveling to the event horizon.  It goes to the mirror and back.

How are you defining distance?

I didn't specify any distance.

Yes, in the experiment the light goes to the mirror and back. But, if the event horizon is a finite distance from the platform then, if the mirror is lowered into the event horizon, the light beam will cease to be reflected when the mirror reaches and passes into the event horizon. The length of rope would be finite.

But, as the experiment makes clear, an infinite length of rope must be paid out for the mirror to reach the event horizon.

6

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 09/01/2019 17:31:17 »

I did this diagram to help make the thought experiment easier to visualize:
https://photos.app.goo.gl/2BqU6nZW85oToXw77

7

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 09/01/2019 17:26:09 »

As I keep repeating, all these effects are quite real, but irrelevant.

I think I see where you're getting confused. The blueshift is not irrelevant but the very crux of the argument.

If the light beam travels from the platform to the event horizon, the beam will be infinitely blueshifted. That means the downward beam will contain infinitely many wave cycles. That means, *before* the front of the light beam can reach the event horizon, the light source must generate an infinite sequence of light waves. This requires infinite time at the light source. This means, before the front of the light beam reaches the event horizon, infinite time must pass at the light source. That is a causal sequence and is therefore frame independent. There are no valid frames of reference from which the front of the beam can reach the event horizon before infinite time has passed at the platform.

And, because the location of the platform is irrelevant to the validity of the thought experiment, the result is true for all points in space.

I hope this clarifies it for you.

8

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 09/01/2019 17:15:36 »

If I put a mirror stationary (relative to the platform) near a black hole

How do you define, "near a black hole"? As the experiment shows, and the Shapiro Delay confirms, light cannot travel from any point in space to an event horizon in finite time. How are you defining two points, stationary WRT each other, to be "near" each other when light cannot travel from one to the other in finite time?

How are you defining distance?

9

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 09/01/2019 17:10:37 »

Correct again, but we're looking at the reflected beam from the frame of the platform from which it was sent, reflected by a mirror stationary relative to that platform.  Regardless of any gravity well in which the mirror might be, that is going to result in no red or blue shift as seen by our platform observer.

Exactly correct. Gravitational redshift is entirely reversible. Traveling into space of lower gravitational potential energy, the light is blueshifted. Then, when the light travels back to the platform, the gravitational blueshift is exactly reversed by the gravitational redshift because the light is returning to a point of the same gravitational potential energy as it started.

If the mirror is moving downward at a constant speed, there will be a Doppler redshift of the light beam but that will be constant throughout the experiment.

10

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 03/01/2019 00:38:06 »

Energy is not conserved over different reference frames, so that property is being applied in an invalid manner here.

No, that's incorrect. All frames under consideration in this problem are stationary with respect to the black hole. All light is traveling only radially. Energy is conserved.

OK, I was speaking of the frame of an observer falling in.  The frame you speak of (inertial, stationary with the BH, at the event horizon) is an invalid reference frame, but an observer in a frame close by (one meter outside the EH) will observe an arbitrarily large blue shift of the distant observer, so I agree in that sense.

No, it's not invalid. The thought experiment is a perfectly valid relativistic thought experiment. Nothing in the experiment entails anything being stationary at the event horizon. Maybe you should read the original post and work through the thought experiment.

11

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 02/01/2019 21:07:27 »

Energy is not conserved over different reference frames, so that property is being applied in an invalid manner here.

No, that's incorrect. All frames under consideration in this problem are stationary with respect to the black hole. All light is traveling only radially. Energy is conserved.

12

Physics, Astronomy & Cosmology / Re: Why is it called dark matter instead of dark gravity?

« on: 02/01/2019 18:37:51 »

Whatever is producing the gravity moves slower than c. This is why it's referred to as "matter". It's something with non-zero rest mass.

13

Physics, Astronomy & Cosmology / Re: Is time dilation rigorously predicted from first principles?

« on: 02/01/2019 18:32:45 »

The time dilation of general relativity can be predicted correctly from first principles (universality of c, conservation of energy, Einstein-Planck relation, and causality).

A light beam generated at a source in space stationary with respect to a gravitational mass and shone down toward the mass will be blueshifted. This is because it is traveling from a point of higher gravitational potential energy, GPE, to one of lower GPE. This means an observer lower in the gravity well will see the light as having a higher frequency. But, the number of light waves reaching the lower observer is identical to the number of light waves generated at the source. So, the same number of light waves pass the lower observer in less time than the time required for them to be produced.

The only way to get this to work is for time to pass more slowly for the lower observer than for the higher observer.

This is how I discovered the Shapiro Delay (I'd never heard of it) and this method yields the correct values for both time dilation and Shapiro delay. It's not surprising such simple models can reveal what's going on since these are the sort of thought experiments Einstein used to produce Relativity in the first place.

14

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 02/01/2019 18:10:44 »

The light does in fact get there, and beyond.  Rocks really do fall into black holes, with nothing unusual about the event.  No Hawking radiation observed by the rock for instance.  It just doesn't fall into the black hole in the frame of this distant observer is all.

As with all of Relativity, the observations of all observers are consistent. However, there is no possible way to make the infinite value of the time observed by any observer (not only distant) stationary with respect to the black hole match the finite time you suggest. If the falling object reaches the event horizon in finite time then that event must be observable outside of the event horizon within finite time. But, as you say, it is not observable.

The Shapiro delay is infinite. That means light cannot travel to an event horizon in finite time. Unless you are suggesting that Shapiro is wrong?

15

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 02/01/2019 18:07:17 »

But not true for the observer falling in.

This is not correct. The falling observer measures finite time in their fall to the event horizon. That does not in any way imply that the fall ever ends. Time for the falling observer (even ignoring special relativistic effects) slows asymptotically approaching zero time passage as the observer approaches the event horizon. Just as the area under a decaying exponential curve is finite while the curve is infinitely long, the forever slowing observer never reaches zero.

16

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 02/01/2019 17:01:15 »

The gravitational potential between those two points is finite, but enough for escape speed to be c. 

No, this is wrong. The event horizon is defined as the point where the gravitational potential energy barrier is infinite and that is why the escape velocity is c. To accelerate a test mass to c requires infinite energy. It's not a finite energy barrier unless there's no event horizon.

17

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 02/01/2019 16:58:51 »

The solution is that the light never quite reaches the event horizon, but slows down to a near halt. The same applies to matter falling in - during the entire lifetime of the universe, that material never reaches the event horizon (unless the event horizon moves further out if the black hole expands). The calculations that suggest that objects can cross the event horizon (and that light crosses it too) are based on the idea that clocks never really slow down, so objects are imagined to go on falling through the event horizon from their own point of view and continue on down to a singularity, but this could only happen after more than an infinite amount of time has gone by for the rest of the universe, which means there are no singularities yet and that all the stuff falling towards a black hole centre is frozen in place at the same distance from the centre as it was when it stopped at where the event horizon was at the time it stopped there. The black holes should evaporate away (due to Hawking radiation) before that material has a chance to move any further in, so in reality most of it can never reach the singularity, but perhaps the light can - as the black hole evaporates, the event horizon will migrate inwards as the energy density just outside the event horizon is reduced, so the light will get a chance to move a bit further in. At some stage when the event horizon disappears and the light is free to to go straight through what was the centre of the black hole, it will be shoot out the other side, liberated, never at any stage being infinitely blue-shifted.

I agree with your interpretation (except for one point). I think you've correctly understood what happens.

I personally interpret the situation a bit differently. Since Relativity is based on the universality of c, I interpret the time delay of  light passing through a gravity well as space dilation... essentially, the rubber sheet model. If space didn't dilate exactly the same amount as time then c wouldn't be universal when measured within every frame of reference. 

18

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 02/01/2019 16:52:56 »

The change to an infinite blue shift happens at the singularity in the middle; not at the EH.

That's wrong. The blueshift from any point in space to the event horizon is infinite just as the redshift up from the event horizon to any point in space above the EH is infinite. The blueshift downward is equal to the redshift upward. That's a simple consequence of conservation of energy.

19

Physics, Astronomy & Cosmology / Re: Does gravity attract masses in space, or does it curve space between them?

« on: 02/01/2019 16:50:34 »

Wouldn’t it be equally reasonable to argue that things fall in the direction in which the strength of the gravitational field increases? 

The problem with attributing the acceleration to a change in field strength is that the rate of acceleration is not related to the rate of change of field strength. Any causal relation will probably have a fixed relationship.

20

Physics, Astronomy & Cosmology / Re: Is there an error in this relativistic thought experiment?

« on: 15/11/2018 01:31:58 »

The solution is that the light never quite reaches the event horizon, but slows down to a near halt.

Yes, this seems like the only explanation. The only thing it doesn't explain is why people think black hole event horizons can exist.