If you could see a desk fall into an even horizon, and on the right of that desk was a slowly flashing light bulb, and on the left was a mirror, positioned so that it reflected the light bulb's light towards a distant observer.

As the desk fell toward the event horizon, due to time dilation, you might see that the time between the flash of the light bulb of the right and the flash from the mirror got greater and greater.

But isn't light supposed to have the same speed in what ever time frame you are in, so that in reality, the time between the flashes would appear the same, but the distance between the right side of the desk and the left would get shorter?

So from this thought experiment, would it be fair to say that objects that fall towards the event horizon, of a black hole, appear, to the distant observer, to get smaller and smaller?

And I suppose, if there is no time experienced at the event horizon, from the distant observer's point of view, that maybe an object shrinks to becoming a single point, but never quite makes it?


I'm not sure, when previewing this post, I wondered if I had got it the wrong way around, and the desk would appear to get bigger.....

So what would happen?

What would happen to the timing of the flashes, and what bearing might that have on the appearance of the size of the desk?

My guess would be that the desk would appear to get flatter. In that sense the light and the mirror would appear to get closer together relative to our reference frame.

The mirror has a warning on it saying that objects appear closer

I've been thinking.

If the time period stays the same, BUT we think/know that the time it must have taken to cross that distance would have been much longer if the desk had stayed the same size, there fore the desk would look smaller, and shorter.....

I'm still not sure.....

been thinking again.

if the time between the light bulb flash, and the mirror flash actually did get longer, then as we assume that light always travels at the same speed; then if the time period doubled, then it would look like the light had traveled twice as far, and therefor the desk would appear twice as LARGE, in both up and down dimensions.

hmm...

In reality, the parts of the desk closest to the hole would accelerate away from the further parts due to tidal forces.

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We're running amok on a little flight of fancy here, I'm afraid.

If we're in Schwarszchild coordinates and considering stationary observers, the spatial part of the metric tells the story:

dr^2/(1 - R/r) + (r dO)^2 + [(r sin O) dphi]^2

where R = 2GM/c^2, the Schwarzschild radius.

Tangential rulers are the same, but radial rulers are shortened by a factor of sqrt(1 - R/r) as one goes deeper in the Schwarzschild well towards the horizon.

The coordinate speed of light is c*(1 - R/r) in the radial direction and
c*sqrt(1 - R/r) in the tangential directions in the asymptotic observer's coordinates. Local observers, as always, see the speed of light as 'c' in all directions.

This is for stationary observers, now. Moving observers, such as radial free fallers and orbiting observers will suffer additional SR contraction effects in the direction of motion.

-Richard

so would the time between light bulb flash ,and mirror flash, get greater, as the desk approached the event horizon?

what frame of reference is the light going between the light bulb and mirror, in?
Is it in the desk's, frame of reference, or the distant observer's?

It's a well-known scientific fact that people and telephone poles shrink (get smaller) the further away from an observer they are. If we use our meter stick to measure them at a distance, they are clearly smaller. However, since their meter stick strinks along with them, they don't notice their shrinkage. In fact, they think it is we who shrink.

For a long time I was under the impression that gravitational lensing
would make objects appear to be smaller (or farther away) as they
approached the event horizon. But it seems that I had it backward.
Lensing should actually make objects approaching the horizon appear
larger. The effect would not continue for a long time, though, since
the light from the object redshifts to invisibility and the number of
photons reaching an outside observer per second rapidly decreases
to zero. Milliseconds, not minutes or years.

-- Jeff, in Minneapolis

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As light travels at normal speed, for say some white mice in a survival cage on the desk, but that the time it takes to go from the bulb to the mirror is dilated for an distant observer, then to that distant observer the time period between the light bulb flash, and the flash from the mirror must increase, so the apparent distance must increase by the same factor that the time period decreased.

That must mean that if the time dilation increases the time period of the flashes by a factor of 2, then the apparent length, and thus height of the desk, is doubled.

maybe?

When will Universal Studios finish their mathematically correct Black Hole Bonanza thrill ride?

I think the reverse. Time dilation accompanies length contraction, but only along the single axis parallel to the relative velocity vector, proportional to the gravitation differential, or the vector sum of each.

Again, for a *stationary* desk (one can imagine moving the desk deeper in the well very slowly) the flash frequency would be dilated by the time dilation factor, sqrt(1 - R/r).

Assuming the desk is aligned so that it's depth is along the radial direction, the tangential distances, the width and height, would not be affected. The depth would get shorter by the same sqrt(1 - R/r) factor.

I don't exactly understand what you mean by "what frame of reference the light is in". The light travels a null path through space-time between events. Being a null path, there is no valid reference frame around the light world line. But all valid references can map the path the light takes in their coordinates.

The light travels at 'c' locally in the desk reference frame. In the distant observer's frame, the coordinate speed of that tangential null path is
c*sqrt(1 - R/r). The time dilation of the local observer just cancels that factor and the local speed is 'c', as it always will be.

-Richard

I just meant, is the light traveling at c, between the light bulb and the mirror, as far as the distant observer can see, or is it slower, due to time dilation?

Does the time period between light bulb flash and mirror reflection of flash slow down, is what I want to know.

Because if it slows down, but the speed of light is c, for the distant observer, then it must have appeared to travel further, hence maybe the desk would look bigger.....

If this were true, then maybe as the desk got closer to the event horizon, the desk would appear to expand and wrap itself around the black holes event horizon....Which makes sense to me as other wise you might have an oddly shaped event horizon like a potato, where more mass had gone in on one side than another, if you see what I mean.


Any way here is a photoshop I made to clarify what I mean by a desk, with flashing light bulb and mirror falling into a black hole.

As the desk fell toward the horizon tidal forces would both pull front to back and squish right to left so as long as the desk remains looking somewhat like a desk it will physically get shorter due to tidal forces.

Lepton,

For Frog March's purpose, you can assume that the desk has not yet
reached a region where tidal forces significantly spaghettify it.

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

The words Frog March and assumption don't go together

Does light travelling in the direction of the tangent? travel faster than light travelling in the direction of the radius? ( please insert answer no here )

If not then what is the proper dialation of time ( to keep SOL constant ) ?

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If my idea is correct and that the length of an object is larger by a factor by which time is slower, ie time it takes something to happen, like radioactive decay, is doubled then the length of an object is doubled, then I have calculated that the Sun appears 2784 meters wider than it really is, or is if you were at the surface.

Sun Mean diameter 1.392×10⁹meters

http://scratchpad.wikia.com/wiki/CAT:time_dilation

Would that mean that it appears 2 parts per 1000,000 dimmer?

Also maybe Mercury's orbit has a few hundred meters smaller radius than it appears, from far off, or roughly on Earth?

Would any of that be measurable?

from my idea(ie not main stream, still no one else was answering), the speed of light is the same in all reference frames(well that isn't my idea, my idea to follow>>); what changes is the apparent size of an object; so if time is dilated by a factor of 2, objects appear twice as long, then it looks like it traveled twice as far(for the distant observer), thus keeping the speed of light the same; so , with my idea, objects get twice as long.

Although this idea seems to suggest that a black hole will appear to get bigger as time goes by, as the matter appears to get closer to the event horizon, maybe...

Can we please keep this one section clear of ATM ideas so it remains a valid educational source?

The light would travel normally until the Black Hole rips the atoms of the desk, lamp, and mirrior apart. That is if I got my facts straight. Black Holes aren't really my forte.

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The thread intrigued me. And whether or not it adds something new does not matter. If I want to give my oppinion on a topic, reguardless of when the last post was, I should be able to.

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