Equivalence Principle and Rindler Horizons

[sbaker8688]

TL;DR Summary

Does standing on the earth (or any massive body) generate a Rindler horizon way off somewhere in the direction of your feet?

I just thought of this. I'm not an expert, so cut me some slack if I get something wrong.

Given:

1) Acceleration is supposed to produce a Rindler horizon.

2) If I understand it correctly, under Relativity and/or the Equivalence Principle, standing on (for example) the Earth is the same as being accelerated upward, i.e. you are being accelerated (where as if you were in free fall towards the earth, you would not be accelerating, you'd just be following a geodesic in warped space).

Question: Does standing on the Earth (or any massive body) generate a Rindler horizon way off somewhere in the direction of your feet? If not, why not?

No equations or techno-babble please.

Thanks.

 

[berkeman]

Summary:: Does standing on the Earth (or any massive body) generate a Rindler horizon way off somewhere in the direction of your feet?

No equations or techno-babble please.

You want to discuss Rindler horizons without any techno-babble?

 

[Ibix]

Does standing on the Earth (or any massive body) generate a Rindler horizon way off somewhere in the direction of your feet?

No.

If not, why not?

Rindler horizons are a flat spacetime phenomenon. The (approximately) equivalent notion in a gravitational field is an event horizon, and whether or not you have one of those depends on whether you are hovering above a black hole or not.

 

[sbaker8688]

Rindler horizons are a flat spacetime phenomenon.

Source? Nothing I've read, and no video I've watched describing Rindler horizons, said anything about flat spacetime.

 

[Ibix]

Source? Nothing I've read, and no video I've watched describing Rindler horizons, said anything about flat spacetime.

The Wikipedia page on Rindler coordinates says it in the first paragraph...

 

[sbaker8688]

If "Rindler coordinates" means "Rindler horizons," and if "techno-babble blah-blah flat Minkowski spacetime" means "Rindler horizons are a flat spacetime phenomenon," then I accept this.

I would ask how warped spacetime cancels or otherwise doesn't allow the effect, and I'd ask how warped does spacetime have to be to cancel the effect (after all, all spacetime is a little warped, even if ridiculously small warpage), but something tells me it's beyond the scope of a simple question-answer forum.

Thanks.

 

[PeroK]

No equations or techno-babble please.

Whoever has the effrontery to study physics while neglecting mathematics should know from the start that he will never make his entry through the portals of wisdom.

Roger Bacon (1214-94)

 

[sbaker8688]

Whoever has the effrontery to study physics while neglecting mathematics should know from the start that he will never make his entry through the portals of wisdom.

Roger Bacon (1214-94)

Most things should be explainable in some version of 'plain speak,' using pictures, analogies, and the like to explain concepts. One should not need PhDs in Mathematics and Physics to try to obtain basic understandings of phenomena and ask basic questions, and if it DOES require that, one may as well not ask the question then.

I've obtained basic understandings of Special and General Relativity without having to delve into differential equations or calculate tensors or whatever. What most should aim for, before anything else, is a "picture in one's head" of what's going on, and be able to visualize things. For instance, Einstein's thought experiments. Did, or does, that require mathematics?

 

[PeroK]

I've obtained basic understandings of Special and General Relativity without having to delve into differential equations or calculate tensors or whatever. What most should aim for, before anything else, is a "picture in one's head" of what's going on, and be able to visualize things. For instance, Einstein's thought experiments. Did, or does, that require mathematics?

I agree with Roger Bacon. In any case, this is not a popular-science forum. The "I" in the thread description implies that undergraduate level physics and mathematics is expected. There is nothing against popular-science sources - there are plenty of reputable ones. But, the aim of this forum is to provide the next level of detail (and the next level of understanding). That requires an acceptance of mathematics.

Our expectation is that you have got as much as you can out of the popular sources and are prepared to roll up your sleeves and take on a bit more of a challenge - by opening an "I" level thread on here.

 

[Ibix]

I would ask how warped spacetime cancels or otherwise doesn't allow the effect, and I'd ask how warped does spacetime have to be to cancel the effect (after all, all spacetime is a little warped, even if ridiculously small warpage)

Rindler horizons boil down to the fact that if you keep accelerating your speed asymptotically approaches light speed and there are regions of spacetime that are too far behind you for light signals to catch you. In curved spacetime, acceleration doesn't necessarily increase your speed, so there's no problem sending you light signals. I suppose you could get a Rindler horizon-like effect in curved spacetime if you stayed in large fairly flat regions (i.e. where you accelerated at $a$ and spacetime curvature length scales were a lot larger than $c^2/a$ over the whole region).

something tells me it's beyond the scope of a simple question-answer foru

It's explainable here, but not without maths. How else are we going to compare acceleration and spacetime curvature?

Most things should be explainable in some version of 'plain speak,' using pictures, analogies, and the like to explain concepts.

As long as you understand that such things are like teaching you how to press play on an iPod, whereas the maths is teaching you how to play an instrument, sure. You can learn things about science that way, but reasoning with such things is risky, as the premise of this thread demonstrates.

 

[vanhees71]

No equations or techno-babble please.

This is weird. You ask a question and forbid us to answer. There's no way to discuss physics without equations. It's the only language adequate to talk about it when it comes to questions like non-inertial reference frames, particularly in the relativistic realm.

 

[Ibix]

For instance, Einstein's thought experiments. Did, or does, that require mathematics?

Absolutely yes. For example the train: certainly you can talk about lightning striking the front and rear of the train simultaneously without maths (edit: or maybe not - simultaneous means at equal times, so we've got a numerical comparison right there), but how do you evaluate whether the light reaches the center of the train simultaneously without using (however unconsciously) that distance traveled is velocity times elapsed time?

 

[sbaker8688]

This is weird. You ask a question and forbid us to answer. There's no way to discuss physics without equations. It's the only language adequate to talk about it when it comes to questions like non-inertial reference frames, particularly in the relativistic realm.

I have to respectfully disagree (I'm a degreed engineer, by the way, meaning I had education in calculus, differential equations, etc).

Math actually does nothing in most cases to give you a concept, and in most cases contributes to no understanding at all, or worse it actually gets in the way. I actually saw this in school, where students merely concentrated on equations some professor was writing on the board, but they had no clue what the equations represented and had zero understanding of the concepts and ideas. They would even admit this to you if you asked them, and couldn't explain the concepts and ideas. Their only concern was regurgitating whatever equations for the test.

In electrical engineering classes I had no idea what a transistor was, because the professor didn't explain it. He just drew mathematical garbage on the chalk board that I was forced to memorize and regurgitate for tests. I didn't figure out that transistors are a combination of switches, or amplifiers, until well after school.

Concepts and visualization are what are important. Einstein thought experiments - for example elevators in free fall vs sitting on the earth, trains moving down tracks while shining a laser off in a direction, or while some guy does juggling in one of the train cars - those are important. And none of that requires mathematics, and in fact sitting at a chalk board writing a bunch of mathematics instead of drawing pictures and explaining concepts for your students does them a disservice.

The mathematics are useful if you actually have to calculate something. Beyond that, they are mostly useless. Numbers on a board are just that - numbers on a board. They are a good way for you to feel superior to others, but they largely aren't going to contribute to you teaching someone anything, or having them understand. Most will just be turned off, and leave.

Numbers are not fundamental. If you see a phenomenon happening that you want to explain, the video of the phenomenon - the movie or picture that forms in your head - that's fundamental. The math is secondary, and is more of a tool.

 

[vanhees71]

There is no way to formulate a concise concept without math. As a degrees engineer you have learned much more math than you need to understand non-inertial reference frames in special relativity!

 

[Nugatory]

If I understand it correctly, under Relativity and/or the Equivalence Principle, standing on (for example) the Earth is the same as being accelerated upward, i.e. you are being accelerated (where as if you were in free fall towards the earth, you would not be accelerating, you'd just be following a geodesic in warped space).

That’s not quite right, even though there are many popular explanations that will misdirect you to that misunderstanding. The equivalence principle doesn’t say that standing on the Earth is “the same” as being accelerated upwards, it says that locally (for example, if we only consider what’s going on inside Einstein’s elevator) acceleration in flat spacetime is experimentally indistinguishable from (“equivalent to”) standing on the surface of the earth.

This equivalence only works locally though. Examine a large enough region and it becomes clear that gravitation and acceleration through space are not at all the same thing. Consider, for example, that in Einstein’s elevator dropped objects fall in the same direction, towards the floor - but on the surface of the Earth an object dropped at the South Pole falls in the opposite direction from an object dropped at the North Pole.
In fact, even locally the equivalence principle is not quite exact. When Einstein’s elevator is at rest on the surface of the Earth dropped objects do not fall exactly straight down perpendicular to the floor. Instead they fall towards the center of the earth, so objects dropped at opposite sides follow very slightly converging paths. If your measuring instruments are good enough you will be able to detect this effect and know whether you are accelerating in empty space or at rest on the surface of the earth. To get the equivalence principle back we’d need a smaller elevator, small enough that our instruments can no longer detect the side to side variation of the gravitational force.

So….

Question: Does standing on the Earth (or any massive body) generate a Rindler horizon way off somewhere in the direction of your feet? If not, why not?

No reason to expect a Rindler horizon here because that horizon is a global phenomenon so the equivalence principle doesn’t apply.

You can see this for yourself if you’re up for doing a bit of easy math - no technobabble, no elaborate relativistic calculations, Newton’s $F=GM_1M_2/r^2$ is all you need. First, consider the volume over which we can approximate the earth’s gravitational field as uniform; this is the maximum size of Einstein’s elevator and with reasonable assumptions about the accuracy of our instruments will be a few kilometers on a side. (But don’t take my word for it! Do the calculation yourself! What’s the difference between the gravitational field at the surface of the Earth and ten kilometers higher? How non-parallel are lines through the center of the Earth from two points ten kilometers apart?). Compare this with the distance to the Rindler horizon for an observer accelerating at a constant 1g and you will see that the equivalence principle just doesn’t apply here.

 

[sbaker8688]

Our expectation is that you have got as much as you can out of the popular sources and are prepared to roll up your sleeves and take on a bit more of a challenge - by opening an "I" level thread on here.

Fair enough. I opened "I" level because I thought there's no way a grade school or high school level has even heard of a Rindler horizon (I know I hadn't), and they only taught basic physics at any high school I ever went to.

 

[Dale]

Summary:: Does standing on the Earth (or any massive body) generate a Rindler horizon way off somewhere in the direction of your feet?

If not, why not?

No equations or techno-babble please.

The Equivalence Principle is a local principle and the Rindler Horizon is not local. So the Equivalence principle cannot be used the infer the existence of a Rindler horizon in curved spacetime.

I have updated the thread to be a B level thread in accordance with the “no math or jargon” request

 

[Dale]

Source? Nothing I've read, and no video I've watched describing Rindler horizons, said anything about flat spacetime.

In addition to the Wikipedia page you can calculate the curvature tensor in the Rindler metric and see that it is flat. That requires math to show, so without the math you will just have to accept the assertion.

I would ask how warped spacetime cancels or otherwise doesn't allow the effect

The Rindler horizon is the boundary of a region of spacetime from which a Rindler observer cannot receive any light signals. No such region exists for a static observer in a spherically symmetric spacetime without a true event horizon.

It isn’t really about the spacetime so much as the observer. In a spherically symmetric spacetime with no event horizon there exist observers that cannot receive signals from some regions of spacetime. A static observer is just not such an observer.

I'd ask how warped does spacetime have to be to cancel the effect

There is no amount of spacetime warping that cancels or activates the effect. It is about the observer, not the spacetime.

Math actually does nothing in most cases to give you a concept, and in most cases contributes to no understanding at all, or worse it actually gets in the way.

This is your thread so it is completely in your discretion to ask for B-level responses. I have answered accordingly. However, I do disagree with this as a general claim. For me, understanding of relativity came from learning about four-vectors. I had studied all of the various thought experiments and so forth and gained no conceptual understanding until I got a unified mathematical framework for thinking of relativity.

It is possible to have a concept-only understanding and it is possible (but rare) to have a math-only understanding, but the best is to have both. So the claim that math contributes nothing to understanding is wrong. A concept-only understanding is possible, but it will always be inferior to a concept-and-math understanding.

 

[Vanadium 50]

Math actually does nothing in most cases to give you a concept, and in most cases contributes to no understanding at all, or worse it actually gets in the way

Is that true? Or does it really keep you from thinking you understand a subject when you only have a superficial knowledge?

But I wasn't here to complain about that. I was complaining about "technobabble". That sounds kind of insulting. Isn't it better to actually get the answer first and only insult it then? Besides, if we can't use numbers and we can't use words, how can we answer your question?

 

[Dale]

I was complaining about "technobabble". That sounds kind of insulting.

I agree. A more neutral term would be “jargon”. I think the non-neutral wording probably exacerbated the usual responses that such comments usually encourage.

 

[vanhees71]

It's not insulting, it's stupid. You cannot expect answers when forbidding the language to be used to give one. I'd recommend just to close this thread!

 

[sbaker8688]

I don't understand how the word "technobabble" is seen to be insulting, when no one was insulted. Indeed no one was even posting at the time when the word "technobabble" was used. It was not meant to be insulting (indeed, there wasn't even anyone here to insult, and one can't insult empty space, or the air), and if someone doesn't like the word for some reason, just replace it with another word you like more. One poster here suggested 'jargon,' so use that one. Or if you don't like that, how about 'technospeak'?

Another poster said it was stupid to not want mathematical or 'technospeak' answers. Okay, at this point, I guess I've come to the wrong place. I can look for another forum, and I will. Having said that, I do believe I got what I came here for. Basically, I was told that Rindler horizons are flat space phenomena. So that answers my question.

Now you may close the thread, if that makes people happy.

 

[Dale]

Having said that, I do believe I got what I came here for. Basically, I was told that Rindler horizons are flat space phenomena.

Again, I would say that it is the observer that is more important than the spacetime. In a spherically symmetric spacetime with no event horizon there exist observers that cannot receive signals from some regions of spacetime. A static observer is just not such an observer.

 

[sbaker8688]

Again, I would say that it is the observer that is more important than the spacetime. In a spherically symmetric spacetime with no event horizon there exist observers that cannot receive signals from some regions of spacetime. A static observer is just not such an observer.

1. I'm not sure what you mean by "spherically symmetric" spacetime. Do you mean curved or warped (non-flat)?

2. I'm not sure what you mean by "static observer." Do you mean one that is not moving? (I get that with relativity, there is no "not moving," there is just "moving or not moving with respect to something else."

 

[PeroK]

1. I'm not sure what you mean by "spherically symmetric" spacetime. Do you mean curved or warped (non-flat)?

2. I'm not sure what you mean by "static observer." Do you mean one that is not moving? (I get that with relativity, there is no "not moving," there is just "moving or not moving with respect to something else."

1) Spherically symmetric refers to a physical system which depends only on some radial parameter and is the same in all directions. To a first approximation the solar system is spherically symmetric about the Sun: the spacetime/gravity around the Sun depends only the distance from the Sun, not on the direction.

2) Static in this case means relative to some implied system of coordinates. In the example of the Solar system it would mean an observer who is at rest relative to the Sun. Or, in your original example, someone standing on the Earth is (approximately) static relative to the Earth.

 

[PeroK]

I've obtained basic understandings of Special and General Relativity without having to delve into differential equations or calculate tensors or whatever. What most should aim for, before anything else, is a "picture in one's head" of what's going on, and be able to visualize things. For instance, Einstein's thought experiments. Did, or does, that require mathematics?

I wanted to answer this point directly. First, we start with Newton's law of gravity. Newton proved mathematically this the inverse square law of gravity led to elliptical orbits. This is not obvious from from the law itself. It requires a page or two of undergraduate mathematics.

Anyone can understand Newton's law of gravity and that it describes the solar system (to a good approximation). But, it could never have been developed or accepted as a theory without the mathematical calculations that showed that it matched reality. To claim that "mathematics gets in the way" is false. Mathematics was so essential to the theory that Newton had to invent the new mathematics of the calculus himself.

Then we have Einstein's theory of relativity. Einstein was only able to realize his theory using advanced differential geometry. Again, rather than getting in the way, mathematics was at the heart of the theory. That GR predicts elliptical orbits is even more obscure and requires more sophisticated mathematics to show.

But, how does anyone know that Einstein's theory trumps Newton's? Without mathematics, you have no way to compare the theories and develop a test. GR, for example, predicts the famous bending of light round the Sun. But, Newton's gravity predicts a common acceleration independent of mass and if we assume that applies to light, then we can say that the Sun should bend light in Newtonian gravity as well.

It turns out, if you do the calculations, that GR predicts twice the bending of light that Newton predicts. There is no way to see this without mathematics.

Ultimately, mathematics is essential for:

Developing a theory of gravity in the first place (anyone can draw pictures of the planets orbiting the Sun - but that is just the experimental data; it's not a theory of gravity).

Confirming that the theory matches experimental data and making predictions for experiments not yet carried out.

 

[Vanadium 50]

That GR predicts elliptical orbits is even more obscure and requires more sophisticated mathematics to show.

I'll do you one better. Where Newton predicts ellipticcal orbits, GR predicts rosettes that are almost, but not quite, elliptical. This difference is measureable, measured, and better agrees with GR than Newton.

 

[Dale]

1. I'm not sure what you mean by "spherically symmetric" spacetime. Do you mean curved or warped (non-flat)?

That is the type of spacetime that you get around a planet, which is what you asked about in your OP. It is a curved spacetime.

Do you mean one that is not moving? (I get that with relativity, there is no "not moving," there is just "moving or not moving with respect to something else."

Yes, I mean one that is not moving with respect to the planet, which is what you asked about in your OP.

Both of those comments were simply indicating that I was answering your specific question in the OP, not making claims about other scenarios in general.

 

[sbaker8688]

Newton proved mathematically this the inverse square law of gravity led to elliptical orbits. This is not obvious from from the law itself. It requires a page or two of undergraduate mathematics.

I totally agree.

But, it could never have been developed or accepted as a theory without the mathematical calculations that showed that it matched reality. To claim that "mathematics gets in the way" is false. Mathematics was so essential to the theory that Newton had to invent the new mathematics of the calculus himself.

I totally agree.

Einstein was only able to realize his theory using advanced differential geometry. Again, rather than getting in the way, mathematics was at the heart of the theory. That GR predicts elliptical orbits is even more obscure and requires more sophisticated mathematics to show.

I totally agree.

Without mathematics, you have no way to compare the theories and develop a test.

I totally agree.

It turns out, if you do the calculations, that GR predicts twice the bending of light that Newton predicts. There is no way to see this without mathematics.

And again, I totally agree.

I never said that Einstein shouldn't have used math to develop his theories, or that they weren't at the heart of them, or that you could and should compare theories and test them without using math, or that you shouldn't use math to see that GR predicts twice the bending of light that Newton's does, etc. I also didn't say that math got in the way of Einstein (or anyone else) developing his theories. What I said was, when lay people are trying to understand this stuff on a basic level, the math gets in the way, and shouldn't be used, or at least not used as much as it is.

 

[vanhees71]

It's the other way around! Einstein always lamented that he had not enough math at his disposal to formulate (at least) GR. He was indeed regretting not having attended the math lectures by Minkowski when he was a student in Zürich. It's ridiculus to think that you can understand physics without math. It's a different issue with popular science. There you have of course to avoid the math to be understandable to the addressed audience. It is, at least as far as I can imagine, impossible to discuss the topic of this thread, i.e., Rindler coordinates and Rindler horizons to locally describe the region close to an event horizon in GR, without using the adequate math.

This is the 30th posting within this thread, and we've not achieved anything to answer the question yet. QED.

 

[sbaker8688]

It is, at least as far as I can imagine, impossible to discuss the topic of this thread, i.e., Rindler coordinates and Rindler horizons to locally describe the region close to an event horizon in GR, without using the adequate math.

The question was if a Rindler Horizon forms when you stand on a massive body. The answers can be yes, no, or nobody knows, and none of those answers require math, nor was math desired.

 

[Dale]

This is the 30th posting within this thread, and we've not achieved anything to answer the question yet.

I disagree. The question has been answered, and at a B level, without math.

 

[vanhees71]

Well, it depends on what you understand as an answer of a scientific question. For me it's answered in the other thread here:

https://www.physicsforums.com/threa...ties-advanced-discussion.1007892/post-6551199

and this is really not overly overambitious math!

 

[Vanadium 50]

The answers can be yes, no, or nobody knows, and none of those answers require math, nor was math desired.

That's disingenuous.

You got an answer like this, immediately challenged it by demanding a source, and then complained that the source used "technobabble".

 

[H_A_Landman]

The weak-field approximation for time dilation is Td = 1 + 𝜙/c². The Rindler horizon occurs when 𝜙 = -c²; in a 1 G field, that is about 1 light year "below" you. At that point, the formula gives Td = 0, i.e. time stops running.

In SR, the Rindler horizon actually exists, because the linear equation is exact. But for gravity, it's only the first order approximation. The actual equation is Td = exp(𝜙/c²). [Einstein 1907] Time never stops unless 𝜙 goes to minus infinity. So there is no Rindler horizon. (There may still be black hole event horizons, etc.)

The Einstein equivalence principle says that gravity and acceleration are locally indistinguishable. Here "locally" means "over short enough distances that the linear approximation is good and you can't see higher order terms". It doesn't say that they are globally indistinguishable. They're not.