ask a physicist

[freyar]

Well, that's quite a few duplicate posts! No saving time or space there...

second, regarding the effects of gravity on time are you suggesting that perhaps the very gravity of 'big blue' earth can effectually alter the time it takes for a signal to traverse in a round trip, moving a velocity of 'C' from a gps to a satellite and back to the gps?

if so, then would it be possible, but not necessarily plausible, that gravity has an affect on RF signals of any frequency? Is there a way to test this, or has it already been tested?

as for Doppler shifts, I know of Doppler radar shifting for radio navigation of aircraft, I guess it works for gravity force as easily as magnetic.

There are two different effects at work. The first, which is what I mentioned before, is about gravitational time dilation. It's really pretty simple though counter-intuitive: suppose you take two precise atomic clocks (or whatever kind of perfect clock you want to imagine). You make sure in a lab that they are running at the same rate when they are sitting side by side. Then you put one on the surface of the earth and one on a rocket that holds position above the earth (ie, not moving compared to the earth). While the one on the ground ticks off one second, the one in the rocket will tick off more time according to general relativity. If you put the clock in an orbiting satellite, you also have to worry about special relativity since the earth and satellite are moving relative to each other, so that would make the clock in the satellite tick off less time. The special relativity and general relativity effects don't quite cancel. The way it effects GPS is that the GPS satellite signal is basically broadcasting the satellite's time, so your phone can compare to its own time and figure out how far the signal travelled. If GPS did not account for how relativity affects the running of time, it just wouldn't work. So this is not only tested but used all over the world every day. But just to be clear, this isn't altering the time for the signal to travel a certain distance, it's really altering how time flows in different places.

The other thing you stumbled on, the change of frequency, as AbduAlhazred says, is the gravitational Doppler shift, which is also due to this time dilation effect but can be thought of as the photon gaining kinetic energy as it falls. This has been measured, first by Robert Pound and Glen Rebka, who "dropped" a photon off the Harvard University physics building. It's actually quite a clever experiment, but I won't get into the details or else this post will go on for too long. But note that the normal Doppler shift is due to the relative speed of emitter and receiver while this is again due to location in a gravitational field.

 

[Scott DeWar]

There are two different effects at work. The first, which is what I mentioned before, is about gravitational time dilation. It's really pretty simple though counter-intuitive: suppose you take two precise atomic clocks (or whatever kind of perfect clock you want to imagine). You make sure in a lab that they are running at the same rate when they are sitting side by side. Then you put one on the surface of the earth and one on a rocket that holds position above the earth (ie, not moving compared to the earth). While the one on the ground ticks off one second, the one in the rocket will tick off more time according to general relativity. If you put the clock in an orbiting satellite, you also have to worry about special relativity since the earth and satellite are moving relative to each other, so that would make the clock in the satellite tick off less time. The special relativity and general relativity effects don't quite cancel. The way it effects GPS is that the GPS satellite signal is basically broadcasting the satellite's time, so your phone can compare to its own time and figure out how far the signal traveled. If GPS did not account for how relativity affects the running of time, it just wouldn't work. So this is not only tested but used all over the world every day. But just to be clear, this isn't altering the time for the signal to travel a certain distance, it's really altering how time flows in different places.

Could you explain further on this, as in Why does the time in a satellite or rocket differ from time on earth? Would time b3 different on Mars? I a guessing yes, and on the moon as well.

What happens? Does time bend in different places? To quote #5,"Need more input!" [movie: short circuit]

 

[AbdulAlhazred]

Could you explain further on this, as in Why does the time in a satellite or rocket differ from time on earth? Would time b3 different on Mars? I a guessing yes, and on the moon as well.

What happens? Does time bend in different places? To quote #5,"Need more input!" [movie: short circuit]

You can understand it in terms of Special Relativity like this: When you stand on the surface of the Earth its indistinguishable from being on an accelerating rocket ship. You can easily equate acceleration and time dilation in SR (I will leave it as an exercise for you, but most intros to SR will present it fairly succinctly). Its effectively the same thing, you'd experience the same time dilation on the surface of the Earth, or on a rocket ship accelerating at 1G, relative to an observer who's not accelerating.

 

[Umbran]

You can understand it in terms of Special Relativity like this

You can, but I wouldn't advise it. While you can deal with accelerating reference frames in special relativity, it is a hassle. And, in fact, the better and more accurate answer comes from general relativity anyway.

 

[Umbran]

Could you explain further on this, as in Why does the time in a satellite or rocket differ from time on earth?

We know that it does. The effect is measurable, and we have a model that can calculate how it changes, to high degrees of accuracy. We can describe, as a sort of physical interpretation of that model, what is happening.

But *why*? I don't think we can actually answer that question yet. To answer a why, we must understand the universe one level down from the thing we are describing. Perhaps a string theory, or whatever quantum gravity we come up with (if we ever come up with one) may answer the why. For now, we can more talk about what happens...

Would time b3 different on Mars? I a guessing yes, and on the moon as well.

Yes.

What happens? Does time bend in different places? To quote #5,"Need more input!" [movie: short circuit]

#5 is alive!

Special Relativity, and by extension, General Relativity, are the inevitable fallout of one simple basic observation - to all observers, everywhere, light travels at the same speed.

Say I am sitting on a train that is moving at 50 mph. Say I pick up a baseball, and throw it to the front of the car. And I measure the throw to be going at 50 MPH, relative to me and the car.

My friend, sitting beside the track as the car and I go by, would say the ball was moving at 100 mph, relative to her and the ground outside. for her, the ball was moving at 50 MPH before I even threw it, after all, so my arm only adds to that speed.

That's not how light works. If I fired a laser toward the front of the car, I'd measure it at 186K miles per second, and my friend would measure it going the *same* speed. The speed of the train doesn't add to the speed of the light.

How is that possible? How can we both see the same speed? There's only one way to do that. Speed is the distance something covers over some period of time. If the speed is immutable, then distance and time must not be! Time and space with bend, fold, and mutilate such that everyone, everywhere, sees light moving at the same speed. Time and space measurements are not absolute and objective for all, but are *relative* to the observer - thus "Relativity".

So, one answer to "Why?" is "Because light moves at the same speed for all observers." But, why does light travel at the same sped for all observers? Um, well, it just does!

(And people tell us quantum mechanics is weird. Piffle!)

Anyway. So, Special Relativity is called that because it is the special case - describing the alteration of time and space in frames that are not accelerating with respect to each other. They can be in motion - like my friend says she's sitting still on the ground, and I'm moving by on the train, but they aren't accelerating.

General Relativity is the general case, more complicated, that also handles frames that are accelerating with respect to each other.

Newton tells us that Force = Mass * Acceleration. Therefore, if you feel a force, you are under an acceleration. So, if you feel your weight, you are under acceleration. So, on the planet, you are under acceleration. If the ground wasn't under you, you'd start to speed up going downwards, right? Thus, General Relativity gives us the answers here. Unfortunately, to really do General Relativity requires some really heavy math - tensor calculus - which I can't even write properly in plain text of these boards. So, I'll go to being descriptive....

You, on the ground, and the satellite in orbit, are under different accelerations - you are accelerating more than the satellite is. So, for both of you to see light move at the same constant speed, you must have different clocks and rulers.

Note that I mentioned clocks *and* rulers. It isn't just that time bends - space bends too. In relativity, space and time are dealt with in largely the same way, which is why you hear us refer to "spacetime", as a unit, inseparable. We can think of a duration as merely a distance traveled through the time dimension, just as a separation between two points is just a distance though a space dimension.

So, you and the satellite are both accelerating. If you compare clocks and rulers, they'll be different. So, somewhere between you and them, space is bent. It is bent because each of you feels the force of gravity. The force of gravity is there because the Earth has mass. Ergo, mass bends spacetime!

Really big masses bend spacetime so much that it curves back in on itself - this is a black hole. Things fall in, and never come out, because all the paths out are bent back around to be paths in! Smaller masses bend spacetime less. So, the clocks on Earth, on the Moon, and on Mars will all be different, as the masses of the bodies they are on are different.

 

[fuindordm]

Newton tells us that Force = Mass * Acceleration. Therefore, if you feel a force, you are under an acceleration. So, if you feel your weight, you are under acceleration. So, on the planet, you are under acceleration. If the ground wasn't under you, you'd start to speed up going downwards, right? Thus, General Relativity gives us the answers here. Unfortunately, to really do General Relativity requires some really heavy math - tensor calculus - which I can't even write properly in plain text of these boards. So, I'll go to being descriptive....

Just to add a gloss to Umbran's very nice answer:

Special Relativity can be derived from the assumption that light travels at the same speed in every reference frame.

General Relativity can be derived from the same assumption, plus a second assumption that inertial mass and gravitational mass are identical (or at least proportional). That second assumption is called the Equivalence Principle, and it can be expressed in several other ways having to do with the nature of reference frames, but that's the simplest and my personal favorite. The tensor calculus required by general relativity stitches together lots of local, small-scale, and essentially flat coordinate systems into global coordinate system with curvature that satisfies both assumptions. It is rather analogous to modeling a curved surface as a patchwork of flat tiles, like what game consoles do to render 3D graphics.

The equivalence principle is one of my favorite mysteries to introduce to first-year physics students. They all learn F=ma and F=mg in short order, but there is nothing in Newtonian physics to explain why the same physical property plays two such different roles. The first one resists a change in motion due to any external force; the second actually creates a force on other objects. Lots of very clever experiments were done before and after Einstein to find out whether the two masses really had the same value in all cases.

Maybe string theory has something to say about that as well? I know it does some very clever things with gravity.

Ben

 

[Umbran]

The tensor calculus required by general relativity stitches together lots of local, small-scale, and essentially flat coordinate systems into global coordinate system with curvature that satisfies both assumptions. It is rather analogous to modeling a curved surface as a patchwork of flat tiles

I think it is important to note that they are an infinite number of infinitely small tiles! As opposed to a few, or some large but finite number.

 

[freyar]

Some very nice answers from Umbran and fuindordm here. I can't say much as I'll be at a workshop all day today, but I'll try to comment on string theory tonight.

 

[fuindordm]

I think it is important to note that they are an infinite number of infinitely small tiles! As opposed to a few, or some large but finite number.

Indeed! Hence the calculus. The local reference frames are infinitesimals, and solving Einstein's equation for general relativity yields a large number of coefficients that fully describe the geometrical properties of the 4D space-time. I had to do this to trace photon trajectories around a black hole for a post-doc projects, and I can testify that the math is quite painful.

 

[Umbran]

I had to do this to trace photon trajectories around a black hole for a post-doc projects, and I can testify that the math is quite painful.

Yah. I walked myself through the details of Hawking's "The Large Scale Structure of Space-time" (which is basically "A Brief History of Time" but with all the math) for fun.

But then, I read the Silmarillion for fun, too.