Basic questions on time dilation (probably already answered, sorry)

[Default]

New to PF, and while I don't know much about the science behind these things, I do come in peace. I have more a philosophical understanding of special relativity, never having worked out a formula, and can't even understand the language of those physics equations. I do, however, grasp the theories behind it (for the most part). Yet, after my basic research, I am (not surprisingly) still need some clarification...


1. Person A is traveling in a straight line, close to c, Person A experiences time pass as normal, but when observing Person B who is stationary, Person B would appear (according to Person A's perspective) to be experiencing life much faster, right?

2. If two people are observing an explosion, person A rotating the central point of explosion at super speeds, person B standing still at the same radius from the explosion point, then person B would observe the explosion before person A, right?

3. If a measurement of a moment in time increases the faster you go (time dilation), and the universe is expanding faster and faster, then our measurement of a moment here on earth, (when compared to someone floating in empty space between two galaxies) is taking longer and longer, so, with that said, what kind of factor are we experiencing time at when compared to the observer floating in empty space/time between the galaxies?

Question 3 might be a little confusing in how I worded things, let me know if you need any clarification...

 

[pervect]

Well, you'll be somewhat handicaped if you can't solve the equations, but if you can draw and interpret a space-time diagram without doing the equations, you can get somewhere.

So - if I asked you to draw the space-time diagram of a non-moving observer, and mark on that space-time diagram the set of points simultaneous with the origin in the stationary frame, then asked you to draw another space-time diagram of a moving observer, and mark the set of points simultaneous with the orgin in the moving frame, could you do it?

Or would you be like - "space-time what?" and have a blank look on your face?

Or would it be like "well, I couldn't do it, but I could understand it, maybe"?

 

[pervect]

Well, you'll be somewhat handicaped if you can't solve the equations, but if you can draw and interpret a space-time diagram without doing the equations, you can get somewhere.

So - if I asked you to draw the space-time diagram of a non-moving observer, and mark on that space-time diagram the set of points simultaneous with the origin in the stationary frame, then asked you to draw another space-time diagram of a moving observer, and mark the set of points simultaneous with the orgin in the moving frame, could you do it?

Or would you be like - "space-time what?" and have a blank look on your face?

Or would it be like "well, I couldn't do it, but I could understand it, maybe"?

 

[Default]

Well, you'll be somewhat handicaped if you can't solve the equations, but if you can draw and interpret a space-time diagram without doing the equations, you can get somewhere.

So - if I asked you to draw the space-time diagram of a non-moving observer, and mark on that space-time diagram the set of points simultaneous with the origin in the stationary frame, then asked you to draw another space-time diagram of a moving observer, and mark the set of points simultaneous with the orgin in the moving frame, could you do it?

Or would you be like - "space-time what?" and have a blank look on your face?

Or would it be like "well, I couldn't do it, but I could understand it, maybe"?

Creating & interpreting a space-time graph from a formula? No.
Theoretical diagram on aspects of space-time? Yes.

Maybe I need more knowledge of the subject before I am allowed to continue further in my questioning of things, but I thought theory was just theory. I didn't imagine my question requiring interpretation of physics formula to be answered, just goes to show how little I know of the subject.
Then again, isn't that where all this came from? Concepts tossed around and then physics brought into give mathematical proof to the theories?

Oh well, live and learn I guess, thank you for your time to read and respond.

 

[Mike_Fontenot]

1. Person A is traveling in a straight line, close to c, Person A experiences time pass as normal, but when observing Person B who is stationary, Person B would appear (according to Person A's perspective) to be experiencing life much faster, right?

No ... just the opposite. Both A and B conclude that the other person is ageing more slowly.

It's necessary to be clear about the meaning of "would appear" in your statement above. In my answer, "appear" does NOT mean "what would a TV image of the other person look like", because the TV image when received is out-of-date, because of the finite speed of the TV signal. To determine the CURRENT age of the other person, the observer has to determine how much the other person has aged since the currently-received image was transmitted. When I said "A would conclude ...", that means that A has properly corrected for the transit time of the TV image.

Mike Fontenot

 

[HallsofIvy]

The key word in relativity is "relative"!

From B's point of view, A is moving very fast relative to him and he sees A's clock as ticking slower than his. But from A's point of view, B is moving very fast relative to him and he sees B's clock as ticking slower than his.

 

[Default]

No ... just the opposite. Both A and B conclude that the other person is ageing more slowly.

It's necessary to be clear about the meaning of "would appear" in your statement above. In my answer, "appear" does NOT mean "what would a TV image of the other person look like", because the TV image when received is out-of-date, because of the finite speed of the TV signal. To determine the CURRENT age of the other person, the observer has to determine how much the other person has aged since the currently-received image was transmitted. When I said "A would conclude ...", that means that A has properly corrected for the transit time of the TV image.

Mike Fontenot

The key word in relativity is "relative"!

From B's point of view, A is moving very fast relative to him and he sees A's clock as ticking slower than his. But from A's point of view, B is moving very fast relative to him and he sees B's clock as ticking slower than his.

So if A is moving super-speed, and B is stationary, they would both observe the other’s clock tick as slower than their own.

Sorry for the limited understanding here, I just figured this forum would be the best place to get real answers that would put things into a personal perspective I could comprehend. I appreciate all patience and help.


How then, is this reconciled…

Two stationary people synchronize clocks and agree to fire off a light at every tick for 10 ticks and then stop.

One person takes off at super-speed in a perfect circle around the stationary one.

The mobile person observes the stationary persons light at longer intervals, and vice versa for the stationary person observing the mobile one.

The stationary person would have to sit around and wait for the mobile person to finish his set of 10 ticks.

If the mobile person is observing the stationary persons ticks as slow, what does he observe when he finishes his 10, and stops, realizing the stationary person finished long before him, yet only observing a few ticks for his 10?

 

[Mike_Fontenot]

So if A is moving super-speed, and B is stationary, they would both observe the other’s clock tick as slower than their own.

That's only true when both people are INERTIAL, i.e., not accelerating.

One person takes off at super-speed in a perfect circle around the stationary one.

The one who is moving at constant speed IN A CIRCLE is accelerating, and so is NOT inertial.

In this scenario, both people agree that the person moving in a circle is ageing more slowly. And, they also both agree about the correspondence between their two ages, at each instant of their lives.

Mike Fontenot

 

[Default]

That's only true when both people are INERTIAL, i.e., not accelerating.



The one who is moving at constant speed IN A CIRCLE is accelerating, and so is NOT inertial.

In this scenario, both people agree that the person moving in a circle is ageing more slowly. And, they also both agree about the correspondence between their two ages, at each instant of their lives.

Mike Fontenot

So the accelerating properties of moving in a circle brings this example back to the principles of general relativity. And the scenario explains itself when changed to moving in a straight line at a steady velocity due to the time and distance light takes reaching to and from each observer at each measure on the space-time plane, justifying the differences in time observation. Right?

Now, if I still have your attention...how silly would a general postulate in regards of time itself be to say that all things past and future (theoretically) have already happened (just like all space is already out there, we just move around in it), and it is only the observers relative position in space-time that creates a feeling of a flow of time?
Light experiences no time, and since light and time have connections, and time is already proven to be completely relative to the observer...am I just veering off into left field here?

 

[Mike_Fontenot]

So the accelerating properties of moving in a circle brings this example back to the principles of general relativity.

General relativity isn't needed unless the two people are being influenced by the gravitational field(s) of one or more very large masses. Special relativity handles accelerated motion just fine.

Mike Fontenot

 

[Default]

General relativity isn't needed unless the two people are being influenced by the gravitational field(s) of one or more very large masses. Special relativity handles accelerated motion just fine.

Mike Fontenot

...and it just keeps getting better. Thanks for the help. I suppose I need to do some more research before I can really understand how this all fits together.

 

[Mike_Fontenot]

I suppose I need to do some more research before I can really understand how this all fits together.

Start with Einstein's own little book by Crown Publishers, called "Relativity, the Special & General Theory". Just read the portion on special relativity ... save the GR stuff until MUCH later, if ever. Read that SR part of the book VERY carefully. Then read it again, and maybe even a third time. Keep at it until you thoroughly understand everything Einstein said.

DON'T skip the equations! That book doesn't require much knowledge and facility with algebra, but what IS there is essential. Do whatever it takes to be able to apply and use the Lorentz equations. You might have to get a little help from a friend who is at least a little familiar with the use of algebra.

And don't be intimidated by those complicated-looking coefficients in the Lorentz equations ... once you have specified a specific relative speed v, where |v| < c, those coefficients are just constant NUMBERS. It helps (in keeping the equations from looking more complex than they really are) to immediately replace the quantity

1 / sqrt( 1 - v*v/(c*c) )

by some single symbol ... most people use the Greek letter "gamma" for that. Then, just remember that for a given speed v, gamma is just some constant number (greater than or equal to one).

It also simplifies things to always use units for time and distance such that c = 1 ... for example, like years and lightyears. Once you do that, you can make the equations look even simpler, by just omitting all the factors of c everywhere in the equations. What remains is actually quite simple and easy to use.

Good luck.

Mike Fontenot

 

[yuiop]

The key word in relativity is "relative"!

From B's point of view, A is moving very fast relative to him and he sees A's clock as ticking slower than his. But from A's point of view, B is moving very fast relative to him and he sees B's clock as ticking slower than his.

So if A is moving super-speed, and B is stationary, they would both observe the other’s clock tick as slower than their own.

That's only true when both people are INERTIAL, i.e., not accelerating.

Hi Default,
It might seem that the answers by HallsofIvy and Mike_Fontenot contradict each other but in a way they are both right.

When the observer moving in a circle passes close by the stationary observer, the circling observer and the stationary observer each measure the others clock to ticking slower than their own. However after the circling observer completes one orbit observers will agree that the time that elapsed on the clock of circling observer during the circumnavigation is less than the time that elapsed on the clock of the stationary (inertial) observer). A little confusing but that is how it works.

The one who is moving at constant speed IN A CIRCLE is accelerating, and so is NOT inertial.

In this scenario, both people agree that the person moving in a circle is ageing more slowly. And, they also both agree about the correspondence between their two ages, at each instant of their lives.

Mike Fontenot

This is a little misleading because it glosses over the fact that they both measure each other's clocks to be ticking slower as they pass close by each other. You cannot say anything definitive about relative tick rates of clocks moving relative to each other and spatially separated until they return to a point where they are adjacent to each other again.

 

[Mike_Fontenot]

[...]
When the observer moving in a circle passes close by the stationary observer, the circling observer and the stationary observer each measure the others clock to be ticking slower than their own.
[...]

It's possible to show that, whenever the traveler is moving perpendicular to the line connecting the home twin and the traveler (according to the home twin), the home twin and the traveler will be in COMPLETE AGREEMENT about the correspondence between their ages. And they will completely agree about their relative rates of ageing, during that type of motion.

Circular motion (where the traveler remains at some constant (non-zero) distance from the home twin (according to the home twin)) is obviously a special case of the above situation (and where the motion remains perpendicular for a finite segment of the traveler's life). The traveler and the home twin remain in complete agreement even if the speed of the traveler isn't constant during that finite segment of his life.

So, in circular motion (with the home twin at the center of the circular arc), they BOTH conclude that the traveler is ageing more slowly than the home twin (and this continues to be the case, as long as the motion remains perpendicular).

Mike Fontenot