Question about frames of reference and clocks

[AndyCiep]

Hey everybody, this is my first post!

I've always had a problem understanding why, if a space-explorer left on a ship, traveled at nearly the speed of light for a while, and then came back to earth, he might have only aged a few months whereas the people of Earth would have aged many years.

Here's what I understand:
1. I understand that every frame of reference has it's own time. Thus, the ship has different time than the earth.
2. I also understand that at faster speeds, time slows down. Thus, on the ship, time will pass more slowly than it does on earth.

Now, due to (1) and (2) - it looks like I've already answered my own question. But here's what trips me up..

3. I also understand that every frame of reference is entitled to regard itself as being "at rest". For example, if two ships pass - both have the right to say they are sitting still and the other one is moving.

So, really - my problem is the following.. isn't it equally correct to say that the space-explorer (from the first paragraph) was sitting still in his spaceship, and that the Earth zoomed away from him, traveled at nearly the speed of light for a while, and then returned back to him?? And thus, shouldn't the earth's time have slowed? So then the people of Earth would have aged only a few months and the space-explorer would be the one who aged many years?

Seems to me that both cases are true. That the earthlings would see the space-explore's time slow relative to theirs, but that the space-explorer would see the Earth's time slow relative to his. So what happens when they meet up in the end and compare watches? Who's watch is ahead and who's is behind??


I'm very excited that I just happened to stumble across this website tonight. I've read a lot of the posts and know that there are a lot of very bright people out there answering questions. I'd love to have this one solved for me (it's been a thorn in my side for a while )

Thanks much!
Andy

 

[chroot]

This is known as the "twin paradox," and is heavily, heavily discussed all over the web.

The essential difference between the stationary and traveling twin is that the traveling twin cannot consider himself at rest. At some point during his trip, he has to fire his thrusters, causing accelerations and changing his direction. The fact that he feels accelerations for some part of the trip indicates he is not always at rest, and no longer has the privilege of considering himself "at rest" with respect to his earth-bound twin.

You can find much, much more analysis here:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

- Warren

 

[robphy]

But here's what trips me up..

3. I also understand that every frame of reference is entitled to regard itself as being "at rest". For example, if two ships pass - both have the right to say they are sitting still and the other one is moving.

Every inertial frame of reference (that is, one moving with constant speed in a straight line) is entitled to regard itself as being "at rest". In such a frame, a ball that is dropped lands directly below where it was released.

 

[yogi]

Hi Andy - the problem you have referred to (the twin paradox) has different solutions for different people. If you initially simply say that two twins pass by each other at some relativistic velocity v, the situation is perfectly symmetrical - since neither is able to claim that he is at rest and the other is moving. But if you then say, the wayfaring twin travels a distance x to a distant planet Alpha, the situation is no longer symmetrical - because you have defined a proper distance in the earth-alpha frame where the stay at home twin kicks back and reads a book. You now have two things defined in the earth-alpha frame - the proper time measured by a clock in the earth-alpha frame, and a distance "x" specified in the Earth alpha-frame. SR asserts that the spacetime interval in each frame is invarient during transformation - so based upon the velocity between the traveling twin and the earth, and using the fact that the spacetime interval is the same in both frames, you can calculate the rate at which the clock escorting the traveling twin must run. It is always less than the rate at which the clock in the Earth frame runs. You do not need to get into the issue of turn-around acceleration etc, because once you specify that the trip distance is to be measured in the earth-alpha frame, there can be only one clock rate in the traveling twin's frame that satisfies the foundational principle of the special theory --- that the intervals in each frame are invarient.

 

[AndyCiep]

Thanks everybody! All three posts helped a lot. I forgot that only inertial frames can be considered at rest. That really changes the situation. I've got it now.

Thanks again.

 

[robphy]

"The test of all knowledge is experiment. Experiment is the sole judge of scientific "truth"." - Feynman, Leighton, Sands

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html asks "What is the experimental basis of Special Relativity?"

 

[Moonbear]

I'm going to start out by pointing out I'm not a physicist, and have only a very basic understanding of special relativity, so my question may be overly simplistic, but this seems to be the place for it as it relates to the topic of this thread.

How do we know that things like time dilation aren't just an experimental artifact? In other words, how do we know our clocks don't just malfunction at speeds close to the speed of light? My understanding is that the evidence for time dilation (or length contraction) is based on the behavior of atomic particles at high speeds. At very slow speeds, we use fairly inaccurate clocks based on crystal vibrations (the average Timex watch), and at those higher speeds, things such as particle decay are used, so the fact that a particle takes longer to decay from the observer's perspective is taken to mean the time in the frame of reference of that particle has dilated, or moved more slowly than for the observer. However, what if those particles just don't behave the same at those high speeds, due to some other factor? For example, what if there is additional vibration that cancels out the intrinsic vibration of the particle and slows its decay, or a dampening of some sort of oscillations? I'm not really sure about how these particles decay to know what other factors could slow that decay without actually altering time, just our ability to measure it. This may be a very naive view, but this seems the place to find out.

 

[swansont]

How do we know that things like time dilation aren't just an experimental artifact? In other words, how do we know our clocks don't just malfunction at speeds close to the speed of light? My understanding is that the evidence for time dilation (or length contraction) is based on the behavior of atomic particles at high speeds. At very slow speeds, we use fairly inaccurate clocks based on crystal vibrations (the average Timex watch), and at those higher speeds, things such as particle decay are used, so the fact that a particle takes longer to decay from the observer's perspective is taken to mean the time in the frame of reference of that particle has dilated, or moved more slowly than for the observer. However, what if those particles just don't behave the same at those high speeds, due to some other factor? For example, what if there is additional vibration that cancels out the intrinsic vibration of the particle and slows its decay, or a dampening of some sort of oscillations? I'm not really sure about how these particles decay to know what other factors could slow that decay without actually altering time, just our ability to measure it. This may be a very naive view, but this seems the place to find out.

It's not particle decay, it's an oscillation between two states.

If there is a different mechanism in action, it exactly mimics the effects of relativity. If the mechanism is wrong, why does it predict the right results? And independent of the clock used - there are different species of atoms used in atomic clocks. They have been compared to quartz oscillators and oscillators based on nuclear interactions as well. All of this confirmation reduces the chance that the theory is wrong.

 

[Phobos]

Perhaps someone else can elucidate, but isn't the fact that we detect muons (very short half-life) from the sun reaching the Earth's surface a clock-free verification of time dilation?

 

[russ_watters]

It's not particle decay, it's an oscillation between two states.

That's an atomic clock. Particle decay (Moonbear) is a separate phenomenon that gives us evidence for time dilation.

 

[Moonbear]

Do the results of such experiments, whether relying on particle decay or on oscillations, "exactly" match predictions by the theory of relativity, or has the theory been modified based on the results of these experiments? Within other areas of science, it is common to modify theories as new experimental evidence becomes available, so I'm wondering to what extent has the same been done with the theory of relativity. Because I take it from the responses I've gotten so far that the strength of the theory is that it has been shown with multiple ways of measuring the time dilation effect, but if every time a new method is employed, the theory is tweaked a bit to account for minor differences in methods, or one of those "physics fudge factors" known as a constant is introduced to the equation, then this might not be the case. I know, it's not very likely a non-physicist with a minimal understanding of the theory is going to come along and find a huge flaw in it, so I know my questions are not likely to poke holes so much as to help me understand where the gaps in my own knowledge lie.

The other thing I've been puzzling over since asking the first question is how do we even define time? I can't think of any way to define it, or to define the measurement of it, without using it in its own definition. For example, I was thinking of the atomic oscillations example...that's the easiest for me to understand...it seems we measure time by the number of oscillations that occur, because we know that a fixed number of oscillations occur in a given time, which already sounds redundant. But, how do we know that number is stable? Don't we need a way to measure time to confirm our time measurement is correct? And does temperature affect the behavior of the particles being used for these experiments? Again, I'm thinking that decay rates, at least of some things, are slowed by lower temperatures, so if this same particle you're using to measure or detect time is held at absolute zero, such that all motion, and thus decay, stops, is time considered to stop?

Also, if there's a place where this has been hashed out over and over again already, pointing me in the direction of a link would be fine too if you don't have "time" to answer these more basic questions.

Thanks for the answers so far!

 

[swansont]

Do the results of such experiments, whether relying on particle decay or on oscillations, "exactly" match predictions by the theory of relativity, or has the theory been modified based on the results of these experiments? Within other areas of science, it is common to modify theories as new experimental evidence becomes available, so I'm wondering to what extent has the same been done with the theory of relativity. Because I take it from the responses I've gotten so far that the strength of the theory is that it has been shown with multiple ways of measuring the time dilation effect, but if every time a new method is employed, the theory is tweaked a bit to account for minor differences in methods, or one of those "physics fudge factors" known as a constant is introduced to the equation, then this might not be the case. I know, it's not very likely a non-physicist with a minimal understanding of the theory is going to come along and find a huge flaw in it, so I know my questions are not likely to poke holes so much as to help me understand where the gaps in my own knowledge lie.

No, the theory is the same. The equations are quite straightforward for special relativity and no "fudge factors" have been added.

The other thing I've been puzzling over since asking the first question is how do we even define time? I can't think of any way to define it, or to define the measurement of it, without using it in its own definition. For example, I was thinking of the atomic oscillations example...that's the easiest for me to understand...it seems we measure time by the number of oscillations that occur, because we know that a fixed number of oscillations occur in a given time, which already sounds redundant. But, how do we know that number is stable? Don't we need a way to measure time to confirm our time measurement is correct? And does temperature affect the behavior of the particles being used for these experiments? Again, I'm thinking that decay rates, at least of some things, are slowed by lower temperatures, so if this same particle you're using to measure or detect time is held at absolute zero, such that all motion, and thus decay, stops, is time considered to stop?

The second is defined in terms of an unperturbed atom - no other interactions. In trying to realize the second, you either have to eliminate perturbations or measure how much of an effect they have. For example, magnetic fields change the oscillation rates (second-order Zeeman shift), but the field cannot be zero in a cesium beam atomic clock (or similar devices) - you need to tell the atoms which way is "up", electromagnetically speaking, so you add a carefully controlled field and calculate the frequency shift from it, and incorporate that into the results.

Nuclear decay is unaffected by temperature. Also there is a distinction to be made between time changing rates and clocks changing rates.