To understand what I mean, you first need to know that Einstein proposed two separate theories of relativity. Special relativity deals with systems that move relative to one another with a constant velocity. General relativity deals with systems that move relative to one another with a variable velocity. In each theory, Einstein’s only concern is that the laws of physics must work the same in both systems, regardless of the fact that they are moving relative to one another. While this seems like a common-sense idea, it leads to conclusions that make little sense.
Special relativity, for example, tells us that when objects move relative to one another, time passes differently for each object. The faster that relative motion is, the more pronounced the difference in the way time passes. For example, if a man gets in a spacecraft that travels at speeds close to the speed of light, time passes very slowly for him relative to those he left behind on earth. As a result, when he returns home, those he left behind might have aged many years, despite the fact that for him, the trip lasted only a few months.
General relativity makes conclusions that are even more strange. For example, general relativity tells us that time passes differently for objects in different gravitational fields. The stronger the field, the more slowly time passes. If a man were to travel to Mercury, for example, time would pass slowly for him compared to those he left behind on earth, because Mercury is so close to the sun that it experiences a larger gravitational field.
Now in general, people don’t travel at speeds high enough to notice how their motion affects the way time passes. In the same way, the gravitational fields we experience on earth are not variable enough to notice how they affect the way time passes. Both of these effects are important in the global positioning system (GPS), however. The satellites used in the GPS travel at high enough speeds that time really does move more slowly for them than it does for us on earth. They also are exposed to a weaker gravitational field than we are, because they are much farther from the center of the earth. As a result, time passes more quickly for them than it does for us. It turns out that this effect is the stronger of the two, so in total, time passes more quickly for the GPS satellites than it does for us here on earth. If both effects were not properly taken into account, your GPS navigational system would not work correctly.1
The important thing to realize, however, is that these effects are real regardless of how fast you are traveling or how much the gravitational field to which you are exposed is varied. It’s just that for most everyday experiences, they are simply too small to be measured…until now! Chou and colleagues have used optical clocks to measure the difference in how time passes between two objects that move at speeds as low as 4 meters per second (about 9 miles per hour) relative to one another! In addition, they have measured the difference in how time passes when an object’s elevation is changed by just 50 centimeters! Not surprisingly, the measured data agree with the predictions made by the equations of special and general relativity. 2
How were they able to perform such an amazing feat? Well, the experiment was very well designed, but the main reason is that optical clocks can provide a much more precise measurement of time than even atomic clocks. The optical clock they used, for example, was about 20 times more precise than the best atomic clock. Because of that, they were able to measure tiny difference in the rate at which time passes.
Now please understand that the importance of this study is not that it confirms the predictions of special and general relativity. Several such confirmations have already been made.3-6 Those studies, however, required either very high speeds (reference 5 used jets, for example) or relatively large differences in height (reference 4 spanned more than 70 feet). This study confirmed the predictions of general and special relativity under normal laboratory conditions.
Since I previously blogged about another confirmation of quantum mechanics, I should point out one more thing. The predictions of quantum mechanics have been confirmed over and over again in many experiments. In the same way, the predictions of general relativity have been confirmed by many experiments, albeit not as many as those that confirm quantum mechanics. However, you need to know that there are specific aspects of quantum mechanics that are in direct conflict with general relativity. One of the most important is how each theory treats the concept of time. Thus, while both have been confirmed by experiment, it is hard to understand how both can be completely correct.
That’s the great thing about science. Even well-confirmed theories present us with entertaining mysteries.
References
1. N. Ashby and M. Weiss, “Global Positioning Receivers and Relativity,” NIST Technical Note 1385, U.S Government Printing Office, March 1999
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2. C. W. Chou, et al., Relativity and Optical Clocks, Science, 329:1630-1633, 2010.
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3. B. Rossi and D. B. Hall, “Variation of the Rate of Decay of Mesotrons with Momentum,” Phys. Rev 59:223-228, 1941
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4. R. V. Pound and J. L. Snider, “Effect of Gravity on Nuclear Resonance,” Phys. Rev. Lett. 13:539-540, 1964
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5. J.C. Hafele and R. E. Keating, “Around the world atomic clocks: predicted relativistic time gains,” Science 177:166, 1972 (this experiment was repeated on its 25th anniversary, and the results confirmed special and general relativity to an even higher degree of precision)
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6. R.F.C. Vessot, et al., “Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser Phys. Rev. Lett. 45:2081-2084, 1980
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I think one of the issues here that confuses thinks is that Einstein’s Theories of Relativity have been used to support a false philosophical conclusion, that all truth is relative. The truth is that while the Theories of Relativity show that certain things once thought of as absolute are relative, it maintains other things such as the physical laws and speed of light in a vacuum as absolute and those things that vary do so in an absolute way. It does not say all things are relative though some have taken it to say so.
You are quite right, Mike. In some ways, the theories of relativity are incredibly absolutist, because they require the laws of physics to work the same everywhere. If that is to happen, then things like time, length, mass, etc. must be relative. If you believe that something like time is absolute, then you are forced to believe that the laws of physics are relative. In the end, the theories of relativity just tell us what things are absolute (the laws of physics) and what things are relative (mass, time, length, etc.).
Dr. Wile, I was excited to see your post on relativity. This is one of my favorite topics in science.
I have a question about velocity time dilation described by Special Relativity. Measured by an observer at rest, an observer in motion experiences time more slowly. However, since all motion is relative, the “moving” observer measures the clock of the observer “at rest” as ticking slower. Thus, both observers will view the other observer’s clock as ticking slower. My question is, if both observers stop moving relative to one another, what does each observer’s clock read in the end? During the journey, both clocks seemed to be ticking slower relative to the other.
Thanks for your help!
Dan, that’s an excellent question. You are quite right in your analysis. Both observers see the OTHER observer’s clock as moving slower. It seems like a conundrum, but it is not, because you are forgetting that Special Relativity tells us about a lot of things besides time dilation, and one of them is that simultaneity is not conserved between moving reference frames.
Let’s suppose we have two observers, A and B. They travel in opposite directions at 0.4c, and they have agreed to stop once they have each traveled one-half of a light year, which has been marked off in advance. When they each hit the mark, they each agree to stop. So…A moves at 0.4c until he sees the mark, and then with his inertial dampeners on, he comes to an immediate halt. To a third observer who is at rest relative to the marks that were made beforehand, this took 1.25 years (time = distance/speed = 0.5 light years/0.4c = 1.25 years). However, to A, it took only 1.15 years, which is 1.25 times the Lorentz factor 1/[square root(1 – 0.42)]. B does the same thing. When he stops, the observer at rest relative to the marks sees that it took 1.25 years, but B measures it as taking only 1.15 years. So B and A both measure that the trip took 1.15 years according to their clocks, but the observer at rest relative to the marks measures 1.25 years with his clock. All three are correct, because time moved more slowly for A and B than for the observer at rest relative to the marks.
Now…what do A and B observe about each other? A sees that B’s clock is running slowly relative to his. However, because light takes time to travel, when A stops, he will see B continuing to move until the light that comes from B’s stop gets to him. In the same way, when B stops, he will see A continuing to move until the light from A’s stop gets to him. In the end, when they each actually see the other stop, the same amount of time will have passed for each of them (1.15 years). However, unless they know special relativity, they will think the experiment failed, because they will think they did not stop at the same time. And, in fact, they did not stop at the same time as measured by THEIR clocks. However, they did stop at the same time as measured by a clock at rest relative to the marks.
Dr. Jay, thanks for posting this! Relativity is a favorite of mine.
You have emphasized in several of your textbooks that a hypothesis must go through a lot of testing before it becomes a theory, and again before it may become a law. How far would you say Einstein’s theories are from becoming scientific law? Also, could you explain the whole ‘gravity is a result of the way mass bends space’ idea? I’ve never quite understood how that ties into relativity (or if my brain is just funny and mixed up the two concepts. :P). Thanks!
Miranda, General Relativity is still relatively new to physics (about 100 years old), so while it is a well-established theory, it is certainly not a law of nature yet. Also, since quantum mechanics is also a well-established theory but is in conflict with General Relativity on some matters, I would say that even if they were both a lot older and had been through a lot more confirmation, we could not consider them laws, since the laws of nature should not contradict one another.
Explaining the “mass bends spacetime” idea is rather difficult. However, think of it this way. A particle travels through space. It doesn’t have any forces acting on it, so it is traveling at a constant velocity. Thus, it is traveling at a constant speed in a straight line. Now…suppose it passes near a planet. What does it do? It no longer moves in a straight line. Instead, its path curves around the planet. To you and me, it looks like a force has acted on it, causing it to change its velocity. We call that force the gravitational force, and we say that the gravitational force that exists between the particle and the planet changed the particle’s velocity.
However, to the particle, no force has acted on it. It is simply traveling in a straight line in space. The planet’s mass, however, has curved space. Thus, the particle is still traveling straight, but its path looks curved to us, not because a force acts on it, but because space in that region is curved. That LOOKS LIKE a force, but it is not. It is simply a consequence of how space is curved by the planet’s mass.
So the idea pertains mostly to objects in space? Last I checked, I get pulled back down no matter how high I jump. :) lol This reminds me of centrifugal ‘force’. Such a cool idea!! Thanks a million.
Miranda, the idea applies to all objects. It is just easiest to understand for objects in space. This is a bit of an oversimplification, but the same basic reasoning applies for you when you jump. You apply a force to your body, which accelerates it in the direction of the force (straight up). Your body travels straight up in space. However, the mass of earth has curved space so much near the surface of the earth that space basically makes a U-turn. Since your body follows space, it makes a U-turn, coming back to hit the earth. All the time, your body was traveling straight through space. However, space is so warped by earth’s mass that it ends up traveling right back down to earth.
Thanks for answering my question about velocity time dilation, Dr. Wile. I have another question that has to do with General Relativity.
I understand that due to the gravitational force of a black hole, there is infinite time dilation at the event horizon, meaning that time stops relative to the outside universe. Suppose a spaceship travels toward a black hole. At one point during the journey, part of the spaceship will be at the event horizon while part of it will be outside the event horizon. Since time literally stops at the event horizon, wouldn’t there be an enormous time difference between the front of the spaceship and the back of the spaceship once it has finished crossing the event horizon?
Dan, remember that for people in the spaceship, time runs normally. It is only relative to a clock far from the black hole that time in the ship runs slowly. Thus, an OBSERVER FAR FROM THE EVENT HORIZON would see a difference in how time passes from the front to the back of the ship, but remember, it is a smooth function. Thus, if you think of time as stopping at the event horizon, then half a meter from the event horizon, time has not completely stopped, but it is moving so slowly that you will think it has stopped unless you watch for a LONG time. Also, remember that at the event horizon, the outside observer will not see ANYTHING of the ship, since light cannot travel to the observer. Thus, the observer will see the ship VERY SLOWLY disappear. When time has stopped in the ship relative to the outside observer, the outside observer will not see anything coming from the ship. To an observer in the ship, nothing seems odd until the ship is destroyed at the event horizon.
Actually, I am neglecting something huge here, and that’s tidal forces. The ship will be obliterated by tidal forces long before it gets swallowed into the event horizon, but what’s a few tidal forces among friends?
What it did was warp my brain!! Just kidding. 🙂 That makes total sense. (Unlike Einstein’s explanation. Yes, I tried reading General/Special Relativity with my dad. 7 hours later, we were still only half sure.) Thanks a million!
Glad I could help, Miranda.
Lol, those annoying tidal forces! I understand that this problem could be avoided in a supermassive black hole, at least.
I know that time dilation is a smooth function as one approaches the event horizon, and that the slowing/stopping of time is only detected by an observers far away from the event horizon. But since time completely stops at the event horizon, there is an infinite gap between the rate of time at the event horizon and the rate of time anywhere outside of the event horizon. Even if an observer is 1 inch from the event horizon, time will be stopped at the event horizon relative to that observer.
So when the front of the spaceship reaches the event horizon, the back of the spaceship will be at some distance from the event horizon. Thus, relative to an observer in the back of the spaceship, time will be stopped at the front of the spaceship, and relative to an observer in the front, time will be moving very quickly in the BACK of the spaceship. (Of course, each observer experiences time normally from their own perspective.) In the end, the time differences between the front and the back of the spaceship would seem to be enormous. Am I understanding this correctly?
Thanks again!
Dan, you are understanding this correctly, but I think you are missing something. Remember, the person at the back of the ship will be unable to observe the front of the ship when the front hits the event horizon. Thus, when time stops (relative to the observer in back) for the front of the ship, the observer will no longer be able to see it. The observer, then, will see time slow down, slow down more, slow down more, and then the front of the ship will be gone. So when time stops, the observation is that existence stops as well. This is actually a philosophically pleasing result as well, at least from my perspective.
Thanks for the link. I had not actually considered that before, but the math does seem to work!
I never would have thought of it that way, that’s an interesting take. But in that case, what does the observer in the back of the ship see when he/she finally crosses the event horizon? Does he enter the black hole, only to find that the front of the spaceship no longer exists? Moreover, does he himself stop existing once he crosses the event horizon? As I understand it, objects do exist within a black hole and do not get obliterated until they reach the singularity at the center.
Dan, the problem is that as material gets absorbed in a black hole, about 10% of its mass gets converted to energy and is radiated outward. This process is called “accretion,” and it will essentially destroy the ship, anything living in it, etc. However, if we ignore that, it is commonly thought that the perception of the passage of time simply stops inside a black hole. All things are traveling to the singularity at the speed of light inside a black hole. Since our perception of time is based on things we can observe moving, when all things move at the speed of light in the same direction, it is impossible to perceive time. Does that mean time “really” stops? I guess that depends on whether time is a real quantity or just a result of human perception.
It is really not known if things get obliterated at the singularity. They become infinitely dense, but does that obliterate them? Hawking once thought the answer was “yes,” but now he says the answer is “no.” He thinks that black holes conserve information, so in the end, things are not completely obliterated. I tend to focus on things we can at least characterize with both mathematics and data, so I remain agnostic on the answer to that question.
You’re right, “obliterated” is not the right word to use; I should have used “crushed” instead. Thanks again for all the info!