Last week I gave a talk to the Northeast Ohio chapter of the Center for Inquiry on the topic “The Strange Behavior of Rulers and Clocks” where I discussed some of the implications of Einstein’s theories of special and general relativity for our notions of distance and time. After the talk, one of the participants whom I know teaches science told me that he had been unaware of one aspect of my talk and I realized that this may be generally true and so here’s a post about it.
Many people are aware of the phenomena of length contraction (which can be roughly and slightly misleadingly stated as moving objects appear to be shorter than their lengths when at rest) and time dilation (that similarly can be roughly and slightly misleadingly stated as clocks in motion appear to run more slowly than clocks at rest). This post will not deal with making those ideas more precise but instead will deal purely with the lesser-known issue of gravitational red shift and what it means.
To understand it, we should first be aware that all atoms emit light with a characteristic set of frequencies that, using diffraction gratings, can be seen as sharp lines. Exactly these same frequencies are absorbed by these atoms when you shine white light on them. The top line of this figure below shows an absorption spectrum for some atom where the pattern of dark lines tells us what frequencies are being absorbed and thus enables us to identify the atom or atoms doing the absorbing.
In stars (like our Sun) where the energy production mechanism produces a continuous range of light frequencies that we see as white light, the atoms near the surface the Sun absorb light at their characteristic frequencies and so the light spectrum that we receive will have gaps at those frequencies. This is how we identify what stars are made of. But what is significant is that while the pattern of absorption lines remains the same as what we see in laboratory analyses on Earth, the actual values of the frequencies are shifted towards lower values as seen in the second line. We say that the light has been ‘red shifted’ because red light has a lower frequency than blue light. (Alternatively we can say that the wavelengths are shifted to longer values.)
How can we explain this strange fact? Think of the frequency of the light as the number of wave peaks passing a point per second. What this experimental observation says is that an atom on the surface of the Sun that is (as a numerically simple hypothetical but unrealistic example) emitting four peaks per second will be seen by an observer on the Earth to arrive with a lower frequency, say two peaks per second. (These numbers are purely for illustrative purposes. In reality, the differences are extremely tiny which is why we do not notice these things in everyday life.) How can that be, since the speed of the light does not change? (The constancy of the speed of light is one of the major tenets of relativity.)
The explanation that we give is that the rate at which clocks run depends on the strength of the gravitational field in which they are. The larger the gravitational field, the slower the clocks and vice versa. Since the gravitational field at the surface of the Sun is larger than that on Earth, that means that the clocks there are running more slowly than the clocks on the Earth. So while the four peaks take one second to leave the surface of the Sun, they take two seconds to go past an observer on the Earth because the clocks on Earth are running twice as fast. We can say figuratively that the light waves lose energy and get stretched as they fight their way to break free of the Sun’s gravitational force and that is why the shift occurs..
This idea that the rate at which clocks run depends on the strength of the gravitational field has been pretty well tested. In fact, it is used in the GPS navigation system. The satellites of the system are at a height of about 22,000 km above the surface of the Earth and thus run at a faster rate than the clocks on the surface of the Earth, since the gravitational field up there is less than the field down here. The corrections due to this have to be built into the system because although the differences are tiny, over time the differences can accumulate and lead to significant errors.
This is one of the fascinating consequences of the theories of relativity, that our everyday notions of distance and time need to be modified.
So pardon my ignorance, but could you maybe say a bit about how these phenomena are related?
Am I wrong to think that the mass gained as one moves faster and faster is directly related to the clock slowing, and that the clock slowing can be shown mathematically to be equivalent whether one calculates it as a slowdown due to the larger gravitation field exerted by one’s spaceship whose mass has increased or whether one calculates it as an effect of velocity without reference to mass? I mean, obviously these have to be identical, but exactly how does that relationship work? Does time drop out of the equation leaving it all dependent on gravity? Or does gravity drop out of the equation leaving it all dependent on velocity? Something else?
I was just about to ask a very similar question. How can you tell precisely how much of the redshift of a star is due to its mass (gravitation) and how much is due to its relative velocity with respect to us? Or can’t you?
@Mano,
Your comment about the absorption lines in the solar spectrum reminds me of time I spent one afternoon looking through the eyepiece of a lab-sized solar spectrometer fed by a heliostat during my undergraduate days. My main memory is that there are so many lines in the spectrum.
Responses to #1 and #2,
There are three possible causes for the red shift. One is the Doppler effect that is due to the observer and the source moving apart. Another is the cosmological redshift which is due to the expansion of space. And the third is the gravitational red shift of this post.
The Doppler effect is not applicable here since the velocities are not only small, the motion of the Earth is tangential to the direction of the light coming from the Sun, so there would be no Doppler shift. The cosmological red shift is a phenomenon that occurs for stars that are very very far away, and the Sun is clearly not in that category. That leaves only the gravitational red shift.
Sunday Afternoon @3,
Yes, the observed spectrum is not nearly as clear as in the image given because there are many different elements and they each produce their spectra and what we see is the combination of all of them. But astrophysicists have ways of fitting the elements to the lines.
The Earth’s orbit is slightly eccentric, while the gravitational redshift for the Sun is very small. So, it turns out that the changing Doppler shift as the Earth travels in its elliptical orbit is comparable in magnitude to the constant gravitational redshift of the Sun. It’s hard to measure gravitational redshifts of stars, but this is almost always a very small correction to the Doppler shifts from their motions in space towards us or away from us. Compact stellar remnants like white dwarfs can be exceptions, and the gravitational redshift from the surfaces of neutron stars are very large.
Mano wrote:
Wow -- you got the subject I was studying in one attempt! The ‘look through the real instrument’ was by way of a demonstration of how complicated real observations are compared with our undergraduate labs where we did spectroscopy of a gas lamp using, wait for it… photographic plates -- remember those???
Years ago, there was a long discussion on the Bad Astronomy forum with a relativity denier who was very confused about time dilation. He seemed to think that relativity was making claims about the effect of velocity on clocks.
The actual physicists in the discussion kept trying to make him understand that the effect was on time itself, not clocks per se. He never got it (or perhaps, consciously or not, refused to get it).
The constancy of the speed of light is one of the major tenets of relativity.
Yay -- finally somebody spelled it right!
Pierce @#9,
Spelled what right?
Mano @ # 10 -- The word usually presented as “tenant”.
Pierce,
Really? I have never seen that.
A Google search for “tenants of liberalism” comes up with 8,670 results (after explicitly eliminating the suggested correction); “tenants of conservatism” produces 6,250.
Actually, I had expected orders of magnitude more hits -- as a copy editor, I notice that all over the place.
CD @1: I’m dreadfully late to this thread, dunno how I missed it.
Yes, you’re wrong. There is no mass increase of the ship. There’s an energy increase relative to slower inertial frames. But the problem with your picture can be readily seen; if you can increase the speed to arbitrarily close to c, the supposed increased mass would eventually form a black hole. But an observer moving with the same instantaneous velocity would simply see a stationary object with the original rest mass; no black hole.
What you’re talking about is what used to be called “relativistic mass”. Einstein hated it, and it might be worth reading a paper by Lev Okun in which he talks about “the pedagogical virus of relativistic mass.”.
Yeah, I’m with Rob and Lev. The concept of relativistic mass leads to all manner of problems of interpretation and should be abandoned.