Did Richards Really Do Away with Einstein?

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As Reed Cartwright noted in a short, brilliantly titled essay yesterday, Discovery Institute Senior Fellow Jay Richards thinks he has found a flaw in the theory of relativity. The theory of relativity is one of the most successful scientific theories ever, and it has been verified time and again with remarkable precision. This month’s issue of Discover Magazine, for example, notes that a clock runs measurably faster at a high altitude than at sea level. A nonscientist criticizing relativity is about like a lawyer criticizing evolution; both are in over their heads.

My own knowledge of relativity, while evidently more profound than Mr. Richards’s, is still not up to par, so I contacted my colleague Victor Stenger, author of Has Science Found God? and asked him to comment on Mr. Richards’s essay. Here is the bulk of his reply, beginning with a quotation from Mr. Richards’s essay.


My vague understanding is that time slows down as you go faster. When travelling at the speed of light, [sic] time stops. If you actually could travel at the speed of light, you would – in your own frame of reference – arrive at your destination instantaneously, no matter how long it took in the frame of reference of your home planet.

This is not quite right. The moving clock slows only for an observer in another reference frame. It does not slow down in its own reference frame (my italics).

So, for the hypothetical photon released just after the big bang, the “time since the big bang” is basically 0.

Only in the photon’s rest frame, and a photon is never at rest.

However, I think I see the point he is trying to make. It is true that an observer moving at a speed near the speed of light relative to Earth would in fact measure a very small time since the big bang.

Just picking a number, let

v=0.999 999 999 999 999 999 999 999 999 999 999 998c,

where c is the speed of light. The Lorentz factor gamma = 1/sqrt[1 - (v/c)2] can be well approximated for v near c by 1/sqrt[2(1-(v/c))].

So here,

v/c = 000 000 000 000 000 000 000 000 000 000 000 002 = 2 x 10-36, and

gamma=1/sqrt(4 x 10-36) = 5 x 1017.

A clock moving at this speed would measure the lifetime of the universe to be

(13.7 x 109 year)/(5 x 1017) = 2.74 x 10-8 year = 0.86 second.

But that’s the whole point of what Einstein said. There is no absolute time. In our reference frame, the universe is 13.7 billion years old.

Mr. Richards is dead wrong when he suggests that thousands of physicists have missed this point. He should learn some physics before he criticizes physicists.


I would add that relativity is conceptually difficult and counterintuitive. It is impossible to understand without knowing the mathematics, and the results often contradict ‘common sense.’ Mr. Richards, who admits to only a ‘vague understanding,’ is simply wrong in saying that the age of the universe is the same everywhere. It is not even the same at the top of Mount Everest as at the shore of the Dead Sea; because clocks run faster on Mount Everest, the universe is older there than on the Dead Sea.

Mr. Richards writes of a subject he does not understand or perhaps chooses not to understand. His essay is of a piece with pronouncements on evolution by Discovery Institute Fellows.

References and notes.

The essay by Mr. Richards may be found at http://www.idthefuture.com/index.ph[…]b=1&pb=1.

Bob Berman, ‘A Twisted Anniversary,’ Discover, May, 2005, p. 30.

Victor J. Stenger is Professor Emeritus of Physics and Astronomy at the University of Hawaii, and Adjunct Professor of Philosophy at the University of Colorado. He is author of five published books including Has Science Found God? (Prometheus, 2003), with two more on the way. http://www.colorado.edu/philosophy/vstenger.

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Over at the Thumb, Matt Young (physicist) has posted Vic Stenger's (physicist) comments on Jay Richards' (not-physicist) post on Einstein. Bottom line: Mr. Richards is dead wrong when he suggests that thousands of physicists have missed this point. He ... Read More

117 Comments

I’m sorry if this is a stupid question, but I thought that clocks would move slower on Mt. Everest than at sea level because points farther from the center of the earth travel with greater velocity than points closer. What am I missing? Thanks.

phaedrus Wrote:

I’m sorry if this is a stupid question, but I thought that clocks would move slower on Mt. Everest than at sea level because points farther from the center of the earth travel with greater velocity than points closer. What am I missing? Thanks.

You are missing the dilatation caused by the curvature of space-time, i.e. gravitation. Gravitation is weaker on Mt.Everest compared to the sea level.

I am very sorry, but the first quotation I sent to Victor Stenger is not by Mr. Richards but from an e-mail by Nicholas Matzke. I somehow conflated Mr. Matzke’s e-mail, which contained quotations from Mr. Richards’s article, with the article itself. Here is what Mr. Richards actually wrote:

If Big Bang cosmology is broadly true, then right now, everywhere in the universe, it’s the same time since the big bang. (There are complexities having to do with the inhomogeneity of the universe here, but let that pass for now.) It’s not like it’s 13.7 billion years old around here, but only 2 billion years old in some other galaxy. Of course we can’t look and see what time it is in the Andromeda galaxy, since it’s a couple of million light years away. But that’s simply a limit on what we can observe directly. It’s still at least roughly the same cosmic time there. So Einstein didn’t do away with a universal time, even if he and his interpreters often say that he did.

Mr. Richards did not “admit” to a “vague understanding,” and I apologize for writing that he did. The error is entirely mine.

You are missing the dilatation caused by the curvature of space-time, i.e. gravitation. Gravitation is weaker on Mt.Everest compared to the sea level.

The point is that the clocks run at different rates in the 2 locations, so the age of the universe (or anything else) is different in the 2 locations. There is no absolute time.

No honest question is stupid.

Although unfortunately Matt Young has inadvertently misled Vic Stenger regarding the quotation from Richards, this in no way makes Richards’s “rebuttal” of Einstein anywhere close to being correct. Stenger’s explanation in itself is correct, even if not directly addressing Richards’s error. As to what Richards has actually written, is just gobbledygook making no sense whatsoever. It hardly can be replied to in a meaningful manner because it is so far from anything scientifically reasonable that there is simply no common ground for a meaningful discussion of that matter between qualified physicists and Richards.

Regarding the time intervals becoming zero in a frame of reference attached to photons (this notion was suggested by Schroeder) such a notion is meaningless because photons, unlike any entities possessing rest mass, cannot be attached to any frame of reference. If they were, they would have zero speed in such a frame, but it is imposssible because all photons always move with the same speed (in vacuum) in all frames of reference (the speed of light). This notion is in fact the seminal concept of special relativity - all the rest of that theory is derived from it. PS. I’ve taught all parts of physics, both on undergraduate and graduate levels, for more than half a century.

In reply to Professor Perakh: In fact I sent Professor Stenger the correct paragraph by Mr. Richards, along with the paragraph by Mr. Matzke. I cut out that paragraph when I prepared the essay for PT. Professor Stenger’s response seems to me to be still pertinent inasmuch as he shows that there is no absolute time. My own comments are also pertinent, except that I should not have accused Mr. Richards of admitting a weak knowledge of relativity; he did not admit that.

I have to admit, Mr.Richardson’s “refutation” has boggled my mind. This caused a serious headache until I have come to an inevitable conclusion: we were all wrong and Richardson is right. He really does away with Einstein with a big, so far unmatched, fashion.

Read his article carefully and you’ll see that the basis of the argument is this:

Right now, my wife is doing something at home. She’s doing it right now even though I don’t know what it is she’s doing.

So he’s not at home and he knows that his wife is doing something (and he doesn’t seem to like it), though he doesn’t know exactly the situation. How does he know it? The only way is numerous past experiences. These are real scientific data!

You have to admit that this is a completely different angle of view, which clearly proves that time is indeed absolute. How many of us share similar experiences? I dare to say that there is some huge amount of data waiting out there to be collected from our wives and girlfriends! [wink]

If a clock is moving faster at the top of Mt. Everest than at the bottom, then wouldn’t the top eventually be (a) day(s) ahead of the bottom? Which, of course, means that the top would count more sunrises and sunsets and the sun would pass overhead more times. But, how can this be when they are affixed to the same point on the Earth?

While the resident cognoscenti are fielding questions, would you mind clearing something up for me? I understand that the usual figure for the speed of light is its speed in a vacuum, which implies that it moves more slowly through other media. But if that’s the case, then how could the speed of light be constant in vacuum? In other words, if light travels at c through a vacuum, then enters an atmosphere and slows down as a result, it would have to accelerate once it re-entered vacuum. The alternative would be that light doesn’t slow down as it passes through a medium, which seems to make the “speed of light in a vacuum” disclaimer superfluous.

Obviously, I’m missing something. Would someone mind filling me in?

AT, you are aware that elapsed time (as measured by a clock) and sidreal time (as measured by days) are entirely different? Or was that remark a joke?

Koly Wrote:

So he’s not at home and he knows that his wife is doing something (and he doesn’t seem to like it), though he doesn’t know exactly the situation. How does he know it?

Um, isn’t it obvious? The designer told him.

While the resident cognoscenti are fielding questions, would you mind clearing something up for me? I understand that the usual figure for the speed of light is its speed in a vacuum, which implies that it moves more slowly through other media. But if that’s the case, then how could the speed of light be constant in vacuum? In other words, if light travels at c through a vacuum, then enters an atmosphere and slows down as a result, it would have to accelerate once it re-entered vacuum. The alternative would be that light doesn’t slow down as it passes through a medium, which seems to make the “speed of light in a vacuum” disclaimer superfluous.

Obviously, I’m missing something. Would someone mind filling me in?

What’s happening is that although the photons always move at c, even in a medium, in a medium, they get absorbed and then re-emitted by the atoms of the medium. That’s what accounts for the differential in velocity. The denser the medium, the shorter the distance a photon travels before being absorbed and re-emitted.

So, ironically, once could say that photons always move at the speed of light, no matter what the medium, but light doesn’t.

Does that help?

Absolute Time -

I think I can answer that. As I understand from Dr. Pratchett’s research, darkness is much faster than light. (That is why a room with no light source is always dark when you first open the door - all the darkness rushes in ahead of the light.) Because mass increases with speed, darkness is also much heavier than light. As more and more days accrue on mountaintops, the darkness flows downwards, eventually accreting on the ocean floor - this is why the ocean’s depths are always dark. The excess light is less dense, and is eventually reflected away by clouds - this is why the tops of clouds, even thunderheads, are always light (except at night, when the falling darkness occludes the light).

Therefore, while extra days and nights are in fact accruing on mountaintops, we never notice it, because the light levels even themselves out. Calendar discrepancies are largely ignored, because no one important lives on mountaintops, except perhaps hermits, who don’t use calendars in any event.

Rilke’s GD -

Yes, that’s as helpful as it is interesting. Thank you very much.

AT, you are aware that elapsed time (as measured by a clock) and sidreal time (as measured by days) are entirely different?

Could you please elaborate? No, it’s no joke. Perfectly valid question.

Colin, you worry me… %:->

Colin Wrote:

In other words, if light travels at c through a vacuum, then enters an atmosphere and slows down as a result, it would have to accelerate once it re-entered vacuum. The alternative would be that light doesn’t slow down as it passes through a medium, which seems to make the “speed of light in a vacuum” disclaimer superfluous.

What happens in matter is that the photons are absorbed by the electrons orbiting the nuclei, these are excited and reemit the photon a little later. This effectively reduces the perceived speed of light when propagating through matter. In reality, photons travel ALWAYS through vacuum, they only interact with charged particles, i.e. are destroyed and recreated.

I am so slow, beaten by RGd…

AT - we’ll take the sunrise as a basic measuring point. Now, the interval between sunrises is based purely on the speed of rotation of the earth. The intervals measured by a clock are not connected to this rotation. For example, a clock which measures time in terms of seconds, uses as the duration of a second 9,192,631,770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at zero kelvins - according to wikipedia. The point is that these two things are unconnected - the speed of rotation of the earth could change and the number of seconds measured by the clock in that day would shorten.

Now what happens in a GR situation is that the ‘seconds’ measured by a clock at sea-level and a clock on Everest would have different lengths. So the apparent interval in seconds between sunrises would be different depending on what clock you used, but both the sea-level and the Everest clock would experience sunrise at the same ‘moment.

One seldom mentioned consequence of special relativity: as you heat a gas, it becomes heavier because of the greater velocity of the molecules that make it up. To get a measurable effect, you have to have a heck of hot gas because the molecules need to reach near-relatavistic speeds to get appreciably more massy.

Followup question - would light travelling through a medium lose energy, then? Photons exciting electrons into emitting another photon can’t (as far as I know) be a free transaction; what is the effect of the energy loss? Does the light move down in the spectrum, or simply become dimmer?

Thanks, by the way, for the answers. Such an interesting thread, bereft of the usual invective.

Absolute Time Wrote:

Could you please elaborate? No, it’s no joke. Perfectly valid question.

I’ll try to help you if I won’t be already beaten by someone else by half an hour…

What you should do when comparing clocks is to do a measurement in your frame, e.g. you measure that the time between two sunsets is 24 hours. Then compare your results with those in different frames, e.g. your buddy on Mt.Everest measured for the same two events 40 hours (the Earth is veeeeery heavy and the Mt.Everest is extreeemely high). With this definition you should be able to conclude answers for your questions easily.

Damn…

Ok, let’s race for the Colin’s follow up!

Now what happens in a GR situation is that the ‘seconds’ measured by a clock at sea-level and a clock on Everest would have different lengths. So the apparent interval in seconds between sunrises would be different depending on what clock you used, but both the sea-level and the Everest clock would experience sunrise at the same ‘moment.

So, then what you are saying is that the clock on top of Mt. Everest is running faster, but time isn’t. If it were time that was running faster, then events (i.e. sunrises, sunsets) would keep in synch with the faster running clock.

Colin Wrote:

Followup question - would light travelling through a medium lose energy, then? Photons exciting electrons into emitting another photon can’t (as far as I know) be a free transaction; what is the effect of the energy loss? Does the light move down in the spectrum, or simply become dimmer?

Your results may vary.

The emitted photon may be the same energy as the initial photon. Or in some cases (fluorescence) a lower energy photon may be emitted. In some cases (multiple photon excitation) you can even get an emitted photon with higher energy than the initial photons, but you end up with a smaller number of photons.

Colin Wrote:

Followup question - would light travelling through a medium lose energy, then? Photons exciting electrons into emitting another photon can’t (as far as I know) be a free transaction; what is the effect of the energy loss? Does the light move down in the spectrum, or simply become dimmer?

“Free transaction” is not a term used in physics. If an electron absorbs a photon, is excited to a different energy level and then reemits the photon while getting back to the original level (one common situation), the energy of the emitted photon will be exactly the same as that of the absorbed one, because of the energy conservation. However, it’s momentum nad thus the direction of propagation can be different. What exactly will happen depends on the matter and the energy spectrum of the light used. You can observe various situations with your own eyes in the visible spectrum: glass does not absorbs too much and let’s most of photons through. Mirror absorbs most of the light and reemits it backwards. Black paint absorbs almost all of the ligth and transforms it to heat - the photons are not reemited properly and their energy is transformed into the kinetic energy of the atoms. A blue thing absorbs all of the spectrum except the blue part, which is bounced back. And so on.

Well, whatever… Just hope I am not completely useless here…

Remember, time always seems to pass at the “normal” rate for you, in your frame of reference. External events (like sunrise/sunset) might measure as taking less or more time depending on where you are in the gravity field, but there is no “absolute” amount of time the event takes… it all depends on where you’re observing it from. Yikes! (grin)

Absolute Time Wrote:

So, then what you are saying is that the clock on top of Mt. Everest is running faster, but time isn’t.

Well imagine my example - a 40 hour day on Mt.Everest would mean your buddy would be very old after 40-50 years (defined as a 365 sunsets, for example). You could watch him age and die, while you would still be only “in the best age”. Is his time running faster or not?

GCT Wrote:

Um, isn’t it obvious? The designer told him.

Well, some call it being jealous… We should ask him whether he has some real data about his wife or he’s just jealous, Einstein’s Theory of Relativity depends on it!

“So, then what you are saying is that the clock on top of Mt. Everest is running faster, but time isn’t. If it were time that was running faster, then events (i.e. sunrises, sunsets) would keep in synch with the faster running clock.”

AT, there’s not a short way to explain what’s wrong with this without you learning the mathematics of (at least Special) Relativity. But the upshot is that, if you insist on absolute time and say that only clock speeds vary based on changes in reference frame, then you have separate general laws of physics that apply to different frames. Sizes, masses, and electrical charges of real objects will be different depending on which frame they are measured in. Relativistic spacetime provides a single, consistent model that works anywhere in the universe …

Seems like at the center of the planet, the “slope” of the gravity well would be zero. But if clocks (i.e., any physical process) run slower there too, it kind of undoes my previously mentioned way of understanding the time slow-down at or above the surface of the planet. (That is, in the middle of the planet, photons don’t have to travel a longer distance to get from atom to atom, so that can’t be used to explain the time dilation there.)

Henry

Don’t look now, but that ID post on Einstein has just been “disappeared”.

It was there a minute ago, with an update.

Randall Wald Wrote:

Is your depth in a gravity well the important thing, or is it the slope of the well at your point? (Actually, that last sentence may not make sense, but it sounds cool.)

Yes, it does sound cool. :-) It’s the depth in the well that counts, relative to the depth of the observer. The acceleration due to gravity is a function of the slope, but has nothing to do with the actual, observed time dilation, except to indicate how quickly it changes as you move towards or away from the local centre of gravity.

Malkuth Wrote:

It’s unfortunate, then, that my understanding of quantum mechanics is only trivial. From my understanding, there are particle-antiparticle pairs that appear in a vacuum and exist for an incredibly short amount of time, after which they annihilate with each other. They can also exist in the intermediate stages of a phenomena, but don’t exist in the initial or final state, which is why they’re called virtual particles. At least, to my trivial understanding. Is this at all correct?

Well, this is correct in the sense that it is the popular interpretation of the underlining mathematics. You have to understand that the theory is not about virtual particles, etc. What is really there is a set of quantum fields. You have a calculational procedure which is used to get observable predictions from the theory, like decay rates and scattering cross-sections. This procedure allows for such an interpretation, but one could also say “well this is nothing else than a calculation, what matters is the result, so what sense does giving catching names to the used tools have?”

We have to be aware that what we want to do is science. Talking about virtual particles is popular and all, but it’s not a prediction that could be tested. It’s a nice label for the mathematics used to get the result. When I say “two point Green’s function consisting of two fermion field propagators” instead of “virtual particle-antiparticle pair” it doesn’t sound as good, does it?

It’s quite sad that what often gets to the public are these popular interpretations and labels physicist often use for hard to grasp phenomena, but not the science itself. Then we, theoretical physicist, look like fools fantasizing outside of reality. This could not be more further away from thruth, when not counting Superstring Theory, which is outside the realm of experiments so far.

The photon propagator is a nice example of how things work. When we want to answer the question, whether the photon is massless or not (and thus propagates with velocity ‘c’), you have to calculate the various algebraic contributions to the propagator function. You can label them “a pair of virtual electron-positron pair” etc., but that’s not important. What is important, that you don’t get any contributions to the mass term and thus you predict that the photon is indeed massless. That can be tested in experiment and if it’s falsified, then all Quantum Electrodynamics or maybe Quantum Field Theory as a whole with the fancy virtual particle interpretation is crap. However, after many decades of experiments, it wasn’t falsified yet, quite the contrary, it’s precision in agreement with experiments is unmatched in the history of science.

Randall Wald Wrote:

Hmm. That seems counterintuitive, at least. I know that a clock closer to a black hole will tick more slowly than one distant from the black hole. Still, isn’t the person at the center of the earth allowed to think that he’s floating in open space? I mean, how could he tell either way? Perhaps my problem is that I’m viewing things too absolutely; I think that to figure out your clock’s rate, you need only calculate how much acceleration/gravity you’re feeling, and you know how your clock ticks with respect to an open-space (no acceleration) clock. Is your depth in a gravity well the important thing, or is it the slope of the well at your point? (Actually, that last sentence may not make sense, but it sounds cool.)

Zim answered your question nicely (and it was right to the point btw), but I want to give you an intuitive understanding what’s going on. And I hope it will help Henry too.

The whole time dilatation in GTR is quite a simple thing. It’s not about time really, it’s about observation. So imagine a gravitational well and any ordinary hole is such a well. If you want to get a ball out of the whole, you kick it, but it will slow down when moving out. If you have several balls and you kick them quickly, they quite slow down when getting out of a deep whole. Your buddy catching the balls up there does not have to be very fast to manage it.

Of course, you can say, yes the balls loose quite much of their velocity, but when I shoot from a gun, buddy won’t make it. But still, even the bullets slows down a little bit. Everything appears to be slower, when observed outside of the whole.

Everything? Light does not slow down, does it? No, but even light has to use some of it’s energy to get out of the hole. It looses frequency and the result is longer wavelength. But when the wavelength is longer and the velocity is the same, it takes MORE time from the arrival of one peak to another. So even when your buddy is watching you kicking the balls, it appears to him an extremely little tiny bit that you do it slower. So if the hole is deep enough, your buddy will comfortably catch the bullets from your gun. And if it is even more deep, your buddy will watch your slowed down version down the hole.

And this is it really. One would be tempted to say that it is only a trick, the time is the same. But when you jump into a black hole, the well is so deep that you will observe the complete future history of the universe. Better think about it like time running with a different pace, because if there is going to be a Big Crash, it will catch you. Even if you stop your fall sooner and get back, all of your buddies will be long gone.

Well, and please ignore my spelling and grammar errors, my English still doesn’t seem to be up to par…

Comment #23933

Posted by Matt Young on April 8, 2005 02:43 PM (e) (s)

Don’t look now, but that ID post on Einstein has just been “disappeared”.

It was there a minute ago, with an update.

His Update should be subtitled “Wherein I contradict myself regarding whether I think Einstein was wrong.”

It’s a pretty awful essay, made awfuler by the update.

Let me clarify: I can fully understand why a person near a black hole thinks his friends in open space appear to have faster clocks. After all, the light he sees coming from them has been blueshifted. To use specific numbers, suppose they thought the light had a frequency of 2*10^15 Hz, and he thinks it has a frequency of 4*10^15 Hz. Frequency is cycles per second, so (dropping the 10^15 for clarity), an event which happens four times per our near-black-hole observer’s second happens two times per our open-space observers’ second. Thus, we see that the open-space observer’s clock is twice as fast as the near-black-hole observer’s clock. Anyway, the point is I get the basic concept of time running at different speeds because of gravity wells.

The only problem I have is with the center of the earth. In particular, I believe (or at least, feel intuitively) that since the middle of the earth feels no gravity, it should be equivalent to open space, and should have a clock that runs at the same rate as an open-space clock. Let’s imagine that our center-of-earth observer has a long tube which goes to the surface and beyond, until there’s no more effect of earth’s gravity (which would take forever, but you get the idea). At the other end is a second observer. Can these two observers figure out which one is in the center of the earth and which one is in open space? If not, then how can the person in the center of the earth have a slower clock than the person on earth’s surface, who would feel a gravity well (just like the person near the black hole)? Shouldn’t the person in the center of the earth have a faster clock? This is the question I don’t understand.

Re “Shouldn’t the person in the center of the earth have a faster clock? This is the question I don’t understand.” I don’t understand the mechanism behind the effect, either, but I think it would cause inconsistencies if clocks started going faster as one went deeper under the surface.

It’s not just time that’s warped, either - distance is contracted; the distance from surface to center is a bit more than would be expected if space obeyed Euclid.

One thought I’m having on the matter, is maybe descending into a gravity well reduces the rest mass of matter particles, and maybe the energy that’s no longer tied up in mass form might be what goes into the kinetic energy as the falling object speeds up? If the particles in the lower altitude object have less mass energy, then an incoming photon would have more energy relative to the mass energy of those particles. I wonder if that thought is consistent with the math?

Henry

I wonder - how about the common (i.e. non-gravity) blue shift? If I travel directly to some place at fast speed, wouldn’t the same logic tell me that time is speeding there (while, according to STR, you can’t see any moving object experiencing faster time than yourself). As far as I understand it, the effects of light shift can be accounted for in STR, leaving clean time dilation as a result, but I would appreciate some thoughts on that.

The only problem I have is with the center of the earth. In particular, I believe (or at least, feel intuitively) that since the middle of the earth feels no gravity, it should be equivalent to open space, and should have a clock that runs at the same rate as an open-space clock.

I remember from my basic physics class that under Genral Relativity, a clock at the top of an accelerating rocket ship runs *faster* than a clock at the bottom, even though both clocks are accelerating at the same speed.

The way I like to think of it is that light forces time to slow down in order to turn what ought to be a speed increase of falling photons into a blue shift.

Marek, I am not a physicist, but here goes. First of all, I’d say that the effects of red shift due to time dilation and blue shift due to length contraction will cancel each other out.

Second, if you think about it, as you observe an object you’re moving towards, you observe their time running faster, hence a blue shift, and you observe time runnng slower in objects that are moving away from you, hence the red shift.

let’s say you’re moving between two planets at half the speed of light. Normal time dilation effects for oberving both planets are the same: they both appear to be about 80 something percent of normal speed.

Except they don’t. The planets are half a light year apart, and at the end of the years travel time, you’ve ovserved 2*80% years on planet two, but only 0.5*80% years on planet 1. So, you see double the frequency from planet two, but you also see their clocks running twice as fast. You see half the frequency from planet 1, but you also see their clocks running at half speed.

Thanks for the example, Boronx. Now that I think about it, I remember the accelerating spaceship example from an excerpt of a Feynman lecture I once read. That shows my naive “acceleration directly relates to clock speed” idea can’t be all right, and is probably mostly wrong. I probably should think more carefully about what exactly happens to light traveling between the surface and the center of the earth, and then figure out what that implies about clock speed.

Well, that doesn’t make sense. Let’s say your spaceship leaves planet 1 at year 1. At that moment it’s seeing light from planet 2 from year 0.5. When you reach planet2 at year 2, you’re seeing light from planet 1 from year 1.5. That says to me that you’ve observed 1.5 years of planet 2 in your 1 year of travel, not 2. And I guess, if I think about the doppler effect, blue shift at 0.5c would be 50% increase in frequency, not 100%.

I made a mistake. Let’s say your spaceship leaves planet 1 at year 1. At that moment it’s seeing light from planet 2 from year 0.5. When you reach planet2 at year 2, you’re seeing light from planet 1 from year 1.5. That says to me that you’ve observed 1.5 years of planet 2 in your 1 year of travel, not 2. And I guess, if I think about the doppler effect, blue shift at 0.5c would be 50% increase in frequency, not 100%.

Randall, Henry,

you don’t seem to like my analogy with kicking the ball out of the hole. But that’s really what’s going on, exactly the same thing happens to photon wavelengths as to ordinary matter. It’s all only about loosing or gaining energy and momentum.

Imagine this - would a ball thrown out of the center of the Earth slow down or accelarate? Why do you then cannot accept that a light looses some energy too (=red shift)?

Randall Wald Wrote:

The only problem I have is with the center of the earth. In particular, I believe (or at least, feel intuitively) that since the middle of the earth feels no gravity, it should be equivalent to open space, and should have a clock that runs at the same rate as an open-space clock.

I am not a physicist but what exactly is it about the center of the earth that causes it to not feel gravitational acceleration? Isn’t that like saying that a black hole feels no acceleration?

It just seems like unless an oberver was infinitely small it would still feel gravitational acceleration. Could be wrong of course.

Thanks

Randall Wald Wrote:

The only problem I have is with the center of the earth. In particular, I believe (or at least, feel intuitively) that since the middle of the earth feels no gravity, it should be equivalent to open space, and should have a clock that runs at the same rate as an open-space clock.

I am not a physicist, but why do you say that the middle of the earth feels no gravity? Doesn’t it feel gravitational acceleration the same as any other point? The exact center may feel it in all directions at once, resulting in no movement, but that is not the same, is it?

Could be wrong of course.

Thanks

Doh! So sorry about that Double now Triple Post! Feel free to delet either! And this one too.

I am not a physicist, but why do you say that the middle of the earth feels no gravity? Doesn’t it feel gravitational acceleration the same as any other point? The exact center may feel it in all directions at once, resulting in no movement, but that is not the same, is it?

Your problem here is the word ‘feeling’. At the center, you wouldn’t feel any gravitational pull, and there also would be no force on you. Force and feeling are related in tricky ways.

Standing on earth’s surface you feel gravity, but don’t move. No net force.

Free-falling toward earth’s center, you would not feel gravity, but you would accelerate. Net force.

Loitering in the exact center, you would not feel gravity, and would not move. No net force.

Now if you really want a messed-up brain, consider the following true statement:

If the earth contained a hollow cavity in the center, you could float around, feeling no force, anywhere in the cavity, not just the very center.

I do not suggest getting stuck on that idea, it’s not possible to understand without spending some time understanding things like Gauss’s Law, and other tedium.

Re “If the earth contained a hollow cavity in the center, you could float around, feeling no force, anywhere in the cavity, not just the very center.”

Depends on the size of the cavity. At a mile from the center, for example, there’d be somewhere around 1/4000 of a G force toward the center. Not much, but not zero.

Henry

Oops, cancel my last post. I just remembered that with a hollow spherical cavity centered at the center, well, it’s the part “under” one that generates the net gravity. The 1/4000 is approximately what one would feel if in a tiny (hopefully air conditioned) cavity offset from the center by a mile.

Henry

Oops, cancel my last post. I just remembered that with a hollow spherical cavity centered at the center, well, it’s the part “under” one that generates the net gravity. The 1/4000 is approximately what one would feel if in a tiny (hopefully air conditioned) cavity offset from the center by a mile.

Henry

Oh great, now cancel one of the two cancellations of the aforementioned post… Good grief.

Steve Wrote:

I do not suggest getting stuck on that idea, it’s not possible to understand without spending some time understanding things like Gauss’s Law, and other tedium.

Let’s try this without Gauss’s Law, but perhaps a bit of tedium. For pics, see a standard 1st year calculus based physics text.

Claim: At any point inside a hollow thin shell, the force from opposing differential(i.e. small) solid angles cancels.

Proof:

Case 1. If you are at the center it’s obvious.

Case 2. If the point under consideration is off center, the only possible direction of force is along the radius*. Now, because the lesser mass from the closer solid angle element is less proportionally by r_close^2 whereas the greater mass from the farther solid angle is greater proportionally by r_far^2.

Since the force is proportional to 1/r^2, the force from these opposing solid angles exactly cancels.

Finally, since a hollow sphere can be thought of as layered thin shells, there is no force from any shell of which the sphere is made. Hence no force inside the hollow sphere.

The hole has to be spherical and concentric with the rest of the sphere. Each shell has to be of uniform density, but the density of each shell can vary with radius.

* Landau would say this is obvious from the symmetry of the problem, and it is if you consider the mirror image of the proposed off radius force about a equatorial plane through the point in question.

Please edit my non-sentence in the post above by joining the paragraphs beginning “Case 2. If the .…” and “Since the force .…” to read:

… by r_far^2, and since the force is …

Thanks.

FH

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This page contains a single entry by Matt Young published on April 6, 2005 11:13 AM.

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