When it comes to physics, there sure are some strange theories -- and even stranger phenomena -- out there. The notion that particles don't have fixed, intrinsic properties that are simultaneously measurable can only be described as weird, and the fact that you can add as much energy as you want to a particle but it will never accelerate to beyond a particular speed is certainly counterintuitive. Yet one theory has them all beat.
For ninety-nine years, now, General Relativity has made a whole host of unique predictions, ranging from time slowing down in a gravitational field to the bending of starlight to the decay of pulsar orbits, that have been observationally confirmed each and every time.
"Since the relative motion along your line of sight at that moment is zero, you might think there would be no shift. But since the object is speeding past you, its time should be dilated. As a result there should be a Doppler shift"
OK, so I think I'm missing something here:
1. Object is moving towards me, light is shifted up in frequency
2. Object is moving away from me, light is shifted down in frequency
Naively, I would expect that if the amount of frequency shift goes from positive to negative then it has to pass thru 0 at some point.
Surely the animation shown completely mises the point.. The mirrors shown are moving in a linear fashion, distance to the observer must therfore be changing, and there must be a component of velocity to produce a doppler shift without time dilation.
Surely the real condition where there classical mechanics show no doppler shift is where the mirrors are moving in a circular path centred on the observer. It is the acceleration required to move this object in its circular path, whether caused by gravity or an external force, that produces the time dilation required to generate the otherwise unexpected doppler shift.
Your analysis is correct for a source moving either directly toward you or directly away from you. In the first case, you observe an increased frequency, in the second a decreased frequency. In the intermediate case, ie the source being at rest relative to you, you would indeed observe zero frequency change.
Things are different, however, if there is a transverse component to the object's velocity. This is totally unexplainable in classical physics. Classical physics indeed would predict a zero Doppler shift. However, relativity predicts that the time dilation of the object moving transversely relative to you would create a frequency shift. In relativity, only sources at rest with respect to you would have a zero Doppler shift.
I read your blog with great interest. Although Einstein's relativity theories are the most elegant and subtle of all theories, insofar as mysterious theories, quantum mechanics reigns.
Relativity may show subtleties in our conceptions of space and time, but does not fundamentally question existence or causality as quantum mechanics appears to do.
Thank you for your explanation.
Two things (dumb layperson question alert;-)
1) Alice is on the train with her "light clock" consisting of a photon bouncing between two mirrors. Bob is standing on the ground watching the train pass. In Alice's frame the movement of the photon is along a vertical axis. In Bob's frame its movement is along an incline, ascending and descending. Is this correct so far?
Now add something to this: As the train passes each of a series of points, an apparatus on the ground sends a time reference signal to the train, where it is recorded. We can go back and observe that the time references are synchronized between what is recorded at the transmitter on the ground, and what is recorded by the receiver aboard the train.
We then query Alice: where is the photon, on a vertical scale between the two mirrors, at each of these points in time when the time reference signals were received? We query Bob, ditto.
If we consider the horizontal movement of the train as a component of the net movement of the photon relative to Bob's frame of reference, then we end up with the counterintuitive result that, at each point where a time reference signal occurs, Alice and Bob will report the photon as located at a different point on the vertical scale between the two mirrors.
Here's the dumb layperson question: Doesn't that necessarily imply that the single photon is demonstrating behavior that would be characteristic of two separate photons?, and how do we reconcile that?
2) About rotation and twisting of space:
Something in my untrained nonexpert guts tells me that there should be an observable tradeoff between the mass of the object and the speed of rotation to produce a given degree of twist of space. More mass + slower rotation should produce the same degree of twisting of space as less mass and faster rotation. This should be reducible to an equation that has strong predictive value.
Is that anywhere near correct, and what sorts of experimental results are there on the matter?
The counterintuitive part of this is, if the object is indeed a uniform sphere, such that the strength of gravity is equal at a given distance above any point on the sphere, then we would expect a static gravitational field around the sphere, and a static condition of altered space around the sphere, but that's not what we observe. By analogy, a marble resting on a thin sheet of stretched rubber produces a static indentation in the sheet of rubber.
So, what's the mechanism by which rotation of the sphere produces a composite gravitational vector (as distinct from a static one) that has a corresponding composite effect on the fabric of space? (The marble rotates and causes rotation as well as depression of the rubber, seen as a roughly whirlpool shape rather than a static indentation.) Or what did I miss?
(I'm trying hard to say "space" rather than "spacetime" as the author of the article did not say "spacetime." Though, I assume that spacetime is what he had in mind, right?)
Relativity isn't strange at all. The speed of light is always measured to be the same because of the wave nature of matter. See The Other Meaning of Special Relativity by Robert Close. It’s measured to be the same, even when it isn’t the same. See Baez where you can read this:
“Einstein talked about the speed of light changing in his new theory. In his 1920 book "Relativity: the special and general theory" he wrote: "... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers.”
Also see Baez re curvature: “in general relativity gravity is not really a ‘force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial.” Space isn’t curved where a gravitational field is, instead it’s inhomogeneous, see Einstein’s 1920 Leyden Address: where you can read this: “the recognition of the fact that “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν)…”.
G: you’re having problems because the bowling-ball analogy is a bad one. A better analogy would be to start off with a block of space. Then you insert the bowling ball, and it pushes space outwards, rendering it inhomogeneous. It doesn’t make space curved. However when you rotate the ball, it does. Gravitomagnetism is akin to electromagnetism in this respect. See The role of the potentials in electromagnetismby Percy Hammond and note this “We conclude that the field describes the curvature that characterizes the electromagnetic interaction."
Doesn’t that necessarily imply that the single photon is demonstrating behavior that would be characteristic of two separate photons?, and how do we reconcile that?
Bob's clock and Alice's clock will no longer be synchronized once Alice accelerates. Once the train has stopped, Bob could look at Alice's clock and see that the photon in her clock was in a different place/had made less bounces than the photon in his clock. Or put more simply, she and her clock have aged slower.
As for what Alice's clock looks like (while in motion) to Bob on the ground, IIRC the discrepancy is accounted for by the fact that Bob must bounce a photon to and from Alice before he can see her clock. There is no way for him to instantly or simultaneously observe her clock. Thus, he will see (eventually) Alice's clock the way Alice sees it, and there is no discrepancy.
What is possibly the strangest effect of time dilation is that a photon, traveling at C, experiences no time at all. A star's light may have been traveling towards us for 10 billion years, but from the photon's perspective, the instant it was emitted it was immediately detected by the observer on earth, 10 billion light years away.
The photon has no time to experience the vast universe it exists in. No matter how far it has to go, it gets there the instant it departs.
your 1st question is really all about special relativity, so gravity and curvatures and all that is irrelevant. Simply by doing time dilation formulas, as Eric pointed out, you see that clocks are no longer in sync between 2 observers where one is moving. Your thought experiment is really how a GPS system works. You have Alice (as a satellite) in orbit with her atomic clock, you have Bob in mission control, and gps recievers are "reference points" on the ground.
So, by studying how gps works, and what effects of spec. relativity are in play, you will have an answer to #1
Your #2 question is a bit unclear to me. What do you mean by "should be a trade off"? In what sense a trade off? Certainly you could have 2 systems that curve spacetime in same manner, one with larger mass and longer period and vice versa, but in the end all mass/energy are just terms in tensor. But I don't understand what correlation and predictive power you mean? i.e. you have our sun and you do the field equestions, and you get certain values of geodesics plot... and you can certainly just use same formula and say ok.. if curvature stays same and I increase mass by 4, what will be the period term of some hypothetical star. Was that a question?
On the other hand, there must be an upper limit before the rotation starts shedding the material from a star and thus start reducing mass to an equilibrium like state.. like i.e. pulsars.
This is a reason why humanity hasn't grown up and left the solar system with technology of science fiction movies.
We still have an intellectual scientific "elite" (shudder worthy) of flat earthed "geo centrism" wannabe intellectuals dominated by big bangers and other nonsense "Theorists " spreading woo.
This is the reason aliens won't visit us.
It's a pretty big universe.
Must suck to live in such a small one (again, dominated by an intellectual flat earthed "elite") that worships theorists instead of people who actually do stuff and prove their beliefs.
Science is the new religion, with its saints, popes, clergy, and worshippers. How sad and pathetic.
John @ 6: I'm not sure that what you've said meshes with the present consensus on those issues. As far as I know, the object in space causes curvature of space, thus we get light bent around not only stars but galaxies, and in such a manner that what we observe does not seem to suggest that the path of the light has been dragged by the rotation of the galaxies but by their mass. I may be mistaken but that's how I have it at the moment. Gravitomagnetism would seem to presuppose a unified field theory, which I know we don't have right now, else we'd be building gravitic propulsion and heading for Mars post-haste.
Eric @ 7: Your second paragraph shows me where my error was. I hadn't accounted for the delay of the photon from Bob bouncing off Alice's clock and returning to Bob. D'oh!;-) Sheesh, just as I'm thinking I have a decent visual model of the phenomenon, we discover a substantial missing piece in the form of Bob's photon. OK, model updated, no anomaly. Thanks.
The part I still don't get is how a nearly perfect sphere that is rotating about its axis can cause the rotation of the curved space around it. Though, assuming it does, is where I get my speculation about the tradeoff between the mass of an object and its rotational speed, as related to the effect upon the rotation of spacetime in its vicinity. That should be testable using a spherical mass rotated at different speeds.
But it still leaves me with the puzzle about how the rotation of the sphere causes rotation of surrounding curved space. Unless (wild speculation) the spacetime occupied by the sphere is connected directly and causally to the spacetime surrounding the sphere, via some mechanism I can't put my finger on at the moment. If that's true, then my hypothetical tradeoff between mass and rotational velocity should be falsified. Right? Or did I miss another critical piece?
"Einstein is a beggar made king using dazzling mathematics to obscure truth"- Nikola Tesla.
Space is a Vacuum; one cannot bend a Vacuum. Light is made of particles with mass; one cannot propagate Waves in a Vacuum.
@ G #10
it's called frame dragging....
This Article is preposterous, which is not surprising, as Einstein's entire Gravitational Theory is preposterous. First, let's mention one big fat truth...NOBODY NOWS WHAT GRAVITY IS. If Einstein was such a Genius, he might have tried to figure out the CAUSE of Gravity, instead of telling us about more of it's Effect's in ant attempt to associate Gravity to Light. "Time" does not exist and cannot be manipulated. The idea that "Space", which also does NOT exist, and "Time" are Mechanically Intertwined is, at best, Pedantic, and is in fact a back-end admission of almost total Cluelessness. Einstein has not helped us. His Poppycock Theory led us, some say intentionally, into a Dead-end tethat cannot be escaped. If Albert Einstein's parenting skills are any indication of his inner Character (and how could they not be) his behavior suggests that Albert Einstein was a man that could not be trusted. "Special Relativity", as far as actual Mechanics are concerned, is Hogwash and will be ridiculed as Ignorance in the near future.
@8 - I believe this is untrue because the relativistic equations we're generally talking about here apply to things with mass, and photons are massless.
So, for example, photons traveling through space have an electrical (E-)component and a perpendicular magnetic (H-)component, and they fluctuate as it moves. A photon couldn't have fluctuating components if it experienced no passage of time in its own reference frame.
The lorentz factor gamma used to calculate time dilation becomes undefined at v = c; while this isn't my area, I believe that you cannot extrapolate the time dilation observed when going near to c to things traveling at c. For things like photons that travel at c, other math applies.
Start over, this time without references to black holes as we all now know do not exist.
You have a point ... all except for the whole "relativity gives the correct result in EVERY SINGLE SITUATION" thing. The test of a theory is whether or not it predicts observation correctly. Relativity (both SR within its more limited domain, and GR) pass this test with flying colors.
It is true that relativity cannot be a complete theory of everything in the universe since it is not compatible with an equally correct theory, namely quantum mechanics. In domains which deal with small particles and high gravitational fields, neither theory really works, so we know that neither is complete. However, in the limit of large scale structures (with large meaning anything about the size of a very small dust speck or bigger) GR works perfectly. In the limit of weak gravitational fields (meaning anything significantly less than the field present near a black hole) QM works perfectly well. It is only under truly extreme conditions that we can't use either QM or GR.
Who precisely is it that you reference when you speak of "people who actually do stuff and prove their beliefs"? Surely, you cannot mean experimental scientists. You, of course, must realize that science cannot prove anything. Experimental evidence only lends support to theory, never proof. Big bang theorists in fact do stuff to "prove" their theories. The look at the results that experimentalists generate and use them to modify the theory and make it better. How else would you suggest that science proceed? Don't try to explain experimental results with theories? How would you determine which experiments to conduct without an underlying theory? Sure, any given theory might turn out to be wrong (or more likely an incomplete description), but even wrong theories are useful.
The lorentz factor gamma used to calculate time dilation becomes undefined at v = c;
Not really true, eric.
See for example the relativistic momentum equations that have gamma (1/(c-sqrt(c-v)) in it that goes to "infinity" but in such a way that the result is that a photon's momentum is hv. A definitely non-infinite number for any wavelength we consider.
A simpler example.
x/x is ALWAYS 1.
But it can also be written in parts as
x * (1/x)
where the second part goes to infinity and our schoolyard maths tells us "anything multiplied by infinity is itself just as infinite!".
Except we know it isn't.
*How you get to infinity* defines the result.
All that can be reliably said is that dividing by a value that tends to zero is undefined unless you define that value's measure.
"First, let’s mention one big fat truth…NOBODY NOWS WHAT GRAVITY IS."
I don't need to know what 2 is to do my two-times table.
I don't need to know what gravity is to be able to fall off a log.
So why do I need to know what gravity is to make a theory about how it works? All I need to to is note, for a start, it makes falling off a log easy.
Step 1 of a theory of gravity.
Einstein went even further than me.
And I went far further there than you did, who gave up before doing a damn thing!
"Space is a Vacuum; one cannot bend a Vacuum. "
Really? How do you know?
"The part I still don’t get is how a nearly perfect sphere that is rotating about its axis can cause the rotation of the curved space around it. "
Rotation requires energy to get going (and it exists when there is no other frame of reference than the object itself: the coriolis force is the result of trying to avoid seeing you're on a rotating frame of reference).
And E=mc2, therefore that rotation has no differentiator to mass.
Therefore if mass bends space, so does rotation.
With the added fillip that since each part of the rotating mass "knows" (i.e. there's a way to see that it or its neighbors are part of a rotating object) it's rotating because of the relative motion of the rest of it, the action of the photons it passes on or interacts with TO those others is also changed.
It's tricky, but not necessarily difficult maths.
Rather like juggling. The idea of how you make the balls go round like that is easy to grasp. The coordination of the actual event is the hard bit!
Wow @19: I believe your calculation of gamma is wrong. It is:
1/sqrt(1-(v/c)^2). Which for photons works out to be 1/sqrt(1-1) or 1/0.
Here is an interesting scenario.Say Alice takes her photon clock next to a black hole and Bob observes the clock from a (safe) distance.Since the clock slows down in strong gravity will Bob see photons bouncing up and down the mirrors at speeds less than light? If so will this be lorentz invariance violation?
since we don't really "see" photons bouncing in macroscopic sense like particles up and down, let's leave that out for a moment. But yes, Bob would observe Alice's clock as running slower, and he would observe light coming from Alice as red shifted. But Alice would observe the same thing when looking at Bob and his clock. To Alice nothing changes really, from her referance frame, her clock runs as it did and it's Bob's clock going out of sync. So that's the lorentz invariance and it's not violated since what bob would measure as gamma or dilation.. the same value would be for Alice's measurment of Bob's clock and reference frame.
You have not addressed the problem of how Alice's clock slows down as seen by Bob.This is a thought experiment which assumes we can see the photon bounce up and down between the mirrors just as Einstein applied it to derive the equation of time dilation in special relativity.Thus your explanation is does not suffice.
because there is no problem. I tried to point that "light" is a bit more complicated phenomenon than a pebble going up and down, which is an image you are trying to paint. You can get a precise answer to what exactly Bob sees for a photon on Alice's side if you do quantum field equations for light and bob's aparatus and then do GR and SR corrections. But that is beyond me and it changes nothing really from the explanation.
Any "time tracking" he observes coming from Alice, he will observe as dilated, and light coming from Alice will be red shifted (you can certainly interpret that as light having different speed in Alice's frame in comparison to Bob's), but wavelength will be different and Bob will still measure that light (when it reaches) to have speed "c". Any "movement" he sees from Alice will be slower. He can't see a single photon moving up and down, because light doesn't work that way, but if it were a pendulum or any macroscopic object that he can actually observe, it would move slower than in his locale. The point being that any light that comes from Alice to Bob, Bob will measure as moving at "c" in his locale when he measures it. In other words, for both Alice and light coming from Alice, Bob will observe that proper time is off.
But your question was about Lorentz invariance, and as I said, it's not violated since Alice will observe the same things for Bob's light and clock. Whatever you want to imagine happens to the photon in A clock observed by B, happens in B clock observed by A. That's the transformation. If Bob sees "light slowing down" in Alice's frame, Alice will see "light slowing down" in Bob's.
Relativistic momentum is rest mass times gamma, *or divided by sqrt(0)*, and since rest mass is zero for a massless particle, the result does not have to be infinity for a massless particle, and is finite for photons (maybe gravitons too, haven't checked, but assume there's nothing different about it).
Lorentz contraction and time dilation means that the distance travelled at light speed in the frame of reference of a photon is zero, and therefore time taken to move zero distance is zero.
Ergo, no time passes.
The fiddle I've never gotten around to doing is what happens with other zero-rest-mass particles that have an intersection with the path taken in another reference frame. I.e. graviton interaction with a photon in a quantum view, rather than a geometrical one, of gravitation.
I just can't keep my concentration when all I KNOW is that I don't know if I have the right mathematical tools to do it, so any answer I get could be false because I apply the wrong tool to the problem.
"Which for photons works out to be 1/sqrt(1-1) or 1/0."
Yes, gamma is 1/.0.
But like I put down, x/x can ALSO be writen as x times 1/x which is 1/0 if x=0, BUT THAT DOES NOT MAKE x/x = infinity when x=0.
Time dilation is not gamma.
SL, Alice sees Bob's light blueshifted and overclocked.
Alice knows she is being accelerated, since she must either be falling in or rotating around the mass, and that CAN be seen because they aren't inertial frames.
This is why the twin paradox doesn't happen: the twin moving at the speed of light must have accelerated to get there, and that is the twin that doesn't age as fast.
"Since the clock slows down in strong gravity will Bob see photons bouncing up and down the mirrors at speeds less than light? "
Since bob is not observing in the frame of reference of Alice, he can see a difference, but if Alice and Bob do an experiment in their own frame of reference, then both see the exact same result.
THAT is why it's invariant.
I can see that a mass is being accelerated BECAUSE IT MOVES FASTER AND FASTER AND HAS A FORCE ACTING ON IT. If I were the one being accelerated, I'd feel a force.
"Alice sees Bob’s light blueshifted"
yes, you are right... she's near massive object while Bob is not, therefore it will add.. my mistake
It's fine, SL, if you already know it, then what you said was understood, and part of the problem with textual discussion of relativity is that the various grunts invented by us to tell us where the next banana was coming from doesn't work too well when it comes to *correctly* specifying different inertial frames.
Several mistakes of mine have been getting the "mirror image right, uh, left, no, it was right, uh, pretty sure..." type.
It's why physicists uses maths with so many greek letters in it. Then *nobody* can tell what's being said.
Or maybe I'm just jaded... :-)
"Then *nobody* can tell what’s being said."
hehehe :))) .. I'll just put some constant here.. I can always take it out later or see if it goes away:)