# Space curve effect on time

1. Nov 7, 2013

### GordonFreechme

So I am new to relativity, and without all the proper math analyzing the equation isn't easy. So I am stuck at this current point until I learn more math, for the most part trying to gain an understanding of how it works, through thought experiments and visualizations.

That being said I have run into a wall in my understanding.

From what I have read there was a wall that was hit in Special Relativity before Length Contraction was thought of, which had to do with the fact that as speed increases time dilates disproportionally. This was explained to me through a Michelson-Morley apparatus with the two sets of perpendicular mirrors traveling through time. Since one mirror (the one in the direction of motion) was moving away from the light as it traveled towards it and away as it moved away, this created an inconsistency. Time dilated in one direction with speed, but differently in another. To solve this length contraction was added, and it allowed time to dilate the same in all directions with speed.

Now when it comes to general relativity I understand that light follows the curves in space time created by the presence of energy. Why it distorts, and how it does it are things I am interested in, but they don't play a role in what I am asking, only the fact that it does curve, and light follows the curves matter for what I am asking. The other effects of the curvature may matter, I am not completely aware of the full effects, if I was I probably wouldn't be asking this question at all.

Now that all being said in the included image (assuming it shows up properly this is my first time on the site) I have set up a Michelson-Morley Apparatus similar to those diagrams I have seen relating to special Relativity, which to a large degree unlike general relativity I have a pretty good understanding of. In the diagram A and B are perpendicular to R and as such the light bends as it moves from A to B, it follows the bends in space created by the mass E. C and D are perfectly in line with R, I haven't labeled R in vector form because I am not the best at it, and because the direction of R doesn't matter so much for what I am asking. Now in this case light from A to B bends and thus it takes a longer path, causing our light clock in that direction to tick slower. However with CD wouldn't the light travel in a straight path? space is bend equally around it, why would it decide to curve in one way and not the other? If it doesn't curve then wouldn't its light path wouldn't be altered and it wouldn't experience the same time dilation as AB. This creates an inconsistently similar to the one first experience with Special Relativity.

I know this forum isn't supposed to be about proposing alternatives to the theory, I am not doing that. All I am asking for is an explanation of why this doesn't actually cause an inconsistency, and I ask because I haven't been able to find one through google searches (its probably labled as something which I am not aware of) and my Astro teacher, who claims to be a physicist as well had no explanation other than he thought my diagram seemed accurate. He actually said to tell him what I find on the matter, which I thought was cool, but it didn't help me at all.

What really makes this hard is almost no understanding of calculus or tensor analysis, it makes the equations really just look like a mess to me. I know I will need both to fully understand what is going on here, but a short simple explanation, with some math as long as it doesn't involve too much Calculus (if it does list it as well I may not know it know, but I could definitely use it later) would be great.

Oh and assume that the bars on top of the vertical lines, in the lower section of the diagram represent 1 second in relation to CD's light clock. Which is why the line in AB just stops, because by the time 1 CD second has passed it hasn't reach A again.

http://img812.imageshack.us/img812/258/xtmp.png [Broken]

Last edited by a moderator: May 6, 2017
2. Nov 7, 2013

3. Nov 7, 2013

### GordonFreechme

I am well aware that curved space changes the path of light. Light follows straight lines in curved space. That isn't what I am asking. See the diagram, in the AB light clock I showed the path of light being bent.

The question here is doesn't this cause inconsistencies with time dilation? Since light traveling along the path R be it negative or positive along that path it couldn't follow a curved path since the bending of space and time would be the same in all directions.

We have one light clock with its beam of light's path is being bent by spacetime, another light clock whose beam of light isn't being bent. This would cause the effect shown in the lower diagram where the beams of light don't return at the same time despite being orientated in the same place. This was one of the big issues with special relativity before length contraction, and unless there is an effect I am unaware of space time couldn't behave the way Einstein described.

Of course I expect I am mistaken, I believe this to be the case, which is why I need this answered, so I can understand what is actually going on.

4. Nov 8, 2013

### A.T.

When was that? SR always contained length contraction, as far as I know.

If your clocks are not free falling, then they are not at rest in an inertial frame.

Also, in SR the inertial frames of reference extend to infinity, so you can use light clocks of arbitrary size there. In curved space-times inertial frames are just local approximations, so the laws of SR hold only for experiments contained in a small area, where the curvature is negligible.

Last edited: Nov 8, 2013
5. Nov 8, 2013

### HallsofIvy

In fact, "length contraction" preceded relativity. Lorenz, in an attempt to explain the Michaelson-Morley experiment, postulated that the moving electrons in the arms of the experiment have a stronger electro-magnetic field and so "contract" the arms exactly enough to give the null result, calculating the Lorenz contraction formula. Einstein's relativity required that empty space itself must contract so it could not be just a matter increased field strength for electrons. The Kennedy experiment, a variation on the Michaelson-Morley experiment showed that it was Einstein, not Lorenz, that was right. Of course, the amount of contraction is the same so we still use the Lorenz contraction formulae.

6. Nov 8, 2013

### GordonFreechme

What I meant was that it was a problem with the theory itself, I know of lorentz transformation, when I look at Special Relativity I see it as a collective work, not completely attributable to Einstein. As I see it as a complete package.

I know the frames are And why would the frames not be at rest? They have to be accelerating yes, but in this case the acceleration in the opposite direction of gravity, is equal to gravitational acceleration so the two cancel out, creating a net change in velocity of Zero.

I know that the frames of reference extend to infinity, that's why in the graph I have selected points, and labeled them. I didn't bother to set exact co ordinance because those depend on the reference frame.

I still am not seeing an answer to my question though. If AB's path is curved due to space time of gravity, it would take longer to get to B. The light Clock would tick slower. Regardless of actual length. However when we line C and D up perfectly with R how could it's path curve? Its a straight line to E. If it warps in Space time and isn't warped in Euclidean space, then why is ABs path curved? Why would one direction cause you to take a warped path in space and not another. And if the beam of light going from CD was traveling in curved space, but its path in our 3Dimensions was straight, wouldn't this imply it was traveling distance we couldn't see it traveling? And if the speed of light is the same no matter what direction or how fast wouldn't that contradict it? This is what was being asked.

The reason it is being asked is because of the formation of length contraction to explain the unequal ticking of light clocks in the unlength contracted model. If it was a problem for light clocks to not have the same time to tick in a local frame there, why would it be okay here? Wouldn't it cause the same problems?

I am sure there are answers to these, but none of you have answered them. At least not clearly. And really we could set any lengths for our light clocks, so long as space is curved. For that show the difference in ticking, it would just be smaller if the length was smaller, and space wasn't warped as much. The more either increase the larger the difference in ticking of our light clocks.

7. Nov 8, 2013

### yuiop

I think the problem is that you expect two orthogonal equal length light clocks to have the same frequency under all conditions, but that is not true. In a MMX type set up in perfectly flat space, we expect a null interference result, no matter how we orientate the apparatus relative to the motion in a given reference frame, because absolute inertial motion in flat space cannot be detected. A similar apparatus in curved space due to gravity or where proper acceleration is present will show a positive interference pattern, because there is no reason to expect that our orientation in a gravity field or our acceleration in a rocket or a centrifuge cannot be detected.

8. Nov 8, 2013

### A.T.

Nobody claimed that "speed of light is the same no matter what direction" in non inertial frames. Therefore no contradiction.

9. Nov 9, 2013

### GordonFreechme

Well thanks, non inertial reference frames. This wasn't something I had heard of before. I am not sure if I mentioned it or not, but I am not in a physics class nor have I taken all the math, so there is a lot of stuff I am missing. This was one of them. Maybe this will answer my question maybe it won't. I can't say as I really don't know the meaning of non inertial reference frames, but at least I have a start which was all I was asking for. I just didn't know a short way of explaining what I was asking, as I was missing more convenient terminology.

10. Nov 9, 2013

### GordonFreechme

One more thing though, doesn't an interference pattern have to do with wavelength? And why would acceleration effect the speed of light? I was under the impression that as we speed up length contracts and time dilates in the direction we are accelerating in to compensate for that effect.

11. Nov 9, 2013

### Staff: Mentor

The best way to analyze this scenario is to suppose that you are in flat spacetime with an interferometer which starts momentarily at rest and accelerates during the travel of the light along both arms. Per the equivalence principle, this is equivalent to a device at rest in a uniform g field. You can obtain the correct expression for delay as a function of g.

12. Nov 9, 2013

### GordonFreechme

What I don't get is why this would effect the time it took the light particles to get their in comparison to each other. Wouldn't length contraction happen only in the direction of acceleration? And wouldn't this cause the particles to still tick at the same time? Isn't this why length contraction was introduced in the first place?

13. Nov 9, 2013

### astrohameed

Sorry actually i can't see the diagram pls send the diagram to me if poscible and from reading ur post i got something and iam trying to answer it hear ok u considers the space time curve is to uniform in all direction but it may not be uniform in all direction or not even same in the same direction in different time . Actually the bending of space time is caused by the gravity and the curved path is called a geodesic the curvature is directly proportional to the gravitty acting on that space but we know any body having a mass can create gravitty so at any space the gravity acting on it will not be a single gravitational force it will be a sum of all gravitational force acting on that place and we have to keep in mind that the gravitty is vector quantity so the directions will effect the gravitty at any point and so the curvature also will change with direction and also due to the motion of heavnly bodies this direction of gravity may change with time .

14. Nov 9, 2013

### yuiop

If an apparatus that has two light clocks mounted at right angles to each other, they are looking for a delay in one of the arms which is effectively due to the light taking a longer path in one of the arms. if the effective path is longer in one arm relative to the other, the waves do not arrive back at the centre in sync and this shows up as an interference pattern. The interferometer is just a very sensitive device to compare light path lengths.

An inertial reference frame has constant velocity in flat space and an accelerometer would register zero acceleration. A non inertial reference frame is an an accelerating reference frame in which the acceleration can be measured by an accelerometer. An example of a non inertial reference frame is standing on the surface of the Earth. You can detect your acceleration by standing on some weighing scales or simply by sensing the pressure on the underside of your feet. Another example was given by Einstein in an accelerating lift in flat spacetime. A light projected across the lift would appear to follow a curved path according to a person inside the accelerating lift, but a straight path according to an inertial observer floating around outside the lift. In an accelerating reference frame, the curved paths followed by light means that the time for light to get from A to B is not the same as in flat spacetime. An easy to visualise example is to time light signals on a rotating disc. If the radius of the disc is r, then the time to go from the centre to a mirror on the rim and back to centre is simply 2*r/c. If we now send the signal from the rim to a mirror at the centre and back to the rim, the time as measured by a clock on the rim is 2*r/c*1/γ, where γ is the gamma factor due to the velocity of the clock at the rim. The rim clock is time dilated and therefore measures a shorter time. The clock on the rim in non inertial because it experiences proper acceleration and it it does not measure the speed of light to be the same in all directions. (Note that the radius of the disc does not length contract because it is at right angles to the velocity.)

15. Nov 9, 2013

### Staff: Mentor

You should work it out as I described to see why the time is affected. Did you understand the setup I proposed earlier?

16. Nov 9, 2013