# Are SR effects caused by spacetime distortion?

1. Jan 4, 2016

### alw34

We now know two things distort space time: relative speed [we call it time dilation and length contraction] and gravity. Gravity IS the 'curvature' of space and time. "Mass tells spacetime how to curve; spacetime tells mass how to move." [John Wheeler, I think.]

Last edited by a moderator: Jan 5, 2016
2. Jan 4, 2016

### Staff: Mentor

One yes, one no. Relative speed does not distort spacetime, and neither time dilation nor length contraction are caused by spacetime curvature. Indeed, special relativity with its length contraction and time dilation only works in flat spacetime.

3. Jan 4, 2016

### alw34

Relative speed does distort space time. Is there a better word than 'distort'??....
because length contraction and time dilation are used to explain how the two way speed of light is the same for all inertial observers. In other words, the speed of light is the constant, not length and not time duration among different inertial observers.

4. Jan 4, 2016

### Staff: Mentor

"Curved" is more often used than "distorted".
This is correct, but it doesn't show that spacetime is being curved or distorted by relative motion.

In the flat uncurved spacetime of special relativity (the form of the theory that deals with relative motion) there is no distortion of spacetime; the spacetime interval and other geometric relationships between any two events is the same for all observers regardless of their state of motion. Time dilation and length contraction appear only because observers in motion relative to one another attach different time and position labels to the same events.

Consider Einstein's train thought experiment, the one that shows the relativity of simultaneity. There's no spacetime distortion going on there, we're just tracing the path of the light signals through space, yet the train and platform observers must assign different times to when the two lightning flashes struck. And once you have relativity of simultaneity, length contraction and time dilation must follow.

5. Jan 5, 2016

### PeroK

You're missing the point that relative motion does not distort spacetime, but gives a different view of it. The analogy is with different observers viewing an object in space. If one observer looks from a different angle then their view of the object is different from the other observer. But the object itself is not changed by being looked at from a dfferent angle.

If, however, the object is deformed, then all observers would agree on the deformation (although, again, they would all be viewing it from a different angle).

Relative motion is analogous to the two observers taking a different view of spacetime, from a different angle.

The other point you're missing is that there is no absolute spacetime and no absolute preferred observer. If there were, it might be fair to say that everyone moving relative to that preferred observer had a distorted view of absolute spacetime. But, there is no preferred observer. Moreover, every inertial observer is moving with every possible velocity relative to some other inertial frame, so how would you quantify the distortion? To every inertial observer, spacetime is flat and undistorted (in SR). Albeit pseudo-Euclidean.

Finally a thought experiment. Two observers are moving relative to each other in an area of SR spacetime. Let's agree for a moment that spacetime is distored by their relative motion. Is it distorted for one, the other or both? Let's assume it must be both. They both agree "spacetime is distorted". One of them vanishes. Leaving just one observer. What does he now conclude? That spacetime is still distorted? Or, that some mysterious force has not only removed his companion but reshaped all of spacetime? In what way does spacetime change by an additional observer being added or removed? The answer is, of course, not at all. Spacetime is not affected by the number of observers, nor their relative motion. If spacetime is curved, it's curved whether or not anyone is moving relative to anyone else.

In fact, you could tidy up that last thought experiment by having one observer, who simply imagines an inertial reference frame moving with respect to himself. By imagining such a reference frame, how can that distort spacetime? Spacetime is unchanged no matter how many reference frames you imagine on it.

6. Jan 5, 2016

### FactChecker

It sounds like the point is that no one can detect any change in their own space-time due to SR. A true "distortion" (like changing the curvature) would be detectable. To an outside stationary observer, it looks distorted, but it really isn't. On the other hand, the change due to gravity and GR is obviously detectable. Is that correct?

7. Jan 5, 2016

### alw34

I can't tell if we have a word difference of if I am missing something technical. It sounds like 'distortion' to you means an effect of curvature, which is ok. But how can the 'geometric relationships' be the 'same' when space and time of one observer is mixed differently than that of the other observer? I do understand this is a coordinate difference, but your last sentence doesn't make sense to me:

I am commenting from the perspective that two observers in different gravitational potentials experience a different passage of time because after they come together and compare time duration in the same reference frame their clocks don't match. Like wise, two observers in relative motion, same gravitational potential, also experience a difference in the passage of time when they come together and compare time duration in the same reference frame. [twin paradox I guess]

To me the differences in time in the two cases is a 'distortion' of space and time.

What have I got wrong here?

PS: FactChecker....if I understand things, a big 'if' of course, this is quite a different view than your post. But thanks for your post, because that enabled me to clarify my thinking.

8. Jan 5, 2016

### bcrowell

Staff Emeritus
"Distortion" is a general term with no specific, widely recognized technical definition. When I teach relativity, I do refer to the Lorentz transformation as a "distortion" of spacetime, but I also refer to the Galilean transformation (which predates relativity by hundreds of years) as a distortion.

9. Jan 5, 2016

### alw34

right....

ok. And I think it is fair to say those transformations explain the differences in elapsed clock times I tried to explain. So what appear to be 'only coordinate differences' as Nugatory said, which can't be directly measured, leads to real differences that can be.

I also recognize the Einstein stress energy tensor formulation for curved spacetime manifests as gravitational tidal forces and this is a different kind of formulation....coordinate free.... a different kind of 'distortion'....yet this formulation simplifies to Lorentz type transformations in the absence of gravity, doesn't it.

Maybe Nugatory limits 'distortion' to the gravitational type??

And maybe it's better to simply say "Both relative motion and gravitational potential affect the passage of time."?? I like that better.

10. Jan 5, 2016

### Staff: Mentor

This is the geometry of four-dimensional spacetime, not three-dimensional space, that we're talking about. Thus, "mixing time and space differently" is just a matter of drawing a different set of coordinate axes in spacetime. If we are moving inertially, our path through spacetime is a straight line. We draw our time axis parallel to that straight line and our space axes perpendicular to it so that our spatial coordinates are constant while the time coordinate is constantly increasing; this pretty much captures our experience sitting in an armchair looking at a clock on the table next to us. Now if we're moving relative to one another, our straight line paths won't be parallel to one another so when we draw our coordinate axes mine won't be parallel to yours.

There's a an analogy from two-dimensional space: The distance between two points is always given by $\Delta{s}^2=\Delta{x}^2+\Delta{y}^2$; if you use a set of coordinate axes that are rotated relative to mine, you'll get different values for $\Delta{x}$ and $\Delta{y}$ but the real physical fact of the distance between the two points will still come out the same. In the flat spacetime of special relativity the distance between two points is given by $\Delta{s}^2=\Delta{x}^2-\Delta{t}^2$ and comes out the same for all observers even if their relative motion leads them to assign different $x$ and $t$ values, and hence to come up with different values of $\Delta{x}^2$ and $\Delta{t}^2$

Differential aging in the twin paradox happens because the two twins take different paths through spacetime. Call the point in spacetime (a point in spacetime is usually called an "event") where they separate at the start of the journey A, the point at which they meet again B, and the point at which the travelling twin changes directions C. The stay-at-home twin follows a straight path from A to B, while the traveller follows an indirect path from A to C and then to B. These are different paths with different lengths - and the length of a (timelike) path through spacetime is the time elapsed for an observer following that path so they experience different times. You'll find more in the Twin Paradox FAQ and especially the section on the "Spacetime diagram analysis".

Gravitational time dilation as it usually presented is a different phenomenon. It's based on comparing the times that you and I assign to two different pairs of two events: A1 and A2 are "my clock ticked" and "my clock ticked again"; B1 and B2 are "your clock ticked" and "your clock ticked again". If the two clocks are of identical construction, the proper time (spacetime distance) between A1 and A2 will be the same (that's what "identical construction" means) as that between B1 and B2; however, if I assign the same time coordinate to events A1 and B1, the curvature of spacetime will make it impossible for me to naturally also assign the same time coordinate to A2 and B2. An analogy from ordinary curved space is that on the surface of the earth I cannot use longitude as a coordinate and require that the distance between any two points of equal latitude and constant longitude difference be the same.

Last edited: Jan 5, 2016
11. Jan 5, 2016

### alw34

Nugatory....thanks for your time...
still trying to understand,
want to think instead of posting...
be back again tomorrow

https://en.wikipedia.org/wiki/Time_dilation
especially: "....From a local perspective, time registered by clocks that are at rest with respect to the local frame of reference (and far from any gravitational mass) always appears to pass at the same rate....In special relativity, the time dilation effect is reciprocal: as observed from the point of view of either of two clocks which are in motion with respect to each other, it will be the other clock that is time dilated.....Observers do not consider their own clock time to be affected, but may find that it is observed to be affected in another coordinate system.

12. Jan 6, 2016

### alw34

Looking back at this, Nugatory's comments imply he reads my use of 'distortion' as 'curvature'.

That's not what I meant. [For others reading this thread, spacetime 'curvature' is meant as 'gravity'. ]

I meant things like the relative difference in the passage of time, and this, as explained in Wikipedia:

"Terrell rotation or Terrell effect is the name of a mathematical and physical effect. Specifically, Terrell rotation is the distortion that a passing object would appear to undergo...."

Anyway, if 'distortion' is too ambiguous in these forums, a more precise wording is:

".... time dilation is a difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from a gravitational mass or masses....
[Wikipedia]

Cheers.

13. Jan 6, 2016

### Ibix

The key words in the passage about Terrell Rotation are "would appear to". It's an optical effect ftom the difference in travel times of light from different points on an object.

Both length contraction and time dilation due to relative motion are coordinate effects. You can change them by changing your choice of simultaneity convention. I don't think this is distortion - it's more closely analogous to a square turning into a diamond when you rotate it. As bcrowell says, whether or not you call this distortion is a semantic issue. But there's a measurable difference between GR curvature and SR coordinate changes - only one of them is keeping you in your seat right now, and the other never can.

14. Jan 6, 2016

### alw34

You touch on an issue I had not thought about enough until Nugatory posted the same. I wanted to read about that issue before I started a new thread.......

Is it the acceleration itself with regard to the SR time dilation in relative motion that induces the physical change in elapsed times which clocks are brought together ? I previously thought not...that SR could handle acceleration just fine.

If acceleration is what induces the physical elapsed time delay, is that due to some tensor like 'curvature' effects? I don't see how since nothing like that is in Lorentz transforms.

Wikipedia tackles the issue here:
https://en.wikipedia.org/wiki/Twin_...lt_of_differences_in_twins.27_spacetime_paths

Last edited: Jan 6, 2016
15. Jan 6, 2016

### Staff: Mentor

SR does indeed handle accelerations just fine. But it sounds as if you're still conflating differential aging and time dilation - they are different phenomena, and differential aging is not caused by (or even especially closely related to) time dilation. One way of seeing this to consider that in the twin paradox case the traveling twin ends up younger, even though the earth clock is moving relative to him so is time dilated and and running slow compared with his clock throughout the entire journey.

(Of course the situation is symmetrical - the stay-at-home twin also considers the traveller's clock to be the moving and dilated one. This symmetry is another hint that time dilation doesn't cause differential aging - time dilation works the same way for both twins, so it shouldn't age them differently).

It's not, which is why you don't see it in the Lorentz transforms. Acceleration shows up in the twin paradox only because you can't send the twins on different paths between the same two events (separation and reunion) without accelerating at least one of them.

You might also consider that the traveller's acceleration at the turnaround point is the same whether he spends a day, a week, a year, or a century coasting between earth and the turnaround, but the age difference will be greater the longer he coasts. That's a hint that the effect is not produced by the acceleration, but rather by the length of the journey.

16. Jan 6, 2016

### Staff: Mentor

If you work through the math on that page, you'll see that the stronger the accelerations are the less they matter. The complicated calculations for the accelerated phases of the journey are just to allow for the fact that the turnaround cannot be quite instantaneous so we should allow for the time elapsed during the turnaround as well as the time spent coasting. A much easier calculation, no integrals or hyperbolic functions needed, is just to take the acceleration so large that time accelerating is a negligible fraction of the total time between separation and reunion.

Somewhere above I linked to the twin paradox FAQ at
If you haven't worked through it already, you should.

(BTW, wikipedia is not in general an acceptable reference at PhysicsForums. We spend a lot of time unconfusing people who have been confused by what they've read there.)

17. Jan 7, 2016

### alw34

I know they have different origins, but exactly how one explains that to one's mother [was it Susskind who said you should be able to do that?] will require some reading on my part.

yes..in the Baez link, which I have only superficially skimmed, I see an example where instead of 'acceleration', the traveling twin 'free falls'..around a planet,say,....that should be interesting.

18. Jan 7, 2016

### PeroK

Here's a classical analogy:

Two people start out at point X and travel to point Y. A travels in a straight line (distance $d$, say) and B travels otherwise (distance $2d$, say). Each has a mileometer (odometer), which they compare when they meet at point Y. They are really confused because A's mileometer reads $d$ while B's reads $2d$ and they are at a loss to explain this difference. Perhaps space is distorted in some way? Perhaps the fact that they took different paths from X to Y distorted space? Perhaps it was the Galilean Transformation that distorted space?

19. Jan 7, 2016

### Staff: Mentor

The Baez link will get through the twin paradox and differential ageing.... and with tongue only slightly in cheek I'm going to recommend that you superficial skimming for wikipedia.

Of course the Baez link won't help you with time dilation because it's not about time dilation, it's about the twin paradox and differential ageing. For time dilation, you will want to start with the relativity of simultaneity (google for "Einstein simultaneity train"), as it is impossible to make sense of time dilation (A says that B's clock is slow; B says that A's clock is slow; they're both right and there is no contradiction or inconsistency) without understanding the relativity of simultaneity.