Nature of Time Dilation and Length Contraction

Projective geometry is a "general geometric system". Euclidean and non-Euclidean geometries would be special cases in projective geometry.

Edit: You know, what I just said would take more explaination to clarify then I care to type. So you can feel free to ignore it. Though it makes for an interesting history lesson for the "evolution of geometry".

 

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The convergence angle of the eyes is only one of about a dozen things that allow you to convert the 2D image on your retina into a 3D perception of the world. Shut one eye and you will still easily preceive a 3D world.

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Why don't you guys for a second disregard the fact that I'm an antirelativist. That's not the issue here. The issue is that I truly don't understand how two physical properties (space and time) can change their physical values based on what an observer observes. Why does space and time care what an observer sees, or care what the speed of light is relative to the observer?

mathman:

But it transforms physically, not perceptually. That's my problem. How can an observer's relative motion influence space and time physically?

przyk:

True, but if a property in the universe changes in a non-inertial way, don't you think that there has to be a reason, and an interaction, for this change to occur?

James:

But the actually physical properties of the house do not change. Relativity claims that the actually physical properties of space and time do change, and that it's not just a matter of perception.

Tom:

I'm not sure I understand your example. Do your questions apply to a situation in which the speed of light is not invariant? If that's the case, then I can say that the light will only care what its speed is relative to a medium, or to it's initial speed, and that it doesn't care what one, or more, observers see or don't see.

Dale:

As I mentioned above, just because the house looks smaller doesn't mean the house is smaller. But in relativity, when space looks contracted, that means it is contracted. Can't you see the difference? One has to do with a physical property remaining constant while the perception of it changes, while the other has to do with the physical property actually changing.

Tom:

In the Lorentz transformations, two physical properties change (time and space). There is no explanation, or reason, for this.

In the Galilean transform, the relativity of the speed of light can be explained by saying that the speed of light is linked to an absolute frame.

You're not claiming that Galilean Relativity is as counterintuitive as Special Relativity, are you?

In Euclidean geometry, the actual physical properties of the house do not change, even if the house looks one inch tall from a distance. In SR, the actual physical properties change, not just the perception of them. That's the big difference between the two.

 

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Yes, I said to imagine that we live in a Galilean universe. The speed of light is not invariant in such a universe, but spatial and temporal intervals are.

But I can just as easily turn that on its head when talking about SR: The lengths and times between intervals only care what their values are in their rest frame, and that they don't care what one, or more, observers see or don't see.

Galilean relativity does not have an absolute frame. It has absolute space and time. That means that spatial and temporal intervals are the same for all inertial observers, while the speed of light changes. In Galilean Relativity, the speed of any given light pulse is linked to nothing other than the rest frame of its source, which cannot be said to be at rest in any other frame. The speed of light changes from one frame to another without any explanation whatsoever, just like spatial and temporal intervals do in SR.

Furthermore if you do assert the existence of an absolute frame then you face the exact same problem, but with a different subject. That is you would have to explain why the laws of electrodynamics are different in any frame other than the absolute frame. They would change, and without any explanation whatsoever. Again, this is no different from the situation with spatiotemporal intervals in SR.

I didn't say anything about that one way or the other. I am claiming that Galilean Relativity is answerable to the same complaint you raise regarding Special Relativity, except the speed of light and spatiotemporal intervals swap places in the two problems. It is readily seen that there is no purely logical reason (that is, nonempirical reason) to accept one over the other. To accept one as logical and reject the other as illogical is then seen to be nothing other than a biased point of view, which is no doubt heavily influenced by everyday experience.

I know. That was my point to James and Dale. That's why I favor my approach to the problem over the shrinking house analogy.

 

I know. Our brains are amazing image processors and very "fault tolerant". But the convergence angle is the easiest to describe and is sufficient to demonstrate that there is enough information available.

-Dale

 

Are they physical properties? Mass is a physical property. Charge is a physical property. Even frame-variant things like energy can be considered physical properties. It seems to me that space and time are not the same kinds of things as mass and charge.

Again, the house is not any smaller, but the angle it subtends is. It is just a feature of the geometry. Similarly, in SR time dilation and length contraction is just part of the geometry. In Euclidean geometry a distance doesn't change, but projections of distances do and so do angles. In an exactly analogous manner in Minkowski gemoetry spacetime intervals don't change, but times dilate and lengths contract.

In both cases, even when I am talking about eyes, I am not talking about perception but about geometry. Your confusion, I suspect, comes from the idea that geometry is somehow a physical property. It is not. Geometry and space and time specify relationships between objects. The angle that a house subtends is not a physical property of the house but only a relationship between the top and the bottom of the house and my eyes. In the same manner the time between two events is not a physical property of either event but a relationship between the two events.

-Dale

 

Hi Dale,

I'm not sure I agree that space and time are not physical properties. After all, isn't the whole point of the general theory of relativity that spacetime is a dynamic physical entity? It seems to me that the spirit of relativity resides in the notion that we ought to stop thinking about spacetime as a kind of immutable background upon which the universe unfolds and instead treat it as a dynamical part of that universe. Our coordinate systems are themselves based on the physical behavior of rods and clocks and light pulses, and general relativity teaches us that this behavior can be dynamic. I think perhaps the point is somewhat moot when talking about special relativity since the geometry there, while different from Newton's conception, is unchanging. However, if one internalizes this view, I think it might be harder to make the jump to general relativity. Just some thoughts.

 

Well, if they are physical properties instead of relationships then I think Prosoothus has a very valid point. What makes them dilate and contract in response to an observer? The curvature of a physical spacetime in response to the presence of matter in GR seems much more "caused" than the dilation and contraction of a physical spacetime in response to a moving observer in SR.

Since my GR background is almost 0 you may be very correct that I am setting myself up for a major paradigm shift down the road. However, at first glance the idea of trying to do Minkowski geometry in a curved spacetime doesn't seem too different from trying to do Euclidean geometry on the surface of the earth.

-Dale

 

Space and time are directions in spacetime, right? But they aren't absolute directions - they're relative to the observer, kind of like length and width.

So it seems to me that when time dilates and lengths contracts, spacetime is not dilating and contracting, you're just getting a different perspective or point of view of the same spacetime.

Consider this joke:

Airhead Airlines, Flight 101, is coming in for a landing, and the pilot is freaking out. The sweat is jumping off his brow. (Planelanding and screeching to a halt.) RRRtttt! He turns to the co-pilot, and he says, "Man, that is the *shortest* runway I ever landed on." The co-pilot says, "Yeah, and so *wide*." ​

 

So what stops us making the next step to the aether model, Physics Monkey?

I've been saying on this forum for a long time now that a dynamic, variable density, compressible (when accelerating) aether which is created by the presence of mass and is carried along with mass could replace the notion of spacetime. I've also put forward the idea that time is non-existent and that our measurements of time are nothing more than one set of arbitrarily chosen PHISICAL oscillations measured and compared against another set. Time dilation is nothing more than the "behaviour" of mass as it is moved through the physical aether. And light's wavelength would be reduced as it approached a massive body (gravitational blue-shifting).

What stops us pursuing this model?

 

I would have said: "...relationship between house width and my eyes," because my eyes are not one above the other.

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What's a "cause"? I agree that length contraction doesn't seem very "caused," but its possible that its just because its not something you experience in everyday life. Why would you accept pressure at both ends of an object as a satisfactory explanation for length contraction, but not relative velocity?

As far as I know, causality is about nothing more than linking an event or state to another, usually preceding, event or state - ie, predictability as opposed to random, spontaneous behaviour. There's just some cause-effect relationships that are more familiar than others. That's just how I see relativity.

 

It's different because no matter how far away you stand from the house, as long as you are in the rest frame of the house, you should obtain the same dimensions for the house. How do you measure the size anyway? Do you hold up a ruler from wherever you're standing and say, "Well this house fits within 1 inch on my ruler, so it must be 1 inch wide."? No, of course not. You determine the width by simultaneously assigning coordinates to two appropriate corners of the house, subtracting them, and taking their absolute value. Now if you translate the origin then surely the coordinates you assign will be different than those used by an observer located an another origin that is at rest to with respect to you. But the differences in the coordinates will be exactly the same.

On the other hand, in relativity when you compare measurements made by observers in different inertial frames, the two observers assign coordinates to the corners of the house whose difference is different, which indicates that the width of the house in the two frames is really not the same. And this has nothing to do with how the house 'looks' to either inertial observer. To determine that you would have to take into account the finite speed of light.

So to directly answer your question, the difference between the two scenarios is that relativity insists on assigning coordinates (and therefore determining lengths) by using local rods and clocks. In your "shrinking house" scenario you get a size difference that is only apparent because you are not heeding that restriction when you use your ruler from a distance.

 

We judge any length whatever by comparing it to our "measing stick" and we judge any time intervals we can measure by comparing them to our clocks. So shouldn't the question be 'Why do our measuring instruments change when we change our motion?'
Or am I looking at it wrong?

 

Perhaps. Our clocks and rulers do not change, ever. It is the clocks and rulers of that guy moving past us that change.

 

I have often wondered if length contraction occurs symmetrically about the center of mass, or if it occurs symmetrically about the location of the force which is causing the acceleration (and if so, does length contraction "propagate" at c?), or if it just occurs everywhere along the axis of motion at the same time. For example, if a rocket accelerates due to firing the rocket engine at its base, is the length contraction any different than it would be if the rocket engine were mounted to the middle of the rocket?

Another thing that puzzles me about length contraction is whether it affects velocity. It seems like it must, (but I am certainly no expert):

If we begin with an extremely long train of length L, parallel to the x-axis of coordinate system K, and it accelerates to relativistic velocity v, the length of the train as measured from K would be contracted such that

L' = L / &gamma; << L

So, as measured from K, it seems like the red caboose of the train had greater speed, and the black engine had lesser speed, so that the extreme ends of the train end up closer together. I assume that the mass of the train prevents the caboose from exceeding c, but when the initial length, acceleration, and final velocity are very great, length contraction demands a very large change in position for the caboose relative to the engine. Perhaps the change in length is always distributed in such a way that it is always the the engine that slows rather than have the caboose exceed v and possibly exceed c?

 

Imagine two observers. One is on an old-time steam train, the other is standing near the tracks. When the train blows its whistle, the observer on the train hears a steady tone. The observer standing near the tracks, as the train approaches, hears a higher-pitched whistle, swiftly descending to a lower-pitched whistle as the train passes.

Does the doppler effect "need to know" how much it needs to contract or expand the distance between the sound waves, to raise or lower the pitch?

No, it doesn't need to "know" anything. Anthropomorphism aside, there's no requirement for an exchange of information between the phenomenon and the observer. The stationary observer hears the doppler effect because that's the way the universe operates, and the doppler effect will happen whether or not there's an observer there to hear it.

Similarly, an observer will see einsteinian contraction of an object moving at relativistic speeds because that's the way the universe operates. Einsteinian time dilation has already been observed using atomic clocks on spacecraft, so we know this isn't "just a theory". It's real.

There is no requirement for the universe to operate in a way that makes sense to us. Quantum effects appear more similar to what happens in Alice in Wonderland than to everyday human experience.

 

BillyT:

With all due respect, this appears illogical to me. Whenever we observe any other object change its state of motion, we observe it's measuring instruments change accordingly. Why should we assume that we are so special that ours do not? If all clocks attached to us change the same amount, we obviously could not detect it...but then again, the other guy cannot detect his clocks change either. Now, if our clocks and yardsticks did change in such a manner then it would certainly appear to us as though everything else (space and time?) changed. Where is this view not logical?