Nature of Time Dilation and Length Contraction

[Prosoothus]

As many of you already know, I'm not someone who is very fond of Relativity. There are several problems I have with relativity, and one of the main ones is the actually cause and effect between spacetime, the speed of light, and the observer. Here's the issue:

Let's say that you have two inertial observers moving at different speeds and one beam of light. Relativity claims that time dilates and length contracts in each observers frame of reference so that they both see the beam of light travelling at c. My questions are:

How does spacetime know how much length needs contracting and how much time needs dilating for an observer? Doesn't spacetime have to observe both the speed of light and the observer to know how much its length needs to contract and its time needs to dilate in order to keep the speed of light invariant for an observer? If spacetime is a seperate entity from the observer, and time dilation and length contraction are not illusions, what interaction causes the physical properties of length and time to change? What exactly is the relationship between spacetime, light, and an observer, and how exactly do they influence each other?

Maybe I'm just old fashioned, but I believe that in order for a physical property to change, it must be influenced by something. Of course, the exceptions would be if that property oscillates, or is entangled in some way. However, in relativity, a property changes without any apparent influence or interaction with the objects that actually determine the amount of change of that property. This doesn't seem logical.

 

[mathman]

How does spacetime know

What is this spacetime you are talking about? Special relativity describes how time and length transform between different inertial coordinate systems.

 

[przyk]

However, in relativity, a property changes without any apparent influence or interaction with the objects that actually determine the amount of change of that property.

As it stands, the universe exists for no apparent reason.

 

[James R]

Prosoothus:

When you view your house from a distance, it looks smaller than when you're close to it. How does your house know how big to appear? Because it would have to know how far away from it you are.

 

[Tom2]

When you view your house from a distance, it looks smaller than when you're close to it. How does your house know how big to appear? Because it would have to know how far away from it you are.

Any antirelativist worth his salt would tell you that the apparent size of the house is just your brain's way of making sense of the input data.

I think a better approach would be to turn the question on its head. Imagine we live in a Galilean universe and that the speed of light from a stationary source is c. Let's say you observe a light pulse from a source moving at speed v in the same direction as the pulse.

How does spacetime know how much the speed of light needs to be changing for an observer? Doesn't spacetime have to observe both the (invariant) spatial and temporal intervals and the observer to know how much the speed of light needs to change in order to keep spatiotemporal intervals invariant for an observer? If spacetime is a seperate entity from the observer, and the variation of the speed of light is not an illusion, what interaction causes the physical property of the speed of light to change? What exactly is the relationship between spacetime, light, and an observer, and how exactly do they influence each other?

 

[DaleSpam]

Tom2, your approach is a very good rhetorical approach, but I do like James_R's comment. The reason that a house looks smaller is simply a feature of the Euclidean geometry of space. Similarly, length contraction and time dilation are simply features of the Minkowski geometry of spacetime. Anti-relativityists (like Prosoothus) simply assume that spacetime must have a Euclidean geometry and get upset when reality and people who study reality don't agree. They think the universe and everyone else must be wrong, not them.

-Dale

 

[przyk]

Personally I find quantum mechanics more "illogical" than SR. It makes no sense to me that people pick on relativity and non-Euclidean geometry rather than the apparent contradictions in QM (which seem to have been too much for even Einstein).

 

[Physics Monkey]

Hi przyk,

I think your view is pretty common in that most people find quantum mechanics rather more unsettling that relativity. It leaves a lot of room to wonder why most people with a bone to pick pick it with special relativity. Just out of curiosity (because I get tired of arguing about relativity all the time ), is it the "usual suspects" that bother you about quantum mechanics?

 

[przyk]

Not sure what you mean. I was referring to the brief introduction to quantum mechanics I read in the first chapter of Feynman's Lectures vol. 3. I don't like the idea that the distribution of electrons on some background after travelling through a double slit is not the sum of the distributions you'd get for each single slit (I'm rushing through the description as I'm assuming you're familiar with it). I feel uncomfortable that the whole theory would break down were it not for the uncertainty principle. Note that its discomfort - I'm not saying anything about QM being logically inconsistent or anything (not that I really know enough to argue about this theory anyway).

I can, to some extent, visualize what's going on in special relativity. But it sounds like particles in quantum mechanics behave like nothing I can relate to.

 

[Tom2]

Tom2, your approach is a very good rhetorical approach, but I do like James_R's comment.

The reason I like mine better is that it leads to a logical problem that most pro-Galilean-relativity people ignore. They usually argue that the Lorentz transformations are just a mathematical accounting tool that keeps the speed of light invariant and that doesn't explain why spatial and temporal intervals are relative. I have no qualm with this view. But these same people often fail to recognize that the Galilean transform is also nothing more than a mathematical accounting tool that keeps spatial and temporal intervals invariant and that doesn't explain why the speed of light is relative.

The dismissal of Special Relativity in favor of Galilean Relativity is then quickly seen to be not a matter of being "old fashioned", but rather a matter of simple bias, and bias against all the experimental evidence at that.

The reason that a house looks smaller is simply a feature of the Euclidean geometry of space.

Is it? Euclid's geometry says that parallel lines never meet, but if you look at two train tracks they sure to appear to be getting closer together. But they aren't, it's just an optical illusion.

Likewise with the house: neither Euclidean geometry, nor Galilean Relativity, nor Special Relativity say that the house should be smaller when you stand further away from it, and indeed it isn't smaller. The apparent reduction in size is just an optical illusion, and is really not analogous to SR at all.

 

[EmptyForceOfChi]

time has not ever been physicaly tested to disstort or dialate, the only dialation maybe is with a clock but a clock is not proof of time,


peace.

 

[Tom2]

I've had this conversation way too many times to want to get into it again. I'll refer you to the following threads:

http://www.scienceforums.net/forums/showthread.php?t=11869
http://www.physicsforums.com/showthread.php?t=106062

If I may quote myself...

In response to the question of whether time itself really slows down, or do the clocks merely slow down while time passes normally:

What's the difference? There are no indicators of time other than clocks. And if all clocks--regardless of the mechanism by which they work--all show the exact same lag in elapsed time when subjected to "twin-paradox" type experiments, then in what sense can it be said that time dilation has not occured? Or should we suppose that the clocks are all conspiring to play a trick on us?

More at the links I posted.

 

[Physics Monkey]

przyk,

Thanks for the reply. I was just curious what it was that you found "discomforting" about QM, and you've answered my question.

 

[Physics Monkey]

Tom2, I didn't realize you were Tom Mattson from Physics Forums! I'm afraid I'm just slow when it comes to such things. How funny.

 

[przyk]

przyk,

Thanks for the reply. I was just curious what it was that you found "discomforting" about QM, and you've answered my question.

I told you pretty much everything I know about QM, actually...

 

[Pete]

Is it? Euclid's geometry says that parallel lines never meet, but if you look at two train tracks they sure to appear to be getting closer together. But they aren't, it's just an optical illusion.

Likewise with the house: neither Euclidean geometry, nor Galilean Relativity, nor Special Relativity say that the house should be smaller when you stand further away from it, and indeed it isn't smaller. The apparent reduction in size is just an optical illusion, and is really not analogous to SR at all.

The size the house appears is just the angle subtended at your eye by the house, right?

So, the reason that things looks smaller if they're further away is because an arc of given length subtends a smaller angle as radius increases.

If an arc of given length subtended a larger angle as radius increased, then things could look larger when you stood further away.

I'm not completely sure, but I'm pretty confident that the relationship between radius and subtended angle is a characteristic of the geometry. Physically, I think that gravitational lensing may produce situations in which an object may appear larger to a particular observer as its distance increases within some limit.

 

[Tom2]

I'm not completely sure, but I'm pretty confident that the relationship between radius and subtended angle is a characteristic of the geometry.

I've just realized why the shrinking house doesn't sit right with me. I agree that it is a geometrical issue, but I disagree that it is a Euclidean geometrical issue. I don't see that Euclid's geometry allows you to deduce the size of the house from measurements made at a distance. To make that deduction I think you have to use projective geometry, aka descriptive geometry. Projective geometry is a branch of geometry that was developed specifically to deal with perspective drawing. A more modern application of it is in the field of computer vision.

This reinforces my conviction that the the Special Relativity/Galilean Relativity analogy is better than the Special Relativity/Shrinking House analogy. Projective geometry aims to describe how things look. Relativity theories aim to describe how things are.

 

[Billy T]

Tom2, I didn't realize you were Tom Mattson from Physics Forums! I'm afraid I'm just slow when it comes to such things. How funny.

PM do you have any relationship to Space Monkey over at Physics Forum? - He is one smart monkey also.

I copied post of his to my computer that shows it is actually harder to notice a small black hole passing relative near the solar system than one passing farther away (via gravitational lensing) because the higher angular rate of change makes the duration of the event too short (perhaps some shot noise limits in any change distant star's intensity are also important?)

I am interested in this as my book Dark Visitor is based on idea that there probably are more pairs of small black hole than all the stars that have ever existed and one (the first or second? of a pair) may have been the true cause of the late 1920s perturbation of Neptune, that lead to Pluto's discovery (by accident as it is much too small to have been the cause of the perturbation).

 

[DaleSpam]

The reason I like mine better is that it leads to a logical problem that most pro-Galilean-relativity people ignore. They usually argue that the Lorentz transformations are just a mathematical accounting tool that keeps the speed of light invariant and that doesn't explain why spatial and temporal intervals are relative. I have no qualm with this view. But these same people often fail to recognize that the Galilean transform is also nothing more than a mathematical accounting tool that keeps spatial and temporal intervals invariant and that doesn't explain why the speed of light is relative.

The dismissal of Special Relativity in favor of Galilean Relativity is then quickly seen to be not a matter of being "old fashioned", but rather a matter of simple bias, and bias against all the experimental evidence at that.

Good point. The bias generally becomes obvious after a little discussion anyway. Particularly with those who are vehemently opposed to relativity but cannot figure out what it actually predicts in a given situation. Your approach allows you to point it out without the discussion.

Is it? Euclid's geometry says that parallel lines never meet, but if you look at two train tracks they sure to appear to be getting closer together. But they aren't, it's just an optical illusion.

Likewise with the house: neither Euclidean geometry, nor Galilean Relativity, nor Special Relativity say that the house should be smaller when you stand further away from it, and indeed it isn't smaller. The apparent reduction in size is just an optical illusion, and is really not analogous to SR at all.

The important lines are not the lines of the train tracks but the lines from your eyes to the tracks. It is not an optical illusion in the sense that your brain is processing the data to give you a mistaken impression. Your eyes and brain are correctly representing the fact that the angle subtended gets smaller as the distance increases despite the fact that the tracks themselves are parallel to each other and the house a constant size. That is simply a feature of Euclidean geometry. In fact, your brain actually compensates as best as it can for this geometrical fact such that you don't actually percieve the football players on the field to be smaller than your little son sitting next to you in the stands.

I admit that the analogy to SR is quite tenuous, but it does show that weird things can happen under any geometry depending on your point of view. We are most familiar with Euclidean geometry since our enormous visual cortexes are designed to process such data. If c were near our "everyday" speeds then we would probably have evolved with brains designed to process Minkowski geometry and it would have seemed natural to us. As it stands, it is not natural for a human to think in Minkowski geometry. It is difficult for some to realize that simply because it is not natural for us to think in that geometry does not imply that the geometry itself is unnatural.

I think that either way we are describing the same thing. You are talking about a bias against c being invariant and I am simply talking about a bias against the geometry under which c is invariant.

-Dale

 

[DaleSpam]

I've just realized why the shrinking house doesn't sit right with me. I agree that it is a geometrical issue, but I disagree that it is a Euclidean geometrical issue. I don't see that Euclid's geometry allows you to deduce the size of the house from measurements made at a distance. To make that deduction I think you have to use projective geometry, aka descriptive geometry. Projective geometry is a branch of geometry that was developed specifically to deal with perspective drawing. A more modern application of it is in the field of computer vision.

This reinforces my conviction that the the Special Relativity/Galilean Relativity analogy is better than the Special Relativity/Shrinking House analogy. Projective geometry aims to describe how things look. Relativity theories aim to describe how things are.

I have never heard of projective geometry, but it sounds like a subset of Euclidean geometry. Obviously, I cannot be sure since I am plainly ignorant.

Euclidean geometry does allow you to deduce the size of the house from measurements made at a distance. Remember, your brain "knows" the distance between your eyes. Given that distance and the angle of the eyes looking at a particular point you can determine the distance to the point and given that distance and the angle subtended by the object you can determine the size of the object. If there were not enough information inherent in the situation then your brain could not "correct" for the effect as it does. It is all just similar triangles etc.

-Dale