# Dilation & Contraction-First Post

1. Oct 22, 2009

### stalnaker

Dilation & Contraction--First Post

Hello! I am a brand-new member here (please be gentle and basic).

I have been listening to a course on special relativity and general relativity—the lecturer is Dr. Richard Wolfson. I have no serious mathematical background but would like to have a much better conceptual understanding of physics since Einstein. In any case, Dr. Wolfson uses the following as an example of the twins paradox:

**One twin remains on earth, while the other twin travels to and back from a nearby star (10 light years away from earth) and is moving at 0.8c.

**While the twin on earth experiences an elapsed time of 25 years, the travelling twin only experiences 15 years of elapsed time.

**So, the travelling twin returns 10 years younger than the twin who remained on earth.

Given this (and I assume it is accurate), I hope that someone might offer me some direction (or correction) concerning my questions below, some of which are very basic in nature.

Thanks for any help!

1) Concerning the example of the twins (one travels to a star and back; one remains on earth), why is the travelling twin (who ages less) to be thought of as moving into the future? Somehow to me, it seems that with that twin being younger, then she would have moved more slowly in time. I am sure that I am missing the obvious here.

2) When an object approaches the speed of light (let’s use the spaceship example again), does only that object experience time dilation? What if there were debris that got caught up in the motion (like dust behind a car)? I take it that, for a brief time (while the debris is at the same speed as the spaceship), the debris would experience time dilation the same way (?). But, as the debris slowed down (changes frame of reference), it would begin to experience a lesser degree of time dilation, right? It seems like that, if we think of each frame of reference (differing speeds), then the spaceship, the debris, and the debris in different frames or sort of wrapped in their own little bubble (or universe?). I am struggling here, but is it fair to say that if we could measure precisely enough and found that almost all objects are moving at slightly different speeds (and with associated effects of time dilation), then all objects would truly not be in the same universe (at least along the lines of time and maybe in terms of space too given what I have just heard about contraction)? It seems as if “the” (wrong word?) universe would become multi-layered in all directions. Maybe there are multiple universes? (Especially if we break speed down in the sort of fashion found in Xeno’s Paradoxes.)

3) What if “inside” the spaceship, I (somehow) throw another object at near the speed of light? Does this create dilation within dilation?

4) I am interested in the concept of “emergent properties.” If from our perspective (not sure that this is even logically possible), we were monitoring several spaceships, say one moving .0001 of the speed of light, one at .001 the speed of light (etc.), until we get to one at .900 the speed of light (and imagine many ships and many gradations of the speed of light); then would we see different things? That is, would we see younger pilots (dilation) or shorter ships (contraction)? If we could monitor one ship that started slowly and then moved towards the speed of light (acceleration), then what would occur? What would we see? If so, at what fraction of the speed of light, would these changes be apparent to human beings?

5) What if an object goes the full speed of light? Can an object go faster than the speed of light?

I would deeply appreciate any help! I am virtually certain that I have at least one foot still planted firmly in Newtonian physics.

Take care.

2. Oct 22, 2009

### mikeph

Re: Dilation & Contraction--First Post

1. I am not certain of the best answer to this (as far as I can see you are right), so I'll leave.

2. The very first line I have to correct- the object approaching the speed of light does not experience anything different. The key is that there is no "approaching speed of light", because that implicitly defines a reference velocity with which to compare the object. No such frame exists. What you could say is, "as the object approaches the speed of light relative to the solar system". Note that the converse is automatically true: "the solar system approaches the speed of light relative to the object". Although this sounds wrong, there is no reason to doubt it- that's relativity.

In this case, you would NOT experience time dilation. If you go at 0.99c relative to the surroundings, you don't "feel" time slow down, or experience a contraction. You only observe these features in objects moving relative to you (read again!). You see your surroundings slow down, and again, they see you slow down. This sounds like it would lead to a lot of paradoxes, but it doesn't when you have a finite speed of light. There is no need for "multi-layered" universes or anything, it is a surprisingly self-consistent model. (you may need to delve into the mathematics a little to believe me on this point though!)

4. Interesting question- you'd see a (very non-linear) increase in the time dilation and contraction effects of clocks on these spacecraft as they, for example, paraded past you at increasing speeds. For the "what fraction"... I'll give you the equation to sue and you can mess around with it and see for yourself (not very complicated):

The factor by which times are slowed, and lengths are contracted, is gamma, where:

gamma = 1 / sqrt[ 1 - (v/c)^2 ]

Where v is the velocity of the object relative to you, and c is the speed of light. Note that v must get pretty close to c for this factor to get much bigger than 1, but when it does get close, gamma explodes.

5. Nope, not possible. This is covered in some other threads in much more detail I believe.

3. Oct 23, 2009

### goter21

Re: Dilation & Contraction--First Post

I am brand new in this forum, I glad to be here.
Is that mean, the traveling twin will see her sister is younger than she is when she has returned, and on the other hand her sister will see that her traveling twin is younger?
May be it is a silly question but I am confused.

When I studied physic I was thought that position and its derivatives are relative, that is we have to attach coordinate frame to describe them. For the light what is its coordinate frame to say that the speed of light is c. Suppose there is nothing in the universe but a finite duration of laser traveling in one direction, can we say that the laser is traveling at speed of c?

Last edited: Oct 23, 2009
4. Oct 23, 2009

### mikeph

Re: Dilation & Contraction--First Post

I don't know the twin paradox that well, so I don't feel I'm the right person to answer that question, but I am sure the symmetry you suggest (both claiming the other is younger) is broken, because the one that actually leaves on the spacecraft will "feel" the inertial force due to acceleration propelling her back to Earth halfway through her journey.

In all inertial frames the speed of light is c. This is really the key point of special relativity and simultaneously the one that makes the least sense. Two people moving relative to each other both observe light travel at c. In a way this agreement is what causes time dilation and length contraction. Laser question: yes.

5. Oct 23, 2009

### jambaugh

Re: Dilation & Contraction--First Post

There are two different but compatible ways of looking at time which you may use but should not mix. You can view a person or object as having a world-line extending across time or you can view the object as "moving through time". The first is better but less intuitive and the second is ok but you must do some qualification.

First and foremost is to understand that in relativity you must pluralize time. There is no absolute "time". Motion is a relational quality of one quantity changing with another. I move across the room in terms of my position as a function of time. You can view that dynamically (position as a function of time and time acting as a parameter) or you can view this geometrically (position and time plotted to show a curve representing motion).

Let me start with the parametric form. If I am just sitting here I am not moving through space but am moving through time at 1 second per second. That sounds kind of obvious and meaningless but there is a distinction. Consider my watch and the clock on the wall here with me. These are two times and the 1sec/sec is the ratio of what they show.

Now let me use my superpowers to jump up and run around the room really fast. I am now moving both through space and time and according to SR my motion through time is actually faster than 1sec/sec if you think of "motion through time" as "motion through clock on the wall time". To get a rate we divide wall time by watch time (we usually carry parameters along with the object). So as far as you (watching from the doorway) are concerned my watch looks like it is running slow because You are moving through (wall)time more slowly than me. Imagine if we compared footprints in a race. If mine are farther apart it means I was running faster.

As to why I move faster instead of slower, that is an issue of space-time geometry which I can only explain fully by taking you through the math. Instead I will use analogies and qualify that Euclidean cases behave opposite from Minkowski cases as far as effect of changes of direction goes.

But I am always traveling at unit "speed" through space-time. Picking up speed across the room as I jump up should be viewed as me changing my space-time velocity (watch time) to point in a different direction. Given I am changing directions it is no longer so mysterious that my motion through my time and my motion through clock on the wall time are different. If you and I are facing different directions then my motion in your forward direction will be different. You may see me taking only a half step distance in your forward direction when I take a full step in my forward direction. (This is an Euclidean case or rotation).

What is weird is not that clocks disagree but that the effect is opposite what you would suppose. Replace steps with clock ticks and you'll see my watch tick duration covering more of your (forward) time and not less. Again this is because space-time has a hyperbolic component (rather than being all elliptic).

As far as all of that goes, its all in the same universe but appears different from different observers. Notice first that an object never "approaches the speed of light." as that is supposing an absolute meaning to speed. You see an object traveling at speed .9c and that is not a statement about the object but about the relationship between you and the object. From the object's perspective it is sitting still and you are traveling at .9c. Forget about not being able to pass the speed of light for a moment. This sort of relativity is common to both Galilean and Einsteinian cases.

Hold this firmly in mind and read back through your thoughts to see if they still make sense.
The object will behave just as you would expect "if the ship were standing still" because from the ship's frame it is standing still. Again remember speeds are rate of change of distances not positions. To measure a distance you must define two points. It isn't that the ship "is moving" it is that "the ship is moving away from or toward some point you choose as defining "stationary".
Imagine we are very thin and that we are walking on a planet the size of say a small house. Now imagine you see me at an angle since I'm some distance away. I am foreshortened (assume we have no depth perception) Put another person a further distance and so on. Each sees all the other's as shorter until the limit of 90deg they have zero height relative to each other. What's more consider the slopes which relate apparent height to proper height. The key point I am making with this analogy is:
when comparing how two people on the little planet see the height of a third we add angles and use the angles with trig to calculate heights and slopes. We do not add slopes!

This happens also with space-time and velocities but in an opposite way. There is no 90deg limit as we are doing hyperbolic rotations (using hyperbolic trig) instead of circular rotations. The key point though is that the speeds are "slopes" in the same sense and will not add normal. Rather you must add the angle-like parameters of the pseudo-rotations and then use hyperbolic trig. In the case of SR all relative speeds are expressed as a hyperbolic tangent: v= c tanh(boost parameter) which is always magnitude less than c.
Spend a lot of (your ) time training your intuition to stop thinking in terms of absolute time. Go back and look at time related concepts such as speeds and change and such and reconsider them in terms of relative time.

Continue to use the "up" analogy I used on the little planet. When we think the planet is flat we all agree that "up" doesn't need qualification and get used to thinking it is an absolute. When we begin understanding the world is round we ask why the people in China (or whatever point is opposite you) don't fall off since everything falls "down". It takes us a while but we learn to apply relativity to direction. We qualify of my "up" in SE Georgia vs. Fred's "up" in England and Beth's "up" in Australia. SR is a relativity of time and you have to realize the "why don't people in China fall off" questions are still assuming absoluteness.

6. Oct 23, 2009

### stalnaker

Re: Dilation & Contraction--First Post

Boy! Thanks for your responses! I will have to think through all of this carefully. I realize that it will be difficult for me grasp all of this due to my lack of mathematical background and to the Newtonian world view which was taught to me as reality; but, I will keep pushing ahead.

I hope to talk with you more after thinking a great deal.