Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

I know very little about relativity, I guess mostly because I have little interest in it. I read a brief explanation in a physics book.

Supposedly if you travel at the speed of light, you travel through time. What if we were to cut a tunnel through earths atmosphere, with no air inside, (a space tunnel) and send a drag racer through it at the speed of light.

Now I'm not sure exactly how fast you would theoretically travel through time, but lets say he traveled a year into the future in one mile's distance. If the locals were to gaze into the tunnel, they would see a vehical travelling so slowly you probably couldn't know it was moving at all. 1/8760 miles an hour, almost a tenthousandth of a mile an hour. But no! Its traveling at the speed of light says the pilot. Who is right?

If someone were to get inside the tunnel, they could lay their hand on the nearly still vehicle, would their hand be going at the speed of light? Or 1/8760 miles an hour?

By that definition, if we see a snail inching its way across the sidewalk, the snail could be traveling at the speed of light, and just have a very very very short life span.

A logarithm is just a misspelled algorithm.

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I also know little about relativity. But it doesn't quite work the way in which you propose.

Imagine a car is traveling away from ** you** at about the speed of light, it starts off one light second away from you. Remember, where you are matters. So the light (photons) travels to your eyes from the starting position, and this takes one second. Now one second later, the object is 2 light seconds away from you, so it takes 2 seconds for you to see the object in its position. But while the light is traveling towards you, the car is still moving away at about the speed of light. So by the time you see the light from when the car was 2 light seconds away, it will already be 4 light seconds away. So here is a chart of what you see over time:

Second : Actual distance : What the distance looks like

0 : 1 : 1

1 : 2 : 1.5

2 : 3 : 1.75

3 : 4 : 1.875

At least I'm pretty sure that's right. So it appears as time is slowing down for the car, because we know that stupid driver wouldn't slow down and mess up our experiment . But if you are in the car, time appears to change normally, and instead, time for the observer (the one watching the car) seems really slow.

Now more crazy things happen, but the point is that the object has to be traveling away from you at the speed of light, and so you aren't going to reach your hand in unless you have a really long arm.

1/8760 miles an hour, almost a tenthousandth of a mile an hour. But no! Its traveling at the speed of light says the pilot. Who is right?

Relativity has that name for a reason. Time is relative to your position/velocity. You are trying to combine the fact that time is universal and that time is relative, and so you come to a contradication. We all think of time as universal, it's very hard not to. That is because for us, for all intensive purposes, time *is* universal. But it isn't.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

It isn't? I thought it was still called the THEORY of relativity.

Anyways, that explains why something might look a certain way at a certain time, but if that guys buddy is standing on the track like a n00b, 10 light seconds away he is definitly going to get pwned in ten seconds, even if the guy doesn't see it till 15 seconds or whatever.

Just like a delayed tv broadcast, it happens when it happens, not when you actually see it. Its just a delayed report. How is that considered traveling through time?

A logarithm is just a misspelled algorithm.

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

It isn't? I thought it was still called the THEORY of relativity.

What exactly do you mean by this?

Just like a delayed tv broadcast, it happens when it happens, not when you actually see it. Its just a delayed report. How is that considered traveling through time?

It's not considered traveling through time. SciFi writers make it seem that way, and often distort it that way, but it isn't. It's simply a change in how time appears from different points of reference.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,582

And, in fact, I think elementary physics is still taught as if Einstein never existed.

I remember reading "an object will continue to move in a certain direction at a certain speed unless acted upon by another object" (or some such wording). No mention of "relative to bla bla". That just perpetuates our ground-centred view of the world (ie "The ground is fixed everything else moves" which is our normal experience). But in reality the ground we stand on is just another part of the universe and could itself be considered to be moving if oserved from that object.

So if you are going to teach physics you should be encouraging people to think that no part of the universe is more important than any other part. It is all "relative".

I like to think of it this way: if there were a stationary reference point in the universe, then there would be 2 types of space, the fixed point, and everything else. But in fact the universe is simpler - just the same everywhere (or so we believe!).

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

**Online**

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I disagree, MathIsFun. The order in which we teach should mimic the order of discovery. In that sense, one who learns it goes through the same series of epiphanies that the scientists themselves would have. Teaching relativity, even abstractly, at a highschool level is useless. The kids won't understand it, either conceptually, mathimatically, or philosophically. This in turn leads to countless misunderstandings. Since they learned it in highschool, people would think they understand it, but in fact have no clue.

Sadly, there are some things that you just have to wait on to be learned. I believe Relativity, in any form, is one of them.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Possibly my favorite quote in understanding General Relativity, the curvature of spacetime:

"A straight line is still the shortest distance between two points, even if it's a straight line that curves."

Offline

**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

It isn't? I thought it was still called the THEORY of relativity.

What exactly do you mean by this?

I mean that relativity it is a theory and not a fact. In otherwords, it cant't yet be proven. Correct?

A logarithm is just a misspelled algorithm.

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Well, sort of.

In science, you can *never* become greater than a theory. "What about a law?" you say? A law and a theory are two fundamentally different things. A law was never a theory and a theory can never become a law.

Laws are simply describing what we see. Theories are describing how/why something happens.

Sure, theories can be false. They are built upon some assumptions and use metaphors in their descriptions. But keep in mind the strength behind the word theory. It means that it has undergone rigorous testing and has been accepted into the scientific community as the best knowledge we have as of now.

Something isn't "just a theory". Theories are the end of the line when it comes to science. If you want something better, look elsewhere. But as the saying goes, "Science is our worse way of finding the truth, besides all the other ways."

Offline

**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

I see. But isn't theory another word for hypothesis?

A logarithm is just a misspelled algorithm.

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

No! This is something I blame the media for because they can never seem to get the definition of a scientific theory right.

Hypothesis: More along the lines of hypothetical, something that has recently been suggested and untested. More or less, a guess, even if an educated one.

Theory: Has already undergone critical tests and generally accepted by the scientific community.

Now of course, this is scientifically speaking. Normal usage is different. For example, someone could say, "Theoretically speaking..." and what they mean is just a guess. But a scientific theory is much different.

Offline

**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

Many different disciplines usually take existing words and define them to have a specific meaning whenever used in that field. In math there's differentiate, integrate, sign, etc. Is theory in science defined to have a different meaning?

A logarithm is just a misspelled algorithm.

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Yep, exactly right.

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Reading over my earlier post, I used poor (at best) or incorrect (at worst) wording. Specifically:

It's simply a change in how time appears from different points of reference.

It's not just how time appears. Time actually changes, known as time dilation.

Imagine you have a spaceship that can travel near the speed of light. Now imagine that it is also one half light second tall. So if you have a lightbulb on the bottom and a mirror on the top, it will take 1 second for light to get from the lightbulb to the mirror and back.

So you are traveling right by earth. You're on the space ship, and you measure time by shooting light to the ceiling and measuring how long it takes to get back, which has to be one second.

Now there is also an observer on earth. To the observer, light is also traveling at the speed of light. But since the spaceship is moving horizontally, the light is also moving horizontally as well as vertically. So from the observer's point of view, it takes longer than one second for the light to get to the top of the spaceship and back.

This is Special Relativity. Now Einstien expanded this idea to say that gravity can have the same exact effect, and called that General Relativity.

Offline

**stardust****Member**- Registered: 2006-04-09
- Posts: 48

MathsIsFun wrote:

And, in fact, I think elementary physics is still taught as if Einstein never existed.

I remember reading "an object will continue to move in a certain direction at a certain speed unless acted upon by another object" (or some such wording). No mention of "relative to bla bla". That just perpetuates our ground-centred view of the world (ie "The ground is fixed everything else moves" which is our normal experience). But in reality the ground we stand on is just another part of the universe and could itself be considered to be moving if oserved from that object.

do you mean 'every object will continue in it's state of rest or uniform acceleration unless acted on by an external force'

That is Newton's first law of motion. I had to do about the laws of motion for the mechanics part of my physics A/s. We were taught that they only apply on the earth, where motion will be relative to the earth.

I also had to do a bit about it in GCSE physics. I think that relativity would not be understood if taught at an earlier level, or have to be simplified for people to get any grasp of it. At GCSE my teacher only went throught the stuff about expanding universe to a very small group as it would have confused most people. I think more complecated areas of the subject should be left to a higher level. simplifying it does not work, when i moved from GCSE to A level I got so confused as I had be taught stuff that had been so over simplified it was basically wrong.

*Last edited by stardust (2006-07-04 01:31:58)*

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

That is Newton's first law of motion. I had to do about the laws of motion for the mechanics part of my physics A/s. We were taught that they only apply on the earth, where motion will be relative to the earth.

That misses the entire beauty of Newton's laws of motion. The greatest thing about them is that they described motion on earth as well as in the heavens. That was his major accomplishment (besides inventing Calculus), something that could never be done before.

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,582

Yes, stardust, it is Newtons First Law (from Wikipedia): *Objects in motion tend to stay in motion, and objects at rest tend to stay at rest unless an outside force acts upon them.*

But that implies that there is something different about an object in motion or at rest. It also assumes that there is an absolute way of measuring the speed, as if all objects were sitting on an x-y graph.

I remember being blown away by the concept that when I walked, I wasn't moving across the ground, I was staying still and my feet were moving the ground under me. Try it, it's real fun! (You are not really moving the earth, but it does give you a new ay of looking at the world)

Maybe "Objects keep their relative speed unless acted upon by an outside force." No ... not quite right ... help me out here guys, we are only re-writing Newton's First Law ...

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

**Online**

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I don't really think there is a need. It's not the relativeness of position or speed that was so revolutionary about Einstein. Newton knew about these two. If he didn't, his theory would have completely failed to explain why the moon stayed with the earth, as it's movement must be measured both relative to the earth and the sun.

Offline

Pages: **1**