# Implications of Einstein's Theories

1. Dec 18, 2013

### JimiJams

What little I've read about Einstein, out of a textbook, regarded his theories on motion at the speed of light. I'm not sure if this is general or special relativity, but it involved observations such as time dilation and length contraction, as well as changes to momentum and energy.

I realize his whole theory, just about, rests on the premise that light will move at the speed of light regardless of your reference frame's velocity. This is a very counter-intuitive notion, when we think of this in terms of classical/Newtonian physics. My question is, does his observations of time dilation and length contraction, or any other observations/realizations he made, serve to explain just why and how light always moves at the speed of light? I mean just thinking about traveling at the speed of light right next to a photon, how can it be that that photon still appears to be moving away at the speed of light while you're traveling at the same speed? Again, does time dilation or anything in his theory at all clarify these observations?

2. Dec 18, 2013

### Staff: Mentor

First, you cannot have an inertial frame of reference that moves at the same speed as a photon. Light always moves at c with respect to any inertial frame.

Second, length contraction, time dilation, and other effects are all interrelated. They are a consequence of the various rules of nature, one of which is that light always moves at c in a vacuum. There is no underlying reason, that we know of, that light always travels at c when viewed from any inertial frame. It is simply what we observe.

3. Dec 18, 2013

### JimiJams

Realistically, no, you can't have an inertial reference frame that moves at the speed of light. But, hypothetically, if you were to move at the speed of light or .9c, whatever makes you more comfortable, light will appear to move at the speed of light.

The classic example of the photon emitting at an angle and reflecting off a mirror back towards a sensor hypothesizes an observer traveling alongside that photon (and the photon appears to move up and down in a straight line rather than any angle...).

Even if you want to entertain the thought of traveling parallel to a photon at .9c, the photon will apear to move away at c rather than c-.9c. I was wondering if anywhere in his theories he can explain how this phenomenon takes place. Does time dilation, length contraction, space-time stretch etc.. serve to explain how light always appears to move away at the speed of light, even if you're traveling at .999999999c?

4. Dec 18, 2013

### Simon Bridge

Um - almost. Relativity applies for all speeds - not just the very fast ones. At light-speed is not covered (except for light) and it is always the other guy who is moving and not oneself.
It takes a bit of practisce to get used to this way of thinking.

If it involves gravity, then it is general relativity, otherwise it is normally special relativity.

your reference frame is always stationary with respect to you. Get used to always talking about who is doing the observing in specific terms - it helps a lot.

The postulate is that all observers will measure the same speed for light in a vacuum.
It does not matter that they may have different velocities with respect to each other.

It doesn't.
The postulate was just that if c is invarient, then that results in a bunch of math that makes sense of a lot of other stuff. It does not explain why the invariant speed has to be c or why light should travel at that speed.

The situation you described is impossible of course - you cannot travel along next to a photon - and the "frame of reference of a photon" is a meaningless concept in relativity.

Imagine that Alice and Bob measure the speed for the same light beam.
Alice is holding the light source while Bob takes off along the beam to do his measurement.

But we realize that, according to regular (Galilean) relativity, if Alice measure Bob's velocity to be $v$, then Bob measures Alice's velocity to be $-v$. By the same relativity, when Alice measured $c_a$ she expected that Bob would measure $c_a-v$ (since he was travelling along the beam in the direction of propagation). Similarly, Bob would expect Alice to measure $c_b+v$. Instead they got $c_b=c_a=c$.

How do you normally measure speed? Why, by timing the thing you want the speed of over a fixed distance. But Alice points out that Bob's rulers are length contracted and his clocks are time-dilated ... when she checks she finds out that they are time dilated by the exact amount needed to make the speed of light come out the same as her's every time.

Bob also noticed that Alice's time was dilated and her lengths were contracted in the same ratios so no wonder she gets the same speed as him.

The time dilation and length contraction relations are what you need to happen for the speed of light to be measured the same by all observers.

5. Dec 18, 2013

### Simon Bridge

In this example the observer is NOT "travelling alongside the photon".
If you have a reference that says this, then the reference is WRONG.

If you and I stood next to each other, and, on your signal, I walked to the far wall and back again while you stayed put ... you would not describe yourself as "moving alongside" me would you?

In "the classic example", you, the observer, are standing in a box with some equipment.
You throw a switch and the equipment emits a pulse of light, and starts a stopwatch. The light reflects of the ceiling and returns to the box, which detects it and stops the stopwatch.

Someone else outside the box has a means to tell when the light was emitted and when it was detected - which is recorded on their own stopwatch.

You and the other person compare notes later.

Thing is that the other guy says you were going amazingly fast while the experiment took place - some 0.9c. But according to you, they were the ones going really fast, the other way. Who's right?

Each of you has a different time for the period between throwing the switch and the pulse returning.
But if you crunch the numbers, the times you get are consistent with the speed of light being the same to both of you.

Last edited: Dec 18, 2013
6. Dec 18, 2013

### JimiJams

Thank you Simon!, This answered just what I was too lazy to do the math to figure out. I learned about time dilation and length contraction but they struck me as only a bizarre phenomenon, I failed to realize that they also explain just WHY light always travels at the speed of light regardless of the observer's velocity.

By the way, I didn't explain very well but the example I was referring to when I said "traveling alongside the photon", is a thought experiment regarding a light box (I think that's what it's called) that was in the same text. It goes; there's a box with a photon emitter in a lower corner, and a mirror on the top of the box inside, and a photon sensor in the other lower corner. If you are standing still observing this box you would see a photon come out at angle theta relative to the ground of the box, hit the mirror and reflect towards the sensor in the other corner at the same angle relative to the ground of the box. Let's say the photon traveled a total 2 meters in time t.

Now, if you hypothetically traveled alongside the photon the very instant it was emitted the photon's path would look like it went straight up and then straight down, rather than at angles. If you do the trigonometry this equates to the photon traveling less of a distance in the same amount of time t than it did when you were standing still. From this, his time dilation and length contraction hypotheses can be surmised.

If you've already heard this example before I'm sorry if I bored or offended you.

7. Dec 18, 2013

### JimiJams

Just to correct myself in my last post, the time is obviously not the same when standing and observing the photon and its distance, and traveling alongside the photon and observing its distance. The distances the photon traveled in both instances are different (for each observer), and the speed of a photon is always c, the speed of light. From that, we can calculate that there is a time difference taking place between the two observers.

8. Dec 18, 2013

### Simon Bridge

The way this is written misses out a very important bit of information - the second observer has to be moving horizontally along with the photon ... i.e. must be travelling at $v=c\sin\beta$ along the floor of the box. We'd normally set up the experiment the other way round since it is easier to think about that way.

Have a look through the FAQ here:
http://www.physicsguy.com/ftl/

9. Dec 18, 2013

### JimiJams

Good point Simon, I should have clarified a horizontal movement by the observer.

10. Dec 18, 2013

### JimiJams

Not to stray off topic, but does Einstein's General Relativity paint a clearer portrait of time dilation and length contraction? I know he developed the theory of space-time and I'm guessing it can be tied into time dilation, length contraction and why observers will experience these events while moving at the speed of light. Something to do with the fabric of space being made of space-time and a certain give and take relationship between the two (time and space).

I would like to get a good book on GR and a supplementary book on the mathematics needed to understand GR, can this be recommended? I've heard Taylor and Wheeler have a good one but it's light on the math. I want something with the math so I can get a clear understanding. It seems Schutz (A First Course in General Relativity), Hartle (Gravity: An Introduction to Einstein's General Relativity) and Carroll (Spacetime and Geometry: An Introduction to General Relativity) all have well-reviewed books on the topic on Amazon, does anyone know which contain the supporting math?

11. Dec 18, 2013

### WannabeNewton

No. Kinematical time dilation and length contraction are effects that come about due to local Lorentz boosts from one local Lorentz frame to another so even in curved space-times it's still analyzed within the framework of SR, GR doesn't offer anything novel there. It just restricts the analysis to local regions of space-time because space-time is locally Minkowski. However GR does introduce the notion of gravitational time dilation.

Peruse the textbook subforum because there have been tons of people who have asked the same thing in the recent past: https://www.physicsforums.com/forumdisplay.php?f=21

12. Dec 18, 2013

### JimiJams

Thanks for the clarification Newton, even though my math studies never took me into local Lorentz boosts or local Minkowski it sounds like there's no tying correlation between time dilation/length contraction and spacetime. Also thanks for the helpful link. Can you by any chance tell me what kind of math text I should look for to supplement study of general relativity?

13. Dec 18, 2013

### WannabeNewton

How much math do you know already? You'll learn about local Lorentz boosts when you study GR so don't worry about that.

EDIT: Also I just saw that you're a Hendrix fan, awesome :)

Last edited: Dec 18, 2013
14. Dec 18, 2013

### JimiJams

I've taken three semesters of college level calc, differential equations, and discrete math fwiw.

Yeah huge Hendrix fan and Page for that matter too, as I'm sure you are haha. You a guitar player?

15. Dec 18, 2013

### Integral

Staff Emeritus
A simple answer to your basic question: Does relativity say anything about why light travels at the speed of light.

No. A constant speed of light is ASSUMED in the postulates. So relativity examines the result of a fixed light speed but does not delve into why it is so.

16. Dec 18, 2013

### WannabeNewton

Learn linear algebra and you'll be all set!

Haha yeah Jimmy Page is my god. And yeah I play guitar.

17. Dec 18, 2013

### JimiJams

sweet, I'll have to grab a good linear algebra text.

Nice, obviously Hendrix is my anointed guitar god, I've been playing for 12 years now. You really can't go wrong looking up to either one though, they are the best in my opinion.

18. Dec 18, 2013

### phinds

No, they most definitely do not explain why light always travels at the same speed regardless of the observers velocity. They are a RESULT of that fact, not an explanation for it. As Simon said we do not have an explanation for it. It just IS and we make use of it. Time dilation / length contraction show up as a result.

19. Dec 18, 2013

### JimiJams

phinds, I mean time dilation and length contraction explain how it's possible for something to appear to be moving at a constant speed even if you're moving at close to the same speed. I don't mean they are the cause, only the result, which helps me to better understand just how an observer would interpret a photon as staying at constant speed c. Sorry for the confusion, I may have been confused myself when I posted that, admittedly.

20. Dec 18, 2013

### Staff: Mentor

They don't, unless you also consider relativity of simultaneity.