Confused by an example in Brian Greene's book and SR in general

[amk0713]

Hi there. I've been reading Brian Greene's book "An Elegant Universe" for the sake of curiosity and one of his examples to demonstrate special relativity really confuses me about the entire concept.

To start, this is my current understanding of SR, so please correct me if I am wrong:

-The faster an object is moving through space, the slower it moves through time.
-Everything is essentially moving at the speed of light through the four dimensions of space time.

Greene's example is about two astronauts floating through black space with the only means to compare their movement is to each other - each can claim that they are stationary. That's pretty easy to understand - they don't know who's moving, it's just a matter of their perception.

However, he later mentions that each has a valid claim that other's clock is running slower. This I don't understand. Shouldn't this also be a way to determine who's moving? Even if they both can say that the other person looks like they are moving, only one is actually moving; therefor, only their clock should slow down since their time is slowing down because of their flow through space.

I would really appreciate some clarification as this subject interests me greatly. I am starting college next year in hopes of going into physics, however, it's troubling to know that after reading the first chapter of Greene's book I still can't fully conceptualize SR.

 

[HallsofIvy]

Although you say that you understand the example of the two astronauts, you appear to be missing the word "relative"! That is, after all, the whole point of "relativity". You can't talk about "The faster an object is moving through space" without saying with respect to what frame of reference.

"Even if they both can say that the other person looks like they are moving, only one is actually moving". NO! Relativity is not just a matter of appearance- each one is motionless in his frame of reference. Each is moving in the frame of reference of the other. Each sees the others clock (and heart beat, how often he blinks, etc.) moving more slowly than his own. Each one's "time" reference is slower than the others.

There is NO "actual" movement- there is only movement relative to another frame of reference.

 

[ZikZak]

To start, this is my current understanding of SR, so please correct me if I am wrong:

-The faster an object is moving through space, the slower it moves through time.
-Everything is essentially moving at the speed of light through the four dimensions of space time.

I know Brian Greene likes this heuristic, but there is a LOT wrong with it if you want a deep understanding of the theory. But it is true that moving clocks run slow.

However, he later mentions that each has a valid claim that other's clock is running slower. This I don't understand. Shouldn't this also be a way to determine who's moving? Even if they both can say that the other person looks like they are moving, only one is actually moving; therefor, only their clock should slow down since their time is slowing down because of their flow through space.

Did I mention there was something wrong with the "traveling at c through spacetime" heuristic? It makes it seem as if there is a privileged reference frame against which all motion may be measured. But Brian Greene is correct and you are wrong here. Each spaceman observes the other's clock to run slow. There is no such thing as "actually moving." That is why it is called "Relativity:" there is no absolute standard of rest against which all motion is measured. There is no such thing as absolute motion, as "actually moving." Motion is measured Relative to your own reference frame and that is as good as it gets.

Spaceman A considers himself at rest, watches spaceman B go by, and because B is moving, his clock is running slow. Exactly the same for B: B has the privilege of considering himself at rest, and as he watches A go by, A's clock is running slow because he is in motion. There is no absolute sense in which one is standing still and the other is not. Each is at rest in his own reference frame and each observes the other's clock running slow.

You are drawing a distinction between "looking like motion" and "actually being in motion." There is no such distinction. If it looks like it's in motion, it's in motion in your reference frame, and there are no signposts stuck in spacetime privileging any reference frame over any other. The laws of physics are the same in every reference frame. There is no special reference frame called "rest." They are all equivalently good.

 

[amk0713]

Ah! That makes a little bit more sense to me now. Thank you.

Just to test my understanding, would this sentence be correct: The "laws of reality" slow down time for everything in relative motion to, well, everything.

I understand that this is meant to be a paradox, but because of this is the only reason that SR can't be disproved because of the fact that any attempt to gauge the relative person's time dilation (communication with cellphones, turning on your jet-pack to fly back to the other person thus disturbing your own time dilation) will distort the results?

Also, let's say that one of the astronauts does in fact turn on his jet-pack to fly towards the other. He is now certain that he is not at rest. Does time now only slow down for him because the perception of who is actually moving is concrete?

 

[ZikZak]

Ah! That makes a little bit more sense to me now. Thank you.

Just to test my understanding, would this sentence be correct: The "laws of reality" slow down time for everything in relative motion to, well, everything.

Not really. It would be correct to say that an observer who observes a clock in motion will observe it running slow.

I understand that this is meant to be a paradox

No it isn't. It's the way the universe is actually observed to behave.

but because of this is the only reason that SR can't be disproved because of the fact that any attempt to gauge the relative person's time dilation (communication with cellphones, turning on your jet-pack to fly back to the other person thus disturbing your own time dilation) will distort the results?

Huh? No! You gauge the time dilation of the other astronaut by looking at his watch and correcting for the time it takes the light to get to you from his changing positions. It's really very simple. You look at his watch. If he is moving, then it is running slow.

Also, let's say that one of the astronauts does in fact turn on his jet-pack to fly towards the other. He is now certain that he is not at rest.

No he isn't. While the jetpack is firing, he can STILL consider himself to be at rest if he likes, in a giant, universal gravitational field. That's why he needed to fire the jetpack: to keep himself stationary while everything else in the universe started falling under the influence of a uniform force of gravity.

Well, that is sort of a quasi-GR way of looking at it anyway.

Does time now only slow down for him because the perception of who is actually moving is concrete?

NO. Stop thinking in absolute terms. Only his ACCELERATION is absolute, not his velocity. While the jetpack is firing, his friend will observe his clock running slow by an amount determined by his instantaneous speed in the friend's reference frame. Therefore when he reaches his friend again, his clock will read less than the friend's.

In his own reference frame, he must indeed do something about the fact that he felt an acceleration. Either he can consider himself at rest in a gravitational field and use the "clocks higher up in a gravity field run fast" rule to account for his friend's very rapidly running clock during that time, or he may simply calculate the difference in simultaneity at the position of his friend in the two (before the jetpack fires, and after) inertial reference frames he inhabits.

 

[ralilu]

Hi there. I've been reading Brian Greene's book "An Elegant Universe" for the sake of curiosity and one of his examples to demonstrate special relativity really confuses me about the entire concept.

To start, this is my current understanding of SR, so please correct me if I am wrong:

-The faster an object is moving through space, the slower it moves through time.
-Everything is essentially moving at the speed of light through the four dimensions of space time.SR.

objects with mass are moving through the time dimension at the speed of light. as soon as they start moving in a spatial dimension then they start moving through the time dimension slower. photons, gravitons etc don't move through the time dimension, time stands still for photons.

 

[amk0713]

Thank you again for the response, but...

"It would be correct to say that an observer who observes a clock in motion will observe it running slow."

Ok. Let's say the clock had some sort of sentience. The clock would also see the observer's blinking, breathing, etc. slow down. So who's right? How can someone see someone else's time slow down if there own perception has slowed down.

Also, what about the twin paradox? The twin that leaves the Earth is the only one that has his time slowed down, as when he comes back he is younger than his 'stationary' twin.

Again, thank you for the help. I know I may be a pain right now. Haha.

 

[Phrak]

It would be correct to say that an observer who observes a clock in motion will observe it running slow.

This isn't quite a conculsion of special relativity. Could you be more precise using an inertial frame of reference? Time dilation compares cojacent clocks.

 

[ralilu]

Ok. Let's say the clock had some sort of sentience. The clock would also see the observer's blinking, breathing, etc. slow down. So who's right? How can someone see someone else's time slow down if there own perception has slowed down.

For the observor in his reference frame, time is flowing normally and he sees the clock slow down relative to his clock. In the clock's reference frame time is flowing normally and the observor's time is slowing down relative to the clock. Both are right.

Also, what about the twin paradox? The twin that leaves the Earth is the only one that has his time slowed down, as when he comes back he is younger than his 'stationary' twin.

When the twin travels he moves in a spatial dimension therefore, time goes slower for him and he ages slower. The stationary twin is not moving so time flows normally for him and he ages at a normal rate.

 

[amk0713]

But if both the clock and observer have their time slowed down by the perception of the other, then wouldn't that equal out and time would flow normally?

And as for the twins; they are the same as the clock and observer. They are moving relative to one another.

 

[atyy]

There are 2 sorts of time.

"Proper time" is the flow of time for each observer - it describes things happening to that observer, and it never slows down or speeds up.

"Coordinate time" is a time that an observer assigns to all events - even those that do not happen to him. There are many ways to assign coordinates to everything. Coordinate time can slow down or speed up.

 

[Fredrik]

-The faster an object is moving through space, the slower it moves through time.
-Everything is essentially moving at the speed of light through the four dimensions of space time.

I haven't read through this thread, so maybe you have all the answers you need already. I was involved in a discussion about this stuff from Greene's book some time ago, and I thought a link to that thread might be useful. See in particular post #18.

 

[A.T.]

-The faster an object is moving through space, the slower it moves through time.
-Everything is essentially moving at the speed of light through the four dimensions of space time.

This is visualized here:
http://www.adamtoons.de/physics/relativity.swf
But as was already said here: This space-time is just a diagram that every inertial observer can draw from his perspective. It is relative.

And as for the twins; they are the same as the clock and observer. They are moving relative to one another.

If they meet again, at least one of them was not inertial and cannot draw such a simple diagram, but rather a highly distorted one. However you can construct the non-inertial path from two inertial frames (flying away and back). This is done here:
http://www.adamtoons.de/physics/twins.swf
The lower diagram (Epstrein) is the one with constant advance rate trough space-time at c, Greene talks about. The nice thing about this diagram, is that you can see the age difference directly, because the temporal axis shows the proper-times of the twins.

Note: observer's time = coordinate time

 

[ZikZak]

Since you are in high school physics, you are probably familiar with those problems that involve a box sliding down an incline. In such problems, you have a choice of defining the x-axis to be horizontal, parallel with the table, or diagonal, parallel with the incline. It makes no difference which you choose; the laws are the same regardless of which set of axes you select.

But now suppose that Heidi has chosen her x-axis to be the horizontal, and Debbie has chosen the diagonal. Now Heidi draws a 1-meter long horizontal line and proclaims: "Verily, I have drawn a line that is 1-meter long in the x direction. Surely anyone who measures this line will agree." But Debbie does not agree. When she measures Heidi's line, it is less than 1 meter long in the x-direction and even has a little bit of y-direction to it. So Debbie draws her own line, diagonally, which she claims is 1 meter in the x direction. Of course to Heidi, Debbie's line is less than 1 meter in her x direction. Debbie's 1-meter x-line is less than one meter of x to Heidi, and Heidi's 1-meter x-line is less than one meter of x to Debbie. Who is correct? Whose line is REALLY shorter in x?

Answer this conundrum and you have answered your question. The two observers each observe the other's clocks running slow, and it is because they do not agree on which direction is the "time" direction in spacetime.