Time dilation, is this correct?

[travis51]

I just watched a video that kind of warped my understanding of time dilation. It said that not only would time appear slow from the point of view of someone standing still looking into something going near the speed of light but if you were going near the speed of light things that are stationary would appear to be slow. Is this true or false information? I always had the idea that if you were let's say going near the speed of light or near the even horizon of a black hole things that are at normal gravity/speed would appear to be faster.

 

[ShayanJ]

Well, That's kind of right. The point is, there is no absolute state of rest and uniform motion is relative. So if A is moving with velocity v w.r.t. B, then either one can consider themselves to be at rest and the other as moving. So from the point of view of A, B's time slows down and from the point of view of B, A's time slows down.

 

[travis51]

How could you travel into the future then with time dilation, if time appears slowed for both of them looking at the other body shouldn't time be the same relative to both when one slows down?

 

[Drakkith]

How could you travel into the future then with time dilation, if time appears slowed for both of them looking at the other body shouldn't time be the same relative to both when one slows down?

It has to do with the fact that an observer in a ship that accelerates to a high velocity is not in an inertial frame the entire time, while someone who stays here on Earth is. (The frame of the Earth isn't actually an inertial frame, but for the purposes of this discussion we can consider it to be)

What you're talking about is known as the twin paradox. See the following link to learn how it is resolved.

http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity

 

[ShayanJ]

How could you travel into the future then with time dilation, if time appears slowed for both of them looking at the other body shouldn't time be the same relative to both when one slows down?

And Relativistic time travel is often considered due to the gravitational time dilation. If A is in a gravitational field which is stronger than the one which B is in, then time passes slower for A than B and that is not relative!

 

[travis51]

http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity

So is this saying that i may be younger once i have left but once i have turned around and came back i would be the same age?

 

[Nugatory]

So is this saying that i may be younger once i have left but once i have turned around and came back i would be the same age?

No, it's not that simple. The problem is that when you say that something is younger than something else, you're really saying that the age (that is, total amount of time experienced) of one of them is less than the age of the other at the same time. It's easy to define "at the same time" when both objects are at the same place, but it's much trickier to do this for objects not in the same place - in fact, if you play around some with the Lorentz transforms and Einstein's famous train thought experiment on the relativity of simultaneity, you'll realize that "at the same time" doesn't have a simple clear meaning for objects at different locations.

 

[pervect]

How could you travel into the future then with time dilation, if time appears slowed for both of them looking at the other body shouldn't time be the same relative to both when one slows down?

What you are most likely missing are the effects due to the "relativity of simultaneity". Different observers regard different events as simultaneous.

Relativity of simultaneity is usually explained using Einstein's train You can find a typical explanation at http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters_2013_Jan_1/Special_relativity_rel_sim/index.html.

It's probably not obvious at first how this explains the twin paradox.

To understand how this applies to the twin paradox, the most useful tool is a space-time diagram. A space-time diagram is basically just a plot of position versus time. Traditaionally, the time axis is drawn vertically.

If you are not familiar with space-time diagrams, they are definitely worth studying until you understand them. The idea behind a space-time diagram is that one event in the physical system must be represented by one point on the diagram, and vica-versa - there is a one to one correspondence between events and points. One can draw several diagrams to describe the same physical situation, just as one can draw several maps of the same terrain. Any valid "map" of the terrain is as good as any other, and so is any space-time diagram.

A resolution of the twin paradox using space-time diagrams would appear as below - the image is from wiki

http://upload.wikimedia.org/wikipedia/commons/c/ce/Twin_Paradox_Minkowski_Diagram.svg

The path through space-time that the traveling twin takes is represented by the pair of bent lines on the right. The path through space-time that the stationary twins takes is represented on the space-time diagram by the vertical line.

Let us assume that the gamma factor is 2:1, and that the traveling twin travels 2 years out and 2 years back by his own watch.

The blue lines on the diagram represent events which are simultaneous from the view point of the traveling twin on the trip out.

Simultaneous events from the viewpoint of the stationary observer would be horizontal lines - but as you can see, simultaneous events from the viewpoint of the moving observer are different, they aren't horizontal.

The diagram represents, amoung other things, the fact that from the viewpoint of the traveling twin, after 2 years of travel only 1 year passes for the stationary twin.

Then the traveling twin changes his velocity. When he changes his velocity, the point he regards as simultaneous shifts. THe diagram idealizes the situation in which this switch happens instantaneously, a realistic scenario would require that the process take some time.

While the blue lines were regarded as simultaneous on the outbound trip, on the inbound trip the RED lines indicate the new simultaneity convention.

Again, while two years of travel pass for the traveling twin, only one year passes for the stationary twin.

However, the total time elapsed for the stationary twin for the complete trip becomes the time spanned by the red lines (where they intersect the worldline of the stationary observer, i.e the vertical axis) plus the time spanned by the blue lines, plus the jump due to the relativity of simultaneity (the big gap in the middle).

It's this gap or "jump" that explains how the stationary twin sees the trip lasting as 4 years. The length of the trip is not just the time spanned by the red lines plus the time spanned by the blue ones. It must include, additionally, the "gap" due to the change in the notion of simultaneity,

 

[ghwellsjr]

A resolution of the twin paradox using space-time diagrams would appear as below - the image is from wiki

http://upload.wikimedia.org/wikipedia/commons/c/ce/Twin_Paradox_Minkowski_Diagram.svg

The path through space-time that the traveling twin takes is represented by the pair of bent lines on the right. The path through space-time that the stationary twins takes is represented on the space-time diagram by the vertical line.

Let us assume that the gamma factor is 2:1, and that the traveling twin travels 2 years out and 2 years back by his own watch.

The blue lines on the diagram represent events which are simultaneous from the view point of the traveling twin on the trip out.

Simultaneous events from the viewpoint of the stationary observer would be horizontal lines - but as you can see, simultaneous events from the viewpoint of the moving observer are different, they aren't horizontal.

The diagram represents, amoung other things, the fact that from the viewpoint of the traveling twin, after 2 years of travel only 1 year passes for the stationary twin.

Could you please point out on the diagram where it shows this. I can't see it.

Then the traveling twin changes his velocity. When he changes his velocity, the point he regards as simultaneous shifts. THe diagram idealizes the situation in which this switch happens instantaneously, a realistic scenario would require that the process take some time.

While the blue lines were regarded as simultaneous on the outbound trip, on the inbound trip the RED lines indicate the new simultaneity convention.

Again, while two years of travel pass for the traveling twin, only one year passes for the stationary twin.

Again, I can't see this on the diagram.

However, the total time elapsed for the stationary twin for the complete trip becomes the time spanned by the red lines (where they intersect the worldline of the stationary observer, i.e the vertical axis) plus the time spanned by the blue lines, plus the jump due to the relativity of simultaneity (the big gap in the middle).

It's this gap or "jump" that explains how the stationary twin sees the trip lasting as 4 years. The length of the trip is not just the time spanned by the red lines plus the time spanned by the blue ones. It must include, additionally, the "gap" due to the change in the notion of simultaneity,

You said the time spanned by the red lines is one year and the same for the blue lines which means the gap would be 2 years to bring the total to 4 years, correct?

But you said the traveling twin travels 2 years out and 2 years back by his own watch and you also said the gamma factor was 2 so wouldn't that mean the stationary twin sees the trip lasting 8 years? Doesn't that mean the gap is 6 years? How does the diagram show any of this?

 

[pervect]

Could you please point out on the diagram where it shows this. I can't see it.

I cheated, the relevant line is actually:

Let us assume that the gamma factor is 2:1, and that the traveling twin travels 2 years out and 2 years back by his own watch.

I'm sure I could have worded it better. However, if you agree that with those assumptions that the situation would be as described it, it might be helpful to reassure the OP about that point, otherwise he might think you are disagreeing with something more substantive.

[add]
On second thought, let me clarify a bit more rather than relying on your goodwill.

The diagram itself isn't to scale, so what the diagram actually shows is the existence of three regions without (yet) assigning any numbers to them.

There is the region covered by the blue lines, the region covered by the red lines, and the gap between the regions.

WHen one assumes a specific gamma factor, one can apply the time dilation concept to say the region covered by the red lines covers less time on the stationary worldline by a factor of gamma than the amount of time it covers on the moving worldline. For brevity, I'll henceforth assume that the gamma factor is 2:1. Note that the region between the red an blue lines covers ALL of the time elapsed for the traveling twin, but only PART of the time elapsed for the stationary twin.

So the two years on the worldline of the traveling twin,covered by the red lines, when divided by the gamma factor, implies that only 1 year of time is covered on the worldline of the stationary twin by the red lines.

From the point of view of the stationary twin, we know that since the time dilation factor was 2:1, and the trip took 4 years for the traveling twins clock, it took 8 years from the point of view of the stationary twin.

However, this 8 years from the POV of the stationary twin includes the region of the gap that happens at turnaround, as well as the two 1-year periods covered by the red and blue lines, respectively.

One can probably pick nits in this explanation too - It would be unrealistic to expect a post to be as clear as a textbook. Hopefully it is clear enough where the basic idea can be comprehended. If not I apologize and recommend finding a good textbook to study...

 

[ghwellsjr]

On second thought, let me clarify a bit more rather than relying on your goodwill.

Thanks, your clarification helps a lot.

The diagram itself isn't to scale, so what the diagram actually shows is the existence of three regions without (yet) assigning any numbers to them.

Let me assign scales to the dots:

The dots on the diagonal lines represent increments of 8 months for a total of 48 months or 4 years, 2 years for the trip out and 2 years for the return trip.

The two regions of dots on the vertical line represent increments of 4 months for a total of 1 year for each region with a third region of no dots representing a gap of 6 years.

So when you say the diagram isn't to scale, you mean that there are actually three different scales, one for the diagonal lines, one for the vertical line where there are dots and one for the vertical line where there are no dots, correct?

Here is a correctly drawn diagram with a single scale:

Note that the dots on the slanted lines are 8 months apart while the dots on the two regions of the vertical line are 4 months apart with a 6-year gap between the two regions. In all cases, the dots represent increments of Proper Time for each twin. The speed of the traveling twin is 0.866c.

Do you concur?