Tags:
1. Jan 21, 2014

### MostlyHarmless

So I just started taking Modern Physics and we are currently discussing special relativity. And needless to say, its giving me a headache.

Here's my confusion:
First, my Professor is Russian, and while his accent isn't so thick that I can't understand him, his grasp of English itself, is such that, I could have a conversation about the weather or politics with him, but its not good enough that he can be perfectly clear with us and cook up familiar analogies etc.. So I'm having trouble there in general.

Specifically though, he was giving an example of Time Dilation where we were to consider the gestation period of like a cow, which he gave as 21 months(why not a human? Who knows.) As our "clock". And we were to suppose this cow was flown out into space at some velocity nearing the speed of light. Ignoring any sort of acceleration for the sake of the example,(I guess?). Then he demonstrated that it would be like 53(or something, not really important right now) months before we got radio transmission of the calf being born. So I asked, what if we were able to receive information from the ship instantly, would it still be some time > 21 months before we heard from the calf? And his response was no, it would just be 21 months. Which, sure, makes sense.

So that left me thinking that all of the peculiarities that we see from relativity are just consequence of the time it takes light to travel.

Then in reading my text while working some practice problems I read something like this in an example: (and I'm paraphrasing) We have a Train, S', moving at velocity, v(from left to right), relative to a platform, S. The train and platform are labeled, from left to right. B, C, A. Two flashes of light occur at points B and A when clocks at points B and A hit some time, t0. (The diagram depicts the train in line w/ the platform, that is, A' is inline with A, etc...) An observer in S at C records these flashes as simultaneous. An observer on the train, in S', at C', records the flash from A first and then the flash from B, he then concludes that the clocks at A and B are not synced.

And I'm good up to here. And then they say this: "All observers in S' would agree with that conclusion after correcting for the time of light travel.[\b]"

I understand that the example in the book isn't meant to describe time dilation, but its kind of thrown me for a loop. I think I might just be over thinking it or something.

2. Jan 21, 2014

### Staff: Mentor

No, although they are a consequence of the fact that the speed of light is the same for all observers.

The time dilation, length contraction, and all of that is what's left after you've allowed for the light travel time. If something happens ten light-seconds away from you, something else happens six light-seconds away, and the light from both events hits your eyes at the same time you will conclude correctly that the second event happened six seconds ago and the first event happened four seconds before that.

However, someone moving relative to you and doing the same analysis with the light hitting his eyes will draw a different conclusion about the timing of the two events. And there's no reason why you're any more right than he is - as far as he's concerned he's at rest and you're the one who is moving. This is the point of the train experiment and relativity of simultaneity that you also mention.

You will get time dilation if you apply this thinking to the events "His clock reads 12:00:00", "His clock reads 12:00:01", "His clock reads 12:00:02", and so forth. Obviously these events are separated by one second for him, but if he's moving relative to you and you're watching his clock, even after you've corrected for the light travel time they won't be separated by one second for you.

The problem here is that the word "instantly" is a just a convenient shorthand for "the message is received at the exact same time that it is sent" - and the train experiment will eventually persuade you that things happening at different locations "at the exact same time" isn't a meaningful concept when people are moving relative to one another.

Last edited: Jan 21, 2014
3. Jan 21, 2014

### MostlyHarmless

Maybe I misunderstood this, but if the light from both events reached my eyes at the same time, how would I conclude that the events took place 4 seconds apart?

4. Jan 21, 2014

### nitsuj

I don't how eliminating the transmission time of the radio transmission some how eliminates the differences in proper time. The cow should seem to take longer than 21 months as measured on Earth.

To Nugatory's point time dilation/ length contraction is "left over" after accounting for "transmission time".

5. Jan 21, 2014

### Staff: Mentor

You know the distance to the two events, so you know how long it took the light to cover that distance.

The speed of light is about 300,000 km/sec, so (for example) if something happened at at a distance of three million kilometers from you, you can calculate that the light was in flight for ten seconds, and therefore that the event happened ten seconds before the light hit your eyes.

So if one event happens 3,000,000 kilometers away and the other event happens only 1,800,000 kilometers away, yet the light from both reaches your eyes at the same time, you will conclude that one of them happened ten seconds ago, one of them happened six seconds ago, and obviously the second event happened four seconds after the first.

6. Jan 21, 2014

### DarkMatterHol

Yes, it seems to me you could illustrate the same time dilatation effect if the cow was to spin around the earth (at the same speed), and yet the gestation period would still be that ~52 months, although the announcement of the birth would only take a few ms. to reach the earth observer. Could the Russian professor have misspoken?

7. Jan 22, 2014

### ghwellsjr

You might conclude that based on what your Professor said, but your Professor was wrong.

Here is a spacetime diagram depicting the scenario. The Earth is the blue line and the cow is the thick black line. After 21 of her months she sends a radio transmission back to earth shown as the thin black line and it arrives 53 months after the cow left. The dots mark off one-month intervals of time for the Earth and the cow:

Notice how the cow's time is dilated or stretched out compared to the Coordinate Time. If the radio transmission could happen instantaneously in the Earth's rest frame, it would arrive almost ten months after the cow delivered at the Earth time of almost 31 months. This is where your Professor was wrong. However, there is a frame in which what he said would be true but unless he explained that to you, we can't give him credit for meaning that frame.

Now you may be wondering how I knew what speed the cow had to travel at to get her Time Dilation to be just the right amount to make the radio transmission arrive exactly after 53 months. It's very easy using the reverse Doppler calculation. Dopper is the ratio of the observed time interval divided by your own clock time interval. In this case, it is 21/53 or 0.3962. We can plug that ratio, R, into the following formula to calculate β, the speed of the cow as a fraction of the speed of light:

β = (R2-1)/(R2+1) = (0.39622-1)/(0.39622+1) = (0.157-1)/(0.157+1) = -0.843/1.157 = -0.7286

The negative sign means that the cow is moving away.

I think it does describe Time Dilation and I think it deserves another spacetime diagram or two. This one's a little more complicated but I need to clarify something. You didn't state that the two observers were in the middle of the platform and the middle of the train. I'm sure your book included that detail or maybe it was implied by a diagram. Anyway, we will assume it to be true.

I start with the rest frame of the platform. The two ends of the platform marked B and A are shown in green with the blue C observer in the center. The two ends of the train are shown in black with the red C observer in the center. The train is moving at 0.6c and dots mark off 1-microsecond intervals of time according to their own clocks. I'm assuming that there are six clocks even if the book didn't say so. At the Coordinate Time of 0, the two ends of the train coincide with the two ends of the platform and two flashes of light occur that propagate toward the observers. At this point, all six clocks were at zero:

Now the two flashes propagate at 45-degree angles and after four microseconds, converge on the blue platform observer. At this point, he concludes that the two flashes were simultaneous in his rest frame since he knows that he is equidistant from the two ends of the platform where the flashes occur.

However, the red train observer sees the first flash at his Proper Time of 2 usecs and the second one at his Proper Time of 8 usecs. Since he knows that he is in the center of the train, he knows that the two flashes did not start out simultaneous in his rest frame or they would have ended up simultaneous, in other words, he would have ended up seeing them simultaneously. If he can also see the times on the two clocks reading zero, then he knows that those two clocks are out of sync in his rest frame. How does he know that? He knows that since he saw the two flashes at different times, then the two clocks would have to be displaying two different times in order to be in sync. Well what could those two times be? Since there is six usecs between the times he saw the two flashes, there must be six usecs difference in the clocks readings in order for them to be synced. So, for example, the first one (A) could have been at -3 usecs and the second one (B) could have been +3 usecs.

And just as a sanity check, here is the scenario transformed into the rest frame of the train:

Note that if we applied the Coordinate Times to the Clocks on the train, then they would have been in sync.

Hope this helps. Any questions?

#### Attached Files:

File size:
23.4 KB
Views:
271
File size:
6.5 KB
Views:
266
• ###### PregnantCow3.PNG
File size:
8.6 KB
Views:
275
8. Jan 22, 2014

### bcrowell

Staff Emeritus
This is wrong. Either your professor is wrong or you misunderstood him. The correct answer to this question is that in SR, the notion of receiving information from the ship instantly is both (a) undefined and (b) impossible. The reason that it's undefined is that simultaneity depends on the frame of reference, so receiving the information "instantly" in one frame will mean that it's not received instantly in other frames. In those other frames, it would be received either after a delay or before it was sent.

9. Jan 22, 2014

### MostlyHarmless

Thank you all, it seems the consensus is that either my professor was wrong, I misunderstood, or he misspoke. I'm thinking there was just lots of misunderstanding I'm the exchange.

I haven't had a chance to read each response in detail, bit rest assured next time I get in front of my text book I will! :)

10. Jan 22, 2014

### pervect

Staff Emeritus
Well, I'm surprised he didn't ask for more information, because the notion of "instantly", like the notion of "simultaneity" and "now", is frame dependent, i.e. it depends on the observer. It's not at all clear whether you were asking "instantly" according to the ship, or "instantly" according to the observer at Earth - there would be two different answers. Presumably one of them is the one your professor gave (I haven't worked out the details).

I wouldn't call the relativity of simultaneity, as above, as "just a consequence of the time it takes light to travel". It does follow from the postulates of relativity, but there's more to those than just a time delay, you have the notion that "c" has the same value for all observers.

11. Jan 23, 2014

### MostlyHarmless

@ghwellsjr: Thanks this reaffirms my understanding before I asked my professor that question.

And now I have a follow up question to be sure I understand what's going on with time dilation. Here's an example given in class.
I'll start with a crude version of the diagram given in class:

We have S, as an observer in the ship, as he measures it the light travels a distance of 2D in some time 2D/c.

Then we have S', an observer who observes the ship moving with some velocity V, close the speed of light. As the observer measures it, the light travels a distance 2L.

So to my understanding, L is obviously greater than D. So it takes the light longer to reflect back to the light source than in the stationary frame. So, it takes the "same event", longer to "happen" in one reference frame than the other.

Is this basically what is going on?

Also, do all these effects apply to non-relativistic speeds too? Just they are immeasurably small?

12. Jan 23, 2014

### Staff: Mentor

I wouldn't phrase it quite that way because events are single points in space-time, such as "the light left the source". Thus, they don't "take time to happen", instead there's time between them. But with that correction, yes, that's pretty much what's going on. The two observers are measuring time and distance differently, but in such a way that they will always get the same answer, $c$, if they divide the distance between the emission and reception of a light signal by the time between those events.

Not necessarily "immeasurably" small, as we have measured them with very precise clocks carried on airplanes; but they're small enough to be quite invisible without specialized instruments. It's a worthwhile exercise to try calculating the time dilation between a clock in automobile moving at 100 km/hr relative to the ground and a clock at rest on the ground. It will take a lot of decimal places before you see anything...

13. Jan 26, 2014

### llynne

I have always had doubts about the twin paradox but this is even worse. The cow 'should' experience expanded time and appear to take longer to give birth. Why is this so? Accelerating mass warps the fabric of space/time, not to mention what it does to the cow. It has traveled through more space than we have measured but less time. Or, technically, through longer seconds. as you can see I still find it confusing ( worse than daylight saving) for the traveller not much time..... For the viewer plenty more time.

Last edited: Jan 26, 2014
14. Jan 26, 2014

### ghwellsjr

It's a result of Einstein's second postulate--assigning the propagation of light to c in all Inertial Reference Frames. We previously only considered the IRF where the earth was at rest and only looked at a signal propagating from the cow to earth. But if we send signals both ways starting at the same number of months, we'll see a symmetry in the scenario. Here is a repeat of the previous diagram I made but with signals sent from both the earth and the cow after 8 months and we see that they each receive the other's signal after 20 months:

That's not true. Who told you that?

Here, let's transform the same scenario to the rest IRF of the cow:

Now you can see that it's the earth that has time stretched out but they still both receive the signals the same way as they did in the first IRF.

Now let's transform to the IRF where both the earth and the cow have their times stretched out to the same extent:

Nothing is happening to space or time when we depict the scenario in different IRF's, It's just a difference in the coordinates that are used.

File size:
19.6 KB
Views:
183
File size:
29 KB
Views:
178
File size:
26.1 KB
Views:
184