General Theory of Relativity Question

[DREAMWALKER]

Ok, I went through a video to understand it more simply. But there is one point I just don't understand.

Which is this:

How does Adam think others' clock is SLOW?

Shouldn't it be FAST?

Here's my breakdown of the video:

Adam is in- Space

Sarah is on - Ground

Beam of light shone from the spaceship

According to the person on EARTH - Takes a longer time for the light to reach the spaceship back due to a V shape

According to the person on the SPACESHIP - Takes a shorter while for the light to return back to the ship

The person on EARTH sees the time passed as MORE

The person on the SPACESHIP sees the time passed as LESS

The person on EARTH sees the time passed as MORE (1 hour),

The person on the SPACESHIP sees the time passed as LESS (1 minute)FOR the person ON EARTH, the clock on the spaceship is SLOWER (BECAUSE for her, the time passed on HER clock is 1 HOUR, but the time passed on HIS clock is JUST 1 MINUTE, hence his is SLOWER compared to hers, hence time is moving SLOWER on HIS clock and FASTER on HER clock)
FOR the person ON THE SPACESHIP, the clock on the EARTH is FASTER - Right??

How does Adam view the clock on Earth as SLOW?

Can someone please explain this..Thanks!

 

[Matterwave]

1) This is the quantum mechanics forum. The special relativity and general relativity forum is ----> thataway

2) It is unclear which effects the video is discussing. There is a gravitational time dilation happening in this scenario because one person is on Earth, in a gravitational well, and one person is in space. In addition, there is a special relativistic time-dilation happening because the person in the spaceship is presumably moving. The general relativistic effect, gravitational time dilation, will have the person in the spaceship observing the person on Earth's time to be slow compared to his own. The special relativistic effect will also have the person in the spaceship observing the person on Earth's time to slow. So both effects will add, and he will see the person on Earth to have a time which is slower than his own.

 

[DREAMWALKER]

So both effects will add, and he will see the person on Earth to have a time which is slower than his own.

This is exactly what I don't understand. How can it be slow for the person in the spacecraft ? Shouldn't it be FAST because

less time passed = slower clock

more time = faster clock

Or am I missing something?

 

[Matterwave]

Less time will have ticked off on the Earth's clock compared to the ship's clock, in the frame of the guy on the ship. So the guy on the ship might see his own clock tick 10 seconds, but the clock on Earth only tick 9 seconds.

 

[DREAMWALKER]

Less time will have ticked off on the Earth's clock compared to the ship's clock, in the frame of the guy on the ship. So the guy on the ship might see his own clock tick 10 seconds, but the clock on Earth only tick 9 seconds.

That's opposite of what the video says:



The video says, the person on Earth will see that the beam takes longer to bounce back to the ship. The Person the spacecraft sees it come quicker. Hence, MORE time has ticked off on the clock on EARTH (takes longer for the beam?) and LESS time on the clock of this ship.

 

[Matterwave]

Where in the video does it say this? I don't really have time right now to watch a 15 minute youtube video front to end.

 

[DREAMWALKER]

Where in the video does it say this? I don't really have time right now to watch a 15 minute youtube video front to end.

From 2:58 to 5:55.

 

[A.T.]

From 2:58 to 5:55.

That part of the video deals only with kinetic time dilation from Special Relativity, which is symmetrical. Gravitational time dilation from General Relativity is ignored here. They could just as well show this in space. far from any big masses.

How does Adam view the clock on Earth as SLOW?

Just apply the same logic in reverse: How will a light beam going vertically up-down from Sarah's perspective look from Adam's perspective?

 

[DREAMWALKER]

That part of the video deals only with kinetic time dilation from Special Relativity, which is symmetrical. Gravitational time dilation from General Relativity is ignored here. They could just as well show this in space. far from any big masses.

Just apply the same logic in reverse: How will a light beam going vertically up-down from Sarah's perspective look from Adam's perspective?

Nope. Didn't get it. For me, it's pretty simple.
This is how I break it down:

less time passed = slower clock

more time = faster clock

So, according to Adam, the EARTH clock SHOULD be fast and not slow.

 

[A.T.]

For me, it's pretty simple.

“Everything should be made as simple as possible, but no simpler.” A. Einstein (paraphrased)

less time passed = slower clock
more time = faster clock

It depends on the reference frame which clock is the faster clock, so you must identify them by name, not their rate.

 

[DREAMWALKER]

“Everything should be made as simple as possible, but no simpler.” A. Einstein (paraphrased)It depends on the reference frame which clock is the faster clock, so you must identify them by name, not their rate.

Ok, but can we talk only in terms of this example..this video particularly? I want to understand this, but this is the only point I am not able to understand.

 

[A.T.]

Ok, but can we talk only in terms of this example..this video particularly?

You are asking about something, that the video doesn't show: Sarah's light-clock from Adam’s perspective. You have to draw you some pictures yourself or find a better video that shows the symmetry.

 

[DREAMWALKER]

You are asking about something, that the video doesn't show: Sarah's light-clock from Adam’s perspective. You have to draw you some pictures yourself or find a better video that shows the symmetry.

I just shared the screenshot above...That's the crux of the problem...I can understand everything, except that bit. It doesn't show the clock, but it DOES show that the time on Sarah's clock is SLOWER as compared to Adam. Which I don't think is right. Adam should see EARTH clock FASTER. Right? More time passed remember relative to Adam's clock?

 

[A.T.]

I can understand everything, except that bit

That "bit" is the whole point of relativity. It's relative whose clock is slower.

but it DOES show that the time on Sarah's clock is SLOWER as compared to Adam. Which I don't think is right.

It is right in Adam's frame of reference.

 

[DREAMWALKER]

That "bit" is the whole point of relativity. It's relative whose clock is slower.

I don't agree then. Because my calculation tells me Adam should see Sarah's clock going FASTER and not SLOWER. Because again, Sarah's clock RELATIVE TO Adam's clock, took longer. Which means her clock is faster compared to Adam's clock which took a shorter time.

 

[A.T.]

Because my calculation tells me Adam should see Sarah's clock going FASTER and not SLOWER.

Then you have done something wrong.

 

[DREAMWALKER]

Then you have done something wrong.

Ok then tell me what's wrong in this:

Adam- Space

Sarah- Ground

Beam of light shone from the spaceship

according to the person on EARTH - Takes a longer time for the light to reach the spaceship back due to a V shape

according to the person on the SPACESHIP - Takes a shorter while for the light to return back to the ship

the person on EARTH sees the time passed as MORE

the person on the SPACESHIP sees the time passed as LESS

the person on EARTH sees the time passed as MORE (1 hour),

the person on the SPACESHIP sees the time passed as LESS (1 minute)

FOR the person ON EARTH, the clock on the spaceship is SLOWER (BECAUSE for her, the time passed on HER clock is 1 HOUR, but the time passed on HIS clock is JUST 1 MINUTE, hence his is SLOWER compared to hers, hence time is moving SLOWER on HIS clock and FASTER on HER clock)

FOR the person ON THE SPACESHIP, the clock on the EARTH is FASTER ...

 

[A.T.]

according to the person on EARTH - Takes a longer time

But what measures the time according to the person on EARTH? You need a second light-clock that bounces light vertically in the EARTH frame, and therefore V-shaped in the SPACESHIP frame. That clock represents the EARTH time, and in the SPACESHIP-frame this EARTH-clock is slower than the SPACESHIP-clock because of the V-shape.

 

[DREAMWALKER]

That clock represents the EARTH time, and in the SPACESHIP-frame this EARTH-clock is slower than the SPACESHIP-clock because of the V-shape.

Man..sorry, but you are just repeating that. I need to know how? and why? I think we have already agreed to disagree on the EARTH clock being slower. But I need an explanation. I am sorry, but I am not quite convinced by your explanation.

 

[A.T.]

I need to know how?

I just told you how. You need to consider a second light clock, which is not shown in the video. And you need to distinguish the two clocks clearly. So far you just keep talking about "time" without specifying according to which clock.

 

[DREAMWALKER]

I just told you how. You need to consider a second light clock, which is not shown in the video. And you need to distinguish the two clocks clearly. So far you just keep talking about "time" without specifying according to which clock.

The black clock belongs to Adam and the red one shown here, belongs to Sarah, i.e the Earth clock, in other words, the "second light clock". The time according to this, red, EARTH clock, is what is worrying me. The super above says "slow" whereas it should be "fast". If you still think I am not clear, I will clear it further.

 

[A.T.]

red one shown here, belongs to Sarah, i.e the Earth clock, in other words, the "second light clock".

You will not understand the red clock behavior, until you actually model it as a light-clock and analyze it's light beam from both frames. In other words, you have to do for the red clock, what the video does for the black clock.

 

[DREAMWALKER]

You will not understand the red clock behavior, until you actually model it as a light-clock and analyze it's light beam from both frames. In other words, you have to do for the red clock, what the video does for the black clock.

I think I know what you mean now...was thinking the same thing...but since I am not well-versed with Physics terms, I couldn't express myself right..thanks!

 

[stevendaryl]

DREAMWALKER:

First of all, when someone says that Adam's clock is running slow, according to Sarah, and Sarah's clock is running slow, according to Adam, they're not talking about what they see, they're talking about what they compute. That distinction isn't made clear in the video. They sort of hint at it, though. From Sarah's perspective, Adam's "light clock" (a light beam bouncing up and down) runs slow, because the light follows a diagonal path. But from Adam's perspective, it is Sarah's light clock that is following a diagonal path, so Adam can equally well reason that Sarah's light clock is running slowly.

How do you reconcile these two seemingly contradictory facts? Adam thinks Sarah's clock is running slower, and Sarah thinks Adam's clock is running slower.

Well, you have to follow the logic and the mathematics. A video can hint at how it works, but you really need to look at the mathematics to understand it in any deep sense.

Let's suppose that Adam is moving so fast (relative to Sarah) that his clock is running at half Sarah's speed. Let's suppose that when Adam passes closest to Sarah, they both set their clocks to 12:00 a.m. Then let's consider a few particular events:

• Event 1: Sarah's clocks shows 12:15 a.m.
  
• Event 2: Adam's clock shows 12:15 a.m.
  
• Event 3: Sarah's clock shows 12:30 a.m.
• Event 4: Adam's clock shows 12:30 a.m.
• Event 5: Sarah's clock shows 1:00 a.m.
• Event 6: Adam's clock shows 1:00 a.m.

Since Sarah thinks that Adam's clock is running slow, she thinks that the order of events is as follows:

1. Event 1 comes first. Her clock shows 12:15
   
2. Event 2 and Event 3 are simultaneous. Her clock shows 12:30 when Adam's clock shows 12:15
3. Event 4 and Event 5 are simultaneous. Her clock shows 1:00 when Adam's clock shows 12:30
4. Event 6 comes last.

Since Adam thinks that Sarah's clock is running slow, he thinks that the order of events is as follows:

• Event 2 comes first. His clock shows 12:15
• Event 1 and Event 4 are simultaneous. When his clock shows 12:30, Sarah's clock shows 12:15
  
• Event 3 and Event 6 are simultaneous. When his clock shows 1:00, Sarah's clock shows 12:30
• Event 5 comes last.

So the relationship between Sarah's time for events and Adam's time for events is not simply that one person's times are slower than the other's. They disagree about the order of events, as well. This is called "relativity of simultaneity". The video gets into the fact that the order of events are different for Sarah and for Adam starting at 6:02.

 

[goce2014]

Hello
Whether there any difference if Sarah is on the equator or at the North Pole in this video?
After 12 hours, Sarah is on the opposite side of the globe if Adam rectilinearly away from Sarah. In the second case Adam at any long remote radius of the Sarah has to be Earth's satellite to maintain the same distance but then has to drive really fast around the Earth like Kimi Raikkonen for example. And finally whether Adam is equally old as Sarah after returning home or he revitalize?

 

[stevendaryl]

Hello
Whether there any difference if Sarah is on the equator or at the North Pole in this video?
After 12 hours, Sarah is on the opposite side of the globe if Adam rectilinearly away from Sarah. In the second case Adam at any long remote radius of the Sarah has to be Earth's satellite to maintain the same distance but then has to drive really fast around the Earth like Kimi Raikkonen for example. And finally whether Adam is equally old as Sarah after returning home or he revitalize?

This particular video didn't get into the complications of (1) the Earth spinning, and (2) gravity's effect on clocks.

 

[jayeshgolhar]

I still not getting how time pass slowly or fastly

 

[stevendaryl]

I still not getting how time pass slowly or fastly

I'm not sure what your question is. If you ignore the effect of gravity, then the elapsed time $\delta \tau$ on a clock that is traveling at speed $v$ for $\delta t$ seconds is given by:

$\delta \tau = \sqrt{1 - \frac{v^2}{c^2}} \delta t$

This formula gives the same answer no matter what inertial reference frame is used to compute $v$ and $t$.

 

[pervect]

Nope. Didn't get it. For me, it's pretty simple.
This is how I break it down:

less time passed = slower clock

more time = faster clock

So, according to Adam, the EARTH clock SHOULD be fast and not slow.

If there were an absolute time, this logic would work. If there were an absolute time, and we have two observers A (Adam) and E (Earth), then we expect that if E concludes that A's clock is slow, A would conclude that E's clock is fast.

The missing concept that exposes the flaw in this argument is the relativity of simultaneity. Unfortunately it's necessary to understand this concept to understand relativity, and the video is most likely not doing a good job of explaining it. I've read some papers which studied how to teach the concept, but it appears the success rate with the usual methods of instruction was low - a bit under 50% - based on attending classes. Presumably attending classes is more effective than watching a youtube video, but I suppose that point hasn't actually been studied.

Anyway - while you shouldn't necessarily let the odds discourage you, you probably do need to realize that more effort than watching this one video is probably required. And that the idea that "you're only missing one point" may be true, but that doesn't make getting the point you're missing any easier.

While I can't guarantee that the paper I mentioned about how to teacah the subject is necessarily the best way to learn it, I can give you the link and hope for the best. See http://www.physics.umd.edu/perg/papers/scherr/ScherrAJP2.pdf, "The challenge of changing deeply held student beliefs about the relativity of simultaneity".

If you do go through the effort of reading this paper, I'd be interested in feedback on whether or not it helped. They claim an 85% success rate using teaching methods based on this paper (though of course, reading the paper isn't the same as being taught using the methods described by the paper.

 

[stevendaryl]

To me, there are two approaches to understanding relativity to the extent that you realize that it is all perfectly consistent, and that no weird twin paradox or barn-and-poll paradox will ever reveal a contradiction:

1. The geometric view.
2. The Lorentz Ether view.

The geometric view treats time as another dimension, just like (or almost exactly like) the other 3 spatial dimensions. There is the weird fact that "lengths" are computed using $\delta s^2 = \delta x^2 - \delta t^2$ (in units were $c=1$ to make time and space look more alike) rather than the Euclidean $\delta s^2 = \delta x^2 + \delta t^2$. If you can get over that weirdness, then relativity becomes a lot more straight-forward using the geometric view, because so many of the paradoxical phenomena in relativity have direct analogies in Euclidean geometry (where they can easily be seen to not be weird at all).

The Lorentz Ether view is really just an extra bit of ontology added to SR. You assume that there is some (unknown) absolute rest frame, and motion relative to this rest frame causes clocks to literally run slower, and causes objects to literally shrink in the direction of their motion. It's clear in this view that there can be no contradictions in relativity coming from thought experiments involving twins and motion and rods and clocks. Any thought experiment has a definite answer to questions such as: what is the length of this, or what is the age of that twin. The weirdness about this view is that this mysterious absolute rest frame always cancels out at the end, and all calculations work just as well assuming that any rest frame is the absolute one.

I'm definitely partial to the geometric view, although I can understand, philosophically, why people might prefer the "undetectable absolute rest frame" alternative, because it makes things more intuitively comprehensible and allows for things such as "instantaneous collapse of the wave function" that make no sense without an absolute rest frame.

 

[Wes Tausend]

...

A better video for just understanding why the observer-pair time difference exists can be found at http://www.learner.org/vod/vod_window.html?pid=611 . Unfortunately the page says it is only available to web addresses within the USA and Canada.

When the page link opens, go down to the little square icon following #42, The Lorentz Transformation, and open it. The 1985 video is meant as a teaching aid for college (or high school) physics classes and is 1/2 hour long. It covers the simple applied math as it progresses and is an unusually good visual aid to comprehending foreshortening and time dilation of Special Relativity (SR) as we still understand it now. Without the Lorentz Transformation, Einstein's SR would likely not be established today.

Wes
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