Newb Question Regarding Special Relativity

[S1lent Echoes]

I am just trying to understand the concept regarding space-time with regards to the observer. I will use the concept I heard of the ping pong ball bouncing straight up and down on a table in a moving train with regards to an observer on the train and one outside of it.

I understand the concept in general that the distance traveled is different between observers but that the light speed is constant. What I do not understand is the point this concept is trying to make.

To the observer on the train, it may not "seem" like the ball traveled the same path or distance as it did to the person outside of the train but surely they acknowledge that fact on some level. Assuming they acknowledge the fact that they are moving. Right? Even if it is only on some subconscious level? Also, regardless of observer perspective the ball did travel along the diagonal path through space-time, right?

Thanks in advance for helping to explain the idea behind this concept to me.

 

[ghwellsjr]

I am just trying to understand the concept regarding space-time with regards to the observer. I will use the concept I heard of the ping pong ball bouncing straight up and down on a table in a moving train with regards to an observer on the train and one outside of it.

I understand the concept in general that the distance traveled is different between observers but that the light speed is constant. What I do not understand is the point this concept is trying to make.

To the observer on the train, it may not "seem" like the ball traveled the same path or distance as it did to the person outside of the train but surely they acknowledge that fact on some level. Assuming they acknowledge the fact that they are moving. Right? Even if it is only on some subconscious level? Also, regardless of observer perspective the ball did travel along the diagonal path through space-time, right?

Thanks in advance for helping to explain the idea behind this concept to me.

You seem to think the observer outside the train has a better appreciation for the path of the ball through space-time but aren't you overlooking another observer outside the Earth who is seeing the ball, the train and both observers traveling at hundreds of miles per hour through space along the surface of the earth? How do you determine the levels for the facts to be acknowledged?

 

[Goodison_Lad]

One of the crucial points of special relativity is that there is no such thing as absolute motion - all motion is relative.
So, the observer on the ground decides that it is the train that is moving. But relativity allows the observer on the train to conclude that it is the observer on the ground (and everything else) that is actually moving in the opposite direction. Both are equally entitled to their views on this. There is nothing at all special about the ground observer - it's just that we're not used to thinking about relative motion this way.

The observers might well disagree over many things e.g. the shape of the path of the ball or the distance it travels. The ground observer will inevitably measure the path traced out by the ball to be longer than what the train observer measures. But he can, by suitable calculation, work out the length of the ball's path as it would appear to the train observer that the train observer. And vice versa. An analogy is how large two people appear to each other when they are standing far apart: I think you look small; you think I look small. Who is right? Both of us. In this analogy, our disagreement grows the further apart we are. In relativity, the 'disagreement' grows the greater the relative velocity.

But although the observers will disagree about certain things (and be equally right), there are some things they will agree on. If it was a beam of light reflecting up and down between two mirrors on the train, both observers would disagree about the shape of the path traced out by the light (just like the ball): to the observer on the train, the light would just be bouncing up and down; but the ground observer would, because of the relative motion of the train, track the light as following an angled path, zig-zagging as the train passed. However, if they each calculated the speed of the bouncing light, they would agree that it was traveling at speed c.

 

[S1lent Echoes]

Awesome, the outside observer viewing it from a huge distance away made it clear to me, tyvm. I knew I was missing something and I knew it was obvious but I just couldn't put my finger on it.

So, you would have to be completely separated from all motion in the universe to know the absolute motion of anything and since that is not possible, all motion is relative because you are in motion with it (?). That is just awesome, I love the philosophy behind physics, again thank you.

 

[S1lent Echoes]

I had another question, that being how objects curve space-time. Specifically the Sun and the planets and how their elliptical orbits are actually straight lines, just curved by the Sun's mass.

Again I understand the concept behind this, if you were to depict this using a graph then the same lines that were straight would be bent if you placed a massive object in the middle of it. This is because of the force generated by the object, correct?

My question is though that space is still there, right? Why is the straightest line or path still not directly through the Sun to the other side of it? Is this concept just for objects like planets trying to stay in motion and not the same for say you and I if we wanted to get from point A to point B (if there is any actual difference between that?)?

 

[Goodison_Lad]

The thing about motion is that any observer can declare themselves to be at rest (as long as there’s no acceleration). So they’d measure the motion of everything else relative to their rest position.

General relativity replaces the idea of gravity as a force with the idea that mass/energy distorts/curves the spacetime around it, and other masses behave accordingly. Objects in spacetime always try to follow the straightest possible path, and if the spacetime has been curved by the presence of a nearby mass, the path of the object through space can appear curved.

It is possible to have the straightest path heading straight for the Sun, if there’s no transverse velocity (which there is in an orbit). When you drop something, it falls in a visibly straight line. Once you have a transverse velocity, though, the straightest path through spacetime that is possible for the object then happens to be appear as a curve through space.

In a simple thought experiment, somebody is in a stationary lift and throws a ball horizontally. They’d see the ball curve downwards towards the ground. If, however, the lift cable snapped and it was plunging freely, when they threw the ball it would appear to them to move in a horizontal straight line – they’d could actually see, if you like, the straightness of its path through spacetime (through the space part anyway). But to observers outside the lift, this straight path would appear curved in the usual way.

 

[S1lent Echoes]

Okay, I think I understand what you are saying though it may take me a little bit to process it all.

Also after thinking about it some more I think I was able to view it another light as well. Since the Sun's mass projects a force then to go to "straight" through it would take X amount of force to get through. If you used that same amount of force but took the "curved" path, then you would still get there faster, therefore making the the actual straightest path. Is that right?

If, given that were true if something were not affected by the Sun's force, then would the straightest line be through the Sun?

 

[Goodison_Lad]

We're in pretty complex territory.

I think a lot of the difficulty of this subject is the use of the word ‘straight’. I’m going to take the liberty of replacing it, for now, with the word ‘natural’. Relativity tells us that the natural path for an object through spacetime is the one for which the object ages the most. The natural path applies to free objects i.e. objects that don’t experience forces or accelerations. In ordinary empty space, far away from massive objects, natural paths look familiar – objects move in straight lines at constant velocity. Spacetime isn’t curved in this case.

Where gravity is concerned, and spacetime is curved, natural paths are not the familiar straight line/constant velocity ones.
Suppose I have a rocket with a clock on board, and I want to send it up and bring it back to the launch pad, say an hour later. I can do this many ways:

1) I might get it to blast off slowly, hover for a while, before landing an hour later;
2) or I could get it to accelerate like mad, then turn around and accelerate back, landing an hour later;
3) or I could simply lob it up at just the right speed, so that it is in free flight all the way up and down, landing (or crashing!) after an hour.

In each case, the start and the end of the journey happens in the same location (the launch pad) at the same times. If I did all these experiments I would find that the ship’s clock in the last experiment showed the greatest amount of time had passed onboard. The ship has followed the natural path through spacetime that joins the beginning and the end of its journey. Anybody on board the ship would not experience any forces or accelerations (apart from the short blast off and landing). This isn’t true for the first two ways – people on board would experience accelerations and forces during the journey.

As I mentioned earlier, scientists no longer talk about gravity as a force in the ordinary sense - they talk about how, for example, the Sun’s mass causes the spacetime around it to curve, so that the natural path that objects follow isn't straight in the everyday sense - it can be curved, because the spacteime the object is traveling through is curved.

The natural route through spacetime isn’t necessarily the one which traces the shortest spatial distance - we have to remember the ‘time’ part of spacetime as well – relativity shows us that it is the route for which the traveller ages the most. And this is the one in which he feels no accelerations or forces.

 

[S1lent Echoes]

Thank you for the clarification, I believe I understand the straight/natural path now (at least enough so that I can sort the rest out in my head). However, the rocket event you described touched on something else and I am having a hard time grasping that concept now. I see how it ties into what we were discussing, I am just having a hard time understanding it.

I know Einstein's theory proved the fact that there is no absolute time and that it is relative, I get that part. I understand that the time passes differently on board than for the time at the launch pad. What I do not get is how this is true? Stephen Hawking explained that there was a test with two clocks at the top and bottom of a water tower and the time was different between the two clocks. Does this tie into that concept? (If that is a different concept, please ignore as I do not want to get off topic.)

 

[Goodison_Lad]

Well, it's all linked, although we are covering an impressive bunch of concepts. Your orginal queation was firmly in the realm of special relativity, but we migrated into general relativity.

General relativity predicts that time runs at different rates for two observers not only according to how fast they move relative to each other (special relativity covers this) but also according to their relative positions in a gravitational field. The closer you are to a mass, the slower your time runs compared with somebody who is further away. So in Hawking's example, the clock at the bottom of the tower would have been running slower than the clock at the top.

In the rocketship examples, both effects will have been combining together: the faster the rocket was moving the slower time ran for it compared with the ground BUT the higher the rocket went the faster time ran for it compared with the ground. They have to take both these effects into account for the GPS system: the high speed of the satellite relative to the ground means that, compared with the ground, there is a slowing effect on time on the satellite; but because the satellite is further away from the Earth's mass, there is a speeding up effect on time on the satellite (or perhaps its better to say that because the ground is closer to the Earth's centre than the satellite, there is a slowing effect on time at the surface).

The two effects aren't equal in size. If they were, time on the satellite would run at excatly the same rate as it does on Earth. The gravitational effect (which makes time at the Earth's surface run more slowly than time at the altitude of the satellite) is larger than the speed effect - overall clocks in GPS orbits run faster than clocks on the ground by about 38 microseconds per day.

 

[S1lent Echoes]

Okay, the concepts themselves make sense to me and I "see" what you are saying. What I still do not understand (or am not "getting") is how/why time is slowed near a mass/gravitational field? Is it the curvature of the space-time around it, i.e. it is more curved close to it than further away from it?

(Btw, thank you for taking the time to explain such a basic/fundamental concept to/for me, much appreciated)

 

[Goodison_Lad]

(Btw, thank you for taking the time to explain such a basic/fundamental concept to/for me, much appreciated)

You’re welcome.

You’re correct – the degree of curvature is greater the closer you get to a mass.

I don’t think anybody knows how mass/energy curves spacetime i.e. what the mechanism is. What Einstein did, though, was give us the mathematical relationship between the mass/energy density in a region and the curvature of spacetime in the neighbourhood. He was struck by a thought: somebody falling freely in the Earth’s gravitational field is completely free of the ordinary effects of the field that we’re familiar with – the feeling of weight. The idea that this effect of gravity could be somehow ‘magicked’ away simply by adopting a different frame of reference to the one we all live in led him to believe the effect of gravity (weight) and the effect somebody in an accelerating object would feel (e.g. a spaceship) were identical (allowing for a few limits). So he pressed on, arriving at the general theory, which allows gravity to be described as the curvature of spacetime.

To explain why time must run more slowly near a mass, I’m going to speak roughly and colloquially. It’s quite long-winded, and won’t please the purists, but it might help. One of the predictions of general relativity is that the radial distance from the centre of a mass to a point on a circle centred on that mass is greater than you’d expect – it’s greater than the circumference of that circle divided by 2∏ (which is what you’d calculate to get the radius of the circle). Somehow, there is more space around a mass than ordinary high-school geometry would suggest. And this effect increases the closer to the mass you get. This is to do with the very curvature of spacetime we’ve been talking about.

Imagine we are located some distance away from a black hole in a circular orbit. We measure the circumference of our orbit to be, say, 6,282 km. So we’d calculate that we must be 1000 km from the centre of the black hole.

We can ascribe a radius to the black hole, which is, let's say, 5km. This would be where its event horizon (the point of no return) is located. Suppose we want to send somebody from our spaceship to hover 3km above its surface, while we stay safely where we are. Ordinarily, we might expect the distance he’d have to travel to be 1000 – 8km = 992km. But in fact, general relativity tells us that, because of the curvature of spacetime, the distance he’d have to cover would be greater than this, say 993km. While I’m just making up these numbers, the principle is quite correct.

So if we aimed a ray of light from our orbiting craft at the black hole, it would have to travel further than we might have expected – it would seem to us to be taking its time to get there. We could only conclude that the light was traveling more slowly than the expected 300,000 km/s. This slowing of light, as measured by us distant observers, is not only allowed by general relativity, but actually predicted by it.

Yet relativity insists that any observer who measures the speed of light locally (i.e. in their immediate neighbourhood) always gets the same value: 300,000 km/s. As the light flashed past our friend, who is hovering just above the black hole, he’d measure its speed to be 300,000 km/s, in accordance with the predictions of relativity.

So we determine the light to be moving ever more slowly as it gets closer to the black hole, yet our hovering shipmate notices nothing unusual about its speed. We can reconcile these two different views only if time for the shipmate is running more slowly than time for us – the slow moving light is moving past him in his slow moving time.

 

[S1lent Echoes]

Ah, okay I believe I understand the concept behind it. In a way it appears to be similar to the ball bouncing on the train and the differences between the observers, since both are in motion albeit relative to each other. At least, that is what helped me understand it (whether they are actually related or not).

Again thank you. I have only just started learning these concepts and am trying to get the basics down, so don't be surprised if you see me on here quite often asking for more explanations on various things as I try to understand more and more. =P