[Kean1 (OP)]

(this is my first post on here so be gentle with me!)
Quoted from latest episode "eggs, eyes etc..., in answer to the question: "How fast a rocket can humans safely travel in?"
"So the Earth rotates at 600 miles an hour. So we're currently on the earth going 600 miles an hour, because we're on the earth we're also going 600 miles an hour. The Earth is speeding around the sun at 70,000 miles per hour. So we are also speeding around the sun at 70,000 miles an hour. The sun is speeding through the galaxy at 450,000 miles an hour, which means we're also spinning at 450,000 miles an hour."

I'm probably dim, but how can I understand "speed" in this statement? Are the references always implicit? For example, in the first statement "we're on earth going 600 mph", should I implicitly understand that the "reference" (if that's even the correct word!) is the centre of the earth, and this jumps to the sun in the second statement "The Earth is speeding around the sun at 70,000 miles per hour". In other words, in astronomy, when speeds are mentioned, should I just assume that I should understand the quoted speed relative to an "obvious" reference.

The reason I'm asking the question is because I simply don't "get" relativity, time dilation etc...e.g. in the classic example of my "twin" charging off in a rocket at near the speed of light aging differently to me, am I not simply "aging" at the same rate relative to my twin, because relative to him/her, I'm charging off in the opposite direction at an equal and opposite speed, therefore cancelling out any warping of time?
Hope that makes (some) sense!

[Halc]

Quoted from latest episode "eggs, eyes etc..., in answer to the question: "How fast a rocket can humans safely travel in?"
"So the Earth rotates at 600 miles an hour.

Maybe where they are (Montreal?). At the equator, it is over 1000 mph.  25000 mile circumference in 24 hours, no?

So we're currently on the earth going 600 miles an hour, because we're on the earth we're also going 600 miles an hour.

We're going 600 mph relative to the center of Earth.  Speed is always relative, so not specifying the relation is wrong.  I'm not moving 600 mph relative to my mailbox. I'm nearly stationary relative to that.

The Earth is speeding around the sun at 70,000 miles per hour. So we are also speeding around the sun at 70,000 miles an hour. The sun is speeding through the galaxy at 450,000 miles an hour, which means we're also spinning at 450,000 miles an hour."

Just so, relative to the sun and the galaxy respectively.

I'm probably dim, but how can I understand "speed" in this statement? Are the references always implicit? For example, in the first statement "we're on earth going 600 mph", should I implicitly understand that the "reference" (if that's even the correct word!) is the centre of the earth, and this jumps to the sun in the second statement "The Earth is speeding around the sun at 70,000 miles per hour". In other words, in astronomy, when speeds are mentioned, should I just assume that I should understand the quoted speed relative to an "obvious" reference.

You got it.  Speed is always relative to something, and language usually lets you get away with letting it be implicit, but the reference is always there.  The speedometer on my car shows speed relative to the road under it, and doesn't bother to say that explicitly.
Velocity (a vector) is also a relation.  So I might be moving at speed 600 mph relative to Earth, and some guy on the planet opposite me also is moving at the same 600 mph speed, but our velocity is very different since we're moving in different directions.  Speed is a scalar, and velocity is a vector.

The reason I'm asking the question is because I simply don't "get" relativity, time dilation etc...e.g. in the classic example of my "twin" charging off in a rocket at near the speed of light aging differently to me, am I not simply "aging" at the same rate relative to my twin, because relative to him/her, I'm charging off in the opposite direction at an equal and opposite speed, therefore cancelling out any warping of time?

Under relativity, it is the other twin that is moving relative to either twin, so in the current inertial frame of either twin, the other twin is aging slower.  Not intuitive, but that's how it works.
When the 'travelling' twin turns around, his inertial frame changes, and in that frame the twin back home simultaneous with the turnaround event is much older than his age in the outbound frame.  That's the relativity of simultaneity in action, and is why one twin is older than the other when they finally meet again.

[jeffreyH]

You are attracted to the earth by gravity. This is important because it puts you in an accelerating frame. But you say, "I'm standing still. How can I be accelerating?" If there was a hole under your feet you would start falling. So the ground is supporting you.

Once you are falling freely you are then in a frame indistinguishable from an inertial or non accelerating frame. But you say "How can I be in an inertial frame? I am accelerating down into a hole."

Welcome to relativity!

[PmbPhy]

(this is my first post on here so be gentle with me!)
Quoted from latest episode "eggs, eyes etc..., in answer to the question: "How fast a rocket can humans safely travel in?"

There is no limit to how fast human in free-fall can move other than the speed of light, which can be shown that nothing can move faster than that. You've been thinking about acceleration and then quoting speed. If the ship is free fall then it can move at any speed less than the speed of light.

[yor_on]

Nice to see you Pmb, and interesting comment that I totally agree too..

As for  'speeds' you always will need to define something from where you measure it. In relativity there is no defined universal platform of a null speed. And all stars planets etc 'uniform motion' then becomes equivalent, as defined locally. By that I mean you f.ex doing a experiment on earth trying to see if it moves, being inside a 'black box' without external information. That also leads us to the equivalence principle in where a uniform constant acceleration becomes inseparable from the gravity you find yourself to have inside that box.
=

Although there is a difference, thinking of it.

Presume you set up a experiment in where you place a light emitter in the middle of your box. Then place two detectors, one at the 'front' of the box, the other at the 'end'. If you're in a gr.....

damn, it won't matter :) The light red and blue shifts both in your gravitational 'field', as well as it will do in a accelerating box. so there will be no difference measured, if we ignore the way earth f.ex spins and  'wobble away'. Will blame this on being away from physics for a while.

What you could use the experiment for is to define the 'gravity' at where the box is situated, but that's all. Excluding outside information it won't tell you a thing about any possible 'speed'. Although if you knew the mass, wouldn't that make a difference?

No not really, if we instead let the box 'float' outside a gravitational potential (aka in 'deep space') you won't see any red and blue shifts, no matter what you would define your speed to be versus some origin.

Ideally that is, because the mass of the box might interfere somewhat with your experiment. Discounting that there will be no proofs for a motion inside that box. This can also be called being in a same 'frame of reference' which just means that you the box and your experiment are 'motionless' relative each other (in this case).

But 'frames of reference' are tricky.
=

spelling and syntax

[Kean1 (OP)]

Thanks all for your replies.
Halc, you wrote (many thanks!):
"Under relativity, it is the other twin that is moving relative to either twin, so in the current inertial frame of either twin, the other twin is aging slower.  Not intuitive, but that's how it works.
When the 'travelling' twin turns around, his inertial frame changes, and in that frame the twin back home simultaneous with the turnaround event is much older than his age in the outbound frame.  That's the relativity of simultaneity in action, and is why one twin is older than the other when they finally meet again."

Really not intuitive... "So in the current inertial frame of either twin, the other twin is aging slower".
What I just can't get past is this idea that time appears to be slowing down for both twins, it just depends on whether you are measuring from one twin's position or the other's...

I'll spare you the ordeal of "banging your head against a brick wall" trying to clarify this further and I'll just have to dig deeper (down the rabbit hole!) and try harder to get my head around it.
Perhaps, if it's not too much of a bother, and you understand my confusion, do you happen to know of any links to explanations that might help me...just idle curiosity as I don't NEED to know this. The trouble I've had is that everything I've read/watched on Youtube that describes, for e.g., the twin thought experiment, always takes as a given that the "reference point" is the twin/you "here on earth", let's say. But if I assume that "I" am the other twin, the one zooming off in the space ship how can I demonstrate/reason that it is "I" that am moving and not the twin on earth that is zooming away from me at an equal and opposite velocity??

[Colin2B]

But if I assume that "I" am the other twin, the one zooming off in the space ship how can I demonstrate/reason that it is "I" that am moving and not the twin on earth that is zooming away from me at an equal and opposite velocity??

Relatively you can’t. But let’s be realistic about this, you are the one travelling in the ‘twins scenario’ and Earth isn’t going to suddenly come and find you in your frame.  However, if you waited hanging in space for the Earth to complete its orbit and return to you, people on earth would have aged less than you as the final measurement is made in your frame.

[Halc]

Really not intuitive... "So in the current inertial frame of either twin, the other twin is aging slower".

That is basic time dilation.  Time 'runs' at full speed if you're stationary, and all objects are stationary in their own frames.  This is consistent with Galilean relativity: "Physics is the same in any frame".  Time dilation means that time slows down for moving things, and in any frame, it is everything not stationary in that frame that is moving.  So relative to the twin in the ship, the Earth twin is the one moving.  Earth is just another ship after all, just a larger one than usual.

What I just can't get past is this idea that time appears to be slowing down for both twins, it just depends on whether you are measuring from one twin's position or the other's...

Be careful about 'appears to be'. Time is computed to be slower in these other frames. The twins are not in each other's presence, and hence neither has a direct way to measure the other.  In fact, if a clock is approaching you fast, it will 'appear' to be running faster, but that's mostly due to Doppler effect, and is why light from approaching galaxies is blue shifted despite being dilated a bit slower.
Say there are twins X and Y moving apart moving fast enough for 2x dilation.
In the frame of one twin X, his clock reads 5 and the clock of the other twin simultaneously (in X's frame) reads say 8.  These are arbitrary numbers, let's just say the value of the minute hand.
Two minutes later (in X's frame), X's clock reads 7 and Y's clock simultaneously (in X's frame) reads 9.
Note that I put 'in X's frame' next to each mention of simultaneous since simultaneity is relative, and two events simultaneous in one frame are not simultaneous in another.  The word is ambiguous without this reference. This (relativity of simultaneity) is the most important part because this explains why one twin comes home objectively younger than the other.

Perhaps, if it's not too much of a bother, and you understand my confusion, do you happen to know of any links to explanations that might help me...just idle curiosity as I don't NEED to know this.

https://en.wikipedia.org/wiki/Relativity_of_simultaneity
That is probably one of the best places to start. They have some nice diagrams/gifs, and there's a description of the classic train thought experiment from which RoS is demonstrated from the postulate of frame independent light speed. Wiki is great for this kind of thing since it is full of hyperlinks you can click on for detail on any part that into which you want to go deeper.

The trouble I've had is that everything I've read/watched on Youtube that describes, for e.g., the twin thought experiment, always takes as a given that the "reference point" is the twin/you "here on earth"

OK, I know that. For that very reason, I always choose the frame of the guy in the ship or the guy in the train, which really helps one discard a lot of the assumptions about absolute motion.  With a westbound train it is pretty much true.  A really fast train going west is actually more stationary (accelerates less) and has Earth rotating underneath it.  Few trains move at fast enough speeds to actually cancel rotation, but jets sometimes do.

But if I assume that "I" am the other twin, the one zooming off in the space ship how can I demonstrate/reason that it is "I" that am moving and not the twin on earth that is zooming away from me at an equal and opposite velocity??

Colin's answer to this is correct. There is no way to detect absolute motion, or more precisely, no local test.  The two twins moving apart at high speed is entirely symmetrical, and thus each ages slower in the frame of the other.  But one of them significantly changes reference frames, and does so a long distance from the other.  That's what makes the difference when they are reunited.  Remember RoS?
Say the rocket takes 5 years (ship time) each way, with 2x time dilation.  At the turnaround point in the outgoing frame, the clock on the stationary ship reads 5 and simultaneous (in that outgoing frame), the clock of the distant (moving away) twin reads 2.5 years.  Now the first twin turns around and is now stationary in a very different inbound frame.  In that frame, his clock still reads 5 (he hasn't gone anywhere yet), but the clock of the distant (moving towards us) twin reads 17.5 years.  During the remaining part of the exercise which the stationary twin waits for Earth to come to him, he ages 5 more years (10 total), and the traveling guy ages 2.5 more (20 total).  The Earth guy has aged twice that of the 'stationary' twin.
RoS is illustrated there.  Relative to two different frames (inbound and outbound), the turnaround event is simultaneous with two very different events (times 2.5 and 17.5) back on Earth.

[Origin]

How fast a rocket can humans safely travel in?"

Any speed won't hurt a person.  As a result of tremendous speed other things like radiation could kill you, but the speed itself is not an issue.  If you are on a plane going at, say 600 mph you would not even feel like you are moving, the same would be true if you were travelling at 10,000,000 kph.

[Bill S]

Perhaps, if it's not too much of a bother, and you understand my confusion, do you happen to know of any links to explanations that might help me...just idle curiosity as I don't NEED to know this.

  http://www.owl232.net/papers/twinparadox.pdf

I found Michael Huemer’s explanation very helpful. 
MTW; never doubt the value of curiosity, it might try the patience of others, but it’s seldom idle.

[LB7]

Any speed won't hurt a person.  As a result of tremendous speed other things like radiation could kill you, but the speed itself is not an issue.  If you are on a plane going at, say 600 mph you would not even feel like you are moving, the same would be true if you were travelling at 10,000,000 kph.

True in translation, not in rotation like a circular path. The links between the atoms are weak and don't like centrifugal forces. Does a pure translation can exist in the Universe ?

[Bored chemist]

Any speed won't hurt a person.  As a result of tremendous speed other things like radiation could kill you, but the speed itself is not an issue.  If you are on a plane going at, say 600 mph you would not even feel like you are moving, the same would be true if you were travelling at 10,000,000 kph.

True in translation, not in rotation like a circular path. The links between the atoms are weak and don't like centrifugal forces. Does a pure translation can exist in the Universe ?

One of the interesting properties of light is rectilinear propagation.

[LB7]

One of the interesting properties of light is rectilinear propagation.

Except when the light is close to a black hole, so like there is matter in the Universe, the trajectory of light is a pure translation ? I mean, EXACTLY a translation ?

[Halc]

Any speed won't hurt a person.

True in translation, not in rotation like a circular path. The links between the atoms are weak and don't like centrifugal forces.

In the rotation case, it is not the speed, but the acceleration that kills a person.

Does a pure translation can exist in the Universe ?

Cannot parse this. What do you mean by 'translation'?

[hamdani yusuf]

Cannot parse this. What do you mean by 'translation'?

I think it's about linear motion, which has straight line trajectory.

[Halc]

I think it's about linear motion, which has straight line trajectory.

OK, so assuming the question is "Can a pure translation exist in the Universe?", I'd have to say that a geodesic is a straight line in a curved space.  If that is an example of a pure translation, then any inertial non-rotating object meets this criteria, but if not, then nothing meets it because space isn't flat at a medium scale.
That said, I cannot think of a single example of a non-rotating object except for fundamental particles that lack a property of angular moment.

[yor_on]

One of the interesting properties of light is rectilinear propagation.

Except when the light is close to a black hole, so like there is matter in the Universe, the trajectory of light is a pure translation ? I mean, EXACTLY a translation ?

Not sure what you mean by translation, but light always take the shortest path between points. That means that light does not 'bend' It just follows the shortest 'path' through SpaceTime according to what I understand. And around a black hole space is not flat but 'curved'.
=

It's like Halc wrote above. And comparing a rotational motion to a geodesic is like comparing a apple to a orange. A rotation (carousel) is GR and accelerations, a geodesic is SR and 'relative/uniform motion', so BC is perfectly correct. As a example you can think of earth rotating the sun. That's not a 'rotation' ala GR, instead it's the 'straightest path' through a 'curved' SpaceTime. And the proof for that is the absence of effects of a acceleration from it, on any of us on earth. It's a 'relative uniform motion' following a geodesic, with only 'proper mass' acting and being acted upon.

(Well, earth do spin around its axis too which could be considered a form of acceleration so it's not as simple as I would like it, and then you have the equivalence principle in where earths gravity becomes a 'acceleration' all on its own)

But if we ignore those two for now the average speed of earth relative its 'orbit' around the sun is 66,627 mph (107,226 km/h).. If we think of the system earth-sun as a merry go round with its axis being the sun I think we should notice a 'force' acting on us.

[Kean1 (OP)]

Rather a long time coming but many thanks for all your replies...the "Corona time warp" now means I have time to try and investigate and understand what you've written!

[yor_on]

Kean, you can think of 'speeds' as a result of what frame of reference you use.

In relativity (SR) a speed is translatable to being still, by choosing the appropriate frame of reference. And the difference between a 'speed' and a acceleration is always local, defined by your weight. All 'speeds', including 'gravitational accelerations' are without 'weight' (when tested by using a scale). So for you being inside a black box all speeds disappear. You need another frame of reference for defining it.

[Bill S]

That said, I cannot think of a single example of a non-rotating object except for fundamental particles that lack a property of angular moment.

Possibly the entire Universe?