2181

Physics, Astronomy & Cosmology / Re: How did scientists measure the mass of the Earth and other planets?

« on: 12/10/2018 22:33:50 »

How did scientists measure the mass of the Earth and other planets?

How did Newton know he'd got his maths right?

This is actually a very good question.  It is sort of a chicken/egg problem, which requires an answer to know the answer.  To illustrate:

Using F = GmM/r² you can calculate the force on a falling object of mass m in terms of M, the mass of the earth, and G, which we assume to be a universal constant.

That doesn’t work.  We’re trying to compute at least a rough G and M here.  We don’t know either of them yet.  We do know force F is 9.8 newtons for a 1KG mass.  We can assume we know r.  We therefore know the product of G and M, but not either separately.

As F = ma, we can measure the acceleration of a falling object or the period of a pendulum to get a value for F/m

F=ma works (F 9.8 = 1 (mass) * 9.8 m/sec acceleration), but that doesn’t yield either mass of Earth M nor G, which are the two things we’re trying to determine here.
The pendulum thing is a function of acceleration (9., not of the mass of Earth.  Put a pendulum in a rocket accelerating at that rate and it will have the same period as here on Earth.  It tells you nothing about the mass of the Earth under you.

So the way to do it is to find an object with known mass and something detectably orbiting it at a known radius.  Then G can be determined, and mass of Earth along with it.  Is that how it was done???  What object possibly fits that description?

2182

Physics, Astronomy & Cosmology / Re: What's a black hole made of?

« on: 12/10/2018 13:02:43 »

This business of things stopping at the event horizon came up before in a discussion here. If the speed of light falls to zero at the event horizon, then nothing can cross the event horizon, ever. Light and matter simply goes more and more slowly, effectively stopping, although it's never technically a complete halt.

I agree that we’re probably wrong about painting the picture just like this. I’ve heard that the official physics line says that things actually do fall in, but a description of how/when from the POV of various frames is typically omitted.  The book from Thorne recommended above perhaps covers this.

From my naive view, one can drop some material ‘on’ a black hole, which gets stuck when time dilates to nothing, but drop anything else and the event horizon expands just enough and swallows the earlier material. That sounds pretty wrong, but at least it gets stuff in there, and allows the original hole to form in the first place.

On another note is the observed behavior of the merger of two black holes, where one gets to observe something big fall in.  The gravity waves come slow at first but with increasing frequency, getting higher and higher until a brief ‘chirp’ at the end when the waves cease abruptly.  That’s a view from a distant frame, and yet it speeds up at the end.  If it got stuck on the surface, wouldn’t the waves slow to imperceptibility instead of speeding up?  This pattern was predicted before it was first witnessed.

On the ‘freeze’ front, I think it was Hawking that was disturbed by the seeming violation of conservation of information when things fell into a black hole, but this was solved by realizing that from any external moment in time, the information never makes its way in, and is thus not actually lost.

I’m just pointing out what I see is evidence on both sides of this fence.

The reason many people imagine that a space ship could cross the event horizon of a large black hole while the people inside it continue to live normally is that the lack of Newtonian time in GR (and SR) leaves the "time" dimension as the only kind of time in the model, and that provides no mechanism to allow any clocks run slow, so for the people in the space ship their clocks must keep on ticking at full speed. However, they will be systematically annihilated before they reach the event horizon because they'll actually be stuck there for countless billions of years while the black hole gradually evaporates - the mechanism behind Hawking radiation will eliminate every single piece of their matter.

The surviving the crossing is hypothetical.  You’re right in that the radiation there (which is only considered Hawking radiation if part of it escapes permanently) would likely explode our traveler as he compresses years of intense radiation into a millisecond.  The gravitational field inside is even more intense, and barring a description of the physics there, it is guesswork if a biological being could exist. The comment was just to point out that little black holes kill you via tidal forces before you ever get that close. The big ones need to use different means to kill you.

The part of the ship clock ticking at full speed is correct.  Except for the clock exploding in a radiation cloud, there would be no discontinuity or anything from a temporal standpoint.

It looks to me as if the only matter that can ever get into a black hole is the matter that collapses to form a black hole, and most of the material of a collapsing body will miss the party and end up sitting just outside the event horizon of the first part to become dense enough to become a black hole. Also, if multiple parts form separate black holes during the collapse of the body, those separate parts may not be able to merge because there may be material around and between them which cannot reach/cross any of the event horizons, so I predict that you'd actually end up with a set of black holes stuck together which collectively form a sphere, but which remain distinct from each other (and the same would happen with any black hole merger).

By that logic, all black holes would be of no size, each preventing additional mass upon reaching the threshold.  For that matter, each would then immediately evaporate, preventing actual formation of black holes.

So the view of stuff getting stuck on the surface is probably wrong, at least when worded that way.  I’d appreciate if somebody more informed (perhaps the answer from the book) would chime in.

All the above is dependent on the idea that the speed of light reaches zero at the event horizon. Perhaps it only reaches zero outwards though.

I think the answer lies on this front.  The event horizon of a BH is very much like the edge of the Hubble Sphere.  Time there is stopped relative to us and the big bang is still banging, because space itself (not just the matter) is moving away at lightspeed.  That is dilation due to relative speed, not gravity, so the analogy might not be appropriate.  I know it is invalid to apply the rules of an inertial frame over distances large enough for space to not be flat.

If [lightspeed] remains higher than that inwards, then there would presumably have to be a mismatch between the speed of light up vs. down at all altitudes in a gravity well.

Doesn’t much matter if time is dilated to zero. Insufficient speed isn’t the problem.  Light speed going down could be 3c, but it isn’t going to help if it has no time to go anywhere.

Bottom line is I don’t know the answers.  I’m no GR expert.

2183

Physics, Astronomy & Cosmology / Re: What is spinning in a spinning black hole?

« on: 11/10/2018 14:50:32 »

I'll pick one of the posts and comment as best I understand things, but I'm not speaking from authority here.

Nothing will break the speed of light in a vacuum. We can only see to the Event Horizon though, so if you want you might assume that past that there can be some other region with different laws of physics.

Some laws are different beyond the event horizon, and some not.  I doubt that local light speed is different beyond the singularity.

As I've seen it described in multiple places, we can consider normal spacetime to be 4 dimensions w,x,y,z.  Let's assign time to w, in a frame where a black hole is stationary somewhere.  x is towards the black hole (down).  y is tangential in the direction of its rotation, and z is the remaining axis.
Beyond the event horizon (EV as you call it), time is suddenly assigned to the x axis and w becomes just another spatial dimension in which matter can move in either direction.  Objects within a black hole can travel back in our time, but cannot get out.  There is no 'down' anymore because that direction is now the future.  Matter cannot get out of the black hole any more than you can travel to your own past.  There is no rotation anymore since there is no radius.  Motion is linear, but space is quite bent.  What appeared to be angular momentum translates into linear momentum in the direction of y.  All stuff is moving that way, and if anything is to accelerate away from that trend, an equal and opposite reaction (Newton still lives in there) is required.

I think it was SoulSurfer(?) that gave a beautiful explanation of where the black hole is thought to get its 'rotational energy' from? It was the direct result of all objects 'spinning', with the angular momentum growing relative its 'size' as it compressed into a 'point'. As it becomes that 'point' all laws of physics breaks down, and its mass becomes 'infinite' as i understands it.

As matter gets closer to the singularity (the end of time in the description above), yes, its mass/energy becomes infinite, but its negative gravitational potential energy becomes negative-infinite, so conservation of energy is preserved.  Yes, that infinite mass multiplied by the infinitesimal proximity to the central singularity yields an angular momentum that is preserved.

The Event horizon is the last outpost for our laws of physics, at least as we can measure, so assuming this is right then it would surprise me if we ever found any black Holes that didn't spin relatively close to light.

Black holes have angular momentum, and that isn't measured in units of 'speed', so no, they don't spin at the speed of light.

It must have to do with what mass they had before they collapsed and their 'spin' at that time.

Yes.  Whatever the cumulative angular momentum of the stuff falling in, the black hole preserves that.  The Hawking radiation will actually dissipate some of that momentum, as will gravitational effects.

Wonder if there are Black Holes of opposite spins?

All different spins.  The axis can be oriented any-which-way, but something like Sagittarius-A has a spin orientation very close to that of Milky-Way at large.  Surely there are pairs that have nearly identical axes but opposite spins.  That would just mean that if they merged, the resulting object would have less overall spin.

And there's one more thing, to me it's the gravity that has 'directions', not space as such. And as 'gravity propagates' at 'c'?

Gravity does not propagate.  It is a static field distortion, else it would be a violation of energy conservation.  Gravitons and gravity waves do propagate at c.

Black holes have less gravity than the stars that originally formed them, since a good deal of the mass of those stars gets blown away in the supernova event that leaves the black hole behind.  So if you were a planet orbiting the star at radius X (and you survived being that close to a supernova), the effect would be orbiting at a new radius greater than X due to the lower gravity, and it going completely dark when your star flashes bright and then goes totally out, exactly like an incandescent light bulb in its final moment.

2184

Physics, Astronomy & Cosmology / Re: What's a black hole made of?

« on: 08/10/2018 19:30:30 »

I would hazard a guess that you would be dead before you reached your destination.

Only the little ones kill you before you get there.  One can cross the event horizon of a big one without even noticing. 

What I meant was you wouldn't live long enough to reach a black hole if traveling from earth.

Maybe I have a really fast ship.  I can get anywhere I want if I go fast enough.  Straight into Sagittarius A is within reach.  I'll still be alive when I get there even if everybody I left behind is long dead.  Not 30000 years dead either.  Weird (but not very interesting) way to achieve immortality.

I think it is just a matter of grammatical tense here.
- We see mechanisms that form black holes from normal matter when a star implodes and/or explodes.
- However, once this matter approaches the singularity, normal matter should be torn apart - it's not clear what the components would be (eg would they be outside the Standard Model?)
- And once it reaches the singularity, normal matter should be mashed together - it's not clear what the result would be
- But really, we can't say much about what happens inside the event horizon of a black hole

Agree to all of that.  The contents are the same stuff as on the outside. I can fall into a black hole and not notice, so my matter hasn't changed significantly from what it has always been.
Even neutron stars are pretty much beyond empirical testing, leaving only the energy bursts to paint a picture of the structure within, but they're in that state because they're in a state of high proper acceleration, a state not seen by matter inside a black hole.

Light is always moving when going into a black hole. It's merely slowing down. A particle like a photon can always be moving towards the event horizon and still never get there. Its sort of like Zeno's paradox. First its moving at c, then later at c/2 then c/4 then c/5 ....... At no time in that sequence is the photon at rest.

Isn't it always going at c?  It's just that time dilates to 'stopped' at the event horizon, at least from an external POV.  It is a singularity, where light moves 0 meters in 0 seconds, which isn't stopped at all.  The speed is just undefined there, but c everywhere else.

2185

Physics, Astronomy & Cosmology / Re: How many black holes are there in the Universe?

« on: 07/10/2018 20:41:12 »

I did read about the event you referenced and thank you for using the word "merger." It is precisely what I needed to advance an argument I've been honing over time.

Merge seems appropriate for two things of similar order of magnitude of mass.  But if one is tiny and the other huge, it seems more like the little one falling into and adding to the bigger one, but the process is really the same.

Does a meteor fall to Earth or do the two just merge?  Or maybe the Earth falls down onto the rock and becomes this huge meteorite on it.

2186

Physics, Astronomy & Cosmology / Re: What's a black hole made of?

« on: 07/10/2018 20:34:11 »

He said "to an outside observer of our universe time does not exist". I didn't realize he was talking about the inside of a black hole. One doesn't call that a universe. It should say "our portion of the universe" or something so people like me don't get confused. Lol.  And its wrong to claim that time doesn't exist because it does.

I agree. Better worded, my statement should simply read that he exits our coordinate space. The interior of a black hole is still spacetime, and (contrary to what I said above) the observer within can still see the universe outside. They just can't see him.

RE - "Not by slowing of velocity..." - That's wrong. All objects slow down and are redshifted to the extent they can't be seen. Even light slows down in a gravitational field and so too for photons moving towards the black hole.

Intuitions are funny here, but you're right I think.  I unrealistically envision fast things approaching light speed and they never hit c but they don't slow down either.  The event horizon is normal spacetime and the rules there are no different.  Yes, at the singularity, things stop in our external reference. Hawking was worried about preservation of information when things fall irretrievably into a black hole, but in coordinate all the information pasting to the surface is not lost information.

2187

Physics, Astronomy & Cosmology / Re: What's a black hole made of?

« on: 05/10/2018 13:59:22 »

I would hazard a guess that you would be dead before you reached your destination.

Only the little ones kill you before you get there.  One can cross the event horizon of a big one without even noticing.  OK, it will still kill you soon enough, but a similar death to being spun at a fatal RPM, which isn't the sort of way I'd choose to go out given a choice.

Answer to the OP then:  It would then be made of you!  You are what you eat.

2188

Physics, Astronomy & Cosmology / Re: Can anyone hear you scream in Space?

« on: 05/10/2018 11:55:30 »

When I am watching spacebattles in the Star Wars I turn off the sound to make it look more realistic 

Might as well leave the sound on.  The battles are in no way realistic, and actually depict WW2 airplane battles.  All the physics was modeled after close quarters aircraft, not spacecraft at all.

Can't say there is much improvement anywhere else for that matter.  They've not yet made a movie of Forever War and they'll probably screw up the battles if they do since the cinema-goers like their standard where it is.

2189

Physics, Astronomy & Cosmology / Re: In deep space, are spacecraft still in freefall?

« on: 02/10/2018 17:39:02 »

Everything has a curved trajectory

...except light that's not being gravitationally lensed, presumably?

Surely even light since it moves in gravitational fields no matter how weak?

Yea, I agree with geordief here.  Sure, one can view light as taking a straight shortest path sort of like airline routes plotting a great circle that appears longer on a flat map, but then gravitational lensing isn't really bending of light.  Two interpretations of the same thing..

Light seems to have inertia even if it doesn't have proper mass.  It can push things, and conservation of momentum laws says that it must thus change direction when it bends around gravity wells since the gravitational object is getting the equal and opposite reaction.  This can indeed be depicted as light traveling in straight lines on bent (non-Euclidean) space.  Sub-light objects cannot take such a locally straight trajectory.

Another POV is that light obviously doesn't take the shortest path.  Enough gravity lensing (a series of hyperbolic turns around at least a pair of black holes say) will bend light back the way it came, and it might take years to make a trip that it could have done in seconds.

2190

Physics, Astronomy & Cosmology / Re: Can we feel gravitational attraction from objects at different velocities?

« on: 02/10/2018 04:15:06 »

Read this and then we'll talk: http://www.newenglandphysics.org/physics_world/gr/grav_force.htm

Notice where the force depends on velocity such as the weight of a moving body depends on its speed (Eq. 20-21).

Sorry.  Way over my head.

I noticed hat you used Newtonian ideas for GR. That's bad juju.   You can't use F =- GMm/r^2 in GR.

Yes, I tried that briefly and it obviously didn't work.  I tried SR, but this is gravity we're talking about and it isn't covered by SR.  I'm fine with being wrong.  I suspected as much.

2191

Physics, Astronomy & Cosmology / Re: Is Wiki right about tidal acceleration?

« on: 01/10/2018 22:44:25 »

As in any physical process within an isolated system, total energy and angular momentum are conserved.

Angular momentum is conserved yes, but a pure Earth/moon system is hardly a closed system.  Total energy is always lost to friction.  I'm surprised to find that wording on a wiki page.  Yes, angular momentum of Earth is transferred to the moon, and the effect is very measurable.  Discard the tidal acceleration hypothesis if you want, but then you need to explain the moon moving away a very measurable 4 cm each year.

Edit: OK, the wiki does admit that only a 30th of the energy is transferred to the moon, and the rest is lost to friction.
The initial comment sort of said otherwise, but I guess 'isolated' system doesn't mean a closed one.

2192

Physics, Astronomy & Cosmology / Re: Can we feel gravitational attraction from objects at different velocities?

« on: 01/10/2018 12:59:44 »

I had sort of questioned the answer being given here and would like somebody to comment on my example.

The replies in the first part of the thread cover the situation at low speeds, but at speeds approaching the speed of light the added kinetic energy (relative to you) of the object will be seen by you as an increase of both it's inertia and it’s gravitational attraction, so you will feel an attraction as it goes past. The faster it goes, the greater the attraction.

My example questioned exactly that.

That paper doesn't touch the subject directly but the one on mass does.

I looked at that but wasn’t sure where the point was spelled out.

I’ll repeat my example:

The earth/moon system orbiting once a month.  Now consider just that in a frame where they're going at .866 c along the orbital axis.  The planets get squashed into a sort of phulka shape, but still have the same separation.  They mass twice as much, and orbit every 2 months, which is half the acceleration as the system at rest.  F=ma: Double the mass, halve the acceleration.  The force must be the same, so the law of gravitation (F=(G(m₀1•m₀2)/r²) is computed with rest-mass (m₀), not with mass (m).
Therefore there is no change in grav. attraction if the moving object changes mass (relativistically).

Did I do that correctly?

Professor Mega-Mind  commented: “Your Relativistic Masses are in constant flux as the bodies orbit”.  I chose velocity along the orbital axis for that very reason.  The velocity of the two objects wobbles around a bit, but the speed and thus relativistic mass of each object is constant.

I computed identical force by applying F=ma, but I have doubts that Newton’s formula scales with relativistic speeds.  The inertia and acceleration I got correct, but Colin2B says the F between the two objects is frame dependent which would mean that Newton’s 2nd law needs relativistic adjustments.

Wiki article on relativistic mechanics address this point:

Force
In special relativity, Newton's second law does not hold in the form F = ma, but it does if it is expressed as

F=dp/dt where p = γ(v)m₀v is the momentum as defined above and m₀ is the invariant mass. Thus, the force is given by

F = γ(v)³m₀a_|| + γ(v)m₀a_†

I did my best to recreate what is written there.  The parallel and perpendicular symbols sort of eluded me.
My example was deliberately pure perpendicular, and so degenerates only into the right side of that equation if I read it right.
I think it says force is the same, contrary to what I think Colin2B is saying.  γ(v)m₀ is the higher relativistic mass, and a_† was computed at half the rest acceleration, due to time dilation.  F is the same, no?

2193

Physics, Astronomy & Cosmology / Re: Einstein's Clock: What happens if you move towards a clock at light speed?

« on: 30/09/2018 16:55:44 »

Well, the ship isn’t going to stay at B is it?  It is going to accelerate and head for A (home presumably), and that makes it stationary in a new different frame in which clocks A and B are not synced.

You’re ahead of me there, I had not considered the return trip. 

My apologies for getting A and B mixed up.  Your scenario was starting at A and going to B, with B being Earth, as per your first post in this topic.  Kindly switch A and B in my quotes where I got that backwards.  Duh…  Of course A then B.  Events are best labeled in alphabetical order as you’ve done.

As mentioned in another thread, some years ago I put quite a lot of time and effort into sorting out in my mind a similar scenario involving three “moving” ships.  A & B were maintaining a constant separation and C was moving relative to them.  Somewhere in the recesses of my brain I must have had the idea that because A & B, in this case, were planets the situation would be different.

Doesn’t matter if any of them were ships or planets or just clocks.  Pretty hard to get a ship up to .866 c but not so hard to blast clocks out of a gun.

They actually have crude clocks that move at well over 99% light speed fired at the observer from say 100 km away, set to self-destruct after a mean of say 2.2 microseconds (time to move about 2/3 km) but it takes light about 3000 microseconds to go that distance so the vast majority of the ‘clocks’ should have self-destructed before that distance is covered, but most of them make it due to time dilation.  This is the muon experiment.  Muons and other decaying particles make pretty good clocks.  Same principle used in carbon dating.

2194

Physics, Astronomy & Cosmology / Re: Why do we have two high tides a day?

« on: 30/09/2018 01:11:09 »

The next question is an interesting one. You introduce the spin of a planet eg Venus that changes the planet’s surface speed. However, I would argue, as I suggested to Le Repteux, that the spin has no effect on the orbit.

I didn’t suggest that the spin has any (short term) effect on the orbit.  Yes, Le Repteux has a thread open about tidal forces slowly pushing orbiting things away, and that is true.  The spin of the sun has a higher angular velocity than any of the planets, so that tide slowly pushes each of them away.  Most planets also spin faster than their orbits, putting thrust on the sun that also contributes to higher orbits.  Venus is an exception there, and its negative spin actually degrades its orbit, but not as much as the tide on the sun expands that orbit.  All this is relevant to the other thread, but your response above seems to concern this point.

The discussion was about tides, with a suggestion that the tides might be partially caused by higher linear speeds at points furthest out, but I pointed out that points on Venus furthest from the sun have the lowest linear speed and should be ‘seeking lower orbit’, and the points closest to the sun have the greatest linear speed and thus should be ‘seeking higher orbit’.  If that were so, the tides on Venus would be to the sides, not towards and away from the sun as all solar tides are.

If you consider the locus of points on the surface the spin does not cause any net increase or decrease in the orbital speed and it is orbital speed which is the prime cause of any centrifugal forces. At any instant in time the forces on any mass on the earth/moon line are the gravitational pull and the centrifugal force and we can treat the spin separately because, it has no effect on the net orbital speed of any part of the mass. Also, as I mentioned to Le Repteux we can treat the spin as a separate component of the overall system and it's only effect is to create centrifugal force causing an equal bulge on the equator of the spin, it does not cause a net motion towards or away from the earth.

All this seems to be about orbital speed, something on which I was not commenting in this topic, until what I wrote above in this post now.

The comment of mine that you quoted in the immediately preceding post concerned centrifugal explanations for the tides.  Instead, I agree with your last line there that we can treat the spin as a separate component of the overall system and yes, all it does is that standing bulge everywhere at the equator.
Tides are partially an effect of spin.  The spin rate coupled with the resonant frequency of oceans and shorelines causes higher tides in some places than others.  Move the continents or alter the spin and the tides will be higher in different places.  But high tide is always towards and away from the gravity gradient and the bulge will form regardless of the axis or intensity of spin.

2195

Physics, Astronomy & Cosmology / Re: Einstein's Clock: What happens if you move towards a clock at light speed?

« on: 30/09/2018 00:06:36 »

  If, at t=0, the ship is stationary relative to A and its clock is synced with A’s clock; the ship’s clock will be synced with Earth’s.

At this point the ship would not be moving relative to A or B, so would its clock be synced with those of A and B?

In the frame where A and B is stationary, and so is the ship still, all three clocks are synced, yes.

As for the ship parked before departure, it is stationary in B’s frame, not the eventual frame of the moving ship.

Possibly the answer is here and I’m missing it.  If “it” is the ship, it is stationary relative to B, that’s fine, but what are you saying is not “stationary” in “the eventual frame of the moving ship”?

Well, the ship isn’t going to stay at B is it?  It is going to accelerate and head for A (home presumably), and that makes it stationary in a new different frame in which clocks A and B are not synced.

2196

Physics, Astronomy & Cosmology / Re: Einstein's Clock: What happens if you move towards a clock at light speed?

« on: 29/09/2018 19:19:28 »

If we consider Earth and A to be stationary relative to each other; their clocks can be synced at t=0.

Synced in the frame in which they are stationary, yes.  Not synced in other frames.

If, at t=0, the ship is stationary relative to A and its clock is synced with A’s clock; the ship’s clock will be synced with Earth’s.

However, if we start the scenario with the ship passing A at 0.866c (or any speed); there will be an instant when the clocks on A and the ship can be synchronised (this we call t=0), but at that point the ship’s clock will not be synced with Earth’s.

No, in the frame of the moving ship, the clock at A is not in sync with the clock at B.  So you can say that there is that instant when the ship clock is synced to the departure event at B (synced to an event, not to a clock).  Both clocks are present at that event and they both read zero (are set to zero actually) at that event.

As for the ship parked before departure, it is stationary in B’s frame, not the eventual frame of the moving ship.

2197

Physics, Astronomy & Cosmology / Re: Einstein's Clock: What happens if you move towards a clock at light speed?

« on: 28/09/2018 19:24:42 »

SR can handle acceleration, the only reason to bring in GR is if you are including gravity in the scenario.

Right you are.  I was mistaken to suggest SR doesn't handle acceleration.  Gravity is not included, nor is non-local scales.  Anything within the galaxy is reasonably local enough for SR.

I was keeping it simple to answer the simple question asked in the OP: Does an approaching clock appear to run faster, and yes, it does.

So for example, if the ship is accelerating from point A to point B, with clocks at these points which are synchronized in the inertial frame, then, if the ship leaves point A at t=0 and T=0, and the ship reaches B when the ship clock reads T, then t will be the time at B according to the ship upon its arrival at B.  The time at A (according to the ship) will depend on the ship's velocity with respect to A and B and the proper distance between A and B( relativity of simultaneity). tB will be greater than T, but tA will be less than T.

I take it that tA is what A clock currently reads in ship frame.  So in my simplified example where the ship is already moving when it departs A, T at B is 5, tB is 10, and tA is 2.5.  Yes, I agree with all this given that the acceleration vector is forwardish (scientific term!) the whole way.  If the ship turns around and accelerates the other way for part of the trip, or maybe makes a detour to Arcturus for nachos, it arrives at B with tA possibly more than T, and tA and tB both synced if the ship velocity becomes zero in the inertial frame of A and B.  So tA is less than T only if acceleration is predominantly away from A.

2198

Physics, Astronomy & Cosmology / Re: Einstein's Clock: What happens if you move towards a clock at light speed?

« on: 27/09/2018 20:19:52 »

Good explanation, Halc.  There are a few points/questions that come to mind.

1. The clock, presumably on a craft, travels from A to B.  We identify B as Earth.

2. The distance from A to Earth is (presumably) already known, so we can calculate that a craft travelling at 0.866c will take 10 years in Earth’s RF, to make the journey.

3. Light takes 8.66 years to make the same journey.

4. We, on Earth, have no way of knowing when the craft left A.  Nor do we have any way of synchronising our clock with that on the craft at the time of its departure.

5. On arrival, would the clock on the craft be 5hrs ahead of clocks on Earth?

6. If the answer to 5 is “yes”, why would that be the case if the clocks were not synchronised when the craft left A.

7. If the craft’s clock differs from Earth’s clock, why would it need “to tick 5 years in only 1.34 remaining years”?  Would the difference not remain?

2: Yes, I said that the departure (A) was 8.66 LY away.

4: Well, we're watching.  At year 8.66, we see the ship depart abruptly already at speed.  Yes, until then, we either don't know, or maybe it was a scheduled thing.  We very much can synchronize our clocks, but we need to assume a frame to do it.  We assume that A is stationary relative to Earth, and thus that synchronized clocks have meaning.  The ship frame is different of course.

5: No...   On arrival, the ship clock is 5 years slow.  It reads 5, and the Earth clock reads 10, assuming both Earth and 'A' read 0 at the same time in their mutual frame.

7: The OP asks how that clock would appear as it approaches rapidly.  We see a zero on the ship clock only 1.34 years before it arrives at time 10.  In that 1.34 years, we see it count from 0 to 5 years, and thus 'appears' to run fast when in fact it is dilated by a factor of 2 and only counts 5 years in a journey that actually takes 10 years in Earth's frame.

2199

Physics, Astronomy & Cosmology / Re: Can we feel gravitational attraction from objects at different velocities?

« on: 27/09/2018 05:16:27 »

Do you feel a change in grav. attraction if the moving object changes mass (relativistically).

Reactionless thrust aside, I never saw this point addressed, and I find it interesting.
What is the gravitational formula for masses moving at relativistic speeds?

I think I worked out that the attraction between objects needs to plug in rest-mass into Newton's formula.

My example was the earth/moon system orbiting once a month.  Now consider just that in a frame where they're going at .866 c along the orbital axis.  The planets get squashed into a sort of phulka shape, but still have the same separation.  They mass twice as much, and orbit every 2 months, which is half the acceleration as the system at rest.  F=ma: Double the mass, halve the acceleration.  The force must be the same, so the law of gravitation (F=(G(m₀1•m₀2)/r²) is computed with rest-mass (m₀), not with mass (m).
Therefore there is no change in grav. attraction if the moving object changes mass (relativistically).

Did I do that correctly?

2200

Physics, Astronomy & Cosmology / Re: Einstein's Clock: What happens if you move towards a clock at light speed?

« on: 26/09/2018 20:26:05 »

Hi,

I watched a video on Youtube about an Einstein thought experiment, in which he realised that if he was travelling away from a clock at light speed the clock would appear to be frozen, but what happens if you travel at the speed of light towards the clock - does the clock appear to speed up?

This is the Doppler effect, the same thing that causes red and blue shift.  The faster a thing moves away from an observer, the slower it appears to go, even without time dilation.  The effect is much stronger than dilation.

So if a clock is coming at you fast (say a big digital clock on the nose of a ship heading this way), the clock will be slower due to dilation, but still appear to run faster due to blue shift.  The clock cannot move at light speed, but it can go as close as you want to it.  If you want it to appear to run 10x fast, there is a speed at which that occurs.

So take a clock coming from 8.66 light years away (Earth frame), moving at .866 c, a 10 year trip in our frame.  Its clock says 0 when it leaves.  At that speed, it will be dilated to half speed and only log 5 years, so it reads 5 years when it gets here.  But it leaves 10 years before it gets here, and we don't see the light from its departure for 8.66 years, leaving us watching the clock appear to tick 5 years in only 1.34 remaining years, so it appears to run about 3.73 the rate of one of our own clocks.
Go even faster, and the clock coming at us appears to run even faster, but it is meaningless to posit a clock moving at actual light speed.