2:36 AM
@Charlie When you stand on the Earth & drop an object, that object accelerates downwards. That could be due to a uniform gravitational field. But Pound-Rebka demonstrates that the gravitational potential up high is lower than what it is down below, so the field can't be uniform. I.e, the acceleration of the dropped object isn't perfectly constant.

2:49 AM
Sorry, the gravitational potential up high is less negative than what it is near the ground. :)

2 hours later…
4:41 AM
Hello
anybody here
Can anybody tell me which metric we would want to use for white holes?
I know they are hypothetical, but still
Mathematically how do we model them?
Would the Schwarschild metric work?
Or do we need something more advanced?

The maximally extended Schwarzschild geometry i.e. the Schwarzschild metric in Kruskal-Szekeres coordinates.

So, that would resemble a black hole with time reversal right
Thanks
Also what metric would we use for a galaxy
Or any other disk shaped oject'
Like I wanted to apply the GR equations for our galaxy
But I don't know what to use

There isn't an analytic solution for a disk. You'd have to use a numerical solution. Fortunately for galaxies the relativistic corrections to Newtonian gravity are vanishingly small.

@John Rennie thanks

If this isn't an appropriate question for here, just let me know and I'll not press it.

Is it theoretically possible for an object with quite a lot of mass (for example a space shuttle) to approach the speed of light? If so, are there any interesting ways of accomplishing that?

4:54 AM
@Beliod approach yes, attain no.

@Beliod actually no

you just need a motor and a lot of fuel :-)

As it approaches light speed, it's inertia would increase and you would more and more enrgy

I know that it can't attain the speed of light, but it should be able to get reasonably close given enough energy right?

@John Rennie that much amount of fuel would exceed the supply of the entire solar system? :)

4:56 AM
@PNS To be fair, I'm considering a very hypothetical scenario. And things which seemed utterly ridiculous (like walking on the Moon) 1,000 years ago are so commonplace that they're not even exciting anymore.

Interesting ways of accomplishing

@Beliod if you do a calculation you'll find that in real life a spaceship could never get close to the speed of light because it could never carry enough fuel. Not unless something outside of it is powering it.

1)get a black hole, enter the ergosphere
That would give it enough energy to approach the speed of light

@JohnRennie That's the situation that I imagine. Something continually speeding it up (like the solar sail concept, but obviously different) from the outside.

@Beliod or laser propulsion i.e. we have a huge laser on Earth that we shine at the object to accelerate it.
We can make protons travel at 99.99999% of the speed of light if that counts ...
They are massive in the sense they have a mass, though obviously that mass is rather small :-)

5:00 AM
@John Rennie just out of curiosity..how much energy would a laser require to get a space shuttle to space

As patently absurd as it is, I'm considering it for the sake of thinking about time travel (going forward in time, obviously). I don't mean to make it plausible, only understand what the limitations are for my own self-interest. For example, if going 60% the speed of light was sufficient enough to make a noticeable impact on your clock, I'd consider that to be a successful concept.
I doubt you'd use the laser to get it into space. Likely just do a typical launcher and then use the laser once the ship is in a vacuum.

@PNS it's a straightforward calculation since the force per watt for a light beam is easily calculated. In fact I'm sure there is at least one question on the main site that asks about this.
@Beliod you'll struggle to make this physically realistic. You'd need to provide a way to slow down again.

@JohnRennie I know, and I'm not guessing that I'll personally solve the issue of time travel lol. I'm just sort of gauging what is within the realm of possibility.
For example, supposing @PNS is correct about the energy required to approach the speed of light with an object that massive, one can reasonably ask about scale. If that close to the speed of light isn't possible, what about 80%, 60%, 40%, etc.

@Beliod a much better way to time travel would be to settle down in a huge planet with a lot of energy
Sorry I meant gravity
You would need a lot of energy to maintain your 0.6c speed
@JohnRennie thanks
I will try searching for it

68

Can photons push the source which is emitting them? Yes. If yes, will a more intense flashlight accelerate me more? Yes Does the wavelength of the light matter? No Is this practical for space propulsion? Probably not Doesn't it defy the law of momentum conservation? ...

5:11 AM
@Beliod with 0.6c speed, I tried calculating it and it seems that the time elapsed according to earth would be one second, while for you it would be 0.8 seconds. Not that much of a deal
@JohnRennie correct me if I am wrong

Thanks for the question. I will look into it for a sec

@Beliod you could ask on the Space Exploration SE

@JohnRennie I'll check it out. These questions always seem to be "too broad."

4

I read that with our current ion propulsion technology it is possible we could send a craft moving the maximum of 100km per second, or around 62 miles. However we seem to be limited by how strong of a power generator we are able to put aboard the craft.. Is it possible that with enough power we c...

5:16 AM
@JohnRennie is there a way to get to space using magnetic fields?

4

What is the maximum (theoretical) velocity that can be achieved by solar-sail technology? Can we get close to the speed of light with that?

I mean we use it for accelerating protons
Maybe a large enough field could be used to accelerate large objects too

Protons are very light :-)

I also read about antimatter propulsion but that seems way too off

Something like a rail gun I guess

5:18 AM
I mean we can only create atomes of antimatter

6

Quite a bit has been written about railguns launching stuff to the earth. But has any work been done on using the moon as a pit stop between the earth and mars.

I guess maybe chirped pulse amplification could be used for creating antimatter
The above answer is correct though
I read in a answer by Emilio Pisanty that CPA could be used for making electron position pairs,
Can that actually happen though?
@JohnRennie

5:52 AM
Anyways.. got to go now, online classes. Will check back in the evening (IST)

6:06 AM
0

I had asked this question on PSE and it was considered off-topic and hence closed quoting that it was "Homework-like question". After that I edited the question following this guidelines. However, even after editing and making it on-topic, the question wasn't reopened. My question is why it was n...

@PNS See math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html which has several useful equations and tables for a rocket with constant acceleration, including how much fuel is required, assuming the rocket carries its own fuel & uses an ideal antimatter engine.
@PNS It takes a lot of energy to attain a speed of 0.6 c, but in a perfect vacuum, it takes no energy to maintain that speed. OTOH, space isn't a perfect vacuum, and when you get up to seriously relativistic speeds with lots of time dilation, you do have to worry about the impact of interstellar gas & dust on your ship. Not to mention the heavily blue-shifted CMB & other EM radiation that you're traveling towards.

6:25 AM
What is a good General relativity book which covers symmetry principles in detail?
(Specifically isometries and Killing tensors and the methods to find them)?

6:50 AM
@PM2Ring you are right about that one!
@PM 2Ring thanks for the webpage

@PNS No worries. You may also enjoy my answer here: physics.stackexchange.com/a/345492/123208
A few years ago, I did a rough calculation of how much energy it takes to maintain 1 g acceleration, assuming you could beam energy to the ship & somehow convert it to kinetic energy (maybe the ship can supply itself with enough reaction mass from the interstellar medium). Anyway, it turns out that the energy production of the whole planet is enough to drive a 15,000 tonne ship.
I don't remember exactly where I got the energy production figure, it was probably something like this: en.wikipedia.org/wiki/Worldwide_energy_supply
So even though I've been a huge science fiction fan for over 50 years, I don't expect that humanity will colonise interstellar space anytime soon. It just consumes too much energy. I suppose slow "generation" ships that take thousands of years could be viable, though.

7:17 AM
@PM2Ringwe would need a very powerful source of energy to actually accomplish that, maybe if we could invent something to harness the energy of the sun, it could work (cough, Dyson sphere, cough)
@PM2Ring
Even that would take us centuries.

@PNS True, the Sun has lots of energy that we could harness.

yeah but harnessing it from earth would not get us enough
for now the best option seems to be building a dyson sphere
which would require a ton lot of energy

I suppose we will send stuff to nearby stars. But probably not people. Unless we figure out a good way of packaging that solar energy. Of course, the ultimate package is antimatter, but our technology is a long way from making (or storing) non-microscopic quantities of antimatter. And then there are the engineering issues of creating an antimatter engine.

7:32 AM
@PM2Ring "engineering issues" can you elaborate?
I have interested in antimatter engines for a long time actually

Why do we even need to leave the Solar System anyway? We could build space habitats that orbit the Sun. The Goldilocks zone here is huge.

@PM2Ring I blame Star Trek.

@PNS Well, the simplest antimatter annihilation reaction, low energy electron + positron, (usually) emits 2 or 3 gamma rays, with a combined energy of 1.022 MeV. Those things aren't healthy! And it's very difficult to control what direction they're released in.
@Philip Fair enough. :) Although to be fair, there were stories about colonising the galaxy at least 50 years before Star Trek.

Heh

@PM2Ring is there any way at all that we can convert gamma rays into lower frequency ones?
I mean, I am no experimentalist but when we conduct experiments we have to take care of some unwanted frequencies of light right
which may tamper the apparartus
so how do we do that
Ans your idea of building habitats here is great, but we also need materials to do so

7:45 AM
Anyway, as I mentioned in that answer I posted earlier, an ideal antimatter engine converts matter + antimatter into photons, and shoots those photons out the back of your rocket. Realistically, you'd use some kind of reaction mass, and chuck that out the back of your rocket. That's because photons have tiny momentum, and because the photons released in annihilation have net zero momentum in the centre of mass frame of the colliding particles.

*and sorry
I am sorry, but what is "reaction masS"?
And in that situation how much antimatter would we need?
Because the photons have a low momentum, and to get a large net momentum, you would need what maybe, metric tons of antimatter

@PNS Sure. You blast normal matter with gamma rays and it heats up. Then you use that heat as in a conventional rocket motor.

Oh that's smart
But then again, how much of that extra matter would we need? That just adds to the payload right?

@PNS A normal rocket works by conservation of momentum. You throw reaction mass in one direction, the rocket moves in the opposite direction.
@PNS Payload normally means stuff apart from the fuel. In most chemical rockets, the fuel supplies the energy, and the reaction mass. But you can have inert reaction mass as well as the chemically active stuff.

Thanks
But what use is the inert reaction mass then?
It has to be used somehow, but if it does not react physically or chemically what does it actually do?
@Philip yep, you are so correct!

7:56 AM
One problem with gamma rays is that they don't just heat up your engine. They tend to knock atoms around, damaging the structure. And they can also knock nuclei around, making them radioactive.

But I have been getting into space expiration and things like that ever done I watched the new COSMOS series
Exploration
But are gamma rays the only by products?
What if we use something else like quark antiquark pair and proton antiprotons

BTW, you can edit chat messages for 2 minutes. If you're on a computer, just hit the up arrow key to get to previous messages.

That is the problem. I am on the phone
The computer is not working since a hour or so
Anyway if we use heavier particles, would be still get gamma rays?
Even though they are harder to make in the first place?

@PNS Ok. I only mentioned the simplest annihilation reaction earlier. When you have stuff like protons & neutrons annihilating with antiprotons & antineutrons, it gets messier. You get things like pions, but they soon decay, giving things like muons, which also decay. Eventually you get gamma rays.

Oh, that's inevitable thenπ€π€
Maybe we can only do stuff like this maybe thousands of years later, huh?

8:07 AM
When high energy gammas hit matter, they can induce pair production, i.e., pairs of electrons + positrons, which of course will soon annihilate. But it means you need a lot of shielding if your engine makes high energy gammas, since you get these chains of gammas -> electrons + positrons -> gammas propagating through your shields, damaging it & possibly making it radioactive. The trick is to use your reaction mass as the sheilding, so you can throw it away. :)

And I set about to design an antimatter engine with just electrons and positrons. That really happened. Well, not practically, but on paper
I made a pretty vague design
Even the people at Star Trek would have included more details than I did
ππ
Anyway got to go, online classes start again at 13:45
@PM2Ring if I have any doubt I can ping you here right?

@PNS Ok . Take a look at en.wikipedia.org/wiki/Positronium

Thanks

@PNS Well, we can certainly continue this discussion later.

8:36 AM
I am not used to adopting the term random to suggest probabilistic, such as random variables, random fields.

2 hours later…
10:36 AM
It takes several days to review your comment before it is presented in Quanta Magazine!

2 hours later…
12:10 PM
Hello :)
I was reading about relativity of simultaneity and read that the precedence order is preserved in all frames of reference. I was wondering why it is like that and how to proof that?

2 hours later…
2:08 PM
@undefined Show that the Lorentz transform doesn't change the sign of the timelike component of the difference between two points
ie $(x_1 - x_2)_0$ doesn't change sign

1 hour later…
3:17 PM
1 day left on this 100-point bounty. It's a very easy one!! Just pick one of the partial charges mentioned in the question, and explain it! Only one person has done so since the bounty was offered, and they picked a rather extremely easy partial charge to explain, so I'd be keen to award the bounty to someone who picks a different partial charge:
21

I am evaluating the atomic charge of an IP system and comparing with a DFT system by using three different charge analysis methods (Mulliken, Bader, Qeq). I wonder what are the differences between the methods, such as pros and cons. Perhaps we can get an answer explaining each of the following ty...

@NikeDattani Unfortunately, I don't think anyone who regularly visits this chat has expertise in this field

@ACuriousMind I had zero experience in it either. I looked up "bader charge" and within an hour wrote down a summary of my research, then got 13 upvotes for it.
So now I'm giving away 100 points to anyone that can do the same thing for one of the other partial charges. I could do it myself, and probably will if no one explains the other types of partial charge, but I will not be able to award my own bounty to myself.

2 hours later…
5:17 PM
@PM2Ring Ah I might be a little unclear on what the PR experiment exactly shows, but is my reasoning that someone stationary on the surface of Earth is not in a locally inertial frame?

5 hours later…
10:37 PM
I am trying to brainwash myself with newton's 3rd law
Help!
After treating space as fabric I cannot digest the fact of newtonian mechanics
It follows that, if there exists one inertial frame, then there exist infinitely many, with each frame moving with constant velocity (and no rotation) relative to any other.
why does it follows that infinitely many frame exist?

Inertial frames can be related by a rotation

rotation is complicated right now think about in straight line
but you can go ahead anyway
If one inertial frame exist then infinitely many frame exist why?

The quote you gave already contains the answer: There are infinitely many different velocities, so there are infinitely many different frames. Doesn't have anything to do with the world being Newtonian or not.

@ACuriousMind Yes I was kinda thinking like this

oh sorry I literally skipped over what you said about rotations

10:52 PM
I think I should be clear about what I am thinking.
@Charlie Oh yes you can start the rotation discussion so it is kinda new to me

what rotation discussion?

Sorry I am just middle school student so I have problems with new concepts.
@ACuriousMind The thing that Charlie was gonna say.
Oh now I remember my real question

I completely misunderstood what you asked because I didn't read it properly, but two inertial frames can be related by both boosts and rotations, don't worry about rotations if you're just learning the basics

can a accelerating frame with accelerating particle with same accleration be inertial?
also same velocity

...what's your definition of "inertial frame"?

11:03 PM
@ACuriousMind where newton first law it true

can't be accelerating in an inertial frame

but the observer will not notice that particle will be accelerating it will find it stationary

"All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration. "
An inertial frame of reference in classical physics and special relativity possesses the property that in this frame of reference a body with zero net force acting upon it does not accelerate; that is, such a body is at rest or moving at a constant velocity. An inertial frame of reference can be defined in analytical terms as a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. Conceptually, the physics of a system in an inertial frame have no causes external to the system. An inertial frame of reference may also be called an inertial...

A reference frame in which the First Law is true is said to be an inertial frame.
book definition
oh I didn't mention relative to what
@bolbteppa Does that means it only needs at least 1 frame to observe? And in order to be true for second frame it should not be accelerating too

Yeah, if there is one frame in which you can detect acceleration, that's enough to say it's not an inertial frame

11:15 PM
Thanks I get it. It's clear now.