is gravity in string theory described just as a gauge boson, like the other 3 interactions in nature, rather than the background spacetime?

As far as I know string theory isn't really a gauge theory regarding forces

But in some limit it's roughly a spin 2 field, yes

@Charlie You can write a state from the superposition of any states, including eigenstates, unless superselection rules apply

@Slereah so as far as you know, the electromagnetic field, strong nuclear force and weak nuclear force are also gauge bosons in that limit of string theory though they aren't formulated by the gauge framework in string theory?

String theory is a theory of strings

There are no fields involved

A string theory that has no gauge field is formulated the same way as one who doesn't

the difference is just the target space

@Slereah what does "one who doesn't" mean?

Well just consider a quantum theory of free scalar fields for instance

This is the diagram of an observer sitting in the space point A sending a superluminal message.

Why is this configuration inconsistent with causality?

How can the observer C know that the message comes from the future and not from some other observer in its past?

@apt45 Well if you string together a lot of such messages, you can form a radio signal

Containing INFORMATIONS ABOUT FUTURE EVENTS

It's possible to make much more obviously causality violating scenarios if you play some tachyonic billiard

The classic scenario is to have a particle going back in time and knocking itself out of its trajectory

Or sending back a tachyon that would knock itself back, anyway

@apt45 well then you'll have to define what "causality" means

Indeed, that's the point

There's various definitions of causality, and tachyons may or may not violate them

In the diagram I showed you, the two observers in A and C cannot communicate instantaneously, therefore they cannot agree on who sent the signal

For example, gamma rays detected with some delay after black hole merging could also have emitted before the merging, as far as we know from the Earth

I can give you the dumbest case of tachyons violating causality

Consider a horizontal line. That tachyon doesn't intersect every spacelike hypersurface

And therefore violates causality

i wonder whether there is a local definition of causality.

ie you cannot predict that this tachyon would appear in this frame

Why tachyons?

There are local definitions of causality, but spacetimes tend to be locally causal

@apt45 What do you mean

And not some other particle? What is the special property of tachyon you are using?

Immagine the message from A to C is so powerful to kill the observer in C. Localilly, this is perfectly fine to me. The observer C does not know that his/her future counterpart will kill him/her. Who can establish that the signal came from the future?

A and C cannot communicate instantaneously, so how do you know that causality is violated?

@apt45 Tachyons can move in spacelike directions

Also you can form loops with tachyons, as long as you have at least 2 spatial dimensions

We don't even know if tachyon do exist 😂

probably not

So let's put aside the tachyons. Let's talk about the diagram I posted

the radius of a Schwarschild black hole is $r_s=2G_NM/c^2$. But a charged black hole always has an inner horizon besides the event horizon. I guess the radius of the inner horizon depends on the charge carried by the black hole. Why is size of the radius of the inner horizon expressed in terms of the charge?

what do you mean

what is the radius of the inner horizon, aka Cauchy horizon, of a charged black hole? I guess it depends on the charge.

actually I also wonder the radius of the event horizon of a charged black hole. Is it different from the radius of a Schwarzschild black hole?

It does depend on the charge, yes

Since it's the zeros of the metric components

Which do depend on the black hole charge

@Charlie Yes, that's right - "superposition" is always relative to a given basis

@Slereah @ACuriousMind I see thank you

Anyone kind enough help why this happens!

@Yuvraj Aren't you just inducing a huge current in the metal blob with the magnet that heats it up and melts it? Kind of like a conduction cooker.

Conduction cooker? Isn't that 'induction' cooker?

lol yes I meant induction

I think there's no permanent magnet here. Just an AC is passed through the copper coil and the current induced in the metal block causes the heating.

But do you know why does the molten metal fall at the end of the video? Is the coil disconnected from the supply or is there any change to the properties of metal due to the increase in temperature?

yes my bad I meant the magnetic field induced by the ac in the wire, apparently I was not thinking while I wrote that entire sentence

No. I was referring to the title which says 'melt metal with magnets'. I didn't notice that missing 'field' in your sentence :P

Since we're at electromagnetic induction, what do you think would happen if you place an utensil on an induction stove? Will it repel or attract? Or nothing? Even small amount of force is taken into account.

it must just mean electromagnets

Maybe, electromagnets with no fixed polarity.

what do you mean will it repel or attract? I assume it just heats up

I guess it would move if it's small enough, I thought induction cookers were just large spinning electromagnets

or something like that

Or in more technical terms, will the force exerted on the utensil by the induction coil, be in the upward direction or in the downward direction? Or is it zero?

I don't know a lot of EM, but wouldn't the utensil have to become magnetic in order for the induction cooker to exert a force?

exactly which direction the force is applied in will depend on which way the electromagnet is spinning etc. no?

It's enough if it's conducting. The induced electric currents would create a magnetic field which would interact with the alternating field in the coil. Have you seen magnets slowed down when they're made to fall through a copper pipe?

Copper isn't magnetic but the induced currents would create a magnetic field which would then slow down the magnet which is falling through it.

yeah sure I've seen that stuff

I don't think induction stoves have 'spinning' electromagnets. Just a coil through which AC is passed. May I know from where you came to know it has 'spinning' magnets?

I have one at home and I thought the noise it made was something spinning, we can easily look it up, it's not something I've given a lot of thought to

so it looks like it's an oscillating current, not a spinning electromagnet

I assume the current being flicked back and forth is the noise I've heard, not physical spinning

I think, the vibrations are due to exhaust fans to cool the induction coil.

I guess it's time to reveal the answer. It repels! Extreme version can be found out in this video.

I have really high myopia and I'm basically blind when I swim. So summer is here and I wanted to try to make my swimming goggles prescription. I have two old glasses that when added up make up the diopter I have now, so I'll take the lenses (4 in total) and hot glue them together and then hot glue them to my swimming goggles. Would that work? Will the hot glue hold in water ?

meh I'm gonna do it

Anyone in solid-state or condensed-matter physics, 21 hours left on this bounty if anyone is interested!

Anyone here know anything about the making of mirrors? Specifically parabolic mirrors.

@Beliod What sort of mirror? Telescope quality, or the kind used as reflectors for car headlights? There are a couple of people on the Astronomy site who've ground their own telescope mirrors.