special relativity - What is the kinematics of a particle with complex mass?

• particles with real-mass have time-like kinematics ($ds^2 > 0$).


• particles with zero-mass have light-like kinematics ($ds^2 = 0$).


• particles with imaginary-mass have space-like kinematics ($ds^2 < 0$) (tachyons).

So the question is pretty simple:

What would be the kinematics of a particle with mass that has both non-zero real and imaginary parts?

Answer

I think the question has no meaningful answer, at least in our universe. If you look at $$E^2 - p^2 = m^2$$ then if $m$ is complex with non-zero real and imaginary components, then $m^2$ is also complex with non-zero real and imaginary components and therefore either $E$ or $p$ (or both) must also be complex with non-zero real and imaginary components. I don't think there is any meaningful description of the kinematics of a particle with complex energy or momentum.

resource recommendations - Books on non-perturbative phenomena in quantum field theory

I am looking for any good places (preferably textbooks) to study about introductory non-perturbative phenomena in Quantum field theory.

Any suggestion will be appreciated.

astrophysics - Is Jupiter a failed star?

In my physics lessons, my teachers have always been keen to tell my class that Jupiter is considered a 'failed star' by scientists. Is this true?

In my own effort I wondered if maybe this could just be being regurgitated from an outdated physics syllabus that still considers the Solar System to have nine planets. From that thought onward, through my research on the Internet, I haven't found people referring to Jupiter as such and people always call it a planet rather than a brown dwarf.

Furthermore, it's my understanding that brown dwarfs possess more mass than Jupiter suggesting to me that Jupiter possesses too little mass for fusion to even be plausible.

So am I correct in thinking that Jupiter is 'only' a planet, or are my physics teachers correct in saying it is a failed star (and if so, why)?

Answer

The answer kind of depends on how old you are. At a very introductory level, say, maybe middle school or younger, it's "okay" to refer to Jupiter as a failed star to get the idea across that a gas giant planet is sort of similar to a star in composition. But around middle school and above (where "middle school" refers to around 6-8 grade, or age ~12-14), I think you can get into enough detail in science class where this is fairly inaccurate.

If you ignore that the solar system is dominated by the Sun and just focus on mass, Jupiter is roughly 80x lighter than the lightest star that undergoes fusion. So it would need to have accumulated 80 times what it already has in order to be a "real star." No Solar System formation model indicates this was remotely possible, which is why I personally don't like to think of it as a "failed star."

Below 80 M_J (where M_J is short for "Jupiter masses"), objects are considered to be brown dwarf stars -- the "real" "failed stars." Brown dwarfs do not have enough mass to fuse hydrogen into helium and produce energy that way, but they do still produce their own heat and glow in the infrared because of that. Their heat is generated by gravitational contraction.

And Jupiter also produces heat through both gravitational contraction and differentiation (heavy elements sinking, light elements rising).

Astronomers are not very good at drawing boundaries these days, mostly because when these terms were created, we didn't know of a continuum of objects. There were gas giant planets, like Jupiter and Saturn, and there were brown dwarf stars, and there were full-fledged stars. The line between brown dwarf and gas giant - to my knowledge - has not been drawn. Personally, and I think I remember reading somewhere, the general consensus is that around 10-20 M_J is the boundary between a gas giant planet and brown dwarf, but I think it's fairly arbitrary, much like what's a planet vs. minor planet, Kuiper belt object (KBO) or asteroid.

So during Solar System formation, was there a chance Jupiter could have been a star and it failed ("failed star!") because the mean Sun gobbled up all the mass? Not really, at least not in our solar system. But for getting the very basic concept across of going from a gas giant planet to a star, calling Jupiter a "failed star" can be a useful analogy.

special relativity - Confusion on Proper time and Proper Length

so I've been looking at special relativity and I have interpretations of the notions of proper length and proper time. Suppose there are two frames S and S'. S' is moving with respect to S. Therefore;

Proper Time is measured by S' Proper Length is measured by S

This is, at least, my way of understanding these two concepts. Is it correct? Thanks

astronomy - Do we know what event caused the Sun and Solar System to form?

Some stellar formation theories suggest that stars are formed by shock waves from trigger events such as supernovae.

This excerpt from Star Formation basically gives the background to my question:

Many astronomers regard the passage of a shock wave through interstellar matter as the triggering mechanism needed to initiate star formation in a galaxy. Calculations show that when a shock wave encounters an interstellar cloud, it races around the thinner exterior of the cloud more rapidly than it can penetrate its thicker interior. Thus, shock waves do not blast a cloud from only one direction. They effectively squeeze it from many directions.

Two questions:

1. 
   

   If the Sun (and Solar System) was formed in this way, rather than a collapse of a cloud of dust and gas, (by itself, through gravity alone), do we have any idea of what event caused it, for example, do we know where a possible ex-supernovae is located, or has it long since vanished by now?

   
   


2. 
   
   

   Stars are often formed in groups. I wonder do we have an age for the nearest stars (using the H-R diagram) or any evidence that they may have been part of the same gas and dust cloud that formed our Sun?

   
   

I do appreciate that:

1. 
   

   Astronomical observations are difficult in many circumstances, e.g. obscuration by dust or gas often prevents an accurate picture of objects located many light years from Earth.

   
   


2. 
   

   The Sun was formed 4,500 million years ago, this fact may make finding evidence of a possible trigger event extremely difficult to discover.

   
   
   

Answer

You're right that the Sun being 4.5 billion years old makes observations difficult. The Sun goes around the Galaxy about once every 225 million years, so since the Sun formed it has gone around the Galaxy perhaps 20 times. The trouble is that the Galaxy is not like the Solar System: stars don't go around on nice nearly circular orbits, everything is a bit jumbled. To give you an idea, here's an estimate of where the stars that are currently in the Solar neighbourhood have been during the last orbit of the Sun around the Galaxy:

As you can see, they span over 80,000 light years (that's basically the full width of the Milky Way) just 1 orbit ago, so a supernova remnant that was near the Sun 20 orbits ago could be virtually anywhere. We can't measure the age of the Sun or supernova remnants accurately enough to help either (as in being able to say "aha! a remnant with exactly the age of the Sun!").

It's similarly difficult to find stars that may have formed near the Sun. About the best we can do is to look for stars with similar age and chemical composition to the Sun, but at 4.5 billion years old, the accuracy of stellar ages isn't terribly good. Asking more broadly what star formation conditions were like in the Milky Way when the Sun formed is also a difficult question and a topic of current research, see for instance this reasonably current review.

A potentially more fruitful approach is to look for Sun-like stars that are forming now and see what conditions look like for their formation - potential triggering mechanisms, how many stars formed in a group, etc. But this only helps inform what the formation of the Sun would have looked like - it's likely the Milky Way was a significantly different beast 4.5 billion years ago in terms of gas supply, morphology, ISM conditions, etc.

Is friction enabling relative motion between bodies in contact?

If the surface object B is placed on is frictionless, on applying a force F on object A, friction will act on object A opposite to the direction of the force applied (opposite to the direction of its tendency of slipping relative to B/ actual slipping relative to B) and will act on object B in the direction of the force applied (opposite to the direction of its tendency of slipping relative to A/ actual slipping relative to A.)

The surface B is on being frictionless can only be an ideal situation, but in this case, friction opposes object A’s tendency of motion towards the right while it enables B’s motion to the right. Is friction enabling relative motion between A and B here?

general relativity - The Time Freezing Room - Theoretically possible?

Imagine a room in your basement with a very special property: The time inside this room runs 60 times faster compared to the outside world. That means when you enter the room and spend there 1 day with working, reading, etc., only 24 minutes are gone in the outside world. Wouldn't such a place be wonderful:

• You would be done with all your university exercises in just a few hours.


• You could read so many books and become one of the most educated people.


• You could practice many skills... you could become a great musician and learn any instruments in just a week (1 week = 14 month), or become expert in any other skill...


• You could run your simulations on a computer in this room and they would be done in little time.


• You could maybe even grow some food in such a room.

The concept of such a room sparked my imagination, so my first question is:

For what would You use such a room? What great possibilities are there?

However, I study physics and I am very curious for the (theoretical) ways to actually build such a room. Of course this room is more like a thought experiment, but: Is it possible to build such a place in accordance with the laws of physics? Or:

How to build such a room?

Thank you for your answers.

Note: Before I asked this question I checked if it matches the physics category, but according to Is non-mainstream physics appropriate for this site? it should be fine: "For example, a question that proposes a new concept or paradigm, but asks for evaluation of that concept within the framework of current (mainstream) physics is OK."