View Full Version : Thought experiment about stars

Copernicus

2019-Mar-05, 08:32 PM

If one has two stars of certain rest mass, that is equal, but one is not moving vs one that is moving at lets say 3^.5/2 the speed of light the one moving would have an effective mass that is 2^.5 times higher than the motionless one. Would the stars burn at different rates, would the faster moving one look smaller by a factor 1/(2^.5)?

George

2019-Mar-05, 09:45 PM

If one has two stars of certain rest mass, that is equal, but one is not moving vs one that is moving at lets say 3^.5/2 the speed of light the one moving would have an effective mass that is 2^.5 times higher than the motionless one. Would the stars burn at different rates, would the faster moving one look smaller by a factor 1/(2^.5)?

This is the sort of question Einstein seem to ask himself in his early years. He was convinced it made no sense to be able to catch up to a wave of light and look at it while traveling next to it.

He originally called his theory the Invariant Theory, or something like that, to emphasize the key point about special relativity, namely that the laws of physics is the same regardless of their initial frame. IOW, both your stars will behave the same within their own inertial frame. How they look to one another will be different, admittedly, but they both would burn at the same rate if we allow them to use their own clocks. But if only one of the clocks is used for the master clock, then we are back to how one appears to the other.

[I will assume your math is correct otherwise, or did you want it checked?]

Ken G

2019-Mar-05, 10:49 PM

If one has two stars of certain rest mass, that is equal, but one is not moving vs one that is moving at lets say 3^.5/2 the speed of light the one moving would have an effective mass that is 2^.5 times higher than the motionless one. Would the stars burn at different rates, would the faster moving one look smaller by a factor 1/(2^.5)?You forgot to say, to whom? Since you stipulated that one star is motionless, it appears you are taking the perspective of that star. That star would certainly reckon that the other star is burning its fuel slowly by the Lorentz factor, and would reckon that the other star diameter in the direction of motion was smaller by that factor as well. However, of course the other star would reckon the exact opposite to be true. These "reckonings" are not statements of fact about the stars, they are descriptions of common coordinate systems that physicists associated with those stars would likely use to try to put language to their experiences. As George said, if one wants to say what is "really happening" for a star, or anything else, one imagines it best to stay with the object in question, for what observer would have a more authoritative view of an object than the object has of itself? But enforcing one's own perspective onto other objects that one is separating from at a vast speed is philosophically questionable.

Copernicus

2019-Mar-06, 01:22 AM

I guess I am asking about relativistic vs expansion of the universe affects. According to current theory the universe is larger than the Hubble Sphere. Would the galaxies have more energy than our galaxy if they are moving away from us at some great velocity, due to expansion, So a galaxy that weighs 10^42 kg and moving at the speed of light away from us due to expansion, would it have an extra energy of 1/2 mc^2?

John Mendenhall

2019-Mar-06, 01:45 AM

As Ken G has so well evplained, the strar's motionns are relative.

Great care must be used when constructing 'thought experiments'.

DaveC426913

2019-Mar-06, 04:22 AM

Simply put: if the star of interest is moving relative to the observer, it will be observed to age slower (by whatever measurement you choose, including comparing it to a similar star in one's own rest frame).

That should clear up any confusion.

Shaula

2019-Mar-06, 05:57 AM

I guess I am asking about relativistic vs expansion of the universe affects. According to current theory the universe is larger than the Hubble Sphere. Would the galaxies have more energy than our galaxy if they are moving away from us at some great velocity, due to expansion, So a galaxy that weighs 10^42 kg and moving at the speed of light away from us due to expansion, would it have an extra energy of 1/2 mc^2?

You are mixing classical and relativistic concepts here. Energy in GR is a complex topic that doesn't lend itself to simple classical read across in realistic models of spacetime. You are also, as has been pointed out, using absolute language when you should be using relative language.

If you want to delve into energy in GR a bit more Baez (http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html) has some good references you can follow.

Ken G

2019-Mar-06, 02:26 PM

What's more, we don't normally think of cosmological expansion as "objects moving away from us at some relativistic speed," we just think the distance to them is increasing-- which is different. In particular, we can see galaxies whose distance from us is now, and has always been, increasing at a rate faster than c. If you tried to apply some relativistic formula to that rate of distance increase, you would get nonsense, because those formulae apply to objects passing each other at the same point in space and time, not to objects that are separated by cosmological distances. At cosmological distances, all distances are just coordinate choices, and there is not even a unique way to measure distance and get a unique answer. So we typically choose "comoving frame coordinates," wherein distance is what you'd get if you laid comoving rulers end-to-end at the same cosmological age, and that's the distance that increases with time at a rate that can be faster than c-- but has no relativistic effects other than what come out of the equations of cosmological evolution. (And since we see objects as they were in the past when the gravitational environment was different, we do see cosmological time dilation, but it doesn't follow the Lorentz factor, and we don't think of it as what is going on "now".)

Copernicus

2019-Mar-06, 06:25 PM

What's more, we don't normally think of cosmological expansion as "objects moving away from us at some relativistic speed," we just think the distance to them is increasing-- which is different. In particular, we can see galaxies whose distance from us is now, and has always been, increasing at a rate faster than c. If you tried to apply some relativistic formula to that rate of distance increase, you would get nonsense, because those formulae apply to objects passing each other at the same point in space and time, not to objects that are separated by cosmological distances. At cosmological distances, all distances are just coordinate choices, and there is not even a unique way to measure distance and get a unique answer. So we typically choose "comoving frame coordinates," wherein distance is what you'd get if you laid comoving rulers end-to-end at the same cosmological age, and that's the distance that increases with time at a rate that can be faster than c-- but has no relativistic effects other than what come out of the equations of cosmological evolution. (And since we see objects as they were in the past when the gravitational environment was different, we do see cosmological time dilation, but it doesn't follow the Lorentz factor, and we don't think of it as what is going on "now".)

This is more what I was asking about. If one does see time dilation, but not following the Lorentz factor, is it known what this relationship is?

Ken G

2019-Mar-06, 06:39 PM

This is more what I was asking about. If one does see time dilation, but not following the Lorentz factor, is it known what this relationship is?

Yes, it's ruled by Einstein's equation applied in the context of the cosmological principle-- it's all in the evolution of the scale factor. This is why when we look at supernovae at high redshift, it seems to take longer to explode than they do when nearby. If you interpret the changes in distance as changes in the length scale, rather than anything moving, then to keep the speed of light constant at c at all past epochs, you have to change the rate that those clocks appear to tick from your perspective. The easiest way to see this is use "light clocks," which are rigid rulers that bounce light back and forth. If distances are increasing when nothing is moving, one perspective we can take is that rigid rulers are shrinking, so light clocks today must tick faster given a fixed c. So the light-clock rulers were longer when the supernova exploded, so it ticked slower, so the supernova seems to take longer to play out. Alternatively, you can take the more popular perspective that rigid rulers are not changing length, but there is "expanding space" between us and the supernova, so the last light the supernova emitted had to cover more distance than the first light did, so it took longer to get here and the supernova seems to play out over a longer time. You get the same answer either way, which description you favor merely reflects your preference about what a coordinate is. Bottom line: it's all in the evolution of the cosmological scale factor, ruled by Einstein's equation, and the reason the supernova takes longer to play out is the same as the reason its spectral lines look redshifted. It's the same factor, so if you calculate the redshift, you calculate the time dilation, they are one and the same physical effect.

Copernicus

2019-Mar-09, 01:40 PM

A little hard to understand. I'm wondering if something is moving, in relationship to something else, simply due to the expansion of space, do the relativity rules, Lorentz factor. It would seem different physics might apply.

Shaula

2019-Mar-09, 03:49 PM

A little hard to understand. I'm wondering if something is moving, in relationship to something else, simply due to the expansion of space, do the relativity rules, Lorentz factor. It would seem different physics might apply.

The problem is, as Ken explains, that your question has a number of complex subjects that appear simple because of the way you have used the terms. The 'expansion of space' doesn't cause movement in the sense you mean, as Ken highlights when he talks about co-ordinate choices and length scale evolution. The Lorentz factor relationship you talk about is only strictly true in cases that can be described by Special Relativity, the cosmological example can't be.

So the answer to your question is that yes, in this case different physics applies - General Relativity.

George

2019-Mar-09, 06:49 PM

A little hard to understand. I'm wondering if something is moving, in relationship to something else, simply due to the expansion of space, do the relativity rules, Lorentz factor. It would seem different physics might apply.

Perhaps it helps to understand that, essentially, the clocks in distant galaxies read the same as ours, ignoring slight gravity well differences, I suppose.

Ken G

2019-Mar-10, 01:23 AM

If someone asks me, "does clock A read the same thing as clock B", I ask them "are the two clocks together in the same room?" If the answer is "no," I say that to even ask the question shows they are confusing an observable truth with an arbitrary choice of coordinates. Perhaps the most central lesson in all of relativity is time is local.

George

2019-Mar-10, 07:32 PM

If someone asks me, "does clock A read the same thing as clock B", I ask them "are the two clocks together in the same room?" If the answer is "no," I say that to even ask the question shows they are confusing an observable truth with an arbitrary choice of coordinates. Perhaps the most central lesson in all of relativity is time is local. True but the analogy was to help "eschew obfuscation"; it's an important point if taken only on the general terms it's presented, namely that if, with a magic wand, we were to go back, say, 5 billion years ago and instantly place a clock adjacent to each and every distant galaxy of our choice, then today, using our wand again, go there - instantly or by freezing time of the universe - and compare their times, they would all have the same time. [Of course, it wouldn't hurt to make sure the gravity wells were all identical to keep hot gum from getting on our shoes while on this mental walk, I suppose.]

This analogy -- I think I saw it from Brian Greene's book originally -- helps me understand the significance of how physics is invariant for inertial frames including big ones. How we actually see one another's clock is helpful in seeing relativity. So it serves both purposes in ways, perhaps, better than other examples.

Ken G

2019-Mar-10, 08:29 PM

True but the analogy was to help "eschew obfuscation"; it's an important point if taken only on the general terms it's presented, namely that if, with a magic wand, we were to go back, say, 5 billion years ago and instantly place a clock adjacent to each and every distant galaxy of our choice, then today, using our wand again, go there - instantly or by freezing time of the universe - and compare their times, they would all have the same time. That's true, but you are talking about cosmological time, which is a bit different from special relativity time, and the question is more like special relativity. The main lesson of special relativity is there is no preferred reference frame in which to mark time, and the main lesson of cosmology is that there is! This bizarre contrast creates a lot of confusion.

ngc3314

2019-Mar-10, 09:06 PM

The main lesson of special relativity is there is no preferred reference frame in which to mark time, and the main lesson of cosmology is that there is!

I was struck by John Peacock's description of the situation in <i>Cosmological Physics</i>: the cosmic scale factor R depends only on time in a comoving frame but not on position, which makes it "suspiciously like a universal time".

(I'm not sure the contrast is that bizarre, because it's common to have preferred frames tied to particular physical systems, which the observable Universe qualifies as, without having frames that are preferred as matters of calculability.)

George

2019-Mar-11, 01:40 PM

That's true, but you are talking about cosmological time, which is a bit different from special relativity time, and the question is more like special relativity. The main lesson of special relativity is there is no preferred reference frame in which to mark time, and the main lesson of cosmology is that there is! This bizarre contrast creates a lot of confusion. You understand far better than I do, but, for me, those clocks help me get a better feel for what an inertial frame represents especially for relativity (invariance theory); it's easier to get laminar flow before turbulent.

I was struck by John Peacock's description of the situation in <i>Cosmological Physics</i>: the cosmic scale factor R depends only on time in a comoving frame but not on position, which makes it "suspiciously like a universal time". The Hubble Flow seems like it is very special, yet not an absolute, apparently.

Ken G

2019-Mar-13, 07:51 AM

I was struck by John Peacock's description of the situation in <i>Cosmological Physics</i>: the cosmic scale factor R depends only on time in a comoving frame but not on position, which makes it "suspiciously like a universal time".

(I'm not sure the contrast is that bizarre, because it's common to have preferred frames tied to particular physical systems, which the observable Universe qualifies as, without having frames that are preferred as matters of calculability.)

Yes, no preferred frame means no frame where the physical laws are different, it doesn't mean there isn't an obviously more convenient set of coordinates staring you in the face. One clear example of this is the center-of-mass reference frame when you have two objects in collision. But I agree with Peacock that cosmological time looks like more than just a clearly convenient set of coordinates, and the cosmological principle is indeed called a "principle", not the "cosmological convenience!" I wouldn't be terribly surprised if there is not some future theory of dynamics in which the laws of physics have to be framed in cosmological time or they do look different, much like Newton's laws have to be framed in inertial coordinates.

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