# Can you make an object have a stronger graviational pull if you make is denser?

zeromodz
If I have 2 objects with equivalent mass. Is there anyway I can make one of them have a stronger pull by changing the density? If so are there any equations the help me predict to what extent?

Thanks.

Gold Member
Sort of. Gravitational force is dependent on mass and distance. If the object is smaller, that means you can reduce the distance.

Consider: here on Earth, you feel gravity at 1g. That is because of exactly two factors:
- the mass of the Earth is 5x10^23g
- your distance from the Earth's centre of mass is ~6200km
This is the best you can do as far as G-pull goes.

But if Earth were crushed down 1/10th of its current diameter, that means you could get ten times closer to its CoM. And that means you would experience a pull of 10^2 or 100gs.

As for formulae, simply use
F=G*m/r^2
where m is the mass of your object and r is its radius - or more relevantly, the minimum distance you can get from the centre of mass of the object.

You will find that, for your smaller object, r can be smaller, therefore F will be larger.

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Homework Helper
Gold Member
If I have 2 objects with equivalent mass. Is there anyway I can make one of them have a stronger pull by changing the density? If so are there any equations the help me predict to what extent?

Thanks.

Loosely speaking, no. The gravitational attraction would be the same between the two.

For example, if the sun were to mysteriously collapse into a black hole (without some big supernova explosion that would tear the Earth apart), the Earth would orbit around around this black hole, just as it did the sun. A Year would still be a year. Gravitationally speaking, we wouldn't see a difference here on Earth (sunlight would be a different story though )

As a more mundane example, consider a dry sponge and a piece of duct-tape. Place both on a scale and measure their combined weight. Now, using the same strip of duct-tape, tightly wrap up the sponge so that its volume decreases. Again weigh the sponge-tape combination. The results are the same. The density increased, but the weight, i.e. gravitational attraction, didn't.

Now if the Earth's volume shrunk down to a much smaller size, you would feel a greater gravitational attraction on its new surface, only because you are now closer to the center of the Earth. But if you were to stand on a platform ≈6371 km (≈3,959 mi) away from the center of the Earth (just as you are now with its current radius), you weight would remain the same as it is now (in both cases you are the same distance from the Earth's center).

Notice I started this response with the phrase "loosely speaking." Getting more technical, the gravitational attraction and gravitational effects are only independent of density if the objects are rigid bodies and the mass distribution of each have spherical symmetry. But even so, it wouldn't matter much. But it can have a non-negligible impact if the objects are close together depending on how you change the orientation of one or both objects. This situation is responsible for ocean tides on Earth. (If the Earth were shrunk down to size of a basketball, there would be no more tides ... of course that would be the least of Earth's problems if that happened. :yuck:) In a similar vein, a neutron star in a close orbit to a large red giant companion could cause the neutron star accrete matter, "taken" from its companion, which wouldn't happen if the companion star was more compact.

Wetmelon
Lots of interesting, well written things

So in other words - No. Unless you are changing the density by adding mass with equivalent volume.

Though you may be able to double the gravitational pull of an object, it won't have much effect in real world... The earth is still going to hold the ball to the ground and friction isn't going to let it go much of anywhere. In deep space however, sure this is theoretically possible:

Force from Gravity = G*(mass of object 1)*(mass of object 2)/(distance between them)^2

where G = 6.67x10^(-11) m^3/(kg*s^2)
masses are in Kg
and distance is in meters

slipperyfish
Not being a physicist myself I got lost in the technical mumbo-jumbo.
So what was the upshot?
That the denser object has a more intense gravitational field immediately around it but from a significant distance they would have the same gravitational pull?

Gold Member
Not being a physicist myself I got lost in the technical mumbo-jumbo.
So what was the upshot?
That the denser object has a more intense gravitational field immediately around it but from a significant distance they would have the same gravitational pull?
Yes.

Earth is ~3900 miles in radius and masses 6x10^24kg.
Imagine a very dense object X, only 1 mile in radius, yet massing 6x10^24kg.

On Earth's surface, 3900 miles from its center, we experience 1g.
If we were in a spaceship 3900 miles from object X, we would experience 1g.

Note that the Earth's surface is the closest we can get to Earth, so it does not exceed 1g.
However, we could fly closer to object X. If we flew to half that distance (1950 miles) we would now experience 2gs. If we flew to within 30 miles of object X (7 halvings) we would experience 128gs (2^7).
The surface gravity on object X (.5mi radius) is 4096gs.

Wolf5370
This is a very interesting subject. I woke up tonight (as I'm wont to do) with Einstein's (Was it his?) thought experiment about bowling balls and marbles on a trampolene surface to show the bending of space-time. I may have taken the analogy a little far, but I suddenly have a problem...I imagined the experiment with a somewhat more elastic surface (perhaps). If we have a marble, say, that has a very high mass, but a small radius (some super dense material) this would cause a deep curve with a small radius - where as a beach ball would produce a shallow dent with a wide radius. For the two to be attracted, then the event horizons of the two curves need to come into contact with each other. So this leads to several questions (that woke me up):
1-Is gravity, being a curvature of space-time as opposed to Newtonian force, of equal density itself or does size affect the curvature as well as mass?
2- Is the flexability of the "surface" (space-time) constant thoughout the universe or is it more apt to curve in some places tha others?
3- Is the "flexability" such that what I suggested (in my apparant dream) impossible in our universe.
4- Is it possible for a super dense object to bend space-time completely around itself - would we know? Maybe this would just be its own little universe/dimension???

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Staff Emeritus
Wolf, the curvature of space due to gravity of an object is only different if you compare two equally massive objects but not of equal density.

Take your marble and beach ball for example. Lets say your marble is 1 in across and the beach ball is 10 in across. If both have the same mass then both have equal curvature at a distance from the center of mass of about 10 in and greater. Once you get INSIDE the surface of the beach ball the gravity is no longer centered at the center of mass. The closer you get to the center the more gravity is pulling "out" instead of "in", since all the matter is no longer on one side of you and is instead surrounding you. In effect you have less gravity per space than the marble does.

The marble, being much smaller and denser, still has all its mass on one side of you, therefore all the gravity is concentrated as well. So once you get closer to the marble than 10 in, you start to experience more gravity than you did with the beach ball.

So, like people said above, replacing the sun with a black hole of equal mass would have almost no difference in the overall gravity of the solar system EXCEPT if you got closer to the black hole than the surface of the sun is to it's center. Make sense?

Homework Helper
Gold Member
Hello Wolf5370,

Welcome to Physics Forums!
This is a very interesting subject. I woke up tonight (as I'm wont to do) with Einstein's (Was it his?) thought experiment about bowling balls and marbles on a trampolene surface to show the bending of space-time. I may have taken the analogy a little far, but I suddenly have a problem...I imagined the experiment with a somewhat more elastic surface (perhaps). If we have a marble, say, that has a very high mass, but a small radius (some super dense material) this would cause a deep curve with a small radius - where as a beach ball would produce a shallow dent with a wide radius. For the two to be attracted, then the event horizons of the two curves need to come into contact with each other.
I wouldn't use the term "event horizon" in your analogy. Event horizon has a very specific meaning, and I don't think it necessarily applies to your beach ball and marble analogy.

But anyway, let's continue with your analogy of the marble and beach-ball on the metaphorical elastic surface.

Imagine that you had a very dense marble and a less dense beach-ball, such that both the marble and beach-ball have the same mass. Also, let's assume that both are perfectly spherical and nothing is rotating.

When the beach-ball is put on the metaphorical surface, it will cause a dent in the surface. The slope (related to curvature) of the dent gradually becomes less as the distance away from the ball increases.

Now put the dense marble on the surface. Near the region of the marble, the slope (curvature) is much, much greater than that region directly under the beach-ball. However, like the case with the beach-ball, as you get further away from the marble, the slope (curvature) decreases.

Now here is the kicker: At a distance greater than or equal to the radius of the beach-ball, the slope (curvature) of each situation is identical. True, the situations differ at distances less than the radius of the beach-ball (namely the marble situation has steeper curvature), but at distances greater than or equal to the radius of the beach-ball, there is no difference at all.
So this leads to several questions (that woke me up):
1-Is gravity, being a curvature of space-time as opposed to Newtonian force, of equal density itself or does size affect the curvature as well as mass?
Umm, I'm not quite sure I follow you here. But I'll take a stab at it anyway. Mass/energy (mass is really just one of several forms of energy) tells spacetime how to curve (how to shape itself). Spacetime curvature tells mass how to move.

The differences between a beach-ball and a marble is the mass distribution. But if you wanted to, you could break up the marble and/or beach-ball into a vast number of tiny, tiny bits of mass (such that each tiny chunk of mass has the same mass as any other tiny chunck). Then each tiny chuck of mass would have the same influence on spacetime curvature as any other tiny chunk of mass. The only difference now in the beach-ball and marble situations is where all the little bits of mass are relative to each other.*

*Technically, if there is any energy binding the pieces of mass together, you'll have to take that into consideration too. But that's pretty negligible on scales greater than atomic nuclei. So let's just assume that we're not ripping atoms apart.
2- Is the flexability of the "surface" (space-time) constant thoughout the universe or is it more apt to curve in some places tha others?
It is a principle that laws of gravitation are the same everywhere in the universe (all else being the same except for position). This is just a principle though. Presently, there is no evidence that would indicate that it isn't true.
3- Is the "flexability" such that what I suggested (in my apparant dream) impossible in our universe.
I don't think I understand the question.
4- Is it possible for a super dense object to bend space-time completely around itself - would we know? Maybe this would just be its own little universe/dimension???
If an object is dense enough, a black-hole will form. Using the analogy of balls on a surface, the dense object would create an incredibly large curvature, near the object. In relativistic terms, the curvature would be large enough, at some close enough distance to the object, that nothing could escape once closer than that distance. This threshold is called the event horizon.

But an important point here is that as you get farther away from the object, the curvature is just like it would be if the object was bigger and less dense.

Imagine that the entire Earth was compressed to the size of a beach-ball. However, also imagine that you were suspended by some sort of platform with a height of exactly the radius of what the Earth is now. In other words, the Earth gets squished to beach-ball size, but you stay put (and don't fall toward the center along with it) due to the platform. From your vantage point up on the platform, gravity is exactly the same as it was before. You would measure g = 9.81 m s-2. You could jump as high as you used to, no more, no less. The moon would continue orbiting the squished up Earth, pretty-much just as it did before the Earth was squished.*

The difference would come into play if you were to climb down the platform toward the newly squished up Earth. Gravitational pull would be much greater the closer you get. If you were to get close enough, the tidal forces would turn you into spaghetti (i.e. you would be spaghettified).

*In this paragraph I'm ignoring certain minor differences that arise from the Earth not being perfectly spherical, rotation, etc.

Wolf5370
Hi guys,
thank you both for the welcome and you answers. I probably was as clear as mud.
I understand what you are both saying in that for the same mass, the curvature in space at the same distance (externally) would be the same.

I was referring to the "strength" of the gravity when I used the density term in Q1 (rather than the density of the object itself).
I guess that this does answer my question if I think about it. If the curvature of space-time is the same at any given point externally, then so is the "strength" of it. My confusion is perhaps more related to the fact that we still tend to talk in terms of Newtonian force instead of curvature (as seen in earlier posts in this thread).

It does make sense to me that the mass of the object is the "force" of the "pull" and thus has the same affect at the same distance regardless how big the "puller" was/is. With a trampoline surface, there is a well around the object (a gap between the object and the trampoline as it rises from the bottom - shallower dips give an apparant greater distance from the surface than a deep one. My problem was, I think, that I was thinking in terms of radii instead of actual measured distance (i.e. how wide the gap is (the curvature) for a given position from the bottom in radii (less than 1 - i.e. where 0.5 would be the vertical centre of the object assuming it is spherical) measuring out in radii until we reach the trampoline fabric).
Thinking about it some more, with your assertions in my mind, it becomes obvious this is an illusion and the fixed distance (outside the boundary of the object) does indeed have the same curvature.

BTW the Q3 question was relating to space-time itself - i.e. if it can stretch (like fabric can) at a specific point, then this will affect the curvature at a given distance as the local stretch will remove some of the energy that would go to bending space-time further away. Not sure if that's any clearer? However, from your answer to Q2, it would seem that (at least in principle) space-time is constant therefore local stretching would not be congruent with our knowledge/understanding.

Q4 I understand the black hole concept (not quite to Hawking's level :D) but that is a curvature great enough that it can trap everything - even light. Does this mean that there is a maximum mass for a black hole? - i.e. that it can not curve greater than that required to hold light (run into Einstein's infinite mass problem?) - if not, then how steep can the curvature become (theoretically) - 90 degrees/infinite? If the "fabric" was more like chewing gum (Q3 can stretch) and I dropped a ball bearing on it, then it would likely wrap right around the ball.
And (the second part of Q4) this being so, would it make any difference other than extending its pull. If the big bang started as a singularity (if it happened at all) then it must have had all the mass/energy of the universe in it (plus more - given that anti-matter/matter would have annihilated each other). So the question was really, is there a maximum at which space-time can curve or is it always fixed to an ever increasable mass? Phew

PS: I knew Event Horizon was specific to black holes, but at 4am here, it seemed as good a descriptor as any even in incorrectly applied - I guessed (correctly) that you would get my gist. Threshold would have been a better term to use - or distance of influence perhaps. :D

PPS: Sorry if my queries seem juvenile, I studied physics to 'A' level (18), then no further - my degrees are in computing - so other than reading New Scientist and trying to keep up with popular science books and popularised theories, I'm stuck in the dark ages (of 1980's). I have kept an interest, but often find myself arguing with theories (to myself!) when I read them, with no sounding board or expert to explain away my exceptions and arguments (which I guess are often flawed!). So, I am happy to have found this forum - just hope I don't wear out that welcome :D

Gold Member
PS: I knew Event Horizon was specific to black holes, but at 4am here, it seemed as good a descriptor as any even in incorrectly applied - I guessed (correctly) that you would get my gist. Threshold would have been a better term to use - or distance of influence perhaps. :D
There is no threshold. Distance of influence is infinite. There is no distance so far from any mass that spacetime is not curved by it.

This is one of the dangers of using analogies, such as trampolines, to extrapolate.

Space Drifter
No. Gravitational pull is governed by mass, not density. Earth is far more dense than Jupiter. But Jupiter's greater mass makes its gravitational pull much stronger.

Oldfart
There is no threshold. Distance of influence is infinite. There is no distance so far from any mass that spacetime is not curved by it.

Dave, does this mean that if I wiggle my little finger, I wiggle the entire universe (well, a little, anyway)?

Calrid
Dave, does this mean that if I wiggle my little finger, I wiggle the entire universe (well, a little, anyway)?

It means that the influence of the gravity of your finger is non 0 at the limit of infinity or the size of the universe or whatever you want to call it yeah. there is no such thing as nothing in field theory, well there is but you get the point.

You wiggle the universe an extremely small amount, and it wiggles you.

ScottTheSculp

A star with higher gravitational pull will cause time to pass more quickly.
This increase in time flow *is* gravity.

Space Drifter

A star with higher gravitational pull will cause time to pass more quickly.
This increase in time flow *is* gravity.

That's interesting. I guess it's in line with how jets at high altitude (hence, further from the earth) will lose a second or so on their clock.

Just thinking out loud here, I could be off my rocker, but I wonder if that means that time may come to a stop altogether for an object drifting alone in deep space, far from any gravitational pull. Could this cause astronauts aboard a spacecraft to successfully make the 20 light-year voyage to Gliese 581g (the recently discovered earth-like exoplanet) without aging? And therefore return to earth still alive? Albeit long after their loved ones here had all passed away.

Shoot, but it would suck for them if during their voyage, which could be a few centuries on earth, we came up with a faster way to travel, and we passed them!

ScottTheSculp
Yep.

To leave the solar system you would be pulling away from the time stream of your star and moving directly against it. You will age quite quickly.
If you head directly at the star there is no time . . .but the end is near.

The time stream is moving passed us at the "speed of light".

Not messing with you. I have a theory ;-)

Space Drifter
Yep.

To leave the solar system you would be pulling away from the time stream of your star and moving directly against it. You will age quite quickly.

If time is faster closer to the sun, then why would you not age slower the further you go from the sun?

And if you kept going, eventually reaching the void of absolute space, outside the influence of any star, then would you not stop aging altogether?

Staff Emeritus
If time is faster closer to the sun, then why would you not age slower the further you go from the sun?

And if you kept going, eventually reaching the void of absolute space, outside the influence of any star, then would you not stop aging altogether?

Time is not faster closer to the sun, it is slower. Also, the effect of the suns gravity on our passage of time is very small. We are far more affected by the earths gravity than we are the suns. (Because the earths gravity is much stronger here. Which is why we stay on earth and don't fly off towards the sun.)

On top of that, the increase in velocity you would get to for interstellar journeys would have far more of an effect on the passage of time than the sun. The closer you get to the speed of light the slower time is going for you compared to a stationary observer.

A star with higher gravitational pull will cause time to pass more quickly.

You've got it backwards. Higher mass = higher gravity = slower time.

All in all, the effect is extremely small unless you are very close to a huge gravity source, such as a neutron star or a black hole.

Space Drifter
Higher mass = higher gravity = slower time.

Good clarification. I recall learning that before, but had forgotten.

The closer you get to the speed of light the slower time is going for you compared to a stationary observer.

That suggests that speed is not relative to nearby objects, but is relative to the entire fabric of the universe, which suggests that the universe is finite.

Let me explain what I mean. A car traveling 60 mph is only doing so relative to its surroundings on earth. But what if the car had no surroundings? Then it would be impossible to determine any speed whatsoever.

Just like if a spacecraft had no apparent surroundings, no stars, no comets, no nebulae, just empty space... then how would its velocity be determined? How could you know if it were traveling at close to the speed of light, if there were nothing to measure against? Is there such a thing as absolute speed irrespective to surroundings? Well, I propose that such absolute speed is only possible in a finite universe. i.e.- the spacecraft's velocity is determined relative to the start and end points of said universe.

For in an open or infinite universe, there would be no official distance markers, no start point, no end point. In other words, there would be no way to determine, between two passing objects, whether both are moving, or one is stationary and the other is moving past it.

I think that is a very simple and solid case for why our universe is finite, not infinite.

Space Drifter
I think my above post is straying from the original topic. I'm going to start a new thread with it.

Staff Emeritus
I think my above post is straying from the original topic. I'm going to start a new thread with it.

No, you pretty much hit a misunderstanding of Relativity on the head with your previous post.

When we say a "Stationary Observer", you are correct. That observer is only stationary because we call it stationary.

For in an open or infinite universe, there would be no official distance markers, no start point, no end point. In other words, there would be no way to determine, between two passing objects, whether both are moving, or one is stationary and the other is moving past it.

This is 100% correct. One cannot tell which object is moving and which is not. We choose our frame and call it stationary or not and base other objects on that frame.

Gold Member
For in an open or infinite universe, there would be no official distance markers, no start point, no end point. In other words, there would be no way to determine, between two passing objects, whether both are moving, or one is stationary and the other is moving past it.

I think that is a very simple and solid case for why our universe is finite, not infinite.

Whether or not the universe is finite or infinite we still have no start or end points or special stationary points.

A finite universe does not have to have a centre, edge or boundary.

Note that the surface of a sphere is finite yet there is no point on the surface that is any more special than any other, no point that could be called start, end, edge or centre. Any coordinate system is utterly arbitrarily applied.

Space Drifter
Whether or not the universe is finite or infinite we still have no start or end points or special stationary points.

A finite universe does not have to have a centre, edge or boundary.

Note that the surface of a sphere is finite yet there is no point on the surface that is any more special than any other, no point that could be called start, end, edge or centre. Any coordinate system is utterly arbitrarily applied.

That makes sense to me. Good explanation.

Okay, so let's forget about open or closed universe for a moment and stick with the idea that no matter what, there are no 'special' markers, start or stop points. I still can't get my head around the idea that speed can be measured without a reference point. For example when we measure the redshift of a distant star, what is that redshift in relation to? Is it the speed that it's moving away from us? Or the speed that it's moving away from the origin point of the big bang? Or is it some sort of absolute speed that can be measure irrespective of any relative marker points? The latter is what I cannot understand.

I mean, if time moves slower closer to massive objects and faster when away from strong gravitational pull, that seems to say that speed MUST be relative to other objects. No?

And finally, the idea that the speed of light is constant, no matter the speed of its observer. That seems related to this whole topic of absolute speed. Bottom line is, I don't understand how anything, including light, can have a measurable speed independent of any surroundings.

(mind you, I am obviously an amateur, so any explanation is greatly appreciated and considered)

Thanks!!!

Homework Helper
Gold Member
For example when we measure the redshift of a distant star, what is that redshift in relation to? Is it the speed that it's moving away from us?
Yes. That and the fact that space itself has expanded since that moment time the light ray was emitted, until the time the ray arrived at Earth. This expansion contributes to a sort of stretching of the wave, giving it a redshift. On cosmological distances, the majority of the redshift of far away galaxies is due to this sort of redshift -- caused by expanding space. That's in addition to any redshift (or blueshift) caused by said object moving through space relative to us.
Or the speed that it's moving away from the origin point of the big bang?
There is no such thing as the "origin point" of the big bang. The big bang happened everywhere at once (perhaps quite literally -- out to infinite distances, but at the very least, distances far greater than our observable universe). The big bang happened where you are sitting right now, just as it happened 40 billion light years away from you (of course, any object at a distance 40 billion light years away from you now was a lot closer back then).
Or is it some sort of absolute speed that can be measure irrespective of any relative marker points? The latter is what I cannot understand.
In relativity, both special and general, there are no absolute speeds. There are no absolute markers. Everything is in relation to arbitrarily defined coordinate systems, which in practice is in relation to other objects (other galaxies for example). All velocities are relative, is the point.
I mean, if time moves slower closer to massive objects and faster when away from strong gravitational pull, that seems to say that speed MUST be relative to other objects. No?
Velocity only means anything when it is relative to some other object (or objects).
And finally, the idea that the speed of light is constant, no matter the speed of its observer. That seems related to this whole topic of absolute speed.

Keep in mind that in relativity, there is no such thing as absolute simultaneity either. (Neglecting that idea might be a source of confusion.) If you measure two events happening at the same time, but separated by a distance, another observer (moving at a velocity relative to your own) may measure the same events at different times from each other (i.e. events did not happen at the same time), and separated by different distances than you measured.

If you are in a spaceship with a clock, in an inertial reference frame (a frame of reference which is not accelerating), and some other guy speeds past you in a spaceship with a clock, also in an inertial reference frame (but different velocity than your own, obviously), you will measure his clock going slower than yours. He will measure your clock going slower than his. Both measurements are equally correct. Neither measurement is any more special than the other. The clocks won't tick at the same rate (and stay that way) until one of you turns around, accelerating in the process, such that you are both in the same inertial frame (i.e. traveling at the same constant velocity).

But while you're drifting relative to each other, it doesn't make any sense to say who is moving and who is not. You know that the both of you are moving relative to each other (that much you know). And that's it.

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Space Drifter
Collinsmark,

Thanks you for such a well thought-out reply.

Interesting, the notion that the big bang happened everywhere. I can comprehend that. I think by referring to the big bang as a big "expansion" rather than a violent bomb-like explosion, it's easy to understand that our known universe is merely larger now than when it was what we refer to as a "singularity."

I also like your explanation of redshift being an expansion of space. This makes more sense to me than if it were measuring "speed." To me, speed is a moot point because it must always be followed by the question, "compared to what?"

And your mention of absolute simultaneity was great. I had never heard the term, but it makes absolute sense. Very easy to understand, the way you explained it.

But I'm still struggling with the speed of light. If every other moving object is subject to relativity, then why is light-speed not relative to anything but itself? Why does light seem exempt from the idea that "in both general and special relativity, there are no absolute speeds."

Space Drifter
Oh, and Collinsmark- if the Big Bang happened everywhere, then it stands to reason that the universe is still a singularity, just a larger singularity.

Gold Member
I also like your explanation of redshift being an expansion of space. This makes more sense to me than if it were measuring "speed."
There are several different types of redshift. One type of red shift is most definitely an indication that some things are receding from us irrespective of any cosmological expansion.

Individividal stars moving away from us will redshift. While galaxies can too. And just as many caqn be blue shifted, meaning they are mocing toward us.

To me, speed is a moot point because it must always be followed by the question, "compared to what?"
Unless specified otherwise, one can assume it means "relative to you".

But I'm still struggling with the speed of light. If every other moving object is subject to relativity, then why is light-speed not relative to anything but itself? Why does light seem exempt from the idea that "in both general and special relativity, there are no absolute speeds."
Light is not like everything else.

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Homework Helper
Gold Member
But I'm still struggling with the speed of light. If every other moving object is subject to relativity, then why is light-speed not relative to anything but itself? Why does light seem exempt from the idea that "in both general and special relativity, there are no absolute speeds."
You're actually asking about something pretty profound. The reason it is profound is that for some reason or another, spacetime warps and curves itself to ensure that everybody and everything measures the same number when measuring the speed of light [Edit: when I say "speed of light" I'm assuming speed of light in a vacuum.]. It's almost as though the whole universe goes out of its way to enforce this -- warping and curving itself by whatever means necessary to make sure every observer observes the same number, no matter what. I'll try to go through two simple examples later (math excluded -- concept only), one dealing with simple special relativity and the other leading toward a first introduction to general relativity.

Why would spacetime do that in the first place? That's a good question. But if it didn't, it would mean would be some sort of preferred velocities -- some sort of preferred markers. But by all experiments in local space, there doesn't seem to be preferred velocities or positions.*

*(Let's ignore cosmological scales, CMB radiation, spacial expansion, etc., and just limit ourselves to local spacetime.)

Let's go back to that example of the guy in the ship that's passing you. Suppose he's moving very, very fast, close to the speed of light, and he turns on a light in the middle of his ship, and he measures how long it takes the light to hit the front and back of the ship (oh, and let's also ignore quantum mechanics too. -- suppose that it's possible to measure the speed of a light ray moving away from you). You'll measure the speed of his light rays moving at the speed of light, relative to yourself. But by your measurements, the front of his ship is almost keeping up with the ray. But you'll also measure his clocks moving much slower. So when you see him measuring how fast his light ray is moving away from the middle of his ship, you'll see him coming up with the same number that your did, because his clocks are moving slower (not to mention that his ship is "shorter" due to Lorentz contractions). When you observe him measuring the light ray moving toward the back of his ship, you'll still see him coming up with the same number. Keep in mind that from your vantage point (your reference frame) the light hits the back of his ship before it hits the front. But he observes both events happening simultaneously. Remember, there is no such thing as absolute simultaneity.

Similarly, when the roles are reversed, he sees your clocks moving slower, and he sees you come up with the same number, when you measure how fast his light rays are moving, the speed of a light ray emanating from your own ship, or any light ray. If that ends up being counter-intuitive, don't forget that there is no such thing as absolute simultaneity. Events that are simultaneous is his frame of reference are not necessarily simultaneous in yours. Time and distance warp into each other differently depending on the frame of reference.

His clocks and his distances have warped themselves (relative to yours) to ensure that he measures the same constant number for the speed of light (and you can even observe him making his measurements). And his result is the same number that you measure. No matter who makes the measurements for the speed of any ray of light (in a vacuum), you'll always observe that person coming up with the same number -- including yourself.

Now let's move to a different example. (And it's a bit more on topic too )

Imagine an elevator in outerspace, that is accelerating. Let's suppose that its instantaneous velocity is zero relative to everything else around the elevator (it doesn't have to be zero -- but let's just say the velocity is zero to keep things as simple as possible). It is accelerating up (imagine that it just finished decelerating down, and now its starting to move back up -- the elevator is actually in empty space so we're simply defining "up" as the direction of positive acceleration).

You can show using just classical, Newtonian mechanics that light moving from the floor to the ceiling of the elevator will be red-shifted, and the light moving from the ceiling to the floor will be blue-shifted. Now suppose there is a clock on the ceiling and another clock on the floor. If you bring only special relativity into the mix, you can show that the clock on the ceiling will tick faster than the clock on the floor. And again, it only takes special relativity to show this. Nothing more. (Rather than go through the derivation/math here, you should be able to find this example by doing a quick google search.) The important point is that if you were to measure the speed of light on the elevator's floor, you would get the usual number. Same for measuring the speed of light at the ceiling of the elevator -- same number. And to necessitate this, the speed of the ceiling clock must tick faster than the floor clock.

The clock on the floor and the clock on the ceiling are not moving relative to one another. They are in the same frame of reference (albeit an accelerating frame). Yet you can prove that one ticks slower than the other. This has nothing to do with relative velocities, and is completely a matter of acceleration (and special relativity). And once again, both clocks are equally correct. There is no one correct clock and another incorrect clock. Both clocks are correct.

Similarly to the previous example, there is no absolute flow of time. You know that one clock ticks faster relative to the other, and the other ticks slower relative to the first. You know that in an elevator accelerating upwards, the flow of time at the top of the elevator is faster relative to the bottom. But that's all you know.

And here is something different from the first example: Since both clocks are not moving relative to each other, there is no disagreement between the respective time rates. In the previous example, both observers claim that the other guy had the slower clock. That's not the case here. Everybody involved is in agreement that the clock on the floor ticks slower, relative to the clock on the ceiling. It does tick slower. All observers agree on that point.

Einstein proposed that this type of acceleration is *equivalent* to being within a gravitational field and not accelerating (not accelerating in a Newtonian sense). Standing in a stationary elevator on Earth is equivalent to standing in an elevator in empty space that is accelerating at g.

Well, almost equivalent. It would be equivalent if the Earth was a big slab of matter that extended infinitely in two dimensions. That's the only configuration that would give rise to a uniform gravitational field, which would be equivalent to the accelerating elevator in space. Of course, Earth is more-or-less spherically shaped, which means that objects in its gravitational vicinity are subject to what are called tidal forces. But you can ignore tidal forces in arbitrarily small elevators only moving within arbitrarily small distances.

Beyond that, a huge portion of the math involved in general relativity is there because these tidal forces, and non-uniform gravitational influences. Tidal forces are an obstruction to making the math simpler. And what's worse is that any time you have more than one body of significant mass (such as the Earth and the Moon, etc.) there simply is no particular coordinate system that is preferred. The math is hard no matter how you look at it, except for the most simplest of cases.

But general relativity all boils down to this equivalence between actual acceleration and gravitational "acceleration" -- the equivalence between inertial mass and gravitational mass. -- in general relativity, it is the person standing still on the ground that is really "accelerating," and the person free-falling is not. The rest is mostly just geometry. (Albeit pretty tough geometry with generalized coordinates including lots and lots of math and special notations -- and maybe some insightful and surprising predictions.)

*[Edit: If you were really crafty, you could accelerate in one direction for a very long time, and then, after you've stopped accelerating, measure the redshift/blueshift cosmic microwave background (CMB) radiation, relative to yourself. You'd likely find it to be blueshifted in front of you and redshifted behind you. In other words, you could measure your velocity relative to the CMB. In that respect maybe there is some sort of preferred velocity on the most cosmic of scales. What that would tell you is your velocity relative to the previous expansion of space. But you would still need some other objects nearby to determine your velocity relative to local space (i.e. relative to other objects residing in your nearby space.) But measuring CMB red/blueshifts is getting way off topic, and it doesn't have anything much to do with general relativity directly (and certainly not the density of an object). So I didn't want to bring it up here.]

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Space Drifter
Collinsmark,

That is an amazing brief on relativity in regard to light. Amazing to me, but perhaps mundane to you folks of the high digit IQ variety! Thank you for taking the time.

I shall cut and paste that into my personal notes. I am not studying toward a degree in astrophysics, but merely extremely curious. Until now, I've only read simple layman-friendly books by Carl Sagan, Michio Kaku and the like. But now plan to dive into the more in-depth realm of the mathematical mechanics of it all.

Your latest post is a great primer and has me understanding the basics a bit more than before I logged on 15 minutes ago. The idea that everything is constantly adjusting, allowing for the speed of light to be the one constant is new and still a bit hazy to me. But I see that it males sense.

The idea that all actions in seemingly different time are actually "correct" in their own respect is a key starting point to understanding. Thank you for the easy-to-understand explanation.

As I begin to understand the amazing mechanics of our universe, it becomes harder to remain agnostic. The machine is so massively complex, and yet so perfect in its math. Astounding. Absolutely astounding.