# Thread: questions on einstein's theories and related topics

1. einstein says that the force needed to accelerate an object increases with velocity...because an object contains greater energy at higher velocity, and energy and mass are effectively equivalent. but the velocity of an object is relative to the reference frame, and an object that is speeding up in one reference frame can be slowing down in another. now i know that time and distance are relative. but does this mean that mass and energy are relative also?

i also want to confirm my understanding of gravity. its my understanding that mass and energy bend space time, causing space time to flow into the depression. and its this flowing that is pushing you down...similar to standing at the bottom of a waterfall, with the water pushing down upon you. is that correct?

also, why do black holes create a hole in space time? its my understanding that a black hole occurs when a star collapses down to the size of a few miles. is that correct? if so, the total mass of the black hole is still the same as the original star. and, at a couple of miles wide, its extremely dense, but its not infinitely dense. so what am i missing?

i know about the four universal forces. but it seems to me that there are other forces outside of this group, such as jet propulsion and friction. so what's so special about the universal forces?

2.

3. Originally Posted by mrjc99
einstein says that the force needed to accelerate an object increases with velocity...because an object contains greater energy at higher velocity, and energy and mass are effectively equivalent.
You can think of it as requiring greater force because the "relativistic mass" increases. But I don't think that is too helpful and can lead to confusion. It is simpler just to consider that velocities do not add up in the simple way we are used to (because we are familiar with low speeds). The sum of two velocities is given by:

but the velocity of an object is relative to the reference frame, and an object that is speeding up in one reference frame can be slowing down in another.
Velocity is relative but acceleration isn't. You may not be able to tell if you are moving and the guy next to you is stationary or vice versa, but if you are accelerating, you know it. To be seen as slowing down in another frame of reference, that frame of reference would need to be accelerating more than you are. At this point, the simple math of special relativity no longer applies (it is possible to make it work with acceleration, but it is tricky. Really you have to use general relativity).

but does this mean that mass and energy are relative also?
Mass isn't; it is invariant. Energy, however, is observer dependent. A simple way to see that is just to consider kinetic energy; this is proportional to velocity but velocity is relative.

its my understanding that mass and energy bend space time, causing space time to flow into the depression. and its this flowing that is pushing you down...similar to standing at the bottom of a waterfall, with the water pushing down upon you. is that correct?
It is an analogy. And perhaps not a very good one. But it is certainly true that gravity is the result of spacetime curvature caused by the presence of mass and energy.

also, why do black holes create a hole in space time? its my understanding that a black hole occurs when a star collapses down to the size of a few miles. is that correct? if so, the total mass of the black hole is still the same as the original star. and, at a couple of miles wide, its extremely dense, but its not infinitely dense. so what am i missing?
So the simple analogy of a black hole (which goes back a very long way) is that the gravity at the surface is so great that the escape velocity is greater than the speed of light, so not even light can escape. A more accurate description would be that the curvature of space-time becomes so great that there are no paths out of the black hole: any attempt to move away from the centre eventually curves back towards the centre again.

The reason it is described as a "hole" is simply that you have a one way surface (the event horizon): things can fall in, but nothing (no matter, no light, no information, nothing) can come out again.

i know about the four universal forces. but it seems to me that there are other forces outside of this group, such as jet propulsion and friction. so what's so special about the universal forces?
All these other forces are ultimately the result of the four fundamental force. In fact, apart from gravity pulling us down to the ground, our entire experience of the world is determined by electromagnetic forces. The reason objects feel "solid" (despite being mainly empty space) is because the electrons in the atoms of your hand repel the electrons in the wood of the table top (simplifying a bit ). Friction is caused by the complex interactions of the surfaces which is, ultimately, electromagnetic forces.

Cool, isn't it!

4. thank you Strange. but i still have some follow up questions. if my analogy about gravity is a bad one, then how exactly does curving of spacetime create gravity? with respect to black holes, i thought they were infinitely dense so that they actually cause a tear in the space time contiuum and time stops completely. but, i would assume that in order to do this, the star would have to collapse to an infinitely small size called the singularity. but the star doesn't collapse to an infinitely small size. so again, i'm not understanding something. with respect to universal forces...if i lay my hands on you, my hand doesn't pass through you because of EM forces. i understand that. but if i push you on top of that, then are you saying that the force of the push is EM in nature as well? thanks again.

5. So the simple analogy of a black hole (which goes back a very long way) is that the gravity at the surface is so great that the escape velocity is greater than the speed of light,
equal to the speed of light, surely?

i thought they were infinitely dense so that they actually cause a tear in the space time contiuum and time stops completely. but, i would assume that in order to do this, the star would have to collapse to an infinitely small size called the singularity. but the star doesn't collapse to an infinitely small size.
spacetime isn't a fabric that can tear. the star does collapse but it gets to a point which we call a "singularity" but really it is just that our current theories breakdown at this point. when we get a quantum theory of gravity this "singularity" will most likely disappear.

"singularity" is just another name for "infinite".

6. Originally Posted by mrjc99
thank you Strange. but i still have some follow up questions. if my analogy about gravity is a bad one, then how exactly does curving of spacetime create gravity?
Well, I'm not sure it is much worse than any other analogy A more accurate description would be that the presence of mass causes the geometry of spacetime to curve so that when things have no force acting on them, they move towards the mass.

with respect to black holes, i thought they were infinitely dense so that they actually cause a tear in the space time contiuum and time stops completely. but, i would assume that in order to do this, the star would have to collapse to an infinitely small size called the singularity. but the star doesn't collapse to an infinitely small size. so again, i'm not understanding something.
So the important thing to understand here is the difference between the black hole's event horizon - that is the black hole that we can "see". That is the point at which things can never escape. Which is why it is called an event horizon: no events inside the horizon can have any effect on the universe outside.

The material that falls through the event horizon gets crushed to a point of zero size and infinite density (according to the best theories we have at present). That may not be realistic and probably just indicates that our theories no longer work at those extreme conditions.

with respect to universal forces...if i lay my hands on you, my hand doesn't pass through you because of EM forces. i understand that. but if i push you on top of that, then are you saying that the force of the push is EM in nature as well?
That's exactly right. EM forces are the main reason that things are solid and can exert pressure, friction, etc on one another.

7. Originally Posted by Chrispen Evan
So the simple analogy of a black hole (which goes back a very long way) is that the gravity at the surface is so great that the escape velocity is greater than the speed of light,
equal to the speed of light, surely?

i have a bit of a "thing" about analogies. i still use some though. *sigh*.

9. now i know that time and distance are relative. but does this mean that mass and energy are relative also?
In special relativity it is better to speak of momentum instead of mass, because that way the description also includes massless particles like the photon.
No, they are not relative - energy and momentum are combined into the momentum 4-vector

which is invariant, i.e. it is the same for all inertial observers.

i also want to confirm my understanding of gravity. its my understanding that mass and energy bend space time, causing space time to flow into the depression. and its this flowing that is pushing you down...similar to standing at the bottom of a waterfall, with the water pushing down upon you. is that correct?
Take the "flow" out, then it is correct. In general relativity space and time are unified into space-time; in the presence of energy this space-time possesses intrinsic curvature. Very simply speaking, in such a space-time, two lines which are initially parallel in space and point into the future will not stay parallel, but approach one another. In practical terms that means, if you have two massive objects next to each other, they will start to move toward one another over time. This is what we call "gravity", and in general relativity it is purely a result of the geometry of space-time. You do not need the "flow" for this, and indeed such an analogy would be misleading.

also, why do black holes create a hole in space time?
They are not holes in space-time, but simply areas with gravitational fields so strong that not even light can escape them.

its my understanding that a black hole occurs when a star collapses down to the size of a few miles. is that correct?
Essentially correct.

if so, the total mass of the black hole is still the same as the original star. and, at a couple of miles wide, its extremely dense, but its not infinitely dense. so what am i missing?
The mass of the black hole is not distributed throughout its volume, but concentrated at the (hypothetical) singularity at its centre. In other words, under pure general relativity, all of the mass is concentrated at a single point, giving it infinite density. It remains to be noted though that in practical terms quantum effects would play a role here also, so it is doubtful that point-singularities actually exist. The problem here is that we do not yet have a model which combines general relativity and quantum mechanics, so we don't really know what happens at the singularity.

i know about the four universal forces. but it seems to me that there are other forces outside of this group, such as jet propulsion and friction. so what's so special about the universal forces?
Be careful not to confuse classic mechanical forces with the fundamental forces. The latter cannot be reduced further, they are just that - fundamental. Other forces like friction can be reduced to things like electromagnetic interactions between the molecules and atoms of the bodies involved. They are not fundamental.

10. thanks markus, and everyone else. but i'm still a little confused. i thought force equals mass time accelleration over the square root of one minus v squared over c squared. the reason why a greater force is needed to accerlerate faster moving objects is that objects contain more energy at higher velocity. but velocity is relative. so wouldn't that make energy relative, as well as the force measured to accelerate the object?

11. Originally Posted by mrjc99
thanks markus, and everyone else. but i'm still a little confused. i thought force equals mass time accelleration over the square root of one minus v squared over c squared. the reason why a greater force is needed to accerlerate faster moving objects is that objects contain more energy at higher velocity. but velocity is relative. so wouldn't that make energy relative, as well as the force measured to accelerate the object?
It's a very valid question, which confuses many students of special relativity. The key to understanding it is to realize that in SR we need to use 4-vectors, because space and time are combined into Minkowski space-time. One important property of 4-vectors in Minkowski space is that they are invariant under Lorentz transformations, which physically means that their magnitude ( not necessarily the components ! ) is the same for all inertial observers, regardless of their state of relative motion.
You are absolutely correct when you say that classic velocity is relative - that is because it is calculated using distance and time, which both are relative concepts. This is why, in special relativity, one does not use velocity ( it is possible though to define an invariant 4-velocity vector ), but impulse instead. Under that picture, the mass of a system - which is now called invariant mass - is the magnitude of the impulse 4-vector, and the force required to change that impulse is its derivate with respect to proper time :

In other words, the greater the impulse of the object, the more force is required to accelerate it further, over a longer time as compared to an observer at rest. If you do the maths and calculate all the magnitudes, you will find that as an object approaches the speed of light the force required to increase the impulse will grow towards infinity.

12. Originally Posted by mrjc99
einstein says that the force needed to accelerate an object increases with velocity...because an object contains greater energy at higher velocity, and energy and mass are effectively equivalent. but the velocity of an object is relative to the reference frame, and an object that is speeding up in one reference frame can be slowing down in another. now i know that time and distance are relative. but does this mean that mass and energy are relative also?
Let's set mass aside and focus on kinetic energy. Imagine you're up in space, and a cannonball is moving towards you at 1000m/s. You would say it has considerable kinetic energy. Now imagine the cannonball is just sitting there, and you're moving towards it at 1000m/s. Where's the kinetic energy now? And how do you really know whether it's you moving or the cannonball? That kinetic energy is really just a label you give to a mass with motion relative to you.

Originally Posted by mrjc99
i also want to confirm my understanding of gravity. its my understanding that mass and energy bend space time, causing space time to flow into the depression. and its this flowing that is pushing you down...similar to standing at the bottom of a waterfall, with the water pushing down upon you. is that correct?
No. You will hear this myth on the Discovery Channel being promoted by people who seem to be reputable physicists, but it is absolutely hopelessly wrong.

Originally Posted by mrjc99
also, why do black holes create a hole in space time? its my understanding that a black hole occurs when a star collapses down to the size of a few miles. is that correct?
Most people will say no, but I say yes. Black holes used to be called "collapsed stars" or "frozen stars" round Oppenheimer's time. In the sixties the name changed to black hole, and people thought of them as something different which involves a point singularity. I think that this interpretation is wrong, and the original "frozen star" interpretation was correct.

Originally Posted by mrjc99
if so, the total mass of the black hole is still the same as the original star. and, at a couple of miles wide, its extremely dense, but its not infinitely dense. so what am i missing?
Infinite gravitational time dilation at the event horizon. Suppose we put you in a bubble of artistic licence, and send you down near the "surface" to set up a super-powerful laser that will blast straight down right through the collapsed star and out the other side. We then haul you back up to watch the show, and then you initiate the laser remotely. When does that laser beam make it through that couple of miles of star-stuff? Answer: never. Because at the surface the coordinate speed of light is zero according to distant observers. The frozen star is a place where light can't go, so it's a hole in spacetime. Check out the Gravastar article on wikipedia. I don't know why it's "an object hypothesized in astrophysics as an alternative to the black hole theory" because it's fairly close to the original frozen-star black hole interpretation. Note this bit: This region is called a "gravitational vacuum", because it is a void in the fabric of space and time."

Originally Posted by mrjc99
i know about the four universal forces. but it seems to me that there are other forces outside of this group, such as jet propulsion and friction. so what's so special about the universal forces?
They're said to be fundamental.

13. Originally Posted by Farsight
No. You will hear this myth on the Discovery Channel being promoted by people who seem to be reputable physicists, but it is absolutely hopelessly wrong.
Farsight, I must ask you to please keep your personal ideas out of this. It is all good and well that you wish to discuss your ideas, but please do so in a separate thread and don't try to promote them as scientifically accepted facts. mrjc99 has asked a serious and valid question, and he expects and deserves an answer which is in accordance with currently accepted physics; the discussion about whether or not you agree with those physics simply does not belong here.

14. Originally Posted by mrjc99
thanks markus, and everyone else. but i'm still a little confused. i thought force equals mass time accelleration over the square root of one minus v squared over c squared. the reason why a greater force is needed to accerlerate faster moving objects is that objects contain more energy at higher velocity. but velocity is relative. so wouldn't that make energy relative, as well as the force measured to accelerate the object?
See what Markus said above. Another way of putting it is that if you said it was the cannonball moving, then you also have to say that its total energy is its rest-mass energy plus its kinetic energy. As far as you're concerned, this is more than the total energy of the cannonball at rest, so it takes more force to accelerate it another 1m/s. Then it's got even more total energy, so it takes even more force to accelerate it by another 1m/s. And so on. The force tends towards infinity as the cannonball's speed tends towards the speed of light. And get this: the speed of light isn't relative. If you're sitting still and I send a light beam past you, you measure its speed to be 299,792,458 m/s. If you then move away from me fast and I send another light beam past you, you still measure its speed to be 299,792,458 m/s. That's because you're time dilated. The "over the square root of one minus v squared over c squared" relates to this, and is the Lorentz factor. It's derived from Pythagoras' theorem, see the wikipedia Simple inference of time dilation due to relative velocity. We've got two parallel-mirror light clocks, one sitting in front of us, the other moving fast. We see the light moving like this ǁ in the local clock and like this /\ in the moving clock. Treat one side of the angled path as a right-angled triangle, and the hypotenuse is the lightpath where c=1 in natural units, the base is the speed v as a fraction of c, and the height gives the Lorentz factor γ = 1/√(1-v²/c²). This is most often used in time dilation and length contraction, but it applies to cannonballs too.

15. Originally Posted by Markus Hanke
Farsight, I must ask you to please keep your personal ideas out of this. It is all good and well that you wish to discuss your ideas, but please do so in a separate thread and don't try to promote them as scientifically accepted facts. mrjc99 has asked a serious and valid question, and he expects and deserves an answer which is in accordance with currently accepted physics; the discussion about whether or not you agree with those physics simply does not belong here.
I'm not giving my personal ideas Markus. The waterfall analogy for a black hole is badly wrong. In no sense is space falling inward within a gravitational field. The idea that it is, absolutely contradicts general relativity, and it's important that people like you and me make this clear to people like mrjc. When it comes to the nature of a black hole, see
The Formation and Growth of Black Holes by Kevin Brown. The "frozen star" interpretation is not some personal idea of mine. I side with it whilst others don't, that's all. It would be improper if you were to suggest that it should be ignored because it's my personal idea. Here's an excerpt:

"Remember that historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock just asymptotically approaches "full stop" (i.e., running at a rate of zero) as it approaches the horizon. It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. This leads to the "frozen star" conception of gravitational collapse..."

16. Originally Posted by Farsight
I'm not giving my personal ideas Markus.
On the contrary. On many other forums for about a decade, you have given your half-informed opinion on physics. You have admitted that you are unable to actually do the mathematics of general relativity--this means that you cannot follow the science. Your mistakes about GR have been corrected by dozens of people. You have been banned from many message boards because when you find yourself unable to defend yourself with actual scientific reasoning, you turn to insults. This is a matter of public record.
The waterfall analogy for a black hole is badly wrong. In no sense is space falling inward within a gravitational field. The idea that it is, absolutely contradicts general relativity, and it's important that people like you and me make this clear to people like mrjc.
Any time-like curve within the interior of the event horizon turns toward the center of the black hole. Thus all points of space do, in a sense, fall toward the center.

If you could work through the mathematics, you would see this. However, you can't so you spout criticism of actual science in an attempt to make yourself seem smarter and sell your book.

Are you really all that different from a spam email scam?

17. Originally Posted by Farsight
The waterfall analogy for a black hole is badly wrong. In no sense is space falling inward within a gravitational field.
Actually it's misleading only in the case of a Schwarzschild black hole, and I had pointed that out already in post 8. The "waterfall analogy" is a fairly good approximation for a Reissner-Nordstroem BH or a Kerr-Newman BH, so long as one understands that it is an analogy only, and that space-time itself does not actually flow anywhere.

18. The waterfall analogy is presented without the caveat that says space does not actually flow anywhere. Here's an example of it: Waterfall

"Imagine light rays, photons, as fishes swimming fiercely in the current. Outside the horizon, space is falling into the black hole at less than the speed of light (or the speed of fishes), and photon-fishes swimming upstream can make way against the flow."

The author also says this:

"Physically, the Gullstrand-Painlevé metric describes space falling into the Schwarzschild black hole at the Newtonian escape velocity."

And then a little later says this:

"I think that even today research into general relativity is too often dominated by abstract mathematical thinking at the expense of conceptual understanding."

See the irony? Now, is the space in the room you're in physically falling down towards the ground? No. The waterfall analogy is absolute trash. It's dangerous cargo-cult pseudoscience being peddled by people who should know better, and you should not side with them in any way.

19. Originally Posted by Farsight
The waterfall analogy is presented without the caveat that says space does not actually flow anywhere.
Because it is an ANALOGY.

Wrong on both points, as far as I can tell.

20. Doublepost deleted. There's a bug or two on this forum.

21. Physbang is a troll, everybody can see that. Don't turn into one yourself. Let me give you some feedback to what he said:

I've been doing this since 2005. The first post of miine I can find on physicsforum is dated May 2006.

You are unable to actually do the mathematics of general relativity--this means that you cannot follow the science.

Both untrue. I've recently given a nice description of the Riemann curvature tensor. It's all pretty simple once it clicks.

I haven't made mistakes, and they haven't been corrected. If they were, PhysBang would link to them or put up a counterargument pointing out what my mistake is. He can't. Instead, I correct him, like here.

They have You have been banned from many message boards because when you find yourself unable to defend yourself with actual scientific reasoning, you turn to insults. This is a matter of public record.

It isn't. It's the PhysBangs of this world who dish out the insults, not me. I've been banned from a number of forums because I'm too bloody good. I embarrass people who like to think they're the experts.

22. hey guys, i know i'm new here. but i wasn't expecting this kind of bickering on a science forum. healthy debate, yes...but not this. you guys are filling up my email with this. please, lets move on. thanks.

23. Sorry mrjc. Sadly this kind of thing is all too common on internet forums. You ask a question and get two different answers that say essentially the same thing whilst giving different nuances, and then people start arguing about the nuances and it's downhill from there. Physics is nothing but a battle of ideas, it's like a constant civil war, and it is ruinous. There's no easy solution I'm afraid. All I can suggest is that you keep asking the questions at multiple locations and take as much value as you can.

24. Originally Posted by Farsight
Physbang is a troll, everybody can see that. Don't turn into one yourself. Let me give you some feedback to what he said:

I've been doing this since 2005. The first post of miine I can find on physicsforum is dated May 2006.
So you have only been making the same mistakes, learning nothing, for seven years. Thanks for the update.
You are unable to actually do the mathematics of general relativity--this means that you cannot follow the science.

Both untrue. I've recently given a nice description of the Riemann curvature tensor. It's all pretty simple once it clicks.
If we look over your posts for the last few years, we see your admission, time and time again, that you cannot follow the mathematics of GR. We can see that you can cut and paste, but we can also see that you have no intentions of ever answering a direct question about a physics scenario. You have made a claim on this board several times, a claim that you have made elsewhere, that the energy of gravity can account for the rotation curves of galaxies. Given you behavior on other boards, you and I both know that you cannot and will not defend this claim. You have turned to insults in an attempt to avoid this problem.

I haven't made mistakes, and they haven't been corrected. If they were, PhysBang would link to them or put up a counterargument pointing out what my mistake is. He can't. Instead, I correct him, like here.
They have You have been banned from many message boards because when you find yourself unable to defend yourself with actual scientific reasoning, you turn to insults. This is a matter of public record.

It isn't. It's the PhysBangs of this world who dish out the insults, not me. I've been banned from a number of forums because I'm too bloody good. I embarrass people who like to think they're the experts.

25. Originally Posted by mrjc99
hey guys, i know i'm new here. but i wasn't expecting this kind of bickering on a science forum. healthy debate, yes...but not this. you guys are filling up my email with this. please, lets move on. thanks.
Sorry, mrjc99. This particular argument has been going on for a while now across several different threads; it is not related to you are your question.
Btw, you can disable the email notifications in your control panel - this way you won't get an email every time someone posts something on thread you are subscribed to.

26. no worries. and i would again like to express gratitude for all the assistance that i have received on this board. i know you guys are just trying to help.

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