Thread: speed/momentum

Hello,
I am going to put a series of questions on this Thread with their connections with speed
first of all:

What is (if there is one) the difference in between speed and momentum?

Originally Posted by sportlaan

What is (if there is one) the difference in between speed and momentum?

Whut?
Speed is distance covered per unit of time.
Momentum is speed x mass.

A 1 kg object moving at 10 m/ sec has the same speed as a 10 kg object moving at 10 m/ sec but 1/10 the momentum.
A 1 kg object moving at 10 m/ sec has the same momentum as a 10 kg object moving at 1 m/ sec but 1/10 the speed.

ok I just didn't know

is speed relative?

It's got to be relative.

So if i accelerate a object to 99.99% of the speed of light and fron this object i accelerate another object also relative to this object to 99.99% of the speed of light why can I or can I not do this scince object 2 woult relative to me be going faster than the speed of light

Originally Posted by sportlaan

So if i accelerate a object to 99.99% of the speed of light and fron this object i accelerate another object also relative to this object to 99.99% of the speed of light why can I or can I not do this scince object 2 woult relative to me be going faster than the speed of light

You CAN do this: as shown by the fact that if you were travelling at 0.9999c and you used a torch the light would still recede from you at c.
BUT to another observer it wouldn't be doing 1.9999 c - velocities don't add that way at relativistic speeds.
Likewise while the velocities of your objects would be 0.9999c relative to each other they wouldn't be faster light according to you.

So what is the reason it doesn't add in that way?
or why would I see the light?

Originally Posted by sportlaan

So what is the reason it doesn't add in that way?

It depends what you mean by "reason".

At one level, it is simply a result from the theory of relativity, describing the geometry of space-time.

In turn, this is an inevitable consequence of the speed of light being constant for all observers, independent of their state of motion, as described in Maxwell's equations.

The reason that light and space-time works like that ...? Well, at present, all we can say is, "that's just the way the universe is." A deeper theory, such as quantum gravity, might give an explanation of that.

I would love to do all this reasearch myself but I don't understand all these "weird" words I find on the internet

Originally Posted by sportlaan

So what is the reason it doesn't add in that way?
or why would I see the light?

Newtonian mechanics defines coordinate transformation between two frames in relative motion with speed as :




This means that , if an object moves with speed in frame F, it will have speed in frame F'.

Turns out that Newtonian mechanics is wrong, the correct transformation between coordinates is:




So, when we try again to calculate (correctly, this time) we obtain .

Could you follow the above?

would you expect me to be able to understand?

Originally Posted by sportlaan

would you expect me to be able to understand?

Yes. Otherwise, you do not have enough math background to understand it for now and you need to wait until you learn basic calculus. How old are you?

Originally Posted by sportlaan

So if i accelerate a object to 99.99% of the speed of light and fron this object i accelerate another object also relative to this object to 99.99% of the speed of light why can I or can I not do this scince object 2 woult relative to me be going faster than the speed of light

So let's try a more intuitive approach.

As you may know, when we observe an object in motion the lengths contract and time slows.

So, the people on your first object accelerate the second object to what they think is 99.99% of the speed of light.

But, when we observe the speed of the second object, relative to the first object, we say it is a much smaller speed difference (because we see their lengths and time different than they do). So we see the total speed of the second object as only slightly faster than the first object.

That is basically what the math in post #10 says.

Thank you
but if you watsh it from the different points of view would the distance seem different?

can your speed be 100% of the speed of light?

can your speed be 100% of the speed of light?

Not if you have mass, for photons and other massless particles it has to be c.

But if speed is relative am i not going on the speed of light for a photon?

This is not really my area of expertise and my understanding of this may not be correct but I think this cannot be the case as there is no reference frame where the photon is at rest (in your question you are implying the photon is at rest and you are travelling at c with respect to it) so asking how things are from the photons point of view does not give a meaningful answer.

What happend PhDemon that you've changed all your customisables to No Bulshit?

I just changed the text under the avatar, some people are allergic to certain things and this is termed an intolerance (like lactose intolerance for example), I seem to be very intolerant to bullshit so changed the text accordingly

Well I'm sorry if I speak bulshit in here (probably all the time) :P I am here becous I want to learn and school is still in the phase where we do a month with just one theory bit, I am quite good at learning new science things but terrible at new languages

Originally Posted by PhDemon

This is not really my area of expertise and my understanding of this may not be correct but I think this cannot be the case as there is no reference frame where the photon is at rest (in your question you are implying the photon is at rest and you are travelling at c with respect to it) so asking how things are from the photons point of view does not give a meaningful answer.

Correct, the fact that a photon is moving at c wrt to you doesn't mean that you are moving at c wrt the photon because one cannot attach a frame of reference to photons.

Originally Posted by sportlaan

Well I'm sorry if I speak bulshit in here (probably all the time) :P I am here becous I want to learn and school is still in the phase where we do a month with just one theory bit, I am quite good at learning new science things but terrible at new languages

No problem, it's not aimed at you but the various cranks we get here, and hey your English is better than my (insert any of the three languages I've tried to learn and failed to get beyond the basics at).

I am terrible at German and Frensh even at Dutch (my native language) I am quite bad I learn English from the countless hours of internet :P

I passed exams at school in French and German (most of which I've forgotten over the last 20 years) and tried to teach myself Italian with very limited success. Luckily I'm British and can be lazy about it

I allways have kind of good grades but to have 60% on frensh i have to learn a long time and for biology or physics I look at it and i can use it

Originally Posted by sportlaan

Thank you
but if you watsh it from the different points of view would the distance seem different?

Distance (and speed and time) is relative: it depends on the observer's frame of reference (i.e. how they are moving with respect to the thing being measured).

Originally Posted by sportlaan

Thank you
but if you watsh it from the different points of view would the distance seem different?

Let's take your example. Relative to you, object 1 and 2 are initially moving at 0.9999c, relative to you. ( And from their perspective, you are moving at 0.9999c relative to them).

Object 2 takes off so that it is now moving at 0.9999c relative to object 1 according to both it and object 1.

According to you, object 2 is now moving at 0.999999995c relative to you. Since object 1 is moving at 0.9999c, object 2 is moving at 0.000099995c (~1/10000 c) with respect to object 1.

According to object 1, you are moving at 0.9999c in one direction and object 2 is moving in 0.999c in the other, and you and object 2 have a speed of 1.9998c with respect to each other.

According to object 2, object 1 is moving at 0.9999c and you are moving at 0.999999995c, and you and object 1 have a respective speed of 0.000099995c to each other.

To put it simply, observers with relative motion with respect to each other measure time and space differently than each other. One way to put this is that these measurements are "frame dependent" .

To give you an idea as to what this means, I'll use an analogy.

Consider the directions North-South and East-West. Now imagine you have a bunch of people facing in different directions to each other in a big open space. You now ask them to point North. They all point in the same direction (assuming they know which direction is North). If there is a tree some distance away, and you ask them how far to the North and how far to the West the tree is, they will all give the same answer. (say 4 miles North and 3 miles West. )

This is analogous to measurements that are frame independent. You get the same answer no matter which direction you face. Your "frame of reference"(direction you are facing) makes no difference.


Now take the same group of people and ask them to all point to the right. They will now be pointing in different directions. If you ask them the distance and direction of the tree, you will also get a range of answers. Some could say " 5 miles to my right", another might say "4 miles in front and 3 miles to the left", while someone else says "3 miles in front and 4 miles to the right" etc.

This is analogous to measurements that are frame dependent. You get different answers depending on which direction you face. (and if you turn to a new direction, the answer changes. Left and right turns with you, where North-South doesn't.) Your answer is tied to your frame of reference.


Now the universe exists in a four dimensional construct called "space-time", which consists of the 3 spatial dimensions and 1 time dimension. You can locate events in this construct by giving them space-time coordinates. For example, I can say that from my present space-time position, my birth was some 55 yrs ago and some 1800 miles away.

Okay, so here's the thing, the "direction" of the 4 dimensions of space-time are not fixed. In other words, they are not like the North-South/East-West from the first example, but are more like the left-right/ forward-backward directions in the second example. Relative motion is what separates the Frames of reference is space-time. For someone moving at some speed with respect to me, The difference between the space-time coordinate between me now and my birth will be different. They they would get a different answer as to how long ago and how far away my birth was. It is like their motion causes a "rotation' in Space-time, so that they measure some of what I measure as distance as time and some of what I measure as time as distance. ( its like the tree in the second example, where one person measured 3 miles along the North-South line and 4 along the East-West line, while another measured it the other way around.)

And just like our notion of left-right turns with us when we turn, Our measurement of space-time changes with us as we change velocity.

As to why this is... It's just the way the universe is put together (and quite frankly, much of what makes our universe possible relies on it being this way.)

Janus, your explanation of frames of reference is superb. Just punching the "like" button isn't enough of a reaction to it. I would like to see that post pinned somewhere appropriate, so it could be easily referred to.