gokul.er137

talking about pushing universes reminds me of Alcubierre drive. Kaku was probably describing the curvature of space time due to the presence of mass. In that sense, space does push' objects closer to the field. The curvature of space is the gravitational redshift of light. The curvature of time is the time dilation in gravitational fields. Both are explained by suitable demonstrations by extending the principle of equivalence.

But again I am not sure why he described it that way. What I have given above is just my interpretation.

vp -> phase velocity

vg -> group velocity

generally vp ->c^2(speed of light squared)/vg

Doing that and substituting does not give me a satisfactory answer.

On a more conceptual note -> group velocity is the rate of change of angular velocity('delta'omega) with the change in wave number('delta'k). Phase velocity is omega/k , that is at any particular instant. So to get the group velocity I could also differentiate omega with respect to k, but I do not know anything about them either.

i was intrigued by how to solve this.

the phase velocity of ocean waves is sqrt(g*lambda/2*pi) where g - acceleration due to gravity, lambda is the wavelength of the wave. The question is find the group velocity.

I tried many things but was not able to get to a proper answer. Any help?

WMAP states that the shape of the Universe within two percent accuracy is flat.

I have this particular question in relation with what we are discussing. - Why can't we assume that the early Universe expanded equally in all directions with a velocity of 'c' (max) for about a second or so? Then within a second, wouldn't we get the volume to be 4/3*pi*c^3?

@ physman - there is hardly any difference between what you are trying to prove and what the MM experiment tried to prove. The only difference is that you have replaced ether with wind. Anyways, it does not hold for light. The speed of light is a constant in physics. Just like the e/m ratio, G constant or Planck's constant. If you measured the ratio of the charge of electron to its mass in Andromeda, it would not change. Same for light.

Thanks for that ajb, D H. btw Griffin seems to be one helluva guy.

D H - Thanks for that info. I am as of now involved in certain physics projects based on spacetime concepts with a PhD professor. Is publishing papers a good indication to top Univ's about my inclination towards physics?

Well, I am going to become a mechanical engineer but I am strongly inclined towards Astrophysics. As you say, I don't know everything. I know a decent level of relativity, quantum mechanics and pure sciences. I am constantly in the learning process and will be publishing a few papers in the near future. Plus, I am involved in a project based on Space time models. Is this an indication to the Universities that I could be a prospective student?

I do not refer to dual programs in which we end up with an engineering degree followed by a post graduate degree. Can we do them separately, like B.E. Mechanical Engineering followed by MS in Physics ? Do Universities like MIT, Caltech accept people with a degree in engineering into their Postgraduate Pure Science programs?

that idea for the most part of it got done with after maxwell. But they have not gone far enough to actually treat it like a medium or field or something like that.

possible. getting a time field into the concept would ease the calculations as far as I know provided it does not get into the way of GR

@swansont - Yes I meant the frequency. The clock will show an entirely different interpretation as it is based on the history of the frame.

I understand what you say. You mean that the clocks on the whole will show a difference when checked after the experiment. But for that particular instance when the velocity is the same, there will be absolutely no difference in the time dilation. Thanks.

I understood the length contraction idea. Thanks.

But what about the time dilation again? I don't understand how the acceleration really affects the dilation at a particular time.

Dilated time between 2 instances in the event = Actual time between 2 instances in the event*gamma factor.

Gamma factor makes use of the velocity. Where does the acceleration come into picture?

the big crunch requires a blackhole of infinite density to take in all the matter. But then if what Hawking told is true, then not all matter that gets into a black hole comes out of it. then again it is speculation.

the physics that holds true within the Universe need not hold for things outside the Universe. So, as of now, we don't have any chance of knowing.

@swansont - if we assume the masses are the same, the frequency is the same, will there be a time dilation with respect to each other? what details do you mean?

I never mentioned that the length becomes 0. almost 0 is what i said. Let us say, the size of an electron. That would hardly hinder the object travelling at such a large speed. So what say?

I have this doubt.

Let us assume an observer independently accelerating from 0 to the speed of light. If an other observer starts accelerating consequently, let us say after a particular time they reach the same speed, let us say 0.95C. Would they observe a time dilation with respect to each other? My idea is yes since with respect to a stationary observer they have a velocity v each. So they have a time dilation with respect to each other though the magnitude is the same. If a cup breaks in one of their frames, the other sees a time dilation. If cup breaks in the other frame, the other observer sees the time dilation.

Another doubt.

If we place a ruler of some particular length. Along the same length a long distance away we have an observer acceleration to the speed of light, let us say he reaches the speed of light (well, almost. let us say v = 0.9999c) before he reaches the ruler. Will he collide with the ruler? I don't think so. The length of the ruler contracts to almost 0. So he will never see himself colliding with the ruler because its not there. Not the same for a stationary observer.

I am not so sure about my deductions. Different views, opinions and of course the right one will be appreciated.

Thanks.

we don't have enough scientific evidence of former Universes.

simultaneity - by itself in science means that things that happen simultaneous is not viewed the same by all observers. if you are sitting in a bus, with respect to a person inside it, you are stationary. with respect to a person outside the moving bus, you are moving. with respect to you, that person is moving. but in a vectorially opposite direction. this by itself is the best example of the loss of simultaneity. the reason for this is because, the reference frames of observers are entirely different.

but the speed of light must be a constant in all frames, irrespective of the velocity or other physical properties. so, in order to maintain a universality of the speed of light, the physical dimensions and the time dimensions are distorted. but again the length contraction does not lead to a change in the measurement of the length of that particular object in its frame. that is because it is purely associated with the the moving frame.so to say, in order to maintain a universality of the speed of light, the basic dimensions bend and curve. more so, even gravity succumbs to the constancy of the speed of light.

simultaneity - by itself in science means that things that happen simultaneous is not viewed the same by all observers. if you are sitting in a bus, with respect to a person inside it, you are stationary. with respect to a person outside the moving bus, you are moving. with respect to you, that person is moving. but in a vectorially opposite direction. this by itself is the best example of the loss of simultaneity. the reason for this is because, the reference frames of observers are entirely different.

but the speed of light must be a constant in all frames, irrespective of the velocity or other physical properties. so, in order to maintain a universality of the speed of light, the physical dimensions and the time dimensions are distorted. but again the length contraction does not lead to a change in the measurement of the length of that particular object in its frame. that is because it is purely associated with the the moving frame.so to say, in order to maintain a universality of the speed of light, the basic dimensions bend and curve. more so, even gravity succumbs to the constancy of the speed of light.

i understand the time dilation part due to velocity. but how is it the clock acceleration direction with respect to him determining the rate at which the time moves? i suppose it is due to the gravitational redshift or blueshift of light is his region depending upon whether it is moving away or towards him.

work function of a metal to the best of my knowledge refers to the work that has to be done in order to remove a valence electron from the metal atom. Essentially, the energy absorbed by the electron must be such that it is at least a bit more larger than the work function. As a basic relation - > E = hc/lambda, the only variable is lambda. As this directly depends upon frequency, you hence need a minimum frequency (threshold frequency) in order to excite the electron from its valence orbit. This frequency of light absorbed by the electron must give it energy greater than threshold frequency. I suppose that is all there is to it.

To calculate the energy levels of hydrogen you can use this formula ->

1/lambda = R(1/n1^2 - 1/n2^2) where R - > Rydberg constant

lambda - > wavelength of light

n1 an n2 represent the orbits of the hydrogen for which the electron "jump" is taking place.

With Respect to the q that this thread started off with : -

Aren't there two cases of time dilation we have to consider? Assuming the spacecraft in which the person moves about is closed,(?) then due to the large forward acceleration, this guy is essentially pushed against the walls behind. So, he is at rest in a pseudo gravitational field. So as an observer he does not obey the principle of equivalence. Thus, there is a sense of time dilation for him.

As the velocity of the craft is close to that of light, so is this guy's. But with respect to the radio, he is at rest as it is also in the craft and with the same velocity as this guy. So there wouldn't be a sense of time dilation in this respect, would it?

yeah. sorry. that's what I mean

In 15 seconds how much of a distance does the police dude cover? In the same 15 seconds, how much of a distance does the car cover? That should be easy now

Well, I am new to the form. I joined because I want to learn new things. Hope you people help me with my endeavour.

From ajb's post I have an idea of where this post is going. The 0/infinity came about probably after using the equations of mass increase, time dilation and length contraction for photons. Since their rest mass is zero, things become 0/infinity.

But again that is exactly why the equations are not applicable to photons. Or any other boson for that matter. Because all of them travel at the speed of light. Einstein's special relativity only defined the change in space-time on a relative basis as a "mass" tends to the speed of light. Not for massless particles at the speed of light. That is for quantum mechanics to deal with .