Search results for query: *

Thanks to all!

Yes. And I want to understand how is it possible that time coordinate assigned to that event is different for the train passenger and the observer. What is reason of this thing?

Yes. I used this term wrong. I don't mean about "time simultaneous" or "at the same time". I mean that when light reach to end of train with point of view of passenger then light reach to end of train with point of view of observer. Is it true?

Is it true that in previous example light reach left end of train with point of view of passenger and with point of view of outside observer simultaneously?

Another example is the propagation of light from the middle of a moving train to its left and right ends. From the train passenger's point of view, the light will simultaneously reach the right and left ends of the train, with point of view of an outside observer - at different times. In this...

I mean another. I mean that in moving frame and in non-moving frame same event happens simultaneously. Ok. For example, light clock. Light reach to end point simultaneously in non-moving and moving frames. https://en.wikipedia.org/wiki/Time_dilation#Simple_inference

I read that light reach to end point simultaneously in different frames.

For example, light clock and mechanical clocks. We can simultaneously start mechanical clocks at initial point and if light reach to end point we can stop simultaneously our mechanical clocks in different frames.

Time dilation is the difference in elapsed time as measured by two clocks due to a relative velocity between them

Does velocity contribute to the time dilation effect?

Hello! I try to understand how in different frames clocks tick and stop simultaneously but show different time? I suppose that velocity is reason of time dilation effect but I'm not sure. Thanks.

Thanks to all! My mistake was that I tried to find time of motion in moving frame but distance in this frame is 0 because clock in moving frame is at rest.

Ok. I'll try to rephrase. Let's write equation for non-moving reference frame: ##(cΔt)^2 = (cΔt0)^2 + (vΔt)^2## How to write equation for moving reference frame?

Why do you say about light beam? I mean another case. Say what time do you measure in moving frame when you travel from A to B?

I wrote that time is Δt0, is it true? But I'm confused because if we're moving from A to B then our distance is vΔt for our reference frame. And if time is Δt0 then distance is vΔt0. It's wrong result.

Sorry, it's my error. Yes. Clock in moving frame is at rest. And I want to know what time is measured by clock in this moving frame.

Ok. I ask about time in moving frame. I want to know time of motion from A to B in moving reference frame. In the rest frame time is Δt.

It represent rest frame with zero velocity with rest clock. But I mean right diagram when I say about moving frame.

No. I mean moving frame with velocity v and with moving clock.

I mean that vΔt is length of path in non-moving reference frame (time in this frame is Δt). And what is time in reference frame with clock?

Sorry. Picture in the first message is wrong.

I considered example of time dilation with light clock. I have a question about measuring time in reference frame with clock. If we know that clock move from A to B in the reference frame with clock then what time of motion is measured in this reference frame? (In non-moving reference frame...

Hello. I read about smooth infinitesimal analysis and I have several questions: 1.What does "ε.1" and "ε.0" mean in this proof? (photo1) (https://publish.uwo.ca/~jbell/basic.pdf , page 5-6) 2. For what purpose do we use Kock-Lawvere axiom when we deal with law of excluded middle? (photo2)...

Hello. How to prove that in smooth infinitesimal analysis every function on R is continuous? (Every function whose domain is R, the real numbers, is continuous and infinitely differentiable.) Thanks.

I read in this source: http://www.bndhep.net/Lab/Math/Calculus.htm The fact that x^2 becomes insignificant compared to x for very small values of x is a fundamental principle of infinitesimal calculus. We say x is infinitesimal when we allow its value to approach zero, but never actually reach...

What is relation between ##\Delta x## and ##dx##? If we want to get term with dx then we discard ##\Delta x^2## and other high-order terms in expression. Is it true?

I didn't fully understand what does it mean? What is it used for?

I read "A treatise on infinitesimal calculus" Bartholomew Price. Integral sum, for ##2xdx##:

Hello. As is known, we can neglect high-order term in expression ##f(x+dx)-f(x)##. For ##y=x^2##: ##dy=2xdx+dx^2##, ##dy=2xdx##. I read that infinitesimals have property: ##dx+dx^2=dx## I tried to neglect high-order terms in integral sum (##dx^2## and ##4dx^2## and so on) and I obtained wrong...

Thank you, it's helpful!

Ok. We have 2 similar expressions: 1. ##2x \Delta x + \Delta x^2## where ##\Delta x## is variable and 2. ##x+x^2## where ##x## is variable. In 1. case we'll get ##2xdx## when ## \Delta x## tends to zero. In 2. case we'll get ##x## when ##x## tends to zero. But in the first case we'll get...

Sorry, I forgot to say that ##x+x^2## is just expression where x is variable. Not differential.

Hello. Let's assume that we have ##2x \Delta x + \Delta x^2##. When ##\Delta x## tends to zero we can neglect ##\Delta x^2## and we'll get ##2xdx##. Let's assume that we have ##x + x^2##. When ##x## tends to zero we can neglect ##x^2##. Will we get an infinitesimal ##x## as such as ##dx##? Thanks.

Hello, @fresh_42 You wrote that "In the first case ##dr \approx \Delta \, r## is an infinitesimal small change in ##r## and in the second it is an infinitesimal small piece of ##r##, so ##dr \approx h##." I have difficulty understanding this topic. How is it possible that ##dr \approx \Delta...

Yes

Hello. There are 4 types of infinitesimals: 1) dx=1/N, N is the number of elemets of the set of the natural numbers (letter N is used to indicate the cardinality of the set of natural numbers) 2) Hyperreal numbers: ε=1/ω, ω is number greater than any real number. 3) Surreal numbers: { 0, 1...

I read about it: change in value from slope

Yes. But we can use dy to represent finite Delta y as sum of infinitesimally small dy and it's right.

Hello! As is known, \Delta y = dy for infinitesimally small dx. It's true. But if we have graph we may see that \Delta y isn't equal to dy even for infinitesimally small dx. Why is that so? Thanks!